Moisture Sensitivity of Plastic Packages of IC Devices (Micro- and Opto-Electronic Materials, Structures, and Systems)

Micro- and Opto-Electronic Materials, Structures, and Systems

Series Editor E. Suhir University of California, Santa Cruz, CA, USA

For further volumes: http://www.springer.com/series/7493

X.J. Fan · E. Suhir Editors

Moisture Sensitivity of Plastic Packages of IC Devices

Foreword by C.P. Wong

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Editors X.J. Fan Department of Mechanical Engineering Lamar University Beaumont, Texas USA [email protected]

E. Suhir ERS Co. Alvina Court 727 94024 Los Altos, California USA [email protected]

ISBN 978-1-4419-5718-4 e-ISBN 978-1-4419-5719-1 DOI 10.1007/978-1-4419-5719-1 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2010927324 © Springer Science+Business Media, LLC 2010 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

Foreword

Moisture, according to the Merriam-Webster dictionary, is defined as “liquid diffused or condensed in relatively small quantity.” It is also defined, by Longman dictionary, as “small amounts of water that are present in the air, in a substance, or on a surface.” Both definitions emphasize on the small quantity, but presumably the state of moisture is in liquid form. In fact, moisture, a small quantity of H2 O molecules, can be in vapor, liquid, or solid phase in air or in any substance. It is interesting to note that moisture sorption is different from water sorption. Moisture sorption process refers to a process in a humid air environment, while water sorption refers to a complete immersion into water. Hydrophobic or superhydrophobic (with water contact angle >150◦ ) materials can effectively prevent water liquid from penetrating through surface, but not for the transmission of moisture (water vapor) in a humid air environment. This interesting phenomenon is illustrated in the first chapter of the book, although the entire book is focused on “moisture” sensitivity of plastic packages of integrated circuit (IC) devices. Most of polymeric materials in IC packaging absorb moisture from an environment. The presence of moisture in plastic materials alters thermal stress through the alteration of thermo-mechanical properties, induces hygroscopic stress through differential swelling, induces vapor pressure that is responsible for the eventual popcorn cracking, reduces interfacial adhesion strength, induces electrical-chemical migration-induced corrosion, and finally alters dielectric properties of materials. Despite the pivotal role of moisture, research activities in moisture-induced failure remain relatively low, compared to the thermally induced failure in IC packaging. This is in part due to the lack of material data and aggravated by the lack of fundamental understanding of moisture transport, material characterization techniques, and procedures. These are reflected in the limited publications and the near absence of such properties from the material vendors. The development of three-dimensional (3D) microelectronics packaging with through-silicon via (TSV), ultrathin, and multi-die stacking technology has become essential to increase functionality with higher memory capacity in more complex and efficient architectures. Wafer thinning is required for such ultrathin die development from the original thickness of 750 μm down to as low as 30 μm. Consequently, new assembly and manufacturing processes must be invented to overcome thin wafer handling and cracking issues. Many new materials such as wafer-level coating v

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films have emerged. As a result, cohesive film rupture may occur due to moisture during reflow. Therefore, one of the major challenges for a practical realization of 3D microelectronics packaging concept is to design materials and meet reliability requirements without cohesive failures subjected to moisture loads. This book provides information on the state-of-the-art technologies and methodologies related to moisture issues in plastic packages. The book covers the wide aspects including moisture diffusion and desorption, characterization and modeling, hygroscopic swelling, interfacial adhesion degradation, accelerated moisture sensitivity/reflow test, electrical-chemical migration, moisture-aging effect on longterm reliability, and several finely selected real-world case studies on various failure mechanisms due to moisture. This is the first book ever to cover the full spectrum of moisture-induced failure mechanisms in IC packages. It is a timely and important contribution to the technical literature for researchers, engineers, and practitioners both in academia and in electronics industry. The editors of the book, Dr. Fan and Dr. Suhir, have rich experience in both theoretical development and industrial practice. They have been offering the professional development courses at various IEEE (Institute of Electrical and Electronics Engineers) CPMT (components packaging and manufacturing technologies) Society conferences, and hundreds of participants have attended their lectures. They have succeeded in bringing together well-recognized experts in this field and present a fine collection of papers covering the full spectrum of the related topics. They are to be congratulated for bringing this very important topic forth in a timely manner. Atlanta, GA November, 2009

C.P. Wong

Preface

Since moisture-sensitive plastic materials were introduced in integrated circuit (IC) device packaging several decades ago, moisture has been one of the major concerns for package designers and reliability engineers. With the recent development of the three-dimensional (3D) microelectronics packaging with through-silicon via (TSV) and multi-die stacking technologies, moisture-induced failures have become even more prominent due to the new materials employed and the overall reduction in package size and thickness. This book provides a comprehensive state-of-the-art and in-depth review of the fundamental knowledge and methodologies in the field of material and structural (“physical”) behavior and performance of various types of moisture-sensitive plastic packages of IC devices. The book consists of 21 chapters divided into six sections: (1) moisture diffusion, absorption and desorption, and adhesion degradation (Chapters 1, 2, 3, and 4); (2) hygroscopic swelling characterization and analysis (Chapters 5, 6, and 7); (3) integrated hydrothermal and thermal stress modeling (Chapters 8, 9, 10, 11, and 12); (4) case studies and applications (Chapters 13, 14, 15, 16, 17, 18, and 19); (5) electro-chemical migration (Chapter 20); and (6) molecular dynamics modeling and characterization (Chapter 21). Brief description of the chapter contents is set forth below. Chapter 1 presents an overview of moisture-induced failures in plastic packages of IC devices, and illustrates the fundamental characteristics of moisture diffusion, hygroscopic swelling, and adhesion degradation. Chapter 2 describes the latest investigations of anomalous moisture diffusion and the corresponding adhesion behaviors in epoxy molding compounds. Chapter 3 provides a method and detailed analysis for real-time moisture absorption and desorption in thin films. Chapter 4 reviews the existing methodologies of moisture diffusion modeling and whole-field vapor pressure analysis. Chapters 5, 6, and 7 describe several characterization methods and techniques for hygroscopic swelling, such as photomechanics measurement techniques and point measurement method using thermo-mechanical and thermo-gravimetric analyzers. Chapters 8, 9, 10, 11, and 12 provide a collection of the most advanced analysis and methods for integrated hydrothermal stress modeling. Chapter 8 describes recent progress in modeling of moisture diffusion and moisture-induced stresses in semiconductor and MEMS packages. Chapter 9 presents a novel methodology for integrated vapor pressure, hygro-swelling, and vii

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thermo-mechanical stress modeling of IC packages. Chapter 10 describes a failure criterion for moisture sensitivity of plastic packages based on the theory of thin flexible plates of large deflections. Chapter 11 develops a continuum theory and describes its application to moisture-induced failures in IC packages. Chapter 12 reviews recent efforts to develop micromechanics-based failure theories/models and computational tools for material and process selection in the design and fabrication of plastic IC packages and provides recommendations for the improvement of their reliability under the anticipated service conditions. Chapters 13, 14, 15, 16, 17, 18, and 19 are dedicated to several case studies on moisture-induced failures in a wide range of package types, such as QFP (quat flat package), QFN (quat flat no-lead), and D2 Pak (Chapter 14), QFN package (Chapter 15), system-inpackages and BGA (ball grid array) packages (Chapter 16), flip chip BGA packages (Chapter 17), and ultrathin 3D stacking die packages (Chapter 18). From material perspectives, epoxy molding compounds, die attach adhesives, and underfill materials are all covered in these case studies. Chapter 13 describes a new methodology for an equivalent acceleration of the IPC/JEDEC moisture sensitivity levels. Chapter 19 reviews an automated simulation system to perform moisture-related modeling for various package types. Chapter 20 describes the fundamentals of the phenomenon of the electrochemical migration (ECM), primarily manifested as bridging metallic dendrites. Chapter 21 shows how molecular dynamics simulation and the nano-scale characterization methods could be used to obtain an insight into the moisture-induced failure modes and mechanisms at the atomistic level. The original scope of the book was based on the professional development course notes of one of the editors, Dr. Fan, on moisture-related reliability in electronic packaging, which has been presented at the IEEE (Institute of Electrical and Electronics Engineers) CPMT (components packaging and manufacturing technologies) Society-sponsored conferences. To present a complete coverage on the latest development and the most recent advances in this field, we have invited experts in this field to bring together a full spectrum of moisture-induced failure mechanisms in IC packages. We are grateful to all the authors from the industry and the academia for their in-depth contributions and their efforts to bring this book to the readers. The first editor, Dr. Fan, would like to express his gratitude to many of his ex-colleagues at Intel, Philips Research, and the Institute of Microelectronics in Singapore. Many of the book chapters reflect the results of numerous collaborative efforts and extensive team work. Without this work our book would never be possible. The second editor, Dr. Suhir, expresses his deep appreciation to his friends and former colleagues at Bell Laboratories, Physical Sciences and Engineering Research Division, at Murray Hill, NJ, and Allentown, PA, for introducing him about 25 years ago to the subject of, and the challenges in, the exciting field of polymeric materials in general and plastic packages of IC devices in particular. Dr. Suhir would like to take this opportunity to acknowledge, with thanks, his collaborations, for almost 20 years, during the “golden age” of Bell Labs, with Shiro Matsuoka, Phil Hubbauer, Lloyd Shepherd, Louis Manzione, Don Dahringer, Harvey Bair, C.P. Wong, Arturo

Preface

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Hale, John Segelken, Alan Lyons, Bonnie Bachman, Charles Cohn, Quazi Ilyas, and many other top-notch materials scientists, physicists, chemists, and chemical engineers. Beaumont, TX Santa Cruz, CA November 2009

X.J. Fan E. Suhir

Series Preface

This title is the second book in the series. The series encompasses a broad area of micro-, opto-electronic, and photonic engineering, with particular emphasis on materials, physics, mechanics, design, reliability, and packaging. The titles in the series feature eminent engineers and scientists as authors and/or editors focused on addressing major issues in the above areas of engineering. Our objective is to have a comprehensive series on the materials, mechanics, physics, packaging, functional performance, and reliability as they pertain to micro- and opto-electronics. The audience for these volumes are those who work in micro- and optoelectronics and photonics, as well as those in many related areas of applied science and engineering. The expected readers are practitioners and professionals, scientists and researchers, along with senior-level undergraduate and graduate students. These volumes can serve as expanded encyclopedias in the field of the mechanics of microand opto-electronic materials and structures. Selected titles could also serve as textbooks, reference works, and as general guidance works for those interested in these subjects. The series contains both descriptions of the state-of-the-art developments in particular fields, as well as new results obtained by authors, editors, and their colleagues. The authors also identify and address crucial, but still unresolved, issues that come up when discussing new developments and issues within the discussed topics. I am thankful to Dr. Fan, the editor of this title, who did the major work by bringing together an excellent team of experts and by putting together many outstanding chapters in this title. It has been a pleasure working with him. I would also like to take this opportunity to thank the authors and editors of the books that are now in the process of being written as well as those authors who have already completed their volume for this series. Potential authors, editors, and those specialists interested in making contributions to the current state of knowledge in a particular field of engineering or applied science within the scope of this book series are invited to send their book proposals to me. Santa Cruz, CA

E. Suhir, Ph.D. Series Editor

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Contents

1 Fundamental Characteristics of Moisture Transport, Diffusion, and the Moisture-Induced Damages in Polymeric Materials in Electronic Packaging . . . . . . . . . . X.J. Fan and S.W.R. Lee

1

2 Mechanism of Moisture Diffusion, Hygroscopic Swelling, and Adhesion Degradation in Epoxy Molding Compounds . . . . M.H. Shirangi and B. Michel

29

3 Real-Time Characterization of Moisture Absorption and Desorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . Y. He and X.J. Fan

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4 Modeling of Moisture Diffusion and Whole-Field Vapor Pressure in Plastic Packages of IC Devices . . . . . . . . . . . . . X.J. Fan, T.Y. Tee, X.Q. Shi, and B. Xie

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5 Characterization of Hygroscopic Deformations by Moiré Interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E. Stellrecht, B. Han, and M. Pecht

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6 Characterization of Interfacial Hydrothermal Strength of Sandwiched Assembly Using Photomechanics Measurement Techniques . . . . . . . . . . . . . . . . . . . . . . . X.Q. Shi, X.J. Fan, Y.L. Zhang, and W. Zhou

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7 Hygroscopic Swelling of Polymeric Materials in Electronic Packaging: Characterization and Analysis . . . . . . J. Zhou, T.Y. Tee, and X.J. Fan

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8 Modeling of Moisture Diffusion and Moisture-Induced Stresses in Semiconductor and MEMS Packages . . . . . . . . . . C. Jang and B. Han

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9 Methodology for Integrated Vapor Pressure, Hygroswelling, and Thermo-mechanical Stress Modeling of IC Packages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T.Y. Tee

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10 Failure Criterion for Moisture-Sensitive Plastic Packages of Integrated Circuit (IC) Devices: Application and Extension of the Theory of Thin Plates of Large Deflections . . . . E. Suhir and X.J. Fan

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11 Continuum Theory in Moisture-Induced Failures of Encapsulated IC Devices . . . . . . . . . . . . . . . . . . . . . . X.J. Fan, J. Zhou, G.Q. Zhang, and A. Chandra

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12 Mechanism-Based Modeling of Thermaland Moisture-Induced Failure of IC Devices . . . . . . . . . . . . H.B. Chew, T.F. Guo, and L. Cheng

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13 New Method for Equivalent Acceleration of IPC/JEDEC Moisture Sensitivity Levels . . . . . . . . . . . . . . . . . . . . . . B. Xie, X.J. Fan, and X.Q. Shi

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14 Moisture Sensitivity Level (MSL) Capability of Plastic-Encapsulated Packages . . . . . . . . . . . . . . . . . . J.K. Fauty

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15 Hygrothermal Delamination Analysis of Quad Flat No-Lead (QFN) Packages . . . . . . . . . . . . . . . . . . . . . . . M.S. Zhang, S.W.R. Lee, and X.J. Fan

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16 Industrial Applications of Moisture-Related Reliability Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . W.D. van Driel, D.G. Yang, C.A. Yuan, and G.Q. Zhang

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17 Underfill Selection Against Moisture in Flip Chip BGA Packages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X.J. Fan, T.Y. Tee, C.Q. Cui, and G.Q. Zhang

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18 Moisture Sensitivity Investigations of 3D Stacked-Die Chip-Scale Packages (SCSPs) . . . . . . . . . . . . . . . . . . . . X.Q. Shi, X.J. Fan, and B. Xie

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19 Automated Simulation System of Moisture Diffusion and Hygrothermal Stress for Microelectronic Packaging . . . . . Y. Liu

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20 Moisture-Driven Electromigrative Degradation in Microelectronic Packages . . . . . . . . . . . . . . . . . . . . . L.F. Siah

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21 Interfacial Moisture Diffusion: Molecular Dynamics Simulation and Experimental Evaluation . . . . . . . . . . . . . . H. Fan, E.K.L. Chan, and M.M.F. Yuen

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About the Editors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Contributors

E.K.L. Chan Department of Mechanical Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, [email protected] A. Chandra Department of Mechanical Engineering, Iowa State University, Ames, IA 50011, USA, [email protected] L. Cheng Department of Mechanical Engineering, National University of Singapore, Singapore, Singapore 117576, [email protected] H.B. Chew Department of Mechanical Engineering, National University of Singapore, Singapore, Singapore 117576, [email protected] C.Q. Cui Compass Technology Co., Ltd., Shatin, Hong Kong, People’s Republic of China, [email protected] H. Fan Department of Mechanical Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, [email protected] X.J. Fan Department of Mechanical Engineering, Lamar University, PO Box 10028, Beaumont, TX 77710, USA, [email protected] J.K. Fauty 46641 East Decatur Street, Mesa, AZ 85205, USA, [email protected] T.F. Guo Department of Mechanical Engineering, National University of Singapore, Singapore, Singapore 117576, [email protected] B. Han Department of Mechanical Engineering, CALCE Electronics Products and Systems Center, University of Maryland, College Park, MD 20742, USA, [email protected] Y. He Intel Corporation, Assembly Test & Technology Development, 5000 W. Chandler Blvd., Chandler, AZ 85226, USA, [email protected] C. Jang Department of Mechanical Engineering, University of Maryland, Glen Martin Hall, College Park, MD 20742, USA, [email protected]

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S.W.R. Lee Department of Mechanical Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, [email protected] Y. Liu Fairchild Semiconductor Corp., 82 Running Hill Rd, South Portland, ME 04106, USA, [email protected] B. Michel Department of Micro Materials Center Berlin (MMCB), Fraunhofer Institute for Reliability and Microintegration (IZM), Volmerstraße 9B, 12489 Berlin, Germany, [email protected] M. Pecht Department of Mechanical Engineering, CALCE Electronics Products and Systems Center, University of Maryland, College Park, MD 20742, USA, [email protected] X.Q. Shi Applied Science & Technologies Research Institute (ASTRI) 5/F, Photonics Center, Science Park, Shatin, Hong Kong, People’s Republic of China, [email protected] M.H. Shirangi Department of Micro Materials Center Berlin (MMCB), Fraunhofer Institute for Reliability and Microintegration (IZM), Volmerstraße 9B, 12489 Berlin, Germany; Robert Bosch GmbH, Automotive Electronics, Development ASIC & Power Packages, Reutlingen, Germany, [email protected] L.F. Siah Assembly Technology Development Q&R – Malaysia (ATD Q&R-M), Intel Technology (M) Sdn. Bhd., Bayan Lepas FTZ Box 121, 11900 Pulau Pinang, Malaysia, [email protected] E. Stellrecht Department of Mechanical Engineering, CALCE Electronics Products and Systems Center, University of Maryland, College Park, MD 20742, USA, [email protected] E. Suhir Department of Electrical Engineering, University of California, 1156 High Street, SOE2, Santa Cruz, CA 95064-1077; Department of Mechanical Engineering, University of Maryland, College Park, MD, ERS Co. LLC, Los altos, CA, USA, [email protected] T.Y. Tee Blk 408, Hougang Ave 10, #07-1082, Singapore, Singapore 530408, [email protected] W.D. van Driel Philips Lighting, Mathildelaan 1,5611 BD Eindhoven, The Netherlands; Delft University of Technology, Mekelweg 2,2628 CD Delft, The Netherlands, [email protected] C.P. Wong Materials Science and Engineering, Georgia Institute of Technology, 771 Ferst Drive, N.W. Atlanta, GA 30332-0245, USA, [email protected] B. Xie Applied Science & Technologies Research Institute (ASTRI) 5/F, Photonics Center, Science Park, Shatin, Hong Kong, People’s Republic of China, [email protected]

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D.G. Yang Guilin University of Electronic Technology, Jinji Road 1, Guilin, China, [email protected] C.A. Yuan TNO IenT, Eindhoven, The Netherlands, [email protected] M.M.F. Yuen Department of Mechanical Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, [email protected] G.Q. Zhang Philips LightLabs, Mathildelaan 1, 5611 BD Eindhoven, The Netherlands; Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands, [email protected] M.S. Zhang Department of Mechanical Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, [email protected] Y.L. Zhang School of Mechanical & Production Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, Singapore 639798, [email protected] J. Zhou Department of Mechanical Engineering, Lamar University, PO Box 10028, Beaumont, TX 77710, USA, [email protected] W. Zhou School of Mechanical & Production Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, Singapore 639798, [email protected]

Chapter 1

Fundamental Characteristics of Moisture Transport, Diffusion, and the Moisture-Induced Damages in Polymeric Materials in Electronic Packaging X.J. Fan and S.W.R. Lee

1.1 Introduction Many failures in microelectronic packages can be traced back to moisture [1, 2]. The mechanical behavior of polymer systems is affected significantly by the absorption of atmospheric moisture [3–8]. In general, there are three types of failure mechanisms when an electronic package is exposed to humidity conditions [8]. The first type of failure is often referred to as “popcorn failure” [4–7]. Packaged microelectronic devices are exposed to factory environmental conditions after the opening of protective dry-bags for surface mounting to printed circuit board (PCB). When moisture, present in the factory environment, is absorbed by the polymeric packaging materials, it condenses in free volumes or micro-/nanopores in the bulk materials and along interfaces. The condensed moisture will vaporize and produce high pressure during the surface mount process. The board and devices are entirely placed in a reflow oven, in which the peak temperature ranges typically from 220 to 260◦ C. The reflow process is completed within a few minutes. Polymer materials, such as dielectric films, adhesives, encapsulants, and plastic printed circuit boards, become extremely compliant when the temperature exceeds their glass transition temperatures. In addition, the interfacial adhesion strength drops substantially. As a result, delamination may occur due to the combined effects of thermo-mechanical stresses, hygroscopic stresses, vapor pressure, material softening, and adhesion degradation. An audible sound may be produced if water vapor is suddenly released due to package cracking. The second type of moisture-induced failure mechanism concerns the package reliability during a lifelong service period under various field environmental conditions. Polymeric materials in packages will swell upon moisture absorption. Hygroscopic swelling creates dimensional changes of materials. Similar to thermal stresses due to the mismatch of thermal expansion, hygroscopic stresses are induced. Moisture will also substantially affect the interfacial adhesion. In addition, aging effect becomes a concern for a long-period exposure to humidity conditions. Consequently, delamination may take place along weaker interfaces

X.J. Fan (B) e-mail: [email protected] X.J. Fan, E. Suhir (eds.), Moisture Sensitivity of Plastic Packages of IC Devices, Micro- and Opto-Electronic Materials, Structures, and Systems, C Springer Science+Business Media, LLC 2010 DOI 10.1007/978-1-4419-5719-1_1, 

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to cause electrical failures of devices. The third type of moisture-assisted failure is due to electrochemical migration (corrosion) in the presence of both electrical bias and moisture (see Chapter 20). There are two kinds of corrosion in electronic packages. The first kind is metal dendritic growth at the cathode side on the substrate surface (e.g., copper trace). Electrolytic dissolution of copper at the anode creates metal ions. Metal ions then migrate to the cathode side as moisture provides transport path (e.g., moisture absorbed by the solder resist). When metal ions reach the cathode, dendritic growth occurs. Continuous reduction of dissolved metal ions leads to the nucleation and growth of metal dendrites, and eventually the formation of anode–cathode short failure. The second kind of corrosion, the so-called conductive anodic filament (CAF) growth, occurs at the sub-surface associated with glass fibers/epoxy resin interface. The CAF grows from anode to cathode along delaminated fiber/epoxy interfaces when moisture is present. A CAF is made from soluble copper salt at the anode and built at the anode by turning to insoluble salt due to pH effect. Dendrites occur as a result of solution at the anode and plating at the cathode. In order to address those moisture effects, three types of accelerated moisture sensitivity/reliability tests are often applied for package reliability qualifications [2]. Moisture/reflow sensitivity test is required prior to environmental stresses for all devices that are surface mounted to PCB. Moisture/reflow sensitivity test has been documented in the joint JEDEC/IPC industry standard J-STD-020D [9]. This test specification has established exposure conditions of temperature, humidity, and time for which the moisture sensitivity ranking of surface mount devices are classified and referenced. Moisture/reflow sensitivity test insures that the temperature, humidity, and/or the shipping requirements are met before assessing the reliability under operation conditions. The so-called highly accelerated stress test (HAST) (without electrical bias) is the second type of accelerated test to evaluate non-hermetic packaged devices in humid environments. The test employs temperature and humidity to accelerate the penetration of moisture through external protective material or along the internal build-up or joined interfaces. Electrical bias is not applied in this test in order to ensure that the failure mechanisms, which may be overshadowed by the bias, can be detected. This test is used to identify failure mechanisms internal to package and is destructive. An autoclave test or pressure cooker test (PCT) is similar to HAST. PCT has a fixed temperature (121◦ C) and fixed RH (100%). During HAST and PCT, the packages are placed in environmental chambers with humidity and temperature controls for a certain period of time. Both HAST and PCT are industrial standards for qualification requirements. Lastly, the biased temperature/humidity (TH) test is a moisture-related test used to evaluate the reliability of a powered device at an elevated temperature and in a high-humidity environment subject to the static bias of the nominal operation state (ranging from 0.1 to 7 V). There are two standard forms of biased moisture test that can be employed. The temperature, humidity, bias (THB) test is performed under the atmospheric pressure, at a temperature between 30 and 85◦ C, and with relative humidity (RH) from 50 to 85%. Highly accelerated stress test with bias (BiHAST) is performed at less than 3 atmospheres of pressure and at a temperature between 110 and 160◦ C.

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Fundamental Characteristics in Polymeric Materials in Electronic Packaging

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In order to fully understand failure mechanisms associated with moisture, it becomes exceedingly important to characterize the moisture absorption behavior of polymeric materials involved in electronic packaging and to quantify polymer matrix damage and adhesion degradation induced by moisture transport. In this chapter, the fundamental characteristics of moisture behaviors in polymer systems and the interactions of moisture with polymer matrix and along interfaces are reviewed. Both Fickian and non-Fickian kinetics of moisture absorption and desorption are investigated. Saturated moisture concentrations at different humidity levels as a function of temperature are discussed for different materials in a wide range of temperature. A specific experiment, which was designed to reveal the passage of moisture vapor through a hydrophobic membrane, is described. The difference of water sorption (immersion in water) and moisture sorption in humid air is discussed. Mercury intrusion method is introduced to measure the sizes of nanopores or free volumes for different types of packaging materials. An approximate method to estimate the free volume fraction is proposed based on moisture weight gain test data. Moiré interferometry technique is applied to study the aging effect of hygroscopic swelling of a polymeric material as a function of time. Adhesion and fracture toughness characterization methods are applied to investigate the influence of moisture on the interfacial fracture toughness or the adhesion strength. Finally, certain issues on the state of moisture in polymer materials, effect of hygroscopic swelling, effects of fillers, and the duration of moisture absorption at different conditions are discussed.

1.2 Fickian and Non-Fickian Moisture Diffusion Fickian transport of moisture in polymers or polymer composites is described by the following equation:   2 ∂ C ∂ 2C ∂ 2C ∂C . =D + + ∂t ∂x2 ∂y2 ∂z2

(1.1)

This equation is known as the general diffusion law or Fick’s second law of diffusion (Fick’s law, for short), C (kg/m3 ) is the moisture concentration, t (s) is time, and D (m2 /s) is the diffusion coefficient or diffusivity (diffusion constant) of the moisture in the material. The temperature dependence of the diffusion constant can be described by the Boltzmann–Arrhenius type of equation: 

Ed D = D0 exp − kT

 ,

(1.2)

where D0 is a pre-factor, Ed is the activation energy, k = 1.38 × 10−23 J/K is the Boltzmann’s constant, and T is the absolute temperature. Note that the pre-factor D0 and the activation energy Ed are different below and above the glass transition

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temperature [1]. In other words, there exist two sets of constants D0 and Ed for a material to fully describe the moisture diffusivity in it as a function of temperature. Consider a one-dimensional case of an infinite plate of thickness h. The general analytical solution, giving the temporal and spatial moisture concentration, C, at time t and the distance x from the mid-plane, can be obtained   ∞ (2n + 1)2 π 2 D C(x,t) − C0 4  ( − 1)n (2n + 1)π exp − x (1.3) = 1− t ·cos 2 Ci − C0 π (2n + 1) h h n=0

for the initial and boundary conditions C = C0 , − h/2 < x < h/2, t = 0 , C = Ci , x = −h/2, x = h/2, t ≥ 0 ,

(1.4)

where Ci is the moisture concentration on the boundary, C0 is the initial moisture concentration, D is the Fickian diffusion coefficient, and h is the thickness of the plate. Assuming the plate is initially dry and then placed into a humid environment, C0 = 0 and Ci = Csat (the saturated moisture concentration), equation (1.3) yields    ∞ (2n + 1)2 π 2 D (2n + 1)π 4  ( − 1)n exp − x t · cos 1− π (2n + 1) h h2 n=0 (1.5)

 C(x, t) = Csat

and describes moisture absorption process as a function of time. With the time progressing, the plate will be fully saturated with a uniformly distributed moisture with the concentration Csat . On the other hand, if C0 = Csat and Ci = 0, equation (1.3) yields

C(x, t) = Csat

  ∞ (2n + 1)2 π 2 D 4  ( − 1)n (2n + 1)π exp − x t · cos π (2n + 1) h h2

(1.6)

n=0

and describes a desorption process, in which an initially fully saturated plate releases moisture into the dry enviroment. The moisture in the plate will be driven out completely as time goes on. Since it is not possible to measure the moisture concentration at an arbitrary inner point experimentally, equation (1.3) should be integrated over the thickness of the bulk plate so that it would be possible to measure at the plate surfaces the ratio of the amount Mt of moisture at a given moment of time t to the amount M∞ of moisture at t → ∞. The total moisture mass in the specimen can be obtained as a function of time as follows:

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  ∞ Mt 1 8  (2n + 1)2 π 2 D =1− 2 exp − t for moisture absorption , M∞ π (2n + 1)2 h2 n=0 (1.7)   ∞ Mt 1 8  (2n + 1)2 π 2 D = 2 exp − t for moisture desorption , M∞ π (2n + 1)2 h2 n=0 (1.8) where Mt is the total mass of moisture at time t and M∞ is the mass related to the saturated concentration Csat by the formula Csat =

M∞ , V

(1.9)

where V is the total volume of the test specimen and M∞ is the saturated mass of moisture over the plate. When analyzing the experimental data, D and M∞ are optimized so that the difference between the experimentally determined mass Mt and its calculated value obtained on the basis of equation (1.3) is minimized [10]. The change in the sample volume caused by the moisture absorption–desorption is small and may be ignored. The accurate evaluation of the parameters Csat and D is critical to understand the physics of the absorption/desorption process and the related reliability issues. Csat determines the moisture absorption capacity of the specimen and D determines how fast the moisture could diffuse into or out of the sample. In equation (1.1) the Fickian diffusion is assumed to be independent of the moisture concentration. While the Fickian diffusion model provides a reasonable approximation to the characteristics of moisture uptake, it rarely provides a full description of the uptake data and is unable to account for the changes in the polymer due to relaxation, material degradation, or cracking. Non-Fickian behavior takes place as the consequence of the relaxation process in polymer molecules and/or as a result of an irreversible reaction between polymer and moisture, such as formation of hydrogen bonds and chemical reactions [11, 12]. It has been found that nonFickian diffusion can take diverse forms [5]. Two-stage or dual-uptake diffusion has been observed in some polymeric materials and is referred to in the literature [5] as an anomalous moisture uptake. Moisture weight gain measurement is a common experimental technique to evaluate the moisture uptake. In order to investigate the kinetics of the Fickian and non-Fickian moisture absorption, moisture weight gain measurements were carried out for several typical packaging materials. The specimen geometries and the temperature/humidity conditions were as follows: 1. A conventional underfill material. The test sample was a 1-mm-thick disk-like specimen with a diameter of 50 mm. Moisture absorption under 85◦ C/85% RH was measured.

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X.J. Fan and S.W.R. Lee

2. A thin bismaleimide-triazine (BT) 70-μm-thick core material with the dimensions 7 mm×7 mm. In this study, moisture absorption–desorption experiments were performed at temperatures 30, 60, and 80◦ C, respectively. At each isothermal temperature, two relative humidity (RH) levels were chosen: 60 and 80%RH. In situ measurements were performed on this thin sample. 3. A 0.6-mm-thick bismaleimide-triazine (BT) core material. The sample size was 50 mm×50 mm. Moisture absorption was measured under 30◦ C/60% RH conditions. 4. A conventional molding compound material sample. Two different sample geometries from the same material in the form of molded disks were fabricated, one with a thickness of 1 mm (MC1) and a diameter of 50 mm and another with a thickness of 2 mm (MC2) and a diameter of 100 mm, respectively. The specimens were exposed to the 85◦ C/85% RH conditions in a humidity chamber. To determine the dry weights, the samples were initially dried (“baked”) at 125◦ C for 24 h. An electronic balance was used for the weight measurements, except for the thin BT core, in which an in situ measurement was performed [10]. The samples were periodically removed and weighed and then returned to the chamber for further soaking. Figure 1.1 is the plot of the Fickian fit for moisture uptake for an underfill sample compared to the experimental data. To determine the diffusivity D and the saturated weight gain M ∞ , the least-squares fitting technique was used. In this approach, the sum of the square of the differences between the experimental weight gain and the  exp cal 2 , was calculated based on equation calculated one, (M)2 = ki=1 Mt,i − Mt,i exp (1.7), using some initial estimated values of the parameters D and M∞ . Mt,i was

Fig. 1.1 Fickian curve fit for a homogeneous underfill material under 85◦ C/85% RH (sample size 50 mm×50 mm×1 mm)

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Fundamental Characteristics in Polymeric Materials in Electronic Packaging

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the ith point of the experimentally determined weight gain at the moment t of time, cal was calculated on the basis of equation (1.7). Here k is the total number of while Mt,i the experimental points used when calculating (M)2 . Then, D and M∞ were varied until (M)2 was minimized. The obtained D and M∞ are taken as the diffusivity and the saturated moisture mass of the sample for that particular temperature/humidity conditions. As one could see from Fig. 1.1, the Fickian diffusion law predicts the experimental behavior of the test specimen within the test period very well. With the increasing time t, the absorption curve smoothly levels off to the saturation level M∞ . The test results in a previous study on different types of underfill also exhibited Fickian behaviors [2]. An example of moisture absorption–desorption experiment for a thin BT core is shown in Fig. 1.2. The temperature was kept at 60◦ C and the RH level was cycled between 0 and 60%. During the first 60 min, a 0% RH condition was imposed to drive residual moisture out of the sample. This was followed by a 200 min of moisture absorption at 60% RH, then a 200-min desorption at 0% RH. The following conclusions could be drawn from Fig. 1.2: (1) During the first 60 min, the moisture was not completely driven out of the sample. A longer time was needed to accomplish that. (2) The subsequent absorption–desorption cycles were reciprocal: the sample reached during re-sorption approximately the same saturated moisture level that the weight was lost as the result of drying. This indicates that the process is completely mechanical (“physical”) and there was no chemical reaction between the water molecules and the material. Figure 1.3 indicates, however, that the Fickian fit is not satisfactory. This could be attributed to the fact that the BT core has a highly inhomogeneous structure involving glass fibers and resin matrix. Rapid moisture diffusion into or out of the substrate at the initial stages of the moisture diffusion might be due to the moisture diffusion through the polymer-based region located at the outer layers of the substrate at the

Weight

RH 60°C

60 50

Weight (%)

100.2

Fig. 1.2 Moisture absorption–desorption experiment conducted using a sorption TGA at 60◦ C with the RH level cycled between 0 and 60% [10]

40 30

100.1

20

100.0

10 99.9

0 0

200

400

600 800 Time (min)

1000 1200

Reference Sensor RH (%)

100.3

8

0

Weight Change (μg)

Fig. 1.3 Desorption curves of a 70-μm BT core. Solid line represents the fitted weight loss versus time curve using D = 1.65 × 10−8 cm2 /s by Fick’s law [10]

X.J. Fan and S.W.R. Lee

Experimental Fitted (D = 1.65 µm2/s)

–5 –10 –15 –20 –25

0

2000

4000

6000

8000

Time (sec)

Fig. 1.4 Moisture weight gain curve for a thick BT core sample with the thickness of 0.6 mm subjected to 30◦ C/60% RH

Weight Gain (%)

beginning of the diffusion process. At the later stages, however, moisture diffusion was forced to progress through fibers which are moisture insensitive. Therefore, the inner components of the substrate acted as a physical barrier against the moisture diffusion, thereby reducing the rate of moisture diffusion or diffusivity. Figure 1.4 is a plot of the moisture weight gain for a 0.6-mm-thick BT core at 30◦ C/60% RH. After the extended hours of moisture absorption, the moisture uptake started to increase again. One could clearly see a two-stage moisture absorption. The material behaved initially as Fickian, and then exhibited a non-Fickian diffusion behavior afterward. The moisture absorption for a molding compound is plotted in Fig. 1.5 for specimens of two different thicknesses. An initial moisture uptake to quasi-equilibrium (the first stage of “virtual” saturation) is followed by a slower linear moisture uptake. This suggests that at least two different mechanisms are present in the moisture absorption process. The first one is the absorption of the water molecules in free volumes or nanovoids. The second mechanism is the hydrogen bonding formation between the water molecules and the polymer chains due to their molecular polarity. The former mechanism reaches a saturation point and is a reversible phenomenon in nature. The latter seems to be linear without a clear saturation, at least

0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0

24

48

72

96 120 144 168 192 216 240 Time (hr)

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Fundamental Characteristics in Polymeric Materials in Electronic Packaging

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Fig. 1.5 Normalized moisture uptake of a conventional mold compound with different thicknesses at 85◦ C/85% RH (x-axis is sqrt(time)/thickness)

for the timescale of observation in this study. The thicker sample (MC2) was further exposed to a humid environment for 8 months. The experimental data showed that the moisture weight gain reached the level of about 0.3% after 8 months compared to the 0.2% at the Fickian saturation point. Our latest experimental data showed that about 40% of residual moisture content was kept for MC2 at 110◦ C after a long period of desorption [11]. Although the composition and chemistry are different for the underfill material, BT, and the molding compound samples, it is not clear what particular mechanisms caused the difference in the moisture uptake for those materials. The molding compound specimen showed a stronger non-Fickian absorption kinetics than the underfill specimen. Vrentas and Duda [13] introduced a diffusion Deborah number (DEB)D to characterize the presence of the non-Fickian effects during absorption experiments. There are a number of non-Fickian diffusion kinetics [5], in which the two-stage non-Fickian type of absorption is widely applied. The general manifestation of the two-stage sorption is characterized by a rapid initial uptake, then a quasi-equilibrium process, followed by a slow approach to the final, true equilibrium. Ultimately, complete saturation will be reached in all instances. A theory that satisfactorily describes the features of a “two-stage” sorption has been suggested by Hopfenberg [14]. In their diffusion relaxation model they considered the absorption process to be composed of two empirical independent contributions: a diffusion part, MF (t), that is governed by Fick’s law, and a structural part, MR (t), resulting from polymer relaxations. The total weight gain at time t may be expressed as the linear superposition of these two contributions: M (t) = MF (t) + MR (t)

(1.10)

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X.J. Fan and S.W.R. Lee

In this equation, MF (t) is given by the solutions to the diffusion equation (1.1). It is assumed that more than one independent relaxation process might be possible, so that the part MR (t) could be expressed by a series M∞ (t) =



M∞,i (1 − e−ki t ) ,

(1.11)

i

where M∞,i represents the equilibrium absorption due to the ith relaxation process and ki is the first-order relaxation constant of the ith relaxation process. It has been shown that such a model is able to describe the non-Fickian behaviors [5]. Whether the non-Fickian effects are considered in the field conditions or in the testing conditions depends on the duration of the time of exposure to moisture. If the exposure time does not exceed the time before polymer relaxation commences, then Fick’s law can be accepted to describe the moisture diffusion. Otherwise non-Fickian’s behavior must be considered. IPC/JEDEC standards require that the duration of moisture exposure at different humidity levels is usually 7–9 days. To determine the exposure time when Fickian law is valid, modeling should be employed. Such modeling should consider material’s chemistry, specimen’s geometry, and humidity level.

1.3 Saturated Moisture Concentration Saturated moisture concentration Csat is a measure of the moisture absorption capacity under given humidity and temperature conditions. According to the definition of the relative humidity as RH =

actual partial water vapor pressure of the air p × 100% = psat saturated partial water vapor pressure of the air

(1.12)

the partial water vapor pressure of the air for the given relative humidity and absolute temperature is p = RH × psat ,

(1.13)

where psat is the saturated water partial vapor pressure and is a function of temperature. Assuming that Henry’s law applies, we have p=

Csat S

(1.14)

S=

Csat , p

(1.15)

or

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Fundamental Characteristics in Polymeric Materials in Electronic Packaging

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where S is the solubility, a material property, which is independent of the ambient relative humidity. From equations (1.13) and (1.15), we obtain Csat = (S × psat )RH .

(1.16)

Equation (1.16) indicates that the solubility S can be obtained when Csat is measured at different temperatures. Since the solubility and the saturated water vapor pressure are functions of temperature, the saturated moisture concentration is proportional to the relative humidity, as long as Henry’s law is fulfilled. Such a linear relationship has been confirmed by the moisture weight gain test obtained for the thin BT sample from the RH step scan experiment, as shown in Fig. 1.6. This figure shows that, at a fixed temperature (30◦ C in this case), Csat is linearly proportional to the RH level. The saturated moisture concentration in the BT sample is shown in Fig. 1.7 as a function of temperature for two different RH levels. The data were obtained from moisture absorption–desorption experiments. Figure 1.7 shows that the parameter Csat in BT core is essentially temperature independent. For most polymer materials at the temperatures well below the glass transition temperature, Csat is temperature independent. This implies that the solubility decreases with temperature according to equation (1.16). The situation is different when the temperature exceeds the glass transition temperature, Tg . The saturated moisture concentration for a die-attach film in the range from 30 to 80◦ C at 60% RH level is shown in Fig. 1.8 as a function of temperature. A strong dependence of temperature is evident. The tested film has a Tg at around 35◦ C. For temperatures exceeding Tg , the saturated moisture concentration depends strongly on the temperature. As a matter of fact, since the saturated moisture concentration has strong dependence on the free volume fraction, the saturated moisture concentration increases significantly when temperature exceeds the glass transition temperature. It is important to investigate the saturated moisture concentration

9 Experimental Data Linear Fit

8

Csat (mg/cm3)

7 6 5 4 3

Slope = 0.11

2 1

Fig. 1.6 Csat as a function of relative humidity at 30◦ C [10]

0

0

10

20

30 40 50 60 Relative Humidity (%)

70

80

90

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X.J. Fan and S.W.R. Lee 10

Csat (mg/cm3)

Fig. 1.7 Saturated moisture content as a function of temperature for two different RH levels [10]

8

6

4

60% R.H. 80% R.H.

70 μm BT core 30

40

50

60

70

80

Temperature (°C)

1.2

Saturated Moisture Uptake (%)

Fig. 1.8 Saturated moisture concentration as a function of temperature for a die-attach film at 60% RH level (Tg of the film is 35◦ C)

Measured Linear Fit

1.0

0.8

0.6 Y = 0.34 + 0.0084T 0.4 30

40

50

60

70

80

Temperature (°C)

at reflow soldering temperatures since an “over-saturation” phenomenon might take place at the reflow soldering conditions [15]. “Over-saturation” is a situation that the material might continue to absorb more moisture despite that desorption takes places during soldering reflow. When saturated moisture concentration is a function of temperature, the moisture diffusion modeling using normalization approach is no longer valid [2]. A direct concentration approach (DCA) has been proposed [15, 16] to conduct moisture diffusion modeling at reflow soldering conditions.

1.4 Water Sorption and Moisture Sorption When a polymer material is immersed into water, the sorption process is referred to as water sorption. For a material that is subjected to a humid air condition with a relative humidity less than 100%, it is referred to as moisture sorption process.

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Fundamental Characteristics in Polymeric Materials in Electronic Packaging

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There are two distinct diffusion mechanisms involved in the transport of moisture: moisture transfer across the surface and through the bulk material, respectively. In order to study the difference between water sorption and moisture sorption, an experiment of moisture sensitivity/reflow test for two groups of quad flat no-lead (QFN) plastic packages was conducted [17]. One group of the packages was coated with a hydrophobic membrane fabricated by a grafting method [18] to prevent water uptake, while the other group was as received. Two types of moisture preconditioning were applied: immersion into water at a constant temperature of 60◦ C and placement in a humidity chamber at 60◦ C/60% RH. Both sorption durations were 192 h. Table 1.1 summarizes the weight gain data and the results after the reflow. The coated packages under water did not exhibit any weight change. However, the coated packages in humid air condition gained almost the same amount of moisture as the uncoated packages either in water or in humid air. Furthermore, the reflow test indicated that the coated packages at 60◦ C/60% RH preconditioning had the same failure rate as the uncoated packages in the same preconditioning conditions, while the coated packages immersed into water did not show any failures after the reflow. These results indicate that a hydrophobic polymer film is very effective in blocking liquid water from penetrating through the package surface, but not for water vapor transmission (see Fig. 1.9). Several other hydrophobic polymeric materials have been found to exhibit similar behavior, as far as water vapor passage in humid air conditions is concerned (Winkler, P., of Badger Meter Inc. 2009, personal communications). Table 1.1 Effect of hydrophobic membrane on moisture sorption versus water sorption Sorption condition

Hydrophobic film coated

Averaged weight gain (%)

Reflow test failure rate

Water immersion (60◦ C) Water immersion (60◦ C) Moisture sorption (60◦ C/60% RH) Moisture sorption (60◦ C/60% RH)

Yes No Yes No

0.03 0.32 0.31 0.31

0/12 7/12 6/12 8/12

1.5 Characterization of Pore Size, Porosity, and Free Volume Porosity of, or free volume fraction in, polymers is a critical material property related to the moisture absorption. Polymer volume is divided into three elements: occupied volume (the “van der Waals” volume), interstitial free volume, and holefree volume [19]. The hole-free volume is accessible for penetrant transport and may be altered by absorption and desorption of penetrants. Changes in the total polymer volume are largely governed by changes in the hole-free volume. Experimental technique known as mercury intrusion porosimetry characterizes material’s porosity by applying various levels of pressure to a sample immersed in mercury [20]. The pressure required to intrude the mercury into sample’s pores

14

X.J. Fan and S.W.R. Lee Water-proof coating film

Water vapor molecules

Water liquid molecules

Fig. 1.9 Schematic diagram for a hydrophobic coating film, which can prevent liquid phase moisture, but not vapor phase moisture, from penetrating into the film

is inversely proportional to the size of the pores. Mercury intrusion porosimetry is based on the capillary law governing liquid penetration into small pores. This law, in the case of a non-wetting liquid like mercury, is expressed by the Washburn’s equation D=

−4γ cos θ , P

(1.17)

where γ is the surface tension of mercury, θ is the contact angle between the mercury and the sample, P is the applied pressure, and D is the pore diameter, all in consistent units. The volume V of mercury penetrating the pores is measured directly as a function of the applied pressure. This P-V curve serves as a unique characterization of the pore structure. The Washburn equation assumes that all pores are cylindrical. Although in reality pores or free volumes are rarely cylindrical, this equation provides a practical representation of pore distributions, providing very useful results for most applications. As pressure increases during an analysis, pore size is calculated at each pressure point, and the corresponding volume of mercury required to fill in these pores is measured. These measurements taken over a range of pressures provide the pore volume versus pore size distribution for the sample material. Mercury porosimetry can determine the pore size distribution quite accurately. Comprehensive data provide extensive characterization of sample porosity and density. Available results include total pore volume, pore size distribution, and pore diameter. Mercury porosimetry is typically applied over a capillary diameter range from 50 nm to 360 μm.

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Several types of polymer materials for electronic packaging applications, such as die-attach films, solder mask, and underfills, were tested using the mercury intrusion technique [21]. Those materials were also examined for moisture weight gain test at 85◦ C/85% RH. The results showed that the relative weight gain ranged from 0.48 to 1.27% for those tested materials. However, no significant pore size down to ∼50 nm was observed for all materials under investigation. This implies that the free volumes, which are occupied by the absorbed moisture, are typically in nanometer range. The same materials were then subjected to a simulated reflow process. An example of microstructures of a die-attach film before and after the reflow is shown in Fig. 1.10. It can be seen that the significant voiding of the film due to the internal vapor pressure was developed after the reflow process [22]. Soles et al. [23] used positron annihilation lifetime spectroscopy (PALS) to quantify the polymer network topology, which produces a nanovoid volume fraction as a function of temperature. A strong correlation was observed between the absolute zero volume fraction and the ultimate moisture uptake. Although the correlation is clear, the absolute moisture zero hole volume fraction is not sufficient to predict the ultimate moisture uptake. An approximate estimate method to obtain the free volume fraction of polymers is proposed using moisture weight gain test. Consider a material with a saturated moisture concentration Csat at the given temperature and humidity. The initial free volume fraction f0 can be found as f0 =

Csat , ρ

(1.18)

where ρ is the moisture density in the pores or free volumes. Since the density of the liquid water is 1.0 g/cm3 , the moisture density in free volume, i.e., the ρ value in equation (1.18), must be less than or equal to 1.0 g/cm3 : f0 ≥ Csat .

(1.19)

Here Csat has the unit of g/cm3 . In general, Csat depends on the relative humidity and temperature. The water liquid will fill in the free volume completely at 100%

Fig. 1.10 Microstructures of a soft die-attach film (a) before and (b) after reflow with moisture absorption

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X.J. Fan and S.W.R. Lee

RH [24, 25]. Therefore, the initial free volume fraction can be estimated from the moisture weight gain test using Csat measurement data extrapolated to 100% RH. This is a lower-bound estimation since the moisture will be usually in the mixture of water and vapor in free volumes. The free volume fraction is usually between 1 and 5% for typical packaging materials [26].

1.6 Hygroscopic Swelling Measurement There are a number of experimental techniques for the characterization of hygroscopic swelling of polymers [27–29]. However, relatively few studies took the time effect into consideration even though polymers exhibit viscoelastic behavior under hygrothermal aging. To address the phenomenon of hydroscopic swelling, a silicon/underfill/FR-4 assembly was built and tested [30]. The purpose of the study was to investigate the hygroscopic swelling behavior of the underfill material in a flip-chip assembly-like configuration. An integrated multi-functional micro-moiré interferometry system was developed [30], by combining moiré interferometry (MI) technique with thermoelectric heating and cooling technique (for thermal cycling) and a humidity environment system (for hygrothermal aging), to investigate the hygroscopic swelling of the underfill. Specimen grating with a frequency of 1,200 lines/mm was replicated onto the surface of the assembly at room temperature. The assembly was then put into the miniaturized moisture chamber with the hygrothermal loading conditioned at 85◦ C/85% RH for 168 h. In order to eliminate thermal effect and investigate the aging effect, a separate thermal aging test without moisture was carried out with the same test configuration and the moiré fringe patterns were acquired at the same time intervals. The detailed experimental procedure and results are presented in Chapter 6. The normal strain and the shear strain obtained from the fringe measurement are plotted in Fig. 1.11. The strain components increased significantly at the beginning.

‘black’ line – pure swelling induced γ xy

‘black’ line – pure swelling induced εx

‘red’ line - γ xy in hygrothermal aging

‘red’ line - εx in hygrothermal aging

‘blue’ line - εx in thermal aging

(a)

‘blue’ line - γxy in thermal aging

(b)

Fig. 1.11 Swelling-induced strains by using superposition method: (a) normal strain εx vs. time (b) shear strain γxy vs. time

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Fundamental Characteristics in Polymeric Materials in Electronic Packaging

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This should correspond to the swelling at the sample surface and the thermal expansion of the underfill material upon moisture absorption and temperature increase. When water migrated into an epoxy-based underfill, it broke the interchain bonds in the material by forming hydrogen bonds with chain interruption. The formation of hydrogen bonds permitted the resin network to expand as a result of the relaxation of the stresses produced by osmotic pressure. With time progressing, the surface portion of the sample was saturated with moisture absorption, and therefore, the strain increase becomes less significant. The red line in Fig. 1.11 represents the change in the measured strain with moisture uptake. It actually consists of two parts: the swelling-induced strain and the thermal-mismatch-induced strain. The blue line represents the experimental results for the same assembly without moisture absorption at a constant temperature of 85◦ C. Therefore, the actual swelling-induced strain should be the black line, which is obtained by the red line subtracted from the blue line. With the consideration of the stress relaxation, the actual swellinginduced strains were expected to be greater than those measured in the process of the hygrothermal aging. The losses of strains induced by thermal aging were added in Fig. 1.11 to the strains measured in hygrothermal aging. As a result, the values of swelling-induced strains were increased by 20–30%. This implies that the time effect and relaxation due to aging must be taken into consideration in order to adequately model the swelling behaviors of polymer materials.

1.7 Effect of Moisture on Fracture Toughness/Adhesion Strength In this section, both fracture mechanics based fracture toughness measurement techniques and the die shear test method are introduced to study the influence of moisture on fracture toughness/adhesion strength. The interface between polyimide on silicon chip and underfill (PI/UF) is used as a carrier in the study.

1.7.1 In Situ Fracture Toughness Measurement A number of test specimens for investigating interfacial fracture energy have been developed over the years [8]. But very few methods could provide rigorous results which might be readily implemented on actual multilayer configurations. The particular difficulties in the measurement of interface fracture toughness are the sample preparation and the design and implementation of test procedures that provide controlled, stable growth of the interface crack. Four-point bend test specimens have been successfully used in semiconductor industries to characterize the interfacial fracture toughness at silicon level with multi-stack layers of thin films. However, the fracture toughness at package level usually has higher fracture toughness (e.g., >20 J/m2 for PI/UF). Most often, when the interface strength is strong, the crack using four-point bend specimen tends not to stay at the interface but goes into the silicon, rendering the interfacial fracture energy measurement meaningless. This has become a major issue when the test is performed in an environmental chamber for

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X.J. Fan and S.W.R. Lee

an in situ measurement. Double cantilever beam (DCB) specimen structure has been applied to measure the interfacial fracture toughness [8]. The details of DCB silicon/underfill/silicon (Si/UF/Si) specimen preparation is described in [8]. A key step in sample preparation is to fill underfill by capillary force. Aluminum end blocks, each with an extended arm, are used to reinforce the silicon beam and prevent it from cracking during testing of Si/UF/Si samples, as shown in Fig. 1.12. Alternatively, the Si/UF/Si specimen can be prepared by dispensing the underfill before the top silicon part was placed (referred to “open face” method). However, it has been shown that underfill filling by capillary force method resulted in much less scattered data for the interface fracture energy measurement than the “open face” dispensing method [8]. This indicates that using capillary force dispensing method to prepare samples for DCB configuration is a critical process step ensuring good quality of interfaces under study. Such an assembly process also mimics the actual underfilling process. Typical load–displacement plots are shown in Fig. 1.13 for a Si/UF/Si specimen. When the load–point displacement increased at a constant rate, the peak

Fig. 1.12 Schematic diagram of a Si/UF/Si sandwiching specimen for the DCB

Force (N)

DCB Load-Disp Curve

Fig. 1.13 Typical loading–unloading curve for a Si/UF/Si DCB specimen

16 14 12 10

Region for data collection

8 6 4 2 0 0

0.1

0.2

0.3 0.4 0.5 0.6 Displacement (mm)

0.7

0.8

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Fig. 1.14 Fracture toughness for a Si/UF/Si assembly under different environmental conditions

normalized energy release rate

load was associated with the onset of the crack growth, and the load drop was associated with the crack jump/arrest. The load-rising portion of each peak is nearly linear and can be used to determine the compliance and peak load needed for the analysis. After stable crack growth occurred (crack length increase from a to a + a), the displacement ramp was interrupted, the specimen was allowed to return to the original undeformed state and was re-loaded again with a constant displacement rate. Compliance C and peak load Pc were determined from each loading curve. The crack length was measured during the re-loading process when the interfaces in front of the crack tip were opened, and the crack tip was located via microscopy. It should be noted that in the beginning of a few cycles for loading and unloading, the data should be discarded because the pre-crack is not sharp enough and the initial stress state of the system was not calibrated. When crack growth becomes substantially large, linear elastic fracture mechanics is not valid. Therefore, those data should be discarded too. Only the middle portion of the data shown in Fig. 1.13 was used to extract the fracture toughness. The details of fracture parameter extraction from the experimental data can be found in [8]. Figure 1.14 plotted the test results in three different conditions. “Case 2” represents the fracture toughness at room condition after the sample was assembled. A significant difference was observed for the fracture toughness at room condition and the one after 1 h bake at 130◦ C. This was possibly due to the moisture effect at room condition, in which a ∼30% RH was expected. Since the underfill was cured following the curing schedule exactly, the suspicion of whether or not the underfill was fully cured was eliminated. As expected, the fracture toughness decreases after moisture preconditioning at 85◦ C/85% RH for 5 days, as shown in Fig. 1.14.

4.5 4 3.5 3 2.5 2 1.5 1 0.5 0

Case 1: 130°C bake for 1 hour Case 2: room condition Case 3: 85°C/85%RH for 5 days

case 1 case 2 case 3 different environmental conditions

1.7.2 Die Shear Test Although interfacial fracture mechanics based fracture toughness measurement provides rigorous definition and results for evaluating interface strength, the sample preparation is very tedious, and the procedure often is not compatible with packaging assembly process. On the other hand, die shear test, by which the samples can

20

X.J. Fan and S.W.R. Lee

be made by standard packaging and assembly processes, provides an effective way for a quick assessment of the adhesion strength. Die shear tests can be performed on a die shear tester system: DAGE Series 4000 with hot plate (temperature range 25–300◦ C). The system has a fixed hot plate and test table with full automatic test process. Several parameters such as shear speed and shear height can be adjusted to control the fracture mode (see Chapter 17 for more details). Figure 1.15 presents the shear adhesion strength results at room temperature for three different underfills under various soaking conditions. It shows that the differences in adhesion among the three underfills at room temperature are not significant. It is also noted that the adhesions for these three underfills are not sensitive to moisture at room temperature. Figure 1.16 plotted the test results for these three underfills at 220◦ C under

Shear Test Strength (PI/UF) At Room Temperature 40

Shear Strength (KG)

35 30 25 20 15 10 5 0 UF1

Fig. 1.15 Adhesion strength at room temperatures under different moisture conditions for three underfills

0 days

UF2 Moisture: 85°C/85RH 11 days

17 days

UF3

21 days

UF/PI 220°C Shear Speed 200um/s Shear Height 30um

Average Shear Strength (KG)

7

Fig. 1.16 Adhesion strength at 220◦ C under different moisture conditions for three underfills

6 5 4 3 2 1 0 Dry

30°C/60RH

UF-3

85°C/60RH

UF-1

85°C/85RH

UF-2

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Fundamental Characteristics in Polymeric Materials in Electronic Packaging

21

various conditions. It shows that the moisture has strong influence on the shear adhesion strength at an elevated temperature. This implies that the adhesion test at high temperature is necessary for the correlation with the actual material performance during moisture sensitivity test.

1.8 Discussions 1.8.1 State of Moisture in Polymers When moisture enters the polymer matrix, it gets condensed into the liquid water phase. Let us consider, for instance, moisture absorption for an underfill subject to the 85◦ C/85% RH condition (see moisture absorption data in Fig. 1.1). Assume that moisture diffusion follows Fickian kinetics with M∞ being the ultimate moisture weight gain for a sample of volume V. The saturated moisture concentration, Csat , as defined by equation (1.9) can be calculated from the weight gain test. The obtained value is Csat = 12.5 mg/cm3 . The ambient moisture vapor density at 85◦ C/85% RH, i.e., ρ ext , can be obtained from the measured saturated water vapor density at 85◦ C/85% RH as follows: ρext = 0.85ρg = 3.04e−4 g/cm3 .

(1.20)

Here ρ g is the saturated water vapor density at 85◦ C. A simple comparison between Csat and ρ ext reveals that Csat = 41ρext . If the free volume fraction is 5% of the total sample volume, then the actual moisture density in the free volume can be estimated according to equation (1.18) as follows: ρ = free volume fraction × Csat = 820ρext .

(1.21)

This implies that the moisture in underfill must be in the binary water liquid/vapor phase. The diffusion process of moisture through polymer systems is a transport process of moisture from ambient vapor phase to the condensed mixed liquid/vapor phase. Water molecules in polymeric materials have been identified to have two distinct states. “Free” or “unbound” state of water is attributed to water molecules that are present in nanopores or free volumes, while “bound” water molecules react with the polymer chains via hydrogen bonding or some chemical reactions [10]. The unbound moisture can be released completely as a result of a desorption process at the same temperature at which the moisture is absorbed. However, in order to release the bound moisture, more energy is needed to break the hydrogen bond and, therefore, a higher temperature is needed. Zhou and Lucas [31] studied the mobility of water in different epoxy systems. The study shows that water molecules bind with epoxy resins through hydrogen bonds. Two types of bound water were found in the epoxy resins. The binding types are classified as type I or type II bonding, depending on the difference in the bond complex and the activation energy. Type I

22

X.J. Fan and S.W.R. Lee

bonding corresponds to a water molecule which forms a single hydrogen bond with the epoxy resin network. This water molecule possesses a lower activation energy and is easier to remove such a molecule from the resin. Type II bonding takes place as a result of a water molecule forming multiple hydrogen bonds with the resin network. This water molecule possesses a higher activation energy and is therefore harder to be removed. Type I bound water is the dominant form of the total amount of the absorbed water. The amount of type II bound water depends strongly on the exposure temperature and time. Higher temperatures and longer exposure times result in a greater amount of the type II bound water.

1.8.2 Total Moisture Volume Versus Volume Expansion Due to Hygroscopic Swelling Consider the underfill tested for hygroscopic swelling; the volume change due to hygroscopic swelling based on the test data under 85◦ C/85% was determined as follows [32]: V = 0.3%, V

(1.22)

where V is the total volume of the sample and V is the volume change due to the moisture absorption at a constant temperature. On the other hand, the material’s free volume fraction is estimated as 3% as a representative value as follows: f0 =

Vfree volume = 3%. V

(1.23)

It shows that the volume change by hygroscopic swelling is only a small fraction of the total free volume. In the previous section, the estimation of the free volume fraction does not consider the effect of hygroscopic swelling. This example inferred that the estimation of free volume fraction using weight gain data without considering the material swelling provides a good approximation if the material does not swell excessively. Equations (1.22) and (1.23) indicate that the major portion of moisture absorption does not contribute to the material’s swelling. It has been suggested that swelling is caused by water molecules bound to the polymer matrix and not by the free water molecules. Because the water molecule is polar, it is capable of forming hydrogen bonds with hydroxyl groups, thereby disrupting interchain hydrogen bonding with the net effect of increasing the intersegmental hydrogen bond length. This concept has been observed and confirmed through spectroscopic methods [33, 34]. If such a postulation holds true, the hygroscopic swelling development would include two stages, which correspond to the dual-stage moisture absorption theory. In the first stage, the absorption of water molecules takes place in free volumes or nanovoids, which is a reversible process. This stage would not contribute to the hygroscopic swelling significantly. In the

1

Fundamental Characteristics in Polymeric Materials in Electronic Packaging

23

second stage, the hydrogen bonding is formed between the water molecules and polymer chains, which will cause the material’s swelling. No published data are available on the history of hygroscopic swelling. In order to characterize the swelling behavior, the coefficient εswelling of hygroscopic swelling (CHS) can be introduced as follows: εswelling = βC,

(1.24)

where β is the coefficient of hygroscopic swelling and C is the moisture concentration. According to the above analysis, the formation of hydrogen bond with polymer materials causes the hygroscopic swelling of materials, while the unbound water liquid/vapor fills in free volumes, which does not cause swelling if the vapor pressure is low at lower temperatures. Therefore, the above equation might need to be modified if only a small fraction of moisture is responsible for the swelling of materials. Instead of using the total moisture concentration in equation (1.24), the moisture concentration fraction which forms the hygrobonding (type II) may be used: εswelling = βCbound water ,

(1.25)

where C bound water is the moisture mass for the bond formation per unit volume.

1.8.3 Effect of Fillers Many polymer materials used in electronic packaging contain fillers. While most fillers are not used with the intent of altering the sorption and transport of water within polymer, this concomitant effect is always unavoidable. Much of the effect of the fillers on the transport properties within the matrix is governed by the degree of interaction between the polymer matrix and the filler at the interphase. In most composites, it is desirable to have a strong adhesive bond between the two materials. The adhesive bonds can be of either a physical or physicochemical nature. Variations in the strength and nature of these bonds lead to three typical situations at the polymer/filler interface [35]. If the bonds are physical, water can be prevented from reaching the interfacial region and the amount of water absorbed depends only on the epoxy fraction of the composites. If physicochemical bonds, such as hydrogen bonds, are involved, the polymer may find its movement restricted in the vicinity of the filler. If this attraction is strong enough, a porton of the polymer matrix as well as the filler volume may be impermeable to the penetrating moistue. If the bonding at the interface is weak, water transport may be enhanced by pathways open along the interface. In this case, the water is transported in the liquid state by capillary forces. Similar capillary transport may occur if microcracks and/or defects are present in the bulk of the epoxy. Voids at the interfcae may increase the Langmuir sites of the composites, allowing higher equilibrium sorption. Water clustering in these voids can cause positive deviations from Henry’s law [36].

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X.J. Fan and S.W.R. Lee

The effect of the interfacial bonding can be taken into account by comparing diffusion and sorption in neat polymer resins and composites. If, after correcting for the fiber content of the composite, there is no difference between these two, interphase effects may be negligible. This in general is found to be true for glass/epoxy systems.

1.8.4 Duration of the Moisture Diffusion In order to illustrate the nature of the moisture diffusion in polymer materials, we consider an example of a simple transient moisture diffusion problem in a slab, with the boundary conditions as shown in Fig. 1.17. The thickness of 2 mm is taken as a typical value for a thick QFP. Three boundary conditions were examined, with the material properties and ambient humid conditions listed in Table 1.2. The results based on equation (1.5) are plotted in Fig. 1.18 for the local moisture concentration at the dry-side as a function of time for three different boundary conditions. It takes hundreds of hours (or even longer) to reach the saturated moisture state. This implies that moisture diffusion is a “slow” process. From equation (1.5), it can be seen that moisture diffusion is strongly dependent on the specimen’s thickness. Therefore, the duration for a material (or structure) to reach saturated state depends strongly on the thickness. For a 30-μm free-standing wafer-level die-attach film at 30◦ C/70RH%, the film is saturated within 5 min [10]. Since newly developed packages become thinner and thinner, the saturated state can be reached much earlier than the required moisture soaking duration (see Chapter 13). In addition, according to equation (1.2), moisture diffusivity increases exponentially with the increase in temperature and, therefore, the diffusivity at reflow peak temperature can be a

x

h = 0.2 cm

Fig. 1.17 One-dimensional moisture diffusion problem

∂C ( x, t ) ∂x

x=h = 0

C (0, t ) = Csat

Table 1.2 Three types of boundary conditions Saturated vapor Moisture density preconditioning ρ g (g/cm3 )

Saturated vapor pressure pg (MPa)

Ambient Ambient vapor vapor density pressure ρ ext (g/cm3 ) pext (MPa)

Moisture diffusivity α D (cm2 /s)

30◦ C/60% RH

4.24 × 10−3 5.87 × 10−2 5.87 × 10−2

0.6 ρ g

0.6pg

3.13 × 10−9 7.86 × 10−3

0.6 ρ g

0.6pg

2.85 × 10−8 8.84 × 10−3

0.85 ρ g

0.85pg

2.85 × 10−8 1.25 × 10−2

85◦ C/60% RH 85◦ C/85% RH

3.04 × 10−5 3.58 × 10−4 3.58 × 10−4

Saturated concentration Csat (g/cm3 )

Fundamental Characteristics in Polymeric Materials in Electronic Packaging

Fig. 1.18 Local moisture concentration at x = h as a function of time for different boundary conditions

25

14.0 30C/60%RH Local moisture concentration at side of x=h (g/cm^3 *e –3)

1

12.0

85C/60%RH 85C/85%RH

10.0 8.0 6.0

x=h

4.0 2.0

h = 0.2 cm

0.0 0

100

200 300 Time (hours)

400

500

few orders higher than the diffusivity at the room temperature. Significant moisture escape from the package during reflow process is expected, which will have a significant impact on package performance at the reflow soldering conditions (see Chapter 18). In Fig. 1.19 the temperature change is plotted for the same configuration as defined in Fig. 1.17 for the thermal diffusion (the thermal diffusivity is taken as 4.0 × 10−3 cm2 /s as a representative value for polymer materials). The structure reaches uniform temperature in about 40 s. The results of Figs. 1.18 and 1.19 show that the heat transfer is much faster than moisture diffusion, even though polymer

Temperature at the side of x=h

1.2

1.0

0.8 x=h

0.6

0.4

0.2

h = 0.2 cm

0.0

Fig. 1.19 Temperature at x = h as a function of time

0

10

20 Time (second)

30

40

26

X.J. Fan and S.W.R. Lee

materials are not good thermal conductive materials. This implies that the package temperature may be assumed to be uniform during the reflow process.

1.9 Concluding Remarks Some epoxy-based polymer materials, e.g., underfills, follow Fick`s diffusion law very well, as far as moisture absorption is concerned. However, for some other materials, e.g., molding compounds, non-Fickian behaviors appear significant even during the standard test period. For BT core materials, the absorption–desorption cycles are repeatable, but Fickian fit is not satisfactory. “Two-stage” sorption theory can describe the non-Fickian diffusion well. The two-stage sorption is characterized by a rapid initial uptake to a quasi-equilibrium state, followed by a slower rate approaching the final true equilibrium state. For practical reasons, if the attention is focused on the moisture diffusion process, when the second stage has not yet been taken into effect, the sole Fickian behavior may be applied. Saturated moisture concentration Csat can be used as a measure of the moisture absorption capacity under given humidity and temperature conditions. For most polymer materials in microelectronics packaging, Csat is temperature independent, but depend on the RH only, provided that the temperature is far below the glass transition temperature. This fact offers theoretical foundation for the accelerated moisture sensitivity test, in which increasing temperature allows fast moisture absorption, while the maximum amount of moisture absorption remains the same. However, the saturated moisture content may increase significantly with the increase in temperature, when the temperature is across the glass transition temperature. Pore sizes and porosity (or free volume fraction of polymer) are critical material properties related to the moisture absorption. For most polymer materials, the free volume or pore sizes are in nanometer range although the free volume fraction is usually in the range of 1–5%. Significant voiding can be developed during the reflow process for soft films. Moiré interferometry technique was applied to study the aging effect of hygroscopic swelling. It was found that hygroscopic swelling is coupled with stress relaxation. Therefore, a nonlinear viscoelastic model should be used to properly model the polymer swelling behaviors. Moisture diffusion can be a slow or fast process, depending on material thickness and temperature. A thick QFP may need hundreds of hours for moisture soaking to reach a saturated state, while a freestanding wafer-level film is saturated with moisture absorption within a few minutes even at room temperature.

References 1. Fan, X.J., “Moisture related reliability in electronic packaging”, Electronic Component Technology Conference (ECTC) Professional Development Course Handout, 2008. 2. Zhang, G.Q., van Driel, W.D., Fan, X.J., Mechanics of Microelectronics. New York, NY: Springer, 2006.

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3. Fan, X.J., Zhang, G.Q., van Driel, W.D., Ernst, L.J., “Interfacial delamination mechanisms during reflow with moisture preconditioning”, IEEE Transactions on Components and Packaging Technologies, 31(2), 252–259, 2008. 4. van Driel, W.D., van Gils, M.A.J, Fan, X.J., Zhang, G.Q., Ernst, L.J., “Driving mechanisms of delamination related reliability problems in exposed pad packages”, IEEE Transactions on Components and Packaging Technologies, 31(2), 260–268, 2008. 5. Bond, D.A., Smith, P.A., “Modeling the transport of low-molecular-weight penetrants within polymer matrix composites”, Applied Mechanics Reviews, 59, 249–268, 2006. 6. Galloway, J.E., Miles, B.M., “Moisture absorption and desorption predictions for plastic ball grid array packages”, IEEE Transactions on Components, Packaging, and Manufacturing Technology Part A, 20(3), 274–279, 1997. 7. Shook, R., Conrad, T., Sastry, V., Steele, D., “Diffusion model to derate moisture sensitive surface mount IC’s for factory use conditions”, IEEE Transactions on Components, Packaging and Manufacturing Technology, 19(2), 110–118, 1996. 8. Fan, X.J., Zhou, J., Chandra A., “Package structural integrity analysis considering moisture”, Proceedings of Electronic Components and Technology Conference (58th ECTC), pp. 1054–1066, 2008. 9. IPC/JEDEC J-STD-020D, “Moisture/reflow sensitivity classification for nonhermetic solid state surface mount devices”, March 2008. 10. He, Y., Fan, X.J., “In-situ characterization of moisture absorption and desorption in a thin BT core substrate”, Proceedings of Electronic Components and Technology Conference (ECTC), pp. 1375–1383, 2007. 11. Shirangi, M.H., Fan, X.J., Michel, B., “Mechanism of moisture diffusion, hygroscopic swelling and adhesion degradation in epoxy molding compounds”, Proceedings of the 41st International Symposium on Microelectronics (IMAPS), pp. 917–923, 2008. 12. van der Wel, G.K., Adan, O.C.G., “Moisture in organic coatings – a review”, Progress in Organic Coatings, 37, 1–14, 1999. 13. Vrentas, J.S., Duda, J.L., “Diffusion in polymer-solvent systems II, a predictive theory for the dependence of diffusion coefficients on temperature, concentration and molecular weight,” Journal of Polymer Science Polymer Physics Edition, 15, 417–439, 1977. 14. Hopfenberg, H.B., Stannett, V.T., Folk, G.M., “Sorption kinetics and equilibrium in annealed Glassy Polyblends”, Polymer Engineering & Science, 15(4), 261–267, 1975. 15. Xie, B., Fan, X.J., Shi, X.Q., Ding, H., “Direct concentration approach of moisture diffusion and whole field vapor pressure modeling for reflow process: part I – theory and numerical implementation”, ASME Journal of Electronic Packaging, 131(3), 031010, 2009. 16. Xie, B., Fan, X.J., Shi, X.Q., Ding, H., “Direct concentration approach of moisture diffusion and whole field vapor pressure modeling for reflow process: part II – application to 3-D ultra-thin stacked-die chip scale packages”, ASME Journal of Electronic Packaging, 131(3), 031011, 2009. 17. Fan, X.J., “Mechanics of moisture for polymers: fundamental concepts and model study”, Proceedings of the International Conference on Thermal and Mechanical Simulation and Experiments in Microelectronics and Microsystems (EuroSimE), pp. 159–172, 2008. 18. Cui, C.Q., Fan, X.J., Unpublished report on the study of a hydrophobolic coating membrane for preventing moisture-induced failures for QFN packages, 1999. 19. Tsenoglou, C.J., Pavlidou, S., Papaspyrides, C.D., “Evaluation of interfacial relaxation due to water absorption in fiber–polymer composites”, Composites Science and Technology, 66, 2855–2864, 2006. 20. Webb, P.A., “An introduction to the physical characterization of materials by mercury intrusion porosimetry with emphasis on reduction and presentation of experimental data”, Norcross, GA: Micromeritics Instrument Corp., 2001. 21. Koning, P., Fan, X.J., Unpublished report on mercury intrusion porosimetry measurement for several kinds of polymer materials, 2006.

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22. Shi, X.Q., Fan, X.J., “Wafer-level film selection for stacked-die chip scale packages”, Proceedings of Electronic Components and Technology Conference (57th ECTC), pp. 1731–1736, 2007. 23. Soles, L.C., Chang, F.T., Bolan, B.A., Hristov, H.A., Gidley, D.W., Yee, A.F., “Contributions of the nanovoid structure to the moisture absorption properties of epoxy resins”, Journal of Polymer Science: Part B: Polymer Physics, 36, 3035–3048, 1998. 24. Fan, X.J., Lim, T.B., “Mechanism analysis for moisture-induced failures in IC packages”, ASME International Mechanical Engineering Congress and Exposition, IMECE/EPE-14, 1999. 25. Fan, X.J., Zhang, G.Q., Ernst, L.J., “A micro-mechanics approach in polymeric material failures in microelectronic packaging”, Proceedings of the 3rd International Conference on Thermal & Mechanical Simulation in Micro-Electronics (EuroSimE), pp. 154–164, 2002. 26. Fan, X.J., Zhou, J., Zhang, G.Q., Ernst, L.J., “A micromechanics based vapor pressure model in electronic packages”, ASME Journal of Electronic Packaging, 127(3), 262–267, 2005. 27. Stellrecht, E., Han, B., Pecht, M.G., “Characterization of hygroscopic swelling behavior of mold compounds and plastic packages”, IEEE Transactions on Components and Packaging Technologies, 27(3), 499–505, 2004. 28. Wong, E.H., Chan, K.C., Rajoo, R., Lim, T.B., “The mechanics and impact of hygroscopic swelling of polymeric materials in electronic packaging”, Proceedings of the 50th Electronic Components and Technology Conference, Las Vegas, NV, pp. 576–580, 2000. 29. Zhou, J., et al., “Effect of non-uniform moisture distribution on the hygroscopic swelling coefficient”, IEEE Transactions on Components and Packaging Technologies, 31(2), 269–276, 2008. 30. Shi, X.Q., Zhang, Y.L., Zhou, W., Fan, X.J. “Effect of hygrothermal aging on interfacial reliability of silicon/underfill/FR-4 assembly”, IEEE Transactions on Components and Packaging Technologies, 31(1), 94–103, 2008. 31. Zhou, J., Lucas, J.P., “Hygrothermal effects of epoxy resin. Part I: the nature of water in epoxy”, Polymer, 40, 5505–5512, 1999. 32. Fan, X.J., Zhou, J., Zhang, G.Q., “Multi-physics modeling in virtual prototyping of electronic packages – combined thermal, thermo-mechanical and vapor pressure modeling”, Microelectronics Reliability, 44, 1967–1976, 2004. 33. Vanderhart, D.L., Schen, M.A., Davis, G.T., “Partitioning of water between voids and the polymer matrix in a molymer compound by proton NMR: the role of larger voids in the phenomena of popcorning and delamination”, International Journal of Microcircuits and Electronic Packaging, 22(4), 1999. 34. Toprak, C., Agar, J.N., Falk, M., “State of water in cellulose acetate membranes”, Journal of the Chemical Society, Faraday Transactions I, 75, 803, 1979. 35. McMaster, M.G., Soane, D.S., “Water sorption in epoxy thin films”, IEEE Transactions on Components, Hybrid, and Manufacturing Technology, 12(3), 373–386, 1989. 36. Delasi, R., Whiteside, J.B., Advances Composite Materials – Environmental Effects, edited by Vinson, J.R., ASTM STP-658, West Conshohocken, PA: ASTM International, 1978.

Chapter 2

Mechanism of Moisture Diffusion, Hygroscopic Swelling, and Adhesion Degradation in Epoxy Molding Compounds M.H. Shirangi and B. Michel

2.1 Introduction In order to design and manufacture robust electronic packages, it is important to understand the response of materials and interfaces to the conditions to which they will be subjected. Moisture diffusion in epoxy molding compounds (EMCs) is one of the major reliability concerns in plastic encapsulated microcircuits (PEMs), because many failure modes observed in these devices are believed to arise from the diffusion of moisture during manufacturing, storage, or operation [1–5]. Interfacial delamination between EMC and copper-based leadframe in PEMs is a common failure problem in semiconductor packages. Despite extreme demands from industrial sectors for the use of simulation tools instead of expensive and time-consuming qualification tests, most of the attempts for predicting interfacial delamination by numerical methods have failed, because the plastic packages undergo complex failure modes arising from the package internal stresses and applied thermo-mechanical loads. It is often believed that failure of the plastic packages during the solder reflow process or accelerated stress testing is due to degrading effects of moisture, such as adhesion loss, hygroscopic swelling, and vapor pressure [6–9]. Using epoxy-based encapsulating materials for protecting semiconductors against environmental attacks is believed to be a turning point in electronic packaging industry. PEMs have many advantages such as lower cost, lighter weight, and better performance over hermetic packages. They are generally applied in all industrial areas including automotive industry, consumer electronics, military, and space applications. Despite all of their advantages, one important disadvantage of PEMs is that the EMC absorbs moisture when exposed to a humid environment [1–10]. EMCs are composite materials made up of an epoxy matrix that encompasses silica fillers, stress relief agents, flame retardants, and other additives [4]. The common resin in epoxy molding compounds used in electronic packaging is epoxy cresol

M.H. Shirangi (B) e-mail: [email protected] X.J. Fan, E. Suhir (eds.), Moisture Sensitivity of Plastic Packages of IC Devices, Micro- and Opto-Electronic Materials, Structures, and Systems, C Springer Science+Business Media, LLC 2010 DOI 10.1007/978-1-4419-5719-1_2, 

29

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M.H. Shirangi and B. Michel

novolac (ECN) and the common hardener and filler are phenolic novolac (PN) and fused silica (FS), respectively [5]. Moisture behavior of EMC is mainly dominated by the diffusion of water through epoxy resin. However, the amount of filler and its shape can influence the moisture diffusivity. Diffusion of moisture in epoxy resins is affected by several factors; however, surface topology and resin polarity are the primary aspects that affect the equilibrium moisture uptake. Soles and Yee [10] found that water traverses the epoxy network through a network of nanopores that is inherent in the epoxy structure. They determined the average size of nanopores diameter to vary from 5 to 6.1 Å and account for 3–7% of the total value of the epoxy material. Since the approximate diameter of a kinetic water molecule is just 3.0 Å, moisture can easily traverse into the epoxy via the nanopores. They found that the volume fraction of nanopores does not affect the diffusion coefficient of water in any of the resin studied and argued that polar groups coincident with the nanopores are the rate-limiting factor in the diffusion process, which could explain why the diffusion coefficient is essentially independent of the nanopore content. There are many speculations on the state of water molecules in polymers. Adamson [11] proposed that moisture can transfer in epoxy resins in the form of either liquid or vapor. Tencer [12] suggested it is also possible that vapor water molecules undergo a phase transformation and condense to the liquid phase. The condensed moisture was reported to be either in the form of discrete droplets on the surface or in the form of uniform layers. These water layers are often quantified in terms of monolayers of water necessary to initiate and support corrosion of the metallization in PEMs. Moisture diffusion in a polymer can be analyzed using the so-called thermal– moisture analogy. The method has been developed by a number of researchers [7, 13] to overcome the discontinuity problem of moisture concentration across the bi-material interfaces using normalized variables. More recently, a direct concentration approach (DCA) has been proposed by Xie et al. [14] to study the moisture diffusion with varying temperature and humidity conditions such as in soldering reflow. Prediction of the problems associated with moisture in PEMs requires a full understanding of the mechanism of moisture diffusion in these materials. In this chapter a detailed analysis of the role of moisture in EMC performance is presented. Moisture diffusion in epoxy molding compounds will be first investigated quantitatively by weight gain measurements of plastic packages as well as standard bulk EMC samples. Then the characteristics of moisture absorption will be studied by performing moisture desorption and re-sorption tests at various baking conditions. Another objective of this chapter is to understand the mechanism of moistureinduced volumetric expansion of molding compounds. This phenomenon is known as hygroscopic swelling and is responsible for an additional mismatch between epoxy molding compound and other package materials. The influence of moisture on the adhesion, one of the most crucial reliability concerns of the epoxy molding compounds, will also be investigated. When the adhesion between a polymer and a substrate like a leadframe is considered in terms

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Mechanism of Moisture Diffusion in Epoxy Molding Compounds

31

of interfacial fracture toughness, the interface is initially under residual stresses. Depending on the amount of cure shrinkage of the EMC during polymerization and the coefficient of thermal expansion (CTE) of the EMC and leadframe, the interface may be under tension or pressure. The situation becomes more complex, when the epoxy molding compound expands due to the moisture absorption, while other components are not affected by moisture. Neglecting any of the mentioned mechanisms may lead to a completely wrong understanding of the effect of moisture on interfacial adhesion. A fracture test setup will be presented and the effect of moisture diffusion on the interfacial fracture toughness will be discussed. The moisture absorption and desorption curves of the bulk EMC samples will be used to explain the fracture results. Moreover, the mechanism of the adhesion loss and its recoverability upon subsequent baking will be discussed in detail.

2.2 Moisture Diffusion in Plastic Encapsulated Microcircuits The objective of this section is to study the diffusion of moisture in plastic encapsulated devices. Four types of plastic packages were selected to investigate how their moisture content changes with time at 85◦ C/85% RH (relative humidity). Table 2.1 lists the type and initial dry weight of these packages. All of the packages were stored more than 1 year in unprotected conditions after their molding process. Since these packages absorb moisture during storage, they should be baked first to reach the dry state. The bake-out condition is believed to depend on the geometry and storage time of the packages. However, a typical and standard baking condition in electronic packaging is 24 h baking at 125◦ C. This baking condition may not necessarily lead to a fully dry state as will be discussed in the next sections. Despite this fact, the bake-out condition for all packages was assumed to be as standard (24 h at 125◦ C) in order to facilitate a consistent comparison between the moisture contents of these devices. Table 2.1 Four types of plastic IC packages for the investigation of moisture diffusion Sample name

Package type

Package dry weight (mg)

EMC used in package

Package dimensions (mm3 )

P1 P2 P3 P4

MO-188 SOIC-24 SOIC-16 PLCC-44

2,209.01 672.13 451.18 2,540.47

MC-1 MC-2 MC-2 MC-3

14 × 14 × 2.75 15.4 × 7.5 × 2.45 10.3 × 7.5 × 2.45 16.5 × 16.5 × 3.8

Package P1 is an MO-188 type which uses solder for the die bonding, while other packages use an epoxy die-attach for bonding the die on leadframe. The packages P1 and P2 use molding compounds MC-1 and MC-2, respectively. Packages P2 and P3 are both SOIC packages that use the same type of molding compound (MC-2). The only difference between P2 and P3 is that P2 is larger and has more pins compared to P3. Package P4 is a PLCC package and is the largest among the four packages. In

32

M.H. Shirangi and B. Michel 5

0.35

4.5

0.3

3.5

P1 P2 P3 P4

3 2.5

Mass uptake, %

Moisture mass, mg

4

2 1.5

0.25 0.2

P1 P2 P3 P4

0.15 0.1

1 0.05

0.5 0

0 0

5

10

15 20 25 30 (time)1/2, (hour)1/2

35

40

0

5

10

15 20 25 30 (time)1/2, (hour)1/2

35

40

(b)

(a)

85◦ C/85%

Fig. 2.1 Moisture absorption of four plastic IC packages at RH: (a) mass of moisture (mg) in package with square root of time and (b) mass uptake (%) with square root of time

order to measure the dry weight of the plastic parts, all plastic packages were first baked at 125◦ C for 24 h, then their weight was measured using an electronic balance (0.01 mg), and finally they were placed in a moisture chamber (85◦ C/85% RH). The plastic parts were removed periodically from the moisture chamber, their weight was measured after reaching the room temperature, and they were placed in the chamber for further sorption. Assuming an initial dry sample at the start of the sorption tests, the weight gain of the packages during the sorption experiment corresponds to the weight of moisture available in the package. Figure 2.1a shows the mass of moisture vs. square root of exposed time. In package P1, the epoxy molding compound is the only organic material that absorbs moisture. The other packages use epoxy dieattach for bonding the silicon die to the leadframe. However, the thickness of the die-attach is very low (20–50 μm) and has therefore no significant influence on the overall mass gain of the plastic package. Hence, it is reasonable to assume for all four packages that only the EMC is responsible for the moisture absorption of the package and other components are whether impermeable to moisture or have no significant contribution to the package mass gain. The mass uptake of the plastic parts at time t can be determined from Mass uptake (% ) =

M(t) − MDry × 100, MDry

(2.1)

where M(t) is the weight of the sample at time t and MDry is the dry weight before moisture preconditioning. In order to ensure that the result of bulk material diffusion can be compared reasonably with that of the package, the weight of the molding compound of each plastic package was estimated using the data provided by the manufacturer and used in equation (2.1), meaning that the dry weight in equation (2.1) represents the weight of the molding compound of the package only and not the whole weight of the package. Using equation (2.1), the mass uptake of the packages was calculated and the results as a function of the

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Mechanism of Moisture Diffusion in Epoxy Molding Compounds

33

square root of exposure time are shown in Fig. 2.1b. These graphs are more suitable for a meaningful comparison between the moisture uptakes of different packages, because they provide comparable information about the moisture uptake of molding compounds. From the graphs in Fig. 2.1b it is not possible to find the moisture diffusion coefficient because usually a bulk material is needed to find the moisture-related material properties of the polymers. However, there are some important results by comparing the package diffusion with standard bulk EMCs, which will be discussed in the next sections.

2.2.1 Moisture Diffusion in a Package vs. in Bulk EMC Using the same transfer molding process, bulk samples of EMCs (MC-1 and MC-2) were provided by the manufacturers in the form of molded disks of 100 mm diameter and 2 mm thickness. Their moisture uptake was also measured using the same method described above. Figure 2.2 shows the moisture uptake curve of a plastic package compared to the moisture uptake curve of the bulk epoxy molding compound used in that package. The results of Fig. 2.2 suggest that the plastic packages and their respective bulk EMCs manifest similar behavior in terms of moisture absorption. For both IC package and bulk EMC, a linear part of moisture absorption curve at the early stages of sorption is followed by a slight plateau and finally a second linear phase. However, there are some differences between a plastic package and its bulk EMC in terms of the diffusion rates, which suggest that for plastic packages additional mechanisms may exist which are explained in the following sections.

2.2.2 Interfacial Moisture Diffusion From Fig. 2.2a and b, it can be postulated that the diffusion of moisture in both packages is faster than that of their respective bulk molding compounds. This can be attributed to the three-dimensional nature of diffusion in the package and also to a higher diffusion rate through the leads/EMC interfaces, while for the thin plates, the diffusion is almost one-dimensional. A review of the diffusion rates available in literature reveals that, in general, the diffusion rate along the interface of adhesive/substrate is faster than that of the bulk adhesive and it becomes more critical to the lifetime of the adhesive joints as the strength of the interface decreases. Vine et al. [15] studied the moisture uptake of an epoxy bonded to aluminum substrates with various surface treatments. They observed faster diffusion in three-layer sandwich specimens than predicted based on mass-uptake experiments performed on bulk diffusion specimens. They attributed this behavior to the presence of micro-cavities in the adhesive layer.

10

15

20

25

30

35

40

(a)

(time)1/2, (hour)1/2

0

5

0

0.1

0.15

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0.25

0.3

0.05

0

MC-2

P2

0.35

0.05

0.1

0.15

0.2

0.25

0.3 Mass uptake, %

0

5

10

20

25 (b)

(time)1/2, (hour)1/2

15

MC-1

P1

Fig. 2.2 Moisture absorption of a plastic IC package compared to its bulk EMC: (a) P1 vs. MC-1 and (b) P2 vs. MC-2

Mass uptake, %

0.35

30

35

40

34 M.H. Shirangi and B. Michel

2

Mechanism of Moisture Diffusion in Epoxy Molding Compounds

35

Davis et al. [16] utilized the technique of electrochemical impedance spectroscopy and investigated epoxies bonded to aluminum with various surface preparations that resulted in either a weak or strong interface and observed that the rate of crack growth was slower for strong interfaces. However, for weak interfaces crack growth was detected almost immediately as moisture appeared at the interface and resulted in a fast rate of crack growth. Zanni et al. [17] compared the calculated diffusion rates between non-bonded adhesive specimens and bonded adhesive joints. They observed that the interfacial diffusion coefficient was greater than that of bulk adhesives and hypothesized the phenomenon of “capillary diffusion,” where the higher surface energy of the dry adhesive effectively pulls moisture along the interface. They used Fickian diffusion to measure water diffusion into bonded joints and related enhanced rate of moisture ingress to water diffusion occurring rapidly in the interface region. These examples all suggest that the diffusion of water into the adhesive joints is not a simple process and may involve several pathways for the moisture ingress, dependent on the system chemistry and interfacial morphology.

2.2.3 Moisture Accommodation at Interfaces An important observation in Fig. 2.2 is the higher amount of maximum moisture content in a package compared to its respective bulk molding compound. This difference can be attributed to the accommodation of water molecules at the interfaces between molding compound and the leadframe. This hypothesis is supported by the study of Chan et al. [18] who performed Fourier transform infrared spectroscopy (FTIR-MIR) technique measurements that showed the maximum moisture concentration at an interface is higher than that at the saturation state of a bulk molding compound. There are many other evidences in the literature on the accumulation of water at the interfaces [19]. Buchwalter [20] suggested that for weak interfaces where secondary bond forces dominate the adhesion, failure occurs almost immediately as water contacts the interface. O’Brien [21] suggested that it is possible for the water to be present in the bulk and interface of the adhesive, yet the integrity of the adhesive bond can be preserved if the interface is strong. This is the case where covalent bonds are present. For strong interfaces, the role of interfacial diffusion becomes less important and the rate-limiting step for failure becomes the chemical reaction at the interface. Wu et al. [22] used neutron scattering by D2 O to show high concentration of water at polyimide interfaces. They showed that the concentration of water at interfaces without adhesion promoters was significantly higher than with them. Nguyen et al. [23] used infrared spectroscopy to measure the accumulation of water at an epoxy/SiO2 interface and correlated it to weakened adhesion. They detected significant diffusion at the interface for poorly adhered adhesive systems where adhesion forces are governed by secondary interactions. Bowden and Throssell [24] found

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M.H. Shirangi and B. Michel

that on aluminum, iron, and SiO2 surfaces, the layer can be up to 20 molecular layers thick at ambient temperatures and humidity. Takahashi [25] used AC impedance spectroscopy to show that at a relative humidity of 80% the interfacial capacitance increased abruptly, suggesting the formation of water clusters in the bulk and at the interfacial regions. Another possible reason for a slightly higher amount of moisture content in plastic packages compared to that of bulk molding compounds may be the presence of residual stresses in packages which causes some nano-scale damages along the interfaces. Buchwalter [20] studied the effect of applied stresses on the moisture-induced damage at interfaces of a plastic package and used a wedge test to externally load the adhesive bonds and concluded that mechanical stresses can work in concert with moisture to cause interfacial damage other than that caused by moisture alone. Since there are many uncertainties when a package is used for the understanding of moisture diffusion in EMCs, for the rest of this work the focus will be on the moisture absorption of bulk molding compounds. MC-1 which is a commercial molding compound will be used further for a systematic investigation of moisture absorption and desorption in EMCs. Moreover, other samples required for the characterization of hygroscopic swelling and interfacial adhesion will be produced from the material MC-1.

2.2.4 Fickian Moisture Diffusion Diffusion of water in polymers has been widely investigated and for most cases the rate of diffusion has been assumed to be constant (Fickian diffusion). Fick’s second law can be applied to describe the moisture diffusion process in many polymeric materials as follows [26]: ∂C = ∇ · (D∇C), ∂t

(2.2)

where D (mm2 /s) is the diffusion coefficient, C (g/mm3 ) is the moisture concentration, t (s) is the time, and x (mm) refers to Cartesian coordinates. For isotropic materials, Fick’s second law can be simplified as follows:   2 ∂ C ∂ 2C ∂ 2C ∂C . =D + + ∂t ∂x2 ∂y2 ∂z2

(2.3)

If the one-dimensional case of an infinite plate of thickness l with appropriate boundary conditions is considered, the analytical solution, giving the temporal and spatial moisture concentration, C, at time t and distance x from the mid-plane is given by

2

Mechanism of Moisture Diffusion in Epoxy Molding Compounds

37

    ∞ −D(2n + 1)2 π2 Ct − C0 4  ( − 1)n (2n + 1)π exp x . =1− t × cos C∞ − C0 π 2n + 1 2l 4 l2 n=0 (2.4) Here C∞ is the maximum equilibrium moisture concentration, C0 is the initial moisture content, and D is the Fickian diffusion coefficient. Since it is not possible to measure the moisture concentration at a point experimentally, the above expression is integrated over the thickness of the bulk film and the fractional mass uptake of the specimen as a function of time is [26]   ∞ 1 8  −D(2n + 1)2 π2 Mt =1− 2 exp t , M∞ π (2n + 1)2 4 l2

(2.5)

n=0

where Mt is the mass of moisture after absorption time t and M∞ is the mass of saturated sample. Equation (2.5) implies that the moisture mass of a polymeric sample exposed to a humid environment obeys an asymptotic behavior, for which a saturation state exists. In other words, if two samples with different thicknesses are exposed to a humid environment, the final moisture uptake defined by equation (2.5) is the same for both samples; however, the time to reach this maximum value depends on the thickness of the sample as shown in Fig. 2.3. x Mt

l1 < l 2

M∞

C ( x = l , t ) = C∞

l C ( x = 0, t ) = C∞

(a)

t

(b)

Fig. 2.3 One-dimensional Fickian diffusion in a plate

2.2.5 Non-Fickian Dual-Stage Moisture Diffusion As observed in Fig. 2.2a and b, there is no equilibrium of moisture absorption even after long-period moisture sorption. It was suspected that this phenomenon may be due to the larger thickness of the bulk samples (2 mm). However later investigations showed a dual-stage moisture absorption for all sample geometries. In order to investigate the role of geometry in the moisture performance of bulk EMCs, two different sample geometries of material MC-1 were produced. The sample with thickness 1 mm has a diameter of 50 mm and the sample with thickness 2 mm has a

38

M.H. Shirangi and B. Michel 0.4

Fig. 2.4 Effect of sample geometry on the non-Fickian behavior

0.35 Mass uptake, %

0.3 0.25 0.2 0.15

thickness: 2 mm

0.1

thickness: 1 mm

0.05 0 0

5

10

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20

25

30

35

40

(time)1/2/l,(hour)1/2/mm

diameter of 100 mm, meaning that for both samples the one-dimensional moisture diffusion can√be assumed. Figure 2.4 shows the percentage of moisture content as a function of t/l, where t is the time of exposure to moisture and l is the thickness of the bulk EMC. It can be observed that the rate of mass uptake per thickness was the same for both sample geometries at the beginning of the exposure to moisture, which√is a typical behavior of Fickian moisture diffusion in polymers. However, after the t/l ratio of around 13, the curves started to deviate from each other. This ratio corresponds to 1 week of sorption for the sample with 1 mm thickness and approximately 3–4 weeks for the sample with 2 mm thickness, respectively. This sorption time will be denoted as virtual saturation in this work and will be used as a virtual border between the two phases of the moisture absorption. It is important to note that in equation (2.3) the diffusivity D in Fickian diffusion is assumed to be independent of moisture concentration C. This assumption may not hold true for many polymers and, consequently, equations (2.3), (2.4), and (2.5) cannot be used directly for the case of non-Fickian diffusion. A prominent feature of non-Fickian diffusion is that there is no characteristic equilibrium mass uptake. There are various types of non-Fickian moisture absorption reported in the literature. Chen and Zhao [27] reported that the moisture absorption in some molding compounds can be characterized by linearly decreasing diffusivity as a function of average moisture content. However, Celik et al. [28] found that for highly nonFickian diffusion of some organic substrates a power-law relation between the diffusivity and moisture content exists. Non-Fickian behavior may be the consequence of a relaxation process in polymer molecules and/or the result of an irreversible reaction between polymer and moisture such as formation of hydrogen bonds. Weitsman [29] proposed various types of non-Fickian moisture absorption and used a combined damage/diffusion model to interpret the non-Fickian moisture uptake of fiber-reinforced polymeric composites. Loh et al. [30] suggested that non-Fickian diffusion is generally considered to occur

2

Mechanism of Moisture Diffusion in Epoxy Molding Compounds

39

when the relaxation of the polymer influences the uptake behavior. Such responses are conventionally divided into two groups. One is known as class II (class I being Fickian diffusion) and generally occurs when the relaxation rate controls the uptake. The other group is termed as anomalous uptake and generally occurs when diffusion and relaxation have comparable rates. Two-stage or dual-uptake diffusion has been observed in many polymeric materials and is one of the most common types of anomalous moisture uptakes. It must be noted that the aging at 85◦ C/85% RH (MSL1) is one of the most severe moisture sensitivity level (MSL) reliability test conditions. Figure 2.5 shows the moisture absorption curves of the material MC-1 in two aging conditions. The rate of diffusion and the maximum mass uptake at MSL1 are higher than that at MSL3 condition (30◦ C/60% RH). The dual-phase moisture absorption can be observed at the MSL1 condition more significantly. However, there seems to be a slight permanent increase in the mass uptake curve at 30◦ C/60% RH, which suggests that the second phase of moisture absorption may exist even at low temperatures. 0.3

Fig. 2.5 Effect of sorption conditions on the non-Fickian behavior Mass uptake, %

0.25 0.2

85°C/85%RH 30°C/60%RH

0.15 0.1 0.05 0 0

5

10

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20

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35

40

(Time)1/2, (hour)1/2

Another mechanism leading to a non-Fickian behavior of moisture absorption may be the swelling of the polymer matrix, which increases the number of active sites available for sorption. Also a chemical degradation of epoxy resins and/or epoxy/filler interface may cause the non-Fickian diffusion. In the latter case, Lekatou et al. [31] observed that the water diffusion initially follows the Fickian model, but then the deviations from the ideal behavior are explained by the flow of water molecules along the filler–matrix interface followed by diffusion into the bulk resin and transport of water by microcracks. Most likely, the dual-phase moisture absorption in epoxy molding compounds can be explained with the two mechanisms of absorbing water by polymers. During the early stages of the sorption, the absorbed molecules reside in the free volumes in the polymer, but their transfer to a bound state with a different energy level requires overcoming some energy barriers and occurs relatively slowly. Possibly the two

40

M.H. Shirangi and B. Michel

bound and unbound mechanisms act simultaneously. However, due to the faster diffusion in free volumes at the beginning of the sorption, the effect of the bonding mechanism can be observed later, when the first mechanism slows down by reaching its saturation state. In this case, most of the bonded water causes non-Fickian diffusion behavior that typically causes a gradual increase of moisture uptake with time. These statements are supported by the results of desorption tests after various sorption times, which will be discussed in Section 2.3. It will be shown that the nonFickian behavior during the absorption process is responsible for a non-reversible sorption process. This supports the hypothesis that there is an energy level for the transition from free volume diffusion to molecular bondings. By using equation (2.5), the diffusion coefficient of bulk materials can be found from the slope of the initial linear part of the moisture uptake curve together with the sample weight at saturation state. The initial stage of moisture absorption (Mt /M∞ < 0.5) can be simplified as follows:   Mt Dt 1/2 =4 . M∞ πl2

(2.6)

However, the problem of moisture diffusion in molding compounds is that from Figs. 2.4 and 2.5, no specific saturation point can be observed. Hence, an estimation of the diffusion coefficient by using Fick’s law is not possible. By considering a virtual saturation level after 168 h, a first value of diffusion coefficient can be estimated. Using a longer soaking time as saturated level will result in obtaining a smaller Fickian diffusion coefficient. This is repeated for various sorption times until a relation between D and M∞ can be obtained. After having the corresponding values of D and M∞ , a transient finite element (FE) analysis is performed for each pair of data and the average moisture content at the end of diffusion process is calculated. Figure 2.6 shows the relation between the apparent diffusion

Diffusion coefficient, mm2/s

2.0E–06 MC-1

1.6E–06

MC-2

1.2E–06 8.0E–07 4.0E–07 0.0E+00 8.0E–6 1.0E–5 1.2E–5 1.4–5

1.6E–5 1.8E–5 average moisture concentration, g/mm3

Fig. 2.6 Diffusion coefficient of two bulk EMC materials as a function of average moisture content at 85◦ C/85% RH condition

2

Mechanism of Moisture Diffusion in Epoxy Molding Compounds

41

coefficients with the average moisture content in the sample. It indicates clearly that the diffusion coefficients of both materials decrease with increasing moisture content. A three-dimensional transient finite element analysis was performed using the thermal–moisture analogy by the simulation tool ANSYS. The dashed lines in Fig. 2.7 show the Fickian simulation of the weight gain process by assuming a final saturated level at the end of absorption process (1,000 h sorption at 85◦ C/85% RH). For this Fickian simulation, D is assumed to be the last point in Fig. 2.6 and C∞ is the assumed saturation moisture concentration, which can be found from C∞ = M∞ /V, V being the specimen volume.

Mass uptake, %

0.25 0.2 0.15

Experimental Data, MC−1 Fickian Simulation, MC−1

0.1

Non−Fickian Simulation, MC−1

0.05 0

0

5

10

15

20

25

30

35

Mass uptake, %

0.25

0.2

0.15 Experimental Data, MC−2 0.1

Fickian Simulation, MC−2 Non−Fickian Simulation, MC−2

0.05

0

0

5

10

15

20

25

30

35

(time)1/2, h1/2

Fig. 2.7 Fickian and non-Fickian simulations of the moisture absorption in two EMC plates

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M.H. Shirangi and B. Michel

In order to determine the non-Fickian dual-stage diffusion properties, the following method proposed by the current authors [1] is used: A first Fickian diffusion with the diffusion coefficient D1 and saturated content level of C1∞ is followed by a second Fickian (D2 and C2∞ = C∞ −C1∞ ) after a specific time (t2 = 168 h). Three independent variables (D1 , D2 , and C1∞ ) are found by using a least mean-square approach to produce the best fit to the experimental curve. The Fickian (D and C∞ ) and non-Fickian (D1 , D2 , and C1∞ ) diffusion parameters are listed in Table 2.2. Table 2.2 Fickian and non-Fickian absorption parameters

MC-1 MC-2

DFickian (mm2 /s)

C∞ (g/mm3 )

D1 (mm2 /s)

D2 (mm2 /s)

C1∞ (g/mm3 )

0.7e–6 0.8e–6

5.4e–6 4.53e–6

1.9e–6 2.3e–6

1.5e–6 1.2e–6

3.7e–6 3.1e–6

As shown in Fig. 2.7 the non-Fickian model that is composed of two parallel Fickian diffusions can be used to obtain the mass uptake of the molding compounds very exactly. The fitting parameters D1 , D2 , and C1∞ are so far used only to get the best fit of the experimental results and may not necessarily have physical meanings. However, they could be further investigated in the future to achieve a meaningful interpretation of sorption phases and their contribution to the overall moisture uptake of molding compounds.

2.3 Moisture Desorption Moisture desorption in epoxy molding compounds takes place at reflow process. Moreover, it is important to understand the mechanism of moisture desorption, since during the assembly of PEMs, the packages undergo baking to remove moisture and thus reduce the probability of moisture-induced failures such as popcorn cracking and interfacial delamination. Experiments on the moisture desorption behavior of the plastic packages listed in Table 2.1 were performed at various temperatures. The packages were stored in an unprotected environment before the sorption tests and thus initially contained moisture due to long-period storage in air. The plastic parts were first baked at 125◦ C for 24 h to remove the initial moisture content. The weight after baking was considered as the dry weight; however, results found from desorption curves of the packages and also from desorption of bulk EMCs revealed that the condition of 125◦ C baking for 24 h may not fully remove all the moisture content. After baking, the packages (three packages for each test category) were placed in a moisture chamber at 85◦ C/85% RH for a sorption time of 168 h. Afterward, the desorption experiments were performed in four infrared chambers at four baking temperatures: 75, 110, 160, and 220◦ C. Since the glass transition temperature of the EMCs used in the packages range from 95 to 130◦ C, the aim was thus to run the desorption experiments at two temperatures below and two temperatures above the glass transition temperature. The desorption period (baking time) was chosen to be 96 h for baking at 75◦ C, 70 h for baking at 110◦ C, 48 h for baking at 160◦ C, and 4 h at 220◦ C, respectively. The

Mechanism of Moisture Diffusion in Epoxy Molding Compounds

P1, 75 °C P1, 110 °C P1, 160 °C P1, 220 °C

1.5 1 0.5 0 0

2

4

6

8

Moisture mass, mg

(time) 0.6 0.5 0.4 0.3 0.2 0.1 0 –0.1 0 –0.2 –0.3 –0.4

1 0.8 0.6 0.4 0.2

–0.2 1/2

0

2

1/2

, (hour) (a)

4

6

(time)1/2, (hour)1/2

(c)

4

6

1/2

(time)

, (hour)

8

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(b) P3, 75 °C P3, 110 °C P3, 160 °C P3, 220 °C

2

P1, 75°C P1, 110 °C P1, 160 °C P1, 220 °C

1.2

0

10

–0.5

43

1.4 Moisture mass, mg

Moisture mass, mg

2

8

10

Moisture mass, mg

2

4.5 4 3.5 3 2.5 2 1.5 1 0.5 0

P4, 75°C P4, 110 °C P4, 160 °C P4, 220 °C

0

2

4

6

8

10

(time)1/2, (hour)1/2

(d)

Fig. 2.8 Moisture desorption of four plastic IC packages at various temperatures: (a) MO-188, (b) SOIC-24, (c) SOIC-16, and (d) PLCC-44

weight measurements of the plastic parts were performed periodically by removing the parts from the oven and measuring at room temperatures similar to the procedure explained in Section 2.2. Figure 2.8a–d shows the temperature-dependent desorption results of the packages P1–P4, respectively. The results of Fig. 2.8 indicate that for all packages studied, the baking condition at 75◦ C cannot lead to a complete removal of moisture content. Even baking at 110◦ C seems to be inappropriate for the removal of moisture from the packages. Interestingly, for the package P3 which is the smallest part among the packages, the final weight of the sample at the end of bake-out was lower than the apparent initial dry weight, which explains why the moisture mass in Fig. 2.8c was a negative value at longer baking times. This can arise from two possible reasons. The first reason may be the out-gassing of the polymer during the baking condition. This assumption was proved not to hold true due to the results found from thermal gravimetric analyzer (TGA) measurements of dry bulk EMC samples that showed insignificant out-gassing even at 220◦ C. The second reason is that, principally, the assumption of gaining a dry package upon 24 h baking at 125◦ C might have been wrong. It seems that this baking condition did not lead to a complete removal of the moisture content and the apparent dry samples contained moisture in reality. It seems to be difficult to understand the mechanism of moisture desorption from the results of baking of

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M.H. Shirangi and B. Michel

plastic IC packages, because other phenomena like interfacial diffusion and moisture accumulation may lead to a misinterpretation of the desorption results. That is why standard bulk samples were later used to understand the intrinsic mechanism of moisture desorption. Samples of bulk EMC (both geometries with 1 and 2 mm thickness of the material MC-1) were placed in humid conditions (85◦ C/85% RH). Some samples were removed after 2 weeks of sorption while the others were removed after 4 weeks of sorption for a subsequent baking in an infrared oven. Polymers lose their moisture content when they are exposed to dry environments at high temperatures. However, not all the moisture may escape from them even upon exposure to high temperature. In this work a systematic approach was chosen to find out at which state of the moisture absorption the formation of the residual moisture content may take place. Figure 2.9a and b illustrates the weight loss of samples at 110 and 160◦ C, respectively. A higher initial moisture content in these figures indicates that the sample was

0.3

Baking at 110°C after virtual saturation (thickness = 1 mm) Baking at 110°C after 2nd phase absorption (thickness = 1 mm) Baking at 110°C after virtual saturation (thickness = 2 mm) Baking at 110°C after 2nd phase absorption (thickness = 2 mm)

Mass loss, %

0.25 0.2 0.15 0.1 0.05 0 0

2

4

6

8

10

(time)1/2, (hour)1/2 (a)

0.35 Baking at 160 °C after Virtual Saturation (thickness = 1 mm) Baking at 160 °C after 2nd Phase absorption (thickness = 1 mm) Baking at 160 °C after Virtual Saturation (thickness = 2 mm) Baking at 160 °C after 2nd Phase absorption (thickness = 2 mm)

Mass loss, %

0.3 0.25 0.2 0.15 0.1 0.05 0 0

2

4

6

(time)1/2, (hour)1/2 (b)

Fig. 2.9 Desorption of an EMC as a function of exposure time to dry environment: (a) desorption at 110◦ C and (b) desorption at 160◦ C

2

Mechanism of Moisture Diffusion in Epoxy Molding Compounds

45

aged for a longer time in humid condition prior to baking and hence the moisture absorption had reached the second absorption phase. This longer aging in a moist environment has a direct influence on the subsequent baking curves. From these desorption curves the following results can be postulated: • A complete removal of moisture was not achieved for any of the samples within the time period investigated. Samples with higher initial moisture content show a higher final residual content, suggesting that a longer time of exposure to moisture leads to a higher amount of “non-reversible” moisture content at a certain temperature. Baking at elevated temperatures (e.g., 160◦ C) leads to more moisture release and a lower amount of residual moisture content. This may mean that for the debonding of hydrogen bonds between water molecules and polymer chains a certain amount of energy is needed, which is not available at lower temperatures (e.g., 110◦ C). • The thicker samples (2 mm thickness) are shown to retain a higher amount of residual moisture content when compared to the thinner samples (1 mm thickness). This is reasonable, as thicker samples normally need more time to reach a certain amount of moisture content during the moisture absorption. A longer exposure to moisture results in a higher amount of non-reversible hydrogen bonds and consequently a higher value of residual moisture contents. This suggests that hydrogen bonding is active from the early stages of exposure to moisture; however, its influence is more dominant when the Fickian mechanism decelerates upon reaching a virtual saturation. • An interesting observation is the parallel initial linear parts of the desorption curves of the samples with similar thickness. For a certain geometry at a constant temperature, the desorption curves of samples with different histories are in parallel. A longer exposure to moisture results in a higher amount of non-reversible absorption mechanism; however, the desorption rate at a constant temperature does not depend on the sorption history and depends only on the baking condition. This means that the non-reversible mechanism arising from the second absorption phase has influence only on the residual moisture content and not on the desorption coefficient. In contrast to the results presented in this section, there are some other studies that suggest a complete removal of moisture content upon baking. He and Fan [32] performed in situ measurements of moisture absorption/desorption on thin film bismaleimide-triazine resin/glass fiber laminates and observed repeatable moisture absorption. It is possible that in these cases only the first phase of moisture absorption was activated within the time period of the recycled test. The Fickian model fails to describe the desorption behavior of such polymers with a dual-stage diffusion, because of two reasons. First, it over-estimates the moisture escape from the polymeric materials and, second, it does not consider the ability of the materials to keep a certain amount of water after a long-term baking. It is worth noting that upon 1 week baking at 110◦ C, a residual moisture content of around 40% of the saturated level was observed in the thick samples. However,

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M.H. Shirangi and B. Michel

not enough effort has been made on solving the failure of Fickian model for predicting these residual moisture contents. A simple non-Fickian moisture desorption model is suggested in this work, which can solve this problem with conventional FE simulation tools. In this model, two parallel diffusion simulations are performed. The first one is a desorption process with the diffusion coefficient D1 and boundary conditions similar to a Fickian desorption (initial nodal moisture concentration of all nodes being C = C∞ and applying C = 0 on the external surfaces of the sample). The second one is a parallel absorption process of an originally dry sample with the diffusion coefficient D2 and the boundary conditions being similar to a Fickian boundary condition with C = Cresidual on the external surfaces. The nodal moisture concentration at each specific time of the first analysis should be added to that at the corresponding time of the second analysis. The result is a non-Fickian moisture desorption with the controlled desorption coefficient and, more importantly, with the residual moisture concentration Cresidual . The residual moisture content can be simply found from experimental data by Cresidual = Mresidual /V, where Mresidual is the residual moisture mass in the sample at the end of desorption process and V is the volume of the sample. The parameters D1 and D2 can be found by fitting the results to the experimental curve, similar to the approach described in the previous section. The non-Fickian desorption model is compared with both experimental data and Fickian model in Fig. 2.10. Table 2.3 summarizes the fitted parameters of the non-Fickian model and compares them with the values of Fickian desorption. It must be mentioned that the desorption experiments were performed in an infrared oven, with possibly some humidity in the air. Some of the residual moisture content in the materials could be the result of a competing parallel absorption due to the moisture available in the air. Another source of error arises from a short time needed for the weighing of the specimens after they are removed from the oven.

0.3 Experiment, T = 110°C Fickian Simulation, T = 110°C

0.25 Weight Loss (%)

Non−Fickian Simulation, T = 110°C

Fig. 2.10 Comparison between experimental, Fickian, and non-Fickian simulations of MC-1 at 110◦ C

0.2 0.15 0.1 0.05 0

0

5

10 timeo.5 (houro.5)

15

20

2

Mechanism of Moisture Diffusion in Epoxy Molding Compounds

47

Table 2.3 Fickian and non-Fickian desorption parameters T (◦ C)

DFickian (mm2 /s)

D1 (mm2 /s)

D2 (mm2 /s)

Cresidual (g/mm3 )

110 160 220

0.7e–6 2.5e–5 15.5e–5

3.5e–6 8.5e–5 20e–5

5.5e–6 8.5e–5 19e–5

2.2e–6 1.5e–6 0.6e–6

Since the electronic balance scale is sensitive to the heat, a time of approximately 5 min is needed, so that the hot samples reach the room temperature. Within this time some moisture uptake from the atmosphere is possible. Assuming Fickian desorption, the desorption coefficient can be estimated from the initial linear part of the experimental data by using equation (2.6). The temperature-dependent desorption coefficient of the material MC-1 is shown in Fig. 2.11. It can be observed that the desorption coefficient fulfills the following equation:   E . (2.7) D = D0 exp − kT The diffusion coefficient D depends on an initial diffusion constant, D0 , temperature, T, and activation energy, E, where k is Boltzmann’s constant. For the sample MC1, the activation energy can be estimated as 0.55 eV. There are some researchers that proposed direct measurements of the diffusion coefficient from the plastic packages. Although these methods are not precise, they enable reasonable comparison between different EMCs and provide more flexibility for the selection of a proper EMC for a specific application. Teverovsky [33, 34] proposed a simple rapid technique for the estimation of temperature dependency of moisture diffusion characteristics directly on the plastic packages of PEMs. The suggested technique is based on substituting the moisture sorption kinetics with the temperature domain measurements of moisture desorption from a flat polymer sample or flat package of PEM that has been pre-saturated with moisture in humidity

ln(D), mm2/s

−8 −10 ln(D) = −6400*(1/T) + 3.5 −12 −14 −16

2

2.1

2.2

2.3

2.4 1/T(1/K)

2.5

Fig. 2.11 Desorption coefficient of MC-1 against adverse temperature

2.6

2.7

2.8 × 10−3

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M.H. Shirangi and B. Michel

chamber. Assumptions for this technique are as follows: (1) temperature dependence of diffusion coefficient follows Arrhenius law, (2) Fickian diffusion holds true, and (3) the temperature in the package is uniform. Using this technique, the diffusion coefficient of a QFP package was found as a function of temperature and the result is shown in Fig. 2.12. It was also found that the diffusion coefficients determined from the packages were 10–60% larger than those found directly from the bulk molding compounds, which is in agreement with the results of this work. Quad flat package QFP-144 1.E–05

1.E–06

D, cm2/s

Fig. 2.12 Arrhenius-like diffusion coefficient found directly from a QFP package. The least-squares fit calculations yield D0 = 0.14 cm2 /s and U = 0.42 eV [35]

1.E–07 y = 0.1416e–5.148x 1.E–08

1.E–09

2

2.25

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2.4 Second Run of Absorption (Re-sorption) The complex mechanism of moisture absorption suggests that a second run of moisture absorption after an absorption/desorption cycle would be even more complicated. In order to achieve logically comparable re-sorption curves, the first run of absorption was stopped after 1 and 2 weeks of sorption for thin and thick samples, respectively. This sorption time corresponds to the time needed to reach the first plateau in sorption curves and will be denoted as “virtual saturation.” After the first sorption, the EMC samples were removed from the humidity chamber and placed in two infrared dry ovens at temperatures of 110 and 160◦ C to release their moisture at a constant temperature. After reaching a “virtual dry state” (the final desorbed state in Fig. 2.9a and b), the samples were placed in the same humidity chamber again for the second run of moisture absorption at 85◦ C/85% RH. Since the samples had undergone an absorption/desorption cycle, they had an initial moisture content (residual moisture content at the end of desorption) as described in the previous section. This initial content was low, because the absorption was stopped as soon as the samples reached the virtual saturation and was not considered in the mass uptake during the re-sorption process. Figure 13a and b shows the comparisons between the first run of moisture absorption and the second run after baking at 110 and 160◦ C for the thin and thick samples, respectively. From these curves the following results can be postulated: • After the desorption at 110◦ C, the second absorption curve before virtual saturation was found to be almost identical to the first run for both 1 and 2 mm samples.

Mechanism of Moisture Diffusion in Epoxy Molding Compounds

Fig. 2.13 Re-sorption experiment of bulk samples after two baking temperatures of 110 and 160◦ C: (a) thin samples (thickness 1 mm) and (b) thick samples (thickness 2 mm)

49

0.3 0.25

Mass uptake, %

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This means the moisture absorption due to the first phase of moisture diffusion is mostly repeatable. The moisture desorption at 110◦ C happens below the glass transition temperature, at which the relaxation of polymer chains and the change of free volumes are not significant. • However, the desorption at 160◦ C affected the second run of moisture absorption significantly. The rate of moisture absorption at the second run was found to be higher than that at the first run. The increase in the rate of moisture uptake can be attributed to the expansion of free volumes in the polymeric materials due to the storage of the material, which was baked at 160◦ C, well above the glass transition temperature. For the thin samples (Fig. 2.13a) the difference between the first and second runs of moisture absorption is much less than the thicker samples (Fig. 2.13b), because of less exposed time to elevated temperature. Consequently, the formation of new free volumes is less, as this is dependent on the time exposure to high temperatures.

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The phenomenon of increasing volumes of EMCs and PEMs was also reported by Teverovsky [34], who observed that after baking, the volume of some PEMs increased by 0.06–0.27%. In order to evaluate how the bake temperature affects the results of the re-sorption, QFP144 packages, which manifested normal volume reduction behavior during baking, were baked at different conditions: 125◦ C for 96 h, 165◦ C for 25 h, and 205◦ C for 2 h. After baking at each condition, the samples were moisturized at 85◦ C, 100% RH for 168 h, and then baking was repeated at the same temperature as before. The results of these measurements are shown in Fig. 2.14 [34]. 0.3

Fig. 2.14 Effect of baking condition on moisture uptake and volume deviation in a QFP package [35]

dm

0.2

dM, (dV), %

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125°C 96hr

dV

0 –0.1 165°C 24hr

–0.2 –0.3 –0.4

205°C 2hr

–0.5 –0.6 Initial

bake

85°C/100% RH/168hr

bake

The phenomenon of non-reversible moisture content was reported by Lin [35], Shirangi et al. [1, 2], and Xie et al. [36]. However, Teverovsky [9] reported that baking resulted in virtually a complete removal of moisture as shown in Fig. 2.14. This may be due to many possible reasons, including short sorption time, lack of measurement accuracy, or type of epoxy used in the molding compounds. However, as shown in Fig. 2.14 the volume variations increased with the bake temperature. The 2-h bake at 205◦ C caused more than 0.4% decrease in the volume compared to only 0.1% after 125◦ C bake.

2.5 Hygroscopic Swelling Water molecules in polymeric materials have been identified to have two distinct states. A “free” or “unbound” state of water is attributed to water molecules that are present in voids and nanopores of the material [7, 21, 37] and can easily move through the free volumes of polymer. Another state is formed by water molecules, which disrupt inter-chain polymer ties and are called “bound” water molecules. The “bound” water molecules react with the polymer chains via hydrogen bonding. It is often believed that the moisture-induced swelling of polymers is due to the hydrogen bonding and the presence of water molecules in free volumes of the polymers has a less contribution to the hygroscopic swelling of polymers [19, 38–42].

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Mechanism of Moisture Diffusion in Epoxy Molding Compounds

51

This identification is further supported by measurement of the ratio of hygroscopic volume expansion to the volume of absorbed water which is less than unity [38], indicating that some of the absorbed water does not contribute to swelling. The hygroscopic mismatch strain at the interfaces between molding compounds and metallic components in a package could be as high as the thermal mismatch strains [7, 38–40]. In order to recognize the impact of the hygroscopic swelling on the overall shape of plastic packages, the surface topography of a plastic IC package was investigated. The measurements were performed via an FRT MicroProf with a chromatic sensor (CWL). The chromatic sensor illuminates the sample by using a white light source and measures the wavelength-dependent (chromatic) distribution of the reflected light and determines the absolute height information. Figure 2.15 shows the outof-plane topography of the top surface of a TQFP-epad package which uses the molding compound MC-1 introduced in the previous sections. The surface topography of a dry package at room temperature is shown in Fig. 2.15a. The sample was then placed in a humidity chamber at 85◦ C/85% RH for 168 h (MSL1). After the sorption, the sample was removed from the humidity chamber and exposed to ambient temperature. Upon cooling to room temperature, the warpage was again measured as shown in Fig. 2.15b. By comparing the warpage of a dry and a moisture-preconditioned package, it becomes clear that the hygroscopic swelling of EMCs alters the overall stress balance in plastic packages. The warpage direction of the package changed from a “smiling” shape to “crying” after moisture preconditioning. At room temperature, the warpage of a dry package is dominated by two factors: The first mechanism is the cure shrinkage of epoxy molding compounds due to the cross-linking of the polymers during the transfer molding. The second mechanism is the mismatch between the coefficient of thermals expansion (CTE) of different materials. When the packages absorb moisture, the hygroscopic swelling of the EMC acts as a third mechanism and affects the warpage direction of the package by introducing a moisture-induced expansion to the epoxy molding compound.

Fig. 2.15 Topography of the upper surface of a TQFP-epad package: (a) dry package and (b) after 168 h aging at 85◦ C/85% RH

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The amount of hygroscopic strain found from the dimensional change is normally assumed to be linearly proportional to the moisture concentration as follows [1–3, 6–8, 38–42]: εh = βC ,

(2.8)

where εh is the hygroscopic strain, β (mm3 /g) is the coefficient of hygroscopic swelling (CHS), and C (g/mm3 ) is the moisture concentration. There has been a long debate and some discrepancy between the different studies over a suitable method in order to find the coefficient of hygroscopic swelling [38–42]. The aim of all these works is to find the hygroscopic swelling strain and to relate it to the local moisture concentration. The next sections of this study provide useful information about the direct effect of hygroscopic swelling by measuring the deflection of specially designed bi-material beams and comparing the results with those found from a well-established characterization method, namely the TMA/TGA approach.

2.5.1 Characterization of CHS by Warpage Measurement of Bi-material Beams Since the direct impact of the hygroscopic swelling on the plastic packages is affecting their warpage, this work investigates the swelling of the EMCs by measuring the deflection of bi-material beams during moisture absorption. Bi-material beams of copper/EMC with two different EMC thicknesses were designed and manufactured as shown in Fig. 2.16a and d. The samples were used later for the characterization of interfacial fracture toughness between the EMC and the copper leadframe. In order to manufacture the bi-material Cu/EMC beams via transfer molding process, copper substrates were first machined into 50 × 10 × 0.4 mm3 strips. After cleaning with acetone the substrates were placed in the cavity of a molding machine. Pellets of a commercial epoxy molding compound (MC-1 in the previous sections) were introduced into the cavity of a pre-heated mold at about 175◦ C and kept under a pressure of 60 bars for 90 s; the molding compound was dispensed automatically on the copper surface at 175◦ C. After molding the samples were placed in an infrared chamber for post-mold curing at 175◦ C for 6 h in order to complete the polymerization process of the epoxy molding compound. Three samples from each type were used to gain a statistically acceptable CHS value. Figure 2.16b and e shows the warpage of the beams in the dry state, which arises from the cure shrinkage of EMC during the manufacturing process and the CTE mismatch between EMC and copper. After the post-mold process, samples were placed in a humidity chamber at 85◦ C/85% RH and were removed periodically from the moisture chamber. Their warpage was measured at room temperature and then they were placed in the humidity chamber for further sorption. During the moisture absorption, the warpage of the thin samples (with an EMC thickness of 0.6 mm) changed from a concave to a convex shape (see Fig. 2.16b and c). The convex shape increased and reached a constant value of approximately 185 μm after 1 week of sorption. Further exposure to moisture

2

Mechanism of Moisture Diffusion in Epoxy Molding Compounds

hEMC = 0.6 mm

53

hEMC = 1 mm EMC

EMC

hCu = 0.4 mm

hCu = 0.4 mm

(a)

(d)

Wdry = +12 µm

Wdry = +186 µm

(b)

(e)

Wmoist = –185 µm (c)

(f)

Hygroscopic swelling changes the stress state

Wmoist = +31 µm

Hygroscopic swelling reduces the stresses

Fig. 2.16 Effect of hygroscopic swelling on the warpage of the bi-material beam

did not affect the warpage significantly. The thick samples (with an EMC thickness of 1.0 mm) had an initial warpage of 186 μm at room temperature in the fully dry state (Fig. 2.16e). During the sorption, their warpage decreased to around 31 μm and remained almost constant after 2 weeks of sorption as shown in Fig. 2.16 f. The warpage values of both samples as a function of exposure time to moisture are shown in Fig. 2.17.

250 200 150 tEMC = 1.0 mm

Warpage, µm

100 50 0 –50 –100 –150

Fig. 2.17 Warpage change of bi-material beams as a function of exposure time to moisture at 85◦ C/85% RH

0

1

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4

tEMC = 0.6 mm

–200 –250 Exposure to 85 C/85%RH, weeks

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M.H. Shirangi and B. Michel

The warpage changing of the bi-material beams is due to the hygroscopic swelling across the exposed surface of the epoxy molding compound. However, since the epoxy molding compounds are viscoelastic materials, stress relaxation can also cause a change in the warpage during the moisture aging at 85◦ C/85% RH [42]. This was confirmed by a separate test regarding the aging of samples in a dry condition at 85◦ C in order to isolate the effect of the thermal aging and to assess the pure effect of the hygroscopic swelling at 85◦ C/85% RH. Nevertheless, in order to calculate the pure hygroscopic swelling strain, one needs the exact amount of the cure and thermal strains. The authors showed in [43] that a simple modification in the CTE values together with applying a viscoelastic model can accurately predict the warpage of these bi-material samples. In this work, the same model was applied to determine the hygroscopic strain of the epoxy molding compound similar to that explained in [42]. The glass transition temperature (Tg ) of the EMC was measured and found to be 109◦ C and the CTE1 and CTE2 were measured 8.9 and 29.6 ppm/K, respectively, as reported in [43]. The cure shrinkage during the molding process of the samples was found by warpage analysis as well. The sample history was modeled with the FE program ANSYS as follows. First, the cure shrinkage at the molding temperature was accounted for by applying the cure strain to the molding compound. Afterward the thermal strains arising from the cooling process from mold temperature (175◦ C) to room temperature (25◦ C) were taken into account. Finally, the hygroscopic swelling and the stress relaxation during the aging at 85◦ C/85% RH were modeled. The hygroscopic strain was obtained from the finite element calculation to be almost 0.061%. The moisture content of the EMC was measured in [1, 2] to be between 4.45E–6 and 6.7E–6 g/mm3 , depending on the sorption history. Consequently, by using equation (2.8), the coefficient of hygroscopic swelling can be estimated at an average value of 134 mm3 /g. Some samples were removed from the moisture chamber after the saturation and were placed in a dry infrared oven at 110◦ C. The warpage of the samples was measured after 10 days of baking. This was done to investigate whether the hygroscopic swelling is reversible. As was expected, not all the moisture-induced warpage due to moisture absorption was recovered. This suggests that the measurement of the hygroscopic swelling by any method that deals with the dimensional change during the desorption of the sample should be avoided, at least for the polymeric materials which show such non-reversible hygroscopic swelling. In the next section another method based on the dimensional measurement of EMCs during the baking will be investigated and the results will be compared to that from the above method.

2.5.2 Characterization of CHS by TMA/TGA Hygroscopic swelling of EMCs has been usually investigated by performing two parallel analyses. In the first one the weight loss of a saturated sample during

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Mechanism of Moisture Diffusion in Epoxy Molding Compounds

55

desorption at a constant temperature is measured. This can be done via a TGA (thermal gravimetric analyzer) or running a finite element simulation of the desorption process of the sample [1]. In the other one the dimensional changes of the sample during desorption are measured. Usually a TMA (thermal mechanical analyzer) measurement [1, 6, 41, 42, 44] or shadow Moiré interferometry [3, 7, 40] is used for the in situ measurement of the hygroscopic strains. In all these methods, the dimensional changes of the sample during the isothermal desorption are considered and it is assumed that the behavior of the polymeric materials in terms of swelling and shrinkage during the absorption and desorption is the same. However, the problem of this method is that, similar to the residual moisture content upon desorption of the molding compounds reported previously, a residual hygroscopic strain may also exist. In other words, not all the swelling during the moisture uptake may be recovered after desorption. This may cause a wrong correlation between the measured strains and the moisture concentrations. In order to determine the CHS of material MC-1, initially moisture-preconditioned (up to virtual saturation) samples of 8 mm length were placed in the TMA for the strain measurement at different temperatures. The average elastic strain along the measuring line was reported by Zhou et al. to be close to zero [41]. The presence of elastic strain due to hygroscopic stress contributes a relatively small analysis error in the determination of the coefficient of hygroscopic swelling [44], compared to the error caused by non-uniform hygroscopic swelling deformation. To eliminate the role of thermal expansion during desorption with TMA, a dry sample was used as reference so that only hygroscopic strains were documented. For the TGA measurement with the available equipments, samples must have a maximum length of 2 mm to fit to the equipment, which makes it difficult to couple the moisture concentration results from TGA with strains from TMA because of different sample geometries. As an alternative for TGA, a finite element analysis of the desorption process was performed and used for the mass loss calculation using the desorption data from Table 2.3. Figure 2.18 shows the experimental results of TMA and the corresponding TGA simulations at three temperatures. From each pair of isotherm TMA/TGA curves of Fig. 2.18, a CHS can be obtained by fitting a linear line and calculating its slope as depicted in Fig. 2.19. The curves do not cross the origin due to the inaccuracy of the TMA at longer stages of desorption. The results show a smooth increase of CHS at higher temperatures due to vapor pressure-induced expansion of the EMC at elevated temperatures. The CHS results found from the TMA/TGA method are in the same order of magnitude as the value determined using the warpage analysis as compared in Table 2.4. However, to the authors’ best knowledge, the warpage analysis should be preferred to estimate the CHS value. This is because of the fact that the hygroscopic swelling develops during the moisture preconditioning and its direct effect is changing the beam warpage. Consequently, the method can be benchmarked by applying the CHS value in the FE analysis and comparing the simulated warpage to the experimental one. This enables the verification of the whole stress analysis, which includes cure, thermal, and hygroscopic strains.

56

M.H. Shirangi and B. Michel x 10−4

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TMA, T = 110 °C

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Fig. 2.18 Results of TMA analysis at three temperatures (left) together with results of TGA from simulation at corresponding temperatures (right)

It must be mentioned that the results from Fig. 2.19 show that the CHS increases with increasing baking temperature. This is a problem of estimating the CHS using the TMA/TGA approach, as during the strain measurements by TMA, especially at elevated temperatures; the expansion of the EMC due to the high vapor pressure is also documented. Consequently, the results at lower temperatures seem to be closer to the real hygroscopic expansion during the sorption at 85◦ C/85% RH.

2.5.3 Characterization of CHS by Archimedes Principle Teverovsky [34] investigated the hygro-thermal expansion of two commercial molding compounds. The volume measurements of molding compounds were done by Archimedes principle based on the weight measurements of the parts in air and then after immersion into a fluid (Galden D02), using the density of the liquid. The volume and weight of the sample were measured two times: after saturation in moisture and after baking at high temperature and the CHS was then found from the following formula:

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Mechanism of Moisture Diffusion in Epoxy Molding Compounds

8

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x 10−4

Strain

Strain versus C at T=110°C 6 CHS=129 mm3/g

4 2 2

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x 10

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1.5

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2

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x 10

x 10−3

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6

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4

3 0

1

2 3 4 Moisture concentration (C), (gr/mm3)

6

5

−6

x 10

Fig. 2.19 Calculation of CHS by combining the results of TMA and TGA Table 2.4 CHS results from different approaches Method

CHS (mm3 /g)

TMA/TGA at 110◦ C TMA/TGA at 160◦ C TMA/TGA at 220◦ C Warpage analysis of a bi-material beam

129 146 168 134

CHS =

1 Vmoist − Vbake Mbake . 3 Mmoist − Mbake Vbake

The results of CHS at different temperatures and humidities are shown in Fig. 2.20. It can be observed that the hygro-thermal expansion is not a constant, but depends on moisturizing conditions and has a trend of increasing with moisture uptake. The results in Fig. 2.20 reveal that moisture uptake is virtually a linear function of the relative humidity for the tested molding compounds.

58

M.H. Shirangi and B. Michel 0.7 0.6

MG70F-0627 MG33F-0520

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Fig. 2.20 Isotherms of the equilibrium moisture uptake: (a) volume swelling and (b) coefficient of moisture expansion (CME) for two epoxy molding compounds [34]

2.6 Moisture-Induced Adhesion Degradation Water is often regarded as the main agent in reducing the service life and reliability of adhesive joints, electronic devices, and composite materials. The mechanism of adhesion loss at a critical relative humidity is the subject of much speculation [21, 45]. The dramatic reduction in adhesion strength has been attributed to both physical and chemical changes resulting from the moisture absorption either in the bulk adhesive or at the interface between the adhesive and substrate. Moisture can influence the interfacial adhesion through three mechanisms. The first mechanism is the intrinsic aggregating effect of water molecules upon direct presence at the interfaces and degrading the interfacial adhesion by bonding to the polymer chains [46–48]. The second mechanism is that the absorbed moisture changes the mechanical properties of polymeric materials. For example, Dudek et al. [47] and Ferguson et al. [49, 48] reported that moisture can change the elastic modulus and shift the glass transition temperature of polymers to lower values. This mechanism leads normally to a slight difference in the mode mixity of the measured fracture toughness of moist sample when compared to that of dry ones. The third mechanism is the swelling of polymeric materials upon exposure to moist environments, thereby causing an additional mismatch between volumetric expansions of substrate and adhesives. This is even more pronounced when the joint between a polymer and metal is investigated. Since the metallic substrate is impermeable to

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Mechanism of Moisture Diffusion in Epoxy Molding Compounds

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moisture, only the polymeric adhesive absorbs moisture and causes a mismatch in hygroscopic strains. In order to measure the intrinsic fracture toughness of a moisture-preconditioned bi-material sample, the influence of hygroscopic swelling which induces an apparent change in the measured fracture toughness should be isolated. Brewis et al. [50] proposed that degradation of the interface is the basic cause for adhesion loss. They suggested that bonds attributable to secondary forces at the interface are broken up by moisture, hydration of the oxide surfaces, and/or water condensation due to the lowering of the vapor pressure by the presence of salt impurities at the interface. In contrast to their results, Lefebvre et al. [51] suggested that the change in the bulk properties of the epoxy adhesive is responsible for the observed onset of adhesion loss at a critical relative humidity. They reported that the solubility, or mass of absorbed water, as a function of relative humidity increased abruptly at the critical relative humidity. Their study suggests that capillary condensation and the depression of glass transition are not responsible for the adhesion loss. They proposed that inter-chain hydrogen bonds are broken by absorption of water. However, using nuclear magnetic resonance, McBrierty et al. [52] opposed the theory that inter-chain hydrogen bonds are broken by absorption of water. They showed in epoxies based on the diglycidyl ether of bisphenol A (DGEBA) that no disruption of the hydrogen bonding network occurs at room temperature in the hydrated epoxy resin. Ferguson [49, 48] suggested that there are three mechanisms that contribute to water penetration at the interface in epoxy adhesive structures: bulk diffusion, wicking along the interface, and capillary action associated with micro-cracking. The first mechanism was discussed in the last sections. The second mechanism for moisture transport to interface is attributed to wicking along the interface and was discussed in previous sections as interfacial diffusion. Comyn et al. [53] found that the rate of wicking of glass-to-lead alloy joints bonded with an epoxy adhesive could not be accounted for by the rate at which water enters the epoxy adhesive by bulk diffusion alone. They concluded that water must also enter the interface by “wicking” along debonded zones along the interface. The final mechanism for moisture transport to the interface is by capillary action associated with voids and cracks present in the epoxy or epoxy composite. Lu et al. [54] found that the addition of fillers to polymers resulted in faster sorption kinetics when compared to the bulk polymer alone. They concluded that water was absorbed not only by the epoxy but also by the interfaces inside the epoxy introduced by the addition of fillers. The intrinsic effect of moisture on the interfacial fracture toughness of copper/EMC interface will be investigated in this section using a combined experimental and numerical method. The end-notched flexure (ENF) test [54] has been widely used to characterize the mode II fracture toughness [2, 42, 43, 55, 56]. A typical ENF testing setup for the bi-material interface is essentially a three-point bending test with an initial crack of length a at one end as shown in Fig. 2.21. The bi-material samples introduced in the previous sections were used for the characterization of interfacial fracture toughness between copper leadframe and epoxy

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Fig. 2.21 End-notched flexure (ENF) test for the measurement of interfacial fracture toughness

molding compound MC-1. Since the upper layer undergoes a larger deflection, the samples were positioned with the copper side facing up. A precrack was generated by coating the desired area of the leadframe with a special spray to prevent it from adhering to the leadframe during the molding process. Later a razor blade was introduced at the end of the beam at the interface to facilitate precracking. After the delamination test, there was a visible trace on the region of the copper leadframe which was precracked and the precrack length was measured by using a ruler. Furthermore, the precrack length was verified for a few samples by C-mode scanning acoustic microscopy. A typical load–displacement curve of an ENF test is shown in Fig. 2.22. For performing each test a specimen was placed on the lower supports. Then the upper

20

16

ENF at 25° C for precrack length of a = 11.8 mm

Point B: Initiation of interfacial delamination upon reaching the B

critical force

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C Point C: Arrest of the crack Propagation.

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A 0 0,0

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Fig. 2.22 Load–displacement curve of an ENF fracture test

0,8

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support was moved down manually and positioned just above the specimen. Next the loading was initiated and the displacement was read off upon reaching a preload of 1 N (point A in Fig. 2.22). At the early stages of applying load, an initial linear relation between force and displacement can be observed. The slope of the curve at this stage represents the bending stiffness of the composite EMC/Cu structure. The peak of the load profile (point B in Fig. 22) corresponds to the critical force and the initiation of the interfacial delamination. This force was used later as the critical force in the finite element analysis. After reaching the peak load the delamination propagates until it stops at a point (point C) which is usually in the middle of the beam. During crack propagation (from point B to point C) the compliance of the beam increases, which means that the energy release rate of the ENF test is dependent on the crack length. After the crack stops at point C, the load increases again linearly. After point C, the slope of the graph represents the stiffness of the EMC only. The fracture load at the onset of crack propagation where the load suddenly drops (point B) was used for the measurement of the interfacial fracture toughness via finite element analysis. For each test condition, between four and eight specimens were used, and each peak load with its corresponding precrack length was used for a separate finite element calculation. In order to prevent large deformations, the span between two lower supports was fixed at 34 mm. Based on the fracture curves obtained from the ENF tests, finite element analyses were carried out to determine the resultant interfacial fracture toughness. A 3D finite element model was built with eight-node elements using the FEM tool ANSYS. For the analysis of the ENF model, contact elements without friction were used in cracked surfaces to avoid element penetrations. The residual stresses during the manufacturing process of the samples were taken into account as follows: First the chemical cure shrinkage during the molding process was introduced in the FEA model as explained by the authors in [43]. Then the cooling process from the molding temperature (175◦ C) to room temperature (25◦ C) was taken into account. Finally the introduction of a precrack, which leads to some stress relaxations in the sample, was modeled by decoupling the selected nodes at the interface. The virtual crack closure technique (VCCT) has successfully been used to obtain the total strain energy release rate (SERR) and the mode mixity for both homogenous and interface cracks based on the results of finite element analysis. VCCT requires only one complete analysis of the structure to obtain the deformations. The method yields the total energy release rate in the direction in which the crack is extended virtually. A macro was written for the FEM tool ANSYS that allows to find all three components of the SERR. Since VCCT is only applicable in the case of linear elastic fracture mechanics (LEFM), it is questionable if this approach would be suitable for the interface crack between the elastic leadframe and the viscoelastic EMC. The authors justified the use of VCCT for the Cu/EMC samples in [43] and suggested that the VCCT is applicable as far as the fracture tests are performed at temperatures below the glass transition temperature of EMCs. Bi-material samples similar to those shown in Fig. 2.16 were used for the calculation of interfacial fracture toughness. At first samples with an EMC thickness of

62 120 100

Normalized interfacial fracture toughness, %

Fig. 2.23 Adhesion degradation of EMC/Cu interface as a function of exposure time to moisture

M.H. Shirangi and B. Michel

80 60 40 20 0 0

1

4 3 5 6 2 Exposure time to 85°C/85%RH, weeks

7

2 mm were produced. The average interfacial fracture toughness was normalized to the value of the dry samples at room temperature. The adhesion loss upon aging in humid environment was compared with the control value at dry state. Except for the samples measured at dry state, all samples were placed in the moisture chamber and five samples were removed after each week. After reaching the ambient temperature, a precrack was introduced in the samples and the fracture test was performed for all five samples. By running an FE simulation of the sample sorption, it was expected that the adhesion is not affected during the first 2 weeks of aging and its maximum decrease takes place after around 6–8 weeks of sorption. However, as shown in Fig. 2.23, it was observed that most of the adhesion loss happened immediately within the first week of moisture sorption. The fracture tests reveal that after 1 week of sorption the highest decrease in interfacial adhesion occurred, followed by a small decrease during the second week of sorption. The interfacial adhesion reached a constant value after approximately 2 weeks of exposure to moisture. This surprising result of rapid adhesion degradation can be attributed to the high rate of moisture diffusion along the interface between the EMC and the leadframe. These results can be justified by the sorption comparisons in Fig. 2.2a and b, which showed a higher diffusion rates across the interfaces. Since the bi-material samples with a high EMC thickness of 2 mm and an open interfacial diffusion path showed such anomalous results of rapid adhesion loss, new samples with thinner EMC thickness of 0.6 mm were used for the later experiments. In the design of the mold cavity some changes were also introduced so that the molding compound covered both sides of the bi-material sample acting as a barrier for interfacial diffusion. This mold flake was later removed by a grinding machine just before the fracture tests. Figure 2.24 shows the intrinsic effect of aging in humid environment on the interfacial fracture toughness of the Cu/EMC interface. All fracture tests were conducted at room temperature with a displacement-controlled rate of 0.1 mm/min. In addition, the effect of moisture on the elastic modulus of the EMC was investigated using three-point bending of bulk EMC bars. It was found

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80 70

Fracture toughness J/m2

Dry 60

dried after virtual saturation

58.7

50 44.9 40 30 26.3 20

virtual saturated

28.8 dried after 2nd phase absorption

10 0

Fig. 2.24 Effect of moisture absorption and desorption on the adhesion of Cu/EMC interface

that moisture does not affect the elastic modulus significantly. Hence, all the fracture toughness measurement can be assumed to be at a constant mode angle as has also been suggested by Ferguson [48]. Using the diffusion coefficient from the experimental results the time to virtual saturation of the samples was found numerically to be almost 2 weeks (0.21% weight gain of the whole sample). Fracture results show that the interfacial fracture toughness initially at 58.7 J/m2 in dry condition reduced to 26.3 J/m2 when the virtual saturation level at the interface was reached. In order to study the effect of an absorption/desorption cycle on the adhesion, moist samples were baked for 24 h at 125◦ C reaching a virtually dry state. A longer exposure to moisture was also investigated by 4 weeks of aging in humid condition (0.25% weight gain of the sample) and subsequent baking for 24 h at 125◦ C. The fracture toughness of these samples was measured again at room temperatures. Some of the adhesion loss due to moisture absorption up to virtual saturation was recovered after drying (44.9 J/m2 ). However, samples that remained longer in humid conditions (4 weeks) showed almost no recoverability upon the same annealing condition (28.8 J/m2 ). This is an important result, which shows the extreme degrading effect of the second phase of moisture absorption. The moisture absorption during the first phase degrades the adhesion due to the intrinsic effect of the presence of water molecules at the interface, which is partially reversible if a proper annealing is performed. However, the second phase of moisture absorption seems to destroy the adhesion bonds permanently, and none of the adhesion loss may be recovered if the moisture level at the interface reaches this critical content. These results are in agreement with the results of Dodiuk et al. [57] who evaluated the effect of moisture on the lap shear strength of four commercial epoxy

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adhesives to aluminum. They found that the exposure of moisture caused a reduction in lap shear strength; however, if the moisture concentration was below 0.3%, the strength was fully reversible after drying, indicating that adhesion loss may be recovered if the moisture content at the interface is still low. They gave no explanation for their results; however, the sorption results depicted in Figs. 2.5 and 2.9 together with the fracture results of Fig. 2.24 can be helpful to understand the moisture-induced degrading effects. The key to understanding the adhesion loss and its recoverability or non-recoverability is the second phase of moisture absorption, which causes a permanent degradation in adhesion by destroying the secondary bonds between polymer and substrate. There are some researchers that observed a critical moisture content for the adhesion degradation. It has been observed that a critical concentration of water may exist where there may be a concentration and associated humidity level below which the interface is not weakened. Kinloch [58] found that epoxy/mild-steel joints suffered no loss in adhesion from environment attack at 50% RH, even though the adhesive still absorbed water up to an equilibrium concentration. As a direct consequence of this observation, Kinloch proposed that a minimum, critical concentration of water must be a requirement for the loss of adhesion due to the presence of moisture. Ferguson and Qu [49, 48] used a water-proof perimeter to the bi-material test specimens before moisture preconditioning to force one-dimensional moisture uptake through the top surface of the test specimen and prevent wicking along the interface. This can enable the assumption of uniform concentration at interface by utilizing the inherent moisture absorption characteristics of the adhesive. They observed that a large portion of the loss in elastic modulus from moisture uptake was recovered upon subsequent drying. They also observed a permanent weight increase in epoxy samples after a subsequent baking which suggests that at least part of the irreversible damage resulted from hydrolysis with a greater extent occurring at higher humidity levels. When they investigated the adhesion under moisture, they observed significant reduction in interfacial adhesion even for low concentrations and concluded that the loss in interfacial fracture toughness from moisture was not recovered upon fully drying. They explained the permanent loss in adhesion with adsorption theory as a primary bonding mechanism for the underfill/copper interface. Contrary to some results regarding the permanent adhesion loss, there are some evidences in the literature that report a full recovery in adhesion upon a subsequent drying. The reversibility of the adhesion loss was reported for organosilicate glass (OSG) film by Lin et al. [59]. Also Shaw et al. [60] found that nearly all of the strength lost after immersing steel/epoxy lap shear joints in distilled water for 3 weeks was recovered after drying. They attributed the loss in strength after moisture preconditioning to plasticization of the epoxy adhesive, which is generally regarded as a reversible process. The discrepancy between the reported results in the literature may be due to different mechanisms available for the adhesion loss. The important result from the moisture diffusion experiments is that the adhesion tests gave reasonable predictive values, in agreement with the observations in moisture absorption and desorption

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behavior. These realistic test conditions can enable a correlation to the response of microelectronic packages to humid conditions.

2.7 Conclusion In this study a systematic investigation of absorption and desorption of moisture in epoxy molding compounds was conducted. Absorption of moisture was found to show a dual-stage non-Fickian behavior. The exposure of an EMC sample upon a virtual saturation (end of the first absorption phase) to a dry environment was found to lead to an almost dry state with only slight residual moisture content at the end. However, a dry state was not achieved when the samples with higher initial moisture content (which were kept in humid environment for a longer time) were baked in dry conditions. A residual moisture content was present which was a complex function of time exposed to moisture, sample geometry, and baking temperature. The schematic picture of the influence of sample history may be depicted as shown in Fig. 2.25. Samples which reached point A (virtual saturation) show a lower residual moisture content upon baking when compared to the samples reached point B (second absorption phase). However, the rate of desorption for both cases was the same, indicating that at least two mechanisms are active during the diffusion of moisture. One is a reversible mechanism that dominates the diffusion rate. The other is a non-reversible mechanism that is a function of time, temperature, and sample geometry. Moisture uptake curve B A Moisture Content

Fig. 2.25 Schematic model for the residual moisture content upon desorption of moisture

Desorption after Desorption after

reaching point B

reaching point A

Cres Cres time ,

(

hour

)

The second run of moisture absorption showed also some differences from the first run. The sample sorption history was found to be the dominating factor. The rate of moisture absorption at the second run was found to be higher than that at the first run. The increase in the rate of moisture uptake can be attributed to the formation of new voids in the polymeric materials, which facilitates the transformation of water molecules in the sample. Higher temperatures lead to the formation of more new free volumes. A schematic picture of the effect of sample history on the rate of the second run of moisture absorption may be depicted like the one in Fig. 2.26.

Fig. 2.26 Schematic model of the second run of the moisture absorption after an absorption/desorption cycle

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Moisture Content

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2nd run of absorption at 85° C/85% RH

1st run of absorption at 85°C/85%RH

Desorption at 110°C Desorption at 160°C time , ( hour )

The coefficient of hygroscopic swelling (CHS) is normally found by relating the dimensional changes of a saturated bulk sample to its mass loss during the isothermal desorption. However, experiments showed that the swelling of EMCs upon moisture intake was not recovered completely after their moisture desorption. This makes a correlation between the actual moisture content and the dimensional changes during the baking process very difficult. Consequently, other methods based on the absorption process should be used for estimating the coefficient of hygroscopic swelling. Warpage measurement of a bi-material beam is a better approach; however, the significant stress relaxation during the aging must be considered in the simulation methods. A detailed analysis of the warpage via FE analysis which considers the effect of cure shrinkage, stress relaxation due to viscoelasticity, and moisture-induced swelling was performed. This method allows for the calculation of the CHS during the moisture absorption of the EMC materials. In this study we also demonstrated that the exposure of a Cu/EMC bi-material beam to moisture prior to fracture tests results in a degradation of the adhesion. This degradation is the result of the diffusion of water in the interface. For samples that were aged shortly in a humid environment the degradation was partially reversible by applying an appropriate heat treatment at mild annealing conditions. However, long-term aging in humid condition caused a permanent adhesion loss, which was attributed to the effect of hydrogen bonding between water molecules and polymer chains at the interface.

References 1. Shirangi, M.H., Auersperg, J., Koyuncu, M., Walter, H., Müller, W.H., Michel, B., “Characterization of dual-stage moisture diffusion, residual moisture content and hygroscopic swelling of epoxy molding compounds,” Proceedings of the 9th EuroSime2008, Freiburg, Germany, pp. 455–462, 2008. 2. Shirangi, M.H., Fan, X.J., Michel, B., “Mechanism of moisture diffusion, hygroscopic swelling and adhesion degradation in epoxy molding compounds,” Proceedings of the 41st International Symposium on Microelectronics (IMAPS), Providence, USA, pp. 1082–1089, 2008. 3. Fan, X.J., Zhou, J., Chandra, A., “Package structural integrity analysis considering moisture,” Proceedings of Electronic Components and Technology Conference (ECTC), Orlando, USA, pp. 1054–1066, 2008.

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4. Pecht, M.G., Nguyen, L.T., Hakim, E.B., Plastic-Encapsulated Microelectronics. New York, NY: Wiley, 1995. 5. Ardebili, H., Hillman, C., Natishan, M.A.E., McCluskey, P., Pecht, M.G., Peterson, D., “A comparison of the theory of moisture diffusion in plastic encapsulated microelectronics with moisture sensor chip and weight-gain measurements,” IEEE Transaction on Components and Packaging Technologies, 25, 132–139, 2002. 6. Fan, X.J., Lee, S.W.R., Han, Q., “Experimental investigations and model study of moisture behaviors in polymeric materials”, Microelectronics Reliability, 49, 861–871, 2009. 7. Fan, X.J., “Mechanics of moisture for polymers: fundamental concepts and model study,” Proceedings of the 9th EuroSime, Freiburg, Germany, pp. 159–172, 2008. 8. Shirangi, M.H., Müller, W.H., Michel, B., “Determination of Copper/EMC interface fracture toughness during manufacturing, moisture preconditioning and solder reflow process of semiconductor packages,” Proceedings of International Conference on Fracture (ICF12), Ottawa, Canada, 2009. 9. Teverovsky, A., Moisture Characteristics of Molding Compounds in PEMs, Lanham, MD: QSS Group, Inc./Goddard Operations. 10. Soles, C., Yee A, “A discussion of the molecular mechanisms of moisture transport in epoxy resins,” Journal of Polymer Science, Part B: Polymer Physics, 38, 792–802, 2000. 11. Adamson, M.J., “Thermal expansion and swelling of cured epoxy resin used in graphite/epoxy composite materials,” Journal of Material Science, 15, 1736–1745, 1980. 12. Tencer, M.,“Moisture ingress into nonhermetic enclosures and packages – a quasisteady state model for diffusion and attenuation of ambient humidity variations,” IEEE 44th Electronic Components Technology Conference, Washington DC, USA, 1994. 13. Wong, E.H., Teo, Y.C., Lim, T.B., “Moisture diffusion and vapor pressure modeling of IC packaging,” Proceedings of Electronic Components Technology Conference (ECTC), Seattle, USA, pp. 1372–1378, 1998. 14. Xie, B., Fan, X.J., Shi, X.Q., Ding, H., “Direct concentration approach of moisture diffusion and whole field vapor pressure modeling for reflow process: part I – theory and implementation”, ASME Journal of Electronic Packaging, 31(3), 031010, 2009. 15. Vine, K., Cawley, P., Kinloch, A.J., “The correlation of non-destructive measurements and toughness changes in adhesive joints during environmental attack,” Journal of Adhesion, 77, 125–161, 2001. 16. Davis, D., Krebs, A., Drzal, L.T., Rich, M.J., Askeland, P., “Electrochemical sensors for nondestructive evaluation of adhesive bonds,” Journal of Adhesion, 72, 335–358, 2000. 17. Zanni-Defarges, M.P., Shanaham, M.E.R., “Evaluation of adhesive shear modulus in a torsional joint: influence of aging,” International Journal of Adhesion and Adhesives, 13, 41–45, 1993. 18. Chan, E., Yuen, M., “Study of interfacial moisture diffusion at Cu/Epoxy interface by FTIRMIR technique,” Proceedings of Electronic and Component and Technology Conference, Reno, Nevada; USA, pp. 1782–1787, 2007. 19. Fan, X.J., “Moisture related reliability in electronic packaging”, Electronic Component Technology Conference (ECTC), Short Course Notes; 2008. 20. Buchwalter, L.P., “Polyimides: fundamental aspects and applications,” Adhesion of Polyimides to Various Substrates. New York, NY: Marcel Dekker, pp. 587–628, 1996. 21. O’Brien, E. P., “Durability of adhesive joints subjected to environmental stress,” Dissertation for Doctor of Philosophy. Blacksburg, VA: Virginia Polytechnic Institute, 2003. 22. Wu, W.L., Orts, W.J., Majkzak, C.J. “Water absorption at a polyimide/silicon wafer interface,” Polymer Engineering & Science, 12, 1000–1004, 1995. 23. Nguyen, T., Byrd, B., Alsheh, D., McDonough, W., Seiler, J., “Interfacial water and adhesion loss of polymer coatings on a siliceous substrate,” Materials Research Society, 385, 57–63, 1995. 24. Bowden, F.P., Throssell, W.R., “Adsorption of water vapour on solid surfaces,” Nature, 167, 601–602 April 1951.

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25. Takahashi, M.K., “AC impedance measurements of moisture in interfaces between epoxy and oxidized silicon,” Journal of Applied Physics, 67, 3419, 1990. 26. Shen, C.H., Springer, G.S., “Moisture absorption and desorption of composite materials,” Journal of Composite Materials, 10, 2–20, 1976. 27. Chen, X., Zhao, S., “Moisture absorption and diffusion characterization of molding compound,” Journal of Electronic Packaging, 127, 460–465, 2005. 28. Celik, E., Guven, I., Madenci, E., “Experimental and numerical characterization of nonFickian moisture diffusion in electronic packages,” Proceedings of Electronic Components and Technology Conference, Reno, Nevada; USA, pp. 1069–1073, 2007. 29. Weitsman, Y.J., “Anomalous fluid sorption in polymeric composites and its relation to fluid induces damage,” Journal of Composites Part A: Applied Science and Manufacturing, 37, 617–623, 2006. 30. Loh, W.K., Crocombe, A.D., Abdel Wahab, M.M., Aschroft, I.A., “Modelling anomalous moisture uptake, swelling and thermal characteristics of a rubber toughened epoxy adhesive,” International Journal of Adhesion & Adhesives, 25, 1–12, 2005. 31. Lekatou, A., Faidi, S.E., Ghidaoui, D., Lyon, S.B., Newman, R.C., “Effect of water and its activity on transport properties of glass/epoxy particulate composites,” Journal of Composites Part A: Applied Science and Manufacturing, 28, 223–236, 1997. 32. He, Y., Fan, X.J., “In-situ characterization of moisture absorption and desorption in thin BT core substrate,” Proceedings of Electronic Components and Technology Conference, Reno, Nevada; USA, pp. 1375–1383, 2007. 33. Teverovsky, A., “A rapid technique for moisture diffusion characterization of molding compounds in PEMs,” NEPP Report, GSFC, 2002. 34. Teverovsky, A., Moisture Characteristics of Molding Compounds in PEMs. Lanham, MD: QSS Group, Inc./Goddard Operations, NASA Technical Report, 2002. 35. Lin, Y.C., “Investigation of the moisture-desorption characteristics of epoxy resin,” Journal of Polymer Research, 13, 369–374, 2006. 36. Xie, B., Fan, X.J., Shi, X.Q., Han, D., “Direct concentration approach of moisture diffusion and whole field vapor pressure modeling for reflow process: part II – application to 3-D ultrathin stacked-die chip scale packages,” ASME Journal of Electronic Packaging, 31(3), 031011, 2009. 37. Fan, X.J., Zhou, J., Zhang, G.Q., Ernst, L.J., “A micromechanics based vapor pressure model in electronic packages,” ASME Journal of Electronic Packaging, 127(3), 262–267,1 2005. 38. Ardebili, H., Wong, E.H., Pecht, M., “Hygroscopic swelling and sorption characteristics of epoxy molding compounds used in electronic packaging,” IEEE Transactions on Components and Packaging Technologies, 26, 206–214, 2003. 39. Shi, X., Zhang, Y., Zhou, W., Fan, X.J., “Effect of hygrothermal aging on interfacial reliability of silicon/underfill/FR-4 assembly,” IEEE Transactions on Components and Packaging Technologies, 31, 94–103, 2008. 40. Stellrecht, E., Han, B., Pecht, M.G., “Characterization of hygroscopic swelling of mold compounds and plastic packages,” IEEE Transactions on Components and Packaging Technologies, 27, 499–506, 2004. 41. Zhou, J., Lahoti, S., Kallolimath, K., “Investigation of non-uniform moisture distribution on determination of hygroscopic swelling coefficient and finite element modelling for a flip chip package,” Proceedings of EuroSimE, Berlin, Germany, 2005. 42. Shirangi, M.H., Müller, W.H., Michel, B., “Effect of nonlinear hygro-thermal and residual stresses on interfacial fracture in plastic IC packages”, Proceedings of the 59th Electronic Components and Technology Conference (ECTC), San Diego, CA, USA, pp. 232–238, 2009. 43. Shirangi, M.H., Wunderle, B., Wittler, O., Walter, H., Michel, B., “Modeling cure shrinkage and viscoelasticity to enhance the numerical methods for predicting delamination in semiconductor packages,” Proceedings of the 10th EuroSime2009, Delft, The Netherlands, 2009.

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44. Zhou, J., “Sequentially-coupled finite element transient analysis with hygroscopic swelling,” Proceedings of the 7th EuroSimE, Como, Italy, 2006. 45. Fan, X.J., Zhou, J., Zhang, G.Q., “Multi-physics modeling in virtual prototyping of electronic packages – combined thermal, thermo-mechanical and vapor pressure modeling,” Microelectronics Reliability, 44, 1967–1976, 2004. 46. Fan, X.J., Zhang, G.Q., van Driel, W.D., Ernst, L.J., “Interfacial delamination mechanisms during reflow with moisture preconditioning,” IEEE Transactions on Components and Packaging Technologies, 31(2), 252–259, 2008. 47. Dudek, R., Walter, H., Michel, B., “Studies on moisture diffusion and popcorn cracking,” Proceedings of the 3rd EuroSimE, Paris, France, pp. 225–232, 2002. 48. Ferguson, T., “Moisture and interfacial adhesion in microelectronic assemblies,” Dissertation for the Degree of Doctor of Philosophy. Atlanta, GA: Georgia Institute of Technology, June 2004. 49. Ferguson, T., Qu, J., “Elastic modulus variation due to moisture absorption and permanent changes upon redrying in an epoxy based underfill,” IEEE Transactions on Components and Packaging Technologies, 29, 105–111, 2005. 50. Brewis, D.M., Comyn, J., Raval, A.K., Kinloch, A.J., “The effect of humidity on the durability of aluminum-epoxide joints,” International Journal of Adhesion and Adhesive, 10, 247–253, 1990. 51. Lefebvre, D.R., Elliker, P.R., Takahashi, K.M., Raju, V.R., Kaplan, M.L., “The critical humidity effect in the adhesion of epoxy to glass: role of hydrogen bonding,” Journal of Adhesion Science and Technology, 14(7), 925–937, 2000. 52. McBrierty, V.J., Martin, S.J., Karasz, F.E., “Understanding hydrated polymers: the perspective of NMR,” Journal of Molecular Liquids, 80(2), 179–205, 1999. 53. Comyn, J, Groves, C., Saville, R., “Durability in high humidity of glass-to-lead alloy joints bonded with an epoxide adhesive,” International Journal of Adhesion and Adhesives, 14, 15–20, 1994. 54. Lu, X., Hofstra, P., Bajkar, R., “Moisture absorption, dielectric relaxation, and thermal conductivity studies of polymer composites,” Journal of Polymer Science: Part B: Polymer Physics, 36, 2259–2265, 1998. 55. Asao, N., Isao, H., Naotaka, T., “A new method for measuring adhesion strength of IC molding compounds,” Journal of Electronic Packaging, 114, 402–412, 1992. 56. Shirangi, M.H., Gollhardt, A., Fischer, A., Müller, W.H., Michel, B., “Investigation of fracture toughness and displacement fields of copper/polymer interface using image correlation technique,” Proceedings of the 41st International Symposium on Microelectronics (IMAPS), Providence, USA, pp. 917–923, 2008. 57. Dodiuk, H., Dori, L., Miller, J., “The effect of moisture in epoxy film adhesives on their performance: I. Lap shear strength,” Journal of Adhesion, 17, 33–44, 1984. 58. Kinloch, A., “Interfacial fracture mechanical aspects of adhesive bonded joints – a review,” Journal of Adhesion, 10, 193–219, 1979. 59. Lin, Y., Tsui, T.Y., Vlassak, J., “Water diffusion and fracture in organosilicate glass film stacks,” Acta Materialia, 55, 2455–2464, 2007. 60. Shaw, G., Rogers, V., Payer, J., “The effect of immersion on the breaking force and failure locus in an epoxy/mild steel system,” Journal of Adhesion, 38, 225–268, 1992.

Chapter 3

Real-Time Characterization of Moisture Absorption and Desorption Y. He and X.J. Fan

3.1 Introduction Moisture plays a key role in the microelectronic packaging reliability. Moisture absorbed by polymer-based packaging materials can cause substantial changes in the polymeric material properties, such as its coefficient of thermal expansion (CTE), Young’s modulus, glass transition temperature (Tg ). Moisture can also change the viscoelastic behavior of the material and its interfacial properties. In cured thermosets, moisture acts as a plasticizer, reducing the Young’s modulus and the Tg and changing the thermal expansion characteristics of the material [1–3]. It has been found, for example (He, Y., Unpublished results, Intel Corporation, 2004), that as a result of moisture saturation during the temperature–humidity bias (THB) conditioning at 85◦ C/85% RH, the glass transition temperature Tg of a cured no-flow underfill material decreased by as much as 25◦ C, while its room temperature Young’s decreased by approximately 8% compared to the values of these characteristics at room temperature. At elevated temperatures, moisture-induced hygroscopic swelling in packaging materials can cause a significant increase in the induced stresses. In some microelectronic packages encapsulated using commercial molding compounds, the strain due to the mismatch in the coefficients of hygroscopic swelling (CHS) can be nearly twice as large as the strain due to the CTE mismatch over a temperature span of T = 60◦ C, when no swelling takes place [4]. For other molding compounds, it has been reported [5] that the strain due to the hygroscopic mismatch ranges from one to nearly four times of the strain caused by the CTE mismatch over a T of 45◦ C for T > Tg or over a T of 100◦ C for T < Tg in a situation when no swelling takes place. For some underfill materials, the strain caused by the hygroscopic swelling is comparable to the strain caused by the thermal expansion over the temperature range of 100◦ C (He, Y., Fan, X.J., Unpublished results, Intel Corporation, 2005). At typical solder reflow temperatures of about 230–260◦ C, vaporization of the residual moisture leads to a sharp buildup in vapor pressure, causing voiding, cracking, interfacial

Y. He (B) e-mail: [email protected] X.J. Fan, E. Suhir (eds.), Moisture Sensitivity of Plastic Packages of IC Devices, Micro- and Opto-Electronic Materials, Structures, and Systems, C Springer Science+Business Media, LLC 2010 DOI 10.1007/978-1-4419-5719-1_3, 

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delaminations, or “popcorn” failures [6, 7]. Moisture can cause degradation in the adhesion (interfacial) strength. For example, the adhesion strength between a solder ball and some underfill materials can decrease by more than 70% as a result of a long-time exposure of the package to 85◦ C/85% RH temperature–humidity bias (THB) [8]. Because many failures in microelectronic packages are attributed to moisture [9], characterization of moisture absorption–desorption and diffusion in electronic packaging materials is essential for understanding moisture-induced failure mechanisms. It is needed also for the adequate modeling of the behavior and performance of plastic packages. Once that has been achieved, one can optimize the package design and the material(s) selection and engineer the manufacturing process so that the likelihood of the moisture-related failure is minimized or, if possible, eliminated. Bismaleimide–triazine (BT) materials are widely used in electronic packaging. This thermosetting resin is obtained from additional polymerization of two monomers, bismaleimide and triazine (a cyanate ester). By blending the BT and the epoxy resin one can achieve better thermomechanical and electrical performance of the compound material compared to standard epoxy systems [10]. The Tg of the BT resin is typically above 185◦ C. Another popular resin used in substrate laminates is the FR-4 resin. FR-4, an abbreviation for Flame Retardant 4, is a type of material used for making printed circuit boards. It describes the board substrate, with no copper layer. The FR-4 used in PCBs is typically UV stabilized with a tetrafunctional epoxy resin system. It has a transparent yellowish color – the green, red, and sometimes blue color of a finished board comes from the solder mask. FR-4 manufactured strictly as an insulator (without copper cladding) is typically a difunctional epoxy resin system and greenish in color. FR-4 has widely replaced G-10 in most applications. Some military applications where destruction of the circuit board is a desirable trait will still utilize G-10. The FR-4 glass transition temperature Tg is typically around 125–135◦ C, although high-temperature FR-4 materials with Tg ∼ 180◦ C are also available [11]. FR-4 resins and BT epoxy resin/glass fiber laminates are commonly used as substrate core materials in electronic packaging. Clearly, their moisture properties have a significant impact on the package reliability. In the recent years, the development of the ultrathin stacked chip scale packaging (UT SCSP) technology has become essential for the increased functionality and higher memory capacity with more complex and more efficient memory architectures in small form-factor packages. In these packages, the wafer must be thinned from the original 750 μm down to as low as 50 μm. The conventional die-attach (DA) paste material and the conventional assembly methods cannot be applied to handle such thin dies. Wafer-level thin adhesive films combined with the corresponding lamination technique provide an acceptable alternative solution. These die-attach films (including wafer-level and “pick-and-place”) are usually very soft, with a tensile modulus less than 10 MPa or even 1 MPa at solder reflow temperature. These small form-factor packages are sensitive to moisture. A new failure mode after preconditioning test has been recently detected – cohesive failure within the die-attach material located between the substrate and the die [12, 13]. The moisture is absorbed through the substrate that consists mainly of a thin BT core and the copper layers. Detailed studies and analyses of the existing information revealed

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that the moisture properties of the thin BT core, including its temperature-dependent moisture diffusivity and saturated moisture content, play a crucial role in modulating the observed failure in ultrathin stackable chip size packages (UT SCSP) [12]. Description of the existing methods to characterize such properties is the objective of this chapter. Traditionally, the characterization of moisture properties of a material involves exposing the sample to a specific temperature–humidity condition, and then monitoring the sample’s weight increase as a function of the exposure time [14]. This procedure requires removing the sample from the temperature–humidity chamber and measuring the sample weight intermittently with an analytical balance, until the moisture saturation is reached. For thick samples, this method works satisfactorily, but has potential problems for thin specimens: the exposure of the sample at room temperature–humidity condition, even for a short time, can cause significant changes in the moisture content of the sample. For example, for a 70 μm thick film saturated with moisture and having a typical moisture diffusivity of 1.0 × 10−8 cm2 /s, it is estimated that it only takes about 2.5 min for the sample to lose 50% of its initial moisture, when it is placed in a dry environment [15, 16].1 For a 50 μm thick film, that time reduces to less than 2 min. Large error can be introduced during moisture absorption measurement if traditional measuring techniques are used. Another problem is that the sensitivity of a typical laboratory balance is only 0.01 mg, and in many cases that is not enough to accurately determine the moisture uptake in a thin film. In addition, the measurement has to be carried out manually. Because of that, new techniques are needed for characterizing moisture properties of thin films. We characterized the moisture absorption–desorption behavior of a 70 μm thick BT core in situ using a TA Instruments Q5000 SA thermogravimetric analyzer (TGA) at 30, 60, and 80◦ C, with the relative humidity cycling in the range of 0–60% and in the range of 0–80%. Based on the experimental data, the diffusion constant and the saturated moisture density, Csat , were determined. We have found that when transitioning from a thin BT core to a thick sample, the glass fibers in the laminates and their structure can have a significant impact on the measured moisture diffusion behavior of the material. Finite element analysis (FEA) modeling can be applied, in addition to the experimental effort, to investigate the moisture distribution in the UT SCSPs during preconditioning.

3.2 Background Moisture diffusion in isotropic materials under constant temperature and relative humidity conditions can be described by Fick’s second law [17]:

easiest way for such estimation is to use a simplified expression of equation (8): MM∞t =  0.75  1 − exp −7.3 Dt , where h is the total thickness. See also, Shen [15] and Ferguson and Qu h2

1 The

[16].

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Y. He and X.J. Fan

  2 ∂ C ∂ 2C ∂ 2C ∂C + + , =D ∂t ∂x2 ∂y2 ∂z2

(3.1)

where C(x,y,z,t) is the moisture concentration in the material (it has a unit of mg/cm3 ), D is the diffusion constant, t is the time, and (x,y,z) are the coordinates. BT/glass fiber laminates are clearly anisotropic; however, for thin samples with large aspect ratios, 1D diffusion model can be nevertheless applied, and the diffusion equation can be simplified as ∂ 2C ∂C =D 2. ∂t ∂x

(3.2)

For a thin plate sample with a thickness of h, one can set up the coordinate system so that the origin is in the center of the sample thickness, and the sample is bounded within −h/2 < x < h/2. The initial and the boundary conditions are [3] C = C0 , − h/2 < x < h/2, t = 0 , C = Ci , x = −h/2, x = h/2, t ≥ 0

(3.3)

where C0 is the initial moisture concentration in the sample and Ci is the constant moisture concentration of the environment. In moisture absorption experiments, C0 < Ci and often C0 = 0. In desorption experiments, C0 > Ci and often Ci = 0. Under these initial and boundary conditions, the diffusion equation (3.2) can be solved using the standard (Fourier) method of variable separation, and the concentration distribution in the sample can be found as [3, 17]   ∞ (2n + 1)2 π 2 D C(x, t) − C0 4  ( − 1)n (2n + 1)π exp − x. =1− t · cos Ci − C0 π (2n + 1) h h2 n=0 (3.4) The change in sample weight due to moisture absorption or desorption can be obtained by integrating the moisture concentration change at the moment of time t over the entire sample volume: 

h/2 Mt =

(C − C0 )dx −h/2

ds,

(3.5)

S

where S is in-plane surface area of the sample. The diffusion from the specimen’s sides is negligible. Substituting equation (3.4) into equation (3.5), and noting that h/2 cos −h/2

2 h( − 1)n (2n + 1)π x · dx = , h (2n + 1)π

(3.6)

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we have 

  ∞ 1 8  (2n + 1)2 π 2 D Mt = (Ci − C0 )S · h · 1 − 2 exp − t . (3.7) π (2n + 1)2 h2 n=0

In equation (3.7), (Ci − C0 )Sh = M∞ is the ultimate change in sample’s weight with t → ∞. In moisture absorption experiments, M∞ is positive, since Ci > C0 . In desorption experiments, M∞ is negative, since Ci < C0 . Thus, the ratio   ∞ Mt 1 8  (2n + 1)2 π 2 D =1− 2 exp − t M∞ π (2n + 1)2 h2

(3.8)

n=0

provides a solution to a 1D diffusion equation [3, 17]. When analyzing the experimental data, D and M∞ were optimized, so that the difference between the experimentally determined Mt and the one calculated using equation (3.8) is minimized. When the number n reaches 50, equation (3.8) converges very fast. In our study, n ran from 0 to 200. The saturated moisture concentration in the material, Csat , is simply M∞ /V, where V is the sample volume. Alternatively, Csat =

M∞ ρ, M

(3.9)

where M is the initial sample weight and ρ is density of the sample. Here the change in the sample volume caused by moisture absorption–desorption is small and can be ignored. Both Csat and D are critical for understanding the moisture-related reliability processes: Csat determines how much moisture can be absorbed by the material, and D determines how fast the moisture can diffuse into and out of the sample. The temperature dependence of the diffusion constant is described by the following Arrhenius equation [18]:   Ed , D = D0 exp − kT

(3.10)

where D0 is a “pre-factor” (diffusion constant for zero activation energy), Ed is the activation energy, k = 1.38 × 10−23 J/K is the Boltzmann’s constant, and T is the absolute temperature.

3.3 Experimental Data 3.3.1 Material The material used in this study was a 70 μm thick BT/glass fiber laminated substrate core material. The general properties of this material have been characterized and are listed in Table 3.1 (He, Y., Unpublished results, Intel Corporation, 2006).

76 Table 3.1 General properties of the 70 μm thick BT core substrate used in this study

Y. He and X.J. Fan Density Fiber content CTE (0–50◦ C) CTE (150–200◦ C) Storage modulus (at 25◦ C) Loss modulus peak Tan δ peak

1.79 g/cm3 56.46 wt% 16 × 10−6 K−1 18.5 × 10−6 K−1 14.65 GPa 207◦ C 215.6◦ C

The dynamic mechanical properties were determined by dynamic mechanical analysis (DMA) experiments conducted under tensile mode with a dynamic frequency of 1 Hz and a heating rate of 3◦ C/min. The fiber content in the specimens was determined by the thermogravimetric (TGA) analysis. The detailed description for these measurements is, however, beyond the scope of this chapter.

3.3.2 Instrumentation The instrumentation used in this study, TGA Instruments, Q5000 SA TGA, is a high-sensitivity thermogravimetric analyzer. It enables one to carry out sorption/desorption analysis of materials under controlled temperature and humidity conditions [19]. The heart of this instrument is a high-performance thermo-balance, which is maintained at a constant temperature of 40◦ C for increased thermal stability. The balance has a signal resolution of 0.01 μg and a sensitivity of 0.1 μg. The humidity chamber is a well-insulated tri-level aluminum block containing deionized water. The block can be refilled as necessary. The humidity surrounding the sample is controlled and maintained by a pair of mass flow controllers. By adjusting the amount of “dry” and “wet” gases flowing through the controller, the software is capable of maintaining a desired relative humidity level. The temperature control is carried out by four thermoelectric devices in conjunction with a thermistor in a closed-loop system. The actual temperature–humidity condition around the sample can be verified by certain salts, such as NaBr, NaCl, KBr, etc. The typical dimensions of a sample used in sorption-TGA experiments were 7 mm × 7 mm with a weight of about 7 mg. Moisture absorption–desorption experiments were performed at 30, 60, and 80◦ C, respectively. At each isothermal temperature, two relative humidity levels were chosen: 60 and 80% RH. During an isothermal experiment, the relative humidity was cycled between 0 and 60% (or 0 and 80%) twice, while the temperature stability was maintained to be better than ±0.05◦ C. At each temperature/moisture conditions, the sample was held for up to 600 min. In such experiments, quartz bowls were used as the sample pan and the reference pan, and the sample was placed inside or on top of the sample bowl, thereby allowing the moisture to diffuse into the sample from both surfaces. Since both the sample and the reference bowls experienced the same temperature and humidity conditions, the net effect on the sample weight change was exclusively from moisture absorption or desorption.

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3.4 Moisture Absorption–Desorption 3.4.1 Moisture Diffusivity Figure 3.1 shows an example of moisture absorption–desorption experiment. The temperature was kept at 60◦ C and the RH level was cycled between 0 and 60%. During the first 60 min, a 0% RH condition was imposed to drive out any residual moisture from the sample. This was followed by a 200 min moisture absorption at 60% RH, then a 200 min desorption at 0% RH. Such a sorption–desorption cycle was repeated one more time, as shown in Fig. 3.1. The following conclusions can be drawn from the results shown in Fig. 3.1: (1) during the first 60 min, the moisture was not completely driven out of the sample; a longer time was needed to accomplish that; (2) the subsequent absorption–desorption cycles were repeatable, i.e., the sample reached approximately the same saturated moisture level during sorption and it lost the same weight upon drying; this indicated that there was no chemical reaction between the water molecules and the material; (3) the saturated moisture level was about 0.33%, so that the saturated moisture content, Csat , is about 5.91 mg/cm3 . The moisture diffusivity for the 70 μm thick BT core at 60◦ C/60% RH can be calculated from the second moisture absorption curve shown in Fig. 3.1. To determine the diffusivity D and the saturated weight gain (M∞ ), the least-square fitting technique was used. In this approach, the sum of the square of the differences between k

 exp cal 2 , the experimental weight gain and the calculated one, (M)2 = Mt,i − Mt,i i=1

was calculated based on equation (3.8), using some initial estimated values of D and

Weight

RH

60

o

60 C

Weight (%)

100.2

50 40 30

100.1

20

100.0

10 99.9

Reference Sensor RH (%)

100.3

0 0

200

400

600 800 Time (min)

1000 1200

Fig. 3.1 Moisture absorption–desorption experiment conducted using a sorption TGA at 60◦ C with the RH level cycled between 0 and 60%. The initial BT core sample weight was 6,560.455 μg

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Y. He and X.J. Fan exp

M∞ . Mt,i was the ith point of the experimentally determined weight gain at time t, cal was the calculated one based on equation (3.8), and k is the total number while Mt,i of points used in calculating (M)2 . Then, D and M∞ were varied until (M)2 was minimized. The obtained D and M∞ were taken as the diffusivity and the saturated moisture content of the sample for that particular temperature–humidity conditions. Figure 3.2 shows the experimentally determined as well as the calculated weight gain as a function of time for a 70 μm thick BT core sample at 60◦ C/60% RH. Curve 1 was calculated using D = 1.85 × 10−8 cm2 /s and M∞ = 21.1 μg, and curve 2 was calculated with D = 1.65 × 10−8 cm2 /s and M∞ = 21.2 μg. Both curves are in a reasonably good agreement with the experimental data. 25 60oC / 60% RH 20

Weight Gain (µg)

Fig. 3.2 Experimentally measured and calculated weight gain for a 70 μm BT core laminate. The experimental data were from the second absorption curve under 60◦ C/60% RH shown in Fig. 3.1. The initial sample weight at t = 0 s (the beginning of the second absorption cycle) was 6,555.472 μg

15 10 Experimental Data Fit 1 Fit 2

5 0 0

1000

2000 Time (sec)

3000

4000

The diffusivity data calculated from the desorption experiment at 60◦ C/60% RH were in the same range as those derived from the absorption experiment, as shown in Fig. 3.3. Similar calculations were performed based on experimental data obtained under different temperature–humidity conditions, and the results enabled us to determine the temperature dependence of the moisture diffusivity. Figures 3.2 and 3.3 indicate that the calculated absorption and desorption curves can fit the experimental data reasonably well, but the fit is less than ideal. One reason for that is that the calculation was based on an assumption that the material was isotropic. In reality, the BT core is a polymer matrix woven composite, and the effect of the glass fiber weave structure and fiber density has to be considered to completely elucidate the moisture diffusion behavior of the BT core [20].

3.4.2 Saturated Moisture Content The saturated moisture content Csat in the BT core is another key material property. Csat is directly related to the vapor pressure inside the material voids during high temperature reflow [21]. While the temperature dependence of diffusivity is

Real-Time Characterization of Moisture Absorption and Desorption

Fig. 3.3 Desorption curves of a 70 μm BT core. Solid line represents the calculated weight loss vs time curve using D = 1.65 × 10−8 cm2 /s

0 Weight Change (µg)

3

79

Experimental Fitted (D = 1.65 µm2/s)

–5 – 10 – 15 – 20 – 25

0

2000

4000 Time (sec)

6000

8000

well established, it is not true for Csat [22]. For many materials, Csat is independent of temperature and depends only on the RH, although exceptions have also been reported. Bao and Yee [22] pointed out that the saturated moisture concentration is related to the heat of moisture absorption:    1 Habs 1 , − Csat = Csat,ref exp − R T Tref

(3.11)

where Csat, ref is the saturated moisture content at a reference temperature Tref , Habs is the heat of moisture absorption, T is the absolute temperature, and R is the universal gas constant. In the absence of chemical reactions between water and the polymer matrix, Habs is small. In addition, for practical reasons, the temperature range of most moisture diffusion studies is restricted to between 25 and 90◦ C. Therefore, the exponential term in equation (3.11) is close to 1 for most polymers that do not react with water, making Csat nearly temperature independent. Figure 3.4 plots the saturated moisture content in the 70 μm BT core as a function of temperature for two different RH levels. These data were obtained from moisture absorption–desorption experiments. It clearly shows that Csat in BT core is essentially temperature independent. Figure 3.5 shows the Csat obtained from the RH step scan experiment. It reveals that at a fixed temperature (30◦ C in this case), Csat is proportional to the RH level. Because of relatively weak molecular interactions and large free volume, saturated moisture content in polymeric materials is much higher than that in ceramic materials. Most of the trapped moisture in the free volume or voids of the polymer condenses into the liquid form. Otherwise, a simple estimation reveals that the internal pressure inside the voids can reach a very high level of more than

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Y. He and X.J. Fan

10

Csat (mg/cm3)

Fig. 3.4 Saturated moisture content as a function of temperature for two different RH levels

8

6 60% R.H. 80% R.H.

70 µm BT core

4

30

40

50

60

70

80

Temperature (°C)

Fig. 3.5 Csat as a function of relative humidity at 30◦ C

9 Experimental Data Linear Fit

8

Csat(mg/cm3)

7 6 5 4 3

Slope = 0.11

2 1 0

0

10

20

30

40

50

60

70

80

90

Relative Humidity (%)

150 times the atmospheric pressure.2 Such high pressure can easily cause internal rupture in the polymeric material. During the reflow process, the condensed water expands rapidly during vaporization. If the vapor cannot escape freely and quickly from the sample, then the built-up internal vapor pressure can cause all kinds of failures in the packages [12–13]. This phenomenon is often referred to as “popcorning.”

Csat = 6 mg/cm3 at 60◦ C, and the volume fraction of the free volume or voids is 5% of the total sample volume. The actual moisture density inside the voids is then 120 mg/cm3 . If the moisture is not condensed into the liquid form but still in gas form, then the internal pressure inside the voids can be calculated using the ideal gas approximation: pV = nRT. For V = 1 cm3 , n = 0.12/18 = 0.0067 mole, R = 8.314 J/mol · K is the universal gas constant, for T = 60◦ C or 333 K, p is estimated to be 18.549 MPa, which is ∼183 atm.

2 Consider

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3.4.3 Temperature Dependence of Diffusivity Based on moisture absorption–desorption experiments and RH step scan experiments performed at various temperatures, one can determine the moisture diffusivity in the BT core material as a function of temperature. The results were plotted in Fig. 3.6. It can be seen that the moisture diffusivity has an Arrhenius temperature dependence with D0 ≈ 6.61 × 10−3 cm2 /s and Ed ≈ 0.368 eV. Using these parameters, one can extrapolate the moisture diffusivity to other temperatures, assuming that the diffusion mechanism does not change. This is usually true for T < Tg . Based on the obtained data, the diffusivity at the reflow temperature of 260◦ C was estimated to be 2.18×10−6 cm2 /s. This is about 121 times higher than the diffusivity at 60◦ C. In reality, the diffusivity could be even higher since the reflow temperature is above the Tg of the BT core. It is estimated that at 260◦ C, it takes less than 1 s for a 70 μm thick saturated BT core to lose 50% of the total moisture and less than 5 s to lose 90% of the total moisture. If the total BT core thickness increases by introducing multiple core layers or by increasing the thickness of each core layer, the time needed for the same amount of moisture to escape from the BT core will increase in

such 2a way that it is proportional to the total thickness of the BT core squared t ∝ h [15, 16]. This should have a significant impact on the package design and materials selection for the optimized preconditioning reliability performance.

This work Linear Fit Neat BT (IBM) BT Laminates (Maryland) Thick BT Core1 (this work) Thick BT Core2 (this work) Wong and Rajoo Galloway and Miles

D(10–9 cm2/s)

100

10

1

0.0028

0.0030

0.0032

0.0034

1/T (K–1) Fig. 3.6 Moisture diffusivity of BT core materials obtained from absorption experiments as a function of temperature. Solid circles: this work; solid line: linear fit of log10 D vs 1/T based on diffusivity data obtained from this work; open diamonds: moisture diffusivity of neat BT resin, as reported in [23]; open squares: diffusivity of BT laminated reported in [11]; dashed line: calculated diffusivity as a function of 1/T using the pre-exponential factor and the activation energy reported in [24]; dash-dotted line: calculated D vs 1/T based on the values of D0 and Ed reported in [7]; open and filled triangles (in-house data): diffusivity of thick BT substrates with thicknesses of 0.72 and 0.812 mm, respectively

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3.5 Comparison with Literature Data Using the standard procedure, which involves exposing the specimen to a specific temperature–humidity condition and monitoring the change in sample weight over time, Liu et al. studied the moisture diffusivity in neat BT resins and in BT/glass fiber laminates [23]. The sample thickness was 0.035 in. (0.89 mm) for the neat resins and 0.030 in. (0.76 mm) for the laminates. Their results showed that for BT neat resin, the diffusivity is 1.29 × 10−8 cm2 /s at 50◦ C/80% RH, and it increases to 2.45×10−8 cm2 /s at 70◦ C/80% RH. At 90◦ C/80% RH, it becomes 5.82 × 10−8 cm2 /s, as shown in Fig. 3.6. Using the Arrhenius equation, the diffusivity of the BT neat resin can be described using D0 = 1.02 × 10−2 cm2 /s and Ed = 8.72 kcal/mol or 0.378 eV. For BT laminates with 280 E-glass fabrics, the diffusivity is reduced by nearly 50% under all the three temperature/RH conditions, with D0 = 1.50 × 10−3 cm2 /s and Ed = 7.93 kcal/mol or 0.344 eV. In their study, the resin content for the laminated samples was measured using thermogravimetric analysis (TGA), but the results were not directly reported in the paper. However, based on the indicated normalized maximum moisture uptake, it could be estimated that for BT/280 laminates, the resin content was approximately 62.5%. The obtained data were the first evidence that suggested that for a relatively thick BT laminate, the addition of glass fiber and its topological or weave structure could have a significant impact on the moisture diffusion behavior of the material. Pecht et al. studied the moisture diffusion in BT/glass fiber laminates [11]. In their study, all of the laminates were woven E-glass fabric with thickness of either 0.038 or 0.053 cm. The reported diffusivity of BT laminates was 1.22 × 10−8 cm2 /s at 50◦ C/50% RH and 1.65 × 10−8 cm2 /s at 50◦ C/85% RH, and it becomes 4.75 × 10−8 cm2 /s at 85◦ C/50% RH and 3.03 × 10−8 cm2 /s at 85◦ C/85% RH. These values were also plotted in Fig. 3.6 (open squares), and the diffusivity values are in reasonable agreement with our data. In the Galloway and Miles’ paper [7], the moisture diffusion constant was reported to follow the Arrhenius equation, with D0 = 1.2 × 10−4 cm2 /s and Ed = 0.295 eV based on absorption data, and the temperature dependence of the diffusivity was calculated using these values and plotted in Fig. 3.6. Based on the desorption data, it has been found that D0 = 6.0 × 10−2 cm2 /s and Ed = 0.465 eV. In their experiments, the sample thickness ranged between 0.155 and 1.05 ± 0.003 mm, but the exact thickness of the BT epoxy was not given. Wong and Rajoo studied the moisture diffusion behavior of a BT core laminate [24]. The sample thickness was 0.4 mm, and the in-plane dimensions were much larger than the thickness, so that 1D diffusion could be assumed. They concluded that for the BT core, the temperature dependence of the transverse moisture diffusivity follows by the Arrhenius equation with D0 = 3.33 × 10−4 cm2 /s and Ed = 0.32 eV, as shown in Fig. 3.6. Thus, at 30◦ C, D ≈ 1.6 × 10−9 cm2 /s and at 60◦ C, D ≈ 4.8 × 10−9 cm2 /s. These results agree very well with Galloway et al.’s data on BT epoxy, but are much lower than the diffusivity data reported in BT neat resin [23]. In addition, the reported Csat was 4.83 mg/cm3 at 30◦ C/60% RH, which is about 18% lower than the result obtained from this study (Fig. 3.1). This is most likely caused

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by higher glass fiber density in their material, although the exact glass fiber content was not reported [24]. In addition to the 70 μm BT core material, using the conventional method with an analytical balance, we have also measured the moisture absorption behavior of two different thick BT substrates with thicknesses of 0.72 mm and 0.812 mm at 85◦ C/85% RH. The diffusivity results are plotted in Fig. 3.6. From the data in Fig. 3.6 it is clear that the moisture diffusivity of 70 μm BT laminated core is much higher than the values reported in [7] and [24], but our results are in good agreement with the diffusivity of BT neat resin [23] or BT laminates reported in [11]. The differences may be attributed to the effect of the volume of the glass fibers in thick BT laminates. In BT/glass laminates, it is expected that the glass fibers absorb essentially no moisture, and all the moisture is absorbed by the BT resin. In a thick BT core, the woven glass fibers form a 3D fabric structure, which hinders the diffusion of moisture. In a thin BT core, however, the woven glass fibers more or less form a 2D grid structure, and the diffusion of moisture is less hindered, leading to a higher diffusivity. This explains why in the 70 μm thick BT core, the observed moisture diffusivity is the same as the one reported in BT neat resin, but it is much less for a thick BT core.

3.6 Application – Moisture Diffusion and Vapor Pressure Modeling for Ultrathin Stacked Chip Scale Packages One major 3D packaging technology is the ultrathin stacked chip scale packaging (UT SCSP) technology. It increases the functionality and memory capacity by incorporating the components into a small form-factor format. In these packages, the substrate is very thin, usually with a total thickness of less than 300 μm. Moisture is absorbed therefore predominantly through the substrate that consists mainly of thin BT core and copper layers. On the other hand, thinner substrates allow moisture to escape out of the package quickly during reflow, thereby reducing the risk of moisture-induced failures. Another important transition from the regular chip scale package (CSP) to the UT SCSP is the use of the wafer-level die-attach (DA) film instead of the die-attach paste. The DA films are usually very soft, with a tensile modulus of less than 10 or even 1 MPa at solder reflow temperature, which could introduce cohesive failure within the DA material located between the substrate and the bottom die, if the internal vapor pressure of vapor exceeds the material strength [12–13]. Previous experimental studies have shown that the failure rate of DA film is very sensitive to the substrate thickness [25]. We investigated the impact of moisture material properties of the BT core on the package performance using finite element analysis (FEA). We studied the impact of substrate core thickness on the moistureinduced failure rate, as well as the effect of the diffusivity of the BT core. In our study the diffusivity values were obtained for thin BT cores. This enabled us to better compare the BT performance and the experimentally observed failure rate in UT SCSP in the case of thin and thick BT cores. In our study, a UT SCSP with five

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Bottom Film MC Die Film SR BT

Fig. 3.7 Schematic structure of 3D ultrathin stacked-die chip scale package. The moisture concentration during reflow at the bottom die-attach film (arrow) was investigated

stacked dice was studied (Fig. 3.7), with two different total substrate thicknesses of 200 and 280 μm, respectively. The SCSP was composed of the molding compound (MC), silicon dice, DA film, solder resist (SR) film, and the BT core. The substrate included two layers of SR and one layer of BT core. In the beginning of the experiment to study the failure rate under different substrate thicknesses, the UT SCSP packages were subjected to moisture preconditioning at 60◦ C and 60% RH for 96 h before sending them through the typical lead-free soldering reflow process. Since the package profile was very thin, the moisture was fully saturated at the bottom of the DA film after the preconditioning and prior to the reflow. The reflow was conducted according to the JEDEC standard. A typical reflow process was completed within 3–5 min. For the results shown here, a typical reflow profile was selected for all cases with the maximum time to reach 260◦ C around 275 s. Due to the symmetry consideration, in the FEA model only half-package needs to be modeled. The direct concentration approach (DCA) was applied to investigate the characteristics of moisture diffusion during reflow process [26]. A multi-scale vapor pressure model, which considers the phase change of moisture, was used to predict the vapor pressure buildup during reflow soldering process [27]. The details of the modeling methodology and theory can be referred to [28]. As discussed in the previous section, all available literature data and the measured data in this chapter on BT core diffusivity fell into two different lines, as shown in Fig. 3.6. The data along the solid line represent the diffusivity of the thin-core or neat BT material (called thin-core diffusivity afterward), and the dashed line data represent the diffusivity of the thick BT core (called thick-core diffusivity). Both sets of data were used in the FEA evaluations. The objective was to investigate the impact of diffusivity on moisture transport during reflow soldering and the effect of the substrate thickness. Figure 3.8 plots the contours of residual moisture concentration in the studied package at 260◦ C with two different diffusivities for the substrate thickness of 200 and 280 μm, respectively. It clearly shows that if the thin-core diffusivity is used,

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Fig. 3.8 FEA contours of moisture concentration at reflowing of 260◦ C for two substrate thicknesses 200 and 280 μm, respectively, when thin-core diffusivity data and thick-core diffusivity data are used. The values inside the box at the top of the figure represent the residual moisture concentration in mg/cm3 (a) Substrate thickness: 200 μm; (b) Substrate thickness: 280 μm

(a) Substrate thickness: 200 μm

(b) Substrate thickness: 280 μm

the local moisture concentration in the DA film between the die and the substrate is significantly lower than that modeled with the thick-core diffusivity. For example, when the substrate core thickness was 280 μm, the local residual moisture content in the DA film with the thin-core diffusivity (Fig. 3.8a) was only 37% of that with the thick-core diffusivity (Fig. 3.8b). The modeling results revealed that the diffusivity played a critical role in determining how much moisture could possibly escape out of the package during reflow soldering process, when the substrate is thin. In order to better understand the effect of the substrate thickness on the local moisture concentration and the impact of the diffusivity, Table 3.2 gives the local moisture concentration in the DA film for two different substrate thicknesses using two different diffusivities data. It can be seen that if the thick-core diffusivity data were used, the moisture concentration remained intact (still saturated at 4.2 kg/m3 ) in the DA film for both thicknesses during reflow. This means that the thick BT core moisture diffusivity was not sufficiently high to allow the release of moisture in the DA film during the short period of reflow process, although significant moisture was released in the exterior of packages and substrates. On the other hand,

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Table 3.2 Maximum local moisture concentration at the bottom die-attach film at 260◦ C for two substrate thicknesses with different sets of moisture diffusivity data Substrate thickness

Thin-core diffusivity data Thick-core diffusivity data

200 μm

280 μm

0.71 kg/m3 4.2 kg/m3

1.55 kg/m3 4.2 kg/m3

Table 3.2 clearly shows that when the thin-core diffusivity data were used, a significant amount of moisture in the DA film could escape during reflow, and the local moisture concentration with a core of 200 μm was 50% lower than that with a core of 280 μm thick. It became obvious that the residual moisture was very sensitive to the substrate thickness. Figure 3.9 plots the whole field vapor pressure contour at 260◦ C with the substrate thicknesses of 200 and 280 μm, respectively, using the thin-core and the

(a). Substrate thickness: 200 μm

Fig. 3.9 FEA contours of vapor pressure at reflowing of 260◦ C for two substrate thicknesses of 200 and 280 μm, respectively, when thin-core diffusivity data and thick-core diffusivity data are used. The values inside the top box are the vapor pressure in Pa (a) Substrate thickness: 200 μm; (b) Substrate thickness: 280 μm

(b). Substrate thickness: 280 μm

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thick-core diffusivities. At the bottom of the DA film between the die and the substrate, the results were very different for two different diffusivities. We conclude therefore that the accurate determination of the diffusivity of BT core is essential for the prediction of the vapor pressure buildup during the reflow process. In Table 3.3, the results for the vapor pressure in the DA film at 260◦ C are given for two different substrate thicknesses and for two different diffusivities data. When the thick-core diffusivity data were applied, local moisture content was high enough to keep the vapor pressure the same as the saturated vapor pressure. However, with the thin-core diffusivity data, a slight reduction of the substrate thickness from 280 to 200 μm resulted in a significant increase in the amount of moisture released from the package; thus the vapor pressure is reduced by 40%. According to the previous experimental study [12, 27], the packages with 280 μm substrate thickness had almost 100% failure rate, while the packages with 200 μm substrate thickness had no failures at all. The FEA data agree well with the experimental data for the thin BT core diffusivity and with the experimental failure rate data [12, 27]. Based on the available literature diffusivity data obtained from the thick BT samples, one would conclude that the moisture concentration in the DA film in a stacked-die chip scale package does not change significantly during the reflow process. However, based on the diffusivity data obtained for the thin BT core in this work, we can show that a small change in the substrate thickness can result in a substantial difference in the residual moisture concentration in the die-attach film, leading to a very different reliability performance. Such reliability results predicted by FEA modeling are in agreement with the experimental data. Table 3.3 Maximum vapor pressure at the bottom die-attach film at 260◦ C for two substrate thicknesses with different sets of moisture diffusivity data Substrate thickness

Thin-core diffusivity data Thick-core diffusivity data

200 μm

280 μm

3.5 MPa 5.84 MPa

5.84 MPa 5.84 MPa

3.7 Conclusions Moisture absorption–desorption behavior of a 70 μm BT laminate used as the UT SCSP substrate core material has been characterized in situ using a sorption TGA equipped with a moisture chamber. Based on the moisture absorption experiments, the moisture diffusivity of this thin BT core has been determined to follow an Arrhenius temperature dependence with D = D0 exp(−Ed /kT), where D0 ≈ 6.61 × 10−3 cm2 /s and Ed = 0.368 eV. The measured diffusivity agrees well with reported value of BT neat resin, but it is much higher than that of the thick BT core materials. This difference is attributed to the effect of glass fiber: in thick BT laminates, glass fibers form a 3D network structure, which greatly hinders moisture diffusion. In thin

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BT cores, the glass fibers are mainly in a 2D structure, which has a much less effect on moisture diffusion in the BT resin. Experimental results revealed that the saturated moisture content of the 70 μm BT core, Csat , has little dependence on temperature, and it depends approximately linearly on relative humidity. At 60% RH, Csat ≈ 5.9–6.1 mg/cm3 ; at 80% RH, Csat ≈ 8.7–8.9 mg/cm3 . Based on literature diffusivity data obtained from the thick BT samples, one would conclude that the moisture concentration in the DA film located between the bottom die and the substrate in a stacked-die chip scale package will not change significantly when the core thickness varies from 280 to 200 μm during reflow process. However, based on the diffusivity data obtained for the thin BT core in this work, we have shown that a small change in substrate thickness can result in a substantial variation in the residual moisture concentration in the die-attach film, leading to a very different reliability performance. Indeed, such reliability results correlated well with the experimental data. Accurate moisture diffusivity data of the BT core combined with finite element modeling provided an important tool in designing a UT SCSP package with more robust reliability performance.

References 1. Prime, R.B., Thermal Characterization of Polymeric Materials, Vol. 2, 2nd edition, edited by Turi, E.A., Ch. 6, New York, NY: Academic, pp. 1702–1704, 1997. 2. Gupta, V.B., Drzal, L.T., Rich, M.J., “The physical basis of moisture transport in a cured epoxy resin system”, Journal of Applied Polymer Science, 30(11), 4467–4493, 1985. 3. Lin, Y.C., Chen, X., “Moisture sorption-desorption-resorption characteristics and its effect on the mechanical behavior of the epoxy system”, Polymer, 46(25), 11994–12003, 2005. 4. Stellrecht, E., Han, B.T., Pecht, M.G., “Characterization of hygroscopic swelling behavior of mold compounds and plastic packages”, IEEE Transactions on Components and Packaging Technologies, 27, 499–506, 2004. 5. Ardebili, H., Wong, E.H., Pecht, M., “Hygroscopic swelling and sorption characteristics of epoxy molding compounds used in electronic packaging”, IEEE Transactions on Components, Packaging and Manufacturing Technology, 26(1), 206–214, 2003. 6. Fukuzawa, I., Ishiguro, S., Nanbu, S., “Moisture resistance degradation of plastic LST’s by reflow soldering”, Proceedings of the 23rd International Reliability Physics Symposium, Orlando, Florida, pp. 192–197, 1985. 7. Galloway, J.E., Miles, B.M., “Moisture absorption and desorption predictions for plastic ball grid array packages”, IEEE Transactions on Components, Packaging and Manufacturing Technology A, 20(3), 274–279, 1997. 8. Park, C.E., Han, B.J., Bair, H.E., “Humidity effect on adhesion strength between solder ball and epoxy underfills”, Polymer, 38(15), 3811–3818, 1997. 9. Fan, X.J., Zhou, J., Chandra, A., “Package structural integrity analysis considering moisture”, Proceedings of 58th Electronic Components and Technology Conference (ECTC), Orlando, Florida, pp. 1054–1066, 2008. 10. Li, Z.F., “A review of BT/epoxy resin—chemistry, composition, processing, properties, and applications”, Internal Project Report, Intel Corporation, July 1995. 11. Pecht, M., Ardebili, H., Shukla, A.A., Hagge, J.K., Jennings, D., “Moisture ingress into organic laminates”, IEEE Transactions on Components and Packaging Technologies, 22(1), 104–110, 1999.

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12. Fan, X., Bekar, I., Fischer, A.A., He, Y., Huang, Z., Prack, E.R., “Delamination/cracking root cause mechanisms for ultra-thin stacked die chip scale packages”, Intel Manufacturing Excellence Conference (IMEC) 2006 technical paper. 13. Huang, Z., Tang, J., Hu, C., Wang, M., Zhang, M., Liu, B., Fan, X., Prack, E., “Moisture induced cohesive delamination in die-attach film in ultra thin stacked chip-scale package”, Intel Assembly and Test Technology Journal, 9, 483–488, 2006. 14. ASTM D5229, Standard Test Method For Moisture Absorption Properties and Equilibrium Conditioning of Polymer Matrix Composite Materials. West Conshohocken, PA: ASTM, 1998. 15. Shen, C.H., Springer, G.S., “Moisture absorption and desorption of composite materials”, Journal of Composite Materials, 10(1), 2–10, 1976. 16. Ferguson, T., Qu, J., “Moisture absorption analysis of interfacial fracture test specimens composed of no-flow underfill materials”, Journal of Electronic Packaging, Transactions of the ASME, 125(1), 24–30, 2003. 17. Crank, J., The Mathematics of Diffusion, 2nd edition. Oxford: Oxford University Press, 1990. 18. Borg, R.J., Dienes, G.J., An Introduction to Solid State Diffusion. San Diego, CA: Academic, p. 60, 1988. 19. Technical Brochure, TA Instruments Q SeriesTM Thermal Analyzers; http://www.tainstruments.com/product.aspx?id=135&n=1&siteid=11, last accessed on March 25, 2010. 20. Tang, X., Whitcomb, J.D., Li, Y., Sue, H.-J., “Micromechanics modeling of moisture diffusion in woven composites”, Composites Science and Technology, 65, 817–826, 2005. 21. Fan, X.J., Moisture Related Reliability Issues in Electronic Packaging, ECTC short course, 2006. 22. Bao, L.-R., Yee, A.F., “Effect of temperature on moisture absorption in a bismaleimide resin and its carbon fiber composites”, Polymer, 43(14), 3987–3997, 2002, and refs. [11–14] cited in this paper. 23. Liu, P.C., Wang, D.W., Livingston, E.D., Chen, W.T., “Moisture absorption behavior of printed circuit laminate materials, advances in electronic packaging”, Proceedings of the 1993 ASME International Electronics Packaging Conference, Vol. 1, American Society of Mechanical Engineers, Binghamton, NY, September 29–October 2, pp. 435–442, 1993. Also quoted in ref. [12]. 24. Wong, E.H., Rajoo, R., “Moisture absorption and diffusion characterization of packaging materials – advanced treatment”, Microelectronics Reliability, 43(12), 2087–2096, 2003. (Notice that Table 2 of this paper contains a typo: the units of D0 should by cm2 /s, not ×10−9 cm2 /s. Also, private communication with Wong, E.H., 2006). 25. Shi, D., Fan, X., “Wafer-level film selection for stacked-die chip scale packages”, Proceedings of 57th Electronic Components and Technology Conference (ECTC), Reno, Nevada, pp. 1731– 1736, 2007. 26. Xie, B., Fan, X.J., Shi, X.Q., Ding, H. “Direct concentration approach of moisture diffusion and whole field vapor pressure modeling for reflow process: part I – theory and numerical implementation,” ASME Journal of Electronic Packaging, 131(3), 031010, 2009. 27. Fan, X.J., Zhou, J., Zhang, G.Q., Ernst, L.J., “A micromechanics-based vapor pressure model in electronic packages,” ASME Journal of Electronic Packaging, 127(3), 262–267, 2005. 28. Fan, X., Zhang, G.Q., van Driel, W.D., Ernst, L.J., “Interfacial delamination mechanisms during soldering reflow with moisture preconditioning”, IEEE Transactions on Components and Packaging Technologies, 31(2), 252–259, 2008.

Chapter 4

Modeling of Moisture Diffusion and Whole-Field Vapor Pressure in Plastic Packages of IC Devices X.J. Fan, T.Y. Tee, X.Q. Shi, and B. Xie

4.1 Introduction Moisture plays an important role in the integrity and reliability of plastic microelectronics packages. Many failures in microelectronics packages are attributed to the presence of moisture [1–3]. When atmospheric moisture is absorbed into the packaged microelectronics devices, it condenses in free volumes or in nano-pores of the polymer materials and at the interfaces. When the condensed moisture evaporates during surface mounting process it produces high vapor pressure. In this process, the peak temperature ranges typically from 220 to 260◦ C. The process is completed within a few minutes. Polymer materials, such as dielectric films, adhesives, encapsulants, and plastic printed circuit boards, become extremely compliant when temperature exceeds their glass transition temperatures. Their Young’s modulus drops by an order of magnitude or even more. In addition, the interfacial adhesion strength may also drop substantially. As a result, delamination may occur at weak interfaces due to the combined effects of thermo-mechanical stresses, hygroscopic stresses, vapor pressure, material softening, and adhesion degradation. An audible sound is sometimes produced if the water vapor is suddenly released due to material cracking. Moisture diffusion analysis is a key to understand the moisture-induced failure mechanism in electronic packaging. Kitano et al. [4] and Tay and Lin [5] investigated the coupled moisture diffusion and heat transfer in plastic electronic packages. In Tay and Lin’s work, the normalized approach is used for a moisture diffusion analysis. Galloway and Miles [6] characterized moisture properties for different packaging materials and introduced thermal-moisture analogy methodology to analyze moisture diffusion. Wong et al. [7] introduced an alternative normalized variable, so-called wetness, which is defined as the ratio of the moisture concentration over the saturated moisture concentration. Commercially available

X.J. Fan (B) e-mail: [email protected]

X.J. Fan, E. Suhir (eds.), Moisture Sensitivity of Plastic Packages of IC Devices, Micro- and Opto-Electronic Materials, Structures, and Systems, C Springer Science+Business Media, LLC 2010 DOI 10.1007/978-1-4419-5719-1_4, 

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heat conduction finite element software can be applied to solve moisture diffusion problems. Typical moisture sensitivity/reflow test comprises two stages, moisture absorption at a constant temperature/humidity condition (preconditioning), followed by a simulated reflow process. Moisture absorbed during preconditioning is partially released at reflow, as the humidity in reflow oven is virtually zero. Traditional analysis usually neglects the moisture loss during the reflow process due to the fact that the local moisture concentration at critical interfaces inside packages remains intact [8, 9]. For ultrathin small-form factor packages, however, the local moisture concentration in packages becomes very sensitive to package geometry [10]. Hence, it is important to understand the moisture redistribution, transport, and diffusion during reflow process. In this chapter, theories and applications of moisture diffusion modeling and vapor pressure analysis are reviewed. The unique characteristics of moisture diffusion in a multi-material system are addressed and described. The commonly used normalization methods to remove interfacial discontinuity are presented, and the details of thermal-moisture analogy and implementations using commercially available finite element software are discussed. The applications of normalization methods to moisture diffusion in a plastic ball grid array (PBGA) package are illustrated. Furthermore, moisture diffusion in a reflow process, in which ambient temperature and humidity loading conditions vary with time, is examined. When ambient temperature and/or humidity loading changes with time, thermal-moisture analogy no longer exists. A so-called direct concentration approach (DCA) is introduced. In the DCA, the moisture concentration is used directly as a basic field variable, which is discontinuous at interfaces. Constraint equations are applied at the interfaces to satisfy the interface continuity requirement. The detailed numerical treatment and implementation procedures using the DCA method are presented. Finally, a whole-field vapor pressure model is introduced. This model is based on a multi-scale micromechanics analysis developed by one of the authors [8, 11, 12]. The interstitial space fraction (or free volume fraction) is introduced to describe the moisture density in the interstitial spaces of a porous material. Phase change of moisture is considered during temperature change. Examples are given to show the differences in moisture and whole-field vapor pressure distributions in a package over time.

4.2 Moisture Diffusion Modeling – Normalization Method 4.2.1 Theory Moisture concentration is discontinuous at interfaces when two materials with different saturated moisture concentrations (Csat ) are joined together. As shown in Fig. 4.1, for unsaturated and saturated situations, respectively, the moisture concentration at the interface is given by

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(a)

93

(b)

Fig. 4.1 Schematic diagram of moisture distribution in bulk and at interface for a bi-material system: (a) unsaturated case and (b) saturated case

C(1) = C(2) ,

(4.1)

where C(1) is the moisture concentration at the interface on the material 1 (Mat1) side and C(2) is the moisture concentration at the interface on material 2 (Mat2) side. The requirement of the interfacial continuity can be expressed as [13] C(1) C(2) = , S1 S2

(4.2)

where S1 and S2 are the solubilities of the Mat1 and Mat2, respectively. Solubility is a material property, which is a function of temperature only. From equations (4.1) and (4.2), the interfacial discontinuity can be excluded by normalizing the moisture concentration C as ϕ = C/S.

(4.3)

Wong et al. [7] introduced an alternative variable, so-called wetness w, defined as

w = C/Csat .

(4.4)

The wetness w is also continuous at the interfaces because the saturated moisture concentration Csat is related to the solubility S according to Henry’s law as follows: S = Csat /pext ,

(4.5)

where pext is the ambient vapor pressure at the given temperature and humid condition. It is noteworthy that Csat is not strictly a material property since it depends on the ambient relative humidity (RH) as well.

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When Fick’s law is used, the transient moisture diffusion is given by the equation 1 ∂C ∂ 2C ∂ 2C ∂ 2C , + 2 + 2 = D ∂t ∂x2 ∂y ∂z

(4.6)

where x, y, and z are coordinates, D is the moisture diffusivity, and t is the time. Other moisture transport mechanisms are ignored in equation (4.6). It has been found that equation (4.6) may not be used for a multi-material system since the field variable, i.e., moisture concentration, C, is discontinuous at interfaces. When equation (4.3) is applied, and only when the solubility S remains constant for each material during the entire time period under study, equation (4.6) can be rewritten using a normalized variable ϕ as ∂ 2ϕ ∂ 2ϕ 1 ∂ϕ ∂ 2ϕ , + + = D ∂t ∂x2 ∂y2 ∂z2

(4.7a)

ϕ1 = ϕ2

(4.7b)

with

and D1 S1

∂ϕ1 ∂ϕ2 = D2 S2 . ∂n ∂n

(4.7c)

Equations (4.7a) to (4.7c) hold at the condition when temperature is constant (ambient humidity may change). Similarly, when the normalized variable w is applied, equation (4.6) can be rewritten in terms of w as ∂ 2w ∂ 2w 1 ∂w ∂ 2w , + 2 + 2 = 2 D ∂t ∂x ∂y ∂z

(4.8a)

w1 = w2

(4.8b)

where

and D1 Csat1

∂w1 ∂w2 = D2 Csat2 ∂n ∂n

(4.8c)

for the case of constant saturated moisture concentration (to be discussed in the next section). The above equations deal with the normalized variables ϕ and w, which are now continuous at interfaces.

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4.2.2 Thermal-Moisture Analogy When Fick’s law is used, the transient moisture diffusion is governed by a similar governing differential equation used for transient heat transfer analysis. Galloway and Miles [6] demonstrated that the commercially available finite element software for transient heat transfer analysis can be effectively used for transient moisture diffusion modeling as long as the field variable of temperature T in a transient thermal analysis is replaced by the normalized field variable ϕ, defined by equation (4.3). Table 4.1 defines the material properties and the corresponding thermal-moisture analogy with the normalized field variable ϕ. Table 4.2 defines the corresponding material properties when the normalized field variable w is used. Both approaches should lead to the same results. For an absorption process, the initial condition is usually set as zero. This is because the package is initially dried up prior to preconditioning. The simplest boundary condition in the case of absorption is that all the exposed surfaces will be set to the saturated moisture concentration Csat (w = 1 when w is used and ϕ = Csat /S when ϕ is used). After the finite element solutions are completed, the volume and the normalized field variables are obtained for each element, and the moisture mass of each element can be calculated. The total weight gain of the package can be calculated by summing up the individual mass contributions for each element at the given time step, as follows: N  I    S(n) ϕi (t) Vi , W (t) =

(4.9)

n=1 i=1

W (t) =

N  I    (n) Csat wi (t) Vi . n=1 i=1

Table 4.1 Thermal-moisture analogy when ϕ = C/S is used as field variable Properties

Heat conduction

Moisture diffusion

Field variable Density Conductivity Specific capacity

Temperature, T ρ k c

ϕ = C/S 1 DS S

Table 4.2 Thermal-moisture analogy when w = C/Csat is used as field variable Properties

Heat conduction

Moisture diffusion

Field variable Density Conductivity Specific capacity

Temperature, T ρ k c

w = C/Csat 1 D 1

(4.10)

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Here W(t) is the total moisture weight gain for the package at time t, N is the number of materials in the package, I is the number of elements for each group of materials, (n) and Vi is the ith element volume. S(n) is the solubility for the nth material and Csat is the saturated moisture concentration for the nth material. The functions ϕi (t) and wi (t) and the volumes Vi are taken from the finite element analysis.

4.2.3 Example – Application to a PBGA Package The geometry and the dimensions of a 68 I/O PBGA package are shown in Fig. 4.2 [6]. Realistic geometry and the attributes of the physical design of the package, such as internal vias, metallization on the die pad, and metallization at the solder joint interconnect, are identified and included in the model. Moisture absorption processes are modeled with a standard finite element analysis (FEA) using a 3-D eight-node transient heat conduction element. The moisture properties of diffusivity (D) and Csat corresponding to the JEDEC specification, level 1, 85◦ C/85% RH, are listed in Table 4.3. Die, copper, gold plate, and solder bump materials do not absorb moisture and are considered in the model with negligibly low values of diffusivity and solubility.

Fig. 4.2 A PBGA package geometry and structure

Table 4.3 Moisture properties of different materials for a PBGA package Material

Diffusivity D (cm2 /s)

Csat (g/cm3 )

BT Die attach Mold compound Solder resist Underfill

8.55e–9 1.68e–7 5.40e–8 2.47e–8 5.60e–9

2.40e–2 5.30e–3 4.00e–3 3.88e–2 2.47e–2

Modeling of Moisture Diffusion and Whole-Field Vapor Pressure

Fig. 4.3 Comparison of finite element analysis results with experimental data on moisture weight gain for a PBGA package

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Mass ratio of moisture, M(t)/Msat

4

850°C/85%RH

0.9 0.8

300°C/60%RH

0.7 0.6 0.5 0.4 0.3

Experiment Experiment

0.2

FEA FEA 0.1 00 0

20

40

60

80

100

120

140

160

Time (hour) Fig. 4.4 Moisture distribution contour in terms of C/Csat in a PBGA package subjected to 85◦ C/85% RH

‘red’ region

42 hrs ‘blue’ region ‘red’ region ‘blue’ region ‘red’ region

‘red’ region

84 hrs ‘red’ region

168 hrs ‘red’ region

‘blue’ region

Transient weight gain predictions at the JEDEC (stands for Joint Electron Device Engineering Council) standard level 1 and level 3 conditions (i.e., 85◦ C/85% RH and 30◦ C/60% RH, respectively) are compared to the experimental data in Fig. 4.3. The agreement between the experimental data and the FEA predictions is within 10% for the absorption process. The moisture distributions over the package length cross section at different times are shown in Fig. 4.4 [8]. The red color in Fig. 4.4 indicates the fully saturated (w=1) conditions and the blue color dry condition (w=0). The wetness ranges from 0 to 1 over the entire package.

4.3 Moisture Desorption Modeling – Direct Moisture Concentration (DCA) Approach 4.3.1 Theory Let us consider now a more general case, when the solubility S varies with time t. Assuming the isothermal condition, the transformation from equation (4.6) leads to

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∂ 2ϕ ∂ 2ϕ ∂ 2ϕ 1 ∂ϕ ϕ ∂S + + = + , 2 2 2 D ∂t D · S ∂t ∂x ∂y ∂z

(4.11)

ϕ ∂S = 0. D · S ∂t

(4.12)

where

Similarly, when the filed variable w is considered, the equation (4.6) becomes ∂ 2w ∂ 2w ∂ 2w w ∂Csat 1 ∂w + , + 2 + 2 = 2 D ∂t D · Csat ∂t ∂x ∂y ∂z

(4.13)

w ∂Csat = 0, D · Csat ∂t

(4.14)

in which

when the saturated moisture concentration Csat is dependent on time t. Equations (4.11) and (4.13) indicate that there is no simple thermal-moisture analogy when the ambient temperature (for ϕ) or the humidity (for w) varies with time (or temperature). In the case of a reflow process, the ambient humidity condition can be assumed constant (zero), while the temperature changes with time. In this case, equation (4.12) is not zero. Equation (4.13) can be reduced to equation (4.7a) only when the saturated moisture concentration is a constant. It has been found that for most polymeric materials Csat is weakly dependent on temperature, but depends on the relative humidity RH, as long as the temperature is well below the glass transition temperature (see Chapter 1). However, the saturated moisture concentration depends strongly on temperature when the temperature exceeds the glass transition temperature [14]. Most polymer materials have glass transition temperatures that are lower than the peak reflow temperature. Hence, the saturated moisture concentration is not constant during the reflow process. A direct concentration approach (DCA) was developed to correctly perform the moisture diffusion modeling under varying temperature and humidity conditions. In the DCA, the moisture concentration C is directly used as the basic field variable. Therefore, the governing differential equation is 1 ∂C ∂ 2C ∂ 2C ∂ 2C . + 2 + 2 = D(t) ∂t ∂x2 ∂y ∂z

(4.15)

It should be pointed out that the diffusivity D is a function of time (or temperature) and C is discontinuous at interfaces. Additional modeling effort is necessary to ensure that the following continuous conditions at interfaces are fulfilled:

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C(1)

=

C(2)

, S (t)1 S (t)2 ∂C (1) ∂C (2) D1 (t) = D2 (t) . ∂n ∂n

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(4.16) (4.17)

Here D1 (t) and D2 (t) are the moisture diffusivities of the materials Mat1 and Mat2, respectively, and n is the normal direction of the location at interfaces. In order to satisfy the continuity conditions at the interface, two separate sets of nodes are applied at a bi-material interface, as shown in Fig. 4.5, to represent the discontinuity of the moisture concentration. A constraint condition C(1)/C(2) = S1 (t)/S2 (t)

(4.18)

should be applied for each pair of nodes based on equation (4.16) to join two materials together. According to the variational principle underlying the FEA procedure, equation (4.17) will be automatically satisfied as long as the finite element formulation is used and equation (4.16) is fulfilled. Fig. 4.5 Special treatment and constrain equations at a bi-material interface in the direct concentration approach (DCA)

4.3.2 Numerical Implementation Because the material solubility is a function of temperature (thus time), the interfacial constraint condition (4.16) changes with time. Commercially available finite element software (such as ABAQUS) does not allow for automatic “updating” of the constraint condition during the analysis. In order to “update” the interfacial continuous condition, a new “job” must be defined and executed with the updated moisture distribution at the previous time step, similar to the initial moisture distribution for the next step analysis. Failure to update the constraint condition will lead to an erroneous result [15, 16]. As has been shown by Tay and Lin [5], the temperature and moisture fields are sequentially coupled during the reflow process. Temperature distribution affects the moisture diffusion, since the diffusivity and the solubility are functions of temperature. It has been shown in Chapter 1 that the heat transfer process is by several orders of magnitude faster than moisture diffusion. This enables one to uncouple the problem. For an ultrathin package, however, the coupling effect must be considered. When ABAQUS is used, the “MASS DIFFUSION” analysis type should be

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Moisture Inputting as Initial Condition

Moisture Diffusion Modeling during Reflow •DCA application

Thermal Modeling during Reflow •“HEAT TRANSFER” analysis type

•“MASS DIFFUSION” analysis type

•T varying with time t

•RH assumed to be zero at exterior boundary •D and S varying with T •Continuous conditionC(1)/C(2)at interface varying withT

Vapor Pressure Modeling •Simplified micromechanics-based vapor pressure model •f required •FORTRAN subroutine

Whole-field Moisture and Vapor Pressure Contour Visualization

Fig. 4.6 Implementation procedures of sequentially coupled heat transfer/moisture diffusion using DCA approach for reflow process

applied for the evaluation of the process of moisture diffusion. The temperature field can be obtained from the “HEAT TRANSFER” analysis type. All material properties can be considered as functions of temperatures. Since the constraint conditions at the interfaces need to be updated at each incremental temperature step, a special program has been written to allow for continuous calculations for an entire reflow process. The general procedures for the analysis of the moisture diffusion and vapor pressure modeling are summarized in Fig. 4.6.

4.3.3 Verification A simple bi-material problem is analyzed, as an illustration of the developed concept, as shown in Fig. 4.7a. Figure 4.7a reflects a two-step loading problem. Step 1 is moisture absorption at 60◦ C/60% RH (for 88 h to guarantee the materials are fully saturated). In step 2, the ambient condition experiences a step change from 60◦ C/60% RH to 260◦ C/0% RH for desorption. This two-step loading problem cannot be solved using traditional normalization methods since the ambient condition experiences a time-dependent change. The problem is now solved using the

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Fig. 4.7 Two equivalent problems: (a) a bi-material with a two-step loading and (b) a singlematerial diffusion problem

DCA according to the procedures described above. The constraint condition at the interface from step 1 to step 2 must be updated accordingly. In order to validate the numerical results, Mat2 is considered as a non-absorbing material. This is realized by assigning the material properties of Mat2 a few orders lower than for the Mat1, as shown in Tables 4.4 and 4.5. The problem in Fig. 4.7a is now equivalent to a single-material problem in Fig. 4.7b. Only the results in step 2 Table 4.4 Material properties at 60◦ C/60% RH for Mat1 and Mat2 60◦ C/60% RH

Mat1

Mat2

Diffusivity D (mm2 /s) Csat (kg/m3 ) Solubility S (kg/m3 ·Pa)

5.14 × 10−7 4.704 3.92 × 10−4

5.14 × 10−10 4.704 × 10−3 3.92 × 10−7

Table 4.5 Material properties at 260◦ C/60% RH for Mat1 and Mat2 260◦ C/60% RH

Mat1

Mat2

Diffusivity D (mm2 /s) Csat (kg/m3 ) Solubility S (kg/m3 ·Pa)

5 × 10−4 2.352 8.37 × 10−7

2.5 × 10−7 1.176 × 10−3 4.185 × 10−10

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are compared. In this case, the problem in Fig. 4.7b can be assumed to be a desorption process with initially fully saturated condition. The analytical solution for the problem in Fig. 4.7b can be obtained as follows [17]: C(x,t) =

  ∞ (2n + 1)π x Dt 1 4Csat  sin exp − 2 (2n + 1)2 π 2 . π (2n + 1) h h

(4.19)

n=0

Here Csat is the saturated moisture concentration of the Mat1 at 60◦ C/60% RH, D is the moisture diffusivity at 260◦ C, h is the double thickness of the Mat1 (as 0.4 mm shown in Fig. 4.7b), and x is the distance of the given cross section from the edge. In this example, the saturated moisture concentration at 60◦ C/60% RH is same as at 260◦ C/60% RH (the next section will illustrate the results without this assumption). In order to eliminate the temperature gradient effect, the thermal conductivity is chosen to be a few orders of magnitude higher than the moisture diffusivity at 260◦ C, so that the temperature becomes rapidly uniform in a very short time period. Figure 4.8 plots the comparison of the local moisture concentration at the interface as a function of time using the DCA and the analytical solution. It shows the excellent agreement between the two solutions. This confirms that the implementation procedure using the DCA is acceptable. It has been also observed that the desorption process is very fast and is completed in less than 200s for the given geometry. In step 1, it needs about 80 h to reach a saturated state at 60◦ C/60% RH. This is because the diffusivity at 260◦ C is several orders of magnitude higher than that at 60◦ C, as shown in Tables 4.4 and 4.5. 5

Concentration (kg/m3)

DCA (Bi-material) 4

Analytical Solution

3 2 1 0 0

50

100

150

200

250

300

350

400

450

500

Time (s)

Fig. 4.8 Comparison of moisture concentration using DCA with the analytical results

4.3.4 Analysis of Moisture Desorption for a Bi-material Model The assembly of a die-attach film with a substrate in a stacked-die chip scale package can be idealized as a bi-material model problem (Fig. 4.9), in which the Mat1

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Fig. 4.9 A bi-material model that represents a substrate/die-attach film structure in a stacked-die chip scale package (Mat2 – die attach, Mat1 – substrate)

Table 4.6 Material properties at 60◦ C/60% RH 60◦ C/60% RH

Mat1

Mat2

Diffusivity D (mm2 /s) Csat (kg/m3 ) Solubility S (kg/m3 ·Pa)

1.28 × 10−5 4.7 3.92 × 10−4

2.93 × 10−5 4.512 3.76 × 10−4

Table 4.7 Material properties at 200◦ C/60% RH 200◦ C/60% RH

Mat1

Mat2

Diffusivity D (mm2 /s) Csat (kg/m3 ) Solubility S (kg/m3 ·Pa)

4.72 × 10−4 4.7 5.05 × 10−6

6.43 × 10−4 9.024 9.7 × 10−6

represents the substrate and the Mat2 represents the die-attach film [16]. Tables 4.6 and 4.7 give the material properties at 60◦ C/60% RH and 200◦ C/60% RH, respectively. It is noted that the saturated moisture concentration for the die attach (Mat2) at 200◦ C/60% RH is as twice as that at 60◦ C/60% RH condition [18]. Two-step loading is applied. Step 1 is a constant temperature/humidity condition at 60◦ C/60% RH for 88 h, followed by step 2 with a step change to 200◦ C/0% RH. Figure 4.10 shows the results of moisture concentration at the interface on the dieattach film side and on the substrate side as a function of time. It is observed that there is a “jump” at the beginning on moisture concentration at the die attach (Mat2), while there is a “drop” at the substrate (Mat1) at time zero, when desorption takes place. This is due to the new continuity requirement according to equation (4.16). It can be seen that the moisture concentration increases in the die-attach film first and then decreases with time. The local moisture gradient drives more moisture

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Mat1

Concentration (kg/m3)

7

Mat2

6 5 4 3 2 1 0 0

20

40

60

80

100

Time (s)

Fig. 4.10 Moisture concentration history plots at a bi-material interface in a desorption process

diffusing through the die-attach film before it reaches the peak value in about 20s. Such a phenomenon is known as “over-saturation.” The distribution of moisture concentration (step 2) in the through-thickness direction at different time is plotted in Fig. 4.11. The moisture concentration at the boundary exterior is always zero. The moisture concentration is obviously discontinuous across the interface. In the beginning of desorption, the moisture concentration at the interface is redistributed according to the new continuity requirement. The redistribution makes the moisture contents at the interface on the Mat1 side less than that in the bulk material. Similarly, the redistribution makes the moisture at the interface on Mat2 side more than in the Mat2 bulk. Such a local moisture gradient drives the moisture further diffusing through the die-attach film across the interface. After a certain time (e.g., 20 s), the moisture in the film eventually starts to decrease. The total amount of moisture content at the interface in the beginning does not change much since the diffusion is not fast enough to result in a significant change in the total amount of moisture at the interface.

4.3.5 Example – Application to a PBGA Package A PBGA package shown in Fig. 4.2 is applied for desorption analysis. If Csat data are the same as those in the preconditioning process, the normalization approach based on w can be applied for conducting moisture desorption analysis. The diffusivity values at reflow temperature are assumed to be a few orders of magnitude higher than in the moisture absorption at preconditioning. Figure 4.12 shows the moisture diffusion distributions of a PBGA package prior to and after 2 min of desorption at 220◦ C [8]. It is found that the moisture desorption during the reflow process affects the moisture distribution greatly, although the time duration is only 2 min. However,

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Fig. 4.11 Moisture distributions in a reflow process for a bi-material model

Before desorption Moisture

After desorption

Fig. 4.12 Moisture distribution contour in terms of C/Csat before and after reflow process

0 0.1 0.2 0.4 0.6 0.7 0.8 0.9 1

even though there is significant amount of moisture loss in the package during the reflow process, the moisture concentration at the underfill/substrate interface remains unchanged.

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4.4 Whole-Field Vapor Pressure Model 4.4.1 Theory Although moisture diffusion is analyzed at a macroscopic level, the vapor pressure model should be considered at a microscopic level. Moisture exists everywhere in polymer materials and stays either in the mixed liquid/vapor phase or in the single vapor phase in nano-pores or in free volumes. Moisture is absorbed into polymeric materials in two ways. The first is as free (“unbound”) water liquid or vapor, which collects at the micro-/nano-pores, in free volumes, at the interfaces, and/or in micro-/ macro-voids. The main portion of the absorbed moisture stays in the unbound water state [14]. Moisture can also be absorbed by water–polymer affinity due to the availability of hydrogen bonding sites along the polymer chains and interfaces known as “bound water.” Unbound moisture will evaporate during the reflow process. In order to determine the vapor pressure, it is necessary to determine if moisture is in the vapor phase or in a binary liquid/vapor phase. To do that, a representative elementary volume (REV) around any considered point in porous medium is introduced. The REV is defined in such a way that wherever it is placed within the considered porous medium domain, it always contains both the solid polymer phase and the porous/free volume phase. The total moisture content in a REV is obtained from the local moisture concentration C at a macroscopic level. If the interstitial space fraction f (or free volume fraction) is known, then the “apparent” moisture density (ρ) in pores can be defined as [12] ρ = C/f .

(4.20)

When the moisture density ρ in pores is less than the saturated water vapor density ρ g , the moisture is in the single vapor phase. In this case, since the total moisture content (C×V, where V is REV volume) and the free volume (f×V) are known, the vapor pressure can be obtained using the ideal gas law as follows: p(T) =

RT ·C MMH2 O f

when C(T)/f < ρg (T).

(4.21)

Here R is the universal gas constant (=8.314 J/(mol·K)) and MNH2 O is the molecular mass of water (=18 g/mol). On the other hand, when the moisture density ρ is equal to or greater than the saturated water vapor density ρ g , the moisture in pores is in the mixed liquid/vapor phase. Therefore the vapor pressure remains as the saturated vapor pressure, as follows: p(T) = pg (T) , when C(T)/f ≥ ρg (T) ,

(4.22)

where pg is the saturated water vapor pressure, which increases exponentially with temperature (see Appendix).

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Fig. 4.13 Two distinct states of moisture in pores in polymer materials

Figure 4.13 illustrates the two distinct moisture states in pores. As shown in Fig. 4.13, these two cases fully describe the moisture states in the pores. The above analysis has greatly simplified the original vapor pressure model [12, 19] in which three distinct cases are identified to describe the moisture states in the pores. This model does not need to relate the current moisture state to a reference moisture state, but yields exactly the same results as the original model does. One of the critical parameters in the above vapor pressure model is the interstitial space fraction f. An approximate estimation method to obtain the free volume fraction of polymers was proposed using moisture weight gain test [12, 14]. Since the density of the liquid water is 1.0 g/cm3 , the moisture density in free volume, according to equation (4.20), must be less than or equal to 1.0 g/cm3 : f0 ≥ Csat

(4.23)

when the Csat uses the unit of g/cm3 . In general, the Csat depends on the relative humidity and temperature. If water liquid fills the free volume completely at 100% RH, the free volume fraction can be estimated from equation (4.23). An initial free volume fraction can be estimated from a moisture weight gain test using Csat measurement data and then extrapolated to the 100% RH condition. The results based on equation (4.23) using the material property data measured by Galloway and Miles [6] showed that the free volume fraction is usually between 1 and 5% for typical packaging materials.

4.4.2 Numerical Implementation A simple transformation from moisture diffusion to a whole-field vapor pressure analysis can be done through the vapor pressure model described in the previous section as long as the interstitial space fraction f is known. A user-defined FORTRAN subroutine is written for ABAQUS to compute the values of vapor pressure and display the contour of vapor pressure at each step. The contours of both

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moisture distribution and vapor pressure can therefore be graphically visualized. Tee et al. [8] developed an APDL language-based program to visualize the vapor pressure contour in ANSYS. In Chapter 19, an automated tool development is introduced to perform moisture diffusion modeling and vapor pressure prediction using ANSYS.

4.4.3 Analysis of Vapor Pressure Development During Reflow for a Bi-material Model

Temperature (oC)

The bi-material model used in Section 4.3.4 is re-examined with a real reflow loading condition, as shown in Fig. 4.14. Several incremental steps are divided to simulate such an actual profile. The interstitial space fraction f is assumed to be 0.05 [8]. Figure 4.15 plots the vapor pressure and moisture concentration at the interface on die-attach (Mat2) side during the reflow soldering process. The results indicate that the vapor pressure increases exponentially and coincides with the saturated vapor pressure curve. This means that the moisture is in the mixed liquid–vapor phase in the materials. Around 220◦ C, the vapor pressure reaches the peak value of about 3 MPa. From 220 to 260◦ C, the vapor pressure starts to decrease gradually, even though temperature increases. This is because there is no sufficient residual moisture remaining in the film, so that the moisture becomes the single vapor phase. In this situation the vapor pressure will not increase with increase in temperature. The competing effect between the temperature rise and the local residual moisture is responsible for the non-monotonic buildups of the vapor pressure.

280 260 240 220 200 180 160 140 120 100 80 60 40 20

Reflow Profile (real) Reflow Profile (for simulation) 0

60

120

Fig. 4.14 A typical reflow profile

180 240 Reflow Time (s)

300

360

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7

5 4.5

Vapor Pressure (MPa)

6

4 5

3.5

4

3 2.5

3

Saturated Vapor Pressure

2

2

Vapor Pressure

1.5

Moisture Concentration

1

1

Concentration (kg/m3)

4

0.5

0

0 60

80

100

120

140

160

180

200

220

240

260

Temperature (oC) Fig. 4.15 History of vapor pressure non-monotonic evolution and moisture concentration at the interface during reflow process for a bi-material model

4.4.4 Whole-Field Vapor Pressure Modeling for FCBGA and PBGA Packages Let the saturated moisture concentrations are constants over the entire reflow temperature range. This allows us to use the normalization approach based on w to perform desorption analysis. A step change is considered from preconditioning at 85◦ C/85% RH to a reflow condition at 220◦ C/0% RH. Different preconditioning times are considered, e.g., 5, 10, and 168 h. The vapor pressure contour is obtained for 2-min reflow at 220◦ C. The finite element data for the vapor pressure for a flip chip ball grid array (FCBGA) are shown in Fig. 4.16a, and the corresponding

5h

5h MPa

0 0.25 0.5 1 1.25 1.5 1.75 2 2.5

10h

0 0.1 0.2 0.4 0.6 0.7 0.8 0.9 1

10h

168h

168h

a

b

Fig. 4.16 (a) Transient vapor pressure distribution in an FCBGA package at JEDEC level 1 at 220◦ C; (b) transient moisture distribution in an FCBGA package at JEDEC level 1 at 220◦ C

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24h 24h MPa 0 0.25 0.5 1 1.25 1.5 1.75 2 2.5

48h

192h

0 0.1 0.2 0.4 0.6 0.7 0.8 0.9 1

48h

192h

a

b

Fig. 4.17 (a) Transient vapor pressure distribution in a PBGA package at JEDEC level 1 at 220◦ C; (b) transient moisture distribution in a PBGA package at JEDEC level 1 at 220◦ C

moisture diffusion distributions are shown in Fig. 4.16b [8]. It is found that the moisture diffusion and the vapor pressure have different distributions. Even though much less moisture is absorbed, the vapor pressure reaches the saturated vapor pressure. Similar conclusions can be made for a PBGA package (Fig. 4.17) [8].

4.5 Summary Understanding of the process of moisture absorption, desorption and diffusion, and vapor pressure evolution is the key to solving the problems of moisture-induced failures in plastic electronic packages. We have presented a review of the existing theories, numerical treatments, and applications of different moisture diffusion modeling methods. In addition, a whole-field vapor pressure model is introduced. The interstitial space fraction f (or free volume fraction) is considered to link a macroscopic moisture diffusion analysis to the microscopic vapor pressure model. The phase change of moisture has been considered. An approximate estimate method to obtain the free volume fraction of polymers using moisture weight gain test is described. The commonly used thermal-moisture analogy based on the normalization methods are described. A simple thermal-moisture analogy does not exist when ambient temperature and/or the humidity varies with time. The direct concentration approach (DCA) can be applied to perform moisture diffusion analysis for the reflow process. In the DCA, the moisture concentration is used as a field variable directly, and the interface continuity requirement is satisfied by using constraint conditions. The numerical implementation procedures for calculating moisture concentration and the ensuing vapor pressure are described in detail. Several examples are presented to compare the finite element predictions with the experimental data for moisture weight gain in packages.

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Appendix: Table of the Saturated Water Vapor Density and Vapor Pressure at Different Temperatures T (◦ C) ρ g (kg/m3 ) pg (MPa)

60 0.13 0.02

70 0.2 0.03

80 0.29 0.05

90 0.42 0.07

100 0.6 0.1

110 0.83 0.15

120 1.12 0.2

T (◦ C) ρ g (kg/m3 ) pg (MPa)

130 1.5 0.28

140 1.97 0.38

150 2.55 0.5

160 3.26 0.65

170 4.12 0.84

180 5.16 1.1

190 6.4 1.37

T (◦ C) ρ g (kg/m3 ) pg (MPa)

200 7.86 1.72

210 9.59 2.14

220 11.62 2.65

230 14 3.25

240 16.76 3.97

250 19.99 4.83

260 23.73 5.84

References 1. Fan, X.J., “Moisture related reliability in electronic packaging”, ECTC Professional Development Course Notes, 2005/2006/2007/2008. 2. Zhang, G.Q., Driel, W.D.V., Fan, X.J., Mechanics of Microelectronics. New York, NY: Springer, 2006. 3. Fan, X.J., Zhou, J., Chandra, A., “Package structural integrity analysis considering moisture”, Proceedings of Electronic Components and Technology Conference. (ECTC), pp. 1054–1066, 2008. 4. Kitano, M., Nishimura, A., Kawai, S., “Analysis of package cracking during reflow soldering process”, Proceedings of IRPS, pp. 90–95, 1988. 5. Tay, A.A.O., Lin, T.Y., “Moisture diffusion and heat transfer in plastic IC packages”, IEEE Transactions on Components, Packaging and Manufacturing Technology, Part A, 19(2), 186–193, 1996. 6. Galloway, J.E., Miles, B.M., “Moisture absorption and desorption predictions for plastic ball grid array packages”, IEEE Transactions on Components, Packaging and Manufacturing Technology, Part A, 20(3), 274–279, 1997. 7. Wong, E.H., Teo, Y.C., Lim, T.B., “Moisture diffusion and vapor pressure modeling of IC packaging”, Proceedings of the 48th Electronic Components and Technology Conference, pp. 1372–1378, 1998. 8. Tee, T.Y., Fan, X.J., Lim, T.B., “Modeling of whole field vapor pressure during reflow for flip chip and wire-bond PGBA Packages”, 1st International Workshop on Electronic Materials & Packaging, 1999. 9. Tee, T.Y., Zhong, Z.W., “Integrated vapor pressure, hygroswelling and thermo-mechanical stress modeling of QFN package during reflow with interfacial fracture mechanics analysis”, Microelectronics Reliability, 44(1), 105–114, 2004. 10. Xie, B., Shi, X.Q., Fan, X.J., “Sensitivity investigation of substrate thickness and reflow profile on wafer level film failures in 3D chip scale packages by finite element modeling”, Proceedings of the 57th Electronic Components and Technology Conference 2007, ECTC 07, pp. 242–248, 2007. 11. Fan, X.J., Lim, T.B., “Mechanism analysis for moisture-induced failures in IC packages”, ASME 1999 International Mechanical Engineering Congress, IMECE/EPE-14, 1999. 12. Fan, X.J., Zhou, J., Zhang, G.Q., Ernst, L.J., “A micromechanics based vapor pressure model in electronic packages”, ASME Journal of Electronic Packaging, 127(3), 262–267, 2005.

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13. Crank, J., The Mathematics of Diffusion. Oxford: Clarendon Press, 1956. 14. Fan, X.J., Lee, S.W.R., Han, Q., “Experimental investigations and model study of moisture behaviors in polymer materials”, Microelectronics Reliability, 49, 861–871, 2009. 15. Xie, B., Fan, X.J., Shi, X.Q., Ding, H., “Direct concentration approach of moisture diffusion and whole field vapor pressure modeling for reflow process: part I – theory and numerical implementation”, ASME Journal of Electronic Packaging, 131(3), 031010, 2009. 16. Xie, B., Fan, X.J., Shi, X.Q., Ding, H., “Direct concentration approach of moisture diffusion and whole field vapor pressure modeling for reflow process: part II – application to 3-D ultra-thin stacked-die chip scale packages”, ASME Journal of Electronic Packaging, 131(3), 031011, 2009. 17. Zhou, J. et al., “Effect of Non-uniform moisture distribution on the hygroscopic swelling coefficient”, IEEE Transactions on Components and Packaging Technologies, 31(2), 269–276, 2008. 18. Fan, X.J., “Mechanics of moisture for polymers: fundamental concepts and model study”, Proceedings of 9th EuroSimE 2008, Freiburg, Germany, pp. 159–172, 2008. 19. Fan, X.J., Zhang, G.Q., van Driel, W.D., Ernst, L.J., “Interfacial delamination mechanisms during reflow with moisture preconditioning”, IEEE Transactions on Components and Packaging Technologies, 31(2), 252–259, 2008.

Chapter 5

Characterization of Hygroscopic Deformations by Moiré Interferometry E. Stellrecht, B. Han, and M. Pecht

5.1 Introduction A plastic encapsulated microcircuit (PEM) consists of a silicon chip, a metal support or a lead frame, wires that electrically attach the chip’s circuits to the lead frame, and a plastic epoxy encapsulating material, or mold compound, to protect the chip and the wire interconnects [1]. The mold compound is a composite material made up of an epoxy matrix that is composed of silica fillers, stress relief agents, flame retardants, and many other additives. Despite having many advantages over hermetic packages in terms of size, weight, performance, and cost, one significant disadvantage of PEMs is that the polymeric mold compound absorbs moisture when exposed to a humid environment. Hygroscopic stresses arise in an electronic package when the mold compound and other polymeric materials swell as they absorb moisture, while the adjacent non-polymeric materials, such as the lead frame, die paddle, and silicon chip, do not experience swelling. The differential swelling that occurs between the mold compound and the non-polymeric materials leads to hygroscopic mismatch stresses in the package [2–5]. This chapter provides a novel experimental procedure for studying the hygroscopic swelling behavior of mold compounds and a PEM package. The procedure utilizes a real-time whole-field displacement measurement technique called moiré interferometry to conduct extremely accurate measurements. Moiré interferometry is a technique with several important advantages over other techniques used for the measurement of hygroscopic swelling. Moiré interferometry boasts a high measurement sensitivity of 0.417 μm/fringe and uses the entire specimen surface as a measurement gage length. It also allows for simultaneous measurement in both the U and V (x and y) directions from a single experiment while effectively canceling any thermally induced deformations.

B. Han (B) e-mail: [email protected]

X.J. Fan, E. Suhir (eds.), Moisture Sensitivity of Plastic Packages of IC Devices, Micro- and Opto-Electronic Materials, Structures, and Systems, C Springer Science+Business Media, LLC 2010 DOI 10.1007/978-1-4419-5719-1_5, 

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5.2 Moiré Interferometry Moiré interferometry is an optical, full-field, in-plane measurement technique with high sensitivity, high spatial resolution, and excellent clarity [6, 7]. Moiré interferometry has the ability to map the deformations of advanced engineering structures with extremely high resolution. The data are output as contour maps of in-plane displacements. A detailed description of moiré interferometry can be found in Refs. [6, 7]. In this method, a high-frequency cross-line grating on the specimen, initially of frequency fs , deforms together with the specimen. A pair of parallel (collimated) beams of laser light strike the specimen and a portion is diffracted back, nominally perpendicular to the specimen, in the +1 and −1 diffraction order of the specimen grating, as shown in Fig. 5.1. Since the specimen grating is deformed as a result of the applied loads, these diffracted beams are no longer collimated. Instead, they are beams with warped wavefronts (w

1 , w

2 ), where the warpages are related to the deformation of the grating. These two coherent beams interfere in the image plane of the camera lens, producing an interference pattern of dark and light bands, which is the moiré pattern.

Fig. 5.1 Diffraction from the specimen grating produces output beams with plane wavefronts w 1 and w 2 for an initial unloaded condition. Warped wavefronts w

1 and w

2 result from the deformation of the sample [6, 7]

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These moiré patterns are contour maps of the U and V displacement fields, i.e., the displacements in the x and y directions, respectively, of each point in the specimen grating. The relationships for every x,y point in the field of view are 1 Nx (x,y) 2fs . 1 Ny (x,y) V(x,y) = 2fs U(x,y) =

(5.1)

In the routine practice of moiré interferometry, fs = 1,200 lines/mm (30,480 lines/in.). The contour interval in the fringe patterns is 1/2fs , which is 0.417 μm displacement per fringe order.

5.2.1 Real-Time Observation and Testing Apparatus Deformation measurements in this procedure were made at an elevated temperature in order to achieve an accurate desorption curve. Therefore, it was necessary to implement real-time moiré interferometry, or the ability to make moiré measurements on a sample subjected to a thermal excursion inside an environmental chamber. A fan inside the chamber circulates the air vigorously to maintain the target temperature. Consequently, the environmental chamber transmits vibrations to the specimen. Moiré interferometry measures tiny displacements, and those inadvertent vibrations cause the moiré fringes to dance at the vibration frequency [8, 9]. Figure 5.2 illustrates the real-time moiré setup used to circumvent the vibration problem. The two major components in this setup are a portable moiré interferometer (PEMI II, Photomechanics, Inc.) and a computer-controlled environmental chamber (EC1A, Sun Systems). The specimen holder is not attached to the chamber. Instead, it is connected directly to the interferometer and is thus essentially free from the environmental chamber. Furthermore, the interferometer and the chamber are mounted on separate tables; this mechanically isolates the interferometer from the chamber. With this arrangement, moiré fringes can be recorded while the chamber is being operated. Further details of the rod assembly and the temperature control are found in Ref. [8].

5.2.2 Tuning and Measurement A critical component in the use of moiré interferometry is the ability to tune the system accurately. The tuning of the interferometer is typically performed with an undeformed reference grating in order to achieve a null field, or zero deformation setting. The experiments described below used a reference specimen to tune the system. Once the null field is set, the specimen with the deformed specimen grating is installed in the interferometer and the moiré fringes are documented. Further details on this topic are found in Refs. [10, 11].

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Fig. 5.2 Experimental apparatus for real-time observation of moiré fringes [8]

Once the tuning procedure is completed, the active specimen with the deformed grating is installed in the interferometer when the desired loading condition has been achieved. In order to correctly utilize the null-field set with the reference grating, it is necessary to correctly align the interferometer to the specimen grating. If the interferometer is not aligned to the specimen, erroneous fringes are immediately introduced due to the effect of out-of-plane rotations.

5.3 Experimental Procedure Using Moiré Interferometry 5.3.1 Initial Preparation An overview of the experimental procedure is illustrated in Fig. 5.3. Two samples were baked in a convection oven (referred to as the baking oven) at 125◦ C to remove

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Fig. 5.3 Overview of experimental procedure

the initial moisture that existed in the mold compound. The weights of the samples were monitored periodically using a Mettler AE100 analytical balance with a resolution of 0.1 mg until the measured weight of each sample remained unchanged for an extended period of time. A prebaking time of 120 h was found to be sufficient for the mold compounds.

5.3.2 Specimen Grating Replication When the bake was completed, a cross-line diffraction grating was replicated onto the samples at an elevated temperature using a high-temperature curing epoxy (TraCon Tra-Bond F230). The grating mold was coated with a very thin, highly reflective metallic film of gold. Gold film was used due to its excellent corrosion resistance characteristics in elevated temperature and relative humidity conditions. The grating replication procedure is illustrated in Fig. 5.4, where the thickness of the grating after replication is very much exaggerated, and it is described in detail in Refs. [6, 7]. The specimens were then returned to the thermal chamber for 24 h to ensure complete polymerization of the epoxy. This procedure ensured that no moisture gain occurred during grating replication.

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Fig. 5.4 Grating replication procedure

5.3.3 Moisture Content Measurement One of the two samples was selected and left in the baking oven so as not to absorb any moisture. This sample, referred to as the reference sample, was needed in order to compensate for the thermal expansion during the measurement. The detailed procedure concerning thermal expansion compensation will be discussed in the following section. The other sample, referred to as the test sample, was removed from the baking oven and placed in a relative humidity chamber at 85◦ C/85% RH. The weight gain of the test sample was periodically monitored with the analytical balance until a “virtual” saturation state was achieved. Virtual saturation is defined as the occurrence of no further weight gain within the resolution of the balance (less than 0.1 mg) for 2–3 days. We refer to a virtual saturation state because achievement of the true saturation state would have required many more days of sorption. The sorption curves of the five mold compounds are shown in Fig. 5.5.

5.3.4 Measurement of Hygroscopic Deformation After the virtual saturation state was achieved, the desorption process proceeded and deformations induced by hygroscopic swelling were documented at a constant temperature of 85◦ C by moiré interferometry. It is important to eliminate undesired thermal expansions of the sample at the measurement temperature so as to document only hygroscopic swelling-induced deformations. This is accomplished by the following procedure:

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Fig. 5.5 Sorption curves of mold compounds

1. Remove the reference sample and the test sample from the baking oven and the relative humidity chamber, respectively, and place them side by side in the convection oven of the real-time moiré system (see the inset in Fig. 5.2). 2. Allow the samples to reach thermal equilibrium at the desorption temperature of 85◦ C. 3. Tune the moiré setup to produce a null field (devoid of fringes) on the reference sample. 4. View the test sample with the moiré interferometer and document the fringe patterns. 5. Remove the test sample immediately after step (4) and weigh it. Place it back in the convection oven. 6. Repeat steps (2)–(5) until the desorption process is complete.

Step (3) in the above measurement procedure is equivalent to the optical subtraction of a uniform strain [10]. This step cancels any thermally induced deformations in the test sample by using the deformed state of the reference sample as a reference. The re-tuning of the null field before each measurement is required to make the measurements completely free from any errors associated with temperature instability of the instruments including the environmental chambers and the interferometer.

5.4 Hygroscopic Swelling Measurement of Mold Compounds The procedure described above was used to analyze five mold compounds manufactured by Sumitomo Bakelite Co. Ltd. The material properties are shown in Table 5.1. The measurement technique was repeated on three different samples of each mold compound to ensure repeatability.

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Properties

EME-6300H

EME7720TA

EME-6600CS

EME7351LS

EMEG700

Ash content (wt%) Filler ratio (spherical/flake) Filler particle size (μm) Epoxy type

70–73 50/50

84–88 100/0

80–83 70/30

85–89 100/0

85–89 100/0

25–31

15–21

13–18

10–16

10–20

O-Cresol Novolac (OCN) Phenol Novolac (PN) 17

Multifunc.

Dicyclopentadiene Biphenyl (DCPD)

Multiaromat.

Multifunc.

Phenol Novolac (PN)

Elastic

Multiaromat.

13

11

10

12

68

40

50

42

49

165

195

165

135

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Hardener

Thermal expansion, α 1 (ppm/◦ C) Thermal expansion, α 2 (ppm/◦ C) Tg (◦ C)

5.4.1 CHS of Mold Compounds The V-field fringe patterns of EME-7720TA obtained during the desorption process are shown in Fig. 5.6. The null-field pattern of the reference sample is shown in (a), and the fringe patterns of the test sample at time intervals of 0, 16, and 400 h are shown in (b), (c), and (d), respectively. The test specimen contracted as desorption progressed, as evidenced by a decrease in the number of fringes in the patterns. The

Fig. 5.6 V-field moiré patterns obtained from mold compound EME-7720TA. (a) Null field obtained from the reference sample; fringe patterns of the test sample at time intervals of (b) 0, (c) 16, and (d) 400 h

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fringe patterns at 0 h (b) represent the hygroscopic swelling at the virtual saturation point. The V-field fringe patterns of the other mold compounds obtained at the virtual saturation point (at 0 h) are shown in Fig. 5.7.

Fig. 5.7 V-field moiré patterns obtained from other mold compounds at the virtual saturation state (time 0): (a) EME-6300H, (b) EME-6600CS, (c) EME7351LS, and (d) EME-G700

It is worth noting that the pattern at 400 h (Fig. 5.6d) has a few residual fringes. These residual fringes were produced by a small amount of moisture (0.04–0.08%) that remained in the mold compounds after the desorption process [4, 5, 12]. If the specimen had returned to its original “dry” condition, the pattern would have been devoid of fringes. This condition was observed for all five mold compounds. It was caused by the lower RH% at the drying temperature (125◦ C) compared to the RH% at the desorption temperature (85◦ C). The hygroscopic strain εh can be determined directly from moiré fringe patterns by using the following equation: εh =

1 N , 2fs L

(5.2)

where fs is the frequency of the specimen grating (1,200 lines/mm), N is the change of fringe orders in the moiré pattern, and L is any gage length across which N is determined. The V-field hygroscopic strains are plotted against moisture content (%) in Fig. 5.8. It is evident that a linear relationship exists between hygroscopic swelling and moisture content. The constant of linearity, called the coefficient of hygroscopic swelling (CHS) [10], is defined as follows: β=

εh , %C

(5.3)

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Fig. 5.8 Hygroscopic strain vs. moisture content (%) obtained from the moiré fringes

where β is the CHS and %C is the moisture content percentage calculated by using the following formula: %C =

Wet weight − dry weight × 100. Dry weight

(5.4)

“Wet weight” is defined as the weight of the sample including the weight of the absorbed moisture. The CHS is a material property of the mold compound and, if known, the hygroscopic swelling can be determined by measuring the moisture content in the mold compound. The test results are summarized in Table 5.2. They include the CHS values, virtual equilibrium moisture content, and the corresponding hygroscopic swelling obtained from equation (5.3). Although only V-field fringes are shown in Figs. 5.6 and 5.7, the corresponding U-field patterns were documented and both fields were used to determine the CHS values. The average CHS value of the five mold compounds was 0.22. The variation of the CHS value was less than 20%. However, the maximum moisture content showed significant variation, which was attributed to the combined effect of the amount of ash content and the resin/hardener system. Table 5.2 Experimental results Properties Average CHS (%εh /%C) Virtual equilibrium moisture content (%C) Hygroscopic swelling (%εh )a CTE (ppm/◦ C) Temperature excursion (◦ C) Thermal mismatch strain (%)b a For b For

85◦ C/85% RH T=100◦ C

EME6300H

EME7720TA

EME6600CS

EME7351LS

EMEG700

0.21 0.54

0.26 0.45

0.21 0.29

0.24 0.26

0.19 0.24

0.11 17 65 0.14

0.12 13 92 0.10

0.06 11 55 0.08

0.06 10 60 0.07

0.05 12 42 0.09

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The moisture content of the first two mold compounds (EME-6300H and EME7720TA) was nearly twice as large as that of the other three mold compounds (EME-6600CS, EME-7351LS, and EME-G700). Consequently, the first two mold compounds exhibited hygroscopic swelling that is almost twice that of the other three compounds.

5.4.2 Comparison Between Hygroscopic and Thermal Deformations The temperature excursion required to produce a thermal expansion equal to the hygroscopic swelling in the mold compound specimen can be calculated as follows: T =

β ·C εh = , α α

(5.5)

where α is the coefficient of thermal expansion (CTE) in ppm/◦ C. This comparison is shown in the lower half of Table 5.2. The deformation caused by hygroscopic swelling can be as significant as the thermal deformation caused by T of 92◦ C. If a mold compound/silicon chip assembly is considered, the hygroscopic mismatch strain component in the direction of the mold compound/chip interface would be identical to hygroscopic swelling in the mold compound at the interface, because the chip does not absorb moisture and does not swell. Assuming that the chip does not deform, the thermal mismatch strain εσ can be approximated as follows: 

εσ = αmold compound − αchip T.

(5.6)

The results are shown in the last row of Table 5.2, where the chip CTE of 3 ppm/◦ C and a temperature excursion of 100◦ C were used. The hygroscopic mismatch strains are compatible with the thermal strains induced by the considerable thermal excursion. The experimental results presented here imply that hygroscopic swelling plays an important role in the cycles to failure of the package when the package is subjected to environments where the relative humidity fluctuates.

5.4.3 Effect of Grating on Sorption and Desorption Characteristics of the Mold Compound In the described method, the test samples were subjected to a high temperature and humidity condition for a long time period. In the original attempt, a room-temperature curing epoxy grating coated with an aluminum layer was used. Preliminary tests revealed that the room-temperature curing epoxy relaxed and the

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aluminum layer corroded in the high temperature/humidity conditions. The hightemperature curing epoxy and the gold coating were used to cope with this problem. With the new grating, high diffraction efficiency was maintained throughout the moiré measurement. The grating was made extremely thin (on the order of 10 μm) compared to the thickness dimension of the test samples (2 mm). The reinforcing effect from the grating on the sample deformation was negligible, as seen in most engineering applications of moiré interferometry. However, two important questions associated with the specimen grating arose in implementing moiré interferometry for the present study. They were (1) the effect of the gold layer on the moisture absorption and desorption from the surface of the sample on which it was applied and (2) the effect of the thin epoxy layer on moisture gain. Supplementary experiments were conducted to address these issues. Three samples without specimen gratings (referred to as bare samples) were subjected to 85◦ C/85% RH along with three test samples with the gold-coated specimen grating attached. Weight gain/loss was documented by the same procedure described earlier. The results from the three bare samples were averaged and compared with the averaged value from the test samples. Comparisons of the absorption and desorption data are plotted in Fig. 5.9a and b, respectively. The results clearly indicate that the gold-coated epoxy grating had virtually no influence on the absorption and desorption characteristics of the test samples.

5.4.4 CHS Measurement Accuracy The accuracy of the hygroscopic swelling measurement depends on the accuracy of the individual parameters used in equation (5.2). It is clear that the accuracy increases proportionally with an increased gage length. With the advent of digital image processing, it is reasonable to assume that the error in gage length measurement is a maximum of one pixel. In this experiment, this one pixel corresponded to a

Fig. 5.9 Comparison of the test samples with the gold-coated grating and the bare samples during the process of (a) sorption and (b) desorption

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real length of about 0.23 mm. With moiré fringes that exhibit a high signal-to-noise ratio, an error in determining a fractional fringe order would be less than 0.2 fringe orders. For the smaller U direction gage length (13 mm) used in the experiments, these two values produced a maximum error of approximately 6 μstrain. The analytical balance used in this experiment had a precision of 0.1 mg and therefore an uncertainty of ±0.05 mg in weight gain/loss measurement. The uncertainty in swelling and weight measurements caused a random error in each data point; so linear regression was performed over the data points to determine the CHS. In order to characterize the potential error in the measured CHS, a separate random analysis was carried out, where the maximum uncertainty was added to each data point randomly and the linear regression coefficients were compared. An error of approximately 1% in the measured CHS was estimated.

5.5 Analysis of Plastic Quad Flat Package The package selected for the test was a square quad flat plastic package with 100 I/Os. The package contained a copper lead frame and a chip with dimensions of 6.36 mm × 6.36 mm × 0.5 mm. The package was prepared as shown in Fig. 5.10 to investigate the interaction between the mold compound and the chip. The opposing sides of the package were trimmed and ground using a precision grinding machine until the silicon chip was exposed on both sides. This specimen configuration preserved the symmetric boundary conditions. After the existing moisture was removed by baking at 125◦ C, the specimen grating was replicated onto the package surface at 85◦ C. The moiré system was tuned at the grating replication temperature, and the null-field patterns were taken as shown in Fig. 5.11a. The package was cooled to 25◦ C and the resulting thermal deformations were measured. The fringe patterns are shown in Fig. 5.11b, which represent in-plane displacement maps induced by T of −60◦ C. The package was then subjected to 85◦ C/85% RH until the saturation state was achieved. The package was installed in the real-time moiré system at 85◦ C, and the deformations caused by hygroscopic swelling at the saturation state were measured.

Fig. 5.10 PQFP package for moiré experiments. The CTE and the CHS of the mold compound of the package were determined from the regions marked by dashed boxes

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Fig. 5.11 (a) Null-field patterns documented at 85◦ C before moisture absorption and (b) fringe patterns induced by cooling the package to 25◦ C (T = −60◦ C)

The resulting fringe patterns are shown in Fig. 5.12. No reference specimen was used for this experiment since it was not practically possible to have two identical package specimens. Instead, the specimen grating was replicated from a special grating mold fabricated on an ultra-low expansion (ULE) glass. The ULE grating mold had a CTE of virtually 0. This negligible CTE allowed the ULE grating to be used as a reference to set a null field at any temperature after moisture absorption [5, 13]. Measurements were taken as the desorption process continued. Representative fringe patterns of the package at time interval of 8 h are shown in Fig. 5.12b. A significant contraction of the package was evident as the number of fringes in the package decreased significantly after 8 h of desorption. The fringe patterns at 0 h (Fig. 5.12a) represent the hygroscopic mismatch deformation at the virtual saturation point. It is important to remember that the measurement was made at the grating replication temperature (85◦ C) and thus the fringe

Fig. 5.12 Fringe patterns obtained at 85◦ C during desorption process: (a) at its virtual equilibrium state and (b) after 8 h

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patterns shown in Fig. 5.12 represent deformations induced only by hygroscopic swelling and do not contain any thermally induced deformations. The displacement fields shown in Figs. 5.11 and 5.12 represent the total deformation of the package, which includes the free thermal (Fig. 5.11) and the free hygroscopic (Fig. 5.12) parts of the deformation and the stress-induced part of the deformation. Mathematically, the total strain of the package is For thermal strain:εαT = εαf + εασ = αT + εασ For hygroscopic strain:εβT = εβf + εβσ = βC + εβσ

,

(5.7)

where εT is the total strain, εf is the free expansion/contraction part of strain, εσ is the stress-induced part of the strain. The subscripts α and β denote the cases of thermal deformation and hygroscopic deformation, respectively. The values of α and β for the mold compound were not known. They were determined from regions (marked by dashed boxes in Fig. 5.10) sufficiently far away from the chip where the deformations represent only εf of the mold compound. The value of α was determined from the fringe patterns in Fig. 5.11b, and it was 14.4 ppm/◦ C. The value of β was determined using the same procedure as described previously for the mold compounds. Fringe patterns at various desorption times were analyzed, and the swelling in these regions was plotted vs. moisture content. The sorption curve is shown in Fig. 5.13a, and the result of swelling vs. moisture content is shown in Fig. 5.13b. The maximum moisture content and the CHS value were determined as C = 0.43% and β = 0.21 (%εh /%C), respectively. The CHS value was approximately the same as the average value of the five mold compounds. The moisture content was similar to that of the two mold compounds with the higher moisture content. The total x-direction strains along a line just above the top of the chip were obtained directly from the U-field fringe patterns. The corresponding stress-induced strains were then calculated using equation (5.7), with T ≈ 60◦ C and C = 0.43%. The results along the dashed line (AA shown in Fig. 5.12) are plotted in Fig. 5.14a, where the x-axis represents a distance from the center of the package, normalized

Fig. 5.13 (a) Sorption curve and (b) free hygroscopic strain vs. moisture content (%) of the mold compound of the package

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Fig. 5.14 (a) Stress-induced strains and (b) bending displacements along the chip/mold compound interface

by the width of the chip. Along the chip/mold compound interface (x < 0.5), εασ was tensile, while εβσ was compressive. The magnitude of the stress-induced strain caused by the CHS mismatch εβσ was nearly twice as large as that produced by the CTE mismatch εασ , with T ≈ 60◦ C. The strains changed abruptly around the edge of the chip. These changes were caused by the material discontinuity. The signs of the strains were reversed, but their magnitudes reduced to a uniform value at a distance of about half the chip width from the edge of the chip. Another interesting phenomenon was observed in the V displacement fields. The bending displacements along the line were determined from the V-field fringe patterns, and they are plotted in Fig. 5.14b. Unlike the strains, the bending displacements have the same sign. The total bending displacement induced by swelling is nearly three times as large as that by thermal deformation. The bending was caused by the fact that the lead frame was not placed in the middle of the package. The CTE of the copper lead frame (17 ppm/◦ C) was reasonably close to that of the molding compound (14.4 ppm/◦ C), and the CTE mismatch was not significant. However, the swelling coefficient of the lead frame was 0 and the swelling mismatch caused a larger bending. The chip also contributed to the bending displacement, but its effect was not significant because of its small relative volume.

5.5.1 Discussion The above results show that hygroscopic swelling effects can have a significant impact on PEM reliability. The hygroscopic strains must be considered for reliability assessment in environments, such as in automotive applications, where packages are subjected to both temperature excursions and relative humidity changes. Accelerated life-testing conditions, such as a highly accelerated stress test (HAST) chamber, where temperature, humidity, and pressure are used, may also witness complications due to hygroscopic swelling issues. The temperature conditions in a HAST chamber are typically from 100 to 150◦ C, the relative humidity is typically over 70%, and the pressure can be up to 50 psi. These conditions will

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drastically increase the amount of moisture absorbed by the polymeric materials in a package and will therefore greatly increase the hygroscopic swelling. It is well known that temperature changes and thermal expansion mismatches can cause stresses and deformations that can lead to reliability problems in PEMs. The experimental evidence here indicates that hygroscopic stresses can also have a significant impact on PEM reliability. In fact, this study shows that hygroscopic swelling-induced deformations can be larger than thermally induced deformations in some packages. Numerical analysis such as finite element analysis has been used extensively to assess the reliability of microelectronic devices. The analysis must include predictive capabilities of hygroscopic swelling if relative humidity is present in the field condition.

5.6 Summary A novel experimental procedure utilizing a whole-field displacement measurement technique was implemented to determine the coefficient of hygroscopic swelling of five commercially available mold compounds. The results showed significant variation (more than 100%) in the moisture content at the virtual equilibrium state but relatively small variation (less than 20%) in the coefficient of hygroscopic swelling. The technique was also used to investigate an actual plastic package with a copper lead frame to evaluate the CHS mismatch strains. The results were compared with the CTE mismatch strains. The magnitude of the stress-induced strain caused by CHS mismatch was nearly twice as large as that produced by CTE mismatch with ΔT of ∼60◦ C. Although the magnitude of the CHS mismatch strain was not large, a significant strain gradient, and thus a large stress gradient at the interface, was expected since the strain of the chip was virtually zero. Hygroscopic strains must be considered for accurate reliability assessment when plastic packages are subjected to environments where the relative humidity fluctuates.

References 1. Pecht, M.G., Nguyen, L.T., Hakim, E.B., Plastic Encapsulated Microelectronics. New York, NY: Wiley, 1995. 2. Ardebelli, H., Wong, E.H., Pecht, M., “Hygroscopic swelling and sorption characteristics of epoxy molding compounds used in electronic packaging,” IEEE Transactions on Components and Packaging Technology, 26(1), 206–214, 2003. 3. Wong, E.H., Chan, K.C., Rajoo, R., Lim, T.B., “The mechanics and impact of hygroscopic swelling of polymeric materials in electronic packaging,” Proceedings of the 50th Electronic Components and Technology Conference, Las Vegas, NV, pp. 576–580, 2000. 4. Stellrecht, E., Han, B., Pecht, M., “Measurement of the hygroscopic swelling coefficient in mold compounds using moiré interferometry,” Experimental Techniques, 27(4), 40–44, 2003. 5. Stellrecht, E., Han, B., and Pecht, M., “Characterization of hygroscopic swelling behavior of mold compounds and plastic packages,” IEEE Transactions on Components and Packaging Technology, 27(3), 499–506, 2004.

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6. Post, D., Han, B., Ifju, P., High Sensitivity Moiré: Experimental Analysis for Mechanics and Materials. Mechanical Engineering Series, New York, NY: Springer, 1994. 7. Post, D., Han, B., Ifju P., “Moiré methods for engineering and science—Moiré interferometry and shadow moiré,” Chap. 7, Photomechanics for Engineers, edited by Rastogi, P. New York, NY: Springer, 2000. 8. Cho, S.M., Cho, S.Y., Han, B., “Observing real-time thermal deformations in electronic packaging,” Experimental Techniques, 26(3), 25–29, 2002. 9. Cho, S.M., Han, B., Joo, J., “Temperature dependent deformation analysis of ball grid array package assembly under accelerated thermal cycling condition,” Journal of Electronic Packaging, Transaction of the ASME, 126, 41–47, 2004. 10. Post, D., Wood, J., “Determination of thermal strains by moiré interferometry,” Experimental Mechanics, 29(3), 318–322, 1989. 11. Joh, D., “Optical–precision alignment of diffraction grating mold in moiré interferometry,” Experimental Techniques, 16(3), 19–22, 1992. 12. Stellrecht, E., “The measurement of hygroscopic swelling in plastic encapsulated microelectronics using moiré interferometry,” MS Thesis, University of Maryland, 2003. 13. Han, B., “Recent advancement of moiré and microscopic moiré interferometry for thermal deformation analyses of microelectronics devices,” Experimental Mechanics, 38(4), 278–288, 1998.

Chapter 6

Characterization of Interfacial Hydrothermal Strength of Sandwiched Assembly Using Photomechanics Measurement Techniques X.Q. Shi, X.J. Fan, Y.L. Zhang, and W. Zhou

6.1 Introduction Flip chip on board (FCOB) designs are being widely used because of their merits, such as high I/O number and small package size. The package is plastically underfilled by epoxy-based material to minimize the consequences of the thermal expansion (contraction) mismatch between the low-expansion chip and high-expansion substrate and to protect the solder joint interconnections from the elevated thermally induced stresses and harsh environmental conditions. The reliability problems, as far as the mechanical performance of solder joints is concerned, are somewhat relieved owing to the underfill adjacent interfaces [1]. Although plenty of effort has been done to address the reliability of the package, the package is still susceptible to the harsh environment, such as moisture conditioning especially under the elevated temperature. Moisture migrating into the plastic packages adversely affects the package reliability. The ingressed moisture causes swelling, degradation of material properties, the popcorn phenomenon, and the loss of interfacial strength and aggravates the possibility of the interfacial delamination during the manufacturing processes and operation. Polymeric materials swell at different rates upon absorbing moisture. The different swelling rates induce the strain and stress, similar to the CTE mismatch [2]. In addition, moisture alters the thermal and mechanical properties of the organic materials, such as coefficient of thermal expansion (CTE), glass transition temperature, Tg, and Young’s modulus. This alteration could result in high thermal stresses in the plastic packages. Moreover, the vapor pressure is responsible for the possible popcorn cracking. The stress generated by the vapor pressure during the solder reflow process can trigger (“activate”) the inherent defects, such as voids and weak joints, and delaminate at the interface [3]. The vapor pressure evolution has been established based on modeling and on a micromechanics approach [3]. Last but not the least, moisture has an adverse effect on the interfacial adhesion, thereby

X.Q. Shi (B) e-mail: [email protected]

X.J. Fan, E. Suhir (eds.), Moisture Sensitivity of Plastic Packages of IC Devices, Micro- and Opto-Electronic Materials, Structures, and Systems, C Springer Science+Business Media, LLC 2010 DOI 10.1007/978-1-4419-5719-1_6, 

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accelerating the possible delamination by deteriorating the polymer interfaces in the package [4–6]. A comprehensive review of moisture-induced failures in electronic packaging could be found in [2]. Many finite element analysis (FEA)-based studies have been conducted to understand the hygrothermal behavior of plastic packages. The results are irradiative to the knowledge of moisture-induced reliability problems. With an appropriate thermal–moisture analogy, moisture diffusion in the polymeric material can be modeled based on the thermal diffusion function of the FEA software. The FEA approach data agree well with the experimental data [7, 8]. To handle the discontinuity of moisture concentration between different adjacent materials, a more general method, the so-called direct concentration approach (DCA), has been recently developed to investigate the moisture absorption, desorption, and diffusion during soldering reflow process for a stack-die chip scale package [7]. On the other hand, it was reported that the decrease in the interfacial adhesion was up to 50% after a long period of aging [4]. It is of interest that a limit exists on moisture-induced strength degradation, beyond which no further degradation occurs [9]. The possible explanation is that the degradation is related to the nature of moisture diffusion, which is Fickian. The above efforts and developments have remarkably improved the knowledge of moisture-induced interfacial problem. However, in order to improve the interfacial reliability, apart from the numerical analysis, it is necessary to realistically understand the failure mechanisms of the FCOB package under the hygrothermal aging. This could be done using the advanced optical measurement techniques. Few studies have taken the time effect into consideration, even though the underfill exhibits the viscoelasticity under hygrothermal aging, which is normally carried out under high temperature for long time. The difficulties of experimental work may exist inherently, since the hygrothermal deformation is a three-dimensional phenomenon, which is affected by the moisture diffusion. It has been estimated that, if the structural response under the saturated condition with Csat can be understood, it is possible to evaluate the reliability status of the assembly under the varying unsaturated moisture concentrations. Therefore, an initial study should be carried out based on the two-dimensional in-situ measurements under an assumption of saturated moisture concentration on the in-plane surface. This assumption should be consistent with the boundary condition applied in the finite element analysis. The delaminated assembly has to be of a particular concern, since the initiation of the delamination or the existence of inherent defects is expected to further degrade the thermal, mechanical, and electrical performance of the package. It should be pointed out, however, that the fracture behaviors under the moisture conditioning have not been well elaborated yet. The experimental technique combined with an appropriate fracture mechanics theory is thought to be a bottleneck in the study of the behavior and performance of a fractured package. In this chapter, a developed moiré interferometry (MI) system with interfacial fracture mechanics method was used to investigate the fracture behavior of a sandwiched assembly under the hygrothermal aging. In order to investigate the time

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effect on the delaminated assembly, the thermal aging study was simultaneously implemented. The representative deformation and stress intensity factors (SIFs) showed that the moisture-induced swelling played a crucial role in the interfacial reliability, in addition to the CTE mismatch between the materials. It is more of importance that the isolation of the time effect and the hygroscopic swelling effect indicated that the time effect was beneficial to alleviate the possibility of a fracture. The positive aspect of the time effect is that the conventional FEA might overestimate the moisture-induced stress compared to the situation when the time effect is not included. Efforts were conducted to measure the critical interfacial fracture toughness between silicon/underfill using the digital image correlation (DIC) technique and to evaluate the possibility of fracture after the hygrothermal loading. The results showed the moisture content diffusing into the assembly had greater potential of the interfacial delamination compared to dry specimens. Finally, the fracture morphologies were studied using a scanning electron microscope (SEM) and remarkable changes of the failure mode were observed.

6.2 Interfacial Fracture Mechanics Approach Interfacial fracture mechanics approach is often employed to determine the resistance of an interface to fracture [10]. For the interface crack shown in Fig. 6.1, the relative crack displacement δ at a distance of r behind the crack-tip (θ = π) is expressed as [11] δ = δy + iδx =

8 (1 + 2iε) cosh (π ε)



r K r iε , 2π E∗ L

(6.1)

where δ x and δ y are the crack-tip opening displacements (CTODs) in the x- and y-directions, respectively; ε is related to material properties defined in [12]. E∗ is the effective Young’s modulus given by

Fig. 6.1 Interface crack problem

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2 1 1 = + , E∗ E1 E2

(6.2)

with Ei = Ei /(1 − νi ) for the plane strain and Ei = Ei for the plane stress. K is the nominal complex interfacial stress intensity factor (SIF) defined as K = K1 + iK2 ,

(6.3)

where K1 and K2 are the nominal mode I and mode II SIF, respectively, and i is the “imaginary unity.” By solving equation (6.1), the individual SIF is obtained: 

       K1 = A cos εIn rL + B sin εIn rLD , K2 = B cos εIn r L − A sin εIn r L D

(6.4)

where ⎧ ⎪ ⎪ ⎨

A = δy − 2εδx B = δx + 2εδy .  8 ⎪ r ⎪ ⎩D = ∗ E cosh (π ε) 2π

(6.5)

Once the deformations around the crack-tip are known, it is possible to evaluate the K1 and K2 parameters. Note that the K1 and K2 in equation (6.4) are nominal SIFs with respect to a distance r from the crack-tip. The exact solutions for the K1 and K2 values at the crack-tip are supposed to be obtained through the extrapolation according to the nominal SIFs as a function of the distance r away from the crack-tip [13]. The effective stress intensity factor Keff is related to the mode I and mode II stress intensity factors as [14] Keff =

 K12 + K22 ,

(6.6)

and the phase angle is defined as ψ = tan−1



Im(Kliε ) Re(Kliε )

 .

(6.7)

β =0

Although the underfill used in this study exhibited significant viscoelastic behavior, the previous investigations [15] demonstrated the validity of linear interfacial fracture mechanics for the interfacial strength analysis.

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6.3 Photomechanics Measurement Techniques 6.3.1 Moiré Interferometry An integrated multi-functional micro-moiré interferometry (M3 I) system was developed, by combining the MI technique with thermoelectric heating and cooling technique (for thermal cycling), the humidity system (for hygrothermal aging), and the microscopic imaging technique, to investigate the interfacial reliability of a sandwiched assembly. The schematic diagram of M3 I system is shown in Fig. 6.2. A miniaturized moisture chamber with ultrasonic humidity excitation was developed to control the hygrothermal conditions within the error of 0.1◦ C and 1%RH. With the system, U and V field moiré fringe patterns can be obtained, and the displacements and strains can be determined as [16] Nx (x, y) , 2f Ny (x, y) V (x, y) = , 2f   1 ∂Nx (x, y) ∂U (x, y) = , εx (x, y) = ∂x f ∂x U (x, y) =

(6.8a) (6.8b)

(6.9a)

Fig. 6.2 Schematic diagram of the M3 I system: 1: computer; 2: driver of phase shifter; 3: microscopic imaging device; 4: phase shifter; 5: moiré interferometer; 6: temperature and humidity controller; 7: six-axis fixture; 8: miniature humidity chamber; 9: chamber support; 10: ultrasonic humidity excitation; 11: optical table

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εy (x, y) = γxy (x, y) =

  1 ∂Ny (x, y) ∂V (x, y) = , ∂y f ∂y

  ∂U (x, y) ∂V (x, y) 1 ∂Nx (x, y) ∂Ny (x, y) + = + , ∂y ∂x f ∂y ∂x

(6.9b)

(6.9c)

where f is the frequency of specimen grating; Nx (x, y) and Ny (x, y) are the fringe orders in the U(x, y) and V(x, y) field moiré patterns, respectively; εx (x, y), εy (x, y), and γxy (x, y) are the normal strain fields in the x- and y-directions and the shear strain field in the x−y plane, respectively.

6.3.2 Digital Image Correlation (DIC) Digital image correlation (DIC) is a technique to measure displacement by correlating with a pair of digital speckle patterns obtained at two different loading conditions and searching for the maximum correlation coefficient C [17]. Since the common coarse-fine search algorithm uses the full-field search and tries many combinations of deformation variables, the calculation becomes time-consuming. Based on our previous work [18, 19], a line search algorithm was developed to improve

Fig. 6.3 Schematic diagram of the integrated μ-DiSC system: 1: computer 1; 2: computer 2; 3: INSTRON microtester; 4: heater; 5: CCD camera; 6: light source; 7: six-axis fixture; 8: microscope; 9: illuminator; 10: attemperator; 11: pedestal

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search accuracy and computational time, which made real-time measurement possible. The bi-cubic spline interpolation method was employed to smoothen the surface of gray-level distribution and determine the maximum correlation coefficient C. The overall arrangement of the experimental setup is schematically shown in Fig. 6.3.

6.4 Experimental Procedures for Interfacial Hydrothermal Strength Characterization 6.4.1 Specimen Preparation Silicon/underfill/FR-4-sandwiched assemblies were prepared as shown in Fig. 6.4. The solder joints were removed from the specimens to simplify the study, since it was found that solder joints played a small role in the warpage of the underfilled flip chip package, while the underfill epoxy played a dominant role [20]. The attention was drawn on the interfacial delamination behavior between the silicon and the underfill materials. The assembly consisted of three materials, namely, silicon, underfill, and FR-4. A commercialized epoxy-based underfill material supR was used in this study. The composition of the material was 60% plied by Loctite

Fig. 6.4 Schematic diagram of the assembly to be studied: (a) flip chip package and (b) silicon/underfill/FR-4 assembly

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epoxy with 40% silica filling from 1 to 4 μm in size. The glass transition temperature (Tg ) of the underfill was determined using differential scanning calorimeter (DSC) to be 105◦ C [21]. The material properties for underfill, silicon, and FR-4 have been indicated in [22]. For the underfill material, the linear relation exists between the hygroscopic strain and moisture concentration. Therefore, the coefficient of moisture expansion (CME) of the underfill is determined to be 0.31 cc/g. A thermal gravimetric analyzer (TGA) and a thermomechanical analyzer (TMA) were used. The dimensions of the assembly were 8 mm(L)×5 mm(W)×1.8 mm(H). The thickness of the underfill was 0.5 mm. No enhanced resistance to progressive debonding was observed under temperature loading [23]. A “pre-crack” was introduced at the silicon/underfill interface by using a 20-μm-thick piece of silicon rubber film. The length a and the ligament of w in front of the crack-tip were 2.7 and 5.3 mm, respectively. This satisfies a, w > H + h + t condition, where H, h, and t are the thickness of the FR-4, the silicon wafer, and the underfill layer, respectively. The selection of these dimensions was such that the edge effects on loading could be neglected. Under these conditions, a steady-state solution was considered to be valid, and the dependence of the stress intensity factors (SIFs) on the crack length could be eliminated [24]. A dispenser and a curing oven were employed to prepare the test specimens. By following flip chip packaging process, an optimized curing condition was defined to be at 165◦ C and 8-min long. Due to the capillary effect, the underfill was dispensed into the gap between the silicon and FR-4. When the specimen was partially cured, the rubber was quickly removed from the specimen and a sharp crack was introduced. After fabrication, each assembly was carefully polished with a fine SiC paper to remove excessive underfill and to obtain the desired dimensions.

6.4.2 Measurement of Thermal and Hygrothermal Deformation The M3 I system was employed to determine the deformation field around the interfacial crack-tip of the assembly subject to thermal and hygrothermal loadings. Specimen grating with a frequency of 1,200 lines/mm was replicated onto the surface of the assembly at room temperature. The assembly was then put for 168 h into the miniaturized moisture chamber with the hygrothermal loading conditioned at 85◦ C/85%RH. The moiré fringe patterns were captured at the times of 0, 1, 3, 7, 11, 24, 48, 96, and 168 h. In order to eliminate the time effect, i.e., the creep of the underfill material, a thermal aging test was carried out for the same assembly, and the moiré fringe patterns were acquired at the same time intervals. The aging temperature was 85◦ C. The humidity level under the thermal aging test was 18%, which was expected to cause negligible moisture absorption in the assembly.

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6.4.3 Determination of Critical Interfacial Fracture Toughness The DIC technique was combined with a sandwiched Brazil-nut (SBN) fixture for characterization of the critical interfacial fracture toughness of silicon/underfill interface under different mixed-mode loading conditions. The sandwich structure was made of silicon/underfill/silicon with a 4-mm pre-crack manufactured at the silicon/underfill interface. The thickness of the underfill was chosen to be 0.5 mm. This is consistent with the specimen thickness in the moiré experiment. The SBNs were aged under 85◦ C/85%RH in a hygrothermal chamber for 168 h beforehand. Artificial speckle patterns were subsequently generated on the specimen surface using white paint and carbon particles to create images with high contrast of gray level, as shown in Fig. 6.5. R The interfacial fracture tests on the samples were conducted with INSTRON micro-tensile machine at room temperature. A high-resolution CCD camera was used to capture speckle patterns at different load levels. With the curve, the speckle pattern at the load level where the interface crack opened could be obtained. This pattern and the initial speckle pattern were used as undeformed and deformed images. With the correlation software, the displacement fields around the crack-tip could be determined [18]. Fig. 6.5 Typical digital speckle pattern of SBN at the crack-tip

6.5 Interfacial Hydrothermal Strength of Sandwiched Assembly 6.5.1 Hygrothermal Displacement of the Assembly The fringe patterns in x- and y-directions at the initial state (t = 0, 85◦ C/dry) and at different time intervals are shown in Fig. 6.6. The number of observed fringe orders increased at the beginning. It was believed to be the result of the swelling of the underfill material upon moisture absorption. When water ingressed into the

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Fig. 6.6 Fringe patterns during hygrothermal aging under 85◦ C/85%RH

epoxy-based underfill, it broke the interchain bonds by forming hydrogen bonds with chain interruption [25]. The formation of hydrogen bonds permitted the resin network to expand through relaxation of the stresses produced by osmotic pressure [26]. Afterward, the increase in the fringe orders was not significant. First, it was found from the experimental results that the absorption property of the underfill was Fickian as shown in Fig. 6.7. Second, the modulus of the underfill material gradually decreased due to the viscoelasticity of the underfill. The combination of both factors lead to inapparent increase in the moiré patterns. The characterization procedures of the moisture properties of the underfill are described in detail in JEDEC standard JEDEC 22-A120. Note that since the moisture diffusion of underfill material in

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Fig. 6.7 Weight gain and Fickian curve fit at 85◦ C/85%RH for underfill

the sandwiched specimen was predominantly one dimensional, the moisture uptake was described by equation (6.10), which was an asymptotic curve as a function of time [27]:   ∞ 1 Mt 8  Dz t 2 =1− 2 exp − 2 [(2n + 1)π ] , Msat π (2n + 1)2 z0 n=1

(6.10)

where D is the diffusion coefficient, z0 is the total film thickness, Mt is the total mass of the diffusing substance absorbed by the sample at time t, and M∞ is the equilibrium mass of the absorbed substance. It was concluded that the initial amount of the moisture uptake caused most of the swelling in the underfill. With the slowing down in the rate of moisture absorption and the amount of the absorbed moisture for a long period of time, the corresponding swelling-induced deformation became inconspicuous. As an evidence, the normal and shear strains at the leftward edge of silicon/underfill interface were determined on the basis of equation (6.9). The results were plotted in Fig. 6.8. As one could see, the strains increased as the time progressed. Both the normal strain and the shear strain showed similar trends, which was in an asymptotic manner. They were analogous to the moisture diffusion in the underfill, since moisture absorbed by the underfill had physical reaction with the interchain bonds and therefore causes swelling [25]. This observation physically, apart from chemical point of view, proved that the swelling of underfill was related to the concentration of the diffused moisture.

6.5.2 Thermal Deformation of the Assembly The objective of the study of the thermal deformation was to understand the time effect on the reliability of the assembly under the hygrothermal aging. The representative fringe patterns under different intervals are shown in Fig. 6.9. The normal and

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Fig. 6.8 Strain gradients at the leftward of silicon/underfill interface in hygrothermal aging (85ºC/85%RH): (a) εx and (b) γxy

U field

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Fig. 6.9 Representative fringe patterns under the thermal aging test (168 h under 85◦ C)

the shear strains at the left of the silicon/underfill interface are plotted in Fig. 6.10. It can be seen from Fig. 6.9 that, analogous to the hygrothermal aging effect, the time effect was significant at the beginning. The strains decreased fast, since the stresses caused by thermal mismatch of the dissimilar materials in the test samples were initially large. As the time went on, the time effect became less obvious. Up to 60–70% decrease in the induced strain occurred at the first 3 h. The remainder released during a relatively long period due to the stress relaxation. Therefore, it was concluded that the thermal aging, which was related to the stress relaxation during aging under the high temperature, helped to gradually reduce the magnitude of the deformation of the sandwiched structure. Wang et al. [28] reported the similar results: FCOB assembly without pre-crack exhibited a significant time effect under high aging temperature, and the stress relaxation happened rapidly at the very beginning of testing that lasts for several hours.

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Fig. 6.10 Strain gradients at the leftward of silicon/underfill interface thermally aged at 85ºC: (a) εx and (b) γxy

The superposition principle has been widely used to separate the deformation caused by thermal aging from that caused by the hygroscopic swelling [1]. With the consideration of stress relaxation, the actual swelling-induced strains were expected to be greater than those measured during the hygrothermal aging (Fig. 6.11). In this figure, the decreases in the strains induced by thermal aging were added to the strains measured in hygrothermal aging. As a result, the values of swellinginduced strains were enlarged 20–30%. It is therefore thought that the time effect should be considered in the case of hygrothermal aging. This is beneficial to the assembly reliability, since it reduces the strains due to the material swelling during moisture ingress. It is necessary to include the time effect, when FEA simulation is performed, otherwise the hygrothermal effect might be unjustifiably overestimated.

pure swelling induced γxy pure swelling induced εx

γxy in hygrothermal aging

εx in hygrothermal aging

εx in thermal aging

a) εx

γxy in thermal aging

b) γxy

Fig. 6.11 Swelling-induced strains by using superposition method: (a) εx and (b) γxy

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6.5.3 Fracture Toughness of the Assembly Under Hygrothermal Aging Adhesion at the interface could be remarkably reduced after moisture conditioning [29, 30]. When the interface toughness is measured as a result of hygrothermal aging, it is convenient to quantitatively evaluate the potential of fracture propagation by comparing with the critical interfacial fracture toughness and thus understand the reliability of the silicon/underfill interface under the moisture attack. Based on the displacement fields obtained by the moiré test, the nominal K1 and

K2 values can be determined using equations (6.1), (6.2), (6.3), (6.4), (6.5), (6.6), and (6.7) for any given distance r from the crack-tip. According to equations (6.1), √ (6.2), (6.3), and (6.4), K1 and K2 are proportional to r, as shown in Fig. 6.12.

It is noticed that √ the value of the nominal K2 value increased as the square root of the distance r, while K1 remained unchanged. The K1 and K2 at the crack-tip can be obtained using extrapolation based on the nominal K1 and K2 with respect to the distance r from the crack-tip [13]. As one could see from √ Fig. 12, the nominal SIFs showed an approximate linear relationship with r. The extrapolation method can then be employed to determine the interfacial fracture toughness at the crack-tip [18]. By curve fitting, the experimental results were extrapolated to r = 0, representing the interfacial toughness K1 and K2 at the crack-tip. With this method, the values of SIFs at different hygrothermal aging times were determined. The results are presented in Fig. 6.13. It was concluded that the majority of the increase in the interfacial fracture toughness took place at the early stage of aging, which is the same as the strain gradients calculated at the interface. K1 increased by 33% and K2 increased by 23%, respectively. Both K1 and K2 increased in an asymptotic manner, i.e., similar to the moisture diffusion in the underfill material. On the other hand, the asymptotic curve suggested that the change in the fracture behavior caused by moisture absorption was rather gradual than instant, although the measured in-plane surface was at the boundary of the saturated moisture concentration.

Fig. 6.12 Representative extrapolation method according to linear relationship under the 85◦ C/85%RH after 168 h

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Fig. 6.13 K1 and K2 with respect to different hygrothermal aging times (85ºC/85%RH)

The values of SIF under the thermal aging were determined and the results are plotted in Fig. 6.14. Both the K1 and K2 decreased faster at the beginning. It was assumed that the creep behavior of the underfill and the solder joints greatly relieved the stress and thereby prevented the interface cracking [28]. Likely, it was observed, for an assembly with crack, that the time effect could considerably affect the interface toughness, although the change in the CTODs was insignificant. Thus, the analyses of the strains and the SIFs showed that the time effect was significant in the hygrothermal aging, especially at the high temperature. In addition, it can be seen that the influence of stresses or fracture parameters on time effect was comparable to that on hygrothermal-induced swelling. Therefore, the results indicated that the interfacial fracture toughness affected by the moisture swelling could possibly be overestimated if the time effect is not considered. Since the interface toughness is an important parameter to evaluate the life of an assembly during thermal cycling, the greater value of the stress intensity factor will eventually result in shorter reliability life. Therefore, if the overestimated interface toughness

Fig. 6.14 K1 and K2 with respect to different thermal aging times (85ºC)

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is used to calculate the fatigue life under moisture conditioning, the reliability issues tend to be more severe and give improper estimation. Viscosity (time–temperature behavior) of the underfill material should be always included into the reliability assessments.

6.5.4 Critical Interfacial Fracture Toughness of the Assembly As long as the values of the parameters of the interfacial fracture toughness under the process of hygrothermal aging were determined, it was easy to estimate the possibility of fracture propagation by comparing the actual fracture toughness with its critical value. Based on the μ-DiSC system and interfacial fracture mechanics, the CTODs obtained in the fracture test were calculated and compared with the critical interfacial fracture toughness with respect to different phase angles. Brazil-nut specimens were used to achieve this variety. The linear extrapolation method was also employed to obtain SIFs at the crack-tip. The measured results are shown in Fig. 6.15. It could be seen that the critical interfacial fracture toughness K1C and K2C followed the ellipse law with respect to different phase angles. By varying the loading angles, different mode mixities were achieved. However, the K1C decreased slowly when K2C increased by changing the loading angle from 90 to 20◦ . This indicated that the K1C played a more critical role in the determination of critical interfacial fracture toughness than K2C . As a result of the hygrothermal aging, the critical interfacial fracture toughness decreased significantly compared to the critical interfacial fracture toughness of dry specimens tested at the room temperature [31]. After 168 h of exposure at the 85◦ C/85%RH, the interfacial adhesion was decreased on average 34.9% for the silicon/underfill interface. Other authors also observed the significant decrease [4], which indicated that the moisture could penetrate into the defects and remarkably decrease the interfacial strength by intercepting the

Fig. 6.15 Critical interfacial fracture toughness of dry and wet (85◦ C/85%RH) SBN specimens

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inter- and intra-molecular hydrogen bonding provided by the hydroxyl groups [25]. It has been demonstrated that the hygrothermal loading would increase the possibility of interfacial delamination in a flip chip package. More significant decrease occurred in mode I (36% for pure mode I fracture and 32% for pure mode II fracture). This means that more severe reliability issues lie in the opening mode. The possible explanation of this phenomenon is due to a displacement-type reaction where water molecules displace the polymer chain in the van der Waals bonding of the polymer adhesive to the glass surface [32]. In order to demonstrate this circumstance, the fracture morphology was to be studied in the next section. Based on the interface toughness parameters K1 and K2 measured by the moiré experiment and the critical interfacial fracture toughness K1C and K2C measured by the μ-DiSC system, it is easy to assess the likelihood of failure by combining the results together. As seen in Fig. 6.16, the interface toughness fell inside the area defined by the boundary of the critical interfacial fracture toughness and x- and yaxes, indicating the interface was safe under the 168-h exposure in 85◦ C/85%RH hygrothermal environment. However, the figure, on the other hand, indicated that the possibility of the interface delamination increased, when the interface toughness increased, by about 24.9% after 168-h aging, and the critical interfacial fracture toughness decreased by about 34.5%.

Fig. 6.16 Failure assessment based on interface toughness and critical interfacial fracture toughness

6.5.5 Reliability of Silicon/Underfill Interface of the Assembly It was found that the major fracture-related failure mode was interfacial delamination with respect to all loading angles. These modes were similar to those observed in dry specimens tested at 125◦ C [31]. However, from the microscopic point of

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view, the morphologies of the interfacial delamination in dry and moisture-sensitive test specimens were surprisingly different. For the delamination that occurred at 125◦ C, it was observed that granular bulges were distributed over the whole fractured interface of the underfill part of the dry sample, as shown in Fig. 6.17a. It indicated that the chemical bonding was destroyed by high stresses at break, which exceeded the local yield stress of underfill material. However, the fracture morphology of a hygrothermal-aged sample showed smooth surface without granulae (Fig. 6.17b). The stresses causing debonding were not large enough to make the underfill material yield locally. From the mechanical point of view, the absorbed moisture led to the bonding interception. This observation also demonstrated that moisture could hydrolyze the chemical bonding between the underfill and the silicon apart from making epoxy-based underfill swell, as has been determined from the moiré experiment.

Fig. 6.17 Fracture morphology of interfacial delamination: (a) interfacial delamination of dry specimen under 125◦ C and (b) interfacial delamination of hygrothermal-aged specimen under the room temperature

6.6 Summary The developed multi-functional micro-moiré interferometry (M3 I) system was introduced to investigate the deformation as well as the interface toughness of a cracked silicon/underfill/FR-4 assembly during 168 h of exposure at 85◦ C/85%RH. The thermal aging test at 85◦ C was carried out to separate the roles of two time effects: (1) moisture diffusion-induced swelling and (2) stress relaxation caused by the viscoelasticity of underfill. The critical interfacial fracture toughness after hygrothermal aging was characterized using the digital image correlation (DIC) technique. The corresponding fracture mechanism was studied by scanning electron microscope (SEM).

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In strain calculation at the interface of silicon/underfill, it was found that both hygrothermal loading and thermal aging had a significant effect on the physical behavior and performance of the moisture-sensitive polymeric materials. It was found also that thermal aging relieved the stresses induced by the hygrothermal mismatch between the dissimilar materials involved. As a result, thermal aging effectively prevented the interfaces from the fracture propagation. Further study on fracture parameters presented the same trend as the conclusions made in strain gradients study. Since the magnitude of the strains and SIFs of thermal aging and hygrothermal loading were quantitatively comparable, time effect was supposed to be considered in hygrothermal aging. The viscoelasticity nature of the underfill material was beneficial to the assembly reliability, since it reduced the strains and the SIFs induced by material swelling during moisture ingress. In the case of simulation of hygrothermal conditioning, the creep behavior of the underfill material, i.e., viscoelastic properties of underfill material, should be included to alleviate the potential fracture threat since time effect can provide a positive impact on the reliability of the assembly. The measured critical interfacial fracture toughness showed that moisture significantly reduced the interfacial strength with comparison to the results of our previous study. The interception of the inter- and intra-molecular hydrogen bonding provided by the hydroxyl groups was thought to take place with respect to wide range of mode mixity. By combining the interface toughness and the critical interfacial fracture toughness, it was concluded that the hygrothermal loading would increase the possibility of the interfacial delamination in a flip chip package. From fracture morphology study, it was observed that granular bulges were distributed over the whole interface of the underfill part at 125◦ C in our study. However, the surface without granula was seen for hygrothermal-aged specimen tested under ambient condition. The observation indicated that moisture adversely affected the chemical bonding, e.g., hydrogen bonding, between the silicon and the underfill materials and reduced the debonding stresses.

References 1. Fan, X.J., Wang, H.B., Lim, T.B., “Investigation of the underfill delamination and cracking for flip chip module during thermal cyclic loading” IEEE Transactions of Components and Packaging Technologies, 24(1), 84–91. 2. Zhang, G.Q., van Driel, W.D., Fan, X.J., Mechanics of Microelectronics. New York, NY: Springer, 2006. 3. Fan, X.J., Zhou, J., Zhang, G.Q., L.J. Ernst, “A micromechanics based vapor pressure model in electronic packages”, ASME Journal of Electronic Packaging, 127(3), 262–267, 2005. 4. Ferguson, T., Qu, J.M., “Effect of moisture on the interfacial adhesion of the underfill/solder mask interface,” Journal of Electronic Packaging, 124, 106–110, 2002. 5. Okura, J.H., Dasgupta, A., Caers, J.F.J.M., “Hygro-mechanical durability of underfilled flipchip-on-board (FCOB) interconnects,” Journal of Electronic Packaging, 124, 184–187, 2002. 6. Fan, X.J., Zhang, G.Q., Ernst, L.J., “Interfacial delamination mechanisms during reflow with moisture preconditioning”, IEEE Transactions of Components and Packaging Technologies, 31(2), 252–259, 2008.

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7. Xie, B., Shi, X.Q., Fan, X.J., “Sensitivity investigation of substrate thickness and reflow profile on wafer level film failures in 3D chip scale packages by finite element modeling”, Proceedings of the Electronic Components and Technology Conference. ECTC ‘07, 57th, Sparks, NV, USA, May 29 2007–June 1 2007, pp. 242–248, 2007. 8. Xie, B., Shi, X.Q., Fan, X.J., “Accelerated moisture sensitivity test methodology for stackeddie molded matrix array package”, Proceedings of EPTC, Electronic Packaging Technology Conference, Singapore, 2007. 9. Park, C.E., Han, B.J., Bair, H.E., “Humidity effect on adhesion strength between solder ball and epoxy underfills,” Polymer, 38(15), 3811–3818, 1997. 10. Kuhl, A., Qu, J.M., “A technique to measure interfacial toughness over a range of phase angles,” Journal of Electronic Packaging, 122, 147–151, 2000. 11. Rice, J.R., “Elastic fracture mechanics concepts for interfacial cracks,” Journal of Applied Mechanics, 55, 98–10, 1988. 12. Dunders, J., “Edge-bonded dissimilar orthogonal elastic wedges,” Journal of Applied Mechanics, 36, 650–652, 1969. 13. Owen, D.R.J., Fawkes, A.J., Engineering Fracture Mechanics: Numerical Methods and Applications. Swansea, UK: Pineridge Press, pp. 43, 1983. 14. Williams, M.L., “The stresses around a fault of crack in dissimilar media,” Bulletin of the Seismological Society of America, 49, 199–204, 1959. 15. Shi, X.Q., Wang, Z.P., Pickering, J.P., “A new methodology for the characterization of fracture toughness of filled epoxy films involved in microelectronics packages,” Microelectronics Reliability, 43, 1105–1115, 2003. 16. Post, D., Han, B., Ifju, P., High Sensitivity Moiré: Experimental Analysis for Mechanics and Materials. New York, NY: Springer, 1994. 17. Bruck, H.A., McNeill, S.R., Sutton, M.A., Peters, W.H., “Digital image correlation using Newton-Raphson method of partial differential correlation,” Experimental Mechanics, 29, 261–267, 1989. 18. Shi, X.Q., Zhang, Y.L., Zhou, W., “Determination of fracture toughness of polymer/inorganic interface with digital image speckle correlation technique,” IEEE Transactions on Components & Packaging Technologies, 30(1), 101–109, 2007. 19. Shi, X.Q., Pang, H.L.J., Zhang, X.R., Liu, Q.J., Ying, M., “In-situ micro-digital image speckle correlation technique for characterization of materials’ properties and verification of numerical models,” IEEE Transactions on Components and Packaging Technologies, 27(4), 659–667, 2004. 20. Zhang, W., Wu, D., Su, B., Hareb, S.A., Lee, Y.C., Materson, B.P., “The effect of underfill epoxy on warpage in flip chip assemblies,” IEEE Transactions on Components and Packaging Manufacturing Technologies, Part A, 21, 323–328, 1998. 21. Shi, X.Q., Wang, Z.P., Pang, H.L.J., Zhang, X.R., “Investigation of effect of temperature and strain rate on mechanical properties of underfill material by use of microtensile specimens”, Polymer Testing, 21, 725–733, 2002. 22. Shi, X.Q., Zhang, Y.L., Zhou, W., “Reliability study of underfill/chip interface with multifunctional micro-moiré interferometry system,” Microelectronics Reliability, 46(2–4), 409–420, 2006. 23. Kook, S.Y., Snodgrass, J.M., Kirtikar, A., Dauskardt, R.H., “Adhesion and reliability of polymer/inorganic interfaces,” Journal of Electronic Packaging, 120, 328–334, 1998. 24. Hutchinson, J.W., Suo, Z.G., “Mixed mode cracking in layered materials,” Advances in Applied Mechanics, 29, 63–191, 1992. 25. Kwei, T.K., “Strength of epoxy polymer I – effect of chemical structure and environmental conditions”, Journal of Applied Polymer Science, 10, 1647, 1966. 26. Xiao, G.Z., Shanahan, W.E.R., “Swelling of DGEBA/DDA epoxy resin during hygrothermal aging,” Polymer, 39(14), 3253–3260, 1998. 27. Crank, J., The Mathematics of Diffusion, 2nd ed. Oxford: Oxford University Press, pp. 477, 1975.

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28. Wang, J., Qian, Z., Zou, D., Liu, S., “Creep behavior of a flip-chip package by both FEM modeling and real time moiré interferometry,” Journal of Electronic Packaging, 120, 179– 185, 1998. 29. Sung, Y., Goh, J.S., Yang, J.C., “Residual stresses in plastic IC packages during surface mounting process preceded by moisture soaking testing,” IEEE Transactions on Components, Packaging, and Manufacturing Technology, Part B, 20(3), 247–254, 1997. 30. Gurumurthy, C.K., Kramer, E.J., Hui, C.Y., “Water-assisted sub-critical crack growth along an interface between polyimide passivation and epoxy underfill,” International Journal of Fracture, 109, 1–28, 2001. 31. Zhang, Y.L., Shi, X.Q., Zhou, W., “Determination of fracture toughness of underfill/chip interface with digital image speckle correlation technique”, Proceedings of ECTC, Las Vegas, USA, vol. 1, pp. 140–147, 2004. 32. Kinloch, A.J., Adhesion and Adhesives: Science and Technology. New York, NY: Chapman and Hall, pp. 56–96, 1987.

Chapter 7

Hygroscopic Swelling of Polymeric Materials in Electronic Packaging: Characterization and Analysis J. Zhou, T.Y. Tee, and X.J. Fan

7.1 Introduction Polymeric materials expand upon moisture absorption. For example, it has been reported that the hygroscopic strain in an encapsulated package is nearly twice as much as the thermal strain over a temperature span of T = 60◦ C due to the hygroscopic swelling of mold compound [1]. For other mold compounds, the hygroscopic mismatch-induced strain ranges from one to nearly four times the strain induced by the thermal mismatch over a T of 45◦ C for T > Tg (glass transition temperature) or over a T = 100◦ C for T < Tg [2]. For some underfill materials, the hygroscopic swelling-induced strain is comparable to the thermal strain caused by thermal expansion over a temperature range of 100◦ C [3–5]. Hygroscopic stresses arise in an electronic package when polymeric materials swell while the adjacent non-polymeric materials, such as silicon chip, do not experience swelling [6–8]. Despite the important role of hygroscopic swelling, there have been no standardbased procedures for swelling measurements. This is partially attributed to the difficulty in setting up a humid control environment for dimensional change measurement. There are several different experimental techniques that have been developed for swelling measurements [6, 7, 9–12]. In this chapter, the characterization of hygroscopic swelling using point-measurement method is described first [6, 7]. In this method, the averaged swelling-induced strain and the averaged moisture concentration are used to determine the coefficient of hygroscopic swelling (CHS). Such an averaged method might introduce some errors in obtaining CHS [13–16]. Analytical solutions based on three-dimensional moisture diffusion analysis are introduced to evaluate the averaged method and to consider the effect of non-uniform moisture distributions during measurement. The discrepancy induced by the averaged method can be predicted by the obtained analytical solutions. Since non-uniform moisture distribution simultaneously introduces transient hygroscopic stresses due to the gradient of moisture concentration, the total measured deformation comprises both hygroscopic swelling strain and elastic strain. A sequentially X.J. Fan (B) e-mail: [email protected] X.J. Fan, E. Suhir (eds.), Moisture Sensitivity of Plastic Packages of IC Devices, Micro- and Opto-Electronic Materials, Structures, and Systems, C Springer Science+Business Media, LLC 2010 DOI 10.1007/978-1-4419-5719-1_7, 

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coupled moisture diffusion and hygroscopic stress finite element analysis is applied to simulate the hygroscopic swelling characterization process. Both hygroscopic swelling strain and elastic strain are calculated numerically. The effect of the hygroscopic stress-induced elastic deformation on the hygroscopic swelling measurement is studied. A nonlinear fully coupled hygroscopic stress modeling technique is developed.

7.2 Hygroscopic Swelling Characterization Using Point-Measurement Methods The moiré interferometry (MI) technique has been developed as an effective tool for achieving a high level of accuracy in hygroscopic swelling measurement [1, 9, 10]. Moiré interferometry measurement is able to obtain the full-field deformation by swelling (see Chapter 5 and 6). Teverovsky [11] used Archimedes principle to obtain the coefficient of hygroscopic swelling. Wong et al. [6] introduced the point-measurement method with a thermo-mechanical analyzer (TMA) and a thermo-gravimetric analyzer (TGA). Such a combined TMA/TGA method has been commonly used in semiconductor industry since standard TMA/TGA instruments are available and they are easy to implement [12]. TGA and TMA do not have humidity control, and thus the samples are preconditioned in a desired temperature/humidity condition until saturation before they are placed into TMA and TGA chambers for hygroscopic swelling measurement. Desorption will then take place during measurement. Figure 7.1 is a schematic of TMA/TGA hygroscopic swelling measurement setup. Two identical samples (same dimensions) are prepared first. The samples are placed into temperature/humidity chamber for moisture absorption until saturation. The moisture absorption time depends on the material and dimensions. After the samples are fully saturated, the specimens are desorbed at a constant temperature in TMA and TGA, respectively. In TMA chamber, the specimen thickness decreases with time due to moisture desorption. A time history of thickness change can be recorded automatically with a TMA. At the same time,

Thermal Mechanical Analyzer

TMA h

h

εave = Δh/h time

TGA

M

ΔM

Moisture absorption Thermal Gravimetric Analyzer

Fig. 7.1 TMA/TGA hygroscopic swelling measurement setup

Cave = ΔM/V time

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another saturated specimen is placed into a TGA chamber. With moisture diffusing out of the material, the mass of the specimen decreases with time. A time history of mass change can be recorded automatically with a TGA. The averaged hygroscopic swelling strain in thickness direction and the averaged moisture mass in samples can be defined as follows: hsat − h(t) , hsat

(7.1)

Msat − M(t) , V0

(7.2)

εave = Cave =

in which the average strain is defined and calculated with respect to a reference state of a fully saturated condition. hsat and Msat are the thickness and the moisture mass of specimen at time zero, respectively, when the specimen is fully saturated. Since TMA and TGA are continuous measurements with time, the averaged hygroscopic strain versus the averaged moisture concentration can be plotted in an X–Y graph, as shown in Fig. 7.2. The trend curve defines the relation between hygroscopic swelling and moisture content. If a linear relation exists between the two, then coefficient of hygroscopic swelling β (CHS, or coefficient of moisture expansion, CME) can be defined as the slope of the curve as follows: εave = βCave .

(7.3)

Figure 7.3 is an actual TMA/TGA data set for a no-flow underfill [7]. The samples are preconditioned with moisture under 85◦ C/85%RH for about 2 weeks. Then the samples are monitored for desorption under TMA and TGA, respectively, and at the same time under 85◦ C constant temperature for about 1 day. The first y-axis in Fig. 7.3 is TGA reading and the second y-axis on the right is TMA reading. It can be seen that the mass change is in microgram and the dimensional change is

ave. strain 0.0012 0.0008 0.0004

Fig. 7.2 A typical average strain/average moisture content plot from TMA/TGA desorption test

0 0.0

1.0

2.0

3.0

4.0

ave. moisture concentration (mg/cm3)

5.0

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TGA and TMA Curves TGA (mg)

TMA (mm) 1.1523

36.07

TGA

36.02

TMA

1.1518 1.1513

35.97

1.1508

35.92

1.1503

35.87

1.1498

35.82

1.1493

35.77

1.1488

35.72 0

200

400 600 Time (min)

800

1.1483 1000

Fig. 7.3 TGA and TMA curves for a no-flow underfill at 85◦ C

Graph of Strain vs. Concentration Strain 0.004 y = 0.31x R2 = 0.99

0.003 0.002 0.001 0 0

0.002

0.004 0.006 0.008 Concentration (mg/mm3)

0.01

0.012

Fig. 7.4 Computation of coefficient of hygroscopic swelling

in sub-micrometer. TMA and TGA are high-resolution instruments capable of handling small specimen. The averaged strain and moisture mass can be calculated from equations (7.1) and (7.2), and Fig. 7.4 can be produced to obtain the coefficient of hygroscopic swelling. In this plot, the origin point is time zero data since saturation state is used as reference state in equations (7.1) and (7.2). Table 7.1 lists the results of the coefficient of hygroscopic swelling measured for various materials [7]. It shows that the coefficient of hygroscopic swelling does not have direct correlation with the amount of moisture absorbed. Some materials absorb more moisture, but have less ability to swell (smaller coefficient of hygroscopic swelling). Some materials absorb less moisture, but swell more. The final hygroscopic strain is the product of the CHS and the saturated moisture concentration.

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Table 7.1 Moisture and hygroswelling material properties at 85◦ C/85%RH Materials

D (mm2 /s)

Csat (mg/mm3 )

CHS (mm3 /mg)

Hygro-strain (Csat × CHS)

Underfill A Underfill B Underfill C Mold compound Solder mask BT substrate

9.02e6 1.55e6 1.14e5 2.79e6 4.83e5 2.13e6

0.0152 0.0329 0.0112 0.0043 0.0143 0.0075

0.18 0.22 0.31 0.4 0.2 0.4

0.0027 0.0072 0.0035 0.0017 0.0029 0.0030

Although it seems to be a good linear fit from Fig. 7.4 to obtain the coefficient of hygroscopic swelling, there are some problems with this method. First, moisture distribution is not uniform across test specimen during desorption in TMA and TGA measurements. During desorption, on the exterior of the specimen surface moisture concentration is zero, but at the center of the specimen, moisture concentration is the highest. It is necessary to understand the effect of non-uniform moisture distribution in determining CHS. Second, moisture concentration gradient introduces hygroscopic swelling mismatch in a homogeneous material; therefore, a mechanical deformation is produced. This means that the measured thickness change during desorption consists of both mechanical deformation and hygroscopic deformation [13–17]. In the following sections, the effects of non-uniform moisture distribution and the elastic deformation during desorption are studied.

7.3 Effect of Non-uniform Moisture Distribution in Determining CHS 7.3.1 Moisture Distribution Consider a rectangular specimen used in TMA measurement, with a dimension hx × hy × hx , as shown in Fig. 7.5. The thickness hx is usually smaller than hy and hz to allow fast desorption and one-dimensional analysis. For a desorption process, the moisture concentration inside the specimen is initially saturated at time zero, that is, C = Csat , where Csat is the saturated moisture concentration of the material. The specimen is then exposed to an absolutely dry environment. The moisture concentration on the exposed faces instantaneously reaches zero. The governing equations for moisture distribution and the initial and boundary conditions for the desorption process are presented by [13]   2 ∂ C ∂ 2C ∂ 2C ∂C . =D + + ∂t ∂x2 ∂y2 ∂z2

(7.4)

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Fig. 7.5 A three-dimensional rectangular specimen in TMA/TGA CHS measurement z

y x

I.C.: C(x, y, z, 0) = Csat .

(7.5a)

B.C.s: C(0, y, z, t) = C(hx , y, z, t) = 0 C(x, 0, z, t) = C(x, hy , z, t) = 0 ,

(7.5b)

C(x, y, 0, t) = C(x, y, hz , t) = 0 where C is the local concentration (g/mm3 , weight of water per unit volume in bulk material); x, y, z are coordinates (mm); D is the moisture diffusivity (mm2 /s); and t is the time (s). The analytical solution for this three-dimensional problem can be obtained as follows [13]: 43 Csat C(x, y, z, t) = π3



  (2n + 1)π x 1 Dt 2 2 sin exp − 2 (2n + 1) π (2n + 1) hx hx n=0  ∞   (2n + 1)π y 1 Dt 2 2 sin exp − 2 (2n + 1) π . (2n + 1) hy hy n=0 ∞    (2n + 1)π z 1 Dt sin exp − 2 (2n + 1)2 π 2 (2n + 1) hz hz n=0 (7.6) ∞ 

7.3.2 Hygroscopic Swelling-Induced Deformation When TMA is used to measure the dimensional change of specimen, the probe reads the instantaneous dimension length at the center of the specimen. Since moisture distribution is not unifrom, the thickness change can be expressed as follows [13]:  hx  hy hz hx = β C x, , , t dx, 2 2 0

(7.7)

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where hx (t) = h(t) − hx ,

(7.8)

h(t) is the thickness at time t, hx is the initial thickness of the specimen at dry condition, and β is the true coefficient of hygroscopic swelling by equation (7.3).

7.3.3 Averaged Approaches In the previous section, an averaged strain and moisture concentration using equations (7.1) and (7.2) are applied to determine the coefficient of hygroscopic swelling. It is noted that equations (7.1) and (7.2) select the saturated state as reference state to obtain the averaged values. In the following, two different averaged approaches are introduced, which will yield different results. 7.3.3.1 Averaged Approach I In this method, the average strain and moisture concentration are defined, respectively, as follows: h(t) − hx hx (t) = , hx hx M(t) − M0 Mmoisture (t) = = , V0 V0

I = εave I Cave

(7.9) (7.10)

in which the averaged strain is defined with respect to the reference point in dry conditions. M(t) is the total weight of the specimen and M0 is the specimen weight in dry condition. Mmoisture is the residual moisture weight at time t and V0 is the initial specimen volume, i.e., ! V0 = hx hy hz !dry ,

(7.11)

where hx , hy , and hz are initial lengths of the specimen in three directions, respectively. The superscript I denotes the averaged approach I. The averaged coefficient of hygroscopic swelling can then be obtained by I I I = βave Cave εave

(7.12a)

or I βave =

I εave . I Cave

(7.12b)

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Thus, the averaged coefficient of hygroscopic swelling in equation (7.12b) can be re-written as  I βave = hx hy hz / C(x, y, z, t)dx dy dz. (7.13) V

We then introduce a parameter RI , which is defined as the ratio of the averaged coefficient of hygroscopic swelling (equation (7.13)) to the true coefficient of hygroscopic swelling (equation (7.7)). After some manipulations, RI can be expressed as follows: RI =

=

I βave β

∞

π 2 n=0 ∞ 4 n=0

(−1)n (2n+1)

1 (2n+1)2



 exp

− Dt (2n + 1)2 π 2 h2y

∞

  n=0 ∞ exp − Dt (2n + 1)2 π 2 h2 y

n=0

(−1)n (2n+1) 1 (2n+1)2

  2π 2 exp − Dt (2n + 1) h2 z

.  2π 2 exp − Dt (2n + 1) h2 z

(7.14) 7.3.3.2 Averaged Approach II Equations (7.1) and (7.2) can be re-written as follows: II = εave

II = Cave

hsat − h(t) , hsat

(7.15)

Msat − M(t) , V0

(7.16)

where the averaged strain is defined with respect to the reference point in a fully saturated condition. hsat and Msat are the thickness and the moisture mass of specimen at time zero when the specimen is fully saturated. The averaged coefficient of hygroscopic swelling can be obtained by II βave =

II εave . II Cave

(7.17)

Equations (7.15) and (7.16) can be re-written as follows: hsat − h(t) (hsat − hx ) − (h(t) − hx ) hx = = βCsat − hsat hsat hsat  hx  , hy hz hx = βCsat − = βCsat − β C x, , ,t dx h0 2 2

II = εave

0

(7.18)

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II = Cave

161

Msat − M(t) [Msat − M0 ] − [M(t) − M0 ] Mmoisture (t) = = Csat − Vsat Vsat Vsat  . Mmoisture (t) = Csat − = Csat − C dx dy dz V0 v

(7.19) We introduce RII as the ratio of the averaged coefficient of hygroscopic swelling to the true coefficient of hygroscopic swelling. RII can be expressed as RII =

=

II βave β





  ∞ ∞ (−1)n (−1)n Dt Dt 2π 2 2π 2 exp − (2n + 1) exp − (2n + 1) 1 − 128 4 2 2 (2n+1) (2n+1) π hy hz n=0  n=0  ∞ 1 exp − Dt (2n + 1)2 π 2 h2x (2n+1)2 n=0  ∞    ∞ 1 1 512 Dt Dt 2 2 2π 2 1 − π6 exp − (2n + 1) π exp − (2n + 1) 2 2 2 2 (2n+1) hy (2n+1) hz n=0 n=0   ∞ 1 exp − Dt (2n + 1)2 π 2 (2n+1)2 h2x n=0 (7.20)

7.3.4 Results It is interesting to note that both equations (7.14) and (7.20) are independent of the saturated moisture concentration Csat . RI and RII depend on specimen dimension and diffusivity of material only. Assume the specimen has the same length in y- and z-directions, that is, hy = hz . The aspect ratio α is defined as α = hy /hx = hz /hx .

(7.21)

First, let us discuss a special case when the size of the specimen is very large in y- and z-directions, which means aspect ratio α goes to ∞. RI in equation (7.14) and RII in equation (7.20) reduce to ∞ RI =

π 2 n=0 ∞ 4 n=0

(−1)n (2n+1)

2 2

1 (2n+1)2

(7.22)

.

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and 1− RII = 1−

128 π4

∞ n=0

∞ 512 π6

n=0

(−1)n (2n+1)

2

∞

2 1 (2n+1)2

n=0 ∞ n=0

1 (2n+1)2 1 (2n+1)2

  2π 2 exp − Dt (2n + 1) 2 h x

.  Dt 2 2 exp − h2 (2n + 1) π

(7.23)

x

As we know ∞  π ( − 1)n = arctan 1 = , (2n + 1) 4

(7.24a)

n=0

∞  n=0

1 π2 ; = 2 8 (2n + 1)

(7.24b)

thus, we have [15, 16] RI = 1 when α → ∞

(7.25)

RII = 1 when α → ∞.

(7.26)

and

The results in equations (7.25) and (7.26) imply that as long as the in-plane specimen size is much greater than the thickness, both averaged methods give the accurate estimate of the coefficient of hygroscopic swelling, even though the moisture in thickness direction is not homogeneous. However, the aspect ratio dependency will appear when the specimen is not sufficiently large. Figure 7.6 plots RI as a function of aspect ratio α, where α ranges from 2 to 50 at times 10, 100, 500, and 2,000 min, respectively. In this calculation, the diffusivity is chosen as a representative value of polymeric materials, that is, D = 4.510–6 mm2 /s. It can be seen that RI is always greater than 1. This means that approach I overestimates the value of hygroscopic swelling, in particular, when the aspect ratio is small. With larger aspect ratio, RI will be closer to 1. The longer time is taken, the more errors are introduced. This is because the specimen starts from a homogeneous moisture distribution at time zero. The moisture becomes non-uniform with time. Different from RI in equation (7.14), RII in equation (7.20) depends not only on the aspect ratio, diffusivity, and time but also on the thickness hx . Figure 7.7 plots RII as a function of aspect ratio α where α ranges from 2 to 50 at 10, 100, 500, and 1,000 min, respectively, and the thickness is taken as 1 mm. Contrary to RI , RII is always less than 1, which implies that approach II underestimates the coefficient of hygroscopic swelling. The smaller the aspect ratio, the more the inaccurate result obtained. With larger aspect ratio, RII will be closer to 1. Another difference with

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Fig. 7.6 Effect of aspect ratio for RI

Fig. 7.7 Effect of aspect ratio for RII

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RI is that the longer time is taken, the more accuracy is obtained for RII . Approach II is based on the reference point with saturation state, in which the moisture loss is employed to estimate the hygroscopic swelling property. With longer desorption time, although the moisture in specimen is highly non-uniform, the total loss of moisture approaches the saturated value. It is evident from both equations (7.14) and (7.20) that RI and RII are time dependent. Figure 7.8 plots RI and RII as functions of time with aspect ratio = 4 and thickness = 1 mm. At the beginning, the specimen is fully saturated; therefore, RI is closer to 1, while RII underestimates the value and is less than 1. With time increasing, the moisture distribution becomes highly non-uniform; errors are introduced when approach I is applied. However, RII approaches 1 with the increase of time and therefore gives more accurate results. Figure 7.8 shows that RI always overestimates the value, while RII always underestimates the value. In other words, RI and RII present an upper and a lower bound estimate in determining the true coefficient of hygroscopic swelling. It is noticed from Figs. 7.6 and 7.8 that RI has an asymptote around 2.5, which means that the maximum ratio of the averaged CHS to true CHS is 2.5 using approch I. This means with approach I, the CHS can be overestimated as much as up to 250%. The value of RII at time zero cannot be found in Fig. 7.8 because the calculation starts from 100 s. Figure 7.9 shows the RII value when the measuring time is within the first 1 min. RII changes its value dramatically from 0.23 to 0.65 during the first 1 min.

Fig. 7.8 RI and RII as a function of time

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0.7 0.65 0.6 0.55

RII

0.5 0.45 0.4 0.35 0.3 0.25 0.2

0

10

20 30 40 Measuring time (seconds)

50

60

Fig. 7.9 RII value within the first 1 min

The bound values can be obtained analytically from equations (7.14) and 7.(20), respectively. When t approaches infinity and zero, respectively, equation (7.14) gives RI =

π2 4

RI = 1

when t → ∞,

(7.27)

when t → 0.

(7.28)

Similarly, when t approaches infinity and zero, respectively, equation (7.20) gives RII = 1 when t → ∞, RII = 0.2667

when t → 0.

(7.29) (7.30)

All the above four limits are proved to be independent of the diffusivity and I and the lower bound β II , aspect ratio. Therefore β always has the upper bound βave ave that is II I ≤ β ≤ βave βave

(7.31)

π2 βI ≥ RI = ave ≥ 1, 4 β

(7.32)

or

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1 ≥ RII =

II βave ≥ 0.267 β

(7.33)

or I ≥β (t → ∞) 2.46β ≥ βave

(t → ∞)

II β ≥ βave ≥ 0.267β

(t → 0),

(7.34)

(t → 0).

(7.35)

The experimental raw data in Fig. 7.3 can be applied using the above analysis. The theoretical predictions and experimental data are presented in Fig. 7.10. It can be seen that the theory corroborates with the experimental results very well. Approach I shows more fluctuations on experimental data. Overall both averaged approaches present upper and lower bounds of the true value of coefficient of hygroscopic swelling.

7.4 Effect of Hygroscopic Stress in Determining CHS Although the above analysis calculates the hygroscopic swelling strain with the consideration of non-uniform moisture distribution, the mechanical deformation is ignored. Since moisture concentration gradient exists, it is inevitable to have both

Fig. 7.10 Experimental validation for RI and RII as a function of time

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mechanical and hygroscopic swelling deformation occurring during desorption process. The variation of thickness at the probe location in TMA measurement is the sum of the hygroscopic swelling and mechanical deformation.

7.4.1 Problem Description The specimen has a prismatic shape with lengths in three dimensions as hx = 1.0368 mm, hy = 4.25 mm, hz = 4.4 mm, respectively. The specimen is fully saturated at the condition of 85◦ C/85%RH before it is placed into a TMA chamber. The TMA chamber temperature is set at a constant temperature of 85◦ C with zero humidity. The particular interest is to find the variation of thickness at the location of specimen center, where the TMA probe is placed. As shown in Fig. 7.11, point O denotes the center of the whole specimen and point A is the surface point at the center on the outer surface. We will be especially interested in the strain and displacement along the measurement line AO or x-direction as a function of time during desorption. The hygroscopic swelling and elastic strain and displacement can be separated from finite element analysis [14, 17]. The following material properties are used. The saturated concentration Csat is 4.5010–2 mg/mm3 and moisture diffusivity is 1.210–6 mm2 /s. Young’s modulus E = 10 GPa and Poisson’s ratio is 0.3. The material is assumed to be homogeneous and linear elastic.

7.4.2 Theory – Sequentially Coupled Field Transient Analysis Considering both hygroscopic swelling strain and thermal strain, Hook’s law for an isotopic material can be expressed as follows: " # " # {ε} = [D]−1 {σ } + εhygro + εth ,

Fig. 7.11 Specimen configuration

(7.36)

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where {σ } is the stress vector,

 T {σ } = σx σy σz σxy σyz σxz ,

(7.37)

{ε} is the strain vector,

 T {ε} = εx εy εz εxy εyz εxz ,

(7.38)

[D]−1 is the flexibility or compliance matrix. Assume E is the Young’s modulus, G is the shear modulus, and ν is the Poisson’s ratio, then ⎡

[D]−1

1/E −ν/E −ν/E 0 0 0 ⎢ −ν/E 1/E −ν/E 0 0 0 ⎢ ⎢ −ν/E −ν/E 1/E 0 0 0 =⎢ ⎢ 0 0 0 1/G 0 0 ⎢ ⎣ 0 0 0 0 1/G 0 0 0 0 0 0 1/G

⎤ ⎥ ⎥ ⎥ ⎥, ⎥ ⎥ ⎦

(7.39)

  where εth is the thermal strain vector. Assume α is the coefficient of thermal expansion, T is the temperature difference, then " #  T εth = T α α α 0 0 0 ;

(7.40)



 εhygro is the hygroscopic swelling strain vector. Assume β is the coefficient of hygroscopic swelling and C is the local moisture concentration, then " #  T εhygro = C β β β 0 0 0 .

(7.41)

During hygroscopic swelling measurement, temperature is constant therefore, thermal strain is zero. The total strain contains hygroscopic strain and elastic strain. Hygroscopic strain is due to the moisture absorption, while the elastic strain is caused by hygroscopic stress due to moisture concentration gradient. This is a transient coupled field analysis between structural and moisture diffusion fields. Moisture diffusion is modeled using standard transient diffusion, which follows the same governing differential equation as the diffusion of heat, but the dependent variable or temperature is replaced by moisture concentration and the thermal diffusivity is replaced by moisture diffusivity. Sequential finite element analysis is adopted to solve this problem, in which one can couple the two fields by applying results from moisture analysis as loads in structural analysis. Only one-eighth of the geometry is simulated due to symmetry. Three symmetric surface conditions are applied. The initial condition is fully moisture saturated, and boundary conditions are that all outer surfaces are absolutely dry with zero moisture concentration, as shown in the following:

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I.C.: C(x, y, z, 0) = Csat . B.C.s: C(0, y, z, t) = C(hx , y, z, t) = 0 C(x, 0, z, t) = C(x, hy , z, t) = 0 . C(x, y, 0, t) = C(x, y, hz , t) = 0

7.4.3 Results Figure 7.12 shows the FEA results of elastic strain and hygroscopic strain in the x-direction at point A versus time. As expected, the hygroscopic strain of point A decreases with time since moisture is gradually diffused out of the specimen. The elastic strain, however, starts from zero and increases to its maximum at ∼180 min, then drops gradually. Both hygroscopic strain and elastic strain eventually approach zero when all moisture is released. The peak elastic strain accounts for about half of the hygroscopic strain, which implies that about one-third of the total strain at the probe location comes from elastic strain.

Fig. 7.12 Elastic strain and hygroscopic strain in the x-direction at the center of the specimen (point O) versus time

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Fig. 7.13 Elastic strain and hygroscopic strain distribution at line OA at t = 180 min

Elastic strain distribution along AO line at the time of 180 min is plotted in Fig. 7.13. The horizontal axis in the figure is the distance from the center point (point O). One can see that the sign of elastic strain changes from positive to negative along the thickness direction. Its average is one order lower than that of hygroscopic strain. This implies that the averaged elastic strain along the x-direction is much smaller than that compared to the average hygroscopic strain. Hygroscopic strain is always positive along the thickness. The total displacement of specimen in the x-direction can be calculated as follows: A hx = 2

A εxtotal dx

O

⎛

= 2⎝

=2

(εxhygro + εxelastic )dx O

A

O

A εxhygro dx +

⎞

.

(7.42)

εxelastic dx⎠

O

Figure 7.14 plots the total displacement and the displacement by hygroscopic swelling. When the time is less than 80 min, the total displacement is very close to the hygroscopic displacement. When the time ranges from 300 to 600 min, the relative error becomes a little higher, but within 10%. This means that the integral of the elastic strain portion in equation (7.42) has negligible contribution to

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Fig. 7.14 Comparison of total displacement with the displacement caused by pure hygroscopic strain

Fig. 7.15 Averaged total strain and averaged hygroscopic strain versus average moisture concentration

the total deformation, even though the elastic strain is significantly comparable to hygroscopic strain at each individual location. Figure 7.15 plots the averaged total strain and averaged hygroscopic strain against averaged moisture content, according to the definitions in equations (7.1) and (7.2). It can be seen that the use of hygroscopic strain analysis in the previous section obtains almost the same results with consideration of the elastic strain. Therefore, the analytical solutions in the previous section are sufficient to give accurate estimates on determining the coefficient of hygroscopic swelling.

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7.5 General Guidelines for Characterizing Hygroscopic Swelling Properties It is obvious that non-uniform moisture distribution during desorption can introduce errors in determining the coefficient of hygroscopic swelling. A general procedure in determining the accurate coefficient of hygroscopic swelling has been suggested as follows: 1. Bake the specimen until it is absolutely dry. 2. Let the specimen absorb moisture at the desired temperature and certain relative humidity until full saturation. 3. Measure the length hsat and weight Msat of the specimen initially and keep the probe at the same location. 4. Let the sample dry out completely and record the length hx and weight M of the specimen, which represent the values at dry conditions, denoted by h0 and M0 , respectively. The coefficient of hygroscopic swelling β is then calculated by β=

(hsat − h0 )/h0 . (M − M0 )/(hx0 hy0 hz0 )

(7.43)

The coefficient of hygroscopic swelling determined in this way is easier and accurate, and it can eliminate the effect of non-uniform moisture distribution. The errors caused by selecting the data sets in certain time range for the linear regression can be avoided. Both moiré interferometry and TGA/TMA method are used to measure a material’s hygroscopic swelling property. For hygroscopic swelling measurements, it is vital to eliminate thermal expansion during moiré measurements so that only hygroscopic swelling is documented. This is accomplished by using a reference sample. The reference and test samples are positioned side by side within the viewing area of the moiré setup. This procedure cancels any thermally induced deformations in the test sample since the deformed state of the reference sample is used as a reference datum for zero hygroscopic deformation of the test sample. Table 7.2 compares the results based on the traditional linear regression method and the simple procedure suggested earlier. It indeed shows that the traditional slope method overestimated the CHS significantly. Further, the moiré interferometry method was used to validate the simple procedure using TMA/TGA method and excellent agreement was obtained, as shown in Table 7.3 [18]. Table 7.2 Comparison of the CHS based on the traditional slope method and new procedure

Sample ID

1

2

3

CHS (new procedure) CHS (averaged method)

0.21 0.29

0.20 0.27

0.22 0.33

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Table 7.3 Comparison between TMA/TGA method and moiré interferometry method

173

Method

CHS

TMA/TGA with new procedure Moiré interferometry

0.21 0.20

7.6 Coupled Nonlinear Thermal–Hygroscopic Stress Modeling The integrated stress modeling under temperature/humidity loading condition requires five types of modeling, i.e., moisture diffusion during moisture preconditioning and reflow, thermal modeling, hygro-mechanical modeling, thermomechanical modeling, and vapor pressure modeling. This is a coupled-field multiphysics problem that involves thermal analysis, moisture diffusion, moisture phase change, and nonlinear stress analysis. There are extensive studies in the literature on thermal–hygroscopic stress modeling [19–26]. However, most of the published work uses linear elastic analysis to simplify the problem. So the superposition method, in which an equivalent coefficient of thermal expansion is introduced, can be applied. For example, if εT is the thermal strain, α the coefficient of thermal expansion, and T the change of temperature, then the thermal strain can be written as follows: εT = α T.

(7.44)

εh = βC,

(7.45)

Similarly,

where εh is the hygroscopic swelling strain and C represents the moisture concentration. When an electronic package is applied to both thermal and hygroscopic loadings, the total expansion strain is ε = α T + βC.

(7.46)

Consider a special case where the temperature and moisture across a material in the package are uniform (the moisture concentration is not necessarily uniform across the whole package). When linear elastic analysis is assumed, the hygroscopic strain can be treated as additional thermal strain. Thus, an equivalent coefficient of thermal expansion α ∗ can be defined as follows: α ∗ = α + βC/T,

(7.47)

ε = α ∗ T.

(7.48)

then

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Equation (7.48) indicates that the equivalent coefficient of thermal expansion α ∗ instead of α can be used to conduct integrated thermal and hygroscopic stress analyses using the conventional thermal stress analysis method. When the effect of thermal aging due to the viscoelastic behavior of underfill is considered, a simple superposition of hygroscopic and thermal strains is not valid anymore. Time dependence and nonlinear behavior of materials must be considered. Unfortunately, commonly used commercial finite element software such as ABAQUS and ANSYS do not explicitly allow the fully coupled time-dependent thermal and hygroscopic nonlinear stress analysis. In the following, a multi-step temperature/humidity loading profile is considered, as shown in Fig. 7.16. Such a loading profile represents a typical loading condition that starts from packaging assembly process and then moves to HAST stress condition. Moisture loading is applied at step 4 when the package is placed into a HAST chamber, where transient moisture diffusion and hygroscopic swelling take place at a constant temperature. The objective is to determine the package deformation and stress buildup history with respect to time during HAST. The nonlinear and temperature-dependent material behavior such as underfill and solder material needs to be considered. The transient moisture diffusion during HAST should be incorporated. Careful examination of the loading profile shown in Fig. 7.16 reveals that the temperature loading can be decoupled from moisture loading in each loading step. In steps 1–3, moisture is not present; therefore, a conventional nonlinear multi-process stress modeling methodology can be applied with the help of element death and birth and multi-constraint functions if necessary. At step 4, the package is exposed to a moisture loading condition at a constant temperature. Since the heat conduction is much faster than moisture diffusion during HAST, it is reasonable to assume the isothermal condition at step 4. The transient moisture diffusion and the subsequent hygro-stress modeling can be performed using the coupled thermal stress analysis provided in the software. It is noted that the built-in temperature field in the software at this step is replaced by the transient moisture field analysis so that the nonlinear hygro-stress analysis can be carried out. An additional field variable should be defined (in ABAQUS keyword ∗ FIELD), which represents the temperature field. The stress state carried over from the previous loading step is considered as initial stresses, and the material properties at step 4 can be updated with the material properties with moisture effect. At step 5, when the package is removed from the HAST chamber and ramped down to the room temperature, the moisture loss

HAST 1

4 3

5 6

2

Time t

Fig. 7.16 A typical multi-step temperature/humidity loading profile

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during step 5 is not significant; therefore, moisture diffusion is not considered. The built-in temperature field is now “switched” back to represent the temperature field to conduct the conventional nonlinear stress analysis. Step 6 is similar to step 4 with transient moisture desorption occurring and the stress state at the end of the previous step is the initial stress state. The above modeling approach is applied to a flip chip package subjected to a loading profile defined in Fig. 7.16. The moiré measurement is also applied to measure the deformation history during HAST at step 4. The moiré system was tuned at the grating replication temperature of 85◦ C. The package was then subjected to 85◦ C/85%RH. Figure 7.17 shows the comparison between the finite element analysis and the moiré measurement. It is noted that the fringe patterns represent the hygroscopic mismatch deformation only and do not contain any thermally induced deformations. Figure 7.18 shows the moisture diffusion history and the progressive hygroscopic swelling-induced package deformation. The particular interest is the stress pattern and distribution of under-bump region along the chip surface, which represents the packaging stresses exerted on the interlayer dielectric (ILD) and under-bump metallurgy (UBM), or ILD/UBM, structures. A global–local modeling scheme is applied. Figure 7.19 shows the bump region structure and local finite element mesh patterns. Figure 7.20 plotted the maximum normal stress and shear stress at the end of step 4. The stresses were taken from a point along the under-chip surface of ILD/UBM structure. Along the UBM or die/bump interface, hygroscopic swelling induces tension while thermal loading itself causes compression. Normal stress due to hygroscopic stress is twice as high as the value of thermal stress. Shear stress due to hygroscopic swelling also increases. FEA simulation results reveal the significance of contribution of hygroscopic swelling-induced tensile stresses under bump region. Since the HAST temperature is lower than the curing temperature, local thermal strain due to the thermal mismatch between bump and underfill is compressive; therefore, the compressive stresses on the under-bump and die surface are applied.

Time zero before HAST at 85°C

Time 168h after HAST at 85°C/85RH

Fig. 7.17 Comparison between moiré measurement and finite element analysis

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Fig. 7.18 Moisture diffusion and package deformation history during HAST

Fig. 7.19 Local finite element model of the inter-layer dielectric (ILD) and under-bump metallurgy (UBM), or ILD/UBM, structures

During HAST, with more moisture absorbed, the underfill and substrate swell to cause the hygroscopic swelling stresses. These stresses are tensile state under bump, which causes ILD/UBM opening failure. Both tensile stress and shear stress reach their highest value near the upper corner of bump, from where the package failure usually initiates [27]. Both hygroscopic swelling-induced tensile and shear stresses impose a potential threat to ILD/UBM failure.

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Fig. 7.20 Maximum normal and shear stress at UBM/ILD region in a flip chip package

177

ILD stresses (MPa) at 85C after HAST

stresses (MPa)

60

with moisture without moisture

50 40 30 20 10 0

Normal stress

Shear Stress

7.7 Conclusions Hygroscopic swelling using point-measurement techniques with TMA/TGA instruments is described. The potential source of errors that are associated with TMA/TGA method is due to the non-uniform moisture distribution. The analytical results show that the TMA/TGA method could overestimate the CHS as much as 250% if the averaged method uses dry condition as reference condition, while the CHS could be underestimated as much as 27% if the averaged method uses fully saturated point as reference condition. In order to obtain the true property of swelling, a simple procedure has been suggested, in which only two points are taken: one point with fully saturated condition and another point with fully dry condition. Those two points satisfy the uniform moisture distribution requirement. Excellent agreement has been reached for the hygroscopic swelling characterization by both TMA/TMA method and moiré interferometry method, when the non-uniform moisture distribution effect is removed. A sequentially coupled moisture diffusion and hygroscopic stress finite element transient analysis is applied to simulate the hygroscopic swelling characterization process. Since the moisture concentration is not uniformly distributed over a test specimen, both hygroscopic swelling and elastic deformation account for the total deformation, which is recorded by a probe in TMA as a function of time. Simulation results show that the peak elastic strain at the center location of the specimen is almost half of the hygroscopic swelling strain at the same location. It is also found that the elastic strain along the measuring direction changes from a tensile state to a compressive state. As a result, the total or averaged elastic strain along the thickness direction is negligible to the hygroscopic swelling strain. This explains well that the analytical models had very good agreement with experimental data even though the elastic deformation is not taken into consideration. A new finite element analysis methodology is presented in this chapter, by which the time-dependent nonlinear analysis of package deformations induced by hygroscopic as well as thermal mismatches can be analyzed. The existing linear superposition method, which couples hygroscopic stress with thermal stress analysis, cannot be applied to the problem with the nonlinear material properties. The

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proposed method allows a fully integrated nonlinear finite element stress modeling during HAST to capture the time-dependent deformation and stress buildup. The moiré interferometry measurement was then applied to a high-density flip chip package to measure the warpage and the strains of package. The numerical results by nonlinear finite element analysis had very good agreement with the experimental data. The results of the effect of hygroscopic swelling on the inter-layer dielectric reveals that the overall ILD stresses under HAST can be twice as high as those considered without the moisture effect.

References 1. Stellrecht, E., Han, B.T., Pecht, M.G., “Characterization of hygroscopic swelling behavior of mold compounds and plastic packages”, IEEE Transactions on Components, Packaging and Technologies, 27, 499–506, 2004. 2. Ardebili, H., Wong, E.H., Pecht, M.G., “Hygroscopic swelling and sorption characteristics of epoxy molding compounds used in electronic packaging”, IEEE Transactions on Components, Packaging and Technologies, 26(1), 206–214, 2003. 3. He, Y., Fan, X.J., “In-situ characterization of moisture absorption and desorption in a thin BT core substrate”, Proceedings of Electronic Components and Technology Conference, pp. 1375–1383, 2007. 4. Fan, X.J., “Moisture related reliability in electronic packaging”, ECTC Professional Development Course Notes, 2005/2006/2007/2008. 5. Zhang, G.Q., van Driel, W.D., Fan, X.J., Mechanics of Microelectronics. New York, NY: Springer, 2006. 6. Wong, E.H., Chan, K.C., Rajoo, R., Lim, T.B., “The mechanics and impact of hygroscopic swelling of polymeric materials in electronic packaging,” Proceedings of the 50th Electronic Components and Technology Conference, pp. 576–580, Las Vegas, NV, USA, 2000. 7. Tee, T.Y., Kho, C.L., Yap, D., Toh, C., Baraton, X., Zhong, Z., “Reliability assessment and hygroswelling modeling of FCBGA with no-flow underfill”, Microelectronics Reliablity, 43(5), 741–749, 2003. 8. Zhou, J., Lahoti, S., Kallolimath, K., “Investigation of non-uniform moisture distribution on determination of hygroscopic swelling coefficient and finite element modeling for a flip chip package,” IEEE International Conference on Thermal, Mechanical and Multiphysics Simulation and Experiments in Micro-Electronics and Micro-Systems (EuroSime), April 17–20, Berlin, Germany, 2005. 9. Shi, X.Q., Zhang, Y.L., Zhou, W., Fan, X.J., “Effect of hygrothermal aging on interfacial reliability of silicon/underfill/FR-4 assembly”, IEEE Transactions of Components and Packaging Technologies, 31(1), 94–103, 2008. 10. Fan, X.J., Lee, S.W.R., Han, Q., “Experimental investigations and model study of moisture behaviors in polymeric materials”, Microelectronics Reliability, 49 ,861–871, 2009. 11. Teverovsky, A., Moisture Characteristics of Molding Compounds in PEMs. Lanham, MD: QSS Group, Inc./Goddard Operations: NASA Technical Report, 2002. 12. Shirangi, M.H., Fan, X.J., Michel, B., “Mechanism of moisture diffusion, hygroscopic swelling and adhesion degradation in epoxy molding compounds,” Proceedings of the 41st International Symposium on Microelectronics (IMAPS), pp. 1082–1089, 2008. 13. Zhou, J., Law J.S., “Effect of non-uniform moisture distribution on the hygroscopic swelling coefficient”, IEEE Transactions on Components and Packaging Technologies, 31(2), 269–276, 2008.

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14. Zhou, J., “Transient analysis on hygroscopic swelling characterization using sequentially moisture diffusion and hygroscopic stress modelling method,” Microelectronics Reliability, 48, 805–810, 2008. 15. Zhou, J., “Analytical and numerical bound analysis of hygroscopic swelling characterization”, Proceedings of the Electronic Components and Technology Conference, ECTC, 2006. 16. Zhou, J., Zhang, X.Q., Tee, T.Y., Luan. J, “Upper and lower bound theoretical analysis in characterizing hygroscopic swelling of polymeric materials,” Proceedings of the 38th International Symposium on Microelectronics (IMAPS), September 25–29, Philadelphia, PA, pp. 673–680, 2005. 17. Zhou, J., Tee, T.Y., Zhang, X., “Transient analysis on hygroscopic swelling characterization using sequentially coupled moisture diffusion and hygroscopic stress modeling approach,” Proceedings of ASME International Mechanical Engineering Congress and Rd & D Expo, November 5–11, Orlando, FL, 2005. 18. Fan, X.J., Zhou, J., Chandra, A., “Package structural integrity analysis considering moisture,” Proceedings of the 58th Electronic Components and Technology Conference (58th ECTC), pp. 1054–1066, 2008. 19. Tee, T.Y., Zhong, Z.W., “Integrated vapor pressure, hygroswelling, and thermo-mechanical stress modeling of QFN package during reflow with interfacial fracture mechanics analysis”, Microelectronics Reliability, 44(1), 105–114, 2004. 20. Fan, X.J., “Mechanics of moisture for polymers: fundamental concepts and model study”, Proceedings of the International Conference on Thermal and Mechanical Simulation and Experiments in Microelectronics and Microsystems (EuroSimE), pp. 159–172, 2008. 21. Fan, X.J., Zhang, G.Q., van Driel, W.D., Ernst, L.J., “Interfacial delamination mechanisms during reflow with moisture preconditioning”, IEEE Transactions on Components and Packaging Technologies, 31(2), 252–259, 2008. 22. van Driel, W.D., van Gils, M.A.J, Fan, X.J., Zhang, G.Q., Ernst, L.J., “Driving mechanisms of delamination related reliability problems in exposed pad packages”, IEEE Transactions on Components and Packaging Technologies, 31(2), 260–268, 2008. 23. Fan, X.J., Zhou, J., Zhang, G.Q., Ernst, L.J., “A micromechanics based vapor pressure model in electronic packages”, ASME Journal of Electronic Packaging, 127(3), 262–267, 2005. 24. Fan, X.J., Zhou, J., Zhang, G.Q., “ Multi-physics modeling in virtual prototyping of electronic packages – combined thermal, thermo-mechanical and vapor pressure modeling “, Journal of Microelectronics Reliability, 44, 1967–1976, 2004 25. Xie, B., Fan, X.J., Shi, X.Q., Ding, H., “Direct concentration approach of moisture diffusion and whole field vapor pressure modeling for reflow process: part I – theory and numerical implementation”, ASME Journal of Electronic Packaging, 131(3), 031010, 2009 26. Xie, B., Fan, X.J., Shi, X.Q., Ding, H., “Direct concentration approach of moisture diffusion and whole field vapor pressure modeling for reflow process: part II – application to 3-D ultra-thin stacked-die chip scale packages”, ASME Journal of Electronic Packaging, 131(3), 031011, 2009. 27. Zhou, J., “Investigation of inner-layer dielectric (ILD) failure by hygroscopic swelling,” Proceedings of IEEE 55th Electronic Components and Technology Conference (ECTC), May 31–June 4, Orlando, FL, 2005.

Chapter 8

Modeling of Moisture Diffusion and Moisture-Induced Stresses in Semiconductor and MEMS Packages C. Jang and B. Han

8.1 Introduction Semiconductor and MEMS packages have a unique engineering structure, in which various polymeric and inorganic materials are densely packed in millimeter- to micrometer-scale configurations. While inorganic materials (silicon, copper, aluminum, etc.) are impervious to moisture, polymers (molding compound, die attach, underfill, solder resist, etc.) absorb moisture and expand because of the absorbed moisture. This mismatch in hygroscopic swelling between the two material groups incurs deformations of semiconductor packages. The consequences of these deformations, as far as the induced stresses are concerned, are similar to the effect of the deformations induced by the mismatch in the thermal expansion. The analysis of moisture-induced deformations is essential to the assessment of the mechanical/functional integrity and performance of semiconductor and MEMS devices subjected to temperature and humidity excursions during their storage, manufacturing, and service life. It involves a moisture diffusion analysis and a subsequent stress analysis, where the combined effect of moisture and temperature distribution on the deformation is calculated [1]. Although moisture diffusion in polymers had been a classical research topic due to the impact of moisture itself on the state of polymers [2], the need to model moisture-related phenomena in complex structures arose quite recently, i.e., just a decade ago, as moisture-related issues such as pop-corning became important in semiconductor packages [3]. This chapter describes recent progress in modeling of moisture diffusion and moisture-induced stresses in semiconductor and MEMS packages. It addresses both basic and practical aspects including (1) the theoretical background of moisture diffusion and hygroscopic swelling, (2) modeling schemes to solve moisture diffusion and combined hygro-thermo-mechanical stresses, and (3) validation of modeling schemes. Much of the chapter is excerpted from [1, 4] and [5] with the kind permission of American Society of Mechanical Engineers (ASME) and Institute of Electrical and Electronics Engineers (IEEE), respectively. C. Jang (B) e-mail: [email protected] X.J. Fan, E. Suhir (eds.), Moisture Sensitivity of Plastic Packages of IC Devices, Micro- and Opto-Electronic Materials, Structures, and Systems, C Springer Science+Business Media, LLC 2010 DOI 10.1007/978-1-4419-5719-1_8, 

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8.2 Technical Background 8.2.1 Moisture Diffusion The majority of gas species including water vapor (moisture) follow Fick’s laws when they permeate through polymer chain structures. Mass flux in polymers is governed by Fick’s first law, which is expressed as J = −D∇C ,

(8.1)

where J is the moisture mass flux vector (kg/m2 s), D is the diffusivity (m2 /s), ∇ is the gradient operator, and C is the moisture concentration (kg/m3 ). The mass conservation of mass within an infinitesimal volume yields Fick’s second law as follows: C˙ = ∇ · (D∇C) .

(8.2)

Henry’s law describes the equilibrium between saturated moisture concentration and ambient vapor pressure at the polymer surface, which is expressed as Csat = Spv ,

(8.3)

where Csat is the saturated moisture concentration, S is the Henry constant or solubility (s2 /m2 ), and pv is the ambient vapor pressure (Pa). Both the diffusivity and solubility are known to follow the Arrhenius relationship     ED ES and S = S0 exp − , (8.4) D = D0 exp − R0 T R0 T where D0 is the diffusivity constant and ED is the activation energy for diffusion, R0 is the universal gas constant (8.3145 J/mol K), S0 is the solubility constant (s2 /m2 ), ES is the activation energy of solution (J/mol), and T is the temperature (K). The permeability of a polymer is defined as the product of diffusivity and solubility:   EP , (8.5) P = DS = P0 exp − R0 T where P0 is the permeability constant (s) and EP is the activation energy of permeation (J/mol). One unique feature of gas diffusion is the concentration discontinuity at the interfaces of different polymeric materials: The maximum amount of moisture that each polymer can absorb is a material property, and therefore the concentration at a bi-material interface can be discontinuous. The concentration at the interface is governed by the Nernst distribution law [6]: χ=

S1 Cint,1 = , Cint,2 S2

(8.6)

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where χ is Nernst partition coefficient at a specific temperature and Cint,1 and Cint,2 are concentrations of two materials at the interface. The corresponding mass continuity is given by D1

! ! ∂C1 !! ∂C2 !! = D , 2 ∂s !s∂s !s+

(8.7)

where s (or s) is a vector perpendicular to the interface plane. A physical illustration of the interfacial conditions is provided in Fig. 8.1. A new term, φ, in the figure will be discussed later. Fig. 8.1 Schematic diagram showing interfacial conditions at a bi-material interface

s

s−

s+

Cint,1

χ=

φi

Cint,2

Mat 1: D1 and S1

D1

Cint,1 Cint,2

∂C1 ∂s

φi =

s–

=

S1 S2

= D2

∂C 2 ∂ s s+

Cint,1 Cint,2 = S1 S2

Mat 2: D2 and S2

In order to analyze moisture diffusion, two diffusion properties out of diffusivity, solubility, and permeability are required. The diffusivity and solubility are in general measured together through well-established moisture weight gain/loss tests [7]. Property data for various packaging polymers are available in the literature (see, e.g., [3, 8–14]). The majority of the reported data were obtained at low temperatures below 100◦ C, where the standard procedure is routinely practiced. A handful of property data at above 100◦ C are found among them [9, 11, 15]. A more extensive work on high-temperature measurement has been conducted recently for more accurate modeling of moisture diffusion during the reflow process [16]. In practice it is very difficult to document accurately the transient moisture weight gain/loss in thin film polymers. Instead of the diffusivity, the permeability is measured through water vapor transmission tests, such as the cup test [17] or well-known MOCON test (http://www.mocon.com) [18]. It is determined from 1-D Fick’s first law J = P (pu − pd ) ⇔ P =

J , pu − pd

(8.8)

where J is the moisture mass flux across the film (kg/m2 s) and pu and pd are the upstream and downstream pressures (Pa), respectively.

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8.2.2 Analytical Solutions of Diffusion Equation Analytical solutions of Fick’s second law are available for some single (homogeneous) material problems with simple geometry,1 which are illustrated in Fig. 8.2. The diffusion equation for an isothermal 1-D problem is reduced to ∂ 2C ∂C =D 2. ∂t ∂x

pu

(8.9)

pu

x p(x,0)=pi

L

p(x,0)=p i

pd

0

(a)

(b)

Fig. 8.2 Schematic diagram of two cases of 1-D moisture diffusion

In the first case (Fig. 8.2a) the one side of a polymer specimen is exposed to an ambient with an upstream vapor pressure (pu ), while the other side is impervious to moisture. It is also equivalent to a polymer specimen with a thickness of 2L, both sides of which are exposed to a humid ambient. The boundary and the initial conditions are δC(0,t) = 0, C(L,t) = Cu = Spu and C(x,0) = Ci = Spi , δx

(8.10)

where Cu is the concentration at the top surface (kg/m3 ), L is the thickness of the substrate (m), and Ci and pi are the initial concentration and pressure. The closedform analytical solution is [19]    ∞  4 (Ci − Cu ) (2n − 1) π x (2n − 1) π 2 n exp − ( − 1) cos Dt . C (x,t) = Cu − 2L 2L (2n − 1) π n=1 (8.11) The moisture content inside the specimen is obtained by integration:   ∞ 1 8  D(2n − 1)2 π 2 t W(t) . =1− 2 exp − Wsat π (2n − 1)2 4L2

(8.12)

n=1

1 Analytical

solutions for 1-D bi-material problems, albeit very limited, can be found in [6].

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Here W is the moisture content (kg) and Wsat is the saturated moisture content. The above solution can be easily extended to a 3-D block specimen subjected to moisture weight gain test where all exterior surfaces of the block are exposed to a humid ambient. The solution is re-written as follows [9]:   ∞ ∞ ∞ W(t) 1 512    Dt , =1− 6 exp − Wsat π Leqv 2 (2 l − 1)2 (2m − 1)2 (2n − 1)2 l=1 m=1 n=1 (8.13) where  Leqv = 2

(2 l − 1) π Lx

2



(2m − 1) π + Ly

2



(2n − 1) π + Lz

2

−1

,

Lx , Ly , and Lz are the length of the block in each direction. Note that Lx in the 1-D case is equal to 2L. Equation (8.13) has been widely used to determine the diffusivity of block-shaped polymer specimens inversely from experimentally measured moisture weight gain data. Figure 8.3 illustrates typical moisture weight gain data along with a curve of the corresponding analytical solution obtained from a nonlinear regression analysis. The second case (Fig. 8.1b) depicts transient moisture transmission through the polymer specimen. The boundary and initial conditions are as follows: C(0,t) = Cd = Spd , C(L,t) = Cu = Spu ,

and C(x,0) = Ci = Spi ,

(8.14)

where Cd is the concentration at the bottom surface (kg/m3 ) and pd is the downstream gas pressure (Pa). The analytical solution of the second case is derived as [20] 3.0

Weight Gain (%wt)

2.4

1.8

1.2

Sample 1 Sample 2 Sample 3 Fickian Fit

0.6

0.0 0

5

10

Time

15

20

25

(hour0.5)

Fig. 8.3 Typical moisture weight gain data and their curve fit using the analytical solution

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Cu − Cd x L   ∞ nπ x  nπ 2 Ci − Cd − (Ci − Cu ) (−1)n +2 exp − Dt . sin nπ L L n=1 (8.15)

C(x,t) = Cd +

The corresponding transient moisture transmission rate is obtained as follows: 

  ∞  Cu − Cd nπ 2 Ci − Cd − (Ci − Cu ) (−1)n J = −D +2 exp − Dt L L L n=1  .   ∞  nπ 2 pu − pd pi − pd − (pi − pu ) (−1)n +2 exp − Dt = −P L L L n=1 (8.16) The above solution has been used to determine the gas diffusivity of thin film specimen as well as the permeability from transient gas transmission tests [21–23].

8.2.3 Hygroscopic Swelling The hygroscopic strain is known to have a linear relationship with moisture concentration as follows [12]: εβ = βC,

(8.17)

where εβ is the hygroscopic strain and β is the coefficient of hygroscopic swelling (CHS). The CHS can be measured by using various tools and techniques including a bending cantilever method [24], a micrometer [25], Michelson interferometry [26], and a thermo-mechanical analysis (TMA) combined with a thermo-gravimetric analysis (TGA) [10]. A full-field deformation analysis can offer a more accurate CHS measurement by coping with the limitation of aforementioned pointmeasurement methods. Moiré interferometry [27] and digital image correlation (DIC) [28] have been utilized for full-field measurement of hygroscopic swelling strains in bulk polymers [29] and thin film polymers [30], respectively.

8.3 Modeling of Moisture Diffusion Fick’s second law can be solved numerically using either in-house codes with an appropriate numerical scheme or a commercially available software package. As long as the semiconductor/MEMS packages are concerned, the commercial software

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is preferred due to complex geometries, material configurations, and loading conditions. However, a practical issue is encountered when moisture diffusion modeling is attempted: Most commercial finite element analysis (FEA) software packages do not offer the moisture (or mass) diffusion function [31].2 Furthermore, when moisture transport into/out of a cavity is involved, the modeling task becomes even more complicated. This section concerns effective ways to address these two issues in modeling moisture diffusion for package applications.

8.3.1 Thermal–Moisture Analogy Heat conduction is a diffusive process and, as such, has a governing equation similar to that of mass diffusion. Fourier’s law of heat conduction is expressed as q = −k∇T,

(8.18)

where q is the heat flux (W/m2 ) and k is the conductivity (W/mK). Assuming no internal heat generation, the energy balance yields the governing equation of heat conduction as follows: ρcp T˙ = ∇ · (k∇T) ,

(8.19)

where ρ and Cp are density (kg/m3 ) and specific heat (J/kg K), respectively. Due to the similarity in governing equations, heat conduction, and mass diffusion have been often treated in a “unified” way [32]. The resulting “thermal–moisture” analogy is very attractive, since moisture diffusion can be solved using the heat transfer function of any FEA software. As a consequence, the thermal–moisture analogy has been utilized extensively to address water diffusion inside semiconductor packages [9, 14, 33–36], food [37], and gas barrier films [20, 38]. 8.3.1.1 Single Material Problems When the density and specific heat are constant, equation (8.19) is reduced to T˙ = ∇ ·



k ∇T ρcp

 = ∇ · (α∇T) ,

(8.20)

where α is the thermal diffusivity (m2 /s). Equations (8.2) and (8.20) have the same form, thus a direct thermal–moisture analogy can be established from direct comparison [31]. It can be expressed as follows:

2 Among

the commercial FEA packages, only ABAQUS provides the general mass diffusion analysis capabilities.

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Field variable: T (temperature) ≡ C (concentration), Diffusivity: α (thermal) ≡ D (moisture).

(8.21)

The direct analogy scheme is simple, physically meaningful, and is easy to understand and utilize. It is noteworthy that this analogy is applicable to only singlematerial or homogeneous problems since it cannot handle the interface discontinuity that occurs in multi-material problems. 8.3.1.2 Interfacial Discontinuity in Multi-material Problems The moisture concentration is discontinuous at a bi-material interface when two materials have different saturated concentrations. There are two ways of handling this discontinuity: (1) to use concentration as it is and (2) to introduce normalized concentration as the independent variable. The former is to solve Fick’s second law equation (equation (8.2)) with imposing Nernst equation (equation (8.6)) as well as mass continuity (equation (8.7)) on the bi-material interface. More preferable in numerical implementation would be to modify the original equation in a normalized form. For non-polar gases, such as oxygen, the driving force of diffusion inside polymers is the partial pressure, and it is by its very nature continuous everywhere. The pressure at the interface is determined as follows (see Fig. 8.1): pi =

C1 C2 = . S1 S2

(8.22)

In the above equation the concentration is normalized by the solubility. Accordingly, the concentration in Fick’s second equations can be replaced with pressure (C = Sp) and boundary conditions can be defined in terms of ambient gas partial pressures. However, this replacement may cause a subtle misunderstanding, when applied to moisture diffusion. Unlike other non-polar gases, the state of polar water molecules is not solely gas phase. Rather, water molecules tend to reside in polymer chains through adsorption and, more likely, hydrogen bonding with polar groups, such as hydroxyl and amide groups [39, 40]. To avoid such a physical misconception, one can introduce a new term, normalized concentration, defined as [31] φ=

C , S

(8.23)

where φ is normalized concentration (Pa). It should be noted that in a numerical implementation perspective, the normalized concentration is equivalent to the existing normalized variables, such as partial vapor pressure [9] and wetness [33]. Substituting equation (8.23) into equation (8.2), Fick’s equation yields ˙ + Sφ˙ = ∇ · [D∇ (Sφ)] . Sφ

(8.24)

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The corresponding boundary condition at the exterior surface is given by equation (8.3): φext = pv .

(8.25)

8.3.1.3 Normalized Analogy The normalized analogy essentially takes account of the interface condition by comparing equation (8.24) to equation (8.19). It can be established as follows: Field variable: T ≡ φ, k ≡ P = DS,

(8.26)

ρcp ≡ S. Since the field variable is the normalized concentration that is continuous at the bi-material interface, this analogy can properly handle the interface condition. It is important to note, however, that the conduction equation of equation (8.19) lacks a few terms in the diffusion equation of equation (8.24). The missing terms are related with the time and spatial gradient of solubility. This indicates that the solubility must be constant in order for the two equations to be truly analogous. Since the solubility is dependent on temperature (equation (8.4)), it is constant only when the loading is isothermal. Thus, the normalized analogy should be applied only to isothermal problems. 8.3.1.4 Advanced Analogy The advanced analogy scheme was proposed to cope with the limitations of the normalized analogy [4]. It was established based on the characteristic of packaging polymers which has been observed in numerous studies [11, 34, 41–46], i.e., the saturated concentration is linearly proportional to the ambient relative humidity but not dependent on the temperature. Figure 8.4 illustrates such a trend for various packaging polymers. The linear relationship between the saturated concentration and the relative humidity originates from Henry’s law (equation (8.3)) as Csat = Spv = Spsat (RH) = M(RH),

(8.27)

where psat is the saturated vapor pressure (Pa), RH is the relative humidity, and M is referred to as “modified solubility” which is constant regardless of temperature. The advanced analogy uses the modified solubility. An advanced normalized concentration, φ, can be defined using the modified solubility as ϕ=

C . M

(8.28)

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Saturated Concentration (%wt)

2.0 Three Samples per Each Case o o o 25 C 55 C 85 C Solder Resist EMC PWB core 1 PWB core 2

1.6

1.2

M

0.8

0.4

0.0 0.0

0.2

0.4

0.6

0.8

1.0

Relative Humidity Fig. 8.4 Measured saturated concentration of various packaging polymers with respect to relative humidity and temperature

Substituting equation (8.28) into equation (8.2), ˙ + M ϕ˙ = ∇ · [D∇ (Mϕ)] ⇒ M ϕ˙ = ∇ · [DM∇ϕ] . Mϕ

(8.29)

Thus, an analogy is established between equations (8.29) and (8.19): Field variable: T ≡ ϕ, k ≡ P = DM,

(8.30)

ρcp ≡ M. The modified solubility automatically satisfies the continuity at the interface. The boundary condition of the new normalized concentration becomes ambient relative humidity (RH). From equations (8.27) and (8.28), the boundary condition is obtained as follows: ϕBC = RH.

(8.31)

The above derivation and the boundary condition (equations (8.29) and (8.31)) clearly indicate that the advanced analogy is valid for multi-material systems subjected to anisothermal loading conditions (non-uniform temperature fields that change with time). It would be instructive to review one of the most widely used normalized variables called “wetness” in respect of the advanced analogy. The wetness is defined as follows [33]:

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Modeling of Moisture Diffusion and Moisture-Induced Stresses

w=

C . Csat

191

(8.32)

The wetness boundary condition is always “unity” according to Henry’s law (equation (8.3)). Since the boundary condition of “unity” cannot be used for anisothermal problems, where Csat changes with ambient conditions, a practical procedure to extend the wetness scheme to temporally anisothermal loading conditions (uniform temperature fields that change with time) was proposed later [47]. For the polymers that satisfy the requirements for the advanced analogy, the wetness can be expressed as w=

C C = . Csat M(RH)

(8.33)

Then, the wetness can be related to the advanced normalized concentration by w=

ϕ . RH

(8.34)

The wetness becomes identical to the advanced normalized concentration only when RH = 1 (or RH% = 100%), i.e., when one uses a saturated concentration at the 100% RH condition for wetness. For this identity, the saturated concentration at 100% RH should be determined from the linear relationship (see equation (8.27)). It is worth noting that the saturated concentration at 100% RH determined from the linear relationship may not be the same as a true Csat at 100% RH since some polymers can absorb more moisture at near 100% RH than what is predicted from the linear relationship (or linear Henry’s law) [16, 48]. This discrepancy near 100% RH is not a concern in typical moisture diffusion analyses, however, since a range of relative humidity of practical importance lies within the region where the linear relationship is valid (e.g., 85◦ C/85% RH).

8.3.1.5 Validation of Analogies A summary of the three analogy schemes is given in Table 8.1. These analogies have been validated with the solution of the original diffusion equation [4, 31], which was obtained numerically using the finite difference method (FDM). As a representative case, a bi-material structure subjected to anisothermal loading is presented. Other cases, such as isotherm/anisothermal single material cases and an isothermal bimaterial case, are found in [4, 31]. The properties of the two materials comprising the bi-material structure are listed in Table 8.2 and the configuration of the structure and loading conditions is illustrated in Fig. 8.5. The problem is solved by using the normalized and advanced analogies, and the results are plotted in Fig. 8.6 together with the solution of the diffusion equation. The advanced analogy scheme predicts

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the moisture concentration accurately, while the normalized analogy significantly deviates from the solution. The FDM scheme to solve the moisture diffusion equation and the procedure and example ANSYS input codes for the advanced analogy are described in detail in Appendices A.1.1 and A.2, respectively.

Table 8.1 Summary of three analogy schemes

T K ρcp BC Multi-material Anisothermal Remark

Direct

Normalized

Advanced

C D 1 Csat X O

φ DS S pv O X

ϕ DM M H O O Not applicable to all polymers

Table 8.2 Material properties for analysis cases illustrated in Figs. 8.4 and 8.5

D0 (m2 /s) S0 (s2 /m2 ) ED (J/mol) ES (J/mol) k (Wm/K) cp (J/kg K) ρ (kg/m3 )

Material I

Material II

5 × 10−3 6 × 10−10 5 × 104 4 × 104 0.001 1,000 1,000

4 × 10−3 2 × 10−10 5 × 104 4 × 104 0.0005 500 1,000

h = 5 W/m2K Ta(t) = 25 + t / 60 (°C)

PVP = P25°C/100%RH 1mm

1mm

Fig. 8.5 Schematic diagram of simulated geometry and boundary condition for the case

anisothermal bi-material  ∇T = 0 and T˙ = 0

Ta(t) = 25 + t / 60 (°C)

PVP = P25°C/100%RH h = 5 W/m2K

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Modeling of Moisture Diffusion and Moisture-Induced Stresses 2.4

t = 1800 sec

FDM Normalized Advanced

4

3

Concentration (kg/m )

3

Concentration (kg/m )

6 5

3 2 1 0 0.0

193

0.5

1.0

1.5

2.0

t = 3600 sec

2.0

FDM Normalized Advanced

1.6 1.2 0.8 0.4 0.0 0.0

0.5

1.0

1.5

2.0

Coordinate along Thickness Direction (mm)

Coordinate along Thickness Direction (mm)

(a)

(b)

Fig. 8.6 Moisture concentrations in the bi-material specimen subjected to the anisothermal loading condition: (a) t =1,800 s and (b) t = 3,600 s

8.3.2 Moisture Transport into/out of a Cavity: Effective-Volume Scheme A semiconductor package can contain cavities within its structure, especially at polymeric interfaces. Such cavities can be produced by defective manufacture and polymeric interface degradation during storage or severe operation. It is generally speculated that the pop-corning failure results from high vapor pressure developed inside the defective cavity during the reflow process [3]. In order to calculate moisture transport into the cavity, Kitano et al. [3] and Tay et al. [8] proposed modeling procedures that employed a recursive procedure considering the vapor pressure-induced cavity volume change. Unlike the semiconductor package, the most critical role of MEMS packaging is to provide an internal cavity for moving parts and to maintain the initial condition of the cavity. The cavity is formed by sealing a gap between a cap and a substrate wafer. More recently, polymers have gained widespread acceptance due to many advantages that they offer [49, 50]. Examples of polymeric seals include benzocyclobutene (BCB), parylene, polyimide, and negative photo-resists [51, 52]. Hermeticity of the MEMS package is a measure of the ability to maintain an acceptable level of stable and sometimes inert ambient in the cavity. It impacts device reliability and hence lifetime expectancy. Poor hermetic performance of seals can lead to ingress of contaminants, ambient gases, and moisture thereby causing performance degradation. Modeling of the moisture transport into and out of a cavity through a polymeric seal is thus crucial in assessment of hermeticity performance of a polymer-sealed MEMS package. Assuming that water vapor obeys the gas law, the evolution of cavity vapor pressure by moisture transport from surrounding polymers or polymeric seals is calculated as follows: pc (t1 ) = pc (0) +

R0 T Mw Vc

  Jc (t) · dA dt , t1

Ac

(8.35)

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where pc is the cavity pressure (Pa), Mw is the molar mass of water (0.018 kg/mol), Vc is the cavity volume (m3 ), Ac is the total area of polymeric surfaces in the cavity, and Jc is the moisture mass flux from the surrounding polymers into the cavity (kg/m2 s). The cavity pressure is also the boundary condition at the cavity surface for polymeric materials surrounding the cavity. Thus, the cavity pressure increment at each time step should be calculated and subsequently used to update the boundary condition at the cavity surface after each time step. This updating process requires a user-defined algorithm (this scheme will be referred to as “the original” scheme). An effective modeling scheme was proposed to avoid the user-defined algorithm (this scheme will be referred to as “effective volume”) [5]. A schematic illustration of the effective volume scheme is shown in Fig. 8.7. It models the package cavity as a fictitious polymer with an extremely large diffusivity and an “equivalent solubility.” The large diffusivity (several orders higher than that of the surrounding polymer) ensures the uniform vapor pressure inside the cavity. It is important to note, however, that the solubility of the fictitious polymer cannot be chosen arbitrary. Instead, the effective solubility should be derived from the gas law and Henry’s law as follows: Sc =

ρ Mw C = = , p nR0 T/V R0 T

(8.36)

where ρ is the water vapor density, which has the same dimension as the moisture concentration (kg/m3 ; note that water vapor density can be interpreted as moisture

x=0 x

x = xi

Dp Sp

φ (xi ,t) = pc (t)

pv

(a)

x=0

φ (xi ) =

x

Fig. 8.7 Schematic illustration of (a) original model and (b) “effective volume” model in a simplified 1-D configuration

Dc >> Dp Sc = M/R0T

Cc (xi –) Cp (xi +) =

Sc

Dp Sp

(b)

Sp

pv

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Modeling of Moisture Diffusion and Moisture-Induced Stresses

195

concentration inside the imaginary polymer), V is the gas volume (m3 ), and n is the number of moles (mol). The effective volume scheme transforms the original single material diffusion problem with transient boundary conditions into a bi-material gas diffusion problem with fixed boundary conditions. Consequently, the Nernst distribution law should be considered for mass continuity at the cavity–polymer seal interface (the inner surface of the polymer seal, x = L in Fig. 8.7b), which can be expressed as [6] φ(L) = p(L) =

Cp (L + ) Cc (L − ) = , Sc Sp

(8.37)

where Cc and Cp is the moisture concentration (or density) of the cavity and the surrounding polymer, respectively. The effective volume scheme can be readily implemented using commercial FEA software packages without a user-defined program, since the mass continuity is automatically satisfied at the interface, and thus the interface condition does not have to be updated manually. It is worth noting that the effective volume scheme must be implemented using the normalized or advanced analogy only for isothermal problems. A mass diffusion module (e.g., ABAQUS) must be used for general anisothermal problems. The effective-volume scheme was validated with the original scheme. In the validation a simple 1-D axisymmetric geometry (Fig. 8.8) was considered, which simulated a MEMS device with a cavity at the center. The axisymmetric form of equation (8.9) can be expressed as  2  ∂ φ 1 ∂φ ∂φ =D + ∂t r ∂r ∂r2

(8.38)

Lp

ri

Fig. 8.8 Schematic diagram of the geometry of 1-D axisymmetric case (the top and bottom surfaces are adiabatic)

ro

h Cavity

Polymer seal

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and the boundary and initial conditions are φ(ro ,t) = pa , φ(ri ,t) = pc , and φ(r,0) = 0 ,

(8.39)

where pa and pc are the ambient and cavity pressures, respectively. Note that in [5] the pressure term is used for the normalized concentration for the sake of general gas applications. The cavity pressure change during each time step (t) can be calculated as follows: Ai R0 T pc (t + t) = pc (t) − MVc

 t

Jr=ri (t)dt,

(8.40)

where Ai is the inner surface area (= 2π ri h), M is the gas molar mass (kg/mol), and Vc is the cavity volume (= π ri2 h). For a more effective validation, equations (8.38), (8.39), and (8.40) are converted into non-dimensional forms by normalizing independent variables (r and φ) with the outer radius (ro ) and the ambient pressure (pa ) as follows: ∂ φ˜ = ∂ ˜t



∂ 2 φ˜ 1 ∂ φ˜ + 2 r˜ ∂ r˜ ∂ r˜

 ,

(8.41)

˜ r,0) = 0. ˜ ˜t) = 1, φ(˜ ˜ ri ,˜t) = p˜ c , φ(˜ φ(1, p˜ c (˜t + ˜t) = p˜ c (˜t) − p˜ =

2r0 Sp ri Sc

 t∗

Dp t r p , r˜ = , ˜t = 2 , and pa r0 r0

J˜ r=ri (˜t)d˜t , J˜ =

Jr0 . Dp Sp pa

(8.42) (8.43) (8.44)

The normalized form of the Nernst distribution law for the effective volume scheme can be written as follows: ˜ ri ) = φ(˜

Sp C C˜ c (˜ri −) = C˜ p (˜ri +), where C˜ = . Sc Sp pa

(8.45)

Since no closed-form solution is available for both schemes, they were solved by a numerical scheme based on FDM [53]; the details of the FDM analysis are described in Appendix A.1.2. Figure 8.9 shows cavity pressure evolution as a function of time for the normalized case of ri /ro = 0.5 (ri = Lp ) and Sp /Sc = 1. The two schemes produce the identical curve, confirming the validity of the effective volume scheme. Validation with experimental measurements can be also found in [5, 54].

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197

1.0

p* (= p / pa)

0.8 0.6 0.4 ri / ro = 0.5

0.2 0.0 0.0

Sp / S c = 1 0.2

0.4 0.6 2 t* (= Dpt / ro )

0.8

0.1

Fig. 8.9 Pressure development inside cavity for the normalized case of ri /r0 = 0.5 and Sp /Sc = 1 (solid line and bullets indicate results by the original model and the effective volume model, respectively)

8.4 Modeling of Hygroscopic Swelling-Induced Stresses 8.4.1 Modeling Strategy for Hygro-thermo-mechanical Stress Analysis When packages are subjected to both temperature excursion and relative humidity change, the total deformation can be represented as ε = εσ + εα + εβ ,

(8.46)

where ε, εσ , εα (= αT; α is the coefficient of thermal expansion), and εβ are the total, mechanical (or stress-induced), free thermal, and free hygroscopic swelling strains, respectively. A constitutive equation defines the relationship among the mechanical strain and other factors such as stress σ , temperature T, and time t: εσ = f (σ ,T,t).

(8.47)

The resulting stress/deformation response caused by temperature excursion and moisture absorption change can be obtained by solving the force equilibrium equation with the above strain definitions and the governing equations of heat conduction (equations (8.18) and (8.19)) and moisture diffusion (equations (8.1) and (8.2)). Solving three field equations simultaneously, however, is too complicated to be practiced in most of engineering applications.

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It would be more practical to solve one field equation at a time and consider the interaction among the fields sequentially. Since they are virtually independent of the stress state, the temperature and moisture concentration fields can be determined through the heat transfer analysis and the moisture diffusion analysis, respectively, prior to a stress analysis, and then they can be incorporated into a subsequent stress analysis. This sequentially coupled analysis has been used to calculate the thermal stresses in a semiconductor package under a transient temperature change. This approach is extended for the combined thermal and hygroscopic loading. Figure 8.10 illustrates the modeling hierarchy of the thermo-hygroscopic stress analysis. The temperature distribution, calculated from the heat transfer analysis or predetermined by a user, is used in the moisture diffusion analysis since the diffusion strongly depends on the temperature (equation (8.4)). Then, both moisture concentration and temperature field are incorporated into the thermal–hygroscopic stress analysis to calculate the stress produced by the combined effect of the temperature and moisture.

Heat Transfer Analysis (or User Definition)

T T(x,t)

Moisture Diffusion Analysis

C C(x,t)

T T(x,t) Thermal Hygroscopic Stress Analysis

ε = εσ + αΔT + βΔC

Fig. 8.10 Modeling hierarchy for thermo-hygroscopic stress analysis

In order to implement the above procedure into the commercial FEA software, a few requirements should be met. First the FEA software must have a capability of mass (moisture) diffusion analysis. Since most commercial FEA softwares do not offer the mass (or moisture) diffusion function, the use of the thermal diffusion (or heat transfer) function for a thermal–moisture analogy could be a practical approach to solve moisture diffusion. Second, the software should have a function to incorporate both the temperature and moisture concentration fields into a stress analysis, where volumetric strains caused by both moisture concentration and temperature can be defined and added. Without this function, this analysis will be limited to only a linear elastic structure where linear superposition of hygroscopic swelling stress and thermal stress is possible. Table 8.3 summarizes the capability of two commonly utilized FEA software packages, ABAQUS and ANSYS, for the hygroscopic stress analysis. ABAQUS satisfies all the above requirements while ANSYS does not support the polymer viscoelasticity in the combined modeling scheme.

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199

Table 8.3 Comparison of ABAQUS and ANSYS for hygroscopic stress modeling ABAQUS

ANSYS

Mass diffusion function

Yes

Moisture concentration as a body force loading in basic features User-definable body force field

N/A

Thermal−moisture analogy N/A

User subroutine for swelling Moisture concentration loading input from external analysis results Nonlinear stress modeling

Any number of any kinds UEXPAN.F Yes (field type change required) No limitation

Fluence only USERSW.F No (programmable using APDL) Does not support viscoelasticity

8.4.2 Implementation Using ABAQUS As mentioned above, ABAQUS provides the general mass diffusion analysis capability and also offers special functions with which a user can manipulate the moisture concentration field and define the hygroscopic swelling in a stress analysis. Nonetheless, a few critical modifications are needed to conduct a thermohygroscopic stress analysis. The temperatures at nodal points, calculated from a heat transfer analysis, can be used in a subsequent diffusion and stress analysis with an option called “∗ TEMPERATURE.” However, the nodal quantities of moisture concentration from a diffusion analysis cannot be used directly in a stress analysis because they cannot be extracted from a result file. They can be extracted from an ABAQUS result file if they have the same record key as the temperature. A sample program to change the record key can be found in Appendix A.3.1. It is important to note that ABAQUS converts only the first 308 MB of a result file if the file size is larger than 308 MB. The size of a result file depends on a node/element count, the number and types of output fields, and an interval of writing output to the result file. These parameters should be controlled so that the size does not exceed the limit. After the record key being changed, the normalized nodal concentration can be used to define the moisture distribution using a “∗ FIELD” command [13]. Finally a volumetric strain caused by both hygroscopic swelling and thermal expansion is defined using a user-defined subroutine (UEXPAN). It is to be noted that ABAQUS does not provide built-in capabilities to define the hygroscopic swelling strain. The subroutine used in the analysis can be found in Appendix A.3.2. The remaining steps of the stress analysis follow a standard procedure of ABAQUS. A final stress field represents the combined effects of moisture and temperature. The scheme allows a systematic coupling of temperature, moisture concentration, and stress without any practical limitation. It is important to note that

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the proposed scheme allows time-independent as well as time-dependent nonlinear constitutive equations of the materials such as plasticity, viscoelasticity, or creep.

8.4.3 Verification of the Modeling Scheme Although the proposed approach does not involve unusually complicated steps, it is instructive to verify the compatibility of the user-defined subroutine with the nonlinear stress analysis function in ABAQUS. A closed-form solution of an annular polymer substrate encasing an inorganic solid bar (axi-symmetric problem) under the generalized plane strain condition is employed to verify the model. It simulates a bi-material system including a polymer–inorganic material interface like a molding compound/silicon chip interface in a semiconductor package. As illustrated in Fig. 8.11, the inner bar has a radius of 10 μm and the polymer substrate has an outer radius of 40 μm. They are assumed to be perfectly bonded. The elastic solution for a general isothermal loading can be found in [55]. Fig. 8.11 Model for the numerical verification

40μm

r 10μm z

The polymer substrate is treated as a viscoelastic material while the inner cylinder is assumed to be elastic. The shear modulus of the polymer can be described by a Prony series [56] G (τ ) = G0 −

NG  i=1

   t , Gi 1 − exp − λi

(8.48)

where G0 is the initial shear modulus; Gi and λi are modulus and time constant of the ith prony element, respectively. The material properties used in the verification are listed in Tables 8.4 and 8.5. The visco-elastic analytical solution was obtained by utilizing the correspondence principle [56]; the problem in the Laplace domain is identical to an “associated” elastic problem in the time domain if boundary conditions are independent of time. It is to be noted that the boundary condition of the problem is the plane strain condition along the axial direction, which is time independent. The reference state is a moisture-free condition at 25◦ C. Then the assembly is subjected to a time-dependent uniform moisture concentration at 85◦ C, which is given as

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201

Table 8.4 Material properties of inner fiber and coating layer

Bulk modulus (GPa) Shear modulus (GPa) CTE (ppm) Solubility (Pa−1 ) CHS (%strain/%wt) a Denotes

Inner fiber

Coating layer

48.6 29.2 0.55 0 0

12.5 5.77a 65 4.93e−7 0.2

initial shear modulus G0 .

Table 8.5 Parameters of the Prony series

i

Gi /G0

τi (s)

1 2 3

0.2 0.2 0.2

100 1,000 10,000



  C (t) = 0.02448 1 − exp −t 100 .

(8.49)

Values Normalized by the Maximum (%)

The moisture concentration increases from zero to the saturated value (0.02448). The above equation simulates approximately a Fickian behavior with an arbitrary diffusivity. Note that the concentration is a non-dimensional quantity in this study. Figure 8.12 shows the normalized moisture content and modulus as a function of time. The moisture is saturated at around 500 s while the modulus continues to relax after the saturation even after 2,000 s. The stress histories are shown in Fig. 8.13, where the radial stresses and the axial stresses at the interface are plotted as a function of time. The initial stresses correspond to thermal loading by the assumed temperature change from 25 to 85◦ C. At the early stage (t < 250 s) the stress increase by hygroscopic swelling is dominant (refer to Fig. 8.12). As the rate of moisture gain decreases, the effect of stress relaxation becomes dominant. The FEA result agrees well with the analytical solution,

Fig. 8.12 Evolution of moisture content and relaxation modulus as a function of time

100 75 50 Moisture Content Modulus

25 0 0

500

1000

Time (sec)

1500

2000

202

C. Jang and B. Han 120 80

σ (MPa)

40 At Interface (r = 10μm) Analytical Solution σrr, FEM

0 –40

σzz, inner bar,FEM σzz, polymer, FEM

–80 –120 0

500

1000

1500

2000

Time (sec) Fig. 8.13 Stress history at the interface calculated from analytic solution and finite element model

which confirms the validity of the user-defined subroutine in the nonlinear stress analysis of ABAQUS.

8.4.4 Discussion: Implementation Using ANSYS Most commercial FEA softwares do not offer the mass (or moisture) diffusion function. In practice, the thermal diffusion (or heat transfer) function can be utilized to simulate the moisture diffusion through a thermal–moisture analogy [4, 31]. An example using ANSYS is described below. ANSYS offers two types of body loads: temperature and fluence. It is important to note that body loads in ANSYS correspond to field variables in ABAQUS. The fluence is a source causing isotropic swelling of materials considered in the model. In the default USERSW option, the relationship between a swelling strain (εsw ) and a fluence is defined as follows: εsw = r (f )n ,

(8.50)

where r is a swelling rate, f is a fluence, and n is an exponent. Equation (8.50) becomes identical to equation (8.17) that defines hygroscopic swelling when n, r, and f are replaced with 1, β, and C, respectively. Since the swelling law of equation (8.50) is available with the default USERSW, neither modification of the user subroutine nor compile/link process is required for the combined hygro-thermo-mechanical analysis. The moisture concentration field, calculated using a proper thermal–moisture analogy, can be imported into the structural analysis using LDREAD command. When the moisture–thermal analogy is employed, however, the initial output is a pseudo-temperature field, not the moisture concentration field. Thus, the field solution imported into each node should be reapplied as a fluence loading using BF

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203

command. A temperature loading can be applied at this point. An example input program is presented in Appendix A.3.3. It is important to note that the USERSW option is available only in the limited elements of ANSYS [57] and the viscoelastic analysis of the combined effect cannot be performed using the current version of ANSYS (ver. 11).

8.5 Application to a Polymer Bi-material Structure The modeling schemes described in this chapter are readily applicable to polymercontaining structures including microelectronic packages and MEMS devices. In this section they are implemented to predict the hygro-thermo-mechanical behavior of a polymer bi-material strip. A numerical model simulates an experimental procedure where a combined hygro-thermal loading is applied to the specimen in a controlled manner and is then validated with experimental measurements.

8.5.1 Bi-material Specimen

4. 10

/2

The bi-material specimen used in the experiment was fabricated by pouring and subsequently curing a liquid state of NCP (non-conductive paste) on an EMC (epoxy mold compound) block. The length and width of the specimen were 13.83 and 4.10 mm, respectively. The thicknesses of NCP and EMC were 1.79 and 1.61 mm, respectively. A mesh setup of the specimen is illustrated in Fig. 8.14. Thermo-mechanical properties of each material were measured using a dynamic material analyzer (DMA) and a thermo-mechanical analyzer (TMA). Hygroscopic properties were also determined through a weight gain test and the moiré interferometry technique [13, 58]. Since moisture soaking was conducted at 85◦ C, the

EMC

1.61

NCP

1.79

Fig. 8.14 Mesh setup of a quarter symmetry model for EMC/NCP bi-material joint (dimensions in millimeters)

13.83 /2

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C. Jang and B. Han Table 8.6 Thermo-mechanical and hygroscopic properties of NCP and EMC (at 85◦ C)

CTE (ppm/◦ C) Poisson’s ratio Young’s modulus (GPa) Diffusivity (mm2 /s) Solubility (1/atm) CHS

NCP

EMC

65 0.35 3.25 (E0 ) 4.509 × 10−6 0.0408 0.28

13 0.3 13 2.8 × 10−6 0.011 0.26

hygroscopic properties were obtained at 85◦ C. All these properties are summarized in Table 8.6. The experiment involved moisture soaking at 85◦ C for 21 h, which should cause stress relaxation of polymers due to viscoelasticity, especially when a glass transition temperature is close to the soaking temperature. The EMC used in this experiment had a glass transition temperature of 165◦ C, which was much higher than the soaking temperature; thus the EMC was assumed to be linear elastic. The viscoelasticity was considered only for the NCP that had a lower glass transition temperature (125◦ C). It was treated as a thermorheologically simple, linear viscoelastic material with a temperature–time shift function [56]. Since a stress relaxation test was carried out in a tensile mode, a Prony series was obtained in terms of tensile moduli as below:  E (τ ) = E0 e∞ +

NG  i=1

  τ ei exp − , λi

(8.51)

where E0 is the initial modulus (Pa), e∞ is the normalized infinite modulus, ei is the normalized modulus of the ith Prony element, and τ is the reduced time (s). The reduced time is related to the actual time and temperature through the integral differential equation t τ=

dt , aT (T)

dτ =

dt , aT (T)

(8.52)

0

where aT is the shift function. The WLF (William–Landel–Ferry) function [59] was used to define a shift function, which is expressed as

 C1 T(t ) − Tref ,

log10 aT (T) = − C2 + T(t ) − Tref

(8.53)

where C1 and C2 are constants and Tref is the reference temperature (K). The constants obtained for the NCP are listed in Table 8.7. Note that E0 is the modulus in Table 8.6.

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Table 8.7 Constants for viscoelastic model of NCP Shift const.

Prony

∞

1

2

3

4

5

6

Tref (K) C1

298 41.28

ei λi (s)

0.0091

0.0507 255

0.0259 5,340

0.0700 1.36e5

0.0682 9.80e5

0.0022 5.20e6

0.0558 5e7

C2 (K)

321.2

Prony

7

8

9

10

11

12

13

ei λi (s)

0.0680 5e7

0.0724 5e8

0.0892 5e9

0.1109 5e10

0.1082 5e11

0.0709 5e12

0.1985 5e13

8.5.2 Experimental Procedure Thermally or hygro-thermally induced deformations of the specimen were documented using the moiré interferometry technique with bi-thermal loading. The details of this optical technique can be found in [27, 60]. The initial moisture concentration of the specimen was made to be zero by prebaking at 125ºC for 48 h. A high-frequency cross-line grating was then replicated on the specimen surface at 85◦ C (“stress-free” temperature). The thermal deformation induced by the temperature change (T = −60◦ C) was first measured by cooling the specimen to 25◦ C. The time durations spent for cooling and deformation measurement were approximately 2 and 5 min, respectively. It was subsequently put into a humidity chamber at 85◦ C/85% RH. After 21 h of moisture absorption, the specimen was taken out of the humidity chamber and cooled to room temperature again to measure combined deformations induced by both the temperature change and moisture intake. The experimental procedure is schematically illustrated in Fig. 8.15.

8.5.3 Simulation Procedure The experimental procedure was simulated using an FE model that encompassed moisture diffusion and combined hygro-thermo-mechanical stress modeling Specimen fabrication

Measurement of hygrothermal deformation (5 min)

Baking at 125°C (48 hours)

Cool down to 25°C (2 min)

Grating replication at 85°C (start of simulation)

Soaking at 85°C/ 85%RH (21 hours)

Fig. 8.15 Loading and deformation measurement procedure

Cool down to 25°C (2 min)

Measurement of thermal deformation (5 min)

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schemes. A 3-D quarter-symmetry model (Fig. 8.14) was built in ABAQUS. The simulation followed the experimental procedure described above. The first step was to determine deformations obtained by cooling the specimen from 85 to 25◦ C. The second step was to simulate moisture soaking at 85◦ C/85% RH for 21 h. While moisture diffusion inside the specimen was solved, moisture concentration fields were stored for subsequent structural analyses as a function of time until the end of soaking time. The history of specimen deformations during the soaking process was calculated by the combined stress model, which considered the viscoelasticity of the NCP. In the last step the specimen temperature was lowered to 25◦ C and deformations by hygro-thermal loadings were calculated. The specimen was assumed to be isothermal throughout the simulation.

8.5.4 Validation of the FE Model The results obtained from the first and third steps of the simulation were compared with the experimental data as shown in Figs. 8.16 and 8.17. The displacement fields in Fig. 8.16 reveal the effect of thermal deformations only (T = −60◦ C). A convex upward (∩) bending deformation was produced by the much larger CTE of the NCP. The experimental data match the numerical prediction very well. The displacements in Fig. 8.17 present the combined effect of thermal contraction and moisture-induced swelling. The swelling expanded the specimen and thus

Fig. 8.16 Temperature-induced deformation (T = −60ºC). The contour interval is 417 nm

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Fig. 8.17 Combined effects of thermal contraction and moisture-induced swelling. The contour interval is 417 nm

the total strains decreased. Reduction of the fringe gradient in the directions of the coordinate axes (or reduction of the total normal strains, ∂U/∂x and ∂V/∂y) is evident in both patterns in Fig. 8.17. The modeling scheme predicts the deformation trend very well in both materials even under the combined loading. Interestingly, while the U displacement fields in Figs. 8.16 and 8.17 were similar, the V displacement field of Fig. 8.17 was completely different from that of Fig. 8.16. It resulted from a hygroscopic swelling mismatch between the NCP and the EMC. Although the swelling coefficients of two materials were comparable, the NCP had much larger hygroscopic swelling due to larger moisture content (equation (8.17)). The swelling deformation, which has an opposite sign to the thermal contraction, reduced the total strain in the y-direction but at a much higher rate for the NCP, which resulted in the closed-loop fringes in the NCP region (the zero displacement gradient or zero total strain in the y-direction). On the other hand, since the modulus of EMC was much larger than that of NCP, the U displacement field of the NCP was constrained by the EMC in spite of its larger swelling deformation. Consequently, the thermally induced bending displacement fields were preserved after the combined loading. A large stress-induced compressive strain of the NCP was resulted. Acknowledgments This work was supported partly by the Center for Advanced Life Cycle Engineering (CALCE) of the University of Maryland and the Integrated Electronics Engineering Center (IEEC) of the State University of New York at Binghamton. Their support is acknowledged gratefully. The authors would also like to thank Prof. Seungbae Park in the State University of New York at Binghamton, Dr. Samson Yoon and Dr. Seungmin Cho in Samsung Techwin Co., Ltd., and Dr. Arindam Goswami in Apple Inc. for their friendly supports and technical contributions.

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Appendix A.1 FDM Schemes for Mass Diffusion Equations A.1.1 Anisothermal 1-D Problem For a 1-D mass diffusion problem, the diffusion equation of equation (8.9) can be reduced to   ∂φ ∂ ∂(Sφ) ∂S +S = D . φ ∂t ∂t ∂x ∂x

(8.54)

The explicit finite difference form of equation (8.54) can be expressed as φ t+t − φxt St+t − Sxt Sxt x + φxt x t t  t t t  t = =

Dx+x +Dx 2



Sx+x φx+x −Sxt φxt − x



Dtx +Dtx−x 2



t t Sxt φxt −Sx−x φx−x x

x

t t t t Dtx + Dtx−x Sx−x φx−x − Dtx+x + 2Dtx + Dtx−x Sxt φxt + Dtx+x + Dtx Sx+x φx+x

2 (x)2

(8.55)

The superscript t and the subscript x denote the time and spatial dependency of φ, respectively. The values of St , St+t , and Dt can be calculated directly from equation (8.4). For an isothermal problem, equation (8.55) is reduced to t t Dφx−x − 2Dφxt + Dφx+x φxt+t − φxt = . t (x)2

(8.56)

For multi-material systems, the normalized concentration at the interface must satisfy a certain condition to ensure a continuous mass flux. Assuming that the materials I and II are located on the left and right sides of the interface, respectively, the continuity requires DI SI

! ! ∂φ !! ∂φ !! = D S II II ∂x !x− ∂x !x+ i

(8.57)

i

where xi − and xi + denote the left side and right side at the interface xi . The discretization of equation (8.57) yields DtI SIt

φxt i − φxt i −x x

= DtII SIIt

φxt i +x − φxt i x

.

(8.58)

.

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Strictly speaking, equation (8.57) is valid for an infinitesimal interface volume whose moisture content is negligible. Once the analysis domain is discretized, however, the interface volume takes finite values and retains a certain amount of moisture. A more rigorous formulation for the interface can thus be derived by considering the moisture accumulation at the interface volume (interface length, dx, after normalized by the area in the 1-D case). It is mathematically expressed as ! !     ∂φ dx ∂φ dx ∂φ !! ∂φ !! + − + SII = −J + J = DII SII − DI SI . (8.59) SI ∂t 2 ∂t 2 ∂x !xi + ∂x !xi − The corresponding finite difference form is obtained as φt − φxt i φ t − φxt i −x − φxt i φxt+t x i t t xi +x t t xi = DII SII − DI SI (SI + SII ) 2 t t x

(8.60)

When node spacing is sufficiently small, equations (8.58) and (8.60) yield practically the same result. It would be worth noting that the implicit scheme can be obtained simply by replacing all superscript t in the right-hand sides of equations (8.55) and (8.60) with t + t.

A.1.2 Isothermal Axisymmetric Problem The explicit finite difference form of equation (8.38) can be expressed as 

t t t t − 2φrt + φr−r − φr−r D φr+r φrt+t − φrt D φr+r . + = t r 2 (r) (r)2

(8.61)

Mass continuity at the volume about the center node (r = 0 ∼ r/2) yields S

∂φ ∂φ dV = −JA = DSA . ∂t ∂r

(8.62)

In the finite difference form, φ0t+t − φ0t · t



r 2

 =D

t − φt φr 0 . r

(8.63)

Since the area is not constant along the r axis, the mass continuity at the interface (r = ri ) depicted in equation (8.59) should be modified as ! ! ! ∂φ ∂φ ∂φ !! − ∂φ ! − D S A . SI dV − + SII dV + = −J + A+ + J − A− = DII SII A+ I I ! ∂t ∂t ∂r ri + ∂r !ri − (8.64)

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The finite difference form is then obtained as SI

φrt+t −φrt i i t



· π ri2 − ri −

= DII SII · 2π ri +

r 2



 r 2 2 ·



+ SII

φrt +r −φrt i i r

φrt+t −φrt i i t

·π



 r 2 2

ri +

− DI SI · 2π ri −

r 2



·

− ri2



φrt i −φrt −r i r

. (8.65)

Re-arranging equation (8.65) yields φrt+t −φrt i i t

 SI ri r −

r2 4

= DII SII (2ri + r)

+ SII ri r +

φrt +r −φrt i i r

r2 4



− DI SI (2ri − r)

φrt −φrt −r i i r

.

(8.66)

A.2 ANSYS Input Templates for the Advance Analogy   A.2.1 Transient Case ∇T = 0 but T˙ = 0 The macro listed below is the portion for the setup of material properties and solution steps included in the modeling program of the case study. Since the system is spatially isothermal, the properties of each material are homogenous. Therefore, they can be defined as constants at each solution step: ! Defining parameters M1=19.74 ! M of material I M2=6.58 ! M of material II R_gas=8.3145 ! Gas constant D01=5e-3 ! D0 of material I S01=6e-10 ! S0 of material I D02=4e-3 ! D0 of material II S02=2e-10e ! S0 of material II Ed1=-5e4e ! D1 = D01 * exp(Ed1/R_gas/T) Es1=4e4 ! S1 = S01 * exp(Es1/R_gas/T) Ed2=-5e4 ! D2 = D02 * exp(Ed2/R_gas/T) Es2=4e4 ! S2 = S02 * exp(Es2/R_gas/T) ! RH = H0*exp(Eh/R_gas/T) for fixed partial vapor pressure (P at 25C/100%RH) ! H0 = S0*Pv/M in Eq. (16), where Pv = 3207 Pa in this case H0=9.742e-8 ! Note: In this program Evp was set 4e4 for consistency with Es ! Its actual value = 4.15e4 Eh=Es1 ! Will be used to calculate phi_BC(T) for fixed Pv T0=298 ! Initial temperature dt=9 ! Time step ! /prep7 et,1,55 ! 2D thermal element

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c,1,M1 ! c = M ("Modified" solubility) c,2,M2 dens,1,1 ! Densities = 1 dens,2,1 !............................................................ ! Solid modeling, meshing, and grouping for IC/BC setup !............................................................ /sol antype,4 ! Initial condition setup. Node components pre-defined ! Phi of exterior surface nodes -> RH of environment ic,exterior,temp,H0*exp(Eh/T0) ! Phi of interior nodes -> zero (initially fully dried) ic,interior,temp,0 ! *do,ii,1,400 time,ii*dt ! System temperature at the current solution step T1=T0+(1/60)*ii*dt ! Calculation of boundary RH at the current solution step d,exterior,temp,H0*exp(Eh/R_gas/T1) ! Update of conductivity of the analogy kxx,1,D01*exp(Ed1/R_gas/T1)*M1 ! k = DM kxx,2,D02*exp(Ed2/R_gas/T1)*M2 nsub,1,1,1 solv *enddo

  A.2.2 Anisothermal Case ∇T = 0 and T˙ = 0 A truly anisothermal loading gives rise to much more complexity in the analogy model. An example of modeling and solving process is illustrated in Fig. 8.18. The key feature is re-assignment of material properties to each element after sorting all elements by materials and temperatures. In ANSYS, the element table feature [57] is useful when this process is to be implemented: ! key part for material property definition and update ! All parameters used in this macro are identical to those in A.1 /prep7 et,1,55 ! 2D thermal element ! Pre-definition of material properties as a function of temperature ! In this program, they are defined from 1C to 100C with one degree step *do,ii,1,100 dens,ii,1 c,ii,M1 kxx,ii,D01*exp(Ed1/(273+ii))*M1 *enddo *do,ii,101,200 dens,ii,1 c,ii,M2 kxx,ii,D02*exp(Ed2/(173+ii))*M2 *enddo

212 Fig. 8.18 General solution process of the anisothermal problem using ANSYS

C. Jang and B. Han Mesh setup

Heat transfer analysis

Modification of model for diffusion analysis Invoking heat transfer analysis result

Calculation of element-to-element temperature

Sorting by element number and material

Re-assignment of element-to-element material property

Solve diffusion

Next time step (Δt)

!........................................................... ! Solid modeling, meshing, and grouping for IC/BC setup !........................................................... ! Total element count = 8000 (4000 for each material) ! Node numbers must be controlled material-by-material (using NUMCMP) n_total=8000 *dim,t_out,array,n_total /sol antype,4 ! *do,ii,1,400 /post1 ! Reading temperature distribution data from aniso_ht.rth (result file) file,aniso_ht,rth set,ii etable,t_res,temp ! Element table of temperature distribution ! Storing temperature data into array *do,jj,1,n_total *get,tt1,etab,1,elem,jj t_out(jj)=tt1 *enddo *if,ii,gt,1,then file„rth *endif ! ! Re-defining element-to-element material numbers /prep7

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*do,jj,1,n_total/2 emodif,jj,mat,nint(t_out(jj))-273 emodif,jj+4000,mat,nint(t_out(jj+4000))-173 *enddo /sol *if,ii,eq,1,then antype,trans ! Initial condition setup. Node components pre-defined ! Phi of exterior surface nodes -> RH of environment ic,exterior,temp,H0*exp(Eh/T0) ! Phi of interior nodes -> zero (initially fully dried) ic,interior,temp,0 *else antype, ,rest *endif ! Environment temperature was assumed to be controlled as in A.1 ! Note: Temperature inside polymers was input from the heat transfer T1=T0+(1/60)*ii*dt time,ii*dt ! Instead of ambient temperature, actual surface temperature ! has to used to calculate BC because of temperature difference ! between environment and solid surface (n_bc: node number at surface) ! If temperature is not uniform over boundary surfaces, ! BC should be input node-to-node d,exterior,temp,t_out(n_bc) nsub,1,1,1 solv *enddo

From a practical point of view, the spatially anisothermal complexity is not needed for most of the problems since spatial temperature gradients during heating or cooling can be ignored (usually less than 1◦ C). In addition, the time step can be controlled in an automatic manner by implementing a customized macro for time step adjustment while taking the rate of concentration change at each step into consideration.

A.3 Templates for the Combined Analysis A.3.1 Program to Change the Record Key This program changes the record key of the nodal concentration (221) obtained from a diffusion analysis using ABAQUS so that the concentration has the record key of the temperature (201). The detailed explanation about subroutines and variables used in this program is available in [61]: SUBROUTINE diff2temp INCLUDE ’aba_param.inc’ DIMENSION ARRAY(513), JRRAY(NPRECD,513) EQUIVALENCE (ARRAY(1), JRRAY(1,1))

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PARAMETER (MXUNIT=21) INTEGER LRUNIT(2,MXUNIT),LUNIT(10) CHARACTER FNAME*80 DATA LUNIT/1,5,6,7,9,11,12,13,20,28/ NRU = 1 LOUTF = 2 LRUNIT(1,1)=8 LRUNIT(2,1)=2 WRITE(6,60) 60 FORMAT(1X,’Enter the name of the input file(s) (w/o extension):’) READ(5,’(A)’) FNAME CALL INITPF (FNAME, NRU, LRUNIT, LOUTF) JUNIT=8 KEYPRV = 0

C

DO 100 INRU = 1, NRU JUNIT = LRUNIT(1,INRU) CALL DBRNU (JUNIT) I2001 = 0 DO 80 IXX2 = 1, 100 DO 80 IXX = 1, 99999 CALL DBFILE(0,ARRAY,JRCD) WRITE(6,*) ’KEY/RECORD LENGTH = ’, JRRAY(1,2), JRRAY(1,1) IF (JRCD .NE. 0 .AND. KEYPRV .EQ. 2001) THEN WRITE(6,*) ’END OF FILE #’, INRU CLOSE (JUNIT) GOTO 100 ELSE IF (JRCD .NE. 0) THEN WRITE(6,*) ’ERROR READING FILE #’, INRU CLOSE (JUNIT) GOTO 110 ENDIF LWRITE=1 IF (INRU.GT.1) THEN IF (JRRAY(1,2).GE.1900 .AND. JRRAY(1,2).LE.1909) LWRITE=0 IF (JRRAY(1,2).GE.1912 .AND. JRRAY(1,2).LT.1922) LWRITE=0 IF (JRRAY(1,2) .EQ. 2001 .AND. I2001 .EQ. 0) THEN I2001 = 1 LWRITE = 0 ENDIF ENDIF IF (INRU .EQ. 1 .OR. LWRITE .EQ. 1) THEN KEY=JRRAY(1,2)

1 2 3

IF((KEY.EQ.1900).OR.(KEY.EQ.1901).OR. (KEY.EQ.1902).OR. (KEY.EQ.1910).OR.(KEY.EQ.1911).OR. (KEY.EQ.1921).OR. (KEY.EQ.1922).OR.(KEY.EQ.1980).OR. (KEY.EQ.2000).OR. (KEY.EQ.2001).OR.(KEY.EQ.1)) THEN CALL DBFILW(1,ARRAY,JRCD) IF (JRCD .NE. 0) THEN

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WRITE(6,*) ’ERROR WRITING FILE’ CLOSE (JUNIT) GOTO 110 ENDIF C C If a current RECORD KEY is 221, the key is changed into 201 and the associated data C are written to an output file. C ELSE IF( (KEY.EQ.221)) THEN JRRAY(1,2)=201 CALL DBFILW(1,ARRAY,JRCD) IF (JRCD .NE. 0) THEN WRITE(6,*) ’ERROR WRITING FILE’ CLOSE (JUNIT) GOTO 110 ENDIF ENDIF ENDIF KEYPRV = JRRAY(1,2) 80 CONTINUE 100 CONTINUE 110 CONTINUE CLOSE(9) C RETURN END

A.3.2 Example Program for UEXPAN The macro listed below combines hygroscopic swelling and thermal expansion to define a total volumetric strain in ABAQUS: SUBROUTINE UEXPAN(EXPAN,DEXPANDT,TEMP,TIME,DTIME,PREDEF,DPRED, STATEV,CMNAME,NSTATV)

$ C

INCLUDE ’ABA_PARAM.INC’ C CHARACTER*80 CMNAME C $ C C C C C

DIMENSION EXPAN(*),DEXPANDT(*),TEMP(2),TIME(2),PREDEF(*), DPRED(*),STATEV(NSTATV) EXPAN(1) : VOLUMETRIC STRAIN TEMP(1) : TEMPERATURE AT T+DT TEMP(2) : TEMPERATURE INCREMENT PREDEF(1): FIELD VARIABLE AT T+DT (I.E., NORMALIZED CONCENTRATION φ) DPRED(1) : FIELD VARIABLE INCREMENT ALPHA = 1.0D-05 BETA = 1.D-1 SOLU = 1 EXPAN(1) = ALPHA*TEMP(2)+ SOLU*BETA*PREDEF(1)

C RETURN END

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A.3.3 ANSYS Input Template for Hygro-Thermal Loading This example program illustrates (1) how to define CHS and (2) how to read the distributions of moisture concentration and temperature from separate external result files: ... ! DEFINE MATERIAL PROPERTIES INCLUDING SWELLING COEFFICIENT (N-MM-SEC-K) EX,1,3E3 NUXY,1,0.4 ALPX,1,30E-6 TB,SWELL,1 ! C72=10 FOR ACTIVATION OF USERSW ! EPS=C67*(FLUENCE)ˆC68 WHERE C67=SWELLING COEFFICIENT AND C68=1 TBDATA,72,10 TBDATA,67,0.1,1 ... ... ! READ MOISTURE CONCENTRATION FIELD FROM RESULT FILE (HYGRO.RTH) ! ELEMENT NUMBER MUST BE COMPRESSED (NUMCMP) IN ADVANCE ALLS LDREAD,TEMP,NO_STEP,NO_SUBSTEP,HYGRO,RTH ! CONVERT DUMPED TEMPERATURE FIELD TO FLUENCE FIELD *DO,II,1,NO_ELEM *GET,BF_MOIST,NODE,II,NTEMP BF,II,FLUE,BF_MOIST *ENDDO ! READ ACTUAL TEMPERATURE FIELD FROM RESULT FILE (TEMPERATURE.RTH) LDREAD,TEMP,NO_STEP,NO_SUBSTEP,TEMPERATURE,RTH ...

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51. Jourdain, A., De Moor, P., Pamidighantam, S., Tilmans, H.A.C., “Investigation of the hermeticity of BCB-sealed cavities for housing (RF-) MEMS devices,” Proceedings of the 15th IEEE International Conference on Micro Electro Mechanical Systems, Las Vegas, NV, USA, pp. 677–680, 2002. 52. Noh, H., Moon, K.S., Cannon, A., Hesketh, P.J., Wong, C.P., “Wafer bonding using microwave heating of parylene for MEMS packaging,” Proceedings of IEEE Electronic Components and Technology Conference, pp. 924–930, 2004. 53. Goswami, A., “Quantitative hermeticity measurement of micro- to nano-liter scale cavities,” PhD Dissertation, College Park, MD: University of Maryland at College Park, 2008. 54. Jang, C., Goswami, A., Han, B., Ham, S., “In-situ measurement of gas diffusion properties of polymeric seals used in MEMS packages by optical gas leak test”, Journal of Micro/Nanolithography, MEMS, and MOEMS (JM3), 8, 043025, 2009. 55. Wang, Y., Han, B., Kim, D.W., Bar-Cohen, A., Joseph, P., “Integrated measurement technique for curing process-dependent mechanical properties of polymeric materials using fiber bragg grating”, Experimental Mechanics, 48, 107–117, 2008. 56. Riande, E., Diaz-Calleja, R., Prolongo, M., Masegosa, R., Polymer Viscoelasticity: Stress and Strain in Practice. New York, NY: Marcel Dekker, 1999. 57. ANSYS release 10 documentation 2005. 58. Yoon, S., Han, B., Cho, S., Jang, C., “Experimental verification of non-linear finite element analysis for combined hygroscopic and thermo-mechanical stresses,” Proceedings of 2005 SEM Annual Conference, Portland, OR, USA, 2005. 59. Williams, M.L., Landel, R.F., Ferry, J.D., “The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids”, Journal of the American Chemical Society, 77, 3701–3707, 1955. 60. Han, B., Post, D., Ifju, P., “Moiré interferometry for engineering mechanics: current practices and future developments”, Journal of Strain Analysis for Engineering Design, 36, 101–117, 2002. 61. ABAQUS, Abaqus 6.4 Analysis User s Manual, Section 6.8. Providence, RI: ABAQUS Inc.

Chapter 9

Methodology for Integrated Vapor Pressure, Hygroswelling, and Thermo-mechanical Stress Modeling of IC Packages T.Y. Tee

9.1 Introduction In addition to the board-level solder joint reliability [1–2], moisture-induced failures during moisture preconditioning and reflow soldering are also a major concern for plastic IC packages. The moisture-induced failures, e.g., popcorning and delaminations, of IC packages are common phenomena during solder reflow. Usually the package is first preconditioned at certain temperatures to absorb moisture. Failures occur due to sudden vaporization of moisture in the package at high-temperature condition. It is critical therefore to evaluate the level of the internal vapor pressure generated in the package during reflow. The popcorn failure was first established by Fukuzawa et al. [3] in 1985 and later reported in many publications [4–6]. JEDEC standard [7] is used to conduct reliability test on moisture sensitivity of the electronic packages. Kitano et al. [5] showed that the package cracking is not controlled by the absolute moisture weight gain, but is due to the local moisture concentration at the critical interfaces. Moisture diffusion modeling is a must in the plastic IC package design for reliability against moisture-induced failures. Modeling of the generated vapor pressure within the package during reflow soldering process is a key element in understanding the failure mechanisms. Previous researchers [4–6] assumed that delamination exists prior to the reflow soldering process and considered the vapor pressure as traction loading caused by the delaminated interfaces. Several studies were carried out and methods were proposed to estimate the vapor pressure acting on the delaminated interface. Since the vapor pressure is generated anywhere in the package, it is necessary to investigate the whole-field vapor pressure distribution in the entire package prior to understanding its effect on the package delamination. The vapor pressure model developed by Fan et al. [8–13] has been widely accepted by the semiconductor industry and has been successfully applied to many cases and validated by experimental data for different packages under different reflow conditions. The model was applied to a plastic BGA and

T.Y. Tee (B) e-mail: [email protected] X.J. Fan, E. Suhir (eds.), Moisture Sensitivity of Plastic Packages of IC Devices, Micro- and Opto-Electronic Materials, Structures, and Systems, C Springer Science+Business Media, LLC 2010 DOI 10.1007/978-1-4419-5719-1_9, 

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flip-chip BGA IC package in the earlier work of the author [8]; however, the integration with thermo-mechanical stress and hygro-mechanical stress was not considered. Recently it has been found that the normalization approach for moisture diffusion modeling based on thermal–moisture analogy cannot be applied to a reflow process [13]. A new approach, the so-called DCA (direct concentration approach), has been developed therefore [12]. The integrated stress modeling during reflow soldering [14] requires five types of modeling, namely (1) moisture diffusion during moisture preconditioning and reflow, (2) thermal modeling, (3) hygro-mechanical modeling, (4) thermomechanical modeling, and (5) vapor pressure modeling. In this chapter, QFN (quad flat non-lead) and FCBGA (flip-chip ball grid array) packages are used as test vehicles for carrying out modeling of the behavior and performance of moisturesensitive plastic packages of IC devices. Different finite element types, boundary conditions, and different loading conditions were considered. The theories and procedures for each type of modeling are briefly described below. In addition, the failure of FCBGA with no-flow underfill during pressure cooker test (PCT) is studied with the combined thermo-mechanical and hygro-mechanical stress modeling [15].

9.2 Moisture Diffusion Modeling 9.2.1 Modeling Methodology In modeling, the transient moisture diffusion equation is analogous to the transient heat conduction equation. It can be described by Fick’s law as follows:   2 ∂ C ∂ 2C ∂ 2C ∂C =D + 2 + 2 . ∂t ∂x2 ∂y ∂z

(9.1)

Here C is the local moisture concentration; x, y, and z are the spatial coordinates; D is the diffusivity (the rate of diffusion); and t is the time. However, unlike temperature, the moisture concentration is discontinuous along the bi-material interface. Therefore, Galloway and Miles [4] introduced a new dependent variable, partial pressure (P = C/S, where S is solubility), to resolve the computational problem. Another similar approach is to use moisture wetness, w, as the field variable. This variable is continuous across the multi-material interface [16–17]. It is defined as follows: w=

C , Csat

1≥w≥0,

(9.2)

where Csat is the saturated moisture concentration. The lower limit, w = 0, refers to the dry condition and the upper limit, w = 1, means that the specimen is fully saturated with moisture. The Equation (9.1) can be rewritten as

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  2 ∂ w ∂ 2w ∂ 2w ∂w + + =D ∂t ∂x2 ∂y2 ∂z2

(9.3)

and could be solved as a typical heat transfer problem, i.e., by using any commercially available FEA software. The above normalization applies only when the saturated moisture concentration is independent of temperature during the reflow process [12]. With this assumption, for the moisture absorption modeling, the initial condition is w = 0 for the whole package and the boundary condition is w = 1 at the external surfaces which are exposed to the ambient moisture. The moisture properties for the molding compound and the die-attach material, i.e., diffusivity and Csat , characterized under 85◦ C/85% RH, are shown in Table 9.1 [14]. The moisture properties can be obtained by curve fitting the moisture weight gain data of a thin disk specimen with the analytical solution to the 1D moisture diffusion equation. The die and the copper leadframe are assumed to be impermeable to moisture (i.e., do not absorb moisture), so that they have zero diffusivity and Csat . Table 9.1 Moisture and hygroswelling material properties of QFN package Material

D (mm2 /s)

Csat (mg/mm3 )

β, CME (mm3 /mg)

Hygro-strain (β × Csat )

Mold compound Die attach

7.43e–7 1.25e–5

7.06e–3 6.20e–3

0.222 0.520

1.57e–3 3.22e–3

The moisture weight gain curve for the molding compound under 85◦ C/85% RH is shown in Fig. 9.1. This is a typical curve with high moisture absorption rate at the beginning (first few days). The curve describes steady state or saturation state at a longer time. It was found that the weight gain curve fitted by Fick’s law overestimated the moisture absorption rate in the long run. The non-Fickian behavior of the test sample could be that moisture diffusion close to the saturation stage is dominant by a slow rate of water condensation from vapor to liquid phase. The Cs of the polymeric material is much higher than the moisture density in the humidity

Moisture Weight Gain Curve

Weight (mg)

160

Fig. 9.1 Moisture weight gain curve for mold compound

120 Experiment Data

80

Equation

40 0 0

200

400

600

800

Time (hr)

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T.Y. Tee

chamber, and therefore some of the vapor phase water must be condensed into the liquid state to make more room for moisture diffusion at the vapor phase from the ambient into the microvoids in the material. At the beginning of weight gain test, moisture density in the microvoid is low, there is no condensation, and the curve can be described well by Fick’s law. At a longer time, the slower condensation process is dominant, so that the moisture diffusivity at vapor phase is reduced at higher moisture concentration. This is the so-called non-Fickian behavior. The effect of this condensation process shall be studied in detail in the future. Moisture desorption diffusivity is also an important material property, especially during the reflow soldering process. This diffusivity determines particularly the moisture weight loss. Moisture diffusivity during desorption at reflow is faster than absorption at the preconditioning temperature. Figure 9.2 shows the effect of temperature (30–220◦ C) on moisture diffusivity during desorption for the molding compound, D (MC), and the die attach, D (DA), material. The diffusivity is faster at higher temperatures and the relationship between the diffusivity and temperature can be described by the following equation: D = D0 eQ/RT ,

(9.4)

where D0 is the diffusion coefficient, Q is the activation energy (eV), R is Boltzmann’s constant (8.83e–5 eV/K), and T is the absolute temperature (K). The D0 and Q for the molding compound and the die attach materials during desorption process are shown in Table 9.2. Diffusivity vs. Temperature 1.E–02

Diffusivity (mm2/s)

0

50

100

150

200

250 Temperature (C)

1.E–03

1.E–04 D (MC) D (DA)

1.E–05 1.E–06

Fig. 9.2 Diffusivity as a function of temperature

Table 9.2 Diffusivity constants of moisture desorption

Material

D0 (mm2 /s)

Q (eV)

Mold compound Die attach

0.18 0.35

−0.304 −0.293

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9.2.2 Modeling Results The transient moisture wetness distribution in QFN (symmetric half model) is shown in Fig. 9.3, ranging from 0 to 100% saturation. The moisture diffuses into the package through the molding compound and gradually spreads out into the die attach layer. At the end of 168 h of moisture preconditioning under 85◦ C/85% RH, the package is almost fully saturated with moisture. During the 5-min solder reflow, external package surface loses a significant amount of moisture due to the high moisture desorption rate. The moisture diffusivity is a few orders higher at the reflow temperature than at the moisture preconditioning temperature. However, the moisture concentration in the interior of the package, including critical die attach and die/molding compound interfaces, still remains relatively unchanged. The local moisture concentration in these critical interfaces determines the strength of the interfacial adhesion and the magnitude of induced internal vapor pressure. This process is partially responsible for the moisture-induced failures in the package, e.g., delamination and popcorning.

Fig. 9.3 Transient moisture wetness distribution

QFN Half Model

Wetness Die DA

MC Cu

1hr

12hr

168hr

Reflow

9.3 Thermal Modeling 9.3.1 Modeling Methodology Similar to the mass diffusion, the following transient heat conduction equation can be solved to obtain the temperature distribution in the package during reflow process:

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∂T = αT ∂t



∂ 2T ∂ 2T ∂ 2T + + ∂x2 ∂y2 ∂z2

 .

(9.5)

Here T is the temperature; x, y, and z are the spatial coordinates; and α T is the thermal diffusivity. The boundary condition used is the external surface temperature, according to the reflow temperature profile measured, within the specification of JEDEC test standard (e.g., maximum temperature of 220◦ C, +5/−0◦ C). The effects of the convection coefficient (h) and the ambient temperature in the multi-zone oven are already considered by measuring the reflow profile. The thermal material properties, specific heat (Cp ), thermal conductivity (k), and density (ρ) are shown in Table 9.3. They are related to the thermal diffusivity by the formula αT =

k . ρ · Cp

(9.6)

Table 9.3 Thermal material properties Material

Cp (J/kg K)

k (W/m K)

ρ (kg/m3 )

Copper Die Mold compound Die attach

385 712 900 800

390 108 0.67 1.2

8,950 2,330 2,088 2,400

9.3.2 Modeling Results The thermal model is analogous to the moisture diffusion model. However, the thermal diffusivity is much faster than the moisture diffusivity. Figure 9.4 shows the temperature distribution in the package during 5-min reflow (from 25◦ C to peak

QFN Half Model Die DA

MC Cu Temperature (°C)

Fig. 9.4 Package temperature distribution during reflow

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227

temperature of 220◦ C). Heat is conducted faster in the die and in the copper leadframe than in the molding compound. When the external surface is heated to 220◦ C after 5 min, the internal package reaches this uniform temperature within a few seconds. Therefore, in the subsequent thermo-mechanical and vapor pressure models, temperature distribution during reflow can be assumed to be uniform throughout the package.

9.4 Vapor Pressure Modeling [11] 9.4.1 Modeling Methodology Representative volume element (RVE) approach is applied to estimate the vapor pressure generated inside the material. Let us take a very small representative material sample, termed RVE. From the microscopic level, the RVE is large enough to be statistically representative of the material properties at this location. Therefore, a field quantity, the void volume fraction, f, can be defined as [8, 9] f =

dVf , dV

1 ≥ f ≥ 0,

(9.7)

where dVf is the void volume and dV is the element volume. When f = 1 (fully voided), it implies that the delamination occurs at this location. The void volume fraction is a field variable and has different evolution at different locations. It evolves faster along the interface than inside the material if the interfacial adhesion is weak. However, the initial microvoids are distributed randomly, but uniformly in the material; thus the initial void volume fraction, f0 , is a material property. A useful quantity, the moisture density in the voids, can be described as ρm =

C dWm dWm /dV = , = dVf dVf /dV f0

(9.8)

where dWm is the moisture weight in an RVE. In addition, the transition temperature, T1 , can be defined [8, 11] as the temperature at which the moisture in the voids is fully transformed to vapor phase, ρm (xi , T0 ) = ρg (T1 ),

(9.9)

where ρ g (T1 ) is the saturated vapor density at temperature T1 and T0 is the preconditioning temperature at which the moisture is absorbed. There are three distinct cases, at which vapor pressure can be computed [8, 11]. It is assumed that the water vapor follows the ideal gas law for the cases 1 and 2. The vapor pressure can be calculated based on the local moisture concentration after preconditioning which determines the transition temperature, T1 .

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The first case is when the moisture density in the voids is low enough, so that all the moisture becomes vaporized at the preconditioning temperature, T0 : p=

Cpg (T0 )T f ρg (T0 )T0

when T0 ≥ T1 ,

(9.10)

where p is the pressure and pg is the saturated vapor pressure. In the second case, the moisture is fully vaporized at the temperature between the preconditioning temperature, T0 , and the peak reflow temperature, T: p=

pg (T1 )T T1

when T ≥ T1 ≥ T0 .

(9.11)

For the last case, the moisture is not fully vaporized even at reflow temperature, T: p = pg (T)

when T1 ≥ T.

(9.12)

This case uses thermodynamics table, instead of the ideal gas assumption, to determine the saturated pressure at a particular temperature. The initial void volume fraction, f0 , can be estimated from the material temperature-dependent moisture property. According to equation (9.8), when saturated, the local concentration, C, is the same as Csat . So, the initial void volume fraction can be expressed as f0 =

Csat . ρm

(9.13)

Since ρm ≈ 1.0 g/cm3 , we have ! f0 ≈ Csat !100◦ C/100% RH ,

(9.14)

where 100◦ C/100% RH is selected as the near-saturated condition and unit of Csat is in g/cm3 or mg/mm3 . Alternatively, one can measure the Csat of test sample in boiling water to accelerate the moisture absorption. Equation (9.14) provides a simple way to measure the approximate magnitude of the voids existing in materials. The estimation is at the lower limit, since the moisture usually exists as a mixture of water and vapor at 100◦ C/100% RH. Table 9.4 lists the results of the initial void volume fraction (f0 ) for the molding compound and the die attach material. The Table 9.4 Initial void volume fraction

Material

f0 (%)

Mold compound Die attach

0.83 0.76

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229

accuracy of f0 is not critical in this particular study, because of its low sensitivity, and will be discussed in a later section. The linear vapor pressure-induced strain can be estimated as ∈p =

1 − 2ν p, E

(9.15)

where ν is Poisson’s ratio, E is Young’s modulus, and p is the average vapor pressure. The modulus of the molding compound drops a few orders at the reflow temperature; thus the vapor pressure strain may become as important as thermal or hygro-strain. For example, for the molding compound with the saturated vapor pressure of 2.32 MPa, the strain is equivalent to CTE of 18 ppm/◦ C under the same 175–220◦ C temperature loading. The magnitude of this vapor pressure induced strain is of the same order of magnitude as hygro- and thermal strains. The vapor pressure strain induces additional mismatch in the package, in addition to the CTE and CME mismatches. It must also be pointed out that such an expansion is directly related to the vapor pressure distribution, rather than to the moisture distribution.

9.4.2 Modeling Results From the transient moisture distribution (see Fig. 9.3), the corresponding vapor pressure distribution at the reflow temperature can be calculated (see Fig. 9.5) based on equations (10), (11), and (12). Case 3 of the saturated pressure is mostly encountered here. QFN Half Model

1hr

12hr

168hr

Reflow

Fig. 9.5 Vapor pressure distribution at reflow temperature

5x fo

Die DA

MC Cu

Vapor Pressure (MPa)

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Moisture diffusion and vapor pressure have very different rates of saturation. Moisture diffusion gradually reaches the near-saturation condition at 168 h of moisture preconditioning. However, for vapor pressure, it reaches saturated pressure at the reflow temperature with only 12 h of moisture preconditioning under 85◦ C/85% RH. This implies that at JEDEC level 1, the void moisture density exceeds its critical density value after about 12 h. Subsequent addition of moisture density has no effect on the saturated pressure. Therefore, the vapor pressure-induced strain is related directly to the vapor pressure distribution, rather than to the moisture distribution. At 1 h of moisture preconditioning (see Fig. 9.5), the void moisture density is below the critical value and, therefore, the vapor pressure has closer distribution pattern as moisture diffusion, with lower vapor pressure inside the package, and gradually increasing toward the external surface. This corresponds to the cases 1 and 2 (equations (10) and (11)), which assume ideal gas behavior for non-saturated pressure conditions. Comparison is made with the thermodynamics table and the ideal gas assumption hassled to less than 5% of error. Anyway, for the JEDEC level 1 with 168 h of moisture preconditioning, saturated pressure (case 3, equation (12)) is always encountered and its magnitude is much larger than in the cases 1 and 2. The effect of the initial void volume fraction (f0 ) was also studied. When f0 was increased five times, the vapor pressure distribution was almost unchanged (see Fig. 9.5), because the void moisture density was still above the critical value. It is important to point out that although f0 (until five times) has little effect on the vapor pressure, it may weaken the interfacial adhesion. Exact measurement of f0 is not critical for level 1, but can be important for the low-moisture conditions, e.g., for level 3 or below, due to the low density of the void moisture.

9.5 Hygro-mechanical Modeling CME is a measure of change in the material strain with moisture concentration. For this study, it is the ability of the material to expand when subjected to moisture absorption during moisture preconditioning. Due to the CME mismatch of dissimilar materials, the hygro-mechanical or hygroswelling stress is induced. The concept is analogous to the CTE mismatch and thermo-mechanical stress which we are more familiar with. The hygro-mechanical problem can be solved using the same procedure as a typical thermo-mechanical solution. The moisture loading applied is from 0 to 100% of moisture concentration. The general hygroswelling characterization technique is well known [14–15, 17–18]. Two identical underfill disk samples are preconditioned with moisture under 85◦ C/85% RH for about 2 weeks. Then the samples are monitored for desorption under TGA (thermo-gravimetric analyzer) and TMA (thermo-mechanical analyzer), respectively, at the same time under 85◦ C constant temperature for about 1 day. Both TMA and TGA show very close time-dependent curves (see Fig. 9.6), because the initial moisture content and desorption condition are also close. The change in the dimension and weight can be related by CME, obtained from the slope of the graph (see Fig. 9.7), strain vs. concentration:

9

Methodology of IC Packages TGA (mg)

231 TMA (mm)

Graphs of TGA and TMA

36.12

TGA

1.0369

36.1

TMA

1.0367 1.0365

36.08

1.0363

36.06

1.0361

36.04

1.0359

36.02

1.0357

36 0

200

400

600

800

1.0355 1000

Time (min)

Fig. 9.6 Hygroswelling material characterization

Fig. 9.7 Computation of mold compound CME

Graph of Strain vs. Concentration Strain 0.0012 y = 0.2223x 0.001

R 2 = 0.9946

0.0008 0.0006 0.0004 0.0002 0 0

0.001

0.002

0.003

0.004

0.005

3

Concentration (mg/mm )

εh = βC,

(9.16)

where εh is the hygro-strain, β is the CME, and C is the moisture concentration. The values of CME measured for the molding compound and the die attach [14] are shown in Table 9.1. The die and the copper leadframe materials are assumed to have zero CME, i.e., have no hygroswelling. For this case, the hygro strain is as high as the thermal strain. For example, the molding compound hygro-strain is equivalent to the molding compound CTE of 34.9 ppm/◦ C under the same temperature loading of 175–220◦ C using the analogous equations (9.16) and (9.17): εT = αT,

(9.17)

where εT is the thermal strain, α is the CTE, and T is the temperature loading. Modeling results will be reported in Section 9.7.

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9.6 Thermo-mechanical Modeling Linear-elastic thermo-mechanical stress model was applied. The temperature loading applied was from the post-mold cure temperature of molding compound, 175◦ C, to the reflow temperature of 220◦ C. The thermo-mechanical material properties used in the modeling are shown in Table 9.5. Poisson’s ratio is assumed to be 0.3 for all the materials. Modeling results will be reported in Section 9.7. Table 9.5 Thermo-mechanical material properties Material

Modulus at 220◦ C (GPa)

Mean CTE (ppm/◦ C)

Copper Die Mold compound Die attach

127.4 131 1.1 0.043

17.4 2.8 34 170

9.7 Integrated Stress Modeling 9.7.1 Modeling Methodology Figure 9.8 illustrates the methodology of the integrated stress modeling to calculate the package stress induced during reflow soldering. The five models mentioned earlier are inter-related. Results of moisture distribution from the moisture diffusion model were used as input data for both the vapor pressure model and the hygro-mechanical model. On the other hand, the temperature distribution from the thermal model was applied to both vapor pressure model and the thermo-mechanical model. The stress and strain induced by vapor pressure, thermo-mechanical, and hygromechanical models are combined into an equivalent stress model to compute the package stress and strain induced reflow. The hygro-strain and vapor pressureinduced strain are converted to an equivalent thermal strain, defined by CTE under the same temperature loading (175–220◦ C).

Vapor Pressure Model Moisture Model

Thermal Model

Package Stress During Reflow Hygro-mechanical Stress Model

Fig. 9.8 Integrated package stress model during reflow

Fracture Mechanics Model

Thermo-mechanical Stress Model

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9.7.2 Modeling Results The total strain induced by the thermo-mechanical, hygro-mechanical, and vapor pressure loadings on the molding compound and the die attach materials are listed in Table 9.6 [14]. For hygro-mechanical and vapor pressure-induced strain, they are converted into equivalent mean CTE, under the same 175–220◦ C temperature loading, so that all the three models can be integrated into a thermo-mechanical model with an equivalent strain. For example, the hygro-mechanical strain of molding compound is 1.57e–3 (see Table 9.1, according to equation (9.16)), and the equivalent mean CTE was computed as 1.57e − 3/(220 − 175◦ C) = 34.9 ppm/◦ C. The total equivalent CTE is much larger than the CTE obtained for an individual model. Therefore, the thermal stress and strain due to the mismatch of these three models is much higher than those for an individual model. Table 9.6 Equivalent CTE in integrated stress model Mold compound

Thermo-mechanical Hygro-mechanical Vapor pressure Integrated (total)

Die attach

Total strain

Equivalent mean CTE (ppm/◦ C) Total strain

Equivalent mean CTE (ppm/◦ C)

1.53e–3 1.57e–3 8.14e–4 3.91e–3

34 34.9 18.1 87

170 71.6 479.6 721.2

7.65e–3 3.22e–3 2.16e–2 3.25e–2

The relative package warpage distribution during the reflow process is shown in Fig. 9.9 for various models (not the same scale). Thermo-mechanical model has upward warpage, opposite in direction as compared to hygro-mechanical and vapor pressure-induced stress models. This is because for hygro-mechanical and

Thermomechanical

Hygromechanical

Vapor Pressure

Integrated

Fig. 9.9 Comparison of warpage distributions

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vapor pressure-induced stress models, the die and copper leadframe materials do not absorb moisture and have therefore zero CME and vapor pressure. For the thermo-mechanical model, all the materials have different non-zero CTEs. As to the integrated model, the warpage distribution is more complex; it is a mixture of all the three models. The integrated model is very different from the individual models. The von Mises stress distribution in the molding compound for the integrated model is shown in Fig. 9.10. The maximum stress occurs at the junction of the die, the die attach, and the molding compound. This location is the same for all the other models, despite that they have different warpage distributions. However, the magnitude of the maximum stress is different (see Fig. 9.11). For the von Mises stress, the principle of superposition is not applicable, because it is an equivalent stress, and linearity is no longer valid. For other stress components, the stress computed by the integrated stress model equals exactly to the sum of the stresses given by the three basic stress models indicated above. Among the three models, the thermomechanical stress is the highest. The integrated stress model shows about 50% larger maximum stress in the molding compound than the thermo-mechanical stress. Without considering the hygro-mechanical and vapor pressure-induced stresses, the package stress during reflow soldering would have been underestimated.

MPa

Mold compound

Maximum stress

Fig. 9.10 Integrated model: von Mises stress distribution

Besides the difference in the stresses, the considerations of the moisture diffusion and vapor pressure have also an impact on the interfacial adhesion strength. The interfacial adhesion should be characterized under the conditions below the reflow temperature with the same level of moisture preconditioning.

9.8 Interfacial Fracture Mechanics Modeling 9.8.1 Modeling Methodology Subsequently, the integrated package stress is analyzed using interfacial fracture mechanics approach. There are several possible ways used by researchers for

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235

Maximum Von Mises Stress in MC 35

Stress (MPa)

30 25

Thermo-mechanical Hygro-mechanical Vapor pressure Integrated

20 15 10 5 0 TM

HM

VP

ITG

Fig. 9.11 Comparison of maximum von Mises stress

fracture mechanics analyses [19], e.g., J-integral method, virtual crack closure (VCC) method, crack flank displacement extrapolation method (CFDEM), depending on the type of application. In this work, VCC method with the non-singular crack-tip element (see Fig. 9.12) is applied to calculate the strain energy release rate, G, for the crack along the die/molding compound and the die/die attach corner interfaces, which are the potential delamination layers. Raju [20] developed a convenient approach to compute the G and the mode mixity, ψ, based on the crack opening displacements and the nodal forces. The work required to extend the crack by a is equivalent to the work needed to close the crack tip by a. The mode I (GI ) and mode II (GII ) components of G and mode mixity are described by

y

Fig. 9.12 Non-singular crack-tip elements

j

i Δa

1

2

x

GI =

1 (Fy1 vj + Fy2 vi ), 2a

(9.18)

GII =

1 (Fx1 uj + Fx2 ui ), 2a

(9.19)

G = GI + GII ,

(9.20)

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. ψ = tan−1

GII , GI

(9.21)

where a is the crack extension; Fx1 , Fx2 , Fy1 , and Fy2 are the x and y components of nodal forces at nodes 1 and 2; ui , uj , vi , and vj are the x and y displacements at nodes i and j (see Fig. 9.12). From equation (9.21), it is clear that when mode I is dominant, GI > GII , mode mixity is less than 45◦ (vice versa for mode II). For energy release rate or stress intensity factors in other configurations, similar methodology can be developed [21].

9.8.2 Modeling Results Two potential failure interfaces, i.e., those at the die/molding compound and the die/die attach interfaces, were further analyzed for delamination. An initial crack of 0.1 mm was assumed at the die corner (both top and bottom interfaces), which was induced by the integrated stress under the thermo-mechanical, hygro-mechanical, and vapor pressure loadings. Once the delamination is initiated, the vapor pressure fills up the cavity quickly and saturated vapor pressure of 2.32 MPa is generated to open up and extend the crack length. The initial delamination propagates when G is larger than Gc , critical interfacial toughness of the bi-material. Gc depends strongly on the mode mixity, generally Gc increases with larger mode mixity. It is the strongest under the pure mode II (mode mixity = 90◦ ). The values of Gc have to be determined experimentally. Figure 9.13 shows that G increases with the increase in the crack length at both interfaces studied. The effect of the crack length is significant for the die/molding compound interface. If this interface has an initial crack, the crack may be extended by the vapor pressure until the whole interface is fully delaminated. Figure 9.14 shows that the mode mixity decreases with the longer crack length, gradually changes from the shear mode (mode II) to the opening mode (mode I). This is because the contribution of the vapor pressure loading increases with an increase

G (N/m)

Graph of G vs. Crack Length

150 Die/MC

125

Die/DA

100 75 50 25

Fig. 9.13 Effect of crack length on strain energy release rate (G)

0 0

0.5

1 Crack Length (mm)

1.5

2

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Methodology of IC Packages

237 Graph of Mode Mixity vs. Crack Length

Fig. 9.14 Effect of crack length on mode mixity Mode Mixity (degree)

90 Die/MC

75

Die/DA

60 45 30 15 0 0

0.5

1

1.5

2

Crack Length (mm)

in the crack length and acts to open up the interfacial gap. For the die/molding compound interface, mode mixity becomes stable, when crack length exceeds 1 mm. However, for the die/die attach interface, mode mixity continues to decrease with the increase in the crack length; therefore, the interfacial fracture toughness is also reduced and is more susceptible to further delamination.

9.9 Integrated Stress Modeling for a Pressure Cooker Test 9.9.1 Modeling Methodology The integrated analysis presented in Sections 9.2, 9.3, 9.4, 9.5, 9.6, 9.7, 9.8, and 9.9 is a comprehensive modeling approach for the detailed study of moisture-induced failures. However, it may take up significant amount of resources in the model development due to its complexity. Depending on the application, simplified integrated modeling methodology may be applied. In this example, an FCBGA package with no-flow underfill material is considered. Pressure cooker test (PCT) (121◦ C/100% RH), which is a stringent accelerated test for moisturesensitive package, is applied. The moisture weakens the interfacial adhesion strength and the tensile hygroswelling stress on UBM is induced by moisture absorption. Previous researches [15, 18, 22–23] have shown that hygroswelling of underfill is the key factor for UBM failure during PCT. Since the magnitude of the water vapor pressure at 121◦ C is much lower than the hygroscopic stress and the thermal stress, vapor pressure modeling is not needed. In addition, temperature maintains at a constant temperature of 121◦ C; therefore, an isothermal condition is assumed during PCT. The moisture and hygroswelling properties of no-flow underfill materials are characterized and the results are shown in Table 9.7. The moisture diffusion modeling (85◦ C/85% RH) is first performed to study the relative moisture distribution of various underfill materials. Then, the results of the moisture diffusion were used in the hygroswelling modeling. The failure criteria applied were the maximum

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Table 9.7 Moisture and hygroswelling material properties of FCBGA package at 85◦ C/85% RH Materials

D (mm2 /s)

Csat (mg/mm3 )

CME (mm3 /mg)

Total hygro-strain (Csat × CME)

Underfill A Underfill B Underfill C Mold compound Solder mask BT substrate

9.02e6 1.55e6 1.14e5 2.79e6 4.83e5 2.13e6

0.0152 0.0329 0.0112 0.0043 0.0143 0.0075

0.18 0.22 0.31 0.4 0.2 0.4

0.0027 0.0072 0.0035 0.0017 0.0029 0.0030

normal peeling stress (Sy ) and the shear (Sxy ) stresses caused by the combined thermo-mechanical and hygro-mechanical loading on UBM, which contributed to the UBM-opening failure during PCT.

9.9.2 Moisture Diffusion From results of the moisture diffusion modeling (see Fig. 9.15), it is shown that the unmolded packages become fully saturated with moisture (wetness, w = 1) after 12 h under the 85◦ C/85% RH. The transient moisture wetness distribution is only dependent on the diffusivity of the materials. Underfill C has the highest diffusivity; therefore, it gets fully saturated the fastest. However, once saturated, the final moisture concentration is only dependent on Csat . Therefore, underfill B has the highest moisture concentration according to equation (9.2). Figure 9.16 shows that the molded package gets saturated slower than the unmolded package, but both types of packages are fully saturated after 168 h of

Fig. 9.15 Transient moisture distribution for different underfill materials (unmolded package)

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Fig. 9.16 Transient moisture distribution of unmolded vs. molded package

moisture preconditioning under 85◦ C/85% RH. Under the more severe PCT condition (121◦ C/100% RH), the packaging materials will have even higher diffusivity and Csat . Therefore, both the unmolded and molded packages will be fully saturated at a faster rate during PCT than under the 85◦ C/85% RH conditions. In the subsequent hygroswelling modeling, the moisture distribution can be assumed to be uniform and equals to the Csat of the materials. There is no moisture concentration gradient within the material. If the package is not fully saturated, the moisture concentration distribution results have to be used in the input information as the final moisture loading in the hygroswelling model, instead of assuming w = 1 (fully saturated) throughout the package.

9.9.3 Hygro-mechanical Stress During PCT Figure 9.17 shows that during PCT, the normal hygro-mechanical or hygroswelling stress (Sy ) acting on UBM and solder bump is mostly tensile (peeling mode), causing the UBM-opening failure. Shear stress of lower magnitude also contributes to the interfacial delamination. The swelling of underfill induces compressive normal stress on die/underfill interface [15], but the UBM (die/bump) is under tensile normal stress, because the solder bump does neither absorb, nor swell with moisture. From the parametric studies, unmolded FCBGA with underfill A exhibits the lowest hygro-mechanical stress. Previous reliability test results [15] show also that the unmolded FCBGA with underfill A has the best performance. Underfill A has the least hygroswelling strain (see Table 9.7), due to the relatively low Csat and CME. Interfacial adhesion strength of the underfill under high temperature and high moisture conditions is also an important consideration. For better UBM reliability

240

T.Y. Tee Hygroswelling Stress during PCT (MPa) Case

Hygroswelling Stress on UBM during PCT

Shear Stress Normal Stress 77.72

266.96

UF B

139.06

491.14

600.00

UF C

85.09

301.16

500.00

UF A (Control)

DT=0.325mm

59.86

206.33 400.00

UF B

SS=6x6mm Molded

UBM

77.36

265.87

101.32

368.88

Stress (MPa)

UF A (Control)

UF C

300.00

DT=0.325mm 200.00

SS=6x6mm

100.00

Molded

0.00

Solder Bump

Shear Stress

Control case:

Normal Stress

Unmolded, UnderfillA, Die

Thickness of 0.525mm, Substrate Size of 8x8mm Normal Stress (MPa) of Control Case

Fig. 9.17 Results of parametric studies on hygroswelling stress induced during PCT

during PCT, material suppliers may need to compromise in the formulation of noflow underfill materials, to achieve low values of both the Csat and the CME. Unmolded FCBGA with smaller die thickness of 0.325 mm exhibits a 23% lower stress than a 0.525-mm-thick die, but the substrate size has little effect on the UBM stress. Molded package has a 38% larger stress than an unmolded package (for underfill A), due to the additional CME mismatch with the molding compound material. This correlates well with the reliability test results: Unmolded package generally performs better during PCT than a molded package. Since the test vehicles experienced several test conditions (moisture preconditioning at level 3, followed by reflow and 168 h of PCT), the actual failure mechanism is more complex and could be mixed mode. The moisture-induced failures could be due to the combined effects of process defects, interfacial adhesion strength, moisture, vapor pressure, thermo-mechanical stress, and hygro-mechanical stress.

9.9.4 Combined Hygro-mechanical Stress and Thermo-mechanical Stress During PCT At PCT condition of 121◦ C/100% RH, there is a combination of both hygromechanical stress and thermo-mechanical stress. During temperature cooling, from underfill curing temperature to 121◦ C of PCT, the thermal stress induced on UBM and solder bump is compressive, acting against the tensile hygro-mechanical stress (see previous results in Section 9.9.3). For the unmolded package with underfill A, the compressive stress is 262 MPa, close to the tensile hygro-mechanical stress of 267 MPa. Compressive thermo-mechanical stress during PCT was also observed by other researchers [18] and it has been found that the glass transition temperature Tg of the material can become up to 20◦ C below its dry state value, when the sample is subjected to humid environment. Therefore, at 121◦ C, all the underfill materials may be above Tg . Under high CTE2 , the induced thermo-mechanical stress is even

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more compressive, 278 MPa, greater than the hygro-mechanical stress. Underfill with the high CTE helps to generate compressive thermo-mechanical stress, against the tensile hygro-mechanical stress. In order for a failure to occur during the PCT, the hygro-mechanical stress must be much greater than the thermal stress. Previous hygro-mechanical stress was performed based on the CME at 85◦ C. Other researches [18] show that CME is a strong function of temperature. At 121◦ C, the material CMEs can be about two times higher than the values measured at 85◦ C. When CME is doubled, the hygro-mechanical stress is doubled accordingly. For the case with the underfill A, the magnitude of the hygro-mechanical stress can be as high as 534 MPa, i.e., much larger than the thermo-mechanical stress of 278 MPa. Therefore, the hygro-mechanical stress is the dominant one. For the relative comparison among the design variations, the previous results based on the assumption of CME at 85◦ C are still valid.

9.10 Conclusions The actual package failure mechanism during the reflow soldering process is complex, due to the combined effects of process defects, interfacial adhesion strength, moisture, vapor pressure, thermo-mechanical stress, and hygro-mechanical stress. Therefore, there is a need for comprehensive studies on moisture diffusion, thermal, hygro-mechanical stress, thermo-mechanical stress, and vapor pressure modeling. An integrated stress model combined with the interfacial fracture mechanics evaluations provides a solid basis for studying the QFN package stress and for computing the strain energy release rate when delamination is initiated. It is a useful tool to analyze and to improve the reliability of a plastic IC package, by minimizing the delamination and the popcorn failures as a result of the reflow soldering. The package vapor pressure distribution during the reflow process is the key factor in understanding the failure mechanisms. Moisture diffusion model is applied for the prediction of the local moisture concentration at the critical interfaces, which can be used for subsequent vapor pressure calculations. High moisture concentration weakens the critical interfacial adhesion, generates vapor pressure during the reflow process, and induces the hygro-mechanical stress in the package. The vapor pressure induces additional mismatch in the package, which is of the same order of magnitude as the CTE and CME mismatches. When the interfacial adhesion is reduced to the level below the stress predicted by the integrated stress model, the delamination will occur. For both the die/molding compound and the die/die-attach interfaces, G increases with an increase in the crack length, while the mode mixity decreases with an increase in the crack length. The propagation of an initial crack depends on the relative values of the G and Gc . The contribution of the vapor pressure to the interfacial delamination is significant, especially when there is a defect or a crack along the interface.

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The simulation methodology was also applied to a pressure cooker test for an FCBGA package with no-flow underfill. Hygro-mechanical stress was found to be more dominant than the thermo-mechanical stress during PCT.

References 1. Tee, T.Y., Ng, H.S., Diot, J., Frezza, G,. Tiziani, R., Santospirito. G,. “Comprehensive design analysis of QFN and PowerQFN packages for enhanced board level solder joint reliability”, Proceedings of 52nd Electronic Components and Technology Conference, ECTC, San Diego, CA, USA, pp. 985–991, 2002. 2. Tee, T.Y., Ng, H.S., Yap, D., Zhong, Z.W., “Comprehensive board-level solder joint reliability modeling and testing of QFN and PowerQFN packages”, Microelectronics Reliabiality, 43(8), 1329–1338, 2003. 3. Fukuzawa, I., Ishiguro, S., Nanbu, S., “Moisture resistance degradation of plastic LSI’s by reflow soldering”, Proceedings of IRPS, pp. 192–197, 1985. 4. Galloway, J.E., Miles, B.M., “Moisture absorption and desorption predictions for plastic ball grid array packages”, IEEE Transactions on Components, Packaging, and Manufacturing Technology Part A, 20(3), 274–279, 1997. 5. Kitano, M., Nishimura, A., Kawai, S., “Analysis of package cracking during reflow soldering process”, Proceedings of IRPS, pp. 90–95, 1988. 6. Tay, A.O., Lin, T., “Moisture diffusion and heat transfer in plastic IC packages”, IEEE Transactions on Components, Packaging, and Manufacturing Technology Part A, 19(2), 186–193, 1996. 7. Joint IPC/JEDEC Standard J-STD-020B, “Moisture/reflow sensitivity classification for nonhermetic solid state surface mount devices”. Arlington, VA: Electronic Industries Alliance, 2002. 8. Tee, T.Y., Fan, X.J., Lim, T.B., “Modeling of whole field vapor pressure during reflow for flip chip BGA and wire bond PBGA packages”, Proceedings of 1st EMAP Conference, Singapore, pp. 38–45, 1999. 9. Fan, X.J., Lim, T.B., “Mechanism analysis for moisture-induced failures in IC packages”, Proceedings of ASME International Mechanical Engineering Congress and Exposition, IMECE/EPE-14, 1999. 10. Fan, X.J., Zhang, GQ, Driel, W.D., Ernst, L.J., “Analytical solution for moisture-induced interface delamination in electronic packaging”, Proceedings of 53rd Electronic Components and Technology Conference, ECTC, New Orleans, LA, USA, pp. 733–738, 2003. 11. Fan, X.J., Zhou, J., Zhang, G.Q., Ernst, L.J., “A micromechanics based vapor pressure model in electronic packages”, ASME Journal of Electronic Packaging, 127(3), 262–267, 2005. 12. Xie, B., Fan, X.J., Shi, X.Q., Ding H., “Direct concentration approach of moisture diffusion and whole field vapor pressure modeling for reflow process: part I – theory and numerical implementation”, ASME Journal of Electronic Packaging, 131(3), 031010, 2009. 13. Fan, X.J., Zhang, G.Q., van Driel, W.D., Ernst, L.J., “Interfacial delamination mechanisms during reflow with moisture preconditioning”, IEEE Transactions on Components and Packaging Technologies, 31(2), 252–259, 2008. 14. Tee, T.Y., Zhong, Z.W., “Integrated vapor pressure, hygroswelling, and thermo-mechanical stress modeling of QFN package during reflow with interfacial fracture mechanics analysis”, Microelectronics Reliabiality, 44(1), 105–114, 2004. 15. Tee, T.Y., Kho, C.L., Yap, D., Toh, C., Baraton, X., Zhong, Z.W., “Reliability assessment and hygroswelling modeling of FCBGA with no-flow underfill”, Microelectronics Reliabiality, 43(5), 741–749, 2003. 16. Wong, E.H., Teo, Y.C., Lim, T.B., “Moisture diffusion and vapour pressure modeling of IC packaging”, Proceedings of 48th Electronic Components and Technology Conference, ECTC, Lake Buena Vista, Florida, USA, 1998, pp. 1372–1378.

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17. Wong, E.H., Chan, K.C., Tee, T.Y., Rajoo, R., “Comprehensive treatment of moisture induced failure in IC packaging”, Proceedings of 3rd IEMT/IMC, Tokyo, Japan, pp. 176–181, 1999. 18. Wong, E.H., Chan, K.C., Rajoo, R., Lim, T.B., “The mechanics and impact of hygroscopic swelling of polymeric materials in electronic packaging”, Proceedings of 50th Electronic Components and Technology Conference, ECTC, Las Vegas, NE, USA, pp. 576–580, 2000. 19. Tay, A.O., “Modeling of interfacial delamination in plastic IC packages under hygrothermal loading”, Proceedings of 3rd EuroSIME Conference, Paris, France, pp. 195–206, 2002. 20. Raju, I.S., “Calculation of strain-energy release rates with higher order and singular finite elements”. Engineering Fracture Mechanics, A8(3), 251–274, 1987. 21. Fan, X.J., Wang, H.B., Lim, T.B., “Investigation of the underfill delamination and cracking for flip chip module during thermal cyclic loading”, IEEE Transactions on Components, Manufacturing and Packaging Technologies, 24(1), 84–91, 2001. 22. van Driel, W.D., van Gils, M.A.J., Fan, X.J., Zhang, G.Q., Ernst, L.J., “Driving mechanisms of delamination related reliability problems in exposed pad packages”, IEEE Transactions on Components and Packaging Technologies, 31(2), 260–268, 2008. 23. Fan, X.J., Zhou, J., Zhang, G.Q., “Multi-physics modeling in virtual prototyping of electronic packages – combined thermal, thermo-mechanical and vapor pressure modeling”, Microelectronics Reliability, 44, 1967–1976, 2004.

Chapter 10

Failure Criterion for Moisture-Sensitive Plastic Packages of Integrated Circuit (IC) Devices: Application and Extension of the Theory of Thin Plates of Large Deflections E. Suhir and X.J. Fan

10.1 Introduction Recent improvements in the properties of molding compounds, plastic package designs, and manufacturing technologies have resulted in a substantial increase in the reliability of plastic packages of IC devices still. There is [1], however, one major industry-wide concern associated with moisture-induced failures in these packages. Such failures typically occur during surface mounting the packages onto printed circuit boards (PCB) by means of high-temperature reflow soldering. The observed failures are usually attributed to, although might not be limited by, high internal water vapor pressure caused by a sudden evaporation of moisture that is contained in plastic materials. In the extreme case, which is most likely to occur in a situation when the molding compound is completely delaminated from the chip or the paddle, rapid propagation of a crack, initiated at the chip’s corner or at the paddle’s edge, can be accompanied by a snapping sound and bulging of the package surface away from the delaminated area (“popcorn effect”). It has been established that the following factors and their unfavorable combinations play an important role, as far as such failures are concerned [1, 2]: • High moisture content: It not only leads to high water vapor pressure, but might also result in a substantial decrease in the interfacial strength, and in the ultimate fatigue and brittle strength of the molding compound. • Interfacial delaminations: These lead to elevated stress concentrations, high water vapor pressure (due to the moisture accumulated in the gap between the delaminated surfaces), and, most importantly, result in considerable weakening of the package, because of its inability to perform as a composite structure: the delaminated portion of the molding compound above and/or below the chip (paddle) becomes isolated from the rest of the package and, as a result of that, bends, independently of the package, as a plate.

E. Suhir (B) e-mail: [email protected] X.J. Fan, E. Suhir (eds.), Moisture Sensitivity of Plastic Packages of IC Devices, Micro- and Opto-Electronic Materials, Structures, and Systems, C Springer Science+Business Media, LLC 2010 DOI 10.1007/978-1-4419-5719-1_10, 

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• Low fracture toughness of the molding compound: This makes the compound unable to effectively withstand the initiation and propagation of fatigue and brittle cracks. • Insufficient thickness (low section modulus) of the molding compound above or below the chip (paddle), especially if delamination occurs. • Elevated thermally induced stresses caused by thermal expansion (contraction) mismatch of the dissimilar materials in the package (mainly between the chip and the molding compound), as well as by the temperature gradients in the molding compound (especially in the through-thickness direction). • Initial stresses and perhaps also initial bowing of the package resulting from the thermal expansion (contraction) mismatch of the materials in the package, when it is cooled down from the manufacturing (curing) temperature to room temperature. Clearly, each of these factors can be of greater or lesser significance, depending on the geometry, materials, and loading in a particular package design. It is also clear that the results of experimental investigations, valuable as they might be, inevitably reflect the combined effect of a variety of factors, whereas what is needed for the understanding of the mechanical behavior, life prediction, and structural and materials optimization is the knowledge of the role of each particular parameter affecting the reliability of the package (see, e.g., [2–4]). Theoretical predictive modeling can be very helpful therefore for understanding, predicting, and optimizing the mechanical behavior of a plastic package during reflow soldering operation. It has been shown [5] that a uniformly loaded rectangular plate clamped around its support contour can be used as a suitable theoretical model for the evaluation of the maximum stresses in a plastic package undergoing surface mounting operation and subjected to water vapor loading (Fig. 10.1). In the analysis that follows a more comprehensive and a more flexible analytical stress model [6], based on von Karman’s equations of large deflection of plates (see, e.g., [7]), is developed for the assessment of the plastic package propensity to moisture-induced structural

Fig. 10.1 A typical plastic package and moisture-induced failure at chip/paddle interface delamination. The portion of the molding compound below the pad or above the chip can be treated, from the viewpoint of structural analysis, as a rectangular plate clamped on the support contour

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failures. This model considers the effect of the thermoelastic strains and is based on an assumption that the maximum von Mises stress can be effectively used as a suitable failure criterion that reflects the cumulative effect of various geometric and material characteristics of the moisture-sensitive plastic package on its propensity to a structural failure. It is envisioned that the application of such a criterion might be helpful in bringing different plastic package designs to a “common denominator,” when comparing (rating) these designs from the standpoint of their propensity to failure. In this connection we would like to point out that von Mises stress is a structural criterion and, as such, is different from both geometric criteria (such as, say, chip-to-paddle area ratio, chip-to-package area ratio, chip-to-paddle width ratio) and fracture criteria (such as fracture toughness of the molding compound or the interfacial energy release rate). The obtained constitutive equations account for the following major factors: (1) Nonuniform distribution of temperature in the molding compound in the inplane and in the through-thickness directions. (2) Temperature dependence of Young’s modulus and the coefficient of thermal expansion (CTE) of the compound (note that such dependence, in combination with temperature gradients, makes the polymeric material anisotropic). (3) Thermally induced stresses caused by the thermal expansion mismatch of the dissimilar materials in the package. (4) Thermally induced stresses due to the thermal expansion mismatch of the materials. (5) Initial stresses and initial curvature (if any).

10.2 Analysis 10.2.1 Constitutive Equations The von Karman equations (see, e.g., [7]) for large deflections of rectangular plates (Fig. 10.2) can be generalized to account for the thermoelastic strains, the initial stresses, and the initial curvature as follows [6]: 0 ∂ w , D∇ 4 w + LD (D, w) = hL(w + w, ¯ φ) + p + ∇ 2 MT − σ¯ x0 ∂∂xw2 − σ¯ y0 ∂∂yw2 − 2τ¯xy ∂x∂y 2

¯ w) − C∇ 4 w + LC (D, φ) = − 21h L(w + 2w,

1−v 2 h ∇ (CNT )

2

,

2

,

(10.1)

where w(x, y) is the deflection function (vertical displacements of the points located in the main plane (z = 0), placed at the distance /h

Ez1 dz1 zC = /0 h 0 Edz1

(10.2)

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Fig. 10.2 Plate dimensions

from the lower surface of the plate), E[T(x, y, z)] is (temperature-dependent) Young’s modulus of the plate’s materials, T(x, y, z) is the temperature at the arbitrary point of the plate, z1 = z + c is the distance of this point from the lower surface of the plate (in the case of a plastic package, the distance z1 is counted from the outer surface of the package), h is the plate’s thickness (in the case of a plastic package, it is the underchip thickness of the molding compound, i.e., the thickness of the molding compound layer between its interface with the chip or the paddle and the outer surface of the package), ϕ = ϕ(x, y) is the Airy (stress) function related to the in-plane (“membrane”) stresses acting in the x–y plane of the underchip portion of the molding compound by the formulae [7, 8] σx0 =

∂ 2φ , ∂y2

σy0 =

∂ 2φ , ∂x2

0 τxy =−

∂ 2φ , ∂x∂y

(10.3)

σx0 = σx0 (x, y, z) and σy0 = σy0 (x, y, z) are the in-plane (“membrane”) normal stresses 0 = τ 0 (x, y, z) is the shearing in-plane stress, in the directions x and y, respectively, τxy xy 0 0 0 is the initial value σ˜ x and σ˜ y are the initial values of the normal in-plane stresses, τ˜xy of the shearing in-plane stress, p ≡ p(x, y) is the lateral load acting on the plate (in the case of a plastic package, it is the lateral water vapor induced pressure), 1 D = D(x, y) = 1 − v2

h−z  C

Ez2 dz = −zC

ED h3 12(1 − v2 )

(10.4)

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is the flexural rigidity of the plate (the underchip molding compound layer), 12 ED = 3 h

h−z  C

Ez2 dz

(10.5)

−zC

is the effective Young’s modulus with respect to bending deformations, v is Poisson’s ratio of the plate’s (molding compound) material (in this study this ratio is considered constant, i.e., temperature independent), ⎛ h−z ⎞−1  C C = C(x, y) = ⎝ Edz)⎠

(10.6)

−zC

is the in-plane compliance of the plate (molding compound layer), ∇2 =  =

∂2 ∂2 + 2 2 ∂x ∂y

is the Laplace operator, ∇ 4 = ∇ 2 ∇ 2 =  =

∂4 ∂4 ∂4 +2 2 2 + 2 4 ∂x ∂x ∂y ∂y

is the biharmonic operator; the operator L of the membrane stresses is expressed as

L(w, φ) =

∂ 2w ∂ 2φ ∂ 2w ∂ 2φ ∂ 2w ∂ 2φ − 2 + ∂x∂y ∂x∂y ∂x2 ∂y2 ∂y2 ∂x2

so that 

∂ 2w ∂ 2φ L(w+2w, ¯ w) = 2 − ∂x2 ∂y2



∂ 2w ∂x∂y

2

 ∂ 2 w ∂ 2 w¯ ∂ 2 w ∂ 2 w¯ ∂ 2 w ∂ 2 w¯ + 2 2 , + 2 2 − ∂x∂y ∂x∂y ∂x ∂y ∂y ∂x

and the operators LD and LC are    2 ∂ 2D ∂ 2w ∂ 2D ∂ 2w ∂ 2D ∂ D LD = LD (D, w) = +v 2 + +v 2 ∂x2 ∂y ∂x2 ∂y2 ∂x ∂y2   ∂D ∂∇ 2 w ∂ 2D ∂ 2w ∂D ∂∇ 2 w +2 + (1 − v) + ∂x ∂x ∂x∂y ∂x∂y ∂y ∂y 

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and    2 ∂ 2C ∂ 2C ∂ 2φ ∂ C ∂ 2C ∂ 2w − v + − v ∂x2 ∂y2 ∂x2 ∂y2 ∂x2 ∂y2   ∂C ∂∇ 2 φ ∂ 2C ∂ 2φ ∂C ∂∇ 2 φ +2 + (1 + v) + ∂x ∂x ∂x∂y ∂x∂y ∂y ∂y 

LC = LC (C, φ) =

(note that the only difference between the operators LD and LC is the sign in front of Poisson’s ratio v),

1 NT = 1−v

h−z  C

EαT dz, −zC

1 MT = 1−v

h−z  C

EαTz dz

(10.7)

−z

are the thermally induced in-plane force and the thermally induced bending moment, respectively, α ≡ α[T(x, y, z)] is the (temperature-dependent) coefficient of thermal expansion (CTE) of the material, and T = T(x, y, z) is the change in temperature at the point (x, y, z). The origin O of the rectangular coordinates x, y, z is at the center of the main plane.

10.2.2 Boundary Conditions The boundary conditions for the deflection function w(x, y) for a plate clamped around its contour are as follows: ⎫ a b ⎪ w = 0 for x = ± , y = ± , ⎪ ⎪ 2 2 ⎪ ⎪ ⎪ ⎬ a ∂w = 0 for x = ± , ⎪ ∂x 2 ⎪ ⎪ ⎪ ∂w b ⎪ ⎪ ⎭ = 0 for y = ± . ∂y 2

(10.8)

Here, a is the dimension (side) of the plate along the x-axis and b is its dimension (side) along the y-axis. The first boundary condition in (10.8) indicates that the deflections must be zero at the plate’s contour. The second and the third conditions indicate that, as long as the edges of the plate are rigidly clamped, the angles of rotation of the plate’s cross sections must be zero at the contour. If the plate’s support contour is nondeformable, i.e., if the plate’s edges cannot move closer as a result the plate’s deformation, the plate will experience reactive inplane (“membrane”) stresses. These stresses should satisfy the following conditions of the nondeformability of the support contour (see, e.g., [8]):

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Failure Criterion for Moisture-Sensitive Plastic Packages of IC Devices

a/2

1 0 (σ − vσy0 ) dx = EC x

a/2

0

0

b/2

b/2

1 0 (σ − vσx0 ) dx = EC y

0

1 EC 1 EC





∂ 2φ ∂ 2φ − v ∂y2 ∂x2 ∂ 2φ ∂x2

0

−v

∂ 2φ



1 dx = 2

a/2 0

 dx =

∂y2

1 2

b/2 0

∂w ∂x ∂w ∂y

251

2

2

⎫ ⎪ ⎪ ⎪ dx , ⎪ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎪ ⎪ dy . ⎪ ⎪ ⎭

(10.9)

Here 1 EC = h

h−z  C −zC

1 Edz = h

h Edz1

(10.10)

0

is the effective Young’s modulus of the material with respect to the in-plane (“membrane”) tension or compression. Conditions (10.9) indicate that the in-plane displacements due to bending should be compensated by the in-plane displacements caused by the membrane stresses, so that the total in-plane displacements of the plate are zero.

10.2.3 Stresses After equation (10.1), with the boundary conditions (10.8) and the conditions (10.9) of the nondeformability of the plate’s contour, is solved, the induced stresses in the molding compound can be evaluated by the formulae [6]  ⎫  αT ⎪ Mx − MT ,⎪ − σx = E C(Nx + NT ) − z ⎪ (1 − v2 )D 1 − v ⎪ ⎪ ⎪  ⎪  My − MT αT ⎬ , σy = E C(Ny + NT ) − z − (1 − v2 )D 1 − v ⎪ ⎪ ⎪   ⎪ ⎪ Mxy ⎪ ⎪ ⎭ . τxy = E CNxy − z 2 (1 − v )D

(10.11)

⎫  ⎪ ∂ 2w ∂ 2w ⎪ Mx = D + v 2 + MT , ⎪ ⎪ ⎪ ∂x2 ∂y ⎪ ⎪ ⎪   2 ⎬ 2 ∂ w ∂ w My = D + M + v , T ⎪ ∂y2 ∂x2 ⎪ ⎪ ⎪ ⎪ 2 ⎪ ∂ w ⎪ ⎪ Mxy = D(1 − v) ⎭ ∂x∂y

(10.12)

Here 

are the bending moments acting in the plate’s cross sections with respect to the axes x,y, and z, respectively, and

252

E. Suhir and X.J. Fan

Nx = h

∂ 2φ ∂ 2φ ∂ 2φ 0 0 0 = hσ , N = h = hσ , N = −h = hτxy y xy x y ∂x∂y ∂y2 ∂x2

(10.13)

are the in-plane forces.

10.2.4 Special Cases Examine several special cases for equation (10.1): (1) The effect of the temperature gradient on the change in Young’s modulus in the x − y plane is small. In this case, the flexural rigidity, D, and the in-plane compliance, C, expressed by formulae (10.4) and (10.6), respectively, are independent of the coordinates x and y, and the basic equations (10.1) can be simplified: D∇ 4 w

= hL(w + w, ¯ φ) + p + ∇

C∇ 4 φ = −

2

∂ 2w MT − σ˜ x0 2 ∂x

1−v 2 1 L(w + w, ¯ w) − ∇ (CNT ) . 2h h

∂ 2w − σ˜ y0 2 ∂y

0 − 2τ˜xy

⎫ ∂ 2w ⎪ ,⎪ ⎬ ∂x∂y ⎪ ⎪ ⎭ (10.14)

If, in addition, there is no initial curvature (w¯ = 0), nor the initial in-plane stresses 0 = 0), then equation (10.14) can be further simplified: (σ˜ x0 = σ˜ y0 = τ˜xy ⎫ D∇ 4 w = hL(w1 φ) + p + ∇ 2 MT , ⎬ 1−v 2 1 ∇ (CNT ). ⎭ C∇ 4 φ = − L(w, w) − 2h h

(10.15)

(2) The temperature changes in the through-thickness direction only. If the temperature gradient in the x − y plane is zero and, in addition, no initial deflections nor initial stresses occur, then the last terms in the right parts of the equations (10.15) are zero as well, and the basic equations (10.1) yield D∇ 4 w = hL(w, φ) + p,

C∇ 4 φ = −

1 L(w, w). 2h

(10.16)

These equations are not different from the “conventional” von Karman equations for large deflections of rectangular plates subjected to a lateral load [7]. The only difference is in how the flexural rigidity D and the in-plane compliance C are computed. These should be evaluated by formulae (10.4) and (10.6), i.e., with consideration of the change in Young’s modulus in the through-thickness direction as a function of temperature. (3) The lateral pressure is zero and the plates edges cannot move in its plane. In this case, the lateral forces become equal to the in-plane force (with an opposite sign): Nx = Ny = −NT , the bending moments become zero everywhere, and, in the absence of the initial stresses and curvatures, formulae (10.11) yield

10

Failure Criterion for Moisture-Sensitive Plastic Packages of IC Devices

 σx = σy = E z

 αT MT − . (1 − v2 )D 1 − v

253

(10.17)

(4) The lateral pressure is zero and the plate is free of any supports. In this case, Nx = Ny = 0, Mx = My = Mxy = 0, and if the initial stresses and curvatures are zero as well, formulae (10.1) yield τxy = 0, so that the stresses are expressed as follows:  σx = σy = E CNT + z

 αT MT . − (1 − v2 )D 1 − v

(10.18)

The deflections in such a plate were examined in detail in Suhir [9] in application to thermally induced bowing of plastic packages. (5) The lateral pressure is zero, the plate’s edges are clamped, and the temperature changes in the through-thickness direction only. In this case, Nx = Ny = −NT and Mx = My = MT , if there are no initial stresses nor forces, and formulae (10.11) yield σx = σy = −

EαT . 1−v

(10.19)

This formula indicates that the plate remains flat and experiences in-plane normal stresses only.

10.2.5 Initial Curvature and Initial Stresses The initial temperature-induced curvature of the plate in question (the underchip portion of the molding compound) and the initial stresses can be determined, if there is a need for that, on the basis of a simplified analysis. The rationale behind such an analysis is as follows. Let the plastic package be subjected to a uniform change T in temperature. The thermally induced forces, Fi, i = 1, 2, 3, 4, acting in the constituent materials and the thermally induced curvature of the composite structure (Fig. 10.3) can be evaluated, assuming perfect adhesion, from the following relationships:

Fig. 10.3 Cross section of a plastic package

254

E. Suhir and X.J. Fan

(1) Strain compatibility conditions: h1 κ0 = −α2 T + C2 F2 − 2 h2 −α2 T + C2 F2 + κ0 = −α3 T + C3 F3 − 2 h3 −α3 T + C3 F3 + κ0 = −α1 T + C4 F4 − 2

−α1 T + C1 F1 +

⎫ h2 κ0 , ⎪ ⎪ ⎪ ⎪ 2 ⎪ ⎬ h3 κ0 , ⎪ 2 ⎪ ⎪ ⎪ h4 ⎪ κ0 . ⎭ 2

(10.20)

(2) Equilibrium equation for the induced forces F1 + F2 + F3 + F4 = 0.

(10.21)

(3) Equilibrium equation for the induced bending moments 

h1 h4 + h2 + h3 + 2 2



 F1 +

h2 h4 + h3 + 2 2



 F2 +

h4 h3 + 2 2

 F3 = EIκ0 (10.22)

In these equations, α1 , α2 , and α3 are the thermal expansion coefficients for the molding compound, the metal paddle, and the silicon chip, respectively, Ci =

1 − vi , Ei hi

i = 1, 2, 3, 4,

(10.23)

are the in-plane compliances of the material layers, Ei and ν i are the elastic constants of the materials, hi , i = 1, 2, 3, 4, are the layers’ thicknesses, κ 0 is the temperatureinduced curvature of the molded body, and EI is its flexural rigidity. The first terms in either parts of conditions (10.20) are unrestricted (“stress-free”) thermal contractions. The second terms are the strains due to the thermally induced forces. The third terms are due to bending. The bending strains have opposite signs on the convex and the concave sides of the given layer. Equations (10.20) are written assuming that the curing temperature of the attachment of the chip to the paddle is the same as the molding temperature, so that the temperature change ΔT can be considered the same throughout the molded body. Equation (10.21) states that, since no other forces, but the thermally induced ones, act on the package, these forces must be self-equilibrated. As to the equilibrium equation for the bending moments, this can be formed with respect to any horizontal axis located in the plane of the given cross section. In our analysis, this equation is written with respect to the midplane of the fourth (i = 4) layer. This led to equation (10.22).

10

Failure Criterion for Moisture-Sensitive Plastic Packages of IC Devices

255

Equations (10.20), (10.21), and (10.22) can be rewritten as C1 F1 − C2 F2 + β12 κ0 = α12 T, C2 F2 − C3 F3 + β23 κ0 = α23 T, C3 F3 − C4 F4 + β34 κ0 = α13 T, F1 + F2 + F3 + F4 = 0, β14 F1 + β24 F2 + β34 F3 − EIκ0 = 0,

⎫ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎭

,

(10.24)

where the following notation is used: ⎫ α12 = α1 − α2 , α23 = α2 − α3 , α13 = α1 − α3 , ⎪ ⎪ ⎪ ⎬ h1 + h2 h2 + h3 h3 + h4 , β23 = , β34 = ,⎪ β12 = ⎪ 2 2 2 ⎪ ⎭ β14 = β12 + β23 + β34 , β24 = β23 + β34 .

(10.25)

These equations have the following solutions: F1

F2

F3

F4

κ0

 ⎫ T 2 2 2 ⎪ = {α12 (C2 C3 + C3 C4 + C2 C4 ) EI + C2 β34 + C3 β24 + C4 β23 ⎪ ⎪ ⎪ D ⎪ ⎪ ⎪ 2 ⎪ ⎪ + α23 [C2 (C3 + C4 )EI + C2 β34 − C3 β12 β24 − C4 β12 β23 ] ⎪ ⎪ ⎪ ⎪ ⎪ + α13 (C2 C3 EI − C2 β23 β34 − C3 β12 β24 )}, ⎪ ⎪ ⎪ ⎪ ⎪ T ⎪ ⎪ {−α12 (C3 C4 EI + C3 β14 β24 + C4 β13 β23 ) = ⎪ ⎪ D ⎪ ⎪ ⎪ 2 ⎪ ⎪ + α23 [C1 (C3 + C4 )EI + C1 β34 + C3 β12 β24 + C4 β12 β23 ] ⎪ ⎪ ⎪ ⎪ ⎪ + α13 (C1 C3 EI − C1 β23 β34 + C3 β12 β14 )}, ⎪ ⎪ ⎪ ⎪ ⎪ T ⎪ ⎪ = {−α12 (C2 C4 EI + C2 β14 β24 − C4 β12 β23 ) ⎪ ⎬ D 2 − α23 [C4 (C1 + C2 )EI + C1 β24 β34 + C2 β14 β34 + C4 β12 ] ⎪ ⎪ ⎪ ⎪ ⎪ + α13 (C1 C2 EI + C1 β23 β24 + C2 β13 β14 )}, ⎪ ⎪ ⎪ ⎪ ⎪ T ⎪ ⎪ {α12 (C2 C3 EI − C2 β13 β34 − C3 β12 β24 ) =− ⎪ ⎪ ⎪ D ⎪ ⎪ ⎪ 2 ⎪ + α23 [C3 (C1 + C2 )EI − C1 β23 β34 − C2 β13 β34 + C3 β12 ] ⎪ ⎪ ⎪ ⎪ 2 2 2 ⎪ + α13 [(C1 C2 + C1 C3 + C2 C3 )EI + C1 β23 + C1 β13 + C3 β12 ]}, ⎪ ⎪ ⎪ ⎪ ⎪ T ⎪ ⎪ ⎪ {α12 (C2 C4 β13 + C3 C4 β12 + C2 C3 β34 ) =− ⎪ ⎪ D ⎪ ⎪ ⎪ ⎪ + α23 (C1 C4 β23 + C1 C3 β24 + C2 C3 β14 + C2 C4 β34 ) ⎪ ⎪ ⎪ ⎭ + α13 (C1 C2 β34 + C1 C3 β24 + C2 C3 β14 )}, (10.26)

256

E. Suhir and X.J. Fan

where 2 2 2 2 2 2 + C1 C3 β24 + C1 C4 β23 + C2 C4 β13 + C2 C3 β14 + C3 C4 β12 D = EIC + C1 C2 β34

is the determinant of equations (10.24) and C = C1 C2 C3 + C1 C2 C4 + C1 C3 C4 + C2 C3 C4 . In order to determine the deflection function from the obtained curvature, we use the following equation for the curvature of the composite plate: ∂ 2w ∂ 2w = = −κ0 . ∂x2 ∂y2 After integration, we obtain 1 w = w0 − κ0 (x2 + y2 ), 2 where w0 is the deflection at the center of the plate. For a rectangular package, the maximum bow can be determined from the condition   a b , = 0, w 2 2 where a and b are the plate sides. This results in the following formula for the maximum bow: w0 =

a2 + b2 κ0 . 8

(10.27)

The equation for the initially deflected surface of the package can be written as    2 a 2 1 b 2 2 w¯ = κ0 −x + −y , 2 2 2

(10.28)

and the initial in-plane stresses can be evaluated by the formula σi0 =

Fi , i = 1, 2, 3, 4. hi

(10.29)

As to the initial bending stresses, they can be determined from the computed curvature κ 0 by the formulae σ1 =

E1 κ0 E1 κ0 h2 , σ2 = h2 , 6(1 − v1 ) 1 6(1 − v1 ) 2

σ3 =

E1 κ0 E1 κ0 h2 , σ4 = h2 . 6(1 − v1 ) 3 6(1 − v1 ) 4 (10.30)

10

Failure Criterion for Moisture-Sensitive Plastic Packages of IC Devices

257

10.2.6 Elongated Package Elastic curve: In this section we examine a special case of equations (10.14), when the plate, experiencing large deflections, is characterized by a sufficiently high aspect ratio (the b/a ratio is larger than, say, 2.5), so that it can be treated as an elongated plate. If this is the case, the solution to equations (10.14) can be simplified significantly. At the same time, the solution obtained for an elongated plate is conservative, i.e., results in a reasonable overestimation of the induced deflections and stresses. In the case of an elongated plate, one can consider a relatively simple problem of bending of a strip oriented along the x-axis, i.e., along the plate’s width. The equation of bending of such a strip can be written as follows: D

∂ 2w ∂ 2w − F = p. ∂x4 ∂x2

(10.31)

Here, w = w(x, y) is the deflection function, D=

Eh3 12(1 − v2 )

is the flexural rigidity of the plate, h is its thickness, E and v are the elastic constants of the material, F is the tensile force, and p is the distributed lateral load. In this analysis it is assumed that the load p is constant within the interval −c/2 ≤ x ≤ c/2 and is equal to zero outside this interval. The origin O of the coordinate x is in the middle of the plate at its neutral plane. Equation (10.31) can be rewritten as 2 p ∂ 4w 2∂ w − k = , 4 2 D ∂x ∂x

where

 k=

F D

(10.32)

(10.33)

is the eigenvalue of the problem. Because of the stress relaxation, the curvature of, and the stresses in, the plastic package at room temperature (prior to reflow soldering) can be different from the residual bow and the residual stresses in a newly fabricated package. If this is indeed the case, the package will not be flat and the stresses in it will not be zero at the reflow soldering temperature. In such a situation the initial curvature at room temperature can be measured, and then the last formula in (10.26) can be used to determine the T/D ratio. After substituting this ratio into the first four formulae in (10.26), one can determine the induced forces. The initial in-plane stresses can then be computed on the basis of formulae (10.29), and the bending stresses can be determined by formulae (10.30). The solution to equation (10.32) can be sought, for the interval −c/2 ≤ x ≤ c/2, as

258

E. Suhir and X.J. Fan

w(x) = C0 + C1 cosh kx −

px2 , 2F

(10.34)

where C0 and C1 are the constants of integration. In expression (10.34), it is taken into account that the deflections w(x) must be symmetric with respect to the origin, and therefore only the even functions should be considered. From equation (10.34) we find ⎫ c kc pc2 ⎪ = C0 + C1 cosh + ,⎪ w ⎪ ⎪ 2 2 8F ⎪ ⎪ ⎪ c ⎪ kc pc ⎪

⎪ ⎬ w = kC1 sinh − , 2 2 2F (10.35) c ⎪ p kc ⎪

2 ⎪ = k C1 cosh − , w ⎪ ⎪ 2 2 F ⎪ ⎪ ⎪ c ⎪ kc ⎪

3 ⎭ w = k C1 sinh . 2 2 The solution to equation (10.34) outside the interval −c/2 ≤ x ≤ c/2 is w1 (x1 ) = C2 + C3 kx1 + C4 cosh kx1 + C5 sinh kx1 ,

(10.36)

where xi = x − (c/2). From equation (10.36) we obtain w1 (0) = C2 + C4 , w 1 (0) = kC3 + kC5 , 3 w

1 (0) = k2 C4 , w

1 (0) = k C5 .

3 (10.37)

The compatibility conditions for the displacements, angles of rotation, bending moments (curvatures), and the lateral forces require that the following relationships take place: w

c 2

= w1 (0), w

c 2

= w 1 (0), w

c 2

= w

1 (0), w

c 2

= w

1 (0). (10.38)

Introducing formulae (10.35) and (10.37) into the compatibility conditions (10.38), we obtain the following equations for the constants of integration: ⎫ kc pc2 ⎪ C0 + C1 cosh + C2 − C4 = ,⎪ ⎪ ⎪ 2 8F ⎪ ⎪ ⎪ ⎪ kc pc ⎪ ⎪ ⎬ C1 sinh − C3 − C5 = , 2 2kF ⎪ kc p ⎪ ⎪ C1 cosh − C4 = 2 , ⎪ ⎪ 2 k F ⎪ ⎪ ⎪ ⎪ kc ⎪ ⎭ − C5 = 0 . C1 sinh 2

(10.39)

In addition to the compatibility conditions (10.38), solution (10.36) must satisfy also the boundary conditions at the plate’s ends:

10

Failure Criterion for Moisture-Sensitive Plastic Packages of IC Devices

 w1

a−c 2

 = 0,

w 1



a−c 2

259

 = 0.

(10.40)

These conditions indicate that both the deflection and the rotation angle must be zero at the clamped edges. The four equations (10.39) and the two conditions (10.40) enable one to determine the six constants of integration Ci , i = 0, 1, 2, 3, 4, 5:    

sinh kc ka p kc 1 kc 2 a 2 2 −1 − C0 = − 2 + cotanh , 1− 2 2 c 2 2 k F sinh ka 2 C1 =

k(a−c) p sinh 2 + k2 F sinh ka 2

kc 2

,

(10.41) (10.42)



sinh kc ka a kc 2 −1 + − cotanh , c 2 2 sinh ka 2 pc , C3 = 2kF   k(a−c) p kc sinh 2 + kc 2 C4 = − 2 , 1 − cosh 2 k F sinh ka 2

(10.44)

k(a−c) kc sinh 2 + p sinh 2 k2 F sinh ka 2

(10.46)

p C2 = 2 k F



kc 2

2

C5 =

kc 2

.

(10.43)

(10.45)

After the constants of integration are evaluated, the maximum deflection f can be determined from equation (10.34) as follows: c f = w(0) = C0 + C1 = w0 χf u, . a

(10.47)

Here w0 =

1 − v2 a4 pa4 = p 384D 32ED h3

(10.48)

is the maximum deflection in the case of zero tensile force (F = 0) and a load distributed over the entire width a of the plate (c = a); the factor  c c 24 c = 4 u (1 − cosh u) + sinh u χf u, a a a u sinh u  2  3  u c c c  + 2− − 1 sinh u + sinh u 1 − a 2 a a

(10.49)

accounts for the effect of the finite width of the loaded area and the finite (nonzero) value of the tensile force; and the parameter u is

260

E. Suhir and X.J. Fan

Fig. 10.4 Factor of the maximum deflection

a ka = u= 2 s



F . D

(10.50)

Factor (10.49) is plotted in Fig. 10.4. When there is no tensile load applied to the plate (F = 0, u = 0), formula (10.49) yields χf =

  c2 c c3 2−2 2 + 3 . a a a

(10.51)

In another special case, when the lateral load is distributed over the entire plate’s width (c = a), formula (10.49) results in the expression χf =

u 24 u − tanh . 3 2 u 2

(10.52)

Clearly, in the case c = a, formula (10.51) yields χf = 1, and so does formula (10.52) in the case u = 0. Bending stress: The bending stress at the clamped edge can be evaluated, using equation (10.36) and formulae (10.43) and (10.46) for the constants of integration, as follows:   c E h

a − c w = σ (10.53) u, , χ σb = − 0 M 1 2 a 1 − v2 2

10

Failure Criterion for Moisture-Sensitive Plastic Packages of IC Devices

261

where σ0 =

pa2 2 h2

(10.54)

is the bending stress in the case of zero tensile force (F = 0, u = 0) and a load distributed over the entire width of the plate (c = a); and the factor



 c 3 u ac cosh u − sinh u ac χM u, = 2 a sinh u u

(10.55)

considers the effect of the finite (nonzero) tensile force and the finite width of the loaded area on the bending moment (bending stress). This factor is plotted in Fig. 10.5. Note that formula (10.53) is based on an assumption that the section modulus of the plate’s cross-section can be evaluated without considering the shift in the neutral plane due to the variable Young’s modulus. For a load, distributed over the entire width of the plate (c = a), formula (10.55) yields χM =

3 (u cotanh u − 1). u2

Fig. 10.5 Factor of the maximum bending moment

(10.56)

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E. Suhir and X.J. Fan

In the absence of the tensile force (F = 0, u = 0), relationship (10.55) leads to the following formula: χM =

  c2 c 3− 2 . 2a a

(10.57)

Clearly, in the case u = 0, formula (10.56) yields χM = 1, and so does formula (10.57) in the case of c = a. When a concentrated lateral force is applied in the middle of the plate’s width (span), formula (10.53) can be written as σb = σ0 χ1 (u),

(10.58)

where σ0 =

3 Pa 3 pca = 2 4h 4 h2

(10.59)

is the bending stress in the case when the tensile load is zero. The factor χ1 (u) =

2 tanh u u

(10.60)

reflects the effect of the finite (nonzero) force. In-plane (“membrane”) stress: The formulae that have been obtained in this section so far were derived for the given in-plane (“membrane”) force F, i.e., assuming that the dimensionless parameter u, expressed by formula (10.50), is known. In the situation in question, however, the in-plane tensile force F depends on the deflection function w(x) that, in its turn, depends on the magnitude of this force. Therefore an additional relationship between the unknown tensile force F and the unknown deflection function w(x) is needed to determine the force F and the induced deflections. Such a relationship can be obtained from the biharmonic equation ∇ 4φ = 0

(10.61)

(this equation simply follows from the second equation in (10.16) in the case of an elongated plate for which the operator L is zero) and conditions (10.9) of the nondeformability of the support contour. In an approximate analysis, the solution to equation (10.61) can be sought in the form φ = Ax2 + By2 .

(10.62)

Then equation (10.61) is fulfilled automatically and also conditions (10.9) of the nondeformability of the contour. With ∂w ∂y = 0 for y = b/2

10

Failure Criterion for Moisture-Sensitive Plastic Packages of IC Devices

A = vB =

vEc K . 4(1 − v2 )

263

(10.63)

The expressions for the “mechanical” in-plane stresses caused by the lateral load p are σ˜ x0 =

∂ 2φ Ec K , = 2B = 2 ∂y 2(1 − v2 )

σ˜ y0 =

∂ 2φ vEc K , = 2B = 2 ∂x 2(1 − v2 )

(10.64)

where 2 K= a

a/2 0

∂w ∂x

2 dx.

(10.65)

Strictly speaking, the K value should be evaluated by introducing solutions (10.34) and (10.36) into the integral in formula (10.65) and by evaluating this integral as a sum of the integrals calculated separately for the intervals 0 ≤ x ≤ c/2 and 0 ≤ x ≤ (a − c)/2. Such a procedure leads, however, to tedious derivations and cumbersome relationships. At the same time, since the angle of rotation ∂w/∂x enters formula (10.65) as an integrand, there is reason to believe that even if an approximate configuration of the elastic curve is used, one can still obtain a sufficiently accurate K value. Whatever the configuration, it should satisfy the boundary conditions (10.8) for a clamped plate. Using the expression   x4 x2 w(x) = f 1 − 8 2 + 16 4 a a for the elastic curve of a strip uniformly loaded over its length a (which is the width of the elongated plate) we obtain

K=

512 f 2 f2 = 4.88 2 . 2 105 a a

(10.66)

If the strip is loaded in its mid-cross section by a concentrated force, then   x2 x4 w(x) = f 1 − 12 2 + 16 4 a a and formula (10.65) yields K=

f2 24 f 2 = 4.80 . 5 a2 a2

(10.67)

264

E. Suhir and X.J. Fan

If the deflection curve is approximated as w(x) = f cos2

πx , a

then K=

f2 π2 f 2 = 4.93 . 2 a2 a2

(10.68)

As one can see, formulae (10.65), (10.66), and (10.67) give close results. It is natural to expect that for a plate partially loaded in its cross-section the coefficient in front of the ( f/a) should be between the values obtained for the extreme cases of a distributed and a concentrated load:   2 f 508 f 2 f2 1 512 24 + = = 4.84 2 . (10.69) K= 2 2 2 105 5 105 a a a Introducing equation (10.68) into the first equation in equation (10.64), we obtain the following relationship between the “mechanical” transverse in-plane stress and the deflection-to-width ratio: f2 254 Ec . (10.70) 105 1 − v2 a2 Since the tensile force F can be evaluated as F = σx0 h, the parameter u can be determined as . .  254 Ec f Ec f a σx0 = = 2.694 . (10.71) u= 2 D 35 ED h ED h σ˜ x0 =

This is the sought additional relationship between the tensile force and the maximum deflection. After the nonlinear problem for the maximum deflection f is solved, the membrane stress σ˜ x0 can be computed by formula (10.69). The longitudinal in-plane stress σ˜ y0 can be evaluated, as evident from equation (10.64), as σ˜ y0 = vσ˜ x0 . In order to simplify the computation of the maximum deflection f, one can use the following relationship, which can be easily obtained from equations (10.48), (10.49), and (10.70): 1 − v2 p¯ = 32

.

254 Ec a 4 p u = χp = . 35 ED h ED χf

(10.72)

Relationship (10.71) is plotted in Fig. 10.6 and enables one to evaluate the parameter u from the computed dimensionless lateral load p. After the u value is determined, the deflection-to-thickness ratio f/h can be found from equation (10.70). Finally, the transverse stress σ˜ x0 can be computed from the calculated maximum deflection by formula (10.69). This formula can be written, considering equation (10.48), as

10

Failure Criterion for Moisture-Sensitive Plastic Packages of IC Devices

265

Fig. 10.6 Factor of the water vapor pressure

σ˜ x0 = 0.002362(1 − v2 )

Ec 2 a 6 2 p χf . 2 h ED

(10.73)

As evident from this formula, the in-plane (“membrane”) stress can be quite large, if the lateral (water vapor) pressure p is appreciable and the ratio a/h is large. This is thought to be the case in thin small outline packages (TSOPs). In addition, it should be pointed out that the maximum bending stress, expressed by formula (10.53), is rather weakly dependent on Young’s modulus of the material. Indeed, Young’s modulus affects the bending stress only through the parameter u, and this parameter, as one can see from equation (10.70), is proportional, for the given deflection-to-thickness ratio, to the square root of the ratio of the effective Young’s modulus in tension and in bending. As the calculations show, these Young’s moduli are not much different. The in-plane (“membrane”) stresses, however, are affected by Young’s modulus of the material quite strongly: as evident from formula (10.72), these stresses decrease with an increase in Young’s modulus of the material. Therefore, one can conclude that when the lateral pressure is large and, as a consequence of that, the membrane stresses are substantial, molding compounds with higher Young’s moduli are expected to result in lower induced stresses, i.e.,

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are less prone to failure. This might not be important for thick packages with small chips, but can have an appreciably adverse effect on the reliability of thin packages with large chips. In this connection we would 1ike to point out that, from the structural analysis standpoint, the difference between “thin” and “thick” packages is due, first of all, to whether the membrane stresses contribute substantially, or not, to the total maximum stress in the molding compound. Effective Young’s modulus: Effective Young’s modulus EC and ED in tension and in bending can always be evaluated numerically. It is more convenient, however, to compute them on the basis of approximate formulas. In this section we derive such formulas assuming that the actual distribution of Young’s modulus of the molding material in the through-thickness direction can be approximated by a parabola: E(z1 ) = E0 [2(e+ + e− − 2)ζ 2 − (3e+ + e− − 4)ζ + e+ ],

(10.74)

where ζ = z1 /h is the dimensionless through-thickness coordinate, counted from the external (“hot”) surface of the plate, E0 is Young’s modulus value in the midplane, and e+ = E+ /E0 and e− = E− /E0 are the ratios of Young’s modulus E+ and E− on the “hot” and “cold” surfaces of the plate, respectively, to the midplane Young’s modulus E0 . With expression (10.74), equations (10.5) and (10.7) result in the following approximate formulae: ED = E0

8(e+ + e− + e+ e− + 1) − (e2+ + e2− ) e+ + e− + 4 , Ec = E0 (10.75) 5(e+ + e− + 4) 6

which can be used in engineering calculations. Total in-plane (“membrane”) stress: The total transverse in-plane stress (i.e., the stress acting along the short side of the plate), calculated with consideration of the effect of the change in the coefficient of thermal expansion, α, can be determined, in accordance with formulae (10.11), as follows: 

αT σx0 = E c(Nx + Nτ ) − 1−υ



⎞ ⎛ h−z  c E 0 E ⎝ 1 = σ˜ + EαTdz − αT ⎠. Ec x 1 − υ Ec h −zc

(10.76) The thermally induced strain αT decreases and the Young’s modulus E of the molding compound increases with the decrease in temperature. Therefore, in an approximate analysis, one can assume that the thermally induced stress EαT remains constant over the plate’s thickness. With such a simplification, one can write formula (10.75) as follows: σx0 =

E Ec

 σ˜ x0 +

 E − Ec αT . 1−ν

(10.77)

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Clearly, for E = Ec , the total stress σx0 becomes equal to the “mechanical” stress σ˜ x0 . Similar to equation (10.76), the total longitudinal in-plane stress (i.e., the stress acting in the direction of the long side of the plate) can be calculated as σy0

E = Ec

 σ˜ y0

E − Ec αT + 1−υ



E = Ec

  E − Ec 0 υ σ˜ x + αT . 1−υ

(10.78)

10.2.7 von Mises Stress von Mises stress (see, e.g., [7]) is defined as  1 σM = √ (σ1 − σ2 )2 + (σ2 − σ3 )2 + (σ3 − σ1 )2 . 2

(10.79)

Here, σ 1 , σ 2 , and σ 3 are the principal stresses. In the case of a plate (twodimensional state of stress), the principal stress σ 3 is zero, and therefore σM =



σ12 + σ22 − σ1 σ2 .

(10.80)

The principal stress in the transverse direction (in the direction of the x-axis) is due to the bending stress σ b and the in-plane (“membrane”) stress σx0 and can be evaluated as σ1 = σb + σx0 . As to the principal stress σ 2 , acting in the y-direction, it is due, in the case of an elongated plate, to the membrane stress σy0 only, so that σ2 = σy0 . Then formula (10.79) yields

σM

 3 αT E − Ec 1/2 2 2 = σb 1 + (2 − υ)η + (1 − υ + υ )η + [1 + (1 + υ)η] η 1 − υ σ˜ x0 (10.81)

where the parameter η is expressed as η=

E σ˜ x0 . Ec σb

(10.82)

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10.2.8 Simplified Approach Although the general analytical stress model, based on the constitutive equations (10.1), accounts for any distribution of temperature in the molding component, in a simplified model only the case when the temperature changes in the throughthickness direction is considered. It is believed that such a simplification is justified for many actual plastic package designs, especially for thin packages, in which the expected stresses are the highest. This situation is described by equations (10.16). The solution to these equations is given in the Appendix. In a simplified engineering approach one can use the following calculation procedure. The input data are chip width, c, paddle width, a, underchip thickness, h, Young’s modulus, E, and the coefficient of thermal expansion, α, of the molding compound as a function of temperature, v, Poisson’s ratio of the molding compound, E, Young’s modulus and coefficients of expansion of the chip and paddle materials (these are needed only if the stresses due to the thermal expansion mismatch of the constituent materials are considered), and the water vapor pressure, p. The calculations can be carried out in the following sequence: 1. For the given temperature gradient, calculate the distribution of Young’s modulus in the through-thickness direction, and compute equivalent Young’s modulus (from the standpoint of bending) and (from the standpoint of in-plane deformations) by formulae (10.15) and (10.10). 2. For the given thickness-to-width ratio h/a and the computed p/ED ratio of the lateral pressure p to the effective Young’s modulus ED in bending, determine the pressure factor χ p from formula (10.71). 3. For the given c/a ratio of the width c of the loaded area (chip’s width) to the width a of the plate and the calculated value, determine the value of the parameter u, characterizing the role of the in-plane (“membrane”) stresses, on the basis of the plot in Fig. 10.6. 4. For the given c/a ratio and the computed u value, calculate the factors, χ p and χ M , reflecting the effects of the c/a and u values on the maximum deflection and the maximum bending moment. These factors can be calculated on the basis of formulas (10.49) and (10.55) or the plots in Figs. 10.4 and 10.5, respectively. 5. Determine the maximum bending stress σ b by formula (10.53), the maximum mechanical in-plane stress σ˜ x0 by formula (10.72), and the parameter η, reflecting the effect of the ratio of these stresses by formula (10.81). 6. Compute the von Mises stress by formula (10.80).

10.3 Numerical Examples (1) Let the temperature gradient in the through-thickness direction for the delaminated portion of the molding compound be such that Young’s modulus of the material is E+ = 0.10 × 106 psi = 70.3 kg/mm2 on the “hot” (external) side

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of the package, E− = 0.15 × 106 psi = 105.5 kg/mm2 on the “cold” (facing the die) side, and E0 = 0.20 × 106 psi = 140.6 kg/mm2 in the midplane area. Then formulae (10.15) and (10.10) result in the following effective Young’s moduli: ED = 0.1538 × 106 psi = 108.1 kg/mm2 and EC = 0.1750 × 106 psi = 123.1 kg/mm2 . Let the pressure of the water vapor be p = 360 psi = 0.253 kg/mm2 (this corresponds to the pressure of a saturated vapor at 220◦ C), the width of the delaminated portion be a = 20 mm, and its thickness be h = 1 mm. Assuming for Poisson’s ratio v = 0.3, formula (10.71) yields p = χp = 28.25. Let the chip be c = 10 mm wide and therefore c/a = 0.5. Then the plot in figure yields u = 5.65 and formula (10.70) results in the following deflection-to-thickness ratio: f/h = 1.966. Hence, the maximum deflection is almost twice as large as the plate’s thickness (the thickness of the delaminated compound). From the plot in Fig. 10.5, for c/a = 0.5 and u = 5.65, we obtain χM = 0.26. In the case, when there are no “membrane” stresses and the lateral load is distributed over the entire width of the delaminated compound, the bending stress σ 0 , as predicted by formula (10.54), would be σ 0 = 72,000 psi = 50.6 kg/mm2 . Thus, the fact that the tensile force is not zero and the lateral load acts only in the midportion of the package leads to a substantial, almost by a factor of 4, reduction of the bending stress: σb = χM σ0 = 0.26 × 72,000 = 8,720 psi = 6.13 kg/mm2 . The “mechanical” transverse in-plane stress (acting in the x-direction) can be determined by formula (10.69): σ˜ x0 = 4,870 psi = 3.42 kg/mm2 . From equation (10.81) we obtain: η = 0.2230. Let the coefficient of thermal expansion of the compound be α = 60 × 10−6 1/◦ C, and the change in temperature from the curing temperature to the reflow soldering temperature be T = 80◦ C. Then, formula (10.80) results in the following von Mises stress: σM = 22,016 psi = 15.5 kg/mm2 . This stress is high and can possibly result in the failure of the molding material. (2) Let us determine now the maximum von Mises stress for a square plate 0 (γ = 1). In this case, formulae (10.99) and (10.100) of the appendix yield f = 4.8444 and α = 0.5965. From equation (10.98) we find μ = 27.9976 and ηf = 0.3579, and formula (10.97) results in the following deflection-to-thickness ratio: f = f/h = 1.7340. Comparing this result with the ratio f/h = 1.9660, obtained previously for an elongated plate, we conclude that the maximum deflection of the delaminated molding compound in a square package is smaller than in an elongated one by a factor of about 1.13. Since the bending stress is proportional to the maximum deflection, this stress can be evaluated for a square plate (package) based on the decreased deflection and is σ b = 16,511 psi = 11.6 kg/mm2 . The factors reflecting the effect of the finite aspect ratio on the in-plane-stresses can be computed, using formulae (10.93) and are as follows: ψx0 (γ ) = 0.8113 and ψy0 (γ ) = 1.6133. The “mechanical” in-plane stresses can then be calculated as σ˜ x0 = 0.4 × 4870 × 1.6133 = 3,143 psi = 2.21 kg/mm2 . The total in-plane stresses are σx0 = 3,279 psi = 2.31 kg/mm2 and σy0 = 1,247 psi = 0.877 kg/mm2 and the principal stresses are σ1 = σb + σx0 = 20,462 psi = 14.39 kg/mm2 and σ2 = σy0 = 1,247 psi = 0.877 kg/mm2 . The predicted von Mises stress is

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σM = 19,868 psi = 14.0 kg/mm2 . This value is only a little lower than the calculated stress in an elongated plate of the same width. (3) Let us assess now whether an increase in the thickness of the molding compound could result in an appreciable decrease in the predicted von Mises stress. Let the thickness of the delaminated portion of the compound be, say, h = 1.5 mm, instead of h = 1.0 mm in the previous example. Then, from formula (10.71) one obtains p = χp = 5.580. From the plot in Fig. 10.6 we find u = 2.65 and formula (10.70) yields f/h = 0.9221. The absolute deflection is f = 1.383 mm and is substantially lower than the deflection f = 1.966 mm in the case of a 1 mm thick compound. The bending stress calculated in the absence of the “membrane” forces for a load distributed over the entire width of the plate is σ0 = 32,000 psi = 22.5 kg/mm2 . The factor χ M considering the effects of the finite c/a ratio and the tensile stress on the maximum bending moment is χM = 0.20 and the predicted stress is σ b = 6,400 psi = 4.50 kg/mm2 . This value is almost three times lower than in the case of a 1 mm thick compound. The “mechanical” in-plane stress, predicted by formula (10.69), is σ˜ x0 = 2,410 psi = 1.695 kg/mm2 . From formula (10.81) we find η = 0.3228 and formula (10.80) results in the following von Mises stress: σM = 8,023 psi = 5.64 kg/mm2 . Thus, an increase in the thickness of the molding compound by a factor of 1.5 led to a 2.74-fold reduction in the von Mises stress.

10.4 Calculated Data The maximum von Mises stresses calculated for several actual plastic package designs are shown in Table 10.1. The calculated data are in satisfactory agreement with the experimental observations. As evident from these data, the level of the calculated stress varies significantly depending on the particular package design. Package design geometry is at least as important as the quality of the molding compound: thick packages with small chips are much less vulnerable (in terms of the level of the induced stresses) than thin packages with large chips.

10.5 Conclusions A practically useful calculation procedure has been developed for the evaluation of the failure criterion (von Mises stress) for a moisture-sensitive plastic package during its surface mounting on a printed circuit board. A situation, when complete delamination between the molding compound and the chip (or the paddle) takes place or is likely to occur during reflow soldering, is examined in detail, and a practical calculation procedure is developed for this case. This procedure can be effectively used to assess the role of materials and geometrical characteristics on the von Mises stress, and, hence, on the package propensity to structural failure. The

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Table 10.1 Numerical results

Package type Vendor #1 132 PQFP 164 PQFP 100 TQFP 28 SOJ 44 PLCC 68 PLCC 84 PLCC 160 EIAJ Vendor #2 68 PLCC Vendor #3 32 PLCC Vendor #4 44 PLCC Vendor #5 80 PQFP Vendor #6 240 PQFP a 30◦ C/60%

Die size, c (mm)

Paddle size, a (mm)

Thickness, h (mm) Crackeda

Calculated von Mises stress. σ M (kg/mm2 )

8.910 × 8.700 8.520 × 8.310 6.850 × 6.950 3.549 × 4.679 9.000 × 8.580 6.700 × 6.760 8.130 × 8.130 6.810 × 10.520

10.160 × 10.160 10.668 × 10.668 8.001 × 8.001 7.620 × 4.826 9.398 × 9.398 8.890 × 8.890 9.144 × 9.144 7.391 × 11.709

1.702 1.702 0.600 1.041 1.778 1.930 1.803 1.626

No No Yes No No No No No

4.465 4.755 14.956 4.478 3.556 2.474 3.221 2.605

4.200 × 4.200

6.800 × 6.800

1.513

No

0.301

6.800 × 5.600

8.900 × 7.380

1.090

No

2.810

8.100 × 6.500

9.000 × 9.000

1.579

No

1.617

8.132 × 8.078

9.205 × 9.201

0.600

Yes

16.477

12.790 × 12.780 1.286

No

5.421

9.650 × 9.410

relative humidity/168 h (Ilyas and Poborets, 1963)

developed stress model can also be applied for the preliminary separation of packages that need to be “baked” and “bagged” (“rebaked” and “rebagged”) from those that do not. This model can be used also to judge whether qualification test conditions for reliable enough packages (say, thick packages with small chips) could be safely “derated” to an actual factory humidity profile. Finally, the calculated data obtained on the basis of the developed model can provide guidance for the selection of the most feasible molding compound for the given package design: highly reliable and expensive compounds might be necessary for thin packages with large chips, but may not be needed for thick packages with small chips. Many additional considerations and recommendations concerning moisture sensitive plastic packages of IC devices could be found in Ref. [10–33].

Appendix. Clamped Plate of Finite Aspect Ratio Experiencing Large Deflections If the temperature in a rectangular plate changes in the through-thickness direction only, then for an initially flat and stress flee plate, equations (10.16) can be used to evaluate the deflections w(x, y) and the stress function φ (x, y).

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The functions w(x, y) and φ (x, y) can be sought in the form [8]: w (x, y) = fw∗ (x, y) , φ (x, y) = f 2 φ ∗ (x, y) ,

(10.83)

where f is the maximum deflection at the center of the plate, the coordinate function w∗ (x, y) is chosen in such a way that the boundary conditions for the deflection function at the plate’s contour be fulfilled, and the function φ ∗ (x, y) is to be determined. Substituting relationships (10.83) into the second equation in equation (10.16), we obtain the following equation for the function φ ∗ (x, y):  ∂ 2 w∗ ∂ 2 w∗ − , ∂x2 ∂y2 (10.84) where the equivalent modulus Ec is expressed by formula (10.10). In an approximate analysis one can assume for a plate clamped at the support contour  Ec  ∇ φ (x, y) = − L w∗ (x, y), w∗ (x, y) = Ec 2 4 ∗

w∗ (x, y) = cos2



∂ 2 w∗ ∂x∂y

πx πy cos2 . a b

2

(10.85)

Then equation (10.84) yields  2π x 2π y 4π x 4π y cos + cos + cos + cos a b a b . 2π y 2π x 4π y 4π x 2π y 2π x cos + cos cos + cos cos + 2 cos a b a b a b (10.86) This equation has the following solution:

∇ 4 φ ∗ (x, y)

π 4 E0 =− 2 2 2a b

2π x 2π y 4π x 4π y + D1 cos + D2 cos + D3 cos a b a b 2π y 4π y 2π y 2π x 2π x 4π x cos + D5 cos cos + D6 cos cos . + D4 cos a b a b a b (10.87) Substituting expression (10.87) into equation (10.86) we obtain the formulae for the constants D0 → D6 . Introducing equation (10.87) into conditions (10.9) of the nondeformability of the contour, we determine the constants A and B. Then, formula (10.87) results in the following expression for the function φ ∗ : φ ∗ (x, y) = Ax2 + By2 + D0 cos

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     υ a2 3π 2 1 1 υ πx 2 2  x y − + + + cos a a2 b2 a2 b2 b2 2 1 − υ2  2

2 a 2 b πy 4π x 4π y a − − cos cos − 2 cos b 4b a 4a b b

E0 φ ∗ (x, y) = 32



2π y a2 b2 4π y 2a2 b2 2π x 2π x  cos cos + cos − 2

2 cos 2 a b a b a +b 4a2 + b2 2 2 2π y 4π x a b cos −

. (10.88) 2 cos 2 2 a b a + 4b The in-plane stresses can then be evaluated as follows: σx0

∂ 2 φ ∗ π 2 E0 f 2 ∂ 2φ = 2 = f2 2 = 32 ∂y ∂y



3 1 − υ2



1 υ + 2 2 a b

 +

1 1 πy 4π y + 2 cos cos 2 b b a a

2π y 16a2 4π y 8a2 2π x 2π x cos +

cos +

2 cos 2 cos 2 2 2 2 a b a b a +b 4a + b  2π y 4π x 4a2 cos , +

2 cos a b a2 + 4b2 σy0 =

2 ∗ ∂ 2φ π 2 E0 f 2 2∂ φ = f = 32 ∂x2 ∂x2



3 1 − υ2



υ 1 + 2 2 a b

 +

1 1 πx 4π x + 2 cos cos 2 a a b b

2π y 16a2 2π y 8b2 2π x 4π x cos +

cos +

2 cos 2 cos a b a b a2 + b2 a2 + 4b2  4π y 2π x cos , +

2 cos a b 4a2 + b2 4b2

0 τxy

π 2 E0 abf 2 ∂ 2φ∗ ∂ 2φ = −f 2 = =− ∂x∂y ∂x∂y 4



1 2π y 2π x sin

2 sin a b a2 + b2

 4π y 1 2π y 2π x 4π x sin +

sin +

. 2 sin 2 sin a b a b 4a2 + b2 a2 + 4b2 (10.89) 1

At the point x = a/2, y = 0, formulae (10.89) yield     ψx0 (γ ) , σy0 = σy0 ψy0 (γ ) σx0 = σx0 ∞

∞

(10.90)

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where  

σx0 σy0

 ∞



∞

5 − 2υ 2 π 2 E0 f 2 1 − υ 2 32a2 3υ 2 π 2 E0 f 2 = 1 − υ 2 32a2 =

⎫ ⎪ ,⎪ ⎬ ⎪ ⎪ ⎭

(10.91)

are the in-plane stresses, calculated for the case of an elongated plate (b → ∞, γ = 0), and the factors

  ⎫ ⎪ 4 1 − υ2 ⎪ 2 4 1 3 ⎪ 2− 4 ⎪ ψx0 (γ ) = 1 + γ γ + − ,





 ⎪ 2 2 2 ⎪ ⎬ 2 2 2 5 − 2υ 2 5 − 2υ 2 1+γ 1 + 4γ 4+γ

  ⎪ 2 ⎪ ⎪ 2 4 1 2 + υ2 2 4 1 − υ ⎪ 0 4 ⎪ ⎪ γ − γ + − ψy (γ ) = 1 + .





 ⎭ 2 2 2 3υ 2 2 2 3υ 2 1+γ 1 + 4γ 4+γ

(10.92) reflect the effect of the finite aspect ratio γ = a/b. The shear stress at the point x = a/2, y = 0 is zero. For an elongated plate (γ = 0), formulae (10.92) yield ψx0 (1) = ψy0 (0) = 1. For a square plate (γ = 1) these formulae result in the expressions ψx0

(1 + υ) (63 + 12υ)  ,

= 25 5 − 2υ 2

ψy0



4 3 + 10υ 2 . =1+ 75υ

(10.93)

If, for instance, v = 0.4, then the finite aspect ratio of the plate results in lower in-plane stresses in the x-direction and in higher stresses in the y-direction. The first equation in equation (10.16) can be solved, using the Galerkin method (see, for instance, [7]). In accordance with the procedure of this method, we substitute formulae (10.83), with consideration of equation (10.84), into the first equation in equation (10.16), multiply the obtained expression by the coordinate function w∗ (x, y), and integrate the result over the plate’s surface A. This leads to the following equation for the dimensionless deflection f = f/h: f¯ + α f¯ 3 = f¯0 ,

(10.94)

/ p (x, y) w∗ (x, y) dA 1 / A f¯0 = Dh A w∗ (x, y) ∇ 4 w∗ (x, y) dA

(10.95)

where

is the dimensionless linear deflection (α = 0) and

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h3 α=− D

/



∗ ∗ ∗ A w /(x, y) L w (x, y), w (x, y) ∗ 4 ∗ A w (x, y) ∇ w (x, y) dA



dA

275

(10.96)

is the parameter of nonlinearity. The solution to equation (10.94) can be written as f¯ = ηf f¯0 ,

(10.97)

where the factor ⎛5 . 6 1 ⎜6 8 7 ηf = √ + ⎝3 1+ 1+ 3 μ 27μ

⎞ 5 . 6 6 8 ⎟ 7 3 1− 1+ ⎠, 27μ

μ = 2α f¯02

(10.98)

considers the effect of nonlinearity (“membrane” stresses). Introducing equation (10.85) into formulae (10.95) and (10.96), we obtain

f¯0 =

α=

a 4 1 − υ2 pa4 12 p  = 4 , π ED 3 + 2γ 2 + 3γ 4 h π 4 D 3 + 2γ 2 + 3γ 4 h

(10.99)





3 1 − υ2

12γ 4 17 9 1 + 2υγ 2 + γ 4 1 + γ4 +

+ 2 2 4 8 1−υ 8 1 + γ2  5γ 4 5γ 4 +

2 +

2 . 1 + 4γ 2 4 + γ2 (10.100)

3 + 2γ 2

+ 3γ 3



Using formulae (10.94) for the bending moments acting in the plate’s cross sections, putting MT = 0 and considering the first formula in equation (10.83), we have ⎫ ∂ 2 w∗ ∂ 2 w∗ ⎪ ⎪ Mx = −Df ,⎪ +υ ⎪ ⎪ ∂x2 ∂y2 ⎪ ⎪ ⎪   2 ∗ ⎬ 2 ∗ ∂ w ∂ w My = −Df , + υ ⎪ ∂y2 ∂x2 ⎪ ⎪ ⎪ ⎪ ⎪ ∂ 2 w∗ ⎪ ⎪ Mxy = −D (1 − υ) f . ⎭ ∂x∂y 

(10.101)

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Using equation (10.85), we obtain ⎫ 2π y υ 2π x ⎪ 1 2π x 2π y cos + cos ,⎪ cos cos ⎪ ⎪ ⎪ a b b a a2 b2 ⎪  ⎪  2π x υ 2π y ⎬ 1 2π y 2π x cos + cos , My = 2π 2 Df cos cos ⎪ b a a b b2 a2 ⎪ ⎪ ⎪ ⎪ 2 ⎪ π 2π x 2π y ⎪ ⎭ Mxy = −D (1 − υ) f sin sin . ab a b 

Mx = 2π 2 Df

At the point x = a/2, y = 0, these formulae yield Mx = −

2π 2 Df , a2

My = −

2π 2 υDf , a2

Mxy = 0 .

The bending stresses caused by these moments can be calculated as σx = −

6Mx 12π 2 Df = , h2 a2 h2

σy = −

In the case of an elongated plate (b → ∞, f¯∞ = f¯0 =

6My 12π 2 υDf = . h2 a2 h2

(10.102)

γ = 0), formula (10.99) yields

pa4 . 3π 4 Dh

Using this formula and formula (10.97), one can calculate the factor η∗ = ¯f /f∞ = ηf (f 0 /f∞ ), which considers the effect of the finite aspect ratio of the plate on its maximum deflection.

References 1. Suhir, E., “Failure criterion for moisture sensitive plastic packages of integrated circuit (IC) devices: application of von-Karman’s equations with consideration of thermoelastic strains”, International Journal of Solids and Structures, 34(23), 2991–3019, 1997. 2. Fan, X.J., Lim, T.B., “Mechanism analysis for moisture-induced failures in IC packages”, ASME International Mechanical Engineering Congress and Exposition, Nashville, TN IMECE/EPE-14, 1999. 3. Fan, X.J., Zhou, J., Zhang, G.Q., Ernst, L.J., 2005. “A micromechanics based vapor pressure model in electronic packages”, ASME Journal of Electronic Packaging, 127(3), 262–267. 4. Fan, X.J., Zhang, G.Q., van Driel, W.D., Ernst, L.J., “Interfacial delamination mechanisms during reflow with moisture preconditioning”, IEEE Transactions on Components and Packaging Technologies, 31(2), 252–25, 2008. 5. Fukuzawa, I., Ishiguro, S., Nambu, S., “Moisture resistance degradation of plastic LSI’s by reflow soldering”, 23rd International Reliability Physics Symposium Proceedings, Orlando, FL, USA, pp. 192–197. 6. Suhir, E., “Failure criterion for moisture-sensitive plastic packages”, IEEE 45th ECTC, Las Vegas, NV, USA, pp. 266–284, 1995.

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7. Timoshenko, S.P., Woinowski, K.S., Theory of Plates and Shells, 2nd edition. New York, NY: McGraw-Hill, 1959. 8. Suhir, E., Structural Analysis in Microelectronics and Fiber Optics, Vol. 1. New York, NY: Van-Nostrand Reinhold, 1991. 9. Suhir, E., “Predicted bow of plastic packages of integrated circuit devices”, Journal of Reinforced Plastics and Composites, 12, 951–972, 1993. 10. Bhattachayya, B.K., Huffman, W.A., Jahshman, W.E., Natarajan, B., “Moisture absorption and mechanical performance of surface mountable plastic packages”, IEEE 38th ECC Proceedings, Los Angeles, CA, USA, pp. 49–58, 1988. 11. Cognett, C., “Popcorn effect in reflow soldering of surface mounted assemblies in plastic housing”. Electron, 37, 116–120 (in German), 1988. 12. Conrad, T.R., Shook, R.L., “Impact of moisture/reflow induced delaminations on integrated circuit thermal performance”, IEEE 44th ECTC Proceedings, Washington, DC, USA, pp. 527–553, 1994. 13. EIA/JEDEC Standard, “Moisture-induced stress sensitivity for plastic surface mount devices”, Test Method A112? A, Arlington, VA: Electronic Industries Association, Engineering Department, 1995. 14. Flood, C.A., White, G.M., “Desorption equilibrium moisture relationships for popcorn”, Transactions of the American Society of Agricultural Engineers, 27, 561–565, 1984. 15. Ganssan, G.S., Berg, H., “Model and analyses for reflow cracking phenomenon in SMT plastic packages”. IEEE 43rd ECTC Proceedings, pp. 653–660, Orlando, FL 1993. 16. Ilyas, QSM, Poborets, B., “Evaluation of moisture sensitivity of surface mount plastic packages”, edited by Suhir, E., Structural Analysis in Microelectronics and Fiber Optics, EEP Vol. 7. New Orleans, LA: ASME, pp. 145–156, 1993. 17. Ilyas, Q.S.M., Potter, M., “Experimental evaluation of moisture induced failures of surface mount plastic packages”, IEEE 46th ECTC Proceedings, Orlando, FL, USA, pp. 56–67, 1996. 18. IPC-SM-786 Standard, “Recommended procedures for handling of moisture sensitive plastic IC packages”,IPC Test Method 650-2.6.20. Plastic Surface Mount Component Cracking. Lincolnwood, IL: IPC (Inst. for Interconnecting and Packaging Electronic Circuits). 19. Klinger, D.J., “Humidity acceleration factor for plastic packaged electronic devices”, Quality and Reliability Engineering International, 7, 365–370, 1991. 20. Lea, C., Tolbrook, D., “Moisture induced failure in plastic surface mount packages”, Soldering and Surface-Mount Technology, 3, 30–34, 1989. 21. Liu, S., “Debonding and cracking of microlaminates due to mechanical and hydro-thermal loads for plastic packaging”, edited by Suhir, E., Structural Analysis in Microelectronics and Fiber Optics, EEP Vol. 7. New Orleans, LA: ASME, pp. 1–11, 1993. 22. Miles, B., Freyman, B., “The elimination of the popcorn phenomenon in overmolded plastic pad array carriers”, IEPS Proceedings, Vol. 1, pp. 605–614, San Diego, CA 1992. 23. Pope, D., Clifton, L., “Package cracking in plastic surface mount components as a function of package moisture content and geometry”, 5th Annual IEEE/IETM/CHMT Syrup. Proceedings, pp. 89–92, 1988. 24. Shook, R.L., “Moisture sensitivity characterization of plastic surface mount devices using scanning acoustic microscopy”, 30th International Reliability Physics Symposium Proceedings, pp. 157–168, 1992. 25. Shoraka, F., “Package and molding compound mechanic”, 6th Annual International Electronics Packaging Conference Proceedings, pp. 294–312, 1986. 26. Steiner, T., Suhl, D., “Investigation of large PLCC package cracking during surface mount exposure”, IEEE CHMT Transactions CHMT-10, pp. 209–216, 1987. 27. Suhir, E., Ilyas, Q.S.M., “‘Thick’ plastic packages with ‘small’ chips vs ‘thin’ packages with ‘large’ chips: how different is their propensity to moisture-induced failure?”, edited by Suhir, E., Structural Analysis in Microelectronics and Fiber Optics. Atlanta, GA: ASME, pp. 101– 125, 1996.

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28. Suzuki, S., Oota, K., “Analysis of solder crack phenomena in LSI plastic packages”, Joint ASME/JSME Conference on Electronic Packaging Proceedings, Milpitas, CA, USA, pp. 343– 347, 1992. 29. Tencer, M., “Moisture ingress into nonhermetic enclosures and packages. A quasi steady state model for diffusion and attenuation of ambient humidity variations”, IEEE 44th ECTC Proceedings, Washington, DC, USA, pp. 196–209, 1994. 30. Thompson, P., “Reliability development and qualification of a low-cost PQFT-based MCM”, IEEE 44th ECTC Proceedings, Washington, DC, USA, pp. 186–190, 1994. 31. van Doorselaer, K., de Zeeuw, K., “Relation between delamination and temperature cycling induced failures in plastic packaged devices”, IEEE CHMT Transactions CHMT-13, pp. 879– 882, 1990. 32. van Vroonhoven, J.C.W., “Effects of adhesion and delamination on stress singularities in plastic-packaged integrated circuits”, ASME Journal of Electronic Packaging, 115, 28–33, 1993. 33. Yamada, S.E., “A bonded joint analysis for surface mount components”, ASME Journal of Electronic Packaging, 114, 1–7, 1992.

Chapter 11

Continuum Theory in Moisture-Induced Failures of Encapsulated IC Devices X.J. Fan, J. Zhou, G.Q. Zhang, and A. Chandra

Nomenclature JEDEC IPC BGA CSP QFP QFN FCBGA MSL IC DMA TMA TGA

Joint Electron Device Engineering Council Institute for Printed Circuits ball grid array chip scale package quad flat package quad flat non-lead package flip chip ball grid array moisture sensitivity level integrated circuit dynamic mechanical analyzer thermo-mechanical analyzer thermogravimetric analyzer

11.1 Introduction Package “popcorning” is a moisture-induced failure. It is a common failure mode that is likely to occur during surface-mount (SM) soldering reflow process. Moisture sensitivity/reflow test is a precursor test specified by the joint JEDEC/IPC industry standard J-STD-020D [1]. Its objective is to quantify the classifications of moisture sensitivity levels for plastic-packaged IC devices at the product development and qualification stage. Package “popcorning” testing generally progresses over four stages [2], as illustrated in Fig. 11.1 (with a BGA package as an example). At stage 1 (moisture preconditioning), the package absorbs moisture from the environment. It is a time-consuming process. According to the J-STD-020D specification, moisture sensitivity level 3 (MSL3) test requires, for instance, 192 h of moisture soaking, under 30◦ C/60%RH environmental condition. When atmospheric X.J. Fan (B) e-mail: [email protected] X.J. Fan, E. Suhir (eds.), Moisture Sensitivity of Plastic Packages of IC Devices, Micro- and Opto-Electronic Materials, Structures, and Systems, C Springer Science+Business Media, LLC 2010 DOI 10.1007/978-1-4419-5719-1_11, 

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a. Stage 1

b. Stage 2

c. Stage 3

d. Stage 4 Fig. 11.1 Schematic diagram of four stages of a popcorning failure of a BGA package during moisture sensitivity/reflow test. (a) Stage 1: moisture absorption; (b) stage 2: delamination; (c) stage 3: package bulge; and (d) stage 4: water vapor release

moisture is absorbed through the packaged microelectronics devices, it condenses in free volumes and/or in nanopores in the bulk of the polymeric material and especially over the interfaces. At stage 2, the devices and the printed circuit boards (PCBs) are placed in an oven for a reflow process, in which the peak temperature typically ranges from 220 to 260◦ C. A reflow process is completed within a few minutes. The condensed moisture is vaporized when the temperature rises during reflow, creating high internal vapor pressure inside the package. In addition, the interfacial adhesion strength may drop substantially. As a result, delaminations may occur at weak interfaces, as shown in Fig. 11.1b for the die-attach (DA)/silicon chip interface. Polymeric materials, such as dielectric films, adhesives, encapsulants, and plastic PCBs, become highly compliant (because of the significant drop in the Young’s modulus), when temperature exceeds the glass transition temperature. The vaporizing moisture instantaneously exerts a pressure as traction loading at the delaminated interface. This aggravates the delamination and might cause the package to bulge at stage 3. Eventually the package cracks initiate and may propagate laterally outward at stage 4. When a crack reaches the package exterior, high-pressure water vapor is suddenly released, producing an audible sound. Package “popcorning” has become a common terminology in semiconductor industry to describe package failures during reflow process due to moisture, even if the packages do not experience package bulge at stage 3 and/or water vapor release at stage 4 [2–12].

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Si

MC

Leadframe

Molten solder extrusion into delamination area Si

Interfacial delamination

Underfill

cracking

Solder

delamination

Substrate

a

b

Si Die-attach film Substrate

delamination

c Fig. 11.2 Interfacial delamination in various packages: (a) mold compound/leadframe interface delamination in a QFP; (b) underfill/silicon interface delamination in a FCBGA package; and (c) die-attach/substrate interface delamination in a three-dimensional stacking-die CSP package

There are two major types of package failures during the reflow process. Type I is the interfacial delamination [4, 5]. Some examples of the interfacial delamination in various plastic packages are shown in Fig. 11.2. Delamination at the leadframe/molding compound (MC) is shown in Fig. 11.2a. Delamination takes place in a quad flat package (QFP) and the cracking in the MC is initiated. Figure 11.2b shows the delamination in a flip-chip ball-grid-array (FCBGA) package between the underfill (UF) and the silicon chip passivated with polyimide (PI). The molten solders are extruded into the delaminated areas and cause electrical failures. Interfacial delamination at the substrate/die-attach (DA) interface in a three-dimensional stacking-die package is shown in Fig. 11.2c. Another type of failure (type II) at the reflow process is cohesive material rupture [9–12]. Some wafer-level die-attach (DA) films have a low glass transition temperature. Such films are therefore extremely soft at elevated temperatures. Figure 11.3 is an example of the DMA measurement on storage modulus of a die-attach film [12]. It can be seen that the modulus decreases substantially (<5 MPa), when the temperature exceeds the glass transition temperature, even without the presence of moisture. Figure 11.4 shows material ruptures at the reflow process. Film rupture in a folded flex CSP package is shown in Fig. 11.4a. Die-attach film voiding in a stacking-die CSP package is shown in Fig. 11.4b. Popcorning failures are usually attributed to the combined effects of the thermomechanical stresses, hygroscopic stresses, vapor pressure, material softening, and adhesion degradation. Numerous studies have confirmed that thermal stresses alone

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NoRH RH No

Modulus (MPa) (normalized)

Fig. 11.3 Storage modulus of a die-attach film with and without moisture absorption

85%%RH RH 85

Temperature (normalized)

Die-attach film rupture

Substrate

a

Si

Si

Die-attach film rupture

Substrate b

Fig. 11.4 Adhesive cohesive failures (a) film rupture in a folded flex package and (b) die-attach voiding in a three-dimensional stacking-die CSP package

do not induce failures at reflow process without preceding moisture preconditioning. Moisture plays, therefore, a pivotal role in affecting package integrity and reliability during reflow. Thermal stresses and other thermal effects should nonetheless be accounted for when evaluating the reliability of a plastic package during reflow soldering process. Fukuzawa et al. [13] first reported and studied popcorning failures in 1985. Kitano et al. [14] and Tay and Lin [15–18] conducted a series of work on moisture diffusion and heat transfer in plastic IC packages and studied the dynamics of moisture diffusion, hygrothermal stresses, and delamination using an interface fracture mechanics approach. Liu and Mei [19–20] investigated the behavior of delaminated plastic IC packages subjected to encapsulation cooling, moisture absorption, and wave soldering. Nguyen et al. [21] presented a failure mechanism study associated with soldering reflow process. Galloway et al. [22] developed a thermal–moisture analogy for moisture diffusion modeling and characterized moisture properties of different packaging materials. Wong et al. [23–25] introduced an alternative method for moisture diffusion analysis and characterized hygroscopic swelling using TMA/TGA method. Suhir [26] developed a failure criterion (“figure of merit”) for moisture-sensitive plastic packages of IC devices. The delaminated under-chip portion of the molding compound is treated as a thin plate subjected to the combined action of the lateral and in-plane stresses and the generalized von Karman’s equations for large deflections of flexible plates are used to evaluate the

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induced stresses and to assess the role of the package geometry on its propensity to moisture-induced failure. Based on the developed model, it has been demonstrated that thick packages with small-sized chips are much less prone to moisture-induced failures than thin packages with large chips. Shook et al. [27] studied diffusion models to derate moisture-sensitive surface mount ICs for factory use conditions. Tee et al. [28–33] developed a fully integrated modeling approach to investigate the moisture behavior. Dudek et al. [34, 35] presented a parametric study on moisture diffusion and popcorning cracking. In this chapter, the continuum theory and its application to moisture-induced failures in encapsulated plastic packages of IC devices are addressed. A single spherical void subjected to internal vapor pressure and thermal stress is investigated. Finitedeformation theory is applied to study unstable void growth under hydrostatic stress loading. Two material models are considered: elastic–plastic model and a hyperelastic model. In addition, the behavior of a single spherical void at the interface is studied. The interface debonding is taken into consideration through a void growth constitutive model. The effects of both moisture and temperature are considered. Vapor pressure effects are incorporated into a continuum description of stresses and strains on the basis of the modified Gurson–Tvergaard’s model. A rigid-plastic model is introduced to analyze package bulge and the limit (ultimate) pressure that leads the package to collapse. Finally, a general framework of the governing equations for a deforming polymer with consideration of moisture transport and phase change is presented.

11.2 Instability of Single Void Growth The interfacial delamination or the material rupture at reflow is considered as the consequence of micro-voids growth, nucleation, and coalescence. An investigation of a single void subjected to vapor pressure is helpful to understand the role of moisture evaporation during the reflow process.

11.2.1 Elasto-Plastic Model The classical plasticity theory assumes that a uniform hydrostatic stress has no influence on material’s yielding [36]. The situation might be different in the presence of voids. The effects of the mean stress on local failure behavior due to void growth have been well studied [37–39]. An exponential rate dependence of a single void growth on a triaxial stress condition was found. When finite deformation is considered, Huang et al. [40] have determined that a critical stress exists, beyond which the void will collapse. A spherical volume of material containing a microvoid of a spherical shape, as shown in Fig. 11.5, is considered. The material is assumed to be incompressible. The inner radial surface is subjected to an internal vapor pressure, induced by the

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σT

p

Fig. 11.5 A single spherical void model. The void will collapse with increasing temperature/vapor pressure

moisture inside. A radial stress σ T is applied to outer radius to represent thermal stress as a function of temperature. True stress–logarithmic strain relation σ = H(ε) = σ0



if |ε| < ε0 ε/ε0 ( |ε| /ε0 )N sign(ε) if |ε| ≥ ε0

(11.1)

is used [36]. Here σ 0 is the yield stress, ε0 is yield strain, and N is hardening coefficient. For a spherical void under consideration, the void volume fraction f can be defined as  f =

r1 r2

3 ,

(11.2a)

where r1 and r2 are inner and outer radii of the spherical void in current configuration. The initial void volume fraction can be expressed as  f0 =

R1 R2

3 ,

(11.2b)

where R1 and R2 are initial inner and outer radii, respectively, before deformation. When finite-deformation theory is used, the equilibrium must be established in the current configuration. Huang et al. [40] obtained the following radial equilibrium solution of a spherically symmetric cell in the current configuration: σ T (T) + p(T, f , T0 , f0 , C0 ) = σ0

ε2 ε1

H(ε)dε . 1 − exp (−3/2ε)

(11.3)

Here ε1 and ε2 are the radial strains at the two end points of the cell, which can be determined by the current and initial void volume fractions as follows:

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  f0 1 − f 2 ε1 = ln , 3 f 1 − f0   2 1−f . ε2 = ln 3 1 − f0

(11.4)

In equation (11.4), the vapor pressure is a function of the moisture content C, initial and current temperature T0 and T, and initial and current void volume fraction f0 and f. Equation (11.4) displays a nonlinear and non-monotonic relation between the current volume fraction f and the sum of the internal vapor pressure p and the externally imposed radial thermal stress σ T . Figure 11.6 presents the numerical results of void volume increase with respect to the applied traction σ T +p, when the initial void volume fraction f0 is 0.01 and 0.05, respectively [41]. The applied traction increases continuously from zero to its peak value and then decreases. This implies that the cell collapses, when the peak value is reached. From Fig. 11.6 it can be seen that the critical stress σcr for unstable void growth is about two to three times higher than the yielding stress σ0 , when the initial void volume fraction is in the range 0.01–0.05. σcr= 3.05σ0

(sigma_T+p)/yielding stress

3.5 3

σcr= 2.09σ0

2.5 2 1.5 1 f_0=0.01 0.5

f_0=0.05

0 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

current void volume fraction f

Fig. 11.6 The sum of vapor pressure and thermal stress as a function of void growth (in terms of the current void volume fraction) (elastic–plastic model)

Moisture analysis by Fan et al. [7] suggests that conventional polymeric materials in IC packages have a void volume fraction ranging from 0.01 to 0.05. Given the initial moisture content C0 , the thermal expansion (to obtain σ T ), and the initial void volume fraction f0 , equation (11.4) can be solved to determine the current void volume fraction as well as the vapor pressure as a function of temperature. Assume that the initial void volume fraction f0 is 0.05 and the thermal stress can be estimated by σ T = αE(T − Tstress free ), in which α = 200 ppm/◦ C and Tstress free = 150◦ C. The critical temperature where the void unstable growth occurs is usually well above the glass transition temperature. Young’s modulus decreases dramatically above the glass transition temperature. At reflow temperature 220◦ C, a typical Young’s modulus may be in the range of 500 MPa [41]. Since the yield strength at high

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temperatures is not available, an estimate can be made based on Young’s modulus by σ0 = Eε0 . Assume that ε0 = 0.01. Then the yield stress is σ0 = 5 MPa. The saturated water vapor pressure at 220◦ C is 2.32 MPa (see Chapter 4). The critical stress σcr is about two to three times higher than σ0 , i.e., σcr = 10 − 15 MPa, when the initial void volume fraction is in the range of 0.01–0.05. It shows that the vapor pressure takes a significant portion over the critical stress. When leadfree solder material is used, the reflow temperature can be as high as 260–270◦ C. Therefore, the saturated vapor pressure can reach 5.51 MPa. Besides, the yield stress σ0 can be even lower. The impact of vapor pressure on the unstable void growth becomes more significant. On the other hand, for a material with Young’s modulus of 500 MPa at reflow temperature, it becomes impossible for the material rupture to occur, other than interfacial delamination [4, 5]. Therefore, elastic–plastic model described above is not able to explain the failures in reality.

11.2.2 Hyperelastic Model Most polymer materials used in electronic packaging are thermosets. They exhibit a rubber-like state above the glass transition temperature. The stress–strain relation described by an elastic–plastic model in equation (11.2) may not be appropriate for a rubber material. Guo and Cheng [42] introduced the neo-Hookean model to study a single void problem. The stored energy function for a rubber material can be written as W=

μ 2 (λ + λ22 + λ23 − 3), λ1 λ2 λ3 = 1, 2 1

(11.5)

where μ is the shear modulus and λI are the principal stretches. It can be seen that the shear modulus is the only material property introduced in this stress–strain relation. The equilibrium solution of a spherically symmetric cell in the current configuration, which is similar to equation (11.3), can then be expressed explicitly in terms of the initial and current void volume fractions f0 and f as follows [42]:     σ T (T) + p( f0 , f , C0 , T, T0 ) 1 − f 1/3 1 f0 1 − f 4/3 =2 + μ 1 − f0 2 f 1 − f0 1/3    f0 1 − f 1 f0 1 − f 4/3 −2 − . f 1 − f0 2 f 1 − f0

(11.6)

Equation (11.6) shows a nonlinear and non-monotonic relation between the applied stress and the void volume fraction f. Figure 11.7 plots the sum of vapor pressure and thermal stress as a function of the current void volume fraction for different values of initial void volume fraction. The unstable void growth takes place when the peak value of the sum of the thermal stress and vapor pressure is reached.

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1.8

σcr =1.546μ

(sigma_a+p)/shear modulus)

1.6 1.4

σcr =1.12μ

1.2 1 0.8

f_0 = 0.01 0.6

f_0 = 0.05 0.4 0.2 0 0

0.2

0.4

0.6

0.8

1

current void volume fraction, f

Fig. 11.7 The sum of vapor pressure and thermal stress as a function of void growth (in terms of the current void volume fraction) (hyperelastic model)

It is noted that using the neo-Hookean model by equation (11.5), the critical stress is of the order of shear modulus μ. Assume that the shear modulus μ = E/2(1+v) = E/3 in an incompressible case, where E is Young’s modulus, is about 168 MPa when E = 500 MPa. This implies that the critical stress predicted by a hyperelastic model is on the order of 168 MPa [43]. This value is about an order of magnitude higher than the predicted critical stress of 10–15 MPa, when the elastic–plastic stress–strain relation is used. The results obtained here indeed explain that the unstable growth of void unlikely happens in bulk material, when material’s Young’s modulus is about 500 MPa at reflow temperature. For a soft film (Fig. 11.3) it is concluded that the saturated water vapor pressure may be higher than the critical stress. Therefore, the material rupture may occur.

11.3 Void Behavior at the Interface The void behavior at the interface is different from that within the bulk of the material. The void growth at the interface is not only controlled by the total stress but also affected by the interfacial strength. Figure 11.8 sketches a possible scenario of void growth at the interface. Three stages of the void growth are involved. At the beginning, the void at the interface has an initial void volume fraction f0 , in which a certain amount of moisture is condensed into a mixed liquid/vapor phase. With the increase in temperature, thermal stress and vapor pressure are developed. The void will reach an equilibrium at the void volume fraction f1 . Stage 1 shows no difference with a void in the bulk material. Due to the fact that the interfacial strength is degraded by moisture at high temperature, the void at the interface will continue to grow, even though stress level remains the same, as shown in stage 2 of Fig. 11.8.

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Fig. 11.8 Schematic diagram of the void behavior at interface

A new equilibrium will be reached at the void volume fraction f2 . At this new equilibrium position, the problem can be treated as an equilibrium for a void with the initial volume void fraction ( f0 + f2 − f1 ). If the applied stress reaches the critical stress with ( f0 + f2 − f1 ), the void growth becomes unstable (third stage). The void growth at stage 2 is related to the interface properties. A general relationship between the void growth, moisture content C, and the temperature may be postulated as follows: ˙ f˙ = kCe−(Q/RT) T,

(11.7)

dimensionless applied stress

where C is the moisture concentration, T the temperature, R the universal gas constant. k and Q are interface constants to be determined. It can be seen that the rate of void growth is proportional to moisture concentration C and temperature T. The exact determination of the material properties such as k is challenging. Instead of determining equation (11.7), in the following, equation (11.6) is applied to determine the critical void growth due to interface debonding in stage 2. Assume that the initial void volume fraction is 0.01. At the beginning the void will deform along the solid line shown in Fig. 11.9. Then void growth enters the second stage, in which the

Fig. 11.9 Void growth at interface

1.6 1.4 1.2 1 0.8

f0=0.01 f0=0.6 Case 2 f0=0.7 Case 1 void growth due to debonding

0.6 0.4 0.2

(stage 2)

0 0

0.2

0.4

0.6

void volume fraction

0.8

1

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stress level does not change but void grows following equation (11.8). This is shown in Fig. 11.8 as a dotted line, which intersects with another equilibrium curve. The void will not grow further if the stress level is below the critical stress. Otherwise, as in the case 2 shown in Fig. 11.9, the collapse will take place.

11.4 Extension of the Gurson Model and Void Evolution Rate The preceding instability analysis applies for proportional loadings to a single spherical void only. In order to consider the interactions of voids, Gurson [44] assumes that the matrix material follows the classical elastic–plastic flow rule with von Mises yielding criterion. Using homogenization method, the relationship between macroscopic and microscopic variables over a representative cell model is obtained. The macroscopic plastic potential that represents the yielding condition has the form  =

e σe

2



3m + 2f cosh 2σe

 − (1 + f 2 ) = 0 ,

(11.8)

in which  e denotes von Mises equivalent macroscopic stress,  m the mean macroscopic stress, σe the current matrix flow strength of matrix, and f the current void volume fraction. Equation (11.8) shows the effect of mean stress and void volume fraction on the material’s yielding. Tvergaard [45] improved the model predictions for periodic arrays of cylindrical and spherical voids by introducing two factors q1 and q2 , as follows:  =

e σe

2

 + 2q1 f cosh

3q2 m 2σe

 − (1 + q1 f 2 ) = 0

(11.9)

A point to note is that the Gurson yield condition was derived originally from a cell containing a traction-free void, and the matrix is assumed to be rigid-plastic. Recalling that macroscopic stress i,j is defined as the average of the microscopic stress σ ij over a cell, the following equation is obtained: i,j =

1 V



 σij dv = (1 − f )VM VM

σij dv ,

(11.10)

VM

where V is the cell volume, VM is the matrix volume, and f is the void volume fraction. Fan et al. [46] developed a modified Gurson yield model on the yield criterion for PMMA at a bone–implant interface, by considering the effect of vapor pressure. The modified Gurson’s model is as follows:  =

e σe

2

 + 2f cosh

3[m + (1 − f )p] 2σe

 − (1 + f 2 ) = 0 .

The Gurson–Tvergaard yield condition is then given by

(11.11)

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 =

e σe

2

 + 2q1 f cosh

3q2 [m + (1 − f )p] 2σe

 − (1 + q1 f 2 ) = 0 .

(11.12)

It is noted that the contribution of vapor pressure to the macroscopic mean stress takes the factor form (1–f)p. A similar factor has appeared in the works of Guo and Cheng [47]. The standard Gurson–Tvergaard relation has two internal variables, σe and f. The void volume fraction f is treated as a field variable: a damage parameter to represent the local material behavior. f = 1 at a particular (continuum) point implies that delamination takes place at this point. The evolution equation is required for the void volume fraction f. For homogeneous material in bulk, the growth rate can be written as f˙ = f˙growth + f˙nucleation ,

(11.13)

f˙growth = (1 − f )E˙ kk ,

(11.14)

˙ m. f˙nucleation = Aσ˙ e + B

(11.15)

In order to consider the debonding effect at the interfaces, the void growth rate equations can be modified as follows [4]: f˙ = f˙growth + f˙nucleation + f˙debonding ,

(11.16)

f˙growth = (1 − f )E˙ kk ,

(11.17)

˙ m, f˙nucleation = Aσ˙ e + B

(11.18)

˙ f˙debonding = kCe−(Q/RT) T.

(11.19)

The extended Gurson–Tvergaard relation as shown in equation (11.12) introduces an additional variable: vapor pressure p. The evolution rule for p should follow the vapor pressure model developed in [9, 48], which is presented in Chapter 4. The original Gurson–Tvergaard model requires that each finite element to be modeled as porous material anywhere over the given structure. This usually gives rise to the difficulties in numerical implementation. Also, the model is very sensitive to the size of the element to be taken. The concept of a cell model was first introduced by Xia and Shih [49] to tackle this problem. In the cell model, only a material layer of characteristic thickness D is modeled by Gurson–Tvergaard relation (see Fig. 11.10). Beyond this region, the conventional material without voids is applied. Therefore, it can be assumed that voids are present only in the material layer from the very beginning. This model has advantage that each cell behaves as a basic material unit containing a void and can be considered as a representative volume element pertaining to the specific material considered. The discrete, threedimensional nature of a cell enables it to capture the important features from the

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Conventional material without voids Void coalescence

Layer of cells

Void growth

Gurson model Fig. 11.10 Schematic diagram of cell model application

crack formation to the propagation of a macro-crack. Since the Gurson–Tvergaard model is not able to capture the coalescence phase, the cell model will use a linear traction–separation law to supersede the Gurson model when the void volume fraction reaches a critical value. The cell model has recently been extended to model the interface delamination in plastic IC packages [50]. In Chapter 12, a detailed analysis on a mechanismbased modeling for thermal- and moisture-induced failures in IC devices will be presented.

11.5 A Rigid-Plastic Model for Package Bulging Analysis The vapor pressure subjected to the delaminated area will cause the package to bulge when a complete delamination takes place, as shown in Fig. 11.1c. Molding compound becomes compliant when temperature exceeds its glass transition temperature. The glass transition temperature for a molding compound is typically around 165◦ C, well below the peak reflow temperature. Figure 11.11a shows a real failure image of a QFP after reflow. The molding compound beneath the die pad (leadframe) experiences large deformations due to vapor pressure. A mechanics model is developed to investigate the critical condition which defines the cracking condition in mold compound [51]. As shown in Fig. 11.11(b), the mold compound under the die pad can be simplified as a plate with all edges clamped, subjected to a pressure on the plate top. The material is treated as a rigid-plastic or perfectly elastoplastic material. According to plasticity theory, the limit pressure can be obtained by the following equation: p∗ =

3σe h2 , L2

(11.20)

292 Fig. 11.11 (a) An image of a QFP bulge after reflow and (b) a clamped plate subjected to a vapor pressure

X.J. Fan et al.

(a)

MC

leadframe

Delamination and package bulge

vapor pressure p

(b)

mold compound

where h is the thickness of mold compound under die pad, L is the length of interface, and σe is yield stress. Such a condition can be considered as a critical cracking condition, since the plate edge becomes plastic hinge, as shown in Fig. 11.12a when equation (11.20) is satisfied. It can be found that reducing die-pad size (L) or increasing the thickness of mold compound (h) can enhance the loading capacity of package. σs

Fig. 11.12 Stress state at clamped plate edge: (a) Bending theory and (b) membrane effect

σs

σs

a

b

The rigid-plastic model provides a useful analysis on package deformation after delamination. The solution by equation (11.20) may not be accurate enough since small deflection is assumed. With bulge increasing, membrane effect becomes increasingly as important as bending effect. The combination of membrane and bending effects will result in a completely yielding stress state at the plate edge, as shown in Fig. 11.12b.

11.6 Governing Equations for a Deforming Polymer with Moisture Considering Phase Transition The phenomenological aspect of moisture-induced damage can be found in the works of Fan et al. [52, 53], Hui et al. [54], Roy et al. [55, 56], Rajagopal [57], and Sullivan et al. [58]. These authors have studied the coupled effect of polymer

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damage with moisture diffusion. However, a complete mathematical formulation on polymeric solids coupled with the thermodynamics of evaporation of moisture has not been developed. In this section the governing equations for a deforming polymer with moisture are developed. Moisture phase transition is considered. Similar to soil or rock mechanics with multiphase flow, the solid phase is assumed to comprise a porous skeleton of polymers surrounded by moisture. The moisture flow is neglected here, while an all-round vapor pressure is exerted on the solid phase. The small strain theory is considered here for clarity, but the theory can be extended to large-deformation case. It is assumed that a vapor pressure by moisture, i.e., p, causes only a uniform, volumetric strain by compressing the solids and that the major deformation of the porous skeleton is governed by the effective stress σ . This is defined as follows, with the sign convention that tension is positive, σ = σ − mp ,

(11.21)

where σ is the total stress and m is equal to unity for the normal stress components and zero for the shear stress components. At each point in the domain, the variables are in fact average values over a representative elementary volume (REV) around any considered point in the porous medium domain. As long as the REV is independent of time and of location in the porous medium, the averaged equations obtained are independent of the geometry of the REV. The volume V of REV is composed by the sum of the volume of solid phase and free volume V = Vs + Vf ,

(11.22)

where Vs is solid phase volume and Vf is the free volume. The (averaged) total stress vector at macroscopic level may be expressed in terms of intrinsic phase averages     1 1 σ dV = σ dV + σ dV V V V Vs Vf   1 V Vs f σs s + σf f , = V V Vf

σ  =

(11.23)

where σπ π =

1 Vπ

 V

σπ dV

(11.24)

which presents the average over one phase. Then we have σ  = (1 − f ) σ s − f m p = σ − m p .

(11.25)

This is how we obtained equation (11.21). For clarity, we do not use the symbol , but one should always keep in mind that the quantities are in average at the macroscopic level. In equation (11.25),

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σ = (1 − f )(σ s + m p)

(11.26)

is the strain-producing stress in the solid skeleton, the effective stress. According to Terzaghi’s definition it is the sum of the pressure and average stress in the solid phase. The constitutive equation relating this effective stress to the strains of the skeleton is now independent of the vapor pressure p, and for a general nonlinear material can be written in a tangential from, thus allowing plasticity to be incorporated. The expression is written in general from as dσ = DT (dε − dε c − dε p − dε 0 )

(11.27)

where dε represents the total strain of the skeleton and represents the overall volumetric strains caused by uniform compression of the particles (as opposed to skeleton) by the pressure of the moisture, with Ks being the bulk modulus of the solid phase. The volumetric strain is relatively insignificant when polymer behaves as rubber where the material is nearly incompressible. The matrix DT is dependent on the level of effective stresses and also, if strain effects are considered, on the total strain of the skeleton ε. The equilibrium equation relating the total stress to the body forces and the boundary traction specified at the boundary of the domain is formulated in terms of the unknown displacement vector u. When the effective stress relationship is incorporated, the following equation is obtained:  

δε T DT 

∂ε d− ∂t

 

δε T m

∂ε0 d − − δε DT ∂t 



T



df =

∂p d + ∂t

 

δε T DT m

∂f ∂ε c d − = 0, δε DT ∂t ∂t 

(11.28)

T



 δu dbd + T





∂p 1 d ∂t 3Ks



δuT dtd .

(11.29)

In order to solve this equation, the vapor pressure evolution model is needed, which was developed in [9, 48] as follows: p(t) =

RTC MMH2 O f

p(T) = pg (T)

when C(x, T) / f < ρg (T), when C(x, T)/f ≥ ρg (T),

(11.30) (11.31)

where R is the universal gas constant (=8.314 J/(mol K)), MMH2 o is the molecular mass of water (=18 g/mol), C is the local moisture concentration, and pg is the saturated water vapor pressure. In equation (11.28) there are two terms related to the vapor pressure. Previously, the concept of vapor pressure-induced expansion was introduced [50]. An integrated

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vapor pressure, hygroswelling, and thermo-mechanical stress modeling methodology during reflow with interfacial fracture mechanics analysis modeling was developed to study the vapor pressure effect. It can be seen that such an effect corresponds to the third term on the left side of equation (11.28). When the material is incompressible, this term vanishes. However, the vapor pressure affects the polymer matrix deformation through the second term, which was not considered in the previous approach.

11.7 Concluding Remarks Continuum mechanics-based analysis for a single spherical void provides new insights on failure mechanism due to moisture. Theoretical results for a microvoid growth under both internal vapor pressure and external loading are obtained within the context of finite deformation. There is a critical surface traction which defines the occurrence of unstable void growth and rupture. When elastic–plastic model is applied, the critical surface traction is about two to three times of the yield stress of the polymer material, which has an initial void volume fraction from 1 to 5%. However, such a prediction contradicts with the experimental observations. When hyperelastic model is used, the critical stress is one order higher than that predicted by the elastic–plastic model. Most polymer materials in electronic packaging are thermoset materials and, therefore, hyperelasticity describes rubber state behavior well. The theoretical results obtained from hyperelastic model are consistent with experimental observations. In addition, a model study is presented on unstable void growth at interface. We simplify the problem, which becomes equivalent to a void problem with an increased initial void volume fraction. The increased initial void volume fraction is induced by the degradation of interface adhesion due to moisture at elevated temperatures. This implies that even though stress level does not change, the debonding due to moisture will increase the void volume fraction significantly. The existence of debonding at interface lowers significantly the critical stress so that the interfacial delamination might occur. It is also possible that a soft film will have a material rupture first before delamination takes place. The Gurson–Tvergaard model has been extended to incorporate vapor pressure effects. At a macroscopic level, the contribution of vapor pressure to the hydrostatic stress takes the factor form (1–f) p, i.e., a fraction of vapor pressure. The void evolution rate equations are extended to an interface with considerations of debonding due to temperature and moisture. In Chapter 12, a comprehensive study will be presented on a mechanism-based analysis for popcorn cracking problems. A rigid-plastic model is introduced to analyze package bulge and the limit pressure that leads package to crack is obtained. The relationship between vapor pressure, encapsulation thickness, and the length of die pad is established. Furthermore, under the general framework of continuum mechanics using homogenization, the governing equations for a polymer with moisture are developed. The vapor pressure will affect the macroscopic material behaviors through

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two separate terms. When the material is considered as incompressible, one of the terms vanishes. The evolution rule for the additional field variable, vapor pressure p, obeys the vapor pressure model that is presented in Chapter 4. The new framework provides a systematic approach to perform full-field analysis of moisture-induced failures in encapsulated IC devices.

References 1. JEDEC/J-STD-020D, “Moisture/reflow sensitivity classification for plastic integrated circuit surface mount devices”, 2008. 2. Fan, X.J., “Moisture related reliability in electronic packaging”, Electronic Component Technology Conference (ECTC) Professional Development Course (PDC) handout, 2005/2006/2007/2008. 3. Zhang, G.Q., van Driel, W.D., Fan, X.J., Mechanics of Microelectronics. New York, NY: Springer, 2006. 4. Fan, X.J., Zhang, G.Q., van Driel, W.D., Ernst, L.J., “Interfacial delamination mechanisms during reflow with moisture preconditioning”, IEEE Transactions on Components and Packaging Technologies, 31(2), 252–259, 2008. 5. van Driel, W.D., van Gils, M.A.J, Fan, X.J., Zhang, G.Q., Ernst, L.J., “Driving mechanisms of delamination related reliability problems in exposed pad packages”, IEEE Transactions on Components and Packaging Technologies, 31(2), 260–268, 2008. 6. Shi, X.Q., Zhang, Y.L., Zhou, W., Fan, X.J., “Effect of hygrothermal aging on interfacial reliability of silicon/underfill/FR-4 assembly”, IEEE Transactions on Components and Packaging Technologies, 31(1), 94–103, 2008. 7. Fan, X.J., Lee, S.W.R., Han, Q., “Experimental investigations and model study of moisture behaviors in polymer materials”, Microelectronics Reliability, 49, 861–871, 2009. 8. He, Y., Fan, X.J., “In-situ characterization of moisture absorption and desorption in a thin BT core substrate”, Proceedings of Electronic Components and Technology Conference (ECTC), pp. 1375–1383, 2007. 9. Xie, B., Fan, X.J, Shi, X.Q., Ding, H., “Direct concentration approach of moisture diffusion and whole-field vapor pressure modeling for reflow process: part I – theory and numerical implementation”, ASME Journal of Electronic Packaging, 131(3), 031010, 2009. 10. Xie, B., Fan, X.J, Shi, X.Q., Ding, H., “Direct concentration approach of moisture diffusion and whole field vapor pressure modeling for reflow process: part II – application to 3-D ultra-thin stacked-die chip scale packages”, ASME Journal of Electronic Packaging, 131(3), 031011, 2009. 11. Xie, B., Shi, X.Q., Fan, X.J., “Sensitivity investigation of substrate thickness and reflow profile on wafer level film failures in 3D chip scale packages by finite element modeling”, Proceedings of Electronic Components and Technology Conference (57th ECTC), pp. 242–248, 2007. 12. Shi, X.Q., Fan, X.J., “Wafer-level film selection for stacked-die chip scale packages”, Proceedings of Electronic Components and Technology Conference (57th ECTC), pp. 1731–1736, 2007. 13. Fukuzawa, I., Ishiguro, S., Nanbu, S., “Moisture resistance degradation of plastic LST’s by reflow soldering”, >Proceedings of 23rd International Reliability Physics Symposium, pp. 192–197, 1985. 14. Kitano, M., Nishimura, A., Kawai, S., “Analysis of package cracking during reflow soldering process”, Proceedings of IRPS, pp. 90–95, 1988. 15. Tay, A.A.O., Lin, T.Y., “Influence of temperature, humidity and defect location on delamination in plastics packages”, IEEE Transactions on Components, Packaging and Manufacturing Technology, Part A, 22(4), 512–518, 1999.

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16. Lin, T.Y., Tay, A.A.O., “Dynamics of moisture diffusion, hygrothermal stresses and delamination in plastic IC packages”, ASME EEP-Vol. 19-1, Advances in Electronic Packaging, 1429–1436, 1997. 17. Tay, A.A.O., Lin, T.Y., “Moisture diffusion and heat transfer in plastic IC packages”, IEEE Transactions on Components, Packaging and Manufacturing Technology – Part-A, 19(2), 186–193, 1996. 18. Tay, A.A.O., Lin, T.Y., “The impact of moisture diffusion during solder reflow on package reliability”, Proceedings of the 49th Electronic Components and Technology Conference, 830–836, 1999. 19. Liu, S., Mei, Y., Wu, T.Y., “Bimaterial interfacial crack growth as a function of mode-mixity”, IEEE Transactions on Components, Packaging, and Manufacturing Technology –Part A, 18(3), 618–626, 1995. 20. Liu, S., Mei, Y.H., “Behavior of delaminated plastic IC packages subjected to encapsulation cooling, moisture absorption, and wave soldering”, IEEE Transactions on Components, Packaging, and Manufacturing Technology – Part A, 18(3), 1995. 21. Nguyen, L.T., Lo, R.H.Y., Belani, J.G., “Molding compound trends in a denser packaging world”, IEEE International Electronics Manufacturing Technology Symposium, Kanazawa, Japan, June, 9–11, 1993. 22. Galloway, J.E., Miles, B.M., “Moisture absorption and desorption predictions for plastic ball grid array packages”, IEEE Transactions on Components, Packaging and Manufacturing Technology – Part A, 20(3), 274–279, 1997. 23. Wong, E.H., Teo, Y.C., Lim, T.B., “Moisture diffusion and vapour pressure modeling of IC packaging”, Proceedings of 48th Electronic Components and Technology Conference, pp. 1372–1378, 1998. 24. Wong, E.H., Rajoo, R., Lim, T.B., “Moisture absorption and distribution characterisation of packaging materials-advanced treatment,” Microelectronics Reliability, 43, 2087–2096, 2003. 25. Wong, E.H., Chan, K.C., Rajoo, R., Lim, T.B., “The mechanics and impact of hygroscopic swelling of polymeric materials in electronic packaging,” Proceedings of 50th Electronic Components and Technology Conference, Las Vegas, NV, pp. 576–580, 2000. 26. Suhir, E., “Failure criterion for moisture-sensitive plastic packages of integrated circuit (IC) devices: application of von-Karman’s equations with consideration of thermoelastic strains”, International Journal of Solids and Structures, 34(23), 2991–3019, 1997. 27. Shook, R., Vaccaro, B.T., Gerlach, D.L., “Method for equivalent acceleration of JEDEC/IPC moisture sensitivity levels”, Proceedings of 36th IRPS, pp. 214–219, 1998. 28. Tee, T.Y., Ng, H.S., “Whole field vapor pressure modeling of QFN during reflow with coupled hygro-mechanical and thermo-mechanical stresses”, Proceedings of 52nd ECTC Conference, USA, pp. 1552–1559, 2002. 29. Tee, T.Y., Fan, X-J., Lim, T.B., “Modeling of whole field vapor pressure during reflow for flip chip and wire-bond PGBA packages”, 1st International Workshop on Electronic Materials & Packaging, Singapore, September 29–October 1, 1999. 30. Tee, T.Y., Kho, C.L., Yap, D., Baraton, X., Sivakumar, K., “Comprehensive moisture diffusion, hygroswelling, and thermo-mechanical modeling of FCBGA package with no-flow underfill”, APACK 2001 Conference, Singapore, pp. 210–216, 1999. 31. Kho, C.L., Tee, T.Y., Yap, D., Toh, C., Baraton, X., “Flip chip in package assembly and reliability with no-flow underfill materials”, SEMICON Advanced Packaging Technology Symposium, Singapore, August 2003, Singapore, pp. 81–88, 2002. 32. Tee, T.Y., Kho, C.L., Yap, D., Toh, C., Baraton, X., Zhong, Z.W., “Reliability assessment and hygroswelling modeling of FCBGA with no-flow underfill”, Microelectronics Reliability Journal, 43(5), 741–749, 2003.

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33. Tee, T.Y., Zhong, Z.W., “Integrated vapor pressure, hygroswelling, and thermo-mechanical stress modeling of QFN package during reflow with interfacial fracture mechanics analysis”, Microelectronics Reliability Journal, 44(1), 105–114, 2004. 34. Dudek, R., Walter, H., Michel, B., Alpern, P., Schmidt, R., Tilgner, R., “Studies on parameters for popcorn cracking”, Proceedings of International Conference POLYTRONIC 2001, Potsdam, Germany, October 21–24, 2001, pp. 140–148, 2001. 35. Dudek, R., Walter, H., Michel, B., “Studies on moisture diffusion and popcorn cracking”, Proceedings of Conference EuroSimE 2002, Paris, France, April 2002, pp. 225–232, 2002. 36. Yu, T.X., Plasticity. Beijing: Higher Education Press, 1990. 37. Mclintock, F.A., “A criterion for ductile fracture by growth of holes”, Journal of Applied Mechanics, 35, 363–371, 1968. 38. Rice, J.R., Tracey, D.M., “On the ductile enlargement of voids in triaxial stress fields”, Journal of Mechanics and Physics of Solids, 17, 201–217, 1969. 39. Huang, Y., Hutchinson, J.W., Tvergaard, V., “Cavitation instabilities in elastic plastic solids”, Journal of Mechanics and Physics of Solids, 39, 223, 1991. 40. Huang, Y., Hu, K.X., Yeh, C.P., Li, N.Y., Hwang, K.C., “A model study of thermal stressinduced voiding in electronic packages”, ASME Journal of Electronic Packaging, 118, 229, 1997. 41. Fan, X.J., Zhang, G.Q., Ernst, L.J., “A micro-mechanics approach in polymeric material failures in microelectronic packaging”, Proceedings of 3rd International Conference on Thermal & Mechanical Simulation in Micro-Electronics (EuroSimE), pp. 154–164, 2002. 42. Guo, T.F., Cheng, L., “Unstable void growth in plastic IC packaging material”, Scripta Materialia, 2001, (unpublished manuscript). 43. Fan, X.J., Zhang, G.Q., van Driel, W.D., Ernst, L.J., “Analytical solution for moisture-induced interface delamination in electronic packaging”, Proceedings of Electronic Components and Technology Conference, pp. 733–738, 2003. 44. Gurson, A.L., “Continuum theory in ductile rupture by void nucleation and growth: part Iyield criteria and flow rules for porous ductile media”, Journal of Engineering Materials and Technology, 99, 2–15, 1977. 45. Tvergaard, V., Hutchinson, J.W., “The relation between crack growth resistance and fracture process parameters in elastic-plastic solids”, Journal of Mechanics and Physics of Solids, 40, 1377–1397, 1992. 46. Fan, X.J., “Yield criterion for PMMA at a bone-implant interface”, edited by Yang, G.T. et al., Proceedings of the 4th China-Japan-USA-Singapore Conference on Biomechanics, pp. 360–363, Beijing: International Academic Publishers, 1995. 47. Guo, T.F., Cheng, L., “Thermal and vapor pressure effects on cavitation and void growth”, Journal of Materials Science, 36, 5871–5879, 2001. 48. Fan, X.J., Zhou, J., Zhang, G.Q., Ernst, L.J., “A micromechanics based vapor pressure model in electronic packages”, ASME Journal of Electronic Packaging, 127(3), 262–267, 2005. 49. Xia, L., Shih, C.F., “Ductile crack growth – I, a numerical study using computational cells with microstructurally-based length scales”, Journal of Mechanics and Physics of Solids, 43, 233–259, 1995. 50. Chew, H.B., Guo, T.F., Cheng, L., “Modeling interface delamination in plastic IC packages”, APACK Conference on Advances in Packaging, Singapore, 2001. 51. Fan, X.J., Lim, T.B., “Mechanism analysis for moisture-induced failures in IC packages”, ASME International Mechanical Engineering Congress and Exposition, IMECE/EPE-14, 1999. 52. Fan, X.J., “Mechanics of moisture for polymers: fundamental concepts and model study”, Proceedings of the International Conference on Thermal and Mechanical Simulation and Experiments in Microelectronics and Microsystems (EuroSimE), pp. 159–172, 2008. 53. Fan, X.J., Zhou, J., Zhang, G.Q., “Multi-physics modeling in virtual prototyping of electronic packages – combined thermal, thermo-mechanical and vapor pressure modeling”, Journal of Microelectronics Reliability, 44, 1967–1976, 2004.

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54. Hui, C.Y., Muralidharan, V., Thompson, M.O., “Steam pressure induced in crack-like cavities in moisture saturated polymer matrix composites during rapid heating”, International Journal of Solids and Structures, 42, 1055–1072, 2005. 55. Roy, S., Xu, W., “Modeling of diffusion in the presence of damage in polymer matrix composites”, International Journal of Solids and Structures, 38, 115–125, 2001. 56. Roy, S., Xu, W., Patel, S., Case, S., “Modeling moisture diffusion in the presence of biaxial damage in polymer matrix composite laminates”, International Journal of Solids and Structures, 38, 7627–7641, 2001. 57. Rajagopal, K.R., “Diffusion through polymers undergoing large deformations”, Material Science Technology, 19(9), 1175–1180, 2003. 58. Sullivan, R.M., Stokes, E.H., “A model for the effusion of water in carbon phenolic composites”, Mechanics of Materials, 26, 197–207, 1997.

Chapter 12

Mechanism-Based Modeling of Thermaland Moisture-Induced Failure of IC Devices H.B. Chew, T.F. Guo, and L. Cheng

12.1 Introduction IC packages are multi-layered structures with a large number of interfaces joining oxides, metals, and polymers. For these structures, interface separation is often the result of nucleation, growth, and coalescence of voids. The larger number of micro-pores and cavities observed within the adhesive film, as well as along the film–substrate interfaces, therefore poses a serious threat to the structural integrity of the IC packages. A common occurrence of interfacial failure is during the surface mounting of electronic packages onto the printed circuit board under reflow temperatures of 220–260◦ C. These temperatures exceed the glass transition temperatures, Tg , of the polymeric adhesives and molding compounds and can induce high thermal misfit stresses at the die/adhesive and die/molding compound interfaces. Prior to reflow soldering, moisture diffuses through the hygroscopic polymeric materials and condenses within the micro-pores. At high reflow temperatures, the condensed moisture rapidly vaporizes into steam, creating high internal pressures on pre-existing voids and particle/matrix interfaces. At the same time, the polymeric adhesive experiences significant loss of mechanical strength due to the decrease of modulus of the adhesive at high temperatures [1]. Under these conditions, thermal and vapor pressure-assisted void growth and coalescence is a key failure mechanism, which can lead to popcorn cracking [2, 3]. The chemistry aspects of moisture-assisted crack growth at epoxy–glass interfaces have been studied by Ritter et al. [4]. They observed that water molecules are preferentially absorbed on glass surface, displacing epoxy molecules and breaking interface secondary bonds. Moisture effects can cause significant reductions in epoxy–glass interface toughness. Gurumurthy et al. [5] examined the water-assisted sub-critical crack growth along a polyimide passivation/epoxy underfill interface. They measured the sub-critical crack growth velocity at various relative humidities

L. Cheng (B) e-mail: [email protected]

X.J. Fan, E. Suhir (eds.), Moisture Sensitivity of Plastic Packages of IC Devices, Micro- and Opto-Electronic Materials, Structures, and Systems, C Springer Science+Business Media, LLC 2010 DOI 10.1007/978-1-4419-5719-1_12, 

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and temperatures as a function of the crack-driving force and showed that the presence of moisture produced a marked decrease (by up to a factor of 12) in the energy release rate for crack growth at measurable velocities. Computational studies on interface delamination and popcorn cracking in IC packages often postulate either fully bonded interfaces or pre-cracked interfaces. These studies have adopted standard stress analysis or conventional fracture mechanics approaches to the problem. For example, Alpern et al. [6, 7], Lau and Lee [8], and Ikeda et al. [9] assumed a pre-existing crack prior to reflow soldering, where vapor pressure was treated as an external traction on the crack surface. Kitano [10] coupled the moisture diffusion analysis and stress and deformation analysis to predict the interfacial failure of a pre-cracked specimen. Liu and Mei [11], Lee and Earmme [12], and Tay and Lin [13] focused on a damage tolerance design through the use of fracture parameters such as stress intensity factor to predict the probability of crack propagation during processing and operational cycles. Such approaches, however, cannot predict ductile crack initiation or damage propagation along the interfaces. Moreover, these aspects of IC package failure lie outside the scope of conventional elastic fracture mechanics based on a crack-tip characterizing parameter, since the combination of high constraint levels and high thermal stresses brings about extensive plastic deformation in the adhesive – the resulting plastic zone can be considerably larger than the adhesive thickness. The situation is exacerbated by the presence and evolution of microscopic defects such as micro-voids and micro-cracks from regions of stress concentration. Recent advances show that the fracture mechanics framework augmented by mechanism-based models has good predictive capabilities [14]. The mechanics is used to link the macroscopic geometry and loads to microscopic fracture processes, which are then calibrated by experiments. Specifically, the structure or specimen of interest is divided into two separate domains that can be analyzed independently and then linked together to express the overall behavior. The first domain represents the fracture process zone near the crack front. This zone incorporates a model of the failure mechanism and its key microstructural variables. Surrounding the process zone is the other domain representing the physically larger plastic zone and outer elastic region that can be described by continuum models of elastic–plastic behavior. Within this framework, fracture resistance consists of two contributions: the intrinsic work of separation in the process zone and the extrinsic plastic dissipation in the plastic zone. Liu et al. [15] employed the traction–separation law as the mechanism-based model to simulate popcorn cracking along critical interfaces of an IC package. The approach has the capability to predict crack initiation and subsequent growth, without the assumption of a pre-existing crack tip. Liu et al.’s work showed that vapor pressure shifts interface mode mixity from sheardominated to tensile-dominated stress fields. In addition, vapor pressure-induced crack-driving force was found to be an increasing function of the crack size (see [16] and references therein). This chapter reviews recent efforts by the authors to develop micromechanicsbased failure theories/models and computational tools for material and process selection of IC packages and to improve their reliability under service conditions.

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Our studies on vapor pressure-assisted void growth in hygroscopic polymeric materials have shown that popcorn cracking could be treated as the unstable growth of a voided cell under the conjoint influence of thermal stress and vapor pressure [17–19]. A continuum description of vapor pressure-assisted void growth was developed in [20] and will be discussed in Section 12.2. This micromechanics model was subsequently adopted to predict the fracture and failure of polymeric adhesives and interfaces [16, 21–25]. A full-field IC package analysis was also performed, where we demonstrate the capability of the mechanism-based approach in simulating the entire failure process – from initiation of debonding to formation and propagation of a macrocrack – without a priori knowledge of the critical interface for delamination [26]. A summary of our main findings is presented in Section 12.3. Noting that the polymeric materials and adhesives used for IC packaging exhibit some levels of pressure sensitivity and plastic dilatancy [27–29], we have also extended our research to the effects these parameters have on void growth and interaction [30–33]. A discussion of these aspects will follow in Section 12.4. In Section 12.5, we conclude this chapter with a brief introduction on two recently developed constitutive models which can account for the separate effects of pressure sensitivity and nonlinear viscosity in porous materials [34, 35].

12.2 Vapor Pressure Modeling in Rate-Independent Elastic–Plastic Solids Around the glass transition temperature, Tg , certain polymers including epoxies behave like elastic–plastic solids exhibiting extensive ductility and hardening. In Section 12.3, we assume that the matrix material of the adhesive film can be described as an elastic–plastic, pressure-independent, power-law hardening material. The plastic response of the film is characterized by a J2 flow theory (isotropic hardening based on Mises yield condition). The uniaxial tensile stress–strain behavior of the film is described by a true stress–logarithmic strain relation ⎧σ ⎪ for σ < σ0 ⎨ E , ε = σ0  σ 1/N ⎪ ⎩ for σ  σ0 E σ0

(12.1)

where σ 0 is the initial yield stress in tension and N the strain hardening exponent. Crack growth and interface delamination can be modeled using Xia and Shih’s cell element approach [36]. A strip of void-containing cell elements is embedded at the film–substrate interface ahead of the crack tip. The behavior of these cell elements is described by the Gurson flow potential  [37, 38] extended to take account of vapor pressure p [20]. It has the form  =

σe σM

2

 + 2q1 f cosh

3q2 (σm + p) 2σM



  − 1 + (q1 f )2 = 0,

(12.2)

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where σ e denotes the equivalent macroscopic stress, σ m the mean macroscopic stress, and σ M the flow stress of the matrix as determined by equation (12.1). The micromechanics parameters q1 and q2 were introduced by Tvergaard [38] to improve model predictions for periodic arrays of cylindrical and spherical voids and are taken to be 1.25 and 1, respectively [39]. Internal vapor pressure can build up to high levels when moisture-infiltrated polymer is subjected to temperature increase well above 100◦ C. If the moisture in the void is fully vaporized, the internal pressure may evolve in accordance with the ideal gas law as the void enlarges its size. On the other hand if the moisture is partially vaporized, a two-phase situation exists. In this case, the pressure can stay relatively constant during subsequent void expansion as additional moisture vaporizes. Which scenario prevails is primarily controlled by temperature and the specific volume of the moisture [40]. The two models of void pressure evolution can be viewed as two extreme scenarios. Vapor pressure-assisted void growth/rupture has been observed for IC packages at reflow temperatures [11] and appears to be the mechanism of “popcorn” failure in IC packages [41]. Another application where internal pressure is known to cause voiding is the formation of methane gas at elevated temperatures in carbon steel [42, 43]. The vapor pressure, p, is a new internal variable given by T f0 1 − f −3αT p = e , p0 T0 f 1 − f0

(12.3)

which relates the current state (p,f ,T) to the initial state (p0 ,f0 ,T0 ). In the above, α is the coefficient of thermal expansion (CTE), T is the temperature rise relative to the reference temperature T0 , and f is the current void volume fraction which obeys the volumetric plastic strain rate relation f˙ = (1 − f ) trdp .

(12.4)

Here, we focus on void growth and neglect micro-void nucleation in the matrix.

12.3 Vapor Pressure and Residual Stress Effects As a first step toward understanding popcorn cracking, moisture analysis was carried out to determine the maximum possible water weight gain per sample volume for a particular ambient condition by measuring the saturation concentration data, e.g., Galloway and Miles [44] for plastic ball grid array (PBGA) packages. The saturated concentration of moisture in BT (bimaleimide triazine) epoxy is 0.0066 g/cm3 at equilibrium for the 23◦ C/70% relative humidity condition, whereas in the die attach it is 0.017 g/cm3 . Such large levels of condensed moisture suggest the materials in question are highly porous. For typical polymeric adhesives, the estimated void volume fractions, from available moisture analysis, range from 1 to 5%. The highly

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porous nature of adhesives in flip-chip-on-board (FCOB) and PBGA packages was also observed by Trigg [45] using infrared microscopy. In a humid environment, moisture diffuses to the voids in the adhesive. During reflow soldering, surface-mount plastic-encapsulated devices are exposed to temperatures between 210 and 260◦ C for periods of 30 s to 5 min. Such temperatures fall near the glass transition temperature Tg of the polymeric materials. The mechanical properties of polymeric materials are highly sensitive to temperature. For example, the behavior of epoxy at the temperatures of interest is listed below: E = 3 GPa, σ0 = 30 − 80 MPa at room temperature (25◦ C), E = 300 MPa, σ0 = 2 − 5 MPa at reflow temperature (220◦ C).

(12.5)

These values are obtained from a modulus diagram for amorphous polymers (e.g., Fig. 3.4 in [46]). Under these conditions, the condensed moisture vaporizes with little time for the moisture or vapor to escape. The fast ramp rate suggests the effects of timedependent void growth to be small. The rapidly expanding water vapor exerts internal pressures on the voids that could reach 3–6 MPa [11]. Such stress levels are comparable to the yield strengths of epoxy molding compounds and epoxy adhesives as listed in (12.5). Other studies indicate that the thermal expansion mismatch between the adhesive and the die can generate stresses exceeding the yield strength of the adhesive [47, 48]. Three types of package cracking have been identified in the literature [49]. In type I, the package crack originates from the die-pad/molding compound interface delamination. In type II, the package crack originates from the die-attach/die-pad interface delamination. Type III refers to package cracking originating from the die surface/mold compound interface delamination. Of these, types II and III could result in failure from cutoff of the lead wire and are consequently more serious than type I [50]. Both the type and extent of package cracking are dependent on the material combinations and package geometry [51, 53]. In this section, we first focus on a ductile polymeric adhesive with a centerline crack joining two elastic substrates, which is representative of the die-attach layer in IC packages, paying particular attention to failure mechanisms which are precursors to popcorn cracking. Thereafter, we examine the moisture and residual stress effects on interfacial toughness for type II failures and type I and III failures, respectively. This section concludes with a full-field analysis of a typical IC package under moisture sensitivity test conditions.

12.3.1 Adhesive Failure Mechanisms The polymeric adhesives in typical electronic packages are highly porous and contain voids and cavities of various size scales [45]. With this in mind, a “fully porous adhesive” (FPA) model is employed in [23] where pre-existing voids are distributed throughout the entire adhesive. The adhesive is stressed by remote mode I loading

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and residual stresses, while voids in the adhesive are pressurized by rapidly expanding water vapor. The growth of these voids is governed by the extended Gurson model described in Section 12.2. We assume that void-containing cells of constant initial porosity f0 are uniformly distributed throughout the entire film. The stress arising from thermal expansion mismatch between the adhesive and the substrate is treated as an initial residual tensile stress of magnitude σR = σ0 . Rapid vaporization of moisture at high temperatures introduces an initial vapor pressure on the void of magnitude p0 = σ0 . Four types of loading are considered: (i) remote load only; (ii) remote load with vapor pressure (p0 = σ0 ); (iii) remote load with residual stress (σR = σ0 ); (iv) remote load with vapor pressure and residual stress (p0 = σR = σ0 ). Three distinct mechanisms of failure are revealed in [23]. Figure 12.1 shows the contour maps of voiding activity in low initial porosity adhesives f0 = 0.01. Under load type (i), voiding occurs near the crack tip at low loads. As the deformation increases, intense voiding activity develops far ahead of the crack with the new damage zone being centered about X1 = 1.5h. At even higher loads, additional zones of void activity form even further ahead of the crack. This voiding pattern is referred to as “multiple damage zone” mechanism. Under load types (ii) and (iv), extended damage zones emanate from the crack and the voiding pattern belongs to the contiguous damage zone mechanism. Interface delamination is the dominant failure

(a) 0.088

J/(σ0h) = 0.088

h

0.070

remote load only (b) J/(σ0h) = 0.088

0.070

p0 = σ 0 (c)

J/(σ0h) = 0.088 0.088

0.070

0.070 0.088

Fig. 12.1 Contours of f = 0.05 for J/(σ0 h) = 0.070 and J/(σ0 h) = 0.088 under four types of loading: f0 = 0.01, (i) remote load only; (ii) p0 = σ0 ,σR = 0; (iii) σR = σ0 ,p0 = 0; (iv) p0 = σR = σ0 [23]

σR = σ0 (d) J/(σ0h) = 0.088 0.070

Contours of f = 0.05 for f0= 0.01

σR = p0 = σ0

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mode under load type (iii), with voiding occurring primarily along the adhesive– substrate interfaces. For high initial porosity adhesives f0 = 0.05, the contiguous damage zone mechanism is the dominant failure mode under load types (i)–(iv). Our computations for f0 = 0.01 and 0.05 under load types (i)–(iv) display a common trend. A small load increase induces a disproportionately large increase in the size of the damage zone. In other words, small load variations with time can cause rapid damage propagation. This behavior could explain the catastrophic nature of popcorn cracking. The fully porous adhesive model used in this study appears capable of simulating all three failure mechanisms noted above under a wide range of conditions. For comparison purposes, computations are also performed in which void growth is confined to a narrow zone directly ahead of the crack. In this case, only one row of void-containing cell elements is deployed ahead of the crack. This “partially porous adhesive” (PPA) model is similar to the geometric models employed in [21] for damage evolution simulations and by Xia and Shih [36] for crack growth studies. The void-free adhesive material is described by a J2 flow theory. With one important exception, the partially porous adhesive model correctly predicts voiding and stress patterns in both low- and high-porosity adhesives. However, it generally overestimates the damage level ahead of the crack (see Fig. 12.2).

a

b

Fig. 12.2 Porosity f and mean stress σm /σ0 ahead of crack (X2 = 0) under remote load only: (a) f0 = 0.01 and (b) f0 = 0.05 [23]

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Fig. 12.3 Schematic of non-uniform initial porosity distribution in the adhesive film [24]

The porosity distributions in typical adhesives are likely to be non-uniform. In [24], we describe the non-uniform initial porosity distribution in the adhesive by a doubly periodic function. A schematic of the initial porosity distribution is shown in Fig. 12.3. The associated initial vapor pressure p0 is constant over the cells in the adhesive. Under pure remote loading, increasing amplitude of non-uniformity results in the formation of multiple damage zones for both high- and low-mean porosity adhesives. As an example, we show the contour maps of void activity f = 0.1 for high-mean porosity adhesives f0 = 0.05 in Fig. 12.4 with three amplitudes

Fig. 12.4 Contours of f = 0.1 for J/(σ0 h) = 0.053 and J/(σ0 h) = 0.070 with f0 = 0.05, p0 = σR = 0: (a) f0 /f0 = 0.0; (b) f0 /f0 = 0.3; and (c) f0 /f0 = 0.6 [24] (© 2008 IEEE)

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of non-uniformity: f0 /f0 = 0,0.3, and 0.6. Observe that increasing non-uniformity in f0 changes the damage pattern from a contiguous damage zone extending from the crack (f0 /f0 = 0) to the formation of multiple damage zones both near and far away from the crack (f0 /f0 = 0.6). These damage sites now span over a much larger region from the crack. The damage patterns for f0 = 0.01 with f0 /f0 = 0.6 resemble those shown in Fig. 12.4c. The effects of non-uniform initial porosity distribution are particularly severe for adhesives subjected to high vapor pressure. As f0 /f0 increases for f0 = 0.01 with p0 = σ0 , the failure pattern evolves from the contiguous damage zone mechanism to adhesive rupture near the adhesive–substrate interfaces (Fig. 12.5). These failure patterns, which depict die-attach failures resulting from both the cracking of the die-attach medium itself (Fig. 12.5(a)) and from delamination of the film– substrate interfaces (Fig. 12.5(b)), have been experimentally observed by Teh et al. [54] for adhesives in flip-chip packages subjected to high-temperature and humidity conditions. Figure 12.6 shows the void evolution contours for f0 = 0.05 with p0 = σ0 . An extended damage zone emanates from the crack tip for adhesives with uniform initial porosity distribution. For adhesives with f0 /f0 = 0.6, failure can be catastrophic, with rapid voiding occurring simultaneously throughout the adhesive. We have also conducted computations for adhesives with non-uniform initial porosity distributions under the influence of residual stresses. The effects of f0 /f0 on the damage patterns were found to be small. In the combined presence of residual stress and vapor pressure, we find the shape of the damage patterns across all f0 /f0 to be similar to those for p0 = σ0 ,σR = 0 (Figs. 12.5 and 12.6). This suggest that

Fig. 12.5 Contours of f = 0.05 for J/(σ0 h) = 0.080 and J/(σ0 h) = 0.094 with f0 = 0.01, p0 = σR , σR = 0: (a) f0 /f0 = 0 and (b) f0 /f0 = 0.6 [24] (© 2008 IEEE)

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Fig. 12.6 Contours of f = 0.1 for J/(σ0 h) = 0.050 and J/(σ0 h) = 0.070 with f0 = 0.05, p0 = σ0 , σR = 0: (a) f0 /f0 = 0 and (b) f0 /f0 = 0.6 [24] (© 2008 IEEE)

while residual stress generally increases the extent of adhesive damage, its influence on the damage patterns diminishes in the presence of vapor pressure.

12.3.2 Interfacial Toughness Attention here is directed at residual stress and vapor pressure effects on cracking and interfacial fracture toughness. Type II failure is modeled by the delamination along the interface of a ductile polymeric film constrained between two identical elastic substrates (also known as adhesive failure), while type I and III failures are studied using a bi-material crack model. For both failure types, interface delamination is modeled using Xia and Shih’s cell element approach [36]. A strip of void-containing cell elements is embedded at the weakly bonded interface ahead of the crack tip. The behavior of these cell elements is described by the extended Gurson flow potential described in Section 12.2. 12.3.2.1 Parallel Delamination Along Interfaces of Adhesive Joints Suo [55] noted that laminated structures subjected to high residual stress could simultaneously debond along both interfaces. With this in mind, we focus on the parallel delamination of the adhesive–substrate interfaces under mode I loading in [22]. Residual stresses are induced by the CTE mismatch between the film and substrate it joins. We show that tensile residual stress, acting in conjunction with remotely applied mode I loading, lowers the joint toughness (Fig. 12.7a). The rising R-curves

b Current crack tip

σR /σ0 = 1.0

σR/σ0 = 0.4

σR/σ0 = 0.2

σR /σ0 = 0.0

Fig. 12.7 Residual stress effect on crack growth along joint interface: (a) Crack growth resistance of the joint and (b) plastic zone shape and size [22]

Initial crack tip

p

0

0.001

∋

a

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in the transient crack growth plots are associated with plastic dissipation in the ductile film. The advance of the plastic zone is displayed in Fig. 12.7b for four residual stress levels, σR /σ0 = 0.0,0.2,0.4, and 1.0. In these plots, the crack has grown a distance of 2h. Observe two features. Initially, the plastic zone spreads out across the full width of the film. As the cracks grow, the plastic zone changes its shape – the new growth of the plastic zone is confined to the vicinity of the interface. It may also be noted that the overall size of the plastic zone decreases with increase of σR /σ0 . Focusing on the vapor pressure effects on the crack growth resistance in Fig. 12.8a, we show that high vapor pressure within cavities accelerates void growth and coalescence. As a result, the toughness of the joint is reduced significantly. The reduction in joint toughness can be further compounded under the conjoint influence of vapor pressure and residual tensile stress (Fig. 12.8b). Figure 12.8c displays plastic zone sizes corresponding to three cases (p0 /σ0 = 0.5, 1.0, and 1.5) considered in Fig. 12.8a. The cracks have grown by 2h and one can see that the plastic zones associated with high vapor pressure levels (p0 /σ0 ≥ 1) are effectively confined to the vicinity of the interface. Figure 12.8d displays plastic zones that develop under the combined action of vapor pressure and residual tensile stress (three cases considered in Fig. 12.8b). The plastic zones are narrow and are confined to the vicinity of the interface. These results suggest that residual stress in the film combined with vapor pressure enhance brittle-like cracking characteristics, bringing about severe reduction in toughness of the joints. 12.3.2.2 Interfacial Toughness Under Mixed Mode Loading Interfaces are among the most critical features of microelectronic packages. In IC packages, residual stress arising from the mismatch in thermal expansion coefficients induces a predominant mode II component on the polymer–silicon interfaces. Void growth and coalescence occur under high vapor pressure superposed on this a b

Fig. 12.8 Vapor pressure effect at film – substrate interface on crack growth resistance of the joint: (a) σR /σ0 = 0; (b) σR /σ0 = 1; (c) and (d) plastic zones corresponding to three cases considered in (a) and (b), respectively [22]

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Initial crack tip

313 Current crack tip

p0/σ 0 = 0.5

∋

p0/σ 0 = 1.0

p

0.001 0 p0/σ 0 = 1.5

d

Initial crack tip

Current crack tip

p0/σ 0 = 0.5

∋ p0/σ 0 = 1.0

p

0.001 0

p0/σ 0 = 1.5

Fig. 12.8 (continued)

background stress. We subject a pre-existing crack along one of the adhesive– substrate interfaces to mixed mode loading in [16]. The transient crack growth resistance plots under several mode mixity levels are displayed in Fig. 12.9. One can see that a higher mode mixity ψ gives rise to a larger work of separation in the process zone. The plastic dissipation surrounding the background material also

Fig. 12.9 Crack growth resistance plots for f0 = 0.05, N = 0.1, under mode mixity levels ψ = 0◦ , 20◦ , and 40◦ . The solid curves are for p0 = 0 and the dotted curves for p0 = σ0 [16]

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increases, resulting in higher joint toughness. In the presence of vapor pressure, the joint toughness is significantly lowered. We have shown that these interfacial toughness levels are comparable with available experimental data [5, 56]. In fact, the joint toughness is greatly enhanced as the mode II component of the applied load increases. However, the adverse effects of vapor pressure are found to be greatest in highly porous adhesives subjected to a strong mode II component – these high levels of vapor pressure can cause a several-fold drop in the joint toughness. The latter denotes the likely state of loading in IC packages since residual stress, resulting from the film–substrate thermal mismatch, induces a predominant mode II component. In the absence of vapor pressure, increasing residual tensile stress lowers the joint toughness. However, when combined with void vapor pressure, we have observed that the damaging effects of vapor pressure dominate over residual tensile stress. In plastic-encapsulated packages, a typical die attach is about 40-μm thick, while the average spacing between voids is on the order of microns. Guided by this observation, the range of adhesive thickness 8 ≤ h/D ≤ 80 can be regarded as representative of some adhesive joints in IC packages. The effects of adhesive thickness on the interfacial fracture toughness are summarized in Fig. 12.10 under four types of loading: (i) purely remote load; (ii) remote load with vapor pressure (p0 = σ0 ); (iii) remote load with residual stress (σR = σ0 ); and (iv) remote load with vapor

a

b

c

d

Fig. 12.10 Interface toughness versus film thickness under four types of loading: remote load only; p0 = σ0 , σR = 0; σR = σ0 , p0 = 0; p0 = σR = σ0 . (a) ψ = 0◦ , (b) ψ = 20◦ , (c) ψ = 40◦ , and (d) ψ = 60◦ [16]

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pressure and residual stress (p0 = σR = σ0 ). For all four load types subjected to ψ = 0◦ , no distinct fracture toughness enhancement is observed with increasing film thickness. At higher mode mixity levels of ψ = 20◦−60◦ under load type (i), increasing film thickness raises the toughness levels considerably. Under load type (iii), the fracture toughness is only enhanced with increasing h/D at high-mode mixity levels of ψ = 60◦ . Under load types (ii) and (iv), negligible enhancement in joint toughness is observed with increasing film thickness. As a direct consequence, vapor pressure can induce a fourfold to fivefold drop in the fracture toughness levels of adhesive films with large h/D subjected to a strong mode II component (compare plots for p0 = 0 and p0 = σ0 in Fig. 12.10c and d). The above results pertain to type II failures in IC packages. Type I and III failures have been studied by Chong et al. [25] using a model problem of a bi-material (die/molding compound or die-pad/molding compound) interface crack loaded by elastic bi-material K-fields. Similar to our type II failure observations, they showed that the damaging effects of vapor pressure were remarkably stronger as loading becomes mode II dominant. Since the actual interface loading in an IC package is predominantly mode II, the beneficial effects of increasing interfacial toughness with mode II loading will be negated by high levels of vapor pressure. Chong et al. [25] also observed that resistance curves for low ψ < 30◦ exhibit brittle-like characteristics, with steady-state crack growth reached after small amounts of crack growth. By contrast, resistance curves for high ψ display more ductile characteristics, with crack growth resistance steadily increasing with crack advance. Hence, it is evident that the presence of vapor pressure induces a dramatic transition from ductile to brittle interfacial fracture.

12.3.3 Full-Field Analysis of IC Packages In this subsection, we demonstrate the capability of our mechanism-based approach in simulating the failure of a typical IC package shown in Fig. 12.11 [26]. Specifically, we study the failure response of a plastic ball grid array (PBGA) packages under moisture sensitivity test (MST) conditions [57]. In the physical test itself,

Fig. 12.11 Geometry of 68 I/O PBGA package

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the package is cured at 175◦ C, where it becomes nearly stress free. When the package has cooled to room temperature, it then undergoes three cycles of heating after moisture preconditioning to the reflow temperature of 235◦ C, and back to room temperature of 25◦ C. The possible crack paths in the molding compound are first examined by modeling the fully porous overmold with void-containing cell elements. The contour plots of the current void volume fraction f at the end of third MST cycle for various vapor pressure levels, p0 /σ0 = 0.5, 1.0, and 1.5, are displayed in Fig. 12.12. Observe that as p0 increases, the damage level within the entire package correspondingly increases. In particular, the regions near the die attach and the die corner experience the highest level of voiding activity and are the probable sites for the onset of cracking and delamination (Fig. 12.12c) under MST conditions. Numerical studies by Lee et al. [58] on anisotropic conductive adhesive joints show that the von Mises stress is larger in the upper portion of the adhesive near the chip, as compared to the lower portion nearer the flexible substrate. Recent moisture reliability assessments of PBGA packages by Lau et al. [59] also indicate that cracks are likely to initiate at the die-attach region near to the die corner. In view of these observations, a detailed analysis of type II cracking was conducted. To this end, the ductile crack growth model proposed by Xia and Shih [36] is adopted, where a single row of

a

b

c

Fig. 12.12 Full-field analysis: contour plots of void volume fraction f at the end of third MST cycle for (a) p0 /σ0 = 0.5, (b) p0 /σ0 = 1, and (c) p0 /σ0 = 1.5, with f0 = 0.05 (reflow temperature = 235◦ C) [26] (© 2009 IEEE)

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void-containing cells is deployed along the die-attach/die-pad interface. The void growth and softening behavior of these porous cell elements is governed by our extended Gurson model (Section 12.2). Figure 12.13 shows the porosity and mean stress distribution along the die/dieattach interface at the end of third MST cycle for f0 = 0.05. Four levels of initial vapor pressure, p0 /σ0 = 0, 0.5, 1.0, and 1.5, are considered. Results show that increasing vapor pressure significantly accelerates void growth (Fig. 12.13a) and reduces the interfacial stress-carrying capacity (Fig. 12.13b). This loss of stresscarrying capacity in the presence of moisture was also observed by Fan et al. [60]. For p0 /σ0 = 0.5 and 1, voiding activity increases along the interface, but is particularly intense near the corner of the die/die-attach interface. This observation is in line with our fully porous overmold analysis. At higher vapor pressure levels of p0 /σ0 = 1.5, voiding activity becomes more localized at the corner of the die/die-attach interface, with a second smoother peak f emerging some distances nearer to the center of the die/die-attach interface. These competing sites of damage eventually lead to the complete and rapid delamination of the entire die/die-attach interface. Their formation can be attributed to the high stress triaxiality along to the high stress triaxiality along the highly constrained interface as observed for the constrained layer studies above. The associated loss of stress-carrying capacity with rising p0 in Fig. 12.13b reflects the extensive damage across the interface. In this manner, the entire failure process – from void growth, coalescence to final fracture – is fully captured by our computational model. a

b

Fig. 12.13 Vapor pressure effects with temperature-independent material properties: (a) current void volume fraction f and (b) mean stress σm /σ0 distribution along the die/die-attach interface at the end of MST with f0 = 0.05 [26] (© 2009 IEEE)

12.4 Pressure Sensitivity and Plastic Dilatancy Contributions In contrast to the pressure-insensitive yielding and plastic incompressibility assumption of the matrix material in the Gurson formulation (Section 12.2), experimental studies have shown that the deformation of polymeric materials is highly sensitive

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to hydrostatic pressure [27]; some have observed that certain polymers exhibit modest levels of plastic dilatancy [28, 29]. Hence, the polymeric adhesives and molding compound in IC packages are expected to exhibit some levels of pressure sensitivity and plastic dilatancy. As such, we have conducted detailed computational studies in [31–33] to ascertain the influence of pressure sensitivity, ψ α , and plastic dilatancy, ψ β , on void growth and interaction in polymer packaging materials. The main findings are highlighted here. We first examine the macroscopic response of porous pressure-sensitive dilatant materials subjected to physical stress states similar to highly stressed regions ahead of a crack. With this background knowledge, we then focus on the damage evolution ahead of a crack in pressure-sensitive polymeric layers. In both cases, the pressuresensitive yielding of the matrix material is described by a linear combination of the mean stress and effective stress, i.e., σe + 3ασm − σˆ = 0,

(12.6)

where σ e is the effective stress, σ m the mean stress, and σˆ the flow stress of the subsequent yield surface. The pressure-sensitive index α is related to the friction angle ψ α by tan ψα = 3α. We assume the flow potential to take the form φ = σe + 3βσm

(12.7)

where β is the index for plastic dilatancy, which is related to the dilation angle ψ β by tan ψβ = 3β. The Drucker–Prager yielding condition together with the flow potential (7) can describe the pressure-sensitive dilatant behavior of the material. The plastic part of the deformation rate dp is given by the non-associated flow rule dp = ε˙ p

∂φ , ∂σ

(12.8)

 where ε˙ p ≡ 23 ep :ep is the equivalent strain rate, in which ep signifies the deviatoric part of dp . For the case of β = α, the normals to the yield surface (12.6) and the flow surface (12.7) in stress space coincide resulting in an associated plastic flow. The utilization of an associated flow rule overstates the extent and role of plastic dilatancy. A non-associated flow, with β < α, offers a more realistic description of plastic flow. / The flow stress σˆ in (12.6) is a function of the accumulated plastic strain εp = ε˙ p dt. A power-law (monotonically) hardening description of plastic flow is given by σ0 E



σˆ σ0

1/N −

σˆ = εp , E

where N is the hardening exponent ranging from 0 to 1.

(12.9)

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In Section 12.5, we describe two continuum models of porous solids with pressure sensitivity and nonlinear viscosity, respectively.

12.4.1 Macroscopic Response on Void Growth and Interaction Ductile fracture occurs by the micromechanical process of void growth and coalescence. Assuming that the voids are uniformly dispersed in the matrix material, the resulting microstructure can then be described by an array of unit cells, each containing a single void. In [31], we study the effects ψ α and ψ β on the macroscopic response of a unit cell subjected to axisymmetric deformation. Results reproduced in Fig. 12.14 show that plastic dilatancy, ψ α , has some effect in raising the postpeak stress levels, resulting in a larger work of separation. The effects of pressure sensitivity, ψ α , are more pronounced: Under an externally applied load, an increase in pressure sensitivity of the material severely lowers its stress-carrying capacity. It was also observed in Fig. 12.15 that high initial porosities and pressure-sensitivity levels in polymeric materials can reduce the critical stress responsible for void instability to levels comparable to the initial yield strength. By varying the void aspect ratio, we note that the mechanical strength of the polymer can be further weakened by an increasingly oblate void.

Fig. 12.14 Stress–strain curves of a cell volume containing a single void showing influence of pressure sensitivity ψ α and plastic dilatancy ψ β under uniaxial straining [31]

To gain insights into the moisture-induced failure of IC packages, we have also examined the pressure-induced void growth of a unit cell with traction-free outer boundaries (see Fig. 12.15). Results show that increasing initial porosity f0 severely lowers the saturated peak pressure, pc , associated with rapid unstable void growth. Interestingly, pc increases with ψ α across all initial porosity levels, which suggests that the damaging effects of vapor pressure can be less severe for a pressure-sensitive material.

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Fig. 12.15 Internal pressure effects for ψα = ψβ = 0◦ and 20◦ on spherical void growth with various f0 [31]

In polymeric solids, the larger voids can originate from cavitated rubber blends or from decohesion of filler particle/polymer matrix interfaces, while crazing can induce the formation of localized microporous zones. The void interaction effects in pressure-sensitive dilatant solids containing two populations of cavities of different size scales have also been studied. The representative material volume adopted consists of a single large void with a population of discrete micro-voids placed at locations where cavitation instability could occur, i.e., along the horizontal axis and along the diagonal of the cell (Fig. 12.16a). Plane strain conditions are imposed on the multi-void cell. The stress–strain behavior of the multi-void cell under uniaxial straining is reproduced in Fig. 12.16b. Results suggest that the presence of microvoids greatly reduces the stress-carrying capacity of the cell across the range of

a

b

Fig. 12.16 (a) Finite element mesh of unit cell volume containing two populations of voids of different size scales. (b) Comparison of stress–strain curves for a unit cell containing a single large cavity and one containing two populations of voids of different size scales under uniaxial straining [31]

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pressure sensitivity levels considered – the peak stress is lowered, with a dramatic drop in the post-peak stress level. As the extent of pressure sensitivity increases, the overall stress in the cell correspondingly decreases. In sum, micro-void interaction and pressure sensitivity can work in concert with reducing the stress-carrying capacity of the material: The former is responsible for the post-peak stress drop while the latter controls the sustainable peak stress level.

12.4.2 Extended Damage Zone Formation Previously in Section 12.3, we adopt Xia and Shih’s cell element approach to model the fracture process zone. In [32, 33], we attempt to replicate the exact void growth behavior by placing a single row of cylindrical discrete voids ahead of the crack in a pressure-sensitive dilatant adhesive sandwiched between elastic substrates. Plane strain conditions are imposed and the adhesive is subjected to mode I loading. A schematic is shown in Fig. 12.17. Our computations reveal that increasing pressure sensitivity significantly intensifies the level of damage as well as increases the spatial extent of damage in the adhesive by several folds. These extended damage patterns are shown in Fig. 12.18 for several adhesive layers, with friction angles of ψα = ψβ = 0◦ to 20◦ spanning the range of pressure sensitivity appropriate

Fig. 12.17 An adhesive with a centerline crack sandwiched between elastic substrates. The process zone is modeled by a single row of discrete cylindrical voids [32]

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b

Fig. 12.18 Distribution of porosity f ahead of crack (X2 = 0) for several pressure sensitivity levels ψ α under associated flow, i.e., ψα = ψβ [32]

to polymers. The formation of extended damage zones for pressure-sensitive adhesives can be attributed to the lower stress-carrying capacity of pressure-sensitive solids, which in turn drives the earlier onset of unstable void growth. Interestingly, the simulated damage patterns for pressure-sensitive layers bear resemblance to the long craze zones. Experimental studies have shown that the plastic volume change in polymers does not commensurate with the predictions of the associated flow rule, i.e., ψβ < ψα . The effects of plastic dilatancy on the damage distribution for polymer–silicon joints, under a non-associated flow rule, are presented in Fig. 12.19. Pressure-sensitivity effects are observed to be even greater when a non-associated flow is deployed – the level and spatial ! extent! of damage increases with the deviation from an associated flow rule, !ψβ − ψα !. These effects can be attributed to the lower stress-carrying capacity in the post-peak regime for ψβ < ψα as compared to ψβ = ψα . This limited study suggests that damage in polymers as well as load-bearing predictions based on an associated flow rule could be conservative. Following the two-dimensional studies in [32], we perform three-dimensional computations in [33] by explicitly modeling spherical voids ahead of the crack.

Fig. 12.19 Distribution of porosity f ahead of crack (X2 = 0) for several plastic dilatancy levels ψ β for ψα = 10◦ and 20◦ [32]

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Such an analysis would provide more realistic failure predictions since the real voids and microstructures in actual polymeric layers are three dimensional in nature. While significant quantitative differences in the damage predictions were observed between the three-dimensional and two-dimensional models, the basic trends with regard to the parametric effects of ψ α and ψ β were found to be qualitatively similar. As aforementioned, plastic-encapsulated microcircuits exposed to a humid environment are susceptible to thin film adhesive failures during reflow soldering. Computational studies highlighted in Section 12.3 adopted void-containing cell elements, based on an extended Gurson constitutive model, to describe the ductile fracture process. The damage model was derived based on the assumption of a rigidplastic matrix, and neglects the elastic deformation. Typical polymeric materials, however, exhibit large elastic strains prior to yield. The inelastic deformation and flow stress of the polymeric matrix may also be affected by high hydrostatic stress. With this in mind, we adopt the two-dimensional discrete void model to investigate vapor pressure and voiding effects on thin film adhesive failure in [30]. We assume the high moisture content case, where moisture in the voids does not fully vaporize leaving a two-phase mixture of water and vapor gas. In such cases, vapor pressure can be taken to be a constant, where each void surface is subjected to the identical constant pressure p. We observed that under increasing internal pressure, large-scale adhesive damage occurs with brittle-like failure characteristics. Under low p/σ0 , pressure sensitivity lowers the stress-carrying capacity of the adhesive and intensifies adhesive damage. The reverse effect, however, was observed under high vapor pressure levels. This suggests that vapor pressure effects could be less severe for a highly pressure-sensitive adhesive. Analytical explanations for this peculiar phenomenon have been offered in [23].

12.5 Porous Solids with Pressure-Sensitivity and Non-linear Viscosity In the above section, we have shown that the effects of pressure sensitivity and plastic dilatancy on void growth and interaction are significant and could explain the crazing phenomenon seen in polymeric materials and adhesives. At the same time, we note that viscous effect probably plays a more crucial role for polymers which exhibit significant creeping behavior. Here, we introduce two recently developed macroscopic constitutive models for porous solids, which can individually account for the effects of pressure sensitivity and nonlinear viscosity [35, 34].

12.5.1 Pressure Sensitivity, Dilatancy, and Softening–Rehardening For a porous material with pressure-sensitive dilatant matrix (β = α), Guo et al. [34] derived an approximate flow potential

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 =

Te  (Tm ,α,f )

2

  + 2f cosh γ −1 ln (1 − 3αTm ) − 1 + f 2 = 0,

(12.10)

where Te and Tm are the normalized macro-effective and mean stresses, respectively, as Te =

e , σ0 + 3αp

Tm =

m + p . σ0 + 3αp

(12.11)

The function  takes the form  = 1 − 3αTm / (1 − f )1−s/2 ,

(12.12)

which is accurate over a wide range of parametric values except in the compressive half of the stress space (Tm < 0) when α takes on values in the neighborhood of 0.25. In the above γ =

2α , 2α + sgn (Tm )

s = 1 + 2αsgn (Tm ) .

(12.13)

The influence of the internal void pressure, p, on the yield surface can be seen in Fig. 12.20; the material parameters are f = 0.05 and ψα = 20◦ . Beyond shifting the yield surface to the compressive half of the stress space, internal void pressure alters the size and shape of the yield surface. The effect on the tensile strength is significant – it can be halved if the internal pressure is of the order of the yield stress. The influence of p on the stress–strain curves and porosity evolution for these two vaporization scenarios was examined in greater details in [34].

Fig. 12.20 Internal void pressure effects on the yield surface for ψα = 20◦ and f = 0.05 [34]

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Based on the above potential, Guo et al. [34] expressed the macroscopic deformation rate through the normality rule Dp = 

∂ , ∂T

(12.14)

where  is a positive flow factor, T is the generalized macroscopic stress tensor T=

+pI , σ0 + 3αp

(12.15)

and I a unit tensor. The effective generalized macroscopic stress tensor is Te and the spherical part Tm . The time evolution of void volume fraction due to growth of the voids during a deformation process is governed by

 f˙ = (1 − f ) trDp − 3α ε˙ p ,

(12.16)

in which ε˙ p is the plastic strain rate of the matrix. Polymers exhibit complex and manifold nonlinear deformation [61, 62]. Some polymers display a true stress–strain curve exhibiting a maximum followed by a softening regime. As deformation proceeds further, polymers exhibit rehardening (related to chain re-orientation). In order to capture a range of yield behaviors, Cheng and Guo [63] proposed the following flow stress model: σˆ εp =1+ σ0 ε0



εp + η 1 + ξ (εp /ε0 )2 1

 ,

(12.17)

where ξ mainly controls the maximum (i.e., the intrinsic yield point), η describes the softening/rehardening shape of the stress–strain curve, and σ 0 the (reference) initial yield stress under shear which is related to the initial tensile and compressive yield stresses σ0t and σ0c , by  σ0 =

(1 + α)σ0t for tension, (1 − α)σ0c for compression.

(12.18)

The pressure-sensitivity index α can be determined by σ0t and σ0c as α=

σ0c − σ0t . σ0c + σ0t

(12.19)

This softening–rehardening effect on void growth and interaction in polymeric materials has been studied in a way of discrete voids [63]. It is straightforward to incorporate such effect into the constitutive model (10) for porous solids by replacing σ 0 by σˆ in (17).

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12.5.2 Nonlinear Viscosity For some amorphous materials, void growth and the fracture process are typically rate-dependent. To this end, a micromechanics-based porous material model incorporating internal pressure effects has been developed by Tang et al. [35]. Following Gurson’s homogenization, the model is derived for internal void pressure-assisted void growth in nonlinear viscous solids. The loading function (12.22) has been validated against full-field finite element computations over a full range of stress triaxialities. This model has been applied to several rate-dependent fracture problems [64–66], showing good agreement with existing experimental data. Here, we highlight the key features as follows. For porous materials with a nonlinear viscous matrix, there exists the macroscopic stress potential 1 (1 − f ) σ0 ε˙ 0 n+1

! (t) =



σ¯ σ0

n+1 ,

(12.20)

where t = σ + p1 = s + (σm + p) 1 is the generalized stress tensor, introduced to account for the hygroscopic behavior of certain polymeric materials infiltrated by moisture with internal pressure p [20, 21], and σ¯ represents an average effective stress of the matrix, which is a function of the void volume fraction f and the generalized stress t. The macroscopic inelastic strain rate ε˙ c is given by ε˙ ijc =

∂! . ∂tij

(12.21)

The average effective stress of the matrix, σ¯ , can be implicitly defined by the Gurson-like loading function =

t 2 e

σ¯



3 tm β1 + 2 (1 − m) f cosh 2 σ¯



t 2

9 m + mf β2 − 1 + f 2 − 2mf = 0, 4 σ¯ (12.22)

where te = σe , tm = σm + p, m is the reciprocal of strain rate exponent n, and β1 = β2 =

ln f (1 − f )

m/(1+m)

((1 − f m )/ (mf m ))1/(1+m) (1 − f )2

f (1 − f )2m/(1+m) ((1 − f m )/ (mf m ))

, (12.23)

. 2/(1+m)

The time evolution of the void volume fraction is c , f˙ = (1 − f ) ε˙ kk

(12.24)

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which follows from the incompressibility of the nonlinear viscous matrix. Our primary interest here is void growth. A further development is to introduce a cavitation law in the model accounting for micro-void nucleation in polymeric materials. Internal pressure can arise, for instance, when moisture-infiltrated polymer is subjected to an increase in temperature well above 100◦ C. If the moisture in the void is fully vaporized, the internal pressure p may evolve in accordance with the ideal gas law [20], see equation (12.3). Under isothermal conditions and the mass conservation of moisture concentration, we then have f0 1 − f p = , p0 f 1 − f0

(12.25)

which relates the current state (p, f) to the initial state (p0 ,f0 ). On the other hand, if the moisture partially vaporizes, a two-phase situation exists. In this case, the internal pressure could remain constant during subsequent void expansion. Both scenarios are examined in Fig. 12.21.

a

b

Fig. 12.21 Steady-state toughness as a function of the crack velocity for several vapor pressure levels; n = 6 and σ0 /E = 0.02. (a) f0 = 0.01 and (b) f0 = 0.05 [35]

Vapor pressure effects on toughness–crack velocity relationship is examined for a moderately rate-sensitive material, n = 6. Figure 12.21a presents results for f0 = 0.01. The solid line labeled p/σ0 = 0 (zero vapor pressure) is included for comparison purpose. This curve displays a U-shaped trend. The solid curves labeled p/σ0 = 0.5 and 1 show vapor pressure effects on toughness–crack velocity relationship under the assumption that the pressure is maintained throughout the growth of the void. For p/σ0 = 1, the computed toughness is a monotonically increasing function of the crack velocity. Vapor pressure effects are less pronounced when the ideal gas law assumption is invoked – see dashed line labeled p0 /σ0 = 1. Figure 12.21b shows toughness–crack velocity behavior for a larger initial porosity, f0 = 0.05. In all the cases considered, toughness is a monotonically increasing function of the crack velocity. It appears that vapor pressure effects are most pronounced at low crack velocities. In the vicinity of a˙ /(˙ε0 D) = 103 , an increase

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in p/σ0 from 0 to 1 causes a 10-fold drop in toughness (compare solid lines in Fig. 12.21a as well as those in Fig. 12.21b). At higher velocities, a˙ /(˙ε0 D) = 105 , the reduction is significantly smaller.

References 1. Luo, S., Wong, C.P., “Influence of temperature and humidity on adhesion of under-fills for flip chip packaging”, IEEE Transactions on Components and Packaging Technologies, 28, 88–94, 2005. 2. Fukuzawa, I., Ishiguro, S., Nanbu, S., “Moisture resistance degradation of plastic LSIs by reflow soldering”, IEEE/IRPS International Reliability of Physics Symposium, Orlando, FL, pp. 192–197, 1995. 3. Fan, X.J., Zhou, J., Zhang, G.Q., “Multi-physics modeling in virtual prototyping of electronic packages – combined thermal, thermo-mechanical and vapor pressure modeling”, Microelectronics Reliability, 44, 1967–1976, 2004. 4. Ritter, J.E., Fox, J.R., Hutko, D.I., Lardner, T.J., “Moisture-assisted crack growth at epoxyglass interfaces”, Journal of Materials Science, 33, 4581–4588, 1998. 5. Gurumurthy, C.K., Kramer, E.J., Hui, C.Y., “Water-assisted sub-critical crack growth along an interface between polyimide passivation and epoxy underfill”, International Journal of Fracture, 109, 1–28, 2001. 6. Alpern, P., Lee, K.C., Dudek, R., Tilgner, R., “A simple model for the Mode I popcorn effect for IC packages with copper leadframe”, IEEE Transactions on Components and Packaging Technologies, 25, 301–308, 2002. 7. Alpern, P., Dudek, R., Schmidt, R., Wicher, V., Tilgner, R., “On the Mode II popcorn effect in thin packages”, IEEE Transactions on Components and Packaging Technologies, 25, 56–65, 2002. 8. Lau, J.H., Lee, S.W.R., “Temperature-dependent popcorning analysis of plastic ball grid array package during solder reflow with fracture mechanics method”, Journal of Electronic Packaging, 122, 34–41, 2000. 9. Ikenda, T., Kim, W.K., Miyazaki, N., “Evaluation of the delamination in a flip chip using anisotropic conductive adhesive films under moisture/reflow sensitivity test”, IEEE Transactions on Components and Packaging Technologies, 29, 551–559, 2006. 10. Kitano, M., Nishimura, A., Kawai, S., Nishi, K., “Analysis of package cracking during reflow soldering process”, Proceedings of IEEE International Reliability of Physics Symposium, pp. 90–95, 1988. 11. Liu, S., Mei, Y., “Behavior of delaminated plastic IC packages subjected to encapsulation cooling, moisture absorption, and wave soldering”, IEEE Transactions on Components, Packaging, and Manufacturing Technology, Part A, 18, 634–645, 1995. 12. Lee, K.W., Earmme, Y.Y., “Effect of geometric parameters on popcorn cracking in the plastic packages during VPS process,” Finite Elements in Analysis and Design, 30, 81–96, 1998. 13. Tay, A.A.O., Lin, T.Y., “Moisture-induced interfacial delamination growth in plastic IC packages solder reflow”, Proceedings of IEEE Electronic Components and Technology Conference, pp. 371–378, 1998. 14. Hutchinson, J.W., Evans, A.G., “Mechanics of materials: top down approaches to fracture”, Acta Materialia, 48, 125–135, 2000. 15. Liu, P., Cheng, L., Zhang, Y.W., “Interface delamination in plastic IC packages induced by thermal loading and vapor pressure – a micromechanics model”, IEEE Transactions on Advanced Packaging, 26, 1–9. 16. Chew, H.B., Guo, T.F., Cheng, L., “Vapor pressure and residual stress effects on mixed mode toughness of an adhesive film”. International Journal of Fracture, 134, 349–368, 2005.

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Chapter 13

New Method for Equivalent Acceleration of IPC/JEDEC Moisture Sensitivity Levels B. Xie, X.J. Fan, and X.Q. Shi

13.1 Introduction Moisture/reflow sensitivity test for plastic surface mount devices (SMDs) is defined and outlined in a joint IPC/JEDEC industry standard J-STD-020D [1]. This test specification has established exposure conditions for temperature, humidity, and time, for which the moisture sensitivity rating of SMDs is classified and referenced. Moisture sensitivity test is a precursor test to most reliability evaluations. However, the time required for moisture preconditioning is too long. This makes the process unproductive and costly. For example, the moisture sensitivity level 3 (MSL3) requires 192 h for moisture preconditioning under 30◦ C/60% relative humidity (RH). The long test time has significantly hindered the time-to-market for new product development and new material evaluation. In order to devise an equivalent accelerated moisture sensitivity test, the IPC/JEDEC specification J-STD-020D has recommended a set of accelerated equivalent soaking times under 60◦ C/60%RH. In these tests the total required moisture soak times for MSL 3–5 are reduced by approximately a factor of five compared to the standard times. To use the “accelerated equivalent” soak conditions, correlation of damage response (including electrical, after soak and reflow) should be established for the “standard” soak conditions. In this chapter, the J-STD-020D standard that includes the specifications of soak requirements and reflow conditions is reviewed first. The accelerated equivalent moisture conditions are then recommended. This recommendation is based on the idea of the local moisture concentration equivalency, proposed by Shook et al. [2–6]. The underlying theory and experimental validations are described and discussed, and the limitations of the existing accelerated moisture sensitivity test are indicated. A new methodology for accelerated moisture sensitivity test is developed based on the equivalency of both the local moisture concentration and the global moisture distribution.

X.J. Fan (B) e-mail: [email protected]

X.J. Fan, E. Suhir (eds.), Moisture Sensitivity of Plastic Packages of IC Devices, Micro- and Opto-Electronic Materials, Structures, and Systems, C Springer Science+Business Media, LLC 2010 DOI 10.1007/978-1-4419-5719-1_13, 

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13.2 Moisture Sensitivity Test Classifications – Joint IPC/JEDEC Industry Standard J-STD-020D Moisture/reflow sensitivity test consists of two stages: moisture soaking and reflow (Fig. 13.1). Moisture soaking stage mimics factory environmental conditions that a plastic-packaged surface mount component can safely be exposed to after opening of the protective dry bags. The reflow stage simulates the surface mount process. Cracking and delamination subjected to moisture/reflow is a key failure mechanism for plastic electronic packages at soldering. The failure is due to the combined effects of thermo-mechanical stress, hygroscopic stress, vapor pressure, material softening, and adhesion degradation [7–12].

G

Stage 1: Moisture absorption

G

Stage 2: Soldering reflow

Fig. 13.1 Two stages of moisture sensitivity/reflow test

To classify the moisture sensitivity rating for plastic packages, the J-STD-020D specification has established various parameters of exposure conditions: ambient temperature, relative humidity, soak time, and reflow profile. The testing procedure could be summarized as below: 1. Initial electrical test: test appropriate electrical parameters; replace failed components to meet test parameters. 2. Initial inspection: perform an external visual and acoustic microscope examination on all the components to establish a baseline for their cracking/ delamination. 3. Bake: bake the sample for 24 h minimum at 125 +5/−0◦ C; this step is intended to dry out the package. 4. Moisture soak: place devices in a clean, dry, shallow container, so that the packages do not touch or overlap each other, and impose on each sample the appropriate soak requirements, as shown in Table 13.1. 5. Reflow: subject the sample to three cycles of the appropriate reflow conditions (to be discussed later). 6. Final external visual: examine the devices using an optical microscope to look for external cracks.

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Table 13.1 Moisture sensitivity levels and soaking requirements [1] Floor life

Soak requirements

Level

Time

Condition

Time (h)

Condition

1 2 2a 3 4 5 5a 6

Unlimited 1 year 4 weeks 168 h 72 h 48 h 24 h Time on label (TOL)

≤30◦ C/85%RH ≤30◦ C/60%RH ≤30◦ C/60%RH ≤30◦ C/60%RH ≤30◦ C/60%RH ≤30◦ C/60%RH ≤30◦ C/60%RH ≤30◦ C/60%RH

168+5/−0 168+5/−0 696+5/−0 192+5/−0 96+2/−0 72+2/−0 48+2/−0 TOL

85◦ C/85%RH 85◦ C/60%RH 30◦ C/60%RH 30◦ C/60%RH 30◦ C/60%RH 30◦ C/60%RH 30◦ C/60%RH 30◦ C/60%RH

7. Final electrical test: perform appropriate electrical testing for all the devices. 8. Final acoustic microscopy: perform acoustic microscope analysis for all the devices.

The moisture sensitivity levels and the established soaking conditions in Step 4 are shown in Table 13.1. Defined are six sensitivity levels ranging from moisture insensitive (MSL1) to extremely sensitive (MSL6: bake before use). This information becomes invaluable for board assembly factories, when establishing proper handling procedures for reflow process. The established level and test conditions are generally meant to simulate average worst case factory environmental conditions that a plastic-packaged surface mount IC can safely be exposed to after opening of the protective dry bag. The exposure times imposed by the classification level relate specifically to the established testing condition, e.g., a MSL3 device must be assembled within 168 h for a factory environment of 30◦ C/60%RH. Immediately after removal from the temperature/humidity chamber, the samples are subjected to three cycles of the appropriate reflow conditions. These conditions are defined in Table 13.2 and Fig. 13.2. Table 13.2 shows the reflow conditions for both SnPb-free and Pb-free assemblies. Peak package body temperature (Tp ) is determined by the classification temperature and is around 220◦ C for a SnPb assembly and 260◦ C for a Pb-free assembly. As it could be seen from the standard soaking requirements (Table 13.1 [1]), there is an obviously large gap for floor life requirements between MSL2 and MSL3, jumping from 1 year to just 1 week. Second, floor life testing for Levels 2a−6 does not provide for an option to perform accelerated testing of the 30◦ C/60%RH condition. Test times can be as long as 8 days for MSL3, which includes a default of 24 h for the manufacturing exposure time (MET). Such a long test time is unacceptable, and therefore a new equivalent accelerated testing procedure for testing plastic surface mount packages has been recommended, as shown in Table 13.3. To use the “accelerated equivalent” soak conditions, correlation of damage response (including electrical, after soak and reflow) should be established with the “standard” soak

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Profile feature Preheat/Soak Temperature min (Ts min ) Temperature max (Ts max ) Time (ts ) from (Ts min to Ts max ) Ramp-up rate (TL to Tp ) Liquidous temperature (TL ) Time (tL ) maintained above TL Peak package body temperature (Tp )

Time (tp )a within 5◦ C of the specified classification temperature (Tc ), see Fig. 13.2 Ramp-down rate (Tp to TL ) Time 25◦ C to peak temperature a Tolerance

Sn–Pb eutectic assembly

Pb-free assembly

100◦ C 150◦ C 60−120 s 3◦ C/s max. 183◦ C 60−150 s For users Tp must not exceed the classification temp. For suppliers Tp must equal or exceed the classification temp. 20 sa

150◦ C 200◦ C 60−120 s 3◦ C/s max. 217◦ C 60−150 s For users Tp must not exceed the classification temp. For suppliers Tp must equal or exceed the classification temp. 30 sa

6◦ C/s max. 6 min max.

6◦ C/s max. 8 min max.

for peak body or profile temperature (Tp ) is defined as a supplier minimum and a user

maximum.

conditions. In addition, if the activation energy for moisture diffusion of the package materials is in the range of 0.40−0.48 eV or 0.30−0.39 eV, the “accelerated equivalent” may be used. Accelerated soak times may vary because of the material properties (e.g., molding compound, encapsulant). This equivalency methodology is developed from moisture diffusion analysis augmented by the use of the critical interface concentration dependency. This will be discussed in detail in the next section.

Fig. 13.2 Reflow profile definition (not to scale) [1]

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Table 13.3 Accelerated equivalent soak time and conditions according to J-STD-020D [1] Soak requirements Accelerated equivalent Standard

0.40−0.48 eV

0.30−0.39 eV

Level

Time (h)

Condition

Time (h)

Time (h)

Condition

1 2 2a 3 4 5 5a 6

168 +5/−0 168 +5/−0 696 +5/−0 192 +5/−0 96 +2/−0 72 +2/−0 48 +2/−0 TOL

85◦ C/85%RH 85◦ C/60%RH 30◦ C/60%RH 30◦ C/60%RH 30◦ C/60%RH 30◦ C/60%RH 30◦ C/60%RH 30◦ C/60%RH

NA NA 120 +1/−0 40 +1/−0 20+ 0.5/−0 15 +0.5/−0 10 +0.5/−0 NA

NA NA 168+1/−0 52+1/−0 24+0.5/−0 20+0.5/−0 13+0.5/−0 NA

NA NA 60◦ C/60%RH 60◦ C/60%RH 60◦ C/60%RH 60◦ C/60%RH 60◦ C/60%RH NA

13.3 Local Moisture Concentration Equivalency-Based Method [2] 13.3.1 Theory In order to devise an accelerated test condition that would be equivalent to the moisture response of 30◦ C/60%RH testing, the behavior of the diffusing moisture into the encapsulating molding compound must be well understood and predicted. The ability to model the shape and the distribution of the time-dependent moisture gradient becomes a primary goal. Included is the need to understand the effect of variables, such as the thickness and moisture diffusivity of the molding compound, the dependency on relative humidity, temperature, and the total elapsed test time. It is also important to point out that internal damage resulting from moisture/reflow testing is directly related to the total amount of moisture that has been accumulated at the internal interfaces [13]. Hence, any attempt to develop an accelerated test procedure must encompass these circumstances before it can be considered equivalent. The first step is to model the moisture diffusion behavior during the package exposure to the 30◦ C/60%RH test condition. A simple one-dimensional solution seems to be sufficient to model the time-dependent through-thickness gradient in the molding compound [2]:   ∞  (2n + 1)π D( − 1)n 2  −D(2n+1)2 π 2 t/4L2 (2n + 1)π x e C(x,t) = cos L 2L 2L 3  t n=0 2 2 2 eD(2n+1) π λ/4L Csat [T(λ),RH(λ)] dλ . 0

(13.1)

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In this equation, D is the diffusivity, t is the elapsed test time, L is the molding compound thickness above the die or below the paddle, x is the through-thickness spatial coordinate, and Csat (T, RH) is the molding compound moisture’s saturation, which is a function of both the temperature and the relative humidity. This equation reveals that four fundamental parameters (diffusivity, thickness, time, and moisture saturation) must be determined in order to establish how an equivalent moisture response can be achieved. This could be accomplished best by a systematic study of the effect of each parameter on the diffusion. Let us consider first the effect of the molding compound diffusivity. Table 13.4 lists several diffusivity measurements and shows the Arrhenius fit for temperature activation, Ea (also included in this list for comparison is the diffusivity for a BT [bismaleimide triazine] resin substrate used in the construction of PBGAs) [2]. These measurements reveal that the average activation energy is close to 0.44 eV with only one outlier, the multi-functional compound B. This information allows one to deduce that a change in temperature will produce a similar ingress response for each compound that has anactivation energy close to 0.44 eV. The largest deviation is expected for the multi-functional compound B. Hence, for all the compounds with a temperature activation of about 0.44 eV, a single accelerated temperature may be chosen to produce equivalent responses. Table 13.4 Molding compound diffusivities expressed as D0 exp (− Ea /kT) [2] Type

D0 (mm2 /s)

Ea (eV)

D (mm2 /s) at 30◦ C

Novalac A Novalac B Multi-functional A Multi-functional B Biphenyl A Biphenyl B BT resin

17.95 10.50 7.22 1.49 10.79 11.11 11.96

0.4546 0.4219 0.4109 0.3522 0.4425 0.4464 0.4805

4.96e−7 1.01e−6 1.06e−6 2.08e−6 4.74e−7 4.20e−7 1.23e−7

Another item to consider is the effect of the Csat . Equation (13.1) shows that if Csat were time-independent, then this equation can be normalized with respect to the absolute concentrations by dividing through Csat . In this case Csat is essentially a scaling factor. As long as the test conditions do not change with time, it will be possible to work with normalized concentrations when comparing the diffusion behavior for any molding compound. It is further recognized that for molding compounds, Csat shows a nearly linear dependence from 20%RH to 100%RH. This is true for any constant temperature. Only a slight temperature dependency could be detected at a constant humidity [14–16]. The Csat (T, RH) behavior represented in EIAJ test method EDX-4701 provides a set of curves for a Novalac epoxy [17]. This information allows one to scale Csat (T, RH) for all the molding compounds into essentially one common set of curves. The error from applying this assumption is expected to be less than 5%.

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Consider now two different moisture conditions. Standard condition represents 30◦ C/60%RH with a diffusivity of Dstd . Accelerated condition represents 60◦ C/60%RH with a diffusivity of Dacc . According to equation (13.1), with the assumption of Csat independent of temperature (see Chapter 1) at a constant humidity (60%RH), the equivalency of the local moisture concentration requires that Dstd tstd = Dacc tacc ,

(13.2)

where tstd is the soaking time required by standard test condition and tacc is the accelerated soaking time under 60◦ C/60%RH. Equation (13.2) can be written as tstd Dacc = . tacc Dstd

(13.3)

Using Arrhenius equation, and introducing the acceleration factor (AF), equation (13.3) can be written as

   a exp − kTEacc 1 tstd Dacc 1 Ea

= exp − , (13.4) AF = = = − tacc Dstd k Tacc Tstd exp − Ea kTstd

where Ea is activation energy for the molding compound (related to moisture diffusivity), k is Boltzmann’s constant (= 8.63 × 10−5 eV/K), and Tacc and Tstd are the temperatures at standard soaking condition (30◦ C in the present case) and accelerated soaking condition (60◦ C in the present case), respectively. Table 13.5 shows two sets of accelerated times according to equation (13.4), compared to the standard soaking times. The first set is calculated based on an activation energy of 0.345 eV, and the second set is calculated based on an activation energy of 0.44 eV. These energies are very close to the accelerated equivalent times recommended by J-STD-020D (Table 13.3). Shook et al. [2] studied the equivalent moisture ingress behaviors for various combinations of the molding compound materials and types and package thickness, including: 1. Novalac epoxy-A and thicknesses = 1.5, 1.0, and 0.5 mm 2. Novalac epoxy-B and a compound thicknesses = 1.5 and 1.0 mm 3. Multi-functional epoxy-B and a compound thickness = 1.5 mm. Table 13.5 Times for equivalent 60◦ C /60%RH testing Soaking times (h) Encapsulant activation energy

MSL3

MSL4

MSL5

MSL5a

tstd tacc (0.345 eV) tacc (0.44 eV)

192 58 42

96 29 21

72 22 16

48 15 11

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Consider a package with a molding compound, in which the diffusivity behavior is represented by Novalac epoxy-A shown in Table 13.4. The normalized moisture gradients that develop with time during the package exposure to 30◦ C/60%RH and 60◦ C/60%RH, for a package of 1.5 mm thickness, are shown in Fig. 13.3. One could see how the accelerated 60◦ C/60%RH moisture gradients match the 30◦ C/60%RH condition. An excellent fit is obtained. The analyses provided in Fig. 13.4 are for one specific molding compound and thickness. A systematic analysis of the effect

Fig. 13.3 Correlation between diffusion behavior at 30◦ C/60%RH and 60◦ C/60%RH Novalac epoxy-A and thickness = 1.5 mm [2]

Fig. 13.4 Correlation between diffusion behavior at 30◦ C/60%RH and 60◦ C/60%RH Novalac epoxy-A and thickness = 1.0 mm [2]

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Fig. 13.5 Correlation between diffusion behavior at 30◦ C/60%RH and 60◦ C/60%RH Novalac epoxy-A and thickness = 0.5 mm [2]

of these variables is needed to make sure that accelerated testing using 60◦ C/60%RH will yield similar results for other thicknesses and molding materials. The results for thicknesses of 1.0 and 0.5 mm are shown in Figs. 13.4 and 13.5, respectively. The calculated data were obtained using the diffusivity for Novalac epoxy-A. Figure 13.4 shows that the gradients for 1.0 mm thickness are well-matched erring by a maximum of 7% at the interface concentration for MSL3. Figure 13.5 shows the largest deviations for 0.5 mm thickness, indicating a 7% mismatch for all the times. This is caused by the higher boundary forcing concentration. Such a 7% mismatch is considered acceptable because achieving a more perfect fit to the 30◦ C/60%RH gradients would require that the relative humidity at 60◦ C be lowered by only 4–6%RH. A 4%RH difference is small enough and should have little effect on the overall reflow performance. Hence, the thickness dependency can be neglected with acceptable errors for this molding compound. In fact, based on equation (13.4), the acceleration factor is independent of the package thickness.

13.3.2 Experimental Validations To confirm that the accelerated 60◦ C/60%RH conditions are indeed equivalent (following the predicted times as listed in Table 13.3), experimental verification tests were performed [2]. Moisture/reflow experiments were conducted on several different package types to establish correlation between the 30◦ C/60%RH testing and the accelerated 60◦ C/60%RH condition. Packages evaluated included PLCCs (44, 68, and 84 pins), a 128 pin TQFP, a 132 pin BQFP, and two overmolded PBGAs (27 and 35 mm). The experimental procedure followed the flow as outlined in J-STD-020,

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e.g., all the packages were first characterized by using acoustic microscopy, then baked dry at 125◦ C, then moisturized to the established conditions and times, then convection oven reflowed to a body temperature of 220◦ C, and then re-evaluated acoustically. Internal damage due to delamination and/or cracking was subsequently assessed by comparing the prior and after convective-reflow acoustic images. All the package types were evaluated at the standard IPC/JEDEC moisture level and compared to the equivalent 60◦ C/60%RH test condition. The accelerated test times used for all the experiments were those established for materials with activation energies of 0.40−0.49 eV (Table 13.3). Before discussing the reflow results, it is first appropriate to elaborate upon weight gain measurements collected on a few different package types. The results are shown in Table 13.6 for exposures to both the 30◦ C/60%RH and 60◦ C/60%RH conditions. The measurements reveal that the percent weight gains for each exposure condition follow one another closely with the largest discrepancy of 5.6% for the PBGA package at the 1 month test point. Given that the theory is based in essence upon matching diffusion gradients, this implies that the integrated response, i.e., weight gains, should also be closely matched during each equivalent exposure. This was indeed observed for the weight gain measurements for all the packages tested. The weight gain data is the first compelling confirmation that the predicted times and exposure conditions are indeed correlated. C-SAM data for all the package types are tabulated in Table 13.7. The 44 pin PLCCs and the 68 pin PLCC die surface delamination distributions show good correlation between the 30◦ C/60%RH and 60◦ C/60%RH tests. No significant

Table 13.6 Percent weight gain measurements [2]

Package 68 pin PLCC 27 mm PBGA 128 pin TQFP 100 pin TQFP

Package 68 pin PLCC 27 mm PBGA 128 pin TQFP 100 pin TQFP

Percent weight gain at 30◦ C/60%RH 48 h 72 h 96 h

192 h

672 h

0.047 0.157 0.060 0.052

0.085 0.253 0.099 0.082

0.144 0.323 0.123 0.100

Percent weight gain at 60◦ C/60%RH 10 h 15 h 20 h

40 h

120 h

0.046 0.152 0.061 0.053

0.087 0.244 0.103 0.085

0.138 0.305 0.127 0.103

0.057 0.183 0.071 0.060

0.054 0.174 0.071 0.059

0.063 0.199 0.079 0.065

0.063 0.194 0.081 0.067

Percent difference between 60◦ C/60%RH and 30◦ C/60%RH Package 68 pin PLCC 27 mm PBGA 128 pin TQFP 100 pin TQFP

−2.1 −3.2 +1.7 +1.9

−5.3 −4.9 0 −1.7

0 −2.5 +2.5 +3.1

+2.3 −3.6 +4.0 +3.6

−4.2 −5.6 +3.3 +3.0

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Table 13.7 Moisture/reflow correlation for several package types [2] Damage assessment 30◦ C/60%RH

60◦ C/60%RH

Package

Time (h)

Result

Time (h)

Result

1. 44 PLCC-A

192 672 192 672 192 192 192 96 192 672 192 672

0(8)[25]/12 0(20)[58]/10 0(80)[100]/10 25(50)[100]/10 0(0)[0]/16 0(38)[100]/16 0(0)[25]/16 80(6)[97]/35 0/18 crack 0/18 crack 0/20 crack 13/18 crack 0 − severe

192

0/20 crack

672

5/20 crack

192 672 96 192 336 504 672

0/8 delam 0/8 delam 0/20 delam 0/20 delam 0/20 delam 8/20 delam 19/20 delam

40 120 40 120 40 40 40 20 40 120 40 120 168 40 96 120 168 40 120 20 40 64 100 120

0(0)[70]/10 6(6)[19]/16 6(50)[88]/16 6(75)[94]/16 0(0)[0]/11 0(45)[100]/11 0(0)[27]/11 77(9)[91]/35 0/18 crack 0/18 crack 0/20 crack 21/25 crack 1 − severea 24/25 crack 7 − severea 0/20 crack 0/20 crack 3/20 crack 13/20 crack 0/8 delam 0/8 delam 0/20 delam 0/20 delam 0/20 delam 1/20 delam 20/20 delam

2. 44 PLCC-B 3. 4. 5. 6. 7.

44 PLCC-C 44 PLCC-D 44 PLCC-E 68 PLCC 128 TQFP-A

8. 128 TQFP-B

9. 132 BQFP

10. 35 mm PBGA 11. 27 mm PBGA

Key: X(Y)[Z] / total numbers of packages X is % of packages with >40% die surface area delam (Y) is % of packages <40% and >5% die surface area delam [Z] is % of packages with >1% die surface area delam a Cracks extend to the outside edge of the package.

divergencies were observed for any of the PLCC devices. Reflow results on the 128 lead TQFP-B package show cracks in the molding materials after exposure to 192 h at 30◦ C/60%RH nor after the equivalent 40 h of 60◦ C/60%RH. After 672 h of 30◦ C/60%RH, 72% of the devices cracked compared to 82% found to crack for the equivalent 120 h of 60◦ C/60%RH condition. Exposure to 168 h of 60◦ C/60%RH shows the highest percentage of cracked devices, 96%, as well as more packages with severe crack development. These results indicate that the 120 h equivalent test point correlates better to the 672 h at 30◦ C/60%RH test, which is in good agreement with the theoretical prediction. A similar cracking transition occurs in the 132 pin BQFP package. Devices reflowed after 96 h of 60◦ C/60%RH show no cracks. Three packages cracked after 120 h at 60◦ C/60%RH, while exposure to a longer time than the theory predicts,

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e.g., 168 h, resulted in a much higher percentage of cracked packages as compared to that observed for 672 h of 30◦ C/60%RH exposure. The percentage of cracked packages, 15%, after 120 h of 60◦ C/60%RH is seen to correlate well with the percentage cracked, 25%, after 672 h of 30◦ C/60%RH exposure. Final correlation studies are shown for the 35 and 27 mm PBGA packages. For the 35 mm PBGA package, a statistical null result is essentially obtained: no delaminations were observed for all the conditions. The 27 mm PBGA, however, resulted in a distinctive delamination response. The data shows that no devices delaminated up to and including an exposure of 2 weeks at 30◦ C/60%RH. A transition was found to occur after 3 weeks of exposure, when 8/20 devices had significant delaminations. After 672 h of 30◦ C/60%RH, gross delamination occurred on 19 out of 20 devices reflowed. For the 60◦ C/60%RH condition a somewhat similar delamination pattern had been observed. No devices delaminated up to the 2 week equivalent test point (determined by theory to be 64 h), and all the packages showed gross delamination at the 1 month equivalent test point. A discrepancy, however, lies with the exact equivalent transition point. The theory predicted that 100 h at 60◦ C/60%RH would be equivalent to the 3 week exposure at 30◦ C/60%RH. After 100 h of 60◦ C/60%RH, only one device was found to delaminate, indicating that the transition point for delamination was just beginning. However, this does not correlate well with the total number of devices seen to delaminate after 3 weeks at 30◦ C/60%RH. It appears that the transition behavior for this PBGA device may be somewhat sharp, and determining the exact equivalency with the test time may require a more detailed analysis. Looking back at the weight gain data in Table 13.6, it was found that the percent weight gain for this PBGA package was consistently slightly higher for the 30◦ C/60%RH condition as compared to the 60◦ C/60%RH condition. This result could represent one of two possibilities. First, the laminate structure of the BT substrate may need to be incorporated in the model because of the possibility of a capillary diffusion path. Second, the multifunctional overmold compound used on this PBGA was not fully characterized for the temperature activation and may not fit the assumed 0.40−0.49 eV activation energy criteria. Therefore, moisture/reflow equivalency for this PBGA package is considered satisfactory, although not perfect.

13.3.3 Discussions Equivalent moisture ingress behavior is shown to be obtainable for any combination of the molding compound type and the package thickness. The accelerated test procedure, based on testing at 60◦ C/60%RH, reduces the total required moisture soak time for MSL3−5 by approximately a factor of five compared to the times required for 30◦ C/60%RH testing. One must keep in mind some important assumptions made when obtaining the accelerated test procedure: 1. The saturated moisture concentration Csat must be independent of temperature in the range from the standard test condition (e.g., 30◦ C) to the accelerated test condition (e.g., 60◦ C). Such an assumption is probably true for most of the molding

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compounds, since the Tg of the molding compounds is far beyond this temperature range. As discussed earlier (Chapter 1), the saturated moisture concentration changes dramatically with temperature across the glass transition temperature. For example, if a low Tg die-attach film is applied and the failure mode is dieattach film cracking and delamination, caution must be made to use the above recommended accelerated test procedure. 2. The developed theory is based on the one-dimensional moisture diffusion analysis in a homogeneous material. One-dimensional model concludes that the accelerated factor is independent of the compound thickness above the die or below the paddle. This means that the failure mode is presumably at the compound/die or compound/paddle interface. If the failure mode occurs at other locations, such as die-attach/die in a leadframe package or die-attach/die in a BGA package or at the underfill/die interface in flip chip packages, then a detailed moisture diffusion/stress analysis must be performed to ensure the equivalency. 3. For ultrathin packages, new problems arise, when the above theory is applied. Under standard testing conditions, e.g., MSL3, 30◦ C/60%RH for 192 h, the package might already be fully saturated. In this case, when accelerated testing condition is used (e.g., 60◦ C/60%RH), the saturation is reached much earlier. There are infinite solutions based on the local moisture concentration equivalency, as shown in Fig. 13.6. This means that only local moisture concentration equivalency is not sufficient to determine the equivalent accelerated time. 4. Local moisture concentration determines the local vapor pressure and the interfacial fracture toughness. However, the moisture-induced failures during reflow are also affected by the thermal stresses due to the thermal expansion mismatch and the hygro-stresses due to the hygroscopic swelling mismatch. A new methodology for the equivalent acceleration of IPC/JEDEC moisture sensitivity levels will be introduced in the next section.

Fig. 13.6 Infinite solutions for local moisture concentration equivalency for ultrathin packages

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13.4 New Method for Equivalent Acceleration of IPC/JEDEC Moisture Sensitivity Test Due to the small thickness of the most chip scale packages, moisture diffusion is faster and moisture concentration at critical interfaces becomes saturated earlier than the required soak time. The test method based on the equivalency of the local moisture concentration cannot define the accurate accelerated soak time for the saturation conditions [18, 19]. In addition, the existing accelerated test assumes that cracking and delamination are predominantly controlled by the local moisture concentration, which induces vapor pressure and reduces interfacial adhesion. However, the moisture-induced failure during the reflow process is also affected by the thermal stresses due to the thermal expansion (contraction) mismatch and hygrostresses due to hygroscopic swelling mismatch. Therefore, an effective methodology of the accelerated IPC/JEDEC moisture sensitivity level test is needed to ensure equivalency of both the local moisture concentration (i.e., equivalency of vapor pressure) and the overall moisture distribution (i.e., equivalency of thermal stresses and hygro-stresses) of packages.

13.4.1 Methodology During the surface mount process, thermal stress is developed due to the thermal expansion (contraction) mismatch of dissimilar materials. The thermal strain, εT , at the soak temperature can be expressed as εT = α T,

(13.5)

where α is the coefficient of thermal expansion (CTE) and T is the temperature change. Similarly, hygroscopic stress is developed due to the hygroscopic swelling mismatch. The hygroscopic swelling strain, εH , at soaking humidity condition can be expressed as εH = βC,

(13.6)

where β is the coefficient of hygroscopic swelling and C is the moisture concentration. During moisture absorption, moisture condenses in micro-/nano-pores or free volumes of materials. The moisture vaporization generates high vapor pressure. The driving forces that induce failures are due to the overall effect of thermal stress, hygro-stress, and vapor pressure: σ = σT + σH + p,

(13.7)

where σ is the total driving force inducing failures and p is the vapor pressure. The existing methodology for accelerated moisture sensitivity test is based on the equivalency of the local moisture concentration at the critical interfaces. The local

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moisture concentration determines the local vapor pressure and the interfacial adhesion. The equivalency of the local moisture concentration can ensure the equivalency of the local vapor pressure and the interfacial adhesion theoretically. However, the equivalency of the local moisture concentration is not enough to ensure the equivalency of the thermal stress and the hygro-stress: the thermal stress and the hygro-stress are affected by the temperature gradient and moisture distributions for the entire structure. To ensure the equivalency of all the driving forces (thermal stress, hygro-stress, and vapor pressure) between the standard and the accelerated tests, not only the local moisture concentration at the critical interfaces but also the overall temperature and moisture distributions for the entire electronic package should be equivalent to achieve the equivalency of failure mode and failure rate. Figure 13.7 is a schematic drawing that illustrates the equivalency of the standard and the accelerated moisture sensitivity testing. Both the adhesion degradation and the total driving force (σT + σH + p) should be equivalent. When the total driving force is below the level of the interfacial adhesion strength, the failure would not occur for either test. Since moisture distribution is same for the two soaking conditions, the combined stress during reflow will follow the same pattern (the curves become parallel to each other).

Fig. 13.7 Methodology of new moisture accelerated test

13.4.2 Finite Element Modeling The objective of the FEA modeling was to determine the accelerated soaking time based on the local moisture concentration and the global moisture distribution for an ultrathin chip scale package (CSP). The standard test condition is MSL3 at

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30◦ C/60%RH. Two accelerated conditions were investigated, 60◦ C/60%RH and 85◦ C/60%RH. A stacked-die CSP was employed as a suitable test vehicle for both the numerical simulations and the experimental validation (Fig. 13.8). Previous studies have shown that the critical failure location is the die-attach film between the first level die and the substrate (bottom layer film) [20, 21]. The package geometries are listed in Table 13.8. The temperature-dependent diffusivity and the solubility for the BT, the die-attach film, the molding compound, and the solder mask are listed in Tables 13.9, 13.10, 13.11, and 13.12, respectively. To implement the new methodology, the direct concentration approach (DCA) was applied to determine the equivalency of the local moisture concentration as well as of the overall moisture distribution under 30◦ C/60%RH, 60◦ C/60%RH, and 85◦ C/60%RH [22, 23]. The moisture soak histories at the bottom film/substrate interface under 30◦ C/60%RH, 60◦ C/60%RH, and 85◦ C/60%RH are shown in Fig. 13.9. The local moisture concentration at the interface was saturated after 100 h under 30◦ C/60%RH conditions, after 40 h under 60◦ C/60%RH conditions, and after 25 h under 85◦ C/60%RH conditions. It means from 40 h under 60◦ C/60%RH and 25 h under 85◦ C/60%RH, the local moisture concentration is equivalent with that under standard MSL3. However, it does not mean that the 40 h under 60◦ C/60%RH and the 25 h under 85◦ C/60%RH conditions are equivalent to the MSL3.

MC Die Film SR

Fig. 13.8 The schematic structure of 3D ultrathin stacked-die CSP

BT

Table 13.8 Geometries of test vehicle Length (mm)

Width (mm)

Thickness (mm)

Solder resist 1 BT core Solder resist 2 DA film 1 Die 1 DA film 2 Die 2 DA film 3 Die 3 DA film 4 Die 4 DA film 5 Die 5

12 12 12 8.62 8.62 7.9 7.9 8.62 8.62 4.82 4.82 5.66 5.66

12 12 12 8.62 8.62 7.9 7.9 8.62 8.62 4.82 4.82 5.66 5.66

0.05 0.15 0.05 0.04 0.075 0.025 0.075 0.025 0.075 0.025 0.075 0.025 0.075

Molding compound

12

12

1.05

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Table 13.9 Material properties of BT BT substrate Temperature (◦ C)

Diffusivity (mm2 /s)

Solubility (kg/m3 Pa)

60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260

1.28E−5 1.83E−5 2.56E−5 3.51E−5 4.74E−5 6.30E−5 8.24E−5 1.07E−4 1.36E−4 1.71E−4 2.14E−4 2.64E−4 3.23E−4 3.92E−4 4.72E−4 5.64E−4 6.69E−4 7.88E−4 9.22E−4 1.07E−3 1.24E−3

3.92E−4 2.61E−4 1.57E−4 1.12E−4 7.83E−5 5.60E−5 3.92E−5 2.90E−5 2.18E−5 1.63E−5 1.26E−5 9.92E−6 7.83E−6 6.22E−6 5.05E−6 4.10E−6 3.38E−6 2.80E−6 2.34E−6 1.97E−6 1.67E−6

Saturated moisture concentration: 4.7 kg/m3

To determine the equivalent soak times under 60◦ C/60%RH and 85◦ C/60%RH conditions, the overall moisture distribution in the package was investigated. Moisture diffusion contours are shown for MSL3, 60◦ C/60%RH at 45 and 70 h, and 85◦ C/60%RH at 25 and 45 h in Fig. 13.10. Comparing Fig. 13.10a with Fig. 13.10b, we conclude that although the local moisture concentration at the bottom film reaches the same level under 45 h at 60◦ C/60%RH conditions as that under MSL3, the overall equivalency of the moisture distribution is not reached yet at this time. Not only the local moisture concentration at the bottom film/substrate interface but also overall moisture distribution under 70 h at 60◦ C/60%RH conditions are equivalent with that of the soak for MSL3. Similarly, the overall equivalency of moisture distribution is not reached yet under MSL3 and 25 h at 85◦ C/60%RH conditions, as shown in Fig. 13.10a and d. Until soak for the 45 h at 85◦ C/60%RH conditions, the overall moisture distribution is equivalent with that of the soak for the MSL3, as shown in Fig. 13.10e and a. Therefore, the moisture distribution at the reflow temperature of 260◦ C after the soak under MSL3, 70 h at 60◦ C/60%RH, and 45 h at 85◦ C/60%RH conditions will also be equivalent due to the same reflow process, inducing the equivalent vapor pressure, thermal stress, and hygro-stress. The equivalent driving forces for cracking/delamination could lead to the equivalent failure modes and failure rates

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Die-attach film Temperature (◦ C)

Diffusivity (mm2 /s)

Solubility (kg/m3 Pa)

60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260

2.93E−5 3.97E−5 5.29E−5 6.93E−5 8.96E−5 1.14E−4 1.44E−4 1.79E−4 2.21E−4 2.70E−4 3.26E−4 3.91E−4 4.65E−4 5.49E−4 6.43E−4 7.49E−4 8.66E−4 9.97E−4 1.14E−3 1.30E−3 1.47E−3

3.76E−4 2.51E−4 1.51E−4 1.08E−4 7.52E−5 5.38E−5 3.76E−5 2.78E−5 2.09E−5 1.56E−5 1.21E−5 9.52E−6 7.52E−6 5.97E−6 4.85E−6 3.93E−6 3.23E−6 2.68E−6 2.24E−6 1.88E−6 1.60E−6

Saturated moisture concentration: 4.5 kg/m3

after the soak under MSL3, 70 h at 60◦ C/60%RH, and 45 h at 85◦ C/60%RH conditions. To validate the equivalency of the vapor pressure at the condition of 70 h at 60◦ C/60%RH and MSL3 during the reflow process, the vapor pressure modeling was performed based on the simplified micromechanics vapor pressure model [22, 23]. Figure 13.11 shows the contours of the vapor pressure distribution under MSL3 and 45 and 70 h at 60◦ C/60%RH conditions at the reflow temperature of 260◦ C. The vapor pressure was equivalent at the conditions of 70 h at 60◦ C/60%RH and MSL3. Also, as has been indicated by the results of the vapor pressure modeling for the 85◦ C/60%RH conditions, the vapor pressure was also equivalent under 45 h at 85◦ C/60%RH and MSL3 conditions.

13.4.3 Experimental Validation In order to validate the simulation results, the detailed matrix study was conducted under different moisture conditions. The moisture/reflow sensitivity tests were performed under the conditions of MSL3, 30, 45, 60, 75, and 88 h at 60◦ C/60%RH,

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Table 13.11 Material properties of molding compound Molding compound Temperature (◦ C)

Diffusivity (mm2 /s)

Solubility (kg/m3 Pa)

60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260

1.52E−7 2.20E−7 3.10E−7 4.29E−7 5.84E−7 7.82E−7 1.03E−6 1.34E−6 1.72E−6 2.19E−6 2.75E−6 3.42E−6 4.21E−6 5.13E−6 6.21E−6 7.45E−6 8.88E−6 1.05E−5 1.24E−5 1.44E−5 1.68E−5

2.50E−4 1.67E−4 1.00E−4 7.14E−5 5.00E−5 3.57E−5 2.50E−5 1.85E−5 1.39E−5 1.04E−5 8.06E−6 6.33E−6 5.00E−6 3.97E−6 3.23E−6 2.62E−6 2.16E−6 1.79E−6 1.49E−6 1.26E−6 1.07E−6

Saturated moisture concentration: 3 kg/m3

and 30, 45, and 60 h at 85◦ C/60%RH. The sample size was 48 units for each condition. Failure mode/location of the package under MSL3, 70 h at 60◦ C/60%RH, and 45 h at 85◦ C/60%RH was examined, and the failure analyses were conducted on the failed samples. As shown in Figs. 13.12, 13.13, and 13.14, the cracking/delamination occurred inside the bottom film for these three conditions, i.e., cohesive delamination. Through-scanning acoustic microscope (TSAM) was used for the final inspection to determine the failure rate. The failure rate was defined as R = nf /nt ,

(13.8)

where R is the failure rate, nf is the number of failed samples, and nt is the number of total samples. The detailed testing conditions and experimental results are listed in Table 13.13, including the soaking condition, the soaking duration, the total sample number, the failed sample number, and the failure rate. The failure rates under various soaking conditions are also plotted in Fig. 13.15 using a logarithmic scale. The failure rate under the condition of MSL3 was 4.6%, as shown in Fig. 13.15. The failure rates under the conditions of 60◦ C/60%RH but different times are also plotted in Fig. 13.15. They can be curve-fitted as

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B. Xie et al. Table 13.12 Material properties of solder resist

Solder resist Temperature (◦ C)

Diffusivity (mm2 /s)

Solubility (kg/m3 Pa)

60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260

1.30E−6 2.10E−6 3.29E−6 5.03E−6 7.52E−6 1.10E−5 1.58E−5 2.23E−5 3.09E−5 4.23E−5 5.69E−5 7.56E−5 9.91E−5 1.29E−4 1.65E−4 2.09E−4 2.63E−4 3.28E−4 4.05E−4 4.96E−4 6.02E−4

4.17E−4 2.78E−4 1.67E−4 1.19E−4 8.33E−5 5.95E−5 4.17E−5 3.09E−5 2.31E−5 1.74E−5 1.34E−5 1.05E−5 8.33E−6 6.61E−6 5.38E−6 4.36E−6 3.59E−6 2.98E−6 2.49E−6 2.09E−6 1.78E−6

Saturated moisture concentration: 5 kg/m3

Moisture Concentration (kg/m3)

5 4.5 4 3.5 3 2.5 2 1.5 30C/60%RH

1

60C/60%RH

0.5

85C/60%RH

0 0

20

40 60 Time (hrs)

80

100

Fig. 13.9 Moisture soak histories under 30◦ C/60%RH, 60◦ C/60%RH, and 85◦ C/60%RH



R=0 R = 100.05(t−57.2)

if t < 57.2 , if t > 57.2

(13.9)

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Fig. 13.10 Moisture distribution contours under (a) MSL3, (b) 45 h at 60◦ C/60%RH, (c) 70 h at 60◦ C/60%RH, (d) 25 h at 85◦ C/60%RH, and (e) 45 h at 85◦ C/60%RH

where t is the soak time. By equaling the failure rates under 30◦ C/60%RH and 60◦ C/60%RH conditions, the soak time under 60◦ C/60%RH conditions can be determined as 68 h to be equivalent with the MSL3 conditions. Similarly, the failure rates under 85◦ C/60%RH conditions but different times were plotted in Fig. 13.15. They can be curve-fitted as 

R=0 R = 100.05(t−36)

if t < 36 . if t > 36

(13.10)

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Fig. 13.11 Vapor pressure contours at reflow temperature of 260◦ C: (a) MSL3, (b) 45 h at 60◦ C/60%RH, and (c) 70 h at 60◦ C/60%RH

Fig. 13.12 (a) Cross-section view of the ultrathin stacked-die CSP under MSL3 and (b) zoom-in view of highlighted region in (a)

(a)

(b)

By equaling the failure rates under 30◦ C/60%RH and 85◦ C/60%RH conditions, the soak time under 85◦ C/60%RH conditions can be determined as 47 h to be equivalent with the MSL3. The experimental moisture/reflow tests validated successfully our new methodology and the modeling analyses.

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Equivalent Acceleration of Moisture Sensitivity Levels

Fig. 13.13 (a) Cross-section view of the ultrathin stacked-die CSP under 70 h at 60◦ C/60%RH and (b) zoom-in view of highlighted region in (a)

355

(a)

(b)

Fig. 13.14 (a) Cross-section view of the ultrathin stacked-die CSP under 45 h at 85◦ C/60%RH and (b) zoom-in view of highlighted region in (a)

(a)

(b) Table 13.13 Failure rate correlation under various conditions of preconditioning testing 30◦ C/60%RH 192 h 8/173 (4.6%) 60◦ C/60%RH 30 h 0/172 (0%)

45 h 0/48 (0%)

85◦ C/60%RH 30 h 0/78 (0%)

45 h 4/141 (2.8%)

Note: nf /nt (R) nf is the number of failed samples nt is the number of total samples R is the failure rate

60 h 3/220 (1.4%)

75 h 7/96 (7.3%) 60 h 22/141 (15.6%)

88 h 33/96 (34.4%)

356 100

Failure Rate (%)

Fig. 13.15 Failure rates under 30◦ C/60%RH, 60◦ C/60%RH, and 85◦ C/60%RH

B. Xie et al.

10 1 0

30 45 60 75 88 50

100

192

150

200

250

30C/60%

0.1

60C/60% 85C/60%

0.01

Time (hrs)

Table 13.14 Accelerated equivalent times for MSL3 testing

Testing condition (30◦ C/60%RH)

tstd tacc (60◦ C/60%RH) tacc (85◦ C/60%RH)

Soaking times (h) 192 70 45

Compared with the analyses of the modeling results and the experimental validation, it is concluded that the conditions of the 70 h at 60◦ C/60%RH and the 45 h at 85◦ C/60%RH tests are equivalent with MSL3 conditions in terms of the global moisture distribution and vapor pressure, the local moisture distribution and vapor pressure, the failure rate, the failure location, and the failure mode. Table 13.14 summarizes the recommended accelerated equivalent soak times. It is noted that the new methodology depends on the package type and size.

13.5 Conclusions This chapter reviewed the existing IPC/JEDEC moisture/reflow sensitivity test standards and procedures and the equivalent acceleration moisture sensitivity levels. A set of equivalent accelerated times were established by J-STD-020D. These times are independent of the molding compound/resin thickness and encompass a wide range of material diffusivities. The existing methodology is based on the equivalency of the local moisture concentration only. In addition, the existing accelerated procedure assumes that the failure is predominantly on the molding compound/leadframe paddle or at the molding compound/die interfaces. For ultrathin electronic packages, since the packages may reach saturated state already in standard soaking conditions, the use of the local moisture concentration equivalency is not enough to obtain a satisfactory correlation for the failure rate. A new methodology has been introduced based on the equivalency of both the local moisture concentration and the overall moisture distribution. The new methodology can ensure the same failure mode/location and the same failure rate of cracking/delamination by requiring the equivalency of the local vapor pressure,

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the interfacial adhesion, and the thermal stress and hygro-stress. Finite element analysis is applied for the moisture diffusion and vapor pressure analysis of an ultrathin stacked-die chip scale package to establish the equivalent conditions under 60◦ C/60%RH and 85◦ C/60%RH conditions, respectively. At 70 h under 60◦ C/60%RH testing and 45 h under 85◦ C/60%RH testing, both the local moisture concentration at critical interface and the overall moisture distribution of package become identical with that under the standard MSL3 condition. This indicates that the 70 h at 60◦ C/60%RH and the 45 h at 85◦ C/60%RH tests are the equivalent soak times compared to the MSL3 conditions. Such equivalencies of the test conditions are proven by the detailed moisture/reflow sensitivity experiments and failure analyses. The new methodology developed in this work can be extended to other packages as well.

References 1. IPC/JEDEC J-STD-020D.1, “Moisture/reflow sensitivity classification for nonhermetic solid state surface mount devices”, March 2008. 2. Shook, R., Vaccaro, R., Gerlach, D., “Method for equivalent acceleration of JEDEC/IPC moisture sensitivity levels”, Annual International Reliability Physics Symposium, pp. 214–219, 1998. 3. Shook, R., Conrad, T., Sastry, V., Steele, D., “Diffusion model to derate moisture sensitive surface mount IC’s for factory use conditions”, IEEE Transaction on Components, Packaging and Manufacturing Technology, 19(2), 110–118, 1996. 4. Shook, R.L., Goodelle, J.P., “Handling of highly-moisture sensitive components – an analysis of low-humidity containment and baking schedules”, IEEE Transaction on Electronics Packaging Manufacturing, 23(2), 81–86, 2000. 5. Shook, R.L., Gilbert, J.J., Thomas, E., “Impact of ingressed moisture and high temperature warpage behavior on the robust assembly capability for large body PBGAs”, Proceedings of Electronic Components and Technology Conference, pp. 1823–1828, 2003. 6. Shook, R., Sastry, V., “Influence of preheat and maximum temperature of the solder-reflow profile on moisture sensitive IC’s”, Proceedings of Electronic Components and Technology Conference, pp. 1041–1048, 1997. 7. Fan, X.J., Zhang, G.Q., van Driel, W.D., Ernst, L.J., “Interfacial delamination mechanisms during reflow with moisture preconditioning”, IEEE Transactions on Components and Packaging Technologies, 31S(2), 252–259, 2008. 8. van Driel, W.D., van Gils, M.A.J, Fan, X.J., Zhang, G.Q., Ernst, L.J., “Driving mechanisms of delamination related reliability problems in exposed pad packages”, IEEE Transactions on Components and Packaging Technologies, 31(2), 260–268, 2008. 9. Fan, X.J., Zhou, J., Zhang, G.Q., Ernst, L.J., “A micromechanics based vapor pressure model in electronic packages”, ASME Journal of Electronic Packaging, 127(3), 262–267, 2005. 10. Fan, X.J., Zhou, J., Zhang, G.Q., “ Multi-physics modeling in virtual prototyping of electronic packages – combined thermal, thermo-mechanical and vapor pressure modeling”, Journal of Microelectronics Reliability, 44, 1967–1976, 2004 11. Fan, X.J., “Moisture related reliability in electronic packging”, ECTC Professional Development Course Handout, 2005/2006/2007/2008. 12. Zhang, G.Q., van Driel, W.D., Fan, X.J., Mechanics of Microelectronics. New York, NY: Springer, 2006. 13. Kitano, M., Nishimura, A., Kawai, S., “Analysis of package cracking during reflow soldering process”, 26th International Reliability Physics Symposium, pp. 90–95, 1988.

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14. Fan, X.J., Lee, S.W.R., Han, Q., “Experimental investigations and model study of moisture behaviors in polymeric materials”, Microelectronics Reliability, 49, 861–871, 2009. 15. He, Y., Fan, X.J., “In-situ characterization of moisture absorption and desorption in a thin BT core substrate”, Proceedings of Electronic Components and Technology Conference (ECTC), pp. 1375–1383, 2007. 16. Fan, X.J., “Mechanics of moisture for polymers: fundamental concepts and model study”, Proceedings of the 8th IEEE International Conference on Thermal and Mechanical Simulation and Experiments in Microelectronics and Microsystems, (EuroSimE), April 20–23, 2008. 17. EIAJ Test Method EDX-4701, “Test method of resistance to soldering heat of surface mounting devices for integrated circuits”, Electronic Industries Association of Japan, 1990. 18. Shi, X.Q., Fan, X.J., Xie, B., “A new method for equivalent acceleration of JEDEC moisture sensitivity levels”, Proceedings of Electronics Components and Technology Conference (ECTC), pp. 907–912, 2008. 19. Xie, B., Shi, X.Q., Fan, X.J., “Accelerated moisture sensitivity test methodology for stacked-die molded matrix array package”, Proceedings of IEEE 9th Electronics Packaging Technology Conference (EPTC), pp. 100–104, 2007. 20. Prack, E., Fan, X.J., “Root cause mechanisms for delamination/cracking in stack-die chip scale packages”, International Symposium on Semiconductor Manufacturing (ISSM), September 25–27, Tokyo, Japan, 2006. 21. Shi, X.Q., Fan, X.J., “Wafer-level film selection for stacked-die chip scale packages”, Proceedings of Electronic Components and Technology Conference (57th ECTC), pp. 1731–1736, 2007. 22. Xie, B., Fan, X.J., Shi, X.Q., Ding, H., “Direct concentration approach of moisture diffusion and whole field vapor pressure modeling for reflow process: part I – theory and numerical implementation”, ASME Journal of Electronic Packaging, 131(3), 031010, 2009. 23. Xie, B., Fan, X.J., Shi, X.Q., Ding, H., “Direct concentration approach of moisture diffusion and whole field vapor pressure modeling for reflow process: part II – application to 3-D ultra-thin stacked-die chip scale packages”, ASME Journal of Electronic Packaging, 131(3), 031011, 2009.

Chapter 14

Moisture Sensitivity Level (MSL) Capability of Plastic-Encapsulated Packages J.K. Fauty

14.1 Introduction While it is fairly common to achieve moisture sensitivity level (MSL) 1 compliance with a standard eutectic tin/lead solder reflow in a temperature range of 220–235◦ C, the ability to extrapolate to 260◦ C is proving very difficult. As shown in Fig. 14.1, water vapor pressure will increase by a factor of almost 2× when the reflow temperature increases just 40◦ C from 220 to 260◦ C [1]. The usual failure mode in moisture sensitivity testing is delamination at various interfaces of the package followed by the fracture of mold compound material, the well-known popcorn cracking phenomena [2]. Epoxy mold compounds (EMCs) are by nature moisture absorbent (hydrophilic). Moisture absorption is a function of mold compound chemistry, relative humidity, time, temperature, water absorption rate, and package leadframe design. Water can be absorbed into EMC in two ways. The first is as free or “unbound” water which collects at interfaces in the package structure and in voids created during mold or post-mold cure (PMC). Moisture can also be absorbed, chemically react with, and subsequently bind to resin polymer matrix. Moisture absorption and reaction with a mold compound is caused by water–polymer affinity for each other due to the availability of hydrogen bonding sites along the polymer chains of the compound. This species is known as “bound” water [3]. Chemically bound water at an interface can reduce mold compound adhesion by replacing the hydrogen bonds between the EMC and leadframe, thereby breaking the connection between the two [4]. Existing thermo-mechanical stresses due to mold compound shrinkage, residual CTE mismatches, solvent evaporation, etc. will further reduce adhesion strength of a mold compound as a package cools down from the stress-free state at the mold temperature. During the MSL moisture-loading phase (85◦ C/85% RH for 168 h for MSL 1), water that is absorbed into and binds with the polymer matrix may also cause hygroscopic swelling. When a package subsequently enters reflow process and is heated to the peak reflow temperature, the combination of

J.K. Fauty (B) e-mail: [email protected]

X.J. Fan, E. Suhir (eds.), Moisture Sensitivity of Plastic Packages of IC Devices, Micro- and Opto-Electronic Materials, Structures, and Systems, C Springer Science+Business Media, LLC 2010 DOI 10.1007/978-1-4419-5719-1_14, 

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Vapor Pressure vs. Temperature 40

Vapor Pressure (MPa)

15.

83

12.

27

10.

0

7.7

3

5.1

7

2.5

0 0.0 100.0

215.4

330.8

446.2

561.6

677.0

Temperature (Kelvin)

Fig. 14.1 Saturated water vapor pressure plotted and fitted with an exponential formula y = exp(a + b/x + c ln(x)) (a = –44.1, b =105.5, c =7.2)

an inherent loss in adhesion strength due to material softening, thermo-mechanical effects, and hygroscopic swelling is further complicated by the absorbed moisture in an unbound (free water) state which turns into vapor and expands, causing a further increase in the stress field through vapor pressure. These various combinations of stress levels add serially and if the combined stresses exceed the adhesion strength or fracture toughness of the mold compound interface, delamination and/or mold compound cracking will occur [2, 5]. In summary, when a package is exposed to 85◦ C/85% RH and subsequent reflow, all the thermo-mechanical and hygrothermal stresses act together to cause delamination and cracking of the mold compound. Sometimes a doming effect can be seen on the outside of the package. If the pressure exceeds the flexural strength of the mold compound, a crack initiates. The crack may propagate to the surface of the package resulting in a “popping” sound as the pressure is released [6–8]. In general, adhesion strength governs resistance to delamination, while epoxy mold compound (EMC) flexural strength controls resistance to cracking at high temperature [2]. Since interface delamination is the most common failure mode, the key to the prevention of delamination centers on the maximization of mold compound adhesion and the reduction of moisture absorption. It is well known that most dry package platforms are capable of 260◦ C reflow without experiencing delamination. Therefore, controlling hygroscopic stress should also be considered. Water that binds to the resin matrix is permanently adhered so that it cannot be desorbed through dry baking. It is also not realistic to assume that a modification to mold compound chemistry can be made to totally eliminate the dangling hydrogen bonds that act as collection points across the polymer chain. Though water that exists as free volume in voids can be desorbed through dry baking, it is also not possible to

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totally eliminate voids through mold process optimization. Hydrogen bonding sites and mold compound voids will always be present. Even though the reduction of interfacial adhesion, and subsequent delamination during reflow, is determined by moisture concentration at critical interface and not the overall or average moisture content [2, 9], the more moisture “resistant” a mold compound is to moisture diffusion, the less likely it is for water to collect at interfaces. Ganesan and Berg [10] developed a quantitative model to predict solder reflow cracking resistance as a function of mold compound properties, adhesion, and package geometry. Their analysis showed that of the mold compound properties tested, including elastic modulus above Tg , flexural strength at 260◦ C, moisture absorption at 85◦ C, and diffusivity at 260◦ C, the most important compound property was moisture diffusivity. Mold compounds with lower moisture diffusivity absorb less moisture during normal preconditioning and therefore end up with less moisture concentration at the die pad/mold compound interface. The authors and other researchers pointed out that in the absence of good adhesion, even the best mold compound properties would not solve the solder reflow cracking problems [11–13]. Various ways to control the stresses that lead to delamination and cracking have been explored by many investigators. These include limiting the availability of moisture to be absorbed by dry packing and storing in a dry box followed by limited floor life before reflow [14, 15]; controlling the reflow process by limiting the maximum temperature, time at maximum temperature, and ramp rates [16–18]; controlling leadframe material properties to increase mold compound adhesion through chemical etching, sandblasting [19, 20], plasma cleaning [21], and deliberate oxidation of copper metal [22]; leadframe design including designing in mold locks; controlling die-to-die flag area ratio and thickness of the die flag [6, 23, 24]; and finally controlling the properties of the mold compound that govern resistance to delamination and cracking [10, 25, 26, 11, 27, 28, 31]. Tada and Fujioka [25] investigated flexural modulus, polymer cross-linking, and Tg to see how they related to EMC cracking and delamination. They showed that when all material properties were kept constant except Tg , delamination increased as Tg increased (119–182◦ C) at constant moisture content. Gallo and Tubbs [26] examined a variety of different mold compounds with different mechanical properties produced by changing the type of resin system, filler particle shape, and different amounts of adhesion promoters. After exposure to moisture loading (35.5 up to 168 h of 85◦ C/85% RH) and solder dip at 260◦ C, they found no strong correlation between high temperature strength (flexural strength at 215◦ C) and popcorn cracking but noted that those properties which enhanced adhesion (i.e., low viscosity at melt and adhesion promoters) took precedence over other properties. The authors noted that while a high Tg material imparts better high-temperature strength, a low Tg with all its attendant properties (low viscosity and good wettability) gave better results. Lee and Earmme [27] modeled Young’s modulus, coefficient of thermal expansion (CTE) of the mold compound, chip size, and EMC thickness above and below the die using crack energy release rate as a response variable. Tay et al. [28] studied mold compound adhesion to alloy 42 leadframes and determined that Young’s modulus had no

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influence on susceptibility to delamination. Their data suggested that the higher the initial adhesion strength after PMC and the lower the CTE of the mold compound, the less the susceptibility. Of all the mold compound properties cited for MSL 1 performance, the one property that does seem to stand out for consistency is maximum adhesion. It is logical to assume that the more tenacious the adhesion is, the harder it is for delamination and subsequent cracking to occur. Therefore, one clear objective of this chapter is to correlate adhesion and subsequent delamination with various mold compound properties in an attempt to determine which properties are important in the selection of a proper chemistry to withstand the stresses induced by MSL 1 moisture loading and subsequent reflow at 260◦ C. Figure 14.2 is a schematic showing the proposed key properties of a mold compound in order to pass MSL 1 moisture preconditioning and reflow and how these properties relate to the various stages of preconditioning and reflow. Since delamination always occurs before mold compound cracking, the concentration on the detection of delamination through surface acoustic tomography (SAT) and adhesion testing are used as gauges of MSL performance. Moisture Loading

Solder reflow

(MSL1: 85°C/85%/168H)

(3 x 260°C) Low water absorption

High fracture (flexural) strength

Package cracks High adhesion Low CTE Low flexural modulus Low stress index

Fig. 14.2 Proposed key properties of mold compound (boxes with italic print) in order to pass MSL 1 moisture preconditioning and 260◦ C reflow

14.2 Experimental Procedures and Setup Two experimental protocols were performed. The first series of experiments investigated specific mold compound chemistries and MSL performance. MSL performance data were collected on actual single-sided QFN packages at both MSL 1 and 3 conditions. A correlation analysis was performed between moisture absorption data, adhesion, and MSL performance. The second series of experiments investigated the physical properties of various mold compound candidates. D2 Pak double-sided molded packages were used for MSL 1 performance evaluation.

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14.2.1 Mold Compound Chemistry/Properties Two approaches to mold compound selection are used. The first entails the type of chemistry used in the base polymer resin system, while the second approach centers on the mold compound properties themselves. Table 14.1 lists the mold compound resin chemistries used in the first series of experiments. Table 14.2 gives the descriptions of various resin and hardener chemistries shown in Table 14.1. The use of a hydrophobic resin system such as biphenyl or DCDP helps to lower moisture absorption. For stability of spiral flow, which governs viscosity and therefore wetting and ultimately adhesion, multifunction epoxides are the best since spiral flow does not degrade during cold storage for up to 2 years. Biphenyl compounds suffer from unstable spiral flows that degrade quickly during storage. Some of the newer compounds contain “low water absorption hardeners.” Hardeners also control free volume; the less the free volume generated after post-mold cure, the better the moisture absorption resistance of the mold compound. Table 14.3 is a compilation of the physical properties of the compound formulations used in the second series of experiments. Glass transition temperature (Tg ), CTE, stress index, moisture absorption, and 260◦ C adhesion strength are actual lot data generated in-house except for those values printed in italics which along with flexural strength and modulus are as reported in vendor specification sheets. Table 14.1 Resin and hardener chemistries for the various mold compounds used in this study

Mold compound

Resin/hardener chemistry

A B C D E

MAR/MAR Biphenyl/hydrophobic OCN/PN DCDP/PN Epoxy A/B–anhydride cured

MAR, Multiaromatic resin system; epoxy A/B, novolac and bisphenol A; OCN, ortho-creosol novolac; DCPD, dicyclopentadienyl; biphenyl, biphenyl-type epoxide resin; PN, phenol novolac

14.2.2 Tensile Pull Sample Description/Instron Machine Setup Figure 14.3 shows both a dimensioned schematic and a photo of a molded tensile strength test sample. The “pull tabs” were fabricated from C151 full-hard copper and specifically designed so that only adhesion of the mold compound to the tab is tested. The molded package body is 15 mm × 6 mm. No mechanical interlocks are present to confound the results. Unless otherwise noted, molding was performed on a CALSEM “Genesis II” conventional single-pot mold press. Pull tab optimization studies were performed before the experiment started. Based on these studies, the mold press was set up as velocity controlled wherein the machine is programed

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Table 14.2 Descriptions of the various resin and hardener chemistries used for those mold compounds listed in Table 14.1 Resins Epoxy A/B OCN ECN DCP/DCPD Biphenyl Multi New Hardeners PN

Multi Flexible

Anhydride LWME

LWAH

Novolac and bisphenol A Ortho-creosol novolac Epoxy cresol novolac Dicyclopentadienyl

OCN stands for ortho-cresol novolac resins and ECN stands for epoxidized cresol High Tg novolac resins. Officially, OCN should refer to just the ortho-cresol phenolic resin but molding compound manufacturers appear to have adopted this acronym to mean the same as ECN resins. So, one High would conclude that they are describing adhesion the same thing, an epoxidized orthoBiphenyl-type Low Tg cresol resin system. One vendor might use epoxide resin one acronym, while another will use the Multifunctional-type High Tg other to mean the same thing epoxide resin Proprietary epoxy formula Phenol novolac

Multifunctional-type hardener resin Elastic-type hardener resin

Bisphenol A is diglycidyl ether of bisphenol A (DBGA), a standard general purpose resin

Strictly speaking, phenolic resins (cresols, novolacs, and bisphenols) are different from epoxy resins

BTDA dianhydride Low molecular weight epoxide hardener (biphenyl based) Low water absorption hardener

to supply enough pressure to maintain a transfer speed of 0.20 in./s (approximately 200–800 psi) until the cavity fills, at which point the program switches to a pressurecontrolled “pack-and-hold” phase programed at 1,500 psi. Since the machine is velocity controlled, the amount of pressure needed to transfer material varies with each mold compound in order to maintain the programed speed. In-mold cure time was set at a constant 180 s; transfer time was less than 12 s, while the pack-andhold phase made up the remaining time. Mold temperature was set at 175 ± 3◦ C for all compounds except mold compound E, which based on optimization studies was molded at 185 ± 3◦ C. As part of the pull tab fabrication process, all panels were cleaned in a dilute muriatic acid bath followed by an alcohol rinse and forced air drying. The panels were cut into arrays and wrapped in corrosion-resistant paper for shipment. After

Epoxy A/B Biphenyl Multifunction LMWE OCN OCN OCN DCPD DCPD + BP OCN OCN Biphenyl Multiaromatic

1 2 3 4 5 6 7 8 9 10 11 12

Anhydride PN PN LWAH LWAH PN PN PN PN PN Multiaromatic Multiaromatic

Hardener 190 105.2 117.9 102.1 67.8 139.5 112.9 159 119.3 175.0 107.9 114.4

Tg (◦ C)a N/A 19 N/A 6.70 8.14 16 22 22 21 15 21 21

N/A 13 N/A 4.9 6.7 6.5 9.5 9.5 12 6.1 6 7.2

Flexural modulus at 240◦ C (×102 N/mm2 )

b Stress

a TMA

analysis with a ramp rate of 10◦ C/min at 300◦ C. No post-mold cure performed. index defined as SI = (CTE2 − CTEchip ) × (240−175) × E240 . c PTH 1 atm, 121◦ C, 24 h after 6 h PMC. d No post-mold cure performed.

Resin

Mold compound

Flexural strength at 240◦ C (N/mm2 ) 68 26.2 30.6 47.9 40.5 58.9 38.3 31 45.0 63.0 42.8 40.5

CTE2 (above Tg )a N/A 2.7 N/A 1.2 1.2 2.7 1.9 2.2 3.3 2.5 1.9 1.7

Stress indexb

Table 14.3 Mechanical/material properties of the mold compounds used in this study

N/A 0.38 N/A 0.19 0.20 0.73 0.35 0.35 0.50 N/A 0.32 0.29

Moisture absorption (%weight gain)c

0.279 0.126 N/A 0.116 0.144 0.083 0.106 0.075 0.128 0.087 0.093 0.084

Adhesion strength at 260◦ C on copper (kg f/mm2 )d

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5mm

6mm

15mm

Cu tab thickness 0.5 mm

5mm 2.75mm 6mm 15mm

Fig. 14.3 Pull tab test sample for adhesion testing

receipt from the supplier, the pull tabs were cleaned again in-house by degreasing the frames in IPA vapor for 15 s and then immediately rinsing in flowing deionized water for 5 s. The arrays were then immersed in a Cu etch solution consisting of concentrated sulfuric acid, nitric acid, hydrochloric acid, and deionized water for 20 s and then rinsed immediately under deionized water for 30 s. The arrays were then immersed in ammonium persulfate solution for 5 s and rinsed thoroughly under deionized water for 30 s followed by forced nitrogen air drying. All arrays were stored in a dry box prior to assembly to avoid excessive oxidation. To establish a baseline for oxide thickness as a result of storage, sample units directly from stock were submitted for oxide thickness measurements. A Physical Electronics 670A Scanning Auger Nanoprobe with a probe beam voltage of 10 kV was used for all data acquisition. Sputter etching was accomplished through the use of a 04-303A differentially pumped Ar+ ion gun built into the spectrometer. Typical oxide thickness was measured in the 12–20 Å range. The mold operation itself was not considered to have any significant effect on further oxide growth. Snooping experiments conducted with pull tabs exposed to 190◦ C for up to 10 min resulted in oxide thickness of only about 75 Å. This thickness is far below the 200–400 Å level established by Takano et al. [33] as being detrimental to mold compound adhesion. When used post-mold cure (PMC) was conducted according to supplier recommendations. An Instron Model 5566 test system with a 10-kN load cell was used to measure the strength of the copper-encapsulated interface. One end of the package was held rigid, while an external force was applied at the other end. All tests were carried out at room temperature with a crosshead speed of 4.0 mm/min. The machine was set up to automatically record load as a function of time. Maximum values of load at failure were automatically recorded from the load versus time curves. Scanning acoustic tomography (SAT) was performed using a Sonix HS1000 Inspection System. Top-side reflection mode scans were performed using a 50-MHz transducer. Bottom-side reflection mode and transmission mode scans for die attach analysis were also performed but are not reported in this work.

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14.2.3 Moisture Absorption Samples Moisture absorption samples were prepared by molding hockey puck discs of 1.550 in. (39.37 mm) diameter and 0.160 in. (4.06 mm) thickness. The hockey pucks were post-mold cured according to supplier recommendations and then subjected to a 72-h dry bake at 125◦ C before moisture loading. Moisture absorption was calculated according to the following equation: Moisture absorbed (%weight gain) =

(wet weight − dry weight) × 100 . (14.1) dry weight

Assuming that the hockey puck diameters are much larger than the thickness, a one-dimensional formula was used to calculate the moisture diffusion coefficient for each mold compound [5]. The formula used was D=

(Mt /t1/2 )2 π L2 , 2 16Meq

(14.2)

where Meq is the saturation level calculated with data taken from moisture graphs at approximately 2,900 h of moisture loading, Mt is the moisture level at time t in the linear region of the moisture graph, and L is the hockey puck thickness.

14.2.4 Moisture Sensitivity Testing Sample units in two package styles, single-sided power QFN packages and doublesided D2 Pak packages, were prepared. The QFN package, assembled in the prototype lab, was used in the first series of experiments, while production-built D2 Pak packages were used in the second series of experiments examining mold compound mechanical properties.

14.2.5 QFN Package Description Leadframe arrays (40 mm × 96 mm) containing eight separate QFN packages (6 mm × 7 mm) were etched from 0.010-in.-thick (0.254 mm) C194 half-hard copper. A half-etch trench on the bottom side of the die flag was incorporated into the design to aid in mold compound adhesion. Mold and PMC conditions were the same as cited above for the pull tabs. The mold cap thickness was set at 0.031 in. (0.8 mm). Figure 14.4 is a photo of a typical die attach site showing the position of the die with respect to the die flag. The die flag measured 0.165 in. on a side (4.2 mm) and the IC chip measured 0.75 × 0.10 in. (1.90 mm × 2.54 mm). Reflow was conducted using a Heller 1809EXL convection furnace with a nitrogen atmosphere. The furnace was allowed to stabilize until the moisture content measured below 500 ppm. Temperature profiles for both the pull tabs and QFN

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Fig. 14.4 Die-bonded QFN sample

packages were set up using a SLIM KICK temperature-profiling system. Moistureloaded samples were reflowed within a 30-min window after removal from the moisture chamber.

14.2.6 D2 Pak Package Description Figure 14.5 shows a sample of the D2 Pak. In this case a production line mold system was used to assemble the product. A Lauffer VSKO single-pot, velocity-controlled mold press was used with a production mold die capable of handling 12 leadframes with 20 units per leadframe for a total of 240 cavities. Transfer speed was set in the 0.15–0.20 in./s range with a transfer pressure of approximately 1,200 psi. Total transfer time was 15–20 s and in-mold cure time was approximately 110 s. Once molded, all samples were post-mold cured at the supplier’s recommended temperature and duration. Eight packages from each mold compound group were then

Fig. 14.5 Top and bottom view of D2 Pak used for moisture sensitivity level testing at 260◦ C. The leadframe material is a half-hard Cu alloy containing Ni and P

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subjected to moisture loading (168 h at 85◦ C/85% RH) and three simulated reflows at 260◦ C peak temperature. In addition, all package groups were also subjected to 100 and then to 500 temperature cycles (–65 to 150◦ C). Inspection for delamination was performed using surface acoustic tomography (SAT).

14.3 Experimental Data and Analysis 14.3.1 First Series of Experiments 14.3.1.1 Pull Tab Adhesion Data Pull tab test samples molded with each compound chemistry were exposed to moisture loading at 85◦ C/85% RH for 168 and 504 h and then submitted for adhesion testing. Half were tested with no reflow and half tested after 260◦ C reflow. In addition, dry pull tab samples were also tested with and without reflow. The mean adhesion strength data are shown in Table 14.4. Table 14.4 Mean adhesion strength as a function of moisture loading and reflow Mean adhesion strength (kg f) Mold compound

Dry, no reflow

Dry, reflow

168 h 168 h 85◦ C/85% 85◦ C/85% RH, no reflow RH, reflow

504 h 504 h 85◦ C/85% 85◦ C/85% RH, no reflow RH, reflow

A B C D E

79.358 80.584 60.919 72.130 45.164

69.423 78.309 51.537 56.393 24.931

74.652 77.038 56.252 65.250 40.964

72.476 74.057 51.292 61.384 34.514

56.193 68.246 10.121 42.742 2.040

42.050 57.656 6.845 25.555 1.576

Mean adhesion strength for each resin chemistry at the three moisture levels with no reflow is shown in Fig. 14.6. As can be seen, there is a decrease in adhesion strength within each test cell as a function of moisture loading, indicating a dependency on moisture interaction with the resin chemistry. Mean adhesion strengths for each resin chemistry system at the three moisture levels after reflow at 260◦ C are shown in Fig. 14.7. There is a general decrease in adhesion strength within each test cell as moisture loading progresses. This suggests that a thinner package exposed to the same moisture conditions will suffer a greater proportional loss of adhesion than will a thicker package and be more susceptible to delamination. Mold compound resin/hardener chemistry in order from best to worst with respect to post-moisture loading/reflow adhesion performance is biphenyl/hydrophobic, MAR/MAR, and DCDP/PN, followed by OCN/PN and then epoxy A/B–anhydride. It should be noted that only one mold compound candidate for each resin chemistry was tested, so performance should be considered general in nature.

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80

60

40

Dry - No Reflow 168 hr 85/85 - No Reflow 540 hr 85/85 - No Reflow

MAR

Dry - No Reflow 168 hr 85/85 - No Reflow 540 hr 85/85 - No Reflow

DCDP

Dry - No Reflow 168 hr 85/85 - No Reflow 540 hr 85/85 - No Reflow

0

Dry - No Reflow 168 hr 85/85 - No Reflow 540 hr 85/85 - No Reflow

20

Dry - No Reflow 168 hr 85/85 - No Reflow 540 hr 85/85 - No Reflow

Mean (Mean Adhesion Strength No Reflow)

100

Biphenyl OCN Anhydride

Fig. 14.6 Pull tab adhesion strength as a function of moisture loading with no reflow performed

14.3.1.2 Moisture Absorption Molded hockey puck discs were subjected to post-mold cure and then dry baked for 48 h at 125◦ C. Weight gain was subsequently recorded as a function of exposure time to 85◦ C/85% RH. Moisture absorption data as a function of 85◦ C/85% RH are shown in Fig. 14.8. The equilibrium moisture content (taken from each plot) along with the calculated diffusion coefficient for each compound is listed in Table 14.5. A primary factor in moisture absorption is filler loading. Filler characteristics for the mold compounds in descending order are given in Table 14.6. The same filler material is used in all compounds, so the only differences are in loading volumes, size, and shape. Figure 14.9 showed a 0.91 correlation coefficient (83% correlation) between moisture absorption and filler loading. The higher the filler loading, the less the moisture absorbed into the mold compound. The fit appears to be curvilinear. It is evident that filler loading is an important variable in early moisture absorption process. Resin chemistry may play a secondary role in the “plateau” regions where the moisture–molecular chain affinity for each other determines the tendency to

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100

Mean Adhesion Strength Reflow

80

60

40

20

DCDP

MAR

Biphenyl

OCN

540 hr 85/85 - Reflow

168 hr 85/85 - Reflow

Dry - Reflow

540 hr 85/85 - Reflow

168 hr 85/85 - Reflow

Dry - Reflow

540 hr 85/85 - Reflow

168 hr 85/85 - Reflow

Dry - Reflow

540 hr 85/85 - Reflow

168 hr 85/85 - Reflow

Dry - Reflow

540 hr 85/85 - Reflow

168 hr 85/85 - Reflow

Dry - Reflow

0

Anhydride

Fig. 14.7 Pull tab adhesion strength as a function of moisture loading with reflow performed at 260◦ C peak temperature

reach saturation. The correlation between adhesion and moisture uptake is shown graphically in Fig. 14.10. 14.3.1.3 Correlation of Adhesion and Moisture Absorption with Package MSL Performance MSL performance was gauged by exposing QFN samples to MSL 1 and 3 moisture loading (85◦ C/85% RH for 168 h and 30◦ C/60◦ C for 192 h) followed by three reflows at 260◦ C peak temperature. Scanning acoustic tomography (SAT) topside reflection mode scans of post-reflowed samples are shown in Fig. 14.11 for EMC D. SAT analysis for delamination of post-reflowed units resulted in the same performance with respect to resin chemistry as both the moisture absorption and adhesion studies. Both biphenyl/hydrophobic and MAR/MAR chemistries showed very little delamination. The DCDP/PN chemistry experienced die flag delamination in MSL 1 testing, while both OCN/PN and epoxy A/B–anhydride exhibited massive

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Fig. 14.8 Moisture absorption plotted as a function of time at 85◦ C/85% RH. The dependency on filler loading can be seen with the filler loading overlay

1

73% 0.5 82% 88.5%

0

0 0

750

1500 Time

2250

3000 3000

Biphenyl/PN MAR/MAR OCN/PN Epoxy AB/Anhydride DCDP/PN

Table 14.5 Equilibrium moisture content and diffusion coefficient for each mold compound

Mold compound A B C D E

MAR/MAR Biphenyl/hydrophobic OCN/PN DCDP/PN Epoxy A/B– anhydride cured

Equilibrium moisture content (wt%)

Diffusion coefficient (10−5 cm2 /h)

0.68 0.38 0.89 0.56 1.56

13.46 6.85 10.92 6.00 6.71

Table 14.6 Filler loading, shape, and size of each mold compound chemistry EMC B A C E B

Biphenyl/hydrophobic MAR/MAR OCN/PN Epoxy A/B–anhydride cured DCDP/PN

Filler loading (%)

Filler shape

Filler size (μm max)

88.5 82 73 70

100% spherical 100% spherical 50/50 spherical/flake 100% flake

74 75 150 126

82

70/30 spherical/flake

125

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S = 0.02356422 r = 0.99544546 2

Moisture Absorption

0.9

9

0.7

5

0.6

2

0.5

9

0.3

5

0.2

2 0.1 68

72

76

79

83

87

90

Filler loading Fig. 14.9 Moisture absorption at 575 h plotted as a function of filler loading (y = a/(1+b∗ exp(–cx)), a = 0.14, b = −24.63, c = 0.048)

Adhesion Strength 504 hours with Reflow

S = 3.79923751 r = 0.98493648 .26

63

.75

52

.23

42

.71

31

.19

21

.68

10

6 0.1 0.12

0.22

0.32

0.42

0.52

0.62

0.72

0.82

0.92

Moisture Absotption at 575 hours Fig. 14.10 Bivariate fit analysis between mean adhesion strength after 504 h of moisture loading followed by reflow at 260◦ C and moisture absorption at 575 h (y = a exp(bx), a = 207.59, b = −6.45)

delamination for both MSL 1 and 3 exposure. In general, the resin chemistries that absorbed the most moisture had the lowest adhesion strengths and the worst performance in MSL preconditioning. A curve fitting analysis was performed between loss in adhesion strength and delamination and is shown in Fig. 14.12.

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EMC ‘D’ post MSL 1

EMC ‘D’ post MSL 3

Percent Decrease in Adhesion Strength at 168 Hrs

Fig. 14.11 SAT scans of QFN after exposure to MSL 1 and 3 (EMC D) S = 14.52125655 r = 0.96146079 .00

100

00

80.

00

60.

00

40.

00

20.

0 0.0 0.0

18.3

36.7

55.0

73.3

91.7

110.0

Percent Delamination

Fig. 14.12 Bivariate fit analysis between normalized adhesion strength after 168 h of moisture loading followed by reflow at 260◦ C and percent delamination after MSL 1 preconditioning (y = 1/(a + bx + cxˆ2), a = 0.066, b = 0.00013, c = −6.89e−006)

14.3.1.4 Experimental Conclusions for Mold Compound Chemistry Experiments Several basic conclusions can be reached based on the experimental results. These include the following: 1. Mold compound adhesion strength decreases as a function of moisture loading with or without reflow. 2. Post-MSL/reflow performance correlates directly with moisture absorption and adhesion strength. The lower the moisture absorption and the more stable the adhesion as a function of temperature, the better the MSL performance of the mold compound.

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14.3.2 Second Series of Experiments 14.3.2.1 Pull Tab Adhesion A list of mold compounds under investigation is given in Table 14.3. Adhesion data at 260◦ C without PMC, supplied by an outside lab, was based on shear testing 2 mm × 2 mm plugs molded to copper substrates. Based on the data available in Table 14.3, it appears that compounds 5, 4, 7, 11, and 12 would offer the best candidates followed by compounds 9, 2, 8, and then 6. Not enough information was available to rank compounds 1, 3, and 10. The working assumption was that of those compounds that show promise, the one with the highest adhesion at room temperature as a function of PMC and moisture loading should be the most likely choice. Subsequent MSL testing would show if this hypothesis is correct. Pull tab test was performed on those mold compounds. Figure 14.13 shows the results of the box plot of adhesion strength versus mold compound. Figure 14.13a shows data collected after post-mold cure. Figure 14.13b shows the results after PMC and MSL testing. Based on adhesion strength alone, compounds 4, 5, and 11 seem to stand out for quality of adhesion after moisture loading and reflow. Compounds 4 and 5 are unique in that their base resin chemistry, OCN, is not known for good performance in moisture testing. These compounds, however, have been specifically formulated for MSL 1 260◦ C applications. Both compounds contain a low water absorption hardening agent. Compound 4, in addition, contains a low molecular weight resin mixed with the OCN compound. Compound 11 is a fairly new-generation formulation with multiaromatic resin and hardener formulated for low moisture absorption. Compound 6, the current compound in use, behaves like a typical OCN compound after moisture loading and is clearly not suited for an MSL 1/260◦ C process. The same conclusion can be made for compound 1. Although this compound showed the highest adhesion strength at 260◦ C without post-mold cure, experimental data indicate most that the strength was lost after post-mold cure. A bivariate linear fit analysis using least squares regression was performed between each predictor variable (compound property) and adhesion strength after PMC and MSL exposure. Figure 14.14 shows the bivariate linear fit for adhesion strength versus moisture absorption. Using moisture absorption as a predictor variable results in a candidate list of 4, 5, 11, and 12 showing the most promise. The adhesion was rearranged, and another correlation analysis was performed between room temperature adhesion after PMC and adhesion strength after PMC and MSL exposure. Multivariate analysis showed an 89% data fit. Figure 14.15 shows the bivariate linear fit analysis. It appears that testing mold compounds at room temperature after PMC will give an indication of performance after moisture loading and reflow. 14.3.2.2 Moisture Sensitivity Testing (Level 1 at 260◦ C) Sample D2 PAK product using solder die attach was assembled at an inhouse production facility with each mold compound using a Lauffer VSKO

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Adhesion Strength (kgf)

80 70 60 50 40 30 20 10 01

02

03

04

05

06

07

08

09

10

11

12

09

10

11

12

Mold Compound (a)

Adhesion Strength (kgf)

80 70 60 50 40 30 20 10 01

02

03

04

05

06

07

08

Mold Compound (b)

Fig. 14.13 Box plot of adhesion strength using pull tab test. (a) After standard post-mold cure. (b) After PMC, moisture loading (85◦ C/85% RH, 168 h), and three reflows at 260◦ C

velocity-controlled mold press. Scanning acoustic microscopy was performed before and after MSL 1 moisture exposure/260◦ C reflow, then again after 100 temperature cycles (−65 to +150◦ C). For information purposes, only temperature cycling was extended out to 500 cycles. Results of the experiment are shown in Table 14.7. Compound 10 was not available in time for testing. Compounds 1 and 3 were purposely left out of the test matrix. Compound 1 is a known failure in previous MSL 1 testing, and compound 3 being designed for single-sided molding was considered inappropriate for D2 PAK product. Of the remaining nine compounds tested, six were halted at temperature cycling due to massive delamination after MSL. Of the three remaining candidates (compounds 4, 5, and 12), only compound 5 passed

MSL Capability of Plastic-Encapsulated Packages

Fig. 14.14 Bivariate fit analysis of adhesion strength after PMC and MSL testing versus moisture absorption

377

70 Adhesion PMC/MSL

14

60 50 40 30 20 10 .2

.3 .4 .5 .6 Moisture Absorption - In-house

.7

Adhesion PMC/MSL

70 60 50 40 30 20 10 20

30

40 50 60 Adhesion PMC

70

80

Fig. 14.15 Bivariate fit analysis of adhesion strength after PMC and MSL exposure versus initial room temperature adhesion with PMC only

all phases of the testing (excluding the 500-temperature cycle data) without delamination. Compound 11 was dropped before temperature cycling due to massive delamination on both the substrate and the die. Compounds 4 and 12 showed some signs of delamination before temperature cycling and subsequently got worse. Only compound 5 survived MSL exposure and 100 temperature cycles before succumbing to delamination after the 500-temperature cycle readout. Figure 14.16 shows the progressive nature of the delamination process. For this particular leadframe design, delamination started in the corners of the die flag and moved in toward the center (IC chip).

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Table 14.7 Results of moisture sensitivity testing with a 260◦ C reflow on actual D2 PAK packages Mold compound MRT

Delamination

2

Assembly

On chip On L/F heatsink On L/F post On chip On L/F heatsink On L/F Post On Chip On L/F heatsink On L/F post On chip On L/F heatsink On L/F Post

0/8 0/8 0/8 0/8 0/8 0/8 0/8 0/8 0/8 0/8 0/8 0/8 0/8 0/8 0/8 0/8 0/8 0/8 6/8 8/8 8M/8 7M/8 8L/8 8L/8 8L/8 9/40 6/40 4/40 35/40 25/40 Not continued due to delamination

MSL 1 3 × 260◦ C TC − 100 cy TC − 500 cy

6

7

8

9

11

12

4

5

0/8 0/8 0/8 2/8 8L/8 3/40

0/8 0/8 0/8 0/8 1SS/8 0/40 0/8 1SS/8 3/40 0/4 4S/4 5/20

0/8 0/8 0/8 0/8 5/8 3/40 0/8 7SS/8 11/40 0/4 4M/4 5/20

0/8 0/8 0/8 0/8 0/8 0/40 0/8 0/8 0/8 0/4 4SS/4 2/20

Delamination criteria (% by area): SS, very small (below 5%); S, small (5–20%); M, medium (20–50%); and L, large (over 50%) Reflow ⇔ thermal mismatch vapor pressure

Delamination

Fig. 14.16 Progressive nature of delamination process

14.3.2.3 Experimental Conclusions for the Second Series of Experiments In summary, based on the analysis of the data, it appears that the combination of high initial adhesion strength and low moisture absorption seems to be a good predictor variable for performance of a mold compound when exposed to MSL testing. Initial adhesion strength data resulted in a candidate list of 4, 5, 7, 8, and 11. Calculating the effects of moisture absorption not only reduced the list to 4, 5, and 11 but also added compound 12 though its adhesion strength was less than that of the other candidates. It is noted that the adhesion strength of compound 12 did remain very stable after MSL testing. Therefore, compounds 4, 5, 11, and 12 should have performed the best. Compound 11 was, however, dropped from the test matrix before temperature cycling due to massive delamination on both the substrate and the die. Of the other three compounds cited, only compound 5 survived MSL 1 moisture loading and 100 temperature cycles when used in a D2 PAK package configuration. Compounds 4 and 12 formed a second group that survived moisture loading but failed temperature cycling. All other compounds failed moisture loading sensitivity testing. In general, the following conclusions can be made:

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1. Of the mold compound properties tested, adhesion strength and moisture absorption appeared to be the most significant variables for MSL performance. 2. Initial adhesion strength and moisture absorption can be used as predictor variables in MSL 1/260◦ C testing but will not guarantee performance. 3. The compound that survived MSL testing in D2 PAK packages was an OCN resin-based system with a low water absorption hardener. However, other OCN compounds without the low water absorption hardener did not perform well. It is not known whether the compound chemistry plays a significant role in MSL performance. 4. Room temperature adhesion after post-mold cure and moisture loading had an 85% correlation with moisture absorption. Adhesion after post-mold cure and moisture loading also correlated well (89% fit) with initial post-mold cure adhesion before application of MSL testing. Room temperature adhesion testing can therefore be used as a good indicator of MSL performance.

14.3.3 Additional Experimental Studies 14.3.3.1 Effect of Mold Cap Thickness of QFN Packages Most published papers studied double-sided molded packages such as SOIC (small outline IC). There is no available information on mold cap thickness as a function of stress level for QFN packages. QFN arrays were assembled using a major manufacturer’s mold compound designed specifically for single-sided molding. Samples were prepared both with and without die. The die attach paste used was again specifically designed for this use. Samples of each type were prepared using different mold cap thicknesses (0.57, 0.80, 1.10, and 1.57 mm). These units were then moisture loaded in 85◦ C/85% RH for 168 h and exposed to 260◦ C solder reflow three times. Post-exposure SAT photos revealed the following: 1. Packages molded with no die do not delaminate. 2. Packages with die suffer delamination on the die flag but not top of the die. 3. The die attach interface also do not suffer any delamination. The results were the same for all test groups, regardless of mold cap thickness. Mold cap thickness made no apparent difference in the response of the QFN packages to MSL exposure. 14.3.3.2 Effect of Mold Compound Compaction Mold compound candidate evaluations can be broken down into two broad categories. The first covers chemical aspects such as cure kinetics, Tg and CTE measurements, and constituent analysis. The second covers the mechanical aspects such as adhesion, mold press parameter optimization, spiral flow, and floor life. With respect to mold press parameter optimization, compaction and adhesion are two of

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the more important tools used in setting up a proper mold profile. Mold parameters are characterized and optimized using compaction (as-molded density) as the response variable. Once optimized, adhesion studies are performed to validate the parameters. Mold compound compaction can be further broken into two categories. True compaction is usually defined as the amount of filler present in a molded part. Compaction can also be defined as the amount of micro/macro voids present and the degree to which polymer chains are pushed closer together. The amount of filler present in a molded part is governed solely by the filler loading in the raw EMC pellet, while the amount of voiding present and the packing density of the polymer chains are functions of mold press parameters. For purposes of this study the operational definition of compaction is the dry weight of a molded part represented by the amount of both the filler and the density of voids present in the part. Both properties can be easily measured using optical photographs. Trapped air pockets are inherent to molding pellets and subsequent viscous epoxy as it is being transferred into mold cavities. The compaction phase of the mold process is supposed to crush these air pockets and produce a denser structure with less free volume. Measuring weight gain as a function of various mold parameters gives insight into the quality of the process. There does not appear to be much published information on the effects mold parameters have on as-molded density and the resultant effect compaction has on adhesion or moisture absorption. Minjin et al. [34] tested saturation levels as a function of filler content and determined that saturated moisture absorption decreased as filler loading increased. In general, one wants the most compacted (highest weight) and highest adhesion strength possible. However, compromises must be made between compaction and adhesion. This is due to the fact it is the resin molecular chains that make adhesion possible. The primary adhesion mechanism is thought to be hydrogen bonding between the resin chains and the leadframe. Resin also bonds filler particles to each other and is the glue that makes the mold compound stick to a leadframe. It is logical to assume that the more the resin, the higher the initial adhesion strength. Compaction has the opposite effect – higher weight means more filler, therefore less resin with an attendant decrease in adhesion strength. Having too much resin and not enough filler has a negative effect on mechanical properties such as CTE, moisture resistance, modulus, and fracture strength since it is the filler that governs these properties. Moon et al. [35] measured mold compound properties as a function of filler level and determined that as filler content increased, several properties such as CTE, moisture absorption, and strength were improved. However, adhesion strength suffered in the dry state and degraded even more with moisture absorption. The experiment presented below investigates the role compaction plays in adhesion and moisture absorption. Maximum compaction is defined as the maximum amount of filler present and the minimum amount of voids present. For this study, void density and polymer chain packing were controlled by using mold press parameters. Void density was examined using a designed experimental approach with a single mold compound having a constant filler loading level. Void/packing density was varied by deliberately manipulating mold press transfer/pack-and-hold

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pressures to induce different weight levels. Moisture absorption studies were conducted using “hockey puck” molded discs. Adhesion studies were performed using pull tab test units. QFN packages were assembled using the best and worst case scenarios and exposed to MSL 1 260◦ C preconditioning to determine if compaction is a viable material parameter for enhanced quality. The end result was to determine if optimized compaction levels result in superior adhesion and moisture resistance. Characterization and Optimization of Mold Press As-molded weight and cull thickness (amount of excess mold compound left behind after the mold process is completed) were used as response variables in a series of experiments designed to optimize mold press parameters. Fractional factorial screening experiments were performed first to gather information on main effects. Once established, more refined screening experiments were used to investigate interaction effects. All statistical analyses were conducted at a 95% confidence level. Conclusions reached from the various experimental designs revealed the following: 1. Pack–and-hold pressure (compaction pressure portion of the mold cycle once the velocity profile ends) was a significant variable. Increasing this pressure has the effect of increasing the weight of the molded part. Pack-and-hold pressure plus mold temperature accounted for almost all of the variance in the weight data. 2. Mold temperature was a significant variable. Within the scope of the experiment weight increased at lower mold temperatures. 3. No interaction effects were observed. The effect of mold press pressure on mold compound density is shown in Fig. 14.17, which shows a box plot of compaction measured as weight versus packand-hold pressure (psi). As pack-and-hold pressure increases, the amount of mold compound left behind, defined as cull thickness, becomes less. The thinner culls provided evidence of more material being packed into the cavity. Molded weight

9.255 9.25

Weight

9.245 9.24 9.235 9.23 9.225

Fig. 14.17 The effect of mold press pressure on mold compound density

9.22 0600

1300 Pack/Hold Press

2000

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0.205

9.255 9.25 9.245 Weight

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0.2 0.195 0.19

9.24 9.235 9.23 9.225

0.185

9.22 0600

1300 Pack/Hold Press

2000

.185

.19 .195 Cull Thickness

.2

.205

Fig. 14.18 (a) Box plot of mold compound cull thickness versus pack-and-hold pressure. (b) Weight versus cull thickness

was shown to be inversely related to cull thickness providing direct evidence of more mold compound being forced into the mold (Fig. 14.18). Effect of Void Density on Moisture Absorption and Adhesion Disc samples molded at a high compaction pressure value of 2,000 psi and a low value of 800 psi were submitted for cross sectioning and analyzed for voiding. Optical photos of both specimens are presented in Fig. 14.19. Though there was no discernible difference in filler loading, void density decreased at the higher compaction pressure level. Sample discs from the most compacted and least compacted test cells were dry baked at 130◦ C for 24 h and then exposed to 85◦ C/85% RH for a maximum of 540 h. Weight gain analysis showed no difference in moisture uptake (Fig. 14.20). Adhesion samples were prepared using pull tabs molded at various pack-andhold pressures ranging from 600 to 1,600 psi. Six samples were tested in each test cell. Adhesion strength results are shown in bar chart form in Fig. 14.21. There did not appear to be any difference in adhesion quality. Though it is possible to optimize packing density and reduce internal voiding by controlling machine parameters, the

Fig. 14.19 Optical photos (500×) of cross sections of hockey puck samples molded at 800 and 2,000 psi

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Thick Hockey Pucks 0.28 0.28 0.25 0.22 %Changethick600 0.19 %Changethick800 0.16 %Changethick1200 0.12 %Changethick1600 0.093 0.062 0.031 0 0

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120 180 240 300 360 420 480 540 600

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600 psi 800 psi 1200 psi 1600 psi Fig. 14.20 Weight gain as a function of moisture loading for discs molded at various pressure levels

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Mean(Adhesion Strength (Kg))

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Fig. 14.21 Adhesion strength as a function of compaction using pull tab test

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improvement in mold quality does not translate into improved moisture resistance or increased adhesion. Effect of Compaction on MSL Performance The designed experiments described above established the best and worst case set of parameters for molding hockey pucks. These two settings were used to mold actual QFN arrays. A 0.254 mm thick bare copper C194 SO8 3–lead array was used with a mold cap thickness of 1.1 mm. The first part of the experiment determined whether a weight difference could be detected between the two parameter settings. Four empty arrays (i.e., no die) were initially molded for each test cell. There was a distinct difference in compaction between the two test cells as shown in Fig. 14.22. Two additional groups of samples populated with die were assembled using the same mold parameters and submitted for MSL testing. PMC was performed at 175◦ C for 6 h. Pre-MSL exposure SAT testing revealed no interface delamination for any of the units molded with both compaction pressures. Post-MSL exposure SAT testing for both groups showed evidence of delamination on the die flag and total die attach delamination. Sample photos are shown in Fig. 14.23. The difference in compaction levels did not appear to affect response to MSL exposure. Die attach paste delamination may be confounding the data but it is not believed so since two of the units molded at high compaction pressure with no die attach delamination showed the same amount of die flag delamination. The conclusion reached from the QFN build was that QFN samples molded with high and low compaction pressure tend to show the same rate of delamination after exposure to MSL 1 260◦ C. Conclusions of Mold Compound Compaction Experiments Within the limits of this experiment it appears that mold press “compaction pressure” controls the amount of free volume and not the amount of filler present in a 6.6

EMC Weight

6.5 6.4 6.3 6.2 6.1

Fig. 14.22 Compaction difference in QFN samples molded at best (2,000 psi) and worst conditions (800 psi)

6 2000 psi

800 psi Test Cell

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High compaction pressure (2000psi)

Fig. 14.23 Post-MSL 1 260◦ C SAT photos of QFN product molded with best and worst mold press machine parameters. Compaction did not appear to affect response to MSL exposure

molded part. The differences in free volume between parts molded at low pressure and those molded at higher pressures are stark but do not translate into better performance. As a consequence, compaction as measured by mold press parameters does not appear to affect adhesion strength, moisture absorption, or MSL performance. This does not mean that compaction should be abandoned as a tool in optimizing molding parameters since it has a positive effect on CTE and mechanical strength of a mold compound. Compaction is particularly important in discovering flow problems in a mold die. Mold cavity analysis by weight can detect those cavities that fill the least, thus giving hints on mold design issues that affect flow properties or identifying worst case cavity positions for reliability testing. Compaction can be used as a valuable statistical process control tool since for automatic mold presses, it can signal when mold springs in the pots are starting to go “soft” a lot sooner than looking at cull heights.

14.4 Conclusions Studies with test samples showed that mean adhesion strength for all resin chemistries dry and moisture loaded at 85◦ C/85% RH for 168 and 504 h with no reflow decreases with moisture loading, indicating a dependency on moisture interaction with the resin chemistry. In addition, mean adhesion strengths of each resin chemistry system at the three moisture levels after reflow at 260◦ C showed a corresponding decrease in adhesion strength as moisture loading progresses. This suggests that a thinner package exposed to the same moisture conditions will suffer a greater proportional loss of adhesion than will a thicker package and be more susceptible to delamination. Experiments with pure mold compound samples showed an 83% correlation between moisture absorption and filler loading. The higher the filler loading, the less the moisture absorbed into the mold compound. The fit appears to be curvilinear. It is evident that filler loading is an important variable in early moisture absorption process. Resin chemistry may play a secondary role in the “plateau” regions where the

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moisture–molecular chain affinity for each other determines the tendency to reach saturation. SAT analysis for delamination of actual product after MSL 1 loading and 260◦ C reflow resulted in the same performance as the test units with respect to resin chemistry as both the moisture absorption and adhesion studies. In general the resin chemistries that absorbed the most moisture had the lowest adhesion strengths and the worst performance in MSL preconditioning. Of the mold compound properties tested, adhesion strength and moisture absorption appeared to be the most significant variables for MSL performance. Initial adhesion strength and moisture absorption can be used as predictor variables in MSL 1/260◦ C testing but will not guarantee performance. A correlation analysis performed between room temperature adhesion after PMC and adhesion strength after PMC and MSL exposure showed an 89% data fit, suggesting that testing mold compounds at room temperature after PMC will give an indication of performance after moisture loading and reflow. Mold cap thickness made no apparent difference in the response of the QFN packages to MSL exposure. Experiments with QFN packages using mold compound compaction (weight density) as a test variable reached the conclusion that samples molded with high and low compaction pressure tend to show the same rate of delamination after exposure to MSL 1 260◦ C. The differences in free volume between parts molded at low pressure and those molded at higher pressures are stark but do not translate into better performance. As a consequence, compaction as measured by mold press parameters does not appear to affect adhesion strength, moisture absorption, or MSL performance. Acknowledgments This chapter was written based on work performed by Joseph Fauty, retired – ON Semiconductor plus Michal Stana, formerly of ON Semiconductor – Czech Republic, and Dr. Leonrina Cada, currently with Intel Technology Philippines, Inc. Dr. Cada also holds the position of an associate professor in the University of the Philippines-Diliman, teaching graduate courses on polymer science, materials degradation, and liquid crystals chemistry.

References 1. Fan, X.J., Zhou, J., Zhang, G.Q., Ernst, L.J., “A amicromechanics based vapor pressure model in electronic packages”, ASME Journal of Electronic Packaging, 127(3), 262–267, 2005. 2. Gallo, A., Munamarty, R., “Popcorning: a failure mechanism in plastic encapsulated microcircuits”, IEEE Transactions on Reliability, 44(3), 362–367, 1995. 3. Stellrecht, E., Bongtae, H., Pecht, M., “Characterization of hygroscopic swelling behavior of mold compound and plastic packages”, IEEE Transactions on Components, Packaging, and Manufacturing Technology, 27(3), 499–506, 2004. 4. Lebbai, M., Kim, J.K., Yuen, M.M.F., “Effects of moisture and elevated temperature on reliability of interfacial adhesion in plastic packages”, Journal of Electronic Materials, 32(6), 574–582, 2003. 5. Ardebili, H., Wong, E.H., Pecht, M., “Hygroscopic swelling and sorption characteristics of epoxy molding compounds used in electronic packaging”, IEEE Transactions on Components and Packaging Technologies, 26(1), 206–214, 2003.

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6. Omi, S., Fujita, K., Tsuda, T., Maeda, T., “Causes of cracks in SMD and type specific remedies”, IEEE Transactions on Components, Hybrids, and Manufacturing Technology, 14(4), 818–823, 1991. 7. Alpern, P., Dudek, R., Schmidt, R., Wicher, V., Tilgner, R., “On the mode II popcorn effect in thin packages”, IEEE Transactions on Components and Packaging Technologies, 25(1), 56–65, 2002. 8. Alpern, P., Lee, K.C., Dudek, R., Tilgner, R., “A simple model for the mode I popcorn effect for IC packages with copper leadframe”, Transactions on Components and Packaging Technologies, 25(2), 301–308, 2002. 9. Tay, A.A.O., Lin, T.Y., “Moisture diffusion and heat transfer in plastic IC package”, IEEE Transactions on Components, Packaging, and Manufacturing Technology, Part A, 19(2), 186–193, 1996. 10. Ganesan, G.S., Berg, H.M., “Model and analysis for solder reflow cracking phenomena in SMT plastic packages”, IEEE Transactions on Components, Hybrids, and Manufacturing Technology, 16(8), 940–948, 1993. 11. Fan, X.J., Zhang, G.Q., van Driel, W.D., Ernst, L.J. “Interfacial delamination mechanisms during reflow with moisture preconditioning”, IEEE Transactions on Components and Packaging Technologies, 31(2), 252–259, 2008. 12. van Driel, W.D., van Gils, M.A.J, Fan, X.J., Zhang, G.Q., Ernst, L.J., “Driving mechanisms of delamination related reliability problems in exposed pad packages”, IEEE Transactions on Components and Packaging Technologies, 31(2), 260–268, 2008. 13. Fauty, J. Cada, L.G. Stana, M., “Effect of 260◦ C reflow on the ability of mold compounds to meet moisture sensitivity level one (MSL1)”, IEEE Transactions on Components and Packaging Technologies, 28(4), 841–851, 2005. 14. Shook, R.L., Goodelle, J.P., “Handling of highly-moisture sensitive components – an analysis of low-humidity containment and baking schedules”, IEEE Transactions on Electronics Packaging Manufacturing, 23(02), 81–86, 2000. 15. Shook, R.L., Conrad, T.R., Sastry, V.S., Steele, D.B., “Diffusion model to derate moisture sensitive surface mount IC’s for factory use conditions”, IEEE Transactions on Components, Packaging and Manufacturing Technology – Part C, 19(2), 110–118, 1996. 16. Mercado, L.L., Chavez, B., “Impact of JEDEC test conditions on new-generation package reliability”, Transactions on Components and Packaging Technologies, 25(2), 204–210, 2002. 17. Huang, Y.E., Hagen, D., Dody, G., Burnette, T., ”How reflow temperatures affect BGA delamination”, Surface Mount Technology, 13(2), 154–157, 999. 18. McCluskey, P., Munamarty, R., Pecht, M., “Popcorning in PBGA packages during IR reflow soldering”, Microelectronics International, No. 42, 20–23, 1997. 19. Love, B., Packman, P., “Effects of surface modifications on the peel strength of copper based polymer/metal interfaces with characteristic morphologies”, Journal of Adhesion, 40, 139–150, 1993. 20. Kim, J-K., Lebbai, M., Liu, J.H., Kim, J.H., Yuen, M., “Interface adhesion between copper lead frame and epoxy molding compound: effects of surface finish, oxidation and dimples”, 50th Electronic Components and Technology Conference, Las Vegas, NV, pp. 601–608, 2000. 21. Chun, D.S., Doane, D.A., “Reduction of popcorning in BGA’s by plasma cleaning”, 2nd Pan Pacific Microelectronics Symposium, Kona, Hawaii, January 1997. 22. Kim, S. “The role of plastic package adhesion in performance”, IEEE Transactions on Components, Hybrids, and Manufacturing Technology, 14(4), 809–817, 1991. 23. Thompson, T., Kohn, R., “Implementation of cost effective, level 1, delamination and crack-free solutions for QFP’s”, Proceedings of 1996 International Electronics Packaging Conference, IEPS, Austin, TX, USA, September 1996, pp. 468–474, 1996. 24. Hagen, D., Downey, S., Hughes, C., Fowkes, G., Lim, M.L., Anuar, K., Ibrahim, R., “JEDEC level 1 moisture performance solution for 20 × 20 × 1.4 mm TQFPs,” Proceedings of 1996 International Electronics Packaging Conference, IEPS, Austin, TX, USA, September 1996, pp. 102–111, 1996.

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25. Tada, K., Fujioka, H., “Properties of molding compounds to improve package reliability of SMD’s”, IEEE Transactions on Components and Packaging Technologies, 22(4), 534–540, 1999. 26. Gallo, A., Tubbs, T.R., “High solder-reflow crack resistant molding compound”, IEEE Transactions on Components, Packaging and Manufacturing Technology – Part A, 18(3), 646–649, 1995. 27. Lee, H., Earmme, Y.Y., “A fracture mechanics analysis of the effects of material properties and geometries of components on various types of package cracks”, IEEE Transactions on Components, Packaging and Manufacturing Technology – Part A, 19(2), 168–178, 1996. 28. Tay, A.A.O., Tan, G.L., Lim, T.B., “Predicting delamination in plastic IC packages and determining suitable mold compound properties”, IEEE Transactions on Components, Packaging and Manufacturing Technology – Part B, 17(2), 201–208, 1994. 29. Chen, A.S., Schaefer, W.J., Lo, R.H.Y.,. Weiler, P., “A study of the interactions of molding compound and die attach adhesive with regards to package cracking”, IEEE Electronic Components Technology Conference, Denver, Colorado, p. 115, 1994. 30. Mosbarger, R.D., Hickey, D.J., “The effects of materials and post-mold profiles on plastic encapsulated integrated circuits”, IEEE International Reliability Physics Symposium, San Jose, CA, 1994. 31. Sauber, J., Lee, L., Hsu, S., Hongsmatip, T., “Fracture properties of molding compound materials for IC plastic packaging”, IEEE Transactions on Components, Hybrids, and Manufacturing Technology – Part A, 17(4), 533–541, 1994. 32. Fan, X.J., Zhou, J., Zhang, G.Q., “Multi-physics modeling in virtual prototyping of electronic packages – combined thermal, thermo-mechanical and vapor pressure modeling”, Microelectronics Reliability, 44, 1967–1976, 2004. 33. Takano, E., Mino, T., Takahashi, K., Sawada, K., Shimizu, S., Yoo, H.Y. “The oxidation control of copper lead frame package for prevention of popcorn cracking”, IEEE 47th Electronic Components and Technology Conference, San Jose, CA, pp. 78–83, 1997. 34. Minjin, K., Kim, M., Shin, D., Lim, I., Moon, M., Park, Y., “The effect of filler on the properties of molding compounds and their moldability”, IEEE Electronic Components and Technology Conference, San Jose, CA, pp. 108–113, 1997. 35. Moon, K.S., Hwang, S.D., Yoon, H.G., Ryu, J.H., Woo, S.S., “High filler loading technique and its effects on the reliability of molding compound”, 1998 IEEE/CPMT Electronics Packaging Technology Conference, Singapore, pp. 318–324, 1998.

Chapter 15

Hygrothermal Delamination Analysis of Quad Flat No-Lead (QFN) Packages M.S. Zhang, S.W.R. Lee, and X.J. Fan

15.1 Introduction Quad flat no-lead (QFN) package is a leadframe-based plastic package, which was developed to replace shrink small outline packages (SSOPs). The general manufacturing process includes leadframe preparation, die bonding, wire bonding, encapsulation, terminal formation, and bottom lead finishing. Since it was first fabricated by Sujimi in 1996, QFN packages are getting popular due to the features such as low cost, low pin count requirements, and excellent heat dissipation. With the increasing applications in industry, the reliability problem becomes more important and interfacial delamination during reflow is one of the main concerns. Interfacial delamination can be traced to thermal mismatch effect, moisture absorption, and the degradation of interfacial adhesion. Tee and Zhong [1] established an integrated finite element model to combine thermo-mechanical, hygromechanical, and vapor stresses into one model. However, the failure mechanism is not clear since the critical interfacial stresses were not discussed and the simulation results lack experimental validation. Driel et al. [2] discussed the initiation of delamination in QFN package using interfacial fracture mechanics. But the simulation results were dependent on the location and the length of the pre-crack. Therefore, the contribution to the failure of each effect needs to be identified with more experimental validations. To bridge the gap between finite element analysis (FEA) and experimental validations, Zhang, Lee, and Fan [3, 4] established a combined experiment/simulation methodology as shown in Fig. 15.1 to study the failure mechanism of hygrothermal delamination. Two kinds of dummy QFN packages with different leadframes are manufactured as test vehicles for this study. The research methodology generally divides into two routes. One follows the simulation route, starting from material characterization to finite element modeling. Stress ratio approach is then employed to evaluate the package reliability. In the other route, dummy QFN packages are

M.S. Zhang (B) e-mail: [email protected] X.J. Fan, E. Suhir (eds.), Moisture Sensitivity of Plastic Packages of IC Devices, Micro- and Opto-Electronic Materials, Structures, and Systems, C Springer Science+Business Media, LLC 2010 DOI 10.1007/978-1-4419-5719-1_15, 

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Fig. 15.1 Research methodology

fabricated and tested to provide experimental results for verification. In this chapter, the main objectives are as follows: (a) A finite element model is established to investigate the interfacial stress distribution along different interfaces when a dummy QFN package is subjected to a pure thermal loading and a hygrothermal loading. An alternative implementation using superposition method to calculate the hygrothermal stresses, in which the non-uniform moisture distribution is considered, is developed. (b) Stress ratio approach is employed to evaluate the package reliability. The highrisk interfaces and locations, where delamination likely occurs, are identified. Complete experimental validations are carried out to verify the stress ratio approach.

15.2 Manufacture of Dummy QFN Packages The manufacturing process of dummy QFN packages is similar to the process used in industry, as shown in Fig. 15.2. First, an “X”-shaped die attach pattern was made on bare leadframe by a dispensing machine in order to make the die attach material uniformly distributed underneath the die. Second, pick-n-place machine was used to place the chip on the leadframe. A die attach curing process was followed to complete the die bonding process. Afterward, transfer molding machine was used to cover the die and leadframe with encapsulation. The curing condition of molding compound was at 175◦ C for 120 s. In addition, a post-curing process under 175◦ C

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Fig. 15.2 Manufacturing process of dummy QFN package

Fig. 15.3 Schematic of dummy QFN package

for 6 h was performed to increase molding compound adhesion to leadframe. After sawing and dicing, the final dimensions of the dummy packages were measured by using microscope shown in Fig. 15.3. The molding compound used in the dummy QFN package was a kind of green molding compound for Pb-free reflow with low cost, high adhesion, and low moisture absorption. The die attach material was designed for QFN package with excellent adhesion to a palladium pre-plated (PPF) leadframe. In this study, two kinds of dummy QFN packages were fabricated and tested. The one with silverplated leadframes is noted as Package 1. The other with PPF leadframes is noted as Package 2.

15.3 Mechanical Tests for Interfacial Strength Mechanical tests for interfacial adhesion provide an evaluation of the interface against delamination. Based on the different failure criteria, several common test methods can be classified into two groups: (i) compact tension, double cantilever

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beam (DCB), tapered DCB, blister, end-notched flexure (ENF), and mixed mode bending (MMB) for interfacial fracture toughness and (ii) peel test, pull tab test, button pull/shear test, and die pull/shear test for interfacial strength measurement. As mentioned earlier, the specific fabrication of a package interface requires the use of specific size specimen in interfacial adhesion test. This would bring difficulty in specimen design, test machine accuracy and sensitivity, test fixture alignment, etc. In this study, button shear and die shear tests are chosen to measure the interfacial strength of molding compound/leadframe (MC/LF) and die attach/leadframe (DA/LF) interfaces, respectively. Button shear and die shear tests have advantages of easy experiment operation, simple sample preparation, and easy use of experimental results. Figure 15.4 shows the setup of shear tests. To make the results comparable, both button shear and die shear tests were implemented on Dage 4000 shear machine under same shear speed and shear height. Also, the leadframes used in shear tests were the same as those used in dummy QFN package fabrications.

(a) Button shear test

(b) Die shear test

Fig. 15.4 Mechanical tests for interfacial adhesion: (a) button shear test and (b) die shear test

The failure modes of shear tests for different interfaces are shown in Fig. 15.5. It should be noted that interface debond is observed in Fig. 15.5a–c except die shear test on PPF leadframe, as shown in Fig. 15.5d. The debond region was in the die attach material itself, which means the interfacial shear strength exceeds the cohesive strength of the die attach. This is correct since the die attach chosen here is designed to exhibit excellent adhesion to PPF leadframe. The results of shear tests are shown in Fig. 15.6. Molding compound shows a better adhesion to Ag leadframe than PPF leadframe. Die attach shows a better adhesion to PPF leadframe than Ag leadframe. Even though it is a cohesive strength value for die shear of DA/PPF LF, the shear strength between DA/PPF LF is the highest among all test results (27 MPa). One thing should be mentioned here that the hygrothermal delamination occurs under high-temperature/humidity condition, so the related interfacial adhesion should be measured under same situation. However, due to the experimental limitations, all the shear tests in this study were performed under room temperature. Therefore, we assumed that the shear strength measured in the room temperature has the same trend as measured in high-temperature/humidity condition.

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(a) Button shear on silver leadframe

(b) Button shear on PPF leadframe

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(c) Die shear on silver (d) Die shear on PPF leadframe leadframe

Fig. 15.5 Failure modes of shear tests: (a) button shear on silver leadframe, (b) button shear on PPF leadframe, (c) die shear on silver leadframe, and (d) die shear on PPF leadframe

Shear Strength (MPa)

30.00 25.00 MC/Ag LF 20.00

DA/Ag LF MC/PPF LF

15.00

DA/PPF LF 10.00 5.00 0.00 MC/Ag LF

DA/Ag LF

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DA/PPF LF

Fig. 15.6 Interfacial shear strength

15.4 Moisture Sensitivity Tests of Dummy QFN Packages Moisture sensitivity level-3 (MSL-3) tests are implemented following the JEDEC standard [5]. The test flowchart is shown in Fig. 15.7. Two groups of tests were performed, namely Test A and Test B. In Test A, pure thermal effect on delamination is examined. Samples are baked at 125◦ C for 24 h, followed by the reflow (lead free) without moisture preconditioning. In Test B, samples are soaked under accelerated MSL-3 preconditioning (60◦ C/60% RH for 40 h), followed by the reflow.

Fig. 15.7 Flowchart of MSL tests

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15.5 Finite Element Model A 2D half finite element mode is established using ANSYS code including 8744 four-node quad elements. A finite element mesh is shown in Fig. 15.8. The finer mesh is given at the junction of the die attach fillet and the package edge. The mesh density around the package edge is very high in order to match the free-edge effect. The same model will be used for subsequent different analyses changing only the element types and material properties. As mentioned early, there are two kinds of packages used in this study. Since the plated layer is very thin, two leadframes have almost same material properties. But these different surface treatments will lead to different adhesions to polymer materials such as molding compound and die attach.

(a) FEM mesh at die attach fillet

(b) FEM mesh at package edge

Fig. 15.8 Two-dimensional half model of dummy QFN package: (a) FEM mesh at die attach fillet and (b) FEM mesh at package edge

15.6 Thermo-mechanical Stress Analysis In order to understand the contribution of pure thermal effect, it is necessary to understand the temperature distribution. The governing equation of transient heat transfer can be described as follows: ∂T = αT ∂t



∂ 2T ∂ 2T ∂ 2T + + ∂x2 ∂y2 ∂z2

 ,

(15.1)

where T is the temperature, x, y, and z are the spatial coordinates, and αT is the thermal diffusivity. The boundary condition applied here is the fixed external surface temperature according to a reflow profile (lead free), as shown in Fig. 15.9. The thermal material properties such as specific heat (Cp ), thermal conductivity (k), and density (ρ) are listed in Table 15.1. It has been found from the finite element analysis that the heat is conducted very fast due to the high conductivity of copper and die. The internal package achieves quite uniform temperature at different sections of reflow. When the package

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Fig. 15.9 Reflow profile Table 15.1 Material properties for thermal analysis Material

Cp (J/kg K)

k (W/m K)

ρ (kg/m3 )

Leadframe Die (Si) MC DA

385 750 2,021 600

385 124 1.26 4

8,960 2,329 1,280 2,000

is heated up to a peak temperature of 260◦ C, the temperature gradient is no more than 1◦ C. Therefore, the temperature distribution during reflow can be assumed to be uniform throughout the package in the subsequent thermo-mechanical analysis. For the thermo-mechanical modeling, the temperature is raised from 175◦ C (curing temperature) to 260◦ C (peak temperature for lead-free reflow). Linear elastic material properties are applied, as shown in Table 15.2: εT = αT.

(15.2)

Figure 15.10 plots the shear and normal stress contours in molding compound and die attach, respectively. Since the main concern is at the interface, only shear stress and peeling stress are plotted. It should be noted that the commercial code Table 15.2 Material properties for thermo-mechanical stress analysis Material

E (GPa)

ν

α (ppm/◦ C)

Leadframe Die (Si) MC DA

80 110 1.10 0.04

0.34 0.28 0.30 0.30

18 4 55.7 151

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(a) Shear stress acting in molding compound

(c) Shear stress acting in die attach

(b) Peeling stress acting in molding compound

(d) Peeling stress acting in die attach

Fig. 15.10 Thermo-mechanical stress distribution at 260◦ C: (a) shear stress acting in molding compound, (b) peeling stress acting in molding compound, (c) shear stress acting in die attach, and (d) peeling stress acting in die attach

will average the stress values at the interface between elements. This would be correct only if the structure is made of one kind of material [6]. When the interface crosses over two different materials, it will lead to wrong results. The procedure to obtain the correct interfacial stress distribution is to select all the elements with the same material and then output the nodal stress results at the related interface. The interfacial stress distributions at different interfaces are shown in Fig. 15.11 along different paths, which are defined in Fig. 15.3. Path 1 is at the die top surface from the die center (point A) to the die edge (point B). In Path 1, interfacial shear stress was dominated and the maximum value achieved was 6.38 MPa at point B. Path 2 is at the molding compound/leadframe interface starting from the junction of the die attach fillet (point C) to the package edge (point D). In Path 2, shear stress was dominated again since the peeling stress was negative (compressive). The shear stress concentrated at point C and point D was about 13.82 and 3.45 MPa, respectively. Path 3 is at the die attach/leadframe interface starting from the die center (point E) to the edge of die attach region (point F). Shear stress remains dominant with maximum value at point F of about −1.7 MPa. Once the interfacial stress distributions are obtained, the failure criterion can be described as follows: τ  , (15.3) Y= S where τ is the shear stress from FEA calculation, S is the interfacial shear strength from the previous mechanical tests (Table 15.3), and Y is the failure factor. A larger value of Y represents a higher possibility to failure. From Table 15.4, the following observations have been made:

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Distance (mm)

Distance (mm)

(a) Path 1, A-B

(b) Path 2, C-D

0.5 0

0

0.5

1

1.5

2

2.5

3

4

3.5

Stress (MPa)

–0.5 –1 –1.5 Shear Stress

–2

Peeling Stress

–2.5 –3 –3.5 –4

Distance (mm)

(c) Path 3, E-F

Fig. 15.11 Interfacial stress distribution from thermo-mechanical stress analysis at 260◦ C: (a) Path 1, A–B; (b) Path 2, C–D; and (c) Path 3, E–F

Table 15.3 Interfacial shear strength (MPa) MC/Si

MC/LFAg

MC/LFPPF

DA/LFAg

DA/LFPPF

10.00

11.23

7.56

7.55

27.33

Table 15.4 Calculation of failure criterion factors Y

Maximum shear stress (MPa) Maximum peeling stress (MPa) YAg = [τ /S] YPPF = [τ /S]

(1) MC/Si (A–B)

(2) MC/LF (C–D)

(3) DA/LF (E–F)

A

B

C

D

E

F

0 0 0 0

6.38 2.01 0.64 0.64

−13.82 −6.23 1.23 1.83

−3.45 −17.91 0.31 0.46

0 0 0 0

−1.70 −3.50 0.22 0.06

The bold numbers are the maximum value for failure factor comparison.

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(a) For both types of leadframe packages (Ag and PPF leadframes), the point C always presents a highest value of Y among other locations and interfaces. This implies that delamination likely takes place at molding compound/leadframe interface around the junction of the die attach fillet. (b) Since Y value in Package 2 is greater than that in Package 1 at the point C, Package 2 has a greater probability to fail than does Package 1. Experimental validations were conducted using Test A without moisture preconditioning. The C-SAM inspections showed that Package 1 passed (as shown in Fig. 15.12), while Package 2 had interface delaminations (as shown in Fig. 15.13). From the C-scan images, it looks like the delamination propagation direction follows the white arrows that are pointing from the junction of the die attach fillet toward the package edge. In addition, most of the delaminated areas (dark area) do not connect to the package edge, indicating that the delamination propagated to the package edge but not yet reached the end. Based on these observations, we may conclude that the delamination was initiated at the molding compound/leadframe interface around the junction of the die attach fillet. This is consistent with the finite element analysis.

(a) C-scan image

(b) T-scan image

Fig. 15.12 C-SAM inspection of Package 1 after Test A: (a) C-scan image and (b) T-scan image

15.7 Hygro-mechanical Stress Analysis In this study, the transient moisture diffusion and the subsequent hygro-mechanical stress modeling were performed using coupled thermal stress analysis. The governing equation of moisture diffusion is described as follows:

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(a) C-scan image

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(b) T-scan image

Fig. 15.13 C-SAM inspection of Package 2 after Test A: (a) C-scan image and (b) T-scan image

∂C = Dm ∂t



 ∂ 2C ∂ 2C ∂ 2C + 2 + 2 , ∂x2 ∂y ∂z

(15.4)

where C is the moisture concentration, Dm is the diffusivity which measures the rate of diffusion, and t is the time. However, the moisture concentration is not continuous at interfaces. To remove the discontinuity, the normalization approach such as wetness approach [7] is applied as follows: w=

C , Csat

1 ≥ w ≥ ,0

(15.5)

where Csat is the saturated moisture concentration and w is the wetness fraction. w = 0 means dry and w = 1 means fully saturated. Then equation (15.4) becomes ∂w = Dm ∂t



 ∂ 2w ∂ 2w ∂ 2w + 2 + 2 . ∂x2 ∂y ∂z

(15.6)

Equation (15.6) can be solved using a thermal element type in ANSYS code. It should be noted that the above thermal–moisture analogy does not hold anymore under varying temperature/humidity conditions such as a reflow process [8, 9]. However, if the saturated moisture concentration is independent of temperature throughout reflow temperature range, the wetness approach still applies [9]. Otherwise, the direct concentration approach (DCA) can be used to solve desorption problems [9]. For moisture absorption modeling, the initial condition is w = 0 for the whole package, and the boundary condition is w = 1 at the external surfaces, which are exposed to ambient moisture. Moisture weight gain test was performed to measure moisture diffusivity and the saturated moisture concentration. According to

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Fig. 15.14 Moisture absorption of molding compound under accelerated MSL-3 preconditioning

ASTM standard [10], a disk sample was fabricated under transfer molding process. Afterward, a moisture weight gain measurement was performed and the experimental data are shown in Fig. 15.14. The Arrhenius equation is used to describe the diffusivity as a function of temperature: Q

Dm = D0 e RT ,

(15.7)

where D0 is the initial diffusion coefficient for moisture desorption, Q is the activation energy (eV), R is the Boltzmann constant (8.83 × 10−5 eV/K), and T is the absolute temperature (K). Dm and Csat of molding compound and die attach were determined by experiments shown in Table 15.5, and other material properties are from Ref. [1]. Figure 15.15 plots the wetness contour after moisture preconditioning and at reflow. The package was fully saturated after the accelerated MSL-3 preconditioning. During the reflow, significant amount of moisture was released out of the package. However, the moisture concentration at the molding compound/leadframe interface remained intact. The hygro-strain can then be calculated as follows:  εM = βC = βCsat

C Csat

 = (βCsat ) w,

(15.8)

Table 15.5 Material properties for moisture analysis

MC DA

Dm (mm2 /s)

Csat (mg/mm3 )

D0 (mm2 /s)

Q (eV)

β (mm3 /mg)

4.44e−6 1.25e−5

5.1e−3 3.2e−3

0.18 0.35

−0.31 −0.29

0.22 0.52

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(a) Wetness distribution after preconditioning

(b) Wetness distribution during reflow at 260°C Fig. 15.15 Moisture absorption and desorption: (a) wetness distribution after preconditioning and (b) wetness distribution during reflow at 260◦ C

where εM is the hygro-strain and β is the coefficient of moisture expansion (CME). In ANSYS, since the temperature field is now replaced with moisture diffusion analysis, the sequential heat conduction/thermal stress analysis is replaced by the moisture diffusion/hygro-stress analysis. Figure 15.16 presents the hygro-mechanical

Fig. 15.16 Shear stress acting in molding compound at 260◦ C under hygro-mechanical loading

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1 0.5 0

0.6

Stress (MPa)

Stress (MPa)

0.8

Shear Stress Peeling Stress

0.4 0.2

–0.5

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

–1 –1.5 –2

Shear Stress Peeling Stress

–2.5 –3

0 0

0.5

1

1.5

2

2.5

3

3.5

–3.5 –4

–0.2

Distance (mm) (b) Path 2, C–D

Distance (mm) (a) Path 1, A–B 0.1

Stress (MPa)

0.05 0

0

0.5

1

1.5

2

2.5

3

3.5

4

–0.05 –0.1

Shear Stress Peeling Stress

–0.15 –0.2

Distance (mm) (c) Path 3, E–F

Fig. 15.17 Interfacial stress distribution from hygro-mechanical stress analysis at 260◦ C: (a) Path 1, A–B; (b) Path 2, C–D; and (c) Path 3, E–F

stress contour in molding compound. Thermal stress is not added yet. An integrated stress analysis will be presented in the next section. The interfacial stresses at different interfaces are plotted in Fig. 15.17. Similar trend as the thermo-mechanical stress is observed, i.e., the interfacial stress subjected to hygro-mechanical loading was dominated by shear stress at point C.

15.8 Integrated Stress Analysis The above two sections have discussed the thermo-mechanical and hygromechanical stress analysis separately. However, the packages are subjected to a combined hygrothermal loading during reflow with moisture preconditioning. Therefore, an integrated stress analysis is required to investigate the total package stresses during reflow. Tee et al. used an equivalent mean CTE method to consider both thermal and moisture effects: εT = α1 T εM = βCsat ⇒ α2 =

εM T

⇒ αtotal = α1 + α2 ,

εtotal = αtotal T,

(15.9) (15.10)

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where α 1 is the original CTE and α 2 is the equivalent mean CTE due to hygro-strain. In this method, the moisture distribution is considered uniform, i.e., the package is fully saturated. As a result, the equivalent mean CTE method assumes that the moisture distribution is uniform during reflow. In the present study, an alternative implementation using superposition method is developed, in which non-uniform moisture distribution and the induced hygrostresses are considered. In this approach, the pure thermal stress (or sequential thermal/stress analysis) and the hygro-stress (or sequential moisture/stress analysis) are executed separately. In pure thermal stress analysis, the temperature gradient can be considered without moisture effect. In hygro-stress analysis, the temperature field is replaced by a moisture diffusion field and therefore the non-uniform moisture distribution can be considered. Since the material is assumed to be linear elastic, the superposition can be applied. The integrated stresses are obtained by summing of two separate analyses as follows: εT = α1 T εM = βC

3 ⇒ σtotal = σT + σM .

(15.11)

The advantage of this approach is that the hygro-mechanical stress analysis is conducted as a function of time and temperature by considering the moisture desorption during reflow. It should be noted that the temperature field is already replaced by moisture. The solution to correlate the moisture field with temperature and time is to divide the reflow profile (shown in Fig. 15.9) into several sections. In each section, the temperature is assumed to be unchanged and the related moisture diffusion coefficient at certain temperature can then be calculated by using the Arrhenius equation [equation (15.7)]. Once the divided sections become shorter, the moisture analysis will be approached to a function of time and temperature during reflow. Figure 15.18 plots the stresses at different temperatures during reflow at point C. It can be seen that the hygro-mechanical stress does not change when temperature

0 160 –2

180

200

220

240

Stress (MPa)

–4 –6 –8 –10 –12 –14

Thermo-mechanical Stress Hygro-mechancial Stress

–16

Fig. 15.18 Stress change during reflow at point C

Integrated Stress

–18

Temperature °C

260

280

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8

10

7

5

6 Stress (MPa)

Stress (MPa)

0 5 Shear Shear Stress Stress Peeling Stress

4 3 2

0.5

1

1.5

2

–10 Shear Stress Peeling Stress

–15

1 0

0

–5

–20 0

0.5

1

1.5

2

2.5

3

3.5

–25

Distance (mm) (b) Path 2, C–D

–1 Distance (mm) (a) Path 1, A–B 0.5 0 0

0.5

1

1.5

2

2.5

3

3.5

4

Stress (MPa)

–0.5 –1 –1.5 –2 –2.5

Shear Stress Peeling Stress

–3 –3.5 –4

Distance (mm) (c) Path 3, E–F

Fig. 15.19 Integrated interfacial stress distribution at 260◦ C: (a) Path 1, A–B; (b) Path 2, C–D; and (c) Path 3, E–F

increases. This is because the local moisture concentration along the molding compound/leadframe interface remains unchanged during reflow. Figure 15.19 plots the integrated interfacial stress along three interfaces. Table 15.6 presents the new Y values for different locations based on the integrated stress analysis with moisture effect. Some observations can be made, which are as follows: (a) Y factor at point C increases about 22% compared to the pure thermal stress loading condition. This means a greater probability to fail when moisture effect is added. (b) Y factor at point C remains the highest among other locations. This means the delamination will initiate at molding compound/leadframe interface around the junction of the die attach fillet. The experimental validations were implemented with Test B. The C-SAM inspections in Figs. 15.20 and 15.21 showed that both Package 1 and Package 2 failed at this time. Significant delamination was found at molding compound/leadframe and molding compound/Si (die top) interfaces. From the C-SAM images, it appears that the delamination propagation direction follows the white arrows, which point from the junction of the die attach fillet toward the package

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Table 15.6 Calculation of integrated failure criterion factors Y

Maximum shear stress (MPa) Maximum peeling stress (MPa) YAg = [τ /S] YPPF = [τ /S]

(1) MC/Si (A−B)

(2) MC/LF (C–D)

(3) DA/LF (E–F)

A

B

C

D

E

F

0 0 0 0

7.20 2.94 0.72 0.72

−16.87 −9.55 1.50 2.23

3.92 −18.98 0.35 0.52

0 0 0 0

−1.81 −3.61 0.24 0.07

The bold numbers are the maximum value for failure factor comparison.

(a) C-scan image

(b) T-scan image

Fig. 15.20 C-SAM inspection of Package 1 after Test B: (a) C-scan image and (b) T-scan image

(a) C-scan image

(b) T-scan image

Fig. 15.21 C-SAM inspection of Package 2 after Test B: (a) C-scan image and (b) T-scan image

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edge. In addition, most of the delaminated areas (dark area) do not connect to the package edge, indicating that the delamination propagated to the package edge but not yet reached the end. It is believed that the delamination was initiated at the junction of the die attach fillet. For the interface between the molding compound and the top of the die, the delamination was generated at the edge of the die, which is consistent with finite element analysis. Furthermore, the cross-sectional analysis was carried out to determine if there was delamination at the die attach area. The scanning electron microscope (SEM) was used to photograph the failure modes at cross sections A–A (failure sample in Fig. 15.20) and B–B (failure sample in Fig. 15.21). From the SEM images shown in Figs. 15.22 and 15.23, it is clear that the delamination was initiated at the MC/LF interface. Also, the opening of the crack in Package 2 is much greater than that in Package 1. This is because Package 2 may already have failed under the pure thermal effect. That reveals that the delamination may initiate earlier in Package 2 and then the vapor pressure may be applied on the delaminated surface. Therefore, the delamination opening is larger in Package 2 due to the vapor pressure effect.

(a) Left part of cross-section A–A

(b) Middle part of cross-section A–A

(c) Right part of cross-section A–A

Fig. 15.22 SEM inspection of Package 1 after three times reflow at 260◦ C with MSL-3 preconditioning: (a) left part of cross section A–A, (b) middle part of cross section A–A, and (c) right part of cross section A–A

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(a) Left part of cross-section B–B

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(b) Middle part of cross-section B–B

(c) Right part of cross-section B–B

Fig. 15.23 SEM inspection of Package 2 after three times reflow at 260◦ C with MSL-3 preconditioning: (a) left part of cross section B–B, (b) middle part of cross section B–B, and (c) right part of cross section B–B

15.9 Discussion Fracture mechanics approach is a common method to predict the delamination by comparing the stress intensity factor (K) or the energy release rate (G) at different locations [1, 2, 11]. In order to derive K or G, a pre-crack is embedded in the finite element model. However, the finite element model with an embedded pre-crack is different from the real situation where the sample is intact before reflow. In addition, the simulation results based on the fracture mechanics method are dependent on the location and the length of the artificial pre-crack. Moreover, the method requires the interfacial fracture toughness. It has been very difficult to characterize the interfacial fracture toughness accurately. On the other hand, the stress ratio approach proposed in this study has advantages compared to fracture mechanics approach such as simpler modeling without pre-crack and available experimental test data on adhesion strength. There are some issues with stress ratio approach. One of those issues is the stress mesh-dependent problem. This problem is less critical if a trend analysis is performed using the stress ratio Y as a failure criterion. Normally when Y>1, failure

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happens. However, Y used in our study represents a possibility of failure. A higher value of Y means a higher opportunity to failure. The main idea of this study is to compare the values of Y in all interfaces to find the most critical locations in packages. When mesh density increases, the results of comparison of stress ratio Y does not change. Another issue in this study is that the interfacial strength is determined at room temperature without moisture. It has been found that room temperature adhesion may not represent the adhesion at high temperature with moisture [8]. In addition, both thermo-mechanical and hygro-mechanical models in the present study use the linear elastic material properties. This would be different from the real situation in that the electronic materials behave as viscoelastic at high temperature. Vapor pressure is another key factor which is usually considered in the moisturerelated failures. Many papers have discussed the applications of vapor pressure calculations (e.g., in [12, 8, 13, 9]). However, there are some issues with the vapor pressure calculations at high temperature. Therefore, we assume that the major contribution of vapor pressure is to induce the crack propagation. In this study, the main concern is focused on the delamination initiation.

15.10 Concluding Remarks A combination of finite element analysis, material characterization, and physical prototype methodology has been established to evaluate the package reliability against delamination during reflow. Both simulation and experimental validations have been implemented to study the failure mechanisms of interfacial delamination. The work can be summarized as follows: (a) Two types of dummy QFN packages have been fabricated as test vehicles. Experimental tests with pure thermal effect and hygrothermal effect on dummy packages were conducted. Detailed inspections of delamination were performed to characterize the failure modes. (b) A finite element model for dummy QFN package subjected to pure thermal loading and hygrothermal loading has been built for stress analysis. For both analyses, the shear stresses were found to be the dominant stress component along all interfaces. The maximum stress value appeared at MC/LF interface around the junction of the die attach fillet. (c) A superposition method was developed to integrate the thermo-mechanical and hygro-mechanical stresses together by considering the non-uniform moisture distribution during reflow. Since the local moisture concentration did not change much along the interfaces when temperature increased, the hygro-mechanical stress change was not obvious. As a result, the integrated stress changes with temperature, which is similar to the thermo-mechanical stress change. (d) Based on the results of stress calculations and adhesion measurement, stress ratio approach was employed to evaluate package reliability and to identify

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the delamination initiation locations. The analyses of stress ratio approach agreed well with the experimental results. Package 1 with silver-plated leadframe has better reliability against delamination than does Package 2 (with PPF leadframe). Also, the delamination is believed to be initiated at the molding compound/leadframe interface around the junction of the die attach fillet in dummy QFN package. Acknowledgments This study was sponsored by Ablestik and Henkel through a grant ICI001N to HKUST. The authors would like to acknowledge this support.

References 1. Tee, T.Y., Zhong, Z.W., “Integrated vapor pressure, hygroswelling, and thermo-mechanical stress modeling of QFN package during reflow with interfacial fracture mechanics analysis,” Microelectronics Reliability, 44, 105–114, 2004. 2. Driel, W.D., van Gils, M.J., Fan, X.J., “Driving mechanisms of delamination related reliability problems in exposed pad packages,” IEEE Transactions on Components and Packaging Technologies, 31(2), 260–268, 2008. 3. Zhang, M.S., Lee, S.W.R., Fan, X.J., “Stress analysis of hygrothermal delamination of quad flat no-lead (QFN) packages,” ASME IMECE, Boston, MA, November 1–6, 2008. 4. Zhang, M.S., Lee, S.W.R., “Investigation of moisture sensitivity related failure mechanism of quad flat no-lead (QFN) packages,” ASME IMECE, Boston, MA, November 1–6, 2008. 5. Joint Industry Standard J-STD-020D, Moisture/Reflow Sensitivity Classification for Plastic Integrated Circuit Surface Mount Devices, IPC (The Institute for Interconnecting and Packaging Electronic Circuits) and JEDEC (Joint Electron Device Engineering Council), 2007. 6. Lau, J.H., “A note on the calculation of thermal stresses in electronic packaging by finite element methods,” Journal of Electronic Packaging, 111, 313–320, 1989. 7. Wong, E.H., Teo, Y.C., Lim, T.B., “Moisture diffusion and vapor pressure modeling of IC packaging,” Proceedings of the 48th Electronic Components and Technology Conference, Seattle, WA, USA, pp. 1372–1378, 1998. 8. Fan, X.J., Zhang, G.Q., van Driel, W.D., Ernst, L.J., “Interfacial delamination mechanisms during reflow with moisture preconditioning”, IEEE Transactions on Components and Packaging Technologies, 31(2), 252–259, 2008. 9. Xie, B., Fan, X.J., Shi, X.Q., Ding H., “Direct concentration approach of moisture diffusion and whole field vapor pressure modeling for reflow process: part I – theory and numerical implementation,” ASME Journal of Electronic Packaging, 131(3), 031010, 2009. 10. ASTM D570, Standard Test Method for Water Absorption of Plastics. West Conshohocken, PA: ASTM International, 1998. 11. Tay, A.A.O., “Modeling of interfacial delamination in plastic IC packages under hygrothermal loading,” Journal of Electronic Packaging, 127, 268–275, 2005. 12. Fan, X.J., Zhou, J., Zhang, G.Q., Ernst, L.J., “A micromechanics-based vapor pressure model in electronic packages,” ASME Journal of Electronic Packaging, 127, 262–267, 2005. 13. Lau, J.H., Lee, S.W.R., “Temperature-dependent popcorning analysis of plastic ball grid array package during solder reflow with fracture mechanics method,” Journal of Electronic Packaging, 122(1), 34–41, 2005.

Chapter 16

Industrial Applications of Moisture-Related Reliability Problems W.D. van Driel, D.G. Yang, C.A. Yuan, and G.Q. Zhang

16.1 Introduction Moisture preconditioning is required prior to reliability testing for all microelectronic devices that are surface mounted to boards. Moisture sensitivity/reflow tests are introduced as a requirement for plastic packages because of “popcorning” failures during surface mount reflow process. The popcorn effect results from expanding steam that is evolved during reflow process. Popcorning problems were first reported in 1985 by Fukuzawa et al. [1]. Others continued this study and conducted a series of work on moisture diffusion, the dynamics of moisture diffusion, hygro-thermal stresses evaluation, and delamination in plastic packages [2–7]. A micro-mechanics approach was introduced to study the whole-field vapor pressure evolution during reflow [8, 9], and the vapor pressure model has been validated experimentally by many case studies [2, 7, 9]. Plastic packages are subjected to moisture during assembly, storage, and transport. Moisture sensitivity/reflow tests insure that these conditions are met before assessing the reliability. As such, moisture sensitivity levels (MSLs) are introduced, MSL from 1 to 6, with 1 being the most severe and 6 being the least severe, according to JEDEC standards. Examples are 1. MSL1: unlimited floor life under a 85% RH and a temperature lower than 30◦ C. In a MSL assessment, IC package should withstand a preconditioning at 85◦ C/85% RH for a period of 168 h, followed by reflow process 2. MSL3: limited floor life of 168 h under a 60% RH and a temperature lower than 30◦ C. In a MSL assessment, IC package should withstand a preconditioning of 30◦ C/60% RH for a period of 168 h, followed by reflow process 3. MSL6: limited floor life of 6 h under a 60% RH and a temperature lower than 30◦ C. In a MSL assessment, IC package should withstand a preconditioning of 30◦ C/60% RH for a period of 6 h, followed by reflow process

W.D. van Driel (B) e-mail: [email protected] X.J. Fan, E. Suhir (eds.), Moisture Sensitivity of Plastic Packages of IC Devices, Micro- and Opto-Electronic Materials, Structures, and Systems, C Springer Science+Business Media, LLC 2010 DOI 10.1007/978-1-4419-5719-1_16, 

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For each package the MSLs are obtained via a so-called MSL assessment (MSLA). In a MSLA, packages are subjected to different MSLs and are subsequently placed in a reflow oven for simulated reflow process. C-mode surface acoustic microscopy (C-SAM) is usually used to inspect delamination failures in packages. Figure 16.1 shows an example of C-SAM images for exposed pad-type packages under different MSLs. The C-SAM analysis shows major delamination at MSL1 and no delamination for MSL3. The transition is at MSL2 where only one package shows minor delamination. The MSL for this package is qualified as a MSL3 package. MSL1

MSL2

MSL3

Fig. 16.1 C-SAM images at various MSLs

The above example explains that moisture is hazardous for interface delamination in a microelectronic device. Interface delamination during reflow can be a root cause of several subsequent reliability problems, such as die crack, body crack, and/or wire bond fatigue during further operation of the device [10], or subsequent reliability tests, such as temperature cycling (TMCL), and highly accelerated stress test (HAST). Figure 16.2 shows the progression of delamination (in white) at die-mold compound interface after MSL1 and TMCL testing. As the number of TMCL cycles increases, the delaminated area progresses. But the onset is caused by moisture ingression. Figure 16.3 lists the observed failure modes that are moisture related. They can be categorized into three groups: delamination (at various interfaces within the device), wire failures (stitch break, ball bond lift, and wire fatigue), and crack failures (body crack, substrate crack, and die crack). In this chapter, three different industrial application studies are presented. Substrate-based BGA packages, leadframe-based wire bond packages, and systemin-packages are investigated under different stress conditions. Experiments and

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Industrial Applications of Moisture-Related Reliability Problems

MSL1

TMCL200

413

TMCL500

TMCL1000

TMCL1500

TMCL2000

Fig. 16.2 Progression of delamination (in white) during temperature cycling after reflow Delamination

Wire Failures

Crack Failures

Fig. 16.3 Moisture-related failure modes in packages

theoretical/numerical modeling are applied to understand, predict, qualify, optimize, and design microelectronic devices against moisture sensitivity requirements.

16.2 Application 1: Wire Bond Reliability of a BGA Package Subjected to HAST This study investigates the prevention of moisture-induced wire bond failures in a BGA package. Fifty percent broken stitch bonds were observed during package development under HAST [11]. In this study, moisture diffusion and subsequent thermo-mechanical moisture simulations are performed with the consideration of delamination during a reflow process. The simulation results for different molding compounds are compared to the experimental observations during HAST qualification testing.

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16.2.1 Description of the Carrier A BGA package with low alpha radiation compound showed 50% failures (broken stitch bonds) during combined thermal-moisture HAST qualification testing due to the excessive delamination of different interfaces. Figure 16.4 plots the package configuration. The package is very thin in nature with a relatively large size. The observed failures are shown in Fig. 16.5, indicating a broken stitch bond and the delamination at compound/substrate interface. Three different molding compounds were experimentally evaluated, and different behaviors were observed: • Compound A: failed qualification with severe delamination at compound/substrate interface and significant stitch breaks (see Fig. 16.5) • Compound B: just within qualification limits, some delamination at compound/substrate interface • Compound C: qualified with minor delamination

Fig. 16.4 A BGA package configuration

Fig. 16.5 Observed stitch failure after HAST test (with compound A)

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Virtual qualification is initiated in order to understand the observed failure modes and differences between the molding compounds used.

16.2.2 Material Characterization All polymer materials in the BGA package are characterized with regard to their moisture and thermo-mechanical behaviors. The diffusivity D and the saturated moisture concentration Csat are determined under 85◦ C/85% RH (equal to MSL1) conditions. For the determination of hygroscopic swelling coefficient, TMA/TGA experiments are performed at 130◦ C on saturated samples. The thermo-mechanical behavior of the polymers is measured using TMA and DMTA techniques. With the DMTA a full viscoelastic characterization of the materials is determined. Table 16.1 lists the measured material properties. The moisture uptake is normalized with the saturated moisture concentration Csat of molding compound B. The coefficient of hygroscopic swelling for the substrate differs significantly in x-, y-, and z-directions due to its orthotropic nature. Table 16.1 Material properties

D/DB Csat /Csat,B CME/CMEB CTE2 (ppm/K) Tg (◦ C) CTE1 (ppm/K)

Compound A

Compound B

Compound C

Substrate

0.33 0.48 1.1 11 155 35

1.0 1.0 1.0 17 189 62

0.35 0.35 1.8 6 108 35

0.25 0.87 xy: 0.3; z: 2.0 xy: 16; z: 51 178 xy: 16; z: 239

The following material models are used for different materials: • The silicon is modeled as a linear elastic material. • The substrate is modeled as an orthotropic-layered material taking into account the thickness and density of copper layers. These copper layers are modeled as an ideal elasto-plastic material. • The gold wire is modeled as an ideal elasto-plastic material. • All polymeric materials are modeled using visoelastic- and temperaturedependent properties. The temperature- and time-dependent properties of the polymers were measured using DMA. The master curves from the measurement data can be built by using the time–temperature superposition principle. A generalized Maxwell model is used to describe their viscoelastic behaviors, and the shift factor is described by the WLF equation [12]. Table 16.2 lists the relaxation times and the corresponding Prony coefficients for the molding compound B. The reference temperature is chosen as 25◦ C, and the constants C1 and C2 for the WLF equation are determined to be 73.79 and 298.15, respectively.

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Table 16.2 Relaxation times and corresponding Prony coefficients of molding compound B No

Relaxation times τ n (s)

Coefficients En (MPa)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

1.00E–32 1.00E–26 1.00E–20 1.00E–14 1.00E–08 1.00E–02 1.00E+04 1.00E+09 3.16E+12 3.16E+14 1.00E+16 1.00E+17 3.16E+18 3.16E+20 1.00E+23

8.66E+02 9.63E+02 8.54E+02 7.74E+02 7.46E+02 7.94E+02 8.80E+02 9.57E+02 1.11E+03 2.90E+03 2.75E+03 8.14E+03 4.54E+03 1.26E+03 4.88E+02

16.2.3 Finite Element Modeling The temperature and humidity conditions during HAST test (130◦ C/85% RH, 96 h) are simulated using commercially available finite element software combined with additional user subroutines. These simulations consist of two consecutive steps: a combined temperature and moisture diffusion simulation, followed by a thermo-mechanical simulation with temperature and moisture field solutions as input. The initial stress-free temperature is the process temperature of 175◦ C. The characteristics of temperature and moisture simulations are the following • Temperature is assumed homogeneous in the package due to the large timescales compared to moisture diffusion. • At the beginning of the HAST condition, moisture boundary condition is set to C/Csat = 1 at the exterior of the package. • The predicted moisture profile after the HAST loading step is further maintained during the cooling down step to simulate the effect of removing the package from the test chamber. • The presence of copper layers in the substrate is taken into account by reducing the diffusivity and moisture concentration relative to the percentage copper. The characteristics of thermo-mechanical simulations are the following: • The effect of delamination between molding compound and substrate/die on resulting strains/forces on the wire is investigated. The delamination is modeled using contact bodies.

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• In order to predict strains/forces on the wire, the wire is modeled as a frictionless contact body within the compound, allowing the wire to move within the compound (tunneling effect). This simulates the lack of adhesion due to the inert properties of the gold with respect to the molding compound. • The wire remains attached to the die and leadframe regardless whether delamination between compound and substrate exists.

16.2.4 Results Figure 16.6 plots the moisture concentration contours in the package using the three different compounds. In all cases, the package is almost saturated after the HAST test. Mold compound B absorbs moisture most, followed by A and then C.

A

B

C

Fig. 16.6 Predicted moisture concentration C/Csat after HAST with three different molding compounds (from top to bottom A, B, and C, respectively)

Using the predicted moisture diffusion distributions combined with the thermomechanical loading, the displacements and stresses due to the HAST test are simulated for the three different molding compounds with or without delamination between molding compound and substrate. Figure 16.7 plots the predicted forces on the stitch bond at the end of the HAST test, with and without delamination. It appears that delamination has a greater impact on the forces for compound A and C than B. Actually, for compound B delamination has a marginal effect making this compound a very robust solution. This is consistent with the experimental observations, in which delamination occurred for A and B, but wire break happened in the package with mold compound A only. Compound C exhibits no delamination in HAST. However, the simulation indicates that if delamination is present, potential stitch problems would arise.

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Normalised forces on stitch

4.0E+00 3.5E+00 3.0E+00 2.5E+00 2.0E+00 1.5E+00 1.0E+00 5.0E–01 0.0E+00

MCA

MCB

MCC

MCA

Nodelam

MCB

MCC

Delam

Fig. 16.7 Predicted normalized forces on the stitch bond at the end of HAST testing for three compound types with and without delamination

To further assess the relationship between moisture content and delamination, simulation is performed for the packages with compound type A, B, and C subjected to a MSLA (MSLs 1, 2, and 3). Figure 16.8 shows the moisture concentration at the compound/substrate interface. Combining this with the experimental observations yields a threshold beyond which the package would fail by stitch cracks. 1.4E–02

C [mgr/mm3]

1.2E–02 1.0E–02

critical for delamination at reflow (by comparison with exp. observations)

8.0E–03 6.0E–03 4.0E–03 2.0E–03 0.0E+00 MCB, MSL3

MCC, MSL3

MCC, MSL2

MCB, MSL1

MCC, MSL1

MCA, MSL1

Fig. 16.8 Moisture concentration at compound/substrate interface (glue fillet area) for compounds A, B, and C under different MSLs

16.3 Application 2: Moisture-Related Structural Similarity Rules Structural similarity determines the extent to which test results from a specific device or family can be considered representative for other similar types [13]. When applied to reliability aspects, structural similarity is indispensable in predicting the

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reliability performance of types similar to those that have been specifically subjected to reliability testing. The need for having structural similarity rules is not only because reliability testing of every type is time and money consuming but also because it is often unnecessary to test all due to the inherited similarity of products. Structural similarity rules for IC designs, wafer fabrication processes, and/or package designs are currently used by the industry to define efficient Qualification and Reliability Monitoring programs. They imply that the reliability results from one product may be used for others if they meet the structural similarity criteria. It is evidential that in the case where a full qualification program is needed, time-tomarket and costs will increase significantly. Thus, any qualification data that can be used to minimize the additional testing will be more cost efficient. For assembly and packaging, a structurally similar package means that it • • • • • • •

belongs to the same package type, such as BGA, QFP, or others, has the same or smaller body size, has the same or larger inner, outer lead or ball spacing, has the same or smaller die–pad size, has the same or smaller die size, has the same materials, for leadframe/die attach/molding compound, and has the same construction characteristic, such as exposed die–pad or fused leads.

By following the package structural similarity rules, the numbers of reliability qualification tests may be greatly reduced. However, when looking at these rules it is clear that they are not reliably defined. For instance, geometrical parameters such as die-to-pad ratio are not quantitatively included and it seems that linear relationships are assumed. Besides that, these rules are mainly deducted from experience and industrial trial–error results, not from reliability physics. This section highlights the results to develop moisture-related structural similarity rules using the state-of-theart virtual prototyping techniques.

16.3.1 Description of the Carrier A variety of leadframe-based plastic packages exist ranging from dual-in-line (DIP), small outline (SO), quad flat packages (QFP) to exposed pad packages such as HTQFP, HTSSOP, and HVQFN. The exposed pad is a standard feature for QFN (quad flat no-lead) packages. For leaded packages with a gull wing lead, exposed pad products are made using leadframes with a deep-downset paddle which is exposed to the outside of the package after the mold process. Figure 16.9 shows some examples of leadframe-based package families. On the other hand, ball grid array (BGA) packages are developed based on multi-layer plastic substrates. The BGA family allows for low profiles and outlines and is currently widely used for high-density I/O packages. Many different variations are available, such as TFBGAs, μBGAs, HBGAs, die up or die down, and tape based (see Fig. 16.9).

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Fig. 16.9 Examples of the leadframe- and substrate-based package family Table 16.3 Parameter ranges for both package types Parameter

Leadframe based

Substrate based

Body size (mm2 ) Body thickness (mm) Pad-to-body ratio (%) Die-to-pad ratio (%) Die thickness (μm)

1 × 1 to 60 × 60 0.5–7.5 15–95 15–95 10–500

4 × 4 to 44 × 44 0.9–1.9 15–80 15–95 280–380

In order to conduct the virtual prototyping study, the total design space of both package families is parameterized. Table 16.3 lists the ranges of some parameters. In a substrate-based package, the die-to-pad ratio is defined as the ratio between the die size and the copper pad structure in the substrate.

16.3.2 Material Characterization Table 16.4 shows MSL data (the level that can be reached before failures are detected) for some typical substrate-based packages, with varying body size,

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thickness, pad-to-body ratio, and die-to-pad ratio. The table contains some conflicting data. For instance, for the LBGA packages with a 17 × 17 mm2 body size, the package with the 61% pad-to-body ratio leads to Level 1, but the one with a 42% ratio to Level 2. It is evident that MSL is more dependent on the die-to-pad ratio. Other conflicting data holds for the BGAs, where increasing the body size to 40 × 40 mm2 may lead to a decreased MSL compared to a body size of only 17 × 17 mm2 (which gives Level 4, again due to the high die-to-pad ratio). For the LFBGA packages, the largest body with the largest die-to-pad ratio leads to the highest MSL, being 2. But what would be the result when instead of 54% a ratio of 35% is used? Virtual prototyping techniques are required in order to understand those package parameters that determine its moisture sensitivity. Table 16.4 MSLs for some typical substrate-based packages Package type

Body size (mm3 )

Pad-to-body ratio (%)

Die-to-pad ratio (%)

MSL

BGA208 BGA217 BGA225 BGA272 BGA329 BGA388 BGA596 LBGA224 LBGA256 LBGA324 LFBGA64 LFBGA72 LFBGA208

17 × 17 × 1.2 23 × 23 × 2.6 27 × 27 × 1.55 27 × 27 × 1.55 31 × 31 × 1.75 35 × 35 × 1.75 40 × 40 × 1.75 17 × 17 × 1.05 17 × 17 × 1.05 19 × 19 × 1.05 7 × 7 × 0.9 7 × 7 × 0.9 15 × 15 × 1.05

28 33 38 26 28 35 43 42 61 48 57 58 57

89 63 80 89 85 91 80 89 65 84 36 36 54

4 3 2 2 2 3 3 2 1 2 1 1 2

16.3.3 Finite Element Modeling 3D non-linear parametric FE models are constructed and are experimentally verified in order to calculate the moisture-related responses, i.e., (i) moisture content and (ii) moisture concentration at the relevant package interfaces. Moisture diffusion modeling described in Chapter 4 is implemented in a commercial FE software. Figure 16.10 shows a comparison between predicted and measured moisture content for a series of substrate-based and leadframe-based packages after 168 h of MSL3 conditions, respectively. For the substrate-based family, 2D and 3D FE models are compared to the experimental results. Both models give good agreement. Consistent results are also obtained for leadframe-based packages. Using the advanced simulation-based optimization methods, such as sequence DOE, stochastic RSMs, and adaptive (sequential) techniques [10, 14, 15], moisture diffusion responses under MSL3 conditions are calculated for a complete design space of both package families.

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Substrate-based - MSL3 Moisture weigth [%]

measured simulated_3D simulated_2D

0.30 0.25 0.20 0.15 0.10 0.05

Moisture weigth [%]

0.07

0.35

0.00

measured simulated_3D

0.06 0.05 0.04 0.03 0.02 0.01 0.00

LBGA256 17×17×1.05

LBGA324 19×19×1.05

HLQFP144 20x20x1.4

BGA596:8.32mm die 40×40×1.75

QFP44 14x14x2.67

LQFP208 28x28x1.4

HVQFN48 7x7x0.85

b)

a)

Fig. 16.10 Predicted versus measured moisture content under MSL3 conditions for (a) substratebased and (b) leadframe-based packages

16.3.4 Results A space-filling Latin-hypercube design is constructed [10], consisting of 100 simulation runs to produce sufficient RSM models. Using the parametric nonlinear 3D FEM models, FEM simulations are carried out for all 100 designs and the output variables (moisture mass and concentration) are used as the response parameters. For all response parameters quadratic models with interactions are used for RSM generation. Using an automatic running procedure based on cross-validation, the unimportant model terms were eliminated. The regression statistics are between 0.95 and 0.98 indicating that for all quadratic models the accuracy requirements are satisfied. Table 16.5 lists the relative importance of the linear polynomial terms describing the RSM functions for moisture mass and moisture concentration. The following can be observed from this table:

Table 16.5 Normalized relative importance of the linear polynomial terms for both response parameters. Moisture concentration is calculated on leadframe/EMC and substrate/EMC interface Leadframe based

Substrate based

Parameter

Moisture mass

Moisture concentration

Moisture mass

Moisture concentration

Body size Body thickness Die thickness Pad-to-body ratio Die-to-pad ratio Leadframe/substrate thickness

1.00 0.42 0.01 −0.05 −0.03 0.04

–0.38 1.00 −0.25 0.25 −0.25 0.13

1.00 0.12 −0.01 −0.01 −0.02 0.01

−0.01 1.00 −0.02 −0.04 −0.08 0.23

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• For moisture mass in the package, the body size and the body thickness are the most dominant parameters. The bigger and thicker the package is, the more moisture the package absorbs. For leadframe-based packages, thickness stands out compared to other parameters. • For moisture concentration at critical interfaces, body size and leadframe or substrate thickness are dominant parameters. For substrate-based packages, die thickness, die-to-pad ratio, and pad-to-body ratios seem to have no significant influence. The reason for this is that the dominant path for moisture to ingress into the interface is through the substrate. For leadframe-based packages, there are multiple equal pathways, being (i) top, (ii) side, and (iii) bottom of the package. The larger the body is, the longer it will take the moisture to ingress to the interface. This explains the negative term for body size. The same holds for die thickness and die-to-pad ratio. However, with a larger pad-to-body ratio, the ingression distance via the package side is shorter. Figures 16.11 and 16.12 show the 3D plots of two response parameters as a function of the dominant input parameters: pad-to-body versus die-to-pad ratios (Fig. 16.11) and body thickness versus size (Fig. 16.12). These 3D responses describe the structural similarity rules for both package families. The moisture concentration at the interfaces is responsible for interface delamination during reflow and subsequent qualification testing [16]. Figure 16.11 shows that when the die-to-pad ratio increases, the risk of interface delamination increases. This explains the MSL results shown in Table 16.3. Figures 16.11 and 16.12 also show that the moisture content in a substrate-based package is a factor 2–4 higher than in a leadframe-based package. This holds for local moisture concentration as well. This does not mean that interface delamination will occur more often in substrate-based packages. On the contrary, failure is often observed in thin leadframe-based packages (for the thick ones it takes too long time for the moisture to reach the interface). This is due to the fact that the interface strength between leadframe and compound is quite low. Figure 16.13 shows the moisture concentration at the die/compound interface for the leadframe-based family. The figure illustrates that for very thick packages, almost no moisture will reach the interface under MSL3 conditions. This occurs for packages with a thickness above 3–4 mm. In this case, no MSLA is required for such packages (the so-called DIP types). The structural similarity rules can be deduced from Figs. 16.11, 16.12, and 16.13, and it becomes very clear that the die-to-pad ratio is an important parameter in the eventual response of both package families. It is therefore advised to include this ratio into the structural similarity rules. The following two rules should be eliminated: • Same or smaller die–pad size, • Same or smaller die size.

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Moisture mass

Moisture concentration

Leadframe-based

Substrate-based

Fig. 16.11 3D responses as a function of pad-to-body and die-to-pad ratios

The strength of the presented optimization technique is that the global non-linear response of package families can be captured in the earliest phases of package development by the response surface models. These models are no more than (polynomial) relationships describing the responses as function of input variables. The polynomial formulas can be transported into easy software tools such as Excel.

16.4 Application 3: Moisture Sensitivity of System-in-Packages Since the last few years, the focus in microelectronics is gradually changing from front-end to packaging. System-in-package (SiP) is an answer for the ongoing function integration trend. In SiP, several dies are placed into one package, either side-by-side or stacking in vertical direction. Several stacking die technologies have been developed. For stacked die packages, a spacer is required between each die

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Moisture mass

Moisture concentration

Leadframe-based

Substrate-based

Fig. 16.12 3D responses as a function of body size and thickness

Fig. 16.13 3D responses for the die/compound interface in leadframe-based packages

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to provide room for the wire bond loop height. Both silicon spacer and ball spacer are used in industry. In silicon-spacer technology, a thin piece of silicon is used to separate the active dies in the stack. In ball-spacer technology, this is accomplished with a filler-filled die attach. Even though the fundamental principles of SiPs and single-die packages are similar, the range of applications requires a variety of different manufacturing processes. SiP development leads to an increased probability of failures due to an increased design complexity. Thermo-mechanical reliability issues have been identified as major bottlenecks in the development of future microelectronic components [10]. Introducing stacks into the package redistributes the stresses in the package and generates more interfaces. There is an increased risk and/or vulnerability for cracks and interface delamination during assembly and/or reliability testing. Therefore, it is imperative to investigate the moisture sensitivity of SiPs and to evaluate the package reliability. In this section, an integrated hygro-thermo-mechanical stress modeling is performed for a stacked-die QFN package to evaluate the package reliability. Virtual prototyping techniques are used to explore the stress/strain “hotspots” in the packages. And further the design space is explored by using optimization techniques.

16.4.1 Carrier Description In the silicon-spacer concept, a thin piece of silicon is used to separate the active dies in the stack. In the glue-spacer concept this is accomplished with a fillerfilled die attach. Figure 16.14 shows schematically both stacking concepts for two dies.

Fig. 16.14 Investigated stacking concepts

Daughter die

Daughter die

Mother die

Mother die

Silicon spacer

Ball spacer

Introducing stacks of such a stiff material, silicon, into the package increases the bending resistance and generates more interfaces. Associated with that is the increased risk and/or vulnerability for cracks and interface delamination during assembly and/or reliability testing, either in the package body (molding compound) or in the die itself. From the experiences of package development, failure modes, such as die crack, body cracking, interface delamination between die–pad/glue and die or leadframe and EMC, and die stack delamination, are possible. Figure 16.15 shows two examples of such failures. In order to prevent these failures in stacked SiP, important issues such as moisture sensitivity and design spaces need to be explored [17].

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Fig. 16.15 Fractures within package body (left) and silicon die (right)

16.4.2 Finite Element Modeling The 2D parametric models are developed to investigate the thermo-mechanical reliability issues, especially the moisture sensitivity of the SiPs. Because of the structure symmetry, only one quarter of the package is modeled. FE models are constructed for both stacking concepts in a QFN package. Figure 16.16 shows the models. For the material properties, the silicon die is considered as isotropic and elastic. The leadframe is assumed as elasto-plastic. The molding compound and the glues are modeled as viscoelastic. All appropriate materials (molding compound, substrate, and die attach) have been characterized with regard to their moisture behavior under MSL1 conditions. The material properties are listed in Tables 16.6 and 16.7.

Fig. 16.16 FE models of stacked QFN packages

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Material

CTE (ppm/K)

E modulus (MPa)

Poisson’s ratio

Yield stress (MPa)

Silicon Leadframe Compound

3.0 17 α 1 = 8; α 2 = 32 (Tg =110◦ C) α 1 = 40; α 2 = 140 (Tg =75◦ C) α 1 = 55; α 2 = 130 (Tg = −30◦ C)

169,000 130,000 Viscoelastic

0.23 0.35

− 600

Glue 1 Glue 2

Viscoelastic Viscoelastic

Table 16.7 Moisture properties Material

CME (mm3 /mg)

Csat (mg/mm3 )

D (mm2 /s)

Silicon Leadframe Compound Glue 1 Glue 2

0 0 0.35 0.3 0.3

0 0 4.72E−3 7.6E−3 4.41E−3

0 0 1.57E−6 1.25E−5 1.25E−5

The temperature loading applied is from the post-mold cure temperature (175◦ C), preconditioning (MSL1), reflow (peak temperature of 260◦ C), and temperature cycling. Moisture loading is applied to the package surfaces only during the preconditioning period.

16.4.3 Results Figure 16.17 shows the moisture concentration over the package cross-section at three different time periods under the MSL1 conditions and compares the silicon- and ball-spacer concept. Clearly, the package is not fully saturated after MSL1. This is in contrast to a single die QFN, which will be fully saturated after MSL1. The moisture gradients are input for further hygro-thermo-mechanical stress calculations. Looking at the calculated stress/strain responses, the FE results identify the hotspots for the two stacking concepts. These hotspots are • • • • • •

Package warpage Die-crack for mother, daughter, and spacer die Die-to-spacer delamination Die-to-compound delamination Compound-to-frame delamination Body crack

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10 hr

50 hr (a) Silicon spacer

168 hr

10 hr

50 hr (b) Glue spacer

168 hr

Fig. 16.17 Moisture concentration contours both stacking concepts in a SiP

260°C

–65°C

Fig. 16.18 Warpage of Si spacer QFN package

Figure 16.18 shows the vertical displacement contours at reflow temperature and the lowest temperature of temperature cycling (–65◦ C). The vertical displacement at the bottom corner is used as an indication of the warpage, and the simulation results indicate that when cooling down to room temperature from preconditioning the moisture swelling causes 30–40% more warpage. Overall, the glue-spacer concept has a slightly higher warpage than the silicon-spacer concept (about 10%). A typical stress response is shown in Fig. 16.19. In this figure, the principal stress maximum in the die for the silicon-spacer concept after MSL1 and at reflow temperature is shown. The corresponding stress “hotspots” are at the center of the top surface of the daughter die and the center of the bottom of the mother die. The results indicate that the silicon-spacer concept has a slightly higher stress in the daughter die, but a slightly lower stress in the mother die. Moisture absorption and swelling have slight influence on the stress level in the die. Figure 16.20 shows the stress distribution in the molding compound. Among all the loading phases, maximum stress level in molding compound occurs at the lowest temperature. The hotspots for the compound stress are at the area around mother die glue fillet, the corner with the leadframe, and the central part above the

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(85°C after MSL1)

(260°C reflow temperature)

Fig. 16.19 Stress response for the silicon-spacer concept

Si spacer concept

Glue spacer concept

Fig. 16.20 Principal stress maximum in the molding compound

die. Overstress in the compound may initiate body cracking. The results show that the moisture swelling has slight influence on the compound stress. Both concepts give similar results. Figure 16.21 presents the interface stress plots for the silicon-spacer concept. For the interface between the daughter die and the glue (A1–A2), highest stress level can be found at the overhanging point. Whereas for the interface of mother die/glue/leadframe, critical point is at the die edge, where the maximum shear stress occurs. Simulation results indicate that moisture swelling has no significant effect on the values of the interface stress. However, it should be noted that generally moisture absorption into the die attaches and the interfaces may significantly reduce the adhesion strength. The design parameters play an important role for stress/strain response. Given the six hotspots mentioned above, optimization techniques can be used to explore the design space for preventing these failures. A space-filling Latin-hypercube DOE consisting of nine input parameters and over 100 calculations is constructed. Using the parametric non-linear 2D FEM models, FEM simulations are carried out for all the 100 numerical experiments, and the earlier mentioned output variables (hotspots) are used as the response parameter. For all response parameters quadratic models with interactions are used for RSM generation. Using OPTIMUS

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Equivalent interface stress (MPa)

16

70

431

Si spacer

60 –65C

50 40

25C after MSL1

30

reflow 260C

20 10 0 0.00

0.50 1.00 1.50 Distance from center (mm)

2.00

Equivalent interface stress (MPa)

(a) 120

Si spacer

100 –65C

80 25C after MSL1

60 40

reflow 260C

20 0 0.00

0.50

1.00

1.50

2.00

Distance from center (mm)

(b)

Fig. 16.21 Interface stress plot for the Si spacer concept: (a) interface between daughter die and glue 2 and (b) interface between mother-die and glue 1

[18] automatic running procedure based on cross-validation, the unimportant model terms were deleted. The regression statistics are indicated that for all quadratic models the accuracy requirements are satisfied (in all cases: R2 > 0.9). Figure 16.22 shows a typical result of the optimization process. The figure shows the stress in the daughter die as a function of its thickness and the thickness of the spacer die for a 12 × 12 mm2 body size, a 75% pad body ratio, a 90% die pad ratio, and a 200-μm leadframe thickness. Assuming an allowable stress level of 150 MPa for silicon [10], a clear risk area can be identified: a thick daughter die with a thick spacer in between. The following design rule can be deducted from this: the silicon spacer should always be thinner than the thickness of the die on top of it. This is

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Fig. 16.22 Response surface for daughter die crack in QFN: daughter die versus spacer die thickness

independent on the amount of stacks created. Other significant parameters that play a role for this stress response are – Body size: larger is worse – Die-to-pad ratio: larger is worse – Leadframe thickness: thinner is better Figure 16.23 shows the response surface for the stress in the compound as a function of pad-to-body and die-to-pad ratio. Other parameters are fixed to 12 × 12 mm2 body size, 150 μm stacked die thickness, 150 μm spacer die thickness, and 200 μm leadframe thickness. For compounds, typical strength is in the order of 80–100 MPa [10]; in Fig. 16.23 this value is not reached. But the figure indicates that when increasing the number of stacks in the package, this risk will be a realistic one. The figure also indicates the effect of the die-to-pad ratio on the stress response

Fig. 16.23 Response surface for compound crack in QFN: pad-to-body versus die-to-pad ratio

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in the compound. While increasing the ratio, the risk for body crack is higher. This needs an experimental verification. A design rule that can be deducted should relate the number of stacks with the maximum allowable.

16.5 Conclusions This chapter shows that the microelectronic industry is faced with moisture-related reliability problems. Reliability is one of the major concerns in developing new advanced packages [19–21]. To demonstrate this, three different industrial application studies are described. The first application focused on the effect of moisture and delamination on the observed wire failures in a BGA package. The results indicate that the occurrence of delamination is the key factor for these failures. The second study concerned advanced structural similarity rules that can be achieved through simulation-based optimization techniques. Advanced structural similarity rules are deduced, which can be used to shorten design cycles. Even more, by combining the accurate 3D non-linear reliability prediction models easy-access structural similarity tools can be created that can be operated by package designers. The third study concerns die stacking in packages, which redistribute the stresses and generate more interfaces, giving rise to the increased risk and/or vulnerability for cracks and interface delamination during assembly and/or reliability testing. According to the calculated stress/strain responses, the results identify the hotspots including package warpage, die-crack for the dice, body crack, and interface delamination. Combining virtual prototyping techniques with smartly chosen reliability tests allows possible failure mechanisms within stacked die packages to be better understood and thus prevented. The variety of these practical problems demonstrates the applicability of virtual prototyping techniques to a wide range of industrial problems in microelectronics. Acknowledgments The author Daoguo Yang acknowledges the National Natural Science Foundation of China (NSFC) for their financial support (grant no. 60666002).

References 1. Fukuzawa, I., Ishiguro, S., Nanbu, S., “Moisture resistance degradation of plastics by reflow soldering”, Proceedings of International Reliability Physics Symposium, San Diego, USA, pp. 192–197, 1985. 2. van Driel, W.D., van Gils, M.A.J, Fan, X.J., Zhang, G.Q., Ernst, L.J., “Driving mechanisms of delamination related reliability problems in exposed pad packages”, IEEE Transactions on Components and Packaging Technologies, 31(2), 260–268, 2008. 3. Galloway, J.E., Miles, B.M., “Moisture absorption and desorption predictions for plastic ball grid array packages”, IEEE Transactions on Components, Packaging and Manufacturing Technology, 20(3), 274–279, 1997. 4. van Gils, M.A.J., van Driel, W.D., Zhang, G.Q., Bressers H.J.L., van Silfhout, R.B.R., Fan, X.J., Janssen, J.H.J., “Virtual qualification of moisture induced failures of advanced packages”, Journal of Microelectronics Reliability, 47(2–3), 273–279, 2007.

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5. Shi, X.Q., Zhang, Y.L., Zhou, W., Fan, X.J., “Effect of hygrothermal aging on interfacial reliability of silicon/underfill/FR-4 assembly”, IEEE Transactions on Components and Packaging Technologies, 31(1), 94–103, 2008. 6. Fan, X.J., Zhou, J., Zhang, G.Q., “Multi-physics modelling in virtual prototyping of electronic packages – combined thermal, thermo-mechanical and vapour pressure modelling”, Microelectronics Reliability, 44, 1967–1976, 2004. 7. Xie, B., Fan, X.J., Shi, X.Q., Ding, H., “Direct concentration approach of moisture diffusion and whole field vapor pressure modeling for reflow process: part I – theory and numerical implementation”, ASME Journal of Electronic Packaging, 131(3), 031010, 2009. 8. Fan, X.J., Zhang, G.Q., van Driel, W.D., Ernst, L.J., “Interfacial delamination mechanisms during reflow with moisture preconditioning”, IEEE Transactions on Components and Packaging Technologies, 31(2), 252–259, 2008. 9. Fan, X.J., Zhou, J., Zhang, G.Q., Ernst, L.J., “A micromechanics based vapour pressure model in electronic packages”, ASME Journal of Electronic Packaging, 127(3), 262–267, 2005. 10. Zhang, G.Q., van Driel, W.D., Fan, X.J., Mechanics of Microelectronics. Dordrecht, The Netherlands: Springer, 2006. 11. van Gils, M.A.J., van Driel, W.D., Zhang, G.Q., Bressers, H.J.L., van Silfhout, R.B.R., Fan, X.J., Janssen, J.H.J., “Virtual qualification of moisture induced failures of advanced packages”, Proceedings of the 5th International Conference on Thermal and Mechanical Simulation and Experiments in Microelectronics and Microsystems (EuroSimE), Brussels, Belgium, pp. 157–162, 2004. 12. Yang, D.G., “Cure-dependent viscoelastic behaviour of electronic packaging polymers: modelling, characterization, implementation and applications”, PhD thesis, Delft: Delft University of Technology, 2007. 13. van Driel, W.D., Mavinkurve, A., van Gils, M.A.J., Zhang, G.Q., Yang, D.G., Ernst, L.J., “Advanced structural similarity rules for the BGA package family”, Microelectronics Reliability, 47, 205–214, 2007. 14. van Driel, W.D., Zhang, G.Q., Janssen, J.H.J., Ernst, L.J., “Response surface modelling for non-linear packaging stresses”, Journal of Electronic Packaging, 125(4), 490–497, 2003. 15. Wymysłowski, A., Zhang, G.Q., van Driel, W.D., Ernst, L.J., “Virtual thermo-mechanical prototyping of microelectronics and microsystems”, edited by Suhir, E., Lee, Y.C., Wong, C.P., Micro- and Opto- Electronic Materials and Structures: Physics, Mechanics, Design, Reliability, Packaging Volume 1 Materials Physics/Materials Mechanics. Volume 2 Physical Design / Reliability and Packaging. New York, NY: Springer, 2007. 16. van der Sluis, O., Yuan, C.A., van Driel, W.D., Zhang, G.Q., “Advances in delamination modelling”, edited by Morris, J.E., Nanopackaging; Nanotechnologies and Electronics Packaging, New York, NY: Springer, 2009. 17. Real, R.A., van Driel, W.D., Yang, D.G., Zhang, G.Q., Pasion, J., “Stacking dies: combined virtual prototyping and reliability testing based design rules”, Proceedings of 57th Electronic Components and Technology Conference, Reno, Nevada, USA, pp. 1720–1724, 2007. 18. OPTIMUS Version 5.0, Optimisation Software Tool, Manual. Arlington, VA: Noesis, 2005. 19. van Driel, W.D., “Virtual thermo-mechanical prototyping for microelectronic devices”, PhD thesis, Delft: Delft University of Technology, 2007. 20. Fan, X.J., Wang, H.B., Lim, T.B., “Investigation of the underfill delamination and cracking for flip chip module during thermal cyclic loading”, IEEE Transactions on Components, Manufacturing and Packaging Technologies, 24(1), 84–91, 2001. 21. Xie, B., Fan, X.J., Shi, X.Q., Ding, H., “Direct concentration approach of moisture diffusion and whole field vapor pressure modeling for reflow process: part II – application to 3D ultra-thin stacked-die chip scale packages”, ASME Journal of Electronic Packaging, 131(3), 031011, 2009.

Chapter 17

Underfill Selection Against Moisture in Flip Chip BGA Packages X.J. Fan, T.Y. Tee, C.Q. Cui, and G.Q. Zhang

17.1 Introduction There is an increasing trend toward miniaturization in electronics industry. Electronics products are getting smaller and lighter and operate faster. This is crucial for more compact and efficient electronic packaging. The employment of flip chip interconnections [1] has inherent advantages over the conventional wire bonding techniques in terms of higher packaging density and better performance. Underfill material is usually applied to strengthen the solder bumps through the redistribution of stresses induced during assembly processes and reliability tests [2]. However, underfill is usually made of a polymeric material, susceptible to moisture-induced failures under moisture/reflow sensitivity tests [3] or temperature/humidity storage tests. The moisture weakens the interfacial adhesion strength of the underfill to the silicon chip and the underfill to the printed circuit board (solder mask layer) by generating internal vapor pressure during the reflow soldering process. Delamination or cracking within packages is often observed as a result of this process [4–13]. In addition, hygroscopic swelling of the underfill exerts tensile stresses in the inter-layer dielectric (ILD) and under bump metallurgy (UBM) structures or in the ILD/UBM structures [14–19]. Excessive stresses cause delamination and cracking in the ILD/UBM layers. In this chapter, we focus on the understanding of key parameters of the underfill material for the optimum selection of underfill with minimum moisture-induced failures in flip chip ball grid array (FCBGA) packages during solder reflow. An integrated study has been carried out, including design of experiments, interfacial adhesion measurement (pull/shear), moisture properties characterization, moisture/reflow sensitivity test, failure analysis, and finite element modeling. The effect of the flux residue, underfill voiding, molding process, and plasma grafting process, are also studied. Good correlation between the moisture/reflow sensitivity performance and the key material parameters is obtained.

X.J. Fan (B) e-mail: [email protected] X.J. Fan, E. Suhir (eds.), Moisture Sensitivity of Plastic Packages of IC Devices, Micro- and Opto-Electronic Materials, Structures, and Systems, C Springer Science+Business Media, LLC 2010 DOI 10.1007/978-1-4419-5719-1_17, 

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17.2 Design of Experiments 17.2.1 Test Vehicles The flip chip BGA package addressed in this study is a 27 mm×27 mm package with 10 mm×10 mm die size, as shown in Fig. 17.1, for both unmolded and molded formats. Figure 17.2 shows the bump layout of the silicon chip, with the depopulated array and 156 I/Os. The substrate is a two-layer (2-L) BT substrate with 0.4 mm of thickness. Figure 17.3 shows the top and bottom views of the substrate design.

(a)

(b)

Fig. 17.1 Flip chip BGA configurations: (a) unmolded format and (b) molded format

Fig. 17.2 Layout of bump structure

(a)

Fig. 17.3 Substrate design: (a) top view and (b) bottom view

(b)

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Two groups of underfill materials are evaluated. In the first group, six types of the underfill are tested. In the second group, three types of the underfill from different vendors are evaluated. Three moisture sensitivity levels (MSL), i.e., MSL1, MSL2, and MSL3, are applied in the moisture/reflow sensitivity tests. Table 17.1 shows the soaking conditions, according to J-STD-020D standard, for the MSL1, 2, and 3, respectively. Table 17.1 Moisture sensitivity test conditions [3] MSL

Soaking time (h)

Temperature/humidity condition

MSL1 MSL2 MSL3

168 168 192

85◦ C/85%RH 60◦ C/60%RH 30◦ C/60%RH

The impact of the following parameters is also evaluated in this study: (1) flux residue, (2) plasma grafting surface treatment, (3) overmolding, and (4) underfill voiding.

17.2.2 “No-flux” Assembly Process To investigate the flux residue effect on moisture sensitivity performance, a special assembly process has been designed to eliminate the flux process. Figure 17.4 shows the “no-flux” (fluxless) assembly process flow compared to the normal assembly process. In “no-flux” process, flux/reflow process is skipped before underfilling. The assembled units by this process have no proper electrical connections. Since the focus of our work is on the possible delamination of the underfill, the interfacial delamination can be inspected by CSAM, rather than by electrical measurement. Our objective is to determine an adequate failure criterion during the moisture/reflow sensitivity tests. Flux ( No Clean Flux) Bump/dice wafer

No Flux Bump/dice wafer

Flux/place die

Place die

Reflow Underfill Underfill

(a)

(b)

Fig. 17.4 Assembly process (a) normal flip chip assembly process and (b) “no-flux” assembly process

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17.2.3 Plasma Grafting Surface Treatment The major concern with moisture-induced failures in flip chip packages is the delamination of the underfill from the silicon chip (coated with polyimide passivation, PI). Plasma grafting surface treatment on polyimide surface has been introduced to improve the surface adhesion [20]. Figure 17.5 shows the attributes of the UV plasma process. The plasma is performed on the PI surface of a bumped chip before assembly. The plasma grafting process is a dry, clean, and fast process that is compatible with the in-line manufacturing process. No extra equipment requirement is needed. Such a process is applicable to all types of the polymer materials. Figure 17.6 is a comparison of surface roughness between the treated and the untreated surfaces. It is clear that the surface roughness is reduced after plasma grafting. Furthermore, the XPS analysis for the polyimide after plasma grafting shows that N1s, contributed from the PI, disappears after the plasma grafting procedure (Fig. 17.7a). This means that the grafted GMA is fully covered on the PI surface. Figure 17.7b is C1s spectra, which shows that the intensity of the C–O– increases after plasma grafting, indicating that the GMA is grafted with the epoxy functional group. Fig. 17.5 Plasma grafting process

Fig. 17.6 Surface roughness comparison for plasma grafting treatment

17.2.4 Underfill Voiding When the substrate is not baked before the underfilling process, it is possible to generate voids in the underfill. Figure 17.8 shows the CSAM images and the crosssection failure analysis for the units without substrate prebaking. Large voids are developed and connected near the interface. A special leg of experiment has been designed to investigate the effect of underfill voiding.

Underfill Selection Against Moisture in Flip Chip BGA Packages

C1s

439 Pristine Polyimide

Intensity (Arb. Units)

Pristine Polyimide

Polyimide graft polymerized with GMA by Plasma

Intensity (Arb. Units)

17

Binding Energy (eV)

C-H

C-N C-O C=O

Polyimide Graft Polymerized with C - O GMA by Plasma

C-H

COO

282

285

288

291

Binding Energy (eV) (a)

(b)

Fig. 17.7 XPS analysis on grafted PI surface

CSAM

Cross section

Voids Void

Fig. 17.8 Void formation for units without substrate prebaking

17.3 Material Characterization 17.3.1 Thermo-Mechanical Properties For the first group (six underfills), DMA and TMA have been used to obtain the glass transition temperature, Tg , the moduli below and above the Tg (E1 and E2), and the coefficient of thermal expansion (CTE) below and above the Tg , as shown in Table 17.2. UF-E and UF-F are in-house formulated underfills used for the purpose of the evaluation only. UF-E and UF-F do not contain fillers; therefore, their CTES are high and their moduli above the Tg are very low. UF-A was used as a reference case.

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Table 17.2 Thermal and mechanical material properties of the first group of six underfills CTE1

CTE2

Tg

E1, E2

UF

ppm/◦ C

ppm/◦ C

◦C

GPa

UF-A UF-B UF-C UF-D UF-E UF-F

31 18 25 27 68 61

90 40 93 78 197 199

133 128 117 144 155 102

8 12 9.6 7 2.2 2.7

1.7 4 1.4 4.5 1.05 0.05

Table 17.3 shows the thermal and mechanical material properties of the second group of three underfills obtained from different vendors. Both the in-house measurement data and the data from the suppliers are indicated. Overall, all the three underfills have similar thermal and mechanical properties.

Table 17.3 Thermal and mechanical material properties of the second group of three underfills Material UF-1 UF-2 UF-3

Vendor’s Measured Vendor’s Measured Vendor’s Measured

CTE1 (ppm/◦ C)

CTE2 (ppm/◦ C)

Tg (◦ C) by DMA

Modulus (GPa) 30◦ C

Modulus (GPa) 220◦ C

25 25.2 18 19.5 37 34.7

– 88.9 – 207.3 101 118.3

148 135 154 142 80 96

10.0 8.3 10.0 117.3 8.6 7.0

– 0.28 – 0.66 – 0.23

17.3.2 Moisture Diffusivity and Saturated Moisture Concentration The moisture weight gain curves of the first group of the six underfills under the 85◦ C/85%RH preconditioning are plotted in Fig. 17.9. The saturated moisture weight gain ranges from 0.5% through 1.6% of the total weight. UF-A exhibits the least moisture absorption among the six materials. Since UF-E and UF-F do not have fillers, both materials show high moisture absorption. All the six underfills show Fickian type of moisture diffusion, even when the soaking duration is extended to 900 h. Table 17.4 gives the diffusivity of the second group of the three underfills, both at 85 and 220◦ C. It can be seen that the diffusivity is three orders higher at the reflow temperature (220◦ C) than that at 85◦ C.

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1.6 1.4

% weight gain

1.2 1 0.8 0.6 0.4 0.2

UF - A

UF - B

UF - C

UF - D

UF - E

UF - F

0 0

60 121 182 244 305 366 425 486 547 609 670 731 790 851 912

No. of moisturized hours Fig. 17.9 Moisture weight gain data for the first group of six underfills under 85◦ C/85%RH preconditioning Table 17.4 Diffusivity and saturated moisture concentration for the second group of three underfills Absorption (85◦ C/85%RH)

Desorption (220◦ C)

Material

Diffusivity cm2 /s

Csat g/cm3

Temperature (◦ C)

Diffusivity cm2 /s

UF-1 UF-2 UF-3

2.441E–09 2.675E–09 1.509E–08

2.430E–02 1.713E–02 1.717E–02

220 220 220

8.929E–06 1.139E–05 8.686E–06

17.3.3 Pull/Shear Adhesion Test and Results The interfacial adhesion characterization, in particular, the measurement at high temperature with moisture, is certainly a challenge. We developed a methodology for the adhesion measurement under high temperature and humidity conditions (pull/shear) and conducted a detailed matrix study for evaluating the adhesion (polyimide passivation) between the chip and the underfill (PI/UF), as well as between the solder mask and the underfill (SM/UF). Interfacial fracture mechanics-based fracture toughness measurement provides rigorous definition for the evaluation of the interface adhesion strength. But the sample preparation is usually tedious, and the procedure is often not compatible with the packaging assembly process. On the other hand, pull/die shear tests, by which the samples can be made by standard packaging and assembly processes, provide an effective way for a quick assessment of the adhesion strength. A new method of sample preparation has been developed to produce a large quantity of samples. For pull test samples, 10 mm×10 mm chip with polyimide layer, or

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10 mm×10 mm BT core with a solder mask, was used on both sides, being “glued” by the underfill materials (see Fig. 17.10a). For shear test samples, on one side 2.5 mm×2.5 mm size was used and on the other side, 10 mm×10 mm was used. The use of the same material on both sides can eliminate the thermo-mechanical stress effect from the global CTE mismatch and, in addition, keeps the interface the same on both sides. Such a configuration can control fracture mode better. Figure 17.11 shows the schematic of the sample preparation process. It starts from a silicon wafer with PI passivation. A stencil is designed and applied to control the area and the height of the underfill dispensation. A flip chip pick and place machine is used to assemble 2 mm×2 mm or 10 mm×10 mm silicon dies on the wafer. The whole assembly is then cured according to each underfill’s prescribed curing schedule. Specimens are ready for the test after dicing. Such a sample preparation process can produce a large number of specimens and minimize the sample-to-sample variations. All specimens have consistent wetting areas, as well as the location and the height of the underfill.

Pull Test Samples

Fig. 17.10 Pull test/shear test sample configurations: (a) pull test samples and (b) shear test samples

chip

Shear Test Samples

substrate

subs .

chip

uf

uf

uf

chip

substrate

chip

(a)

uf

substrate

(b)

Wafer/Substrate with PI/SM coating

Curing

Chip attachment

Stencil printing for underfill

Dicing

Test Samples

Fig. 17.11 Schematic of die shear test specimen preparation process

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The pull test setup is shown in Fig. 17.12 within a temperature-controlled chamber. Additional fixture design is needed to ensure that the failure occurs at the UF/PI interface. Die shear tests are conducted on a die shear tester system: DAGE Series 4000 with hot plate (temperature range 25–300◦ C) (Fig. 17.13). The system has a fixed hot plate and a test table with full automatic test process. Several parameters such as shear speed and shear height can be adjusted to control the fracture mode. In the present study, the shear height was set equal to the underfill height and the shear speed was set as 200 μm/s. For all the experimental legs shown later, the sample size was 16 units per leg. One-hundred percent failure along the interface was achieved

pull tester

fixture chip uf

chip fixture

pull fixture

clamp Fig. 17.12 Pull test setup

Fig. 17.13 Die shear test setup

temperature chamber

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for all the legs in shear tests. The standard deviations for the measured adhesion data were less than 15%. Figure 17.14 shows the adhesion results for the second group of the underfills. For the three underfill materials, when tested under room temperature, the pull strength was lower than shear strength, but the difference was insignificant. Subsequently, shear tests were performed further under different durations of moisture preconditioning (85◦ C/85%RH). Figure 17.15 shows that the shear strength (PI/UF) at the room temperature was not sensitive to moisture. This implies that in order to correlate with moisture sensitivity performance, the adhesion test must be conducted at high temperature and with moisture.

Fig. 17.15 Effect of moisture on PI/UF shear strength tested under room temperature

Shear Strength (KG)

Strength (MPa)

Fig. 17.14 Comparison of pull strength and shear strength for PI/UF

32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2 0

Pull Shear

UF - 1

UF -2

UF - 3

40 35 30 0days

25

11days

20

17days

15

21days

10 5 0

UF - 1

UF - 2

UF - 3

Moisture: 85°C/85RH

Figure 17.16 plots the adhesion test results at reflow temperature (220◦ C) for the six underfills (first group). It shows that the UF-C has the strongest adhesion in the presence of moisture at high temperature, while UF-A has the poorest adhesion. In comparison to the moisture absorption data shown in Fig. 17.9, there is no correlation between the moisture absorption and the adhesion at high temperature. At the reflow temperature with moisture preconditioning, the adhesion strength at PI/UF interface is very sensitive to moisture. This has been further confirmed by the shear test for the second group of underfill under various moisture conditions (Fig. 17.17). Higher moisture concentration results in weaker adhesion strength. Failure analysis indicates that almost 100% of the failure mode is located along

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Underfill Selection Against Moisture in Flip Chip BGA Packages

shear strength (kg)

30

445

with moisture without moisture

25 20 15 10 5 0

UF - A

UF - B

UF -C

UF - D

UF - E

UF - F

underfill Fig. 17.16 Adhesion test results at 220◦ C at underfill/PI (the first group of underfill)

Average Shear Strength (KG)

UF/PI 220°C Shear Speed 200um/s Shear Height 30um

7 6 5 UF -1

4

UF -2

3

UF - 3

2 1 0

Dry

30°C/60RH 85°C/60RH 85°C/85RH

Fig. 17.17 Adhesion test results at 220◦ C at underfill/PI (the second group of underfill)

the PI/UF interface. This correlates well with the actual moisture sensitivity test of FCBGA packages. At SM/UF interface, however, the high temperature adhesion is not very sensitive to moisture (see Fig. 17.18). The failure mode for the SM/UF interface is also more complicated. Some tests show mixed failure paths, and about 70% of them belong UF/SM 220°C Shear Speed 200um/s Shear Height 30um

Average Shear Strenght (KG)

6 5 UF - 1

4 3

UF - 2

2

UF - 3

1 0 Dry

30°C/60RH 85°C/60RH 85°C/85RH

Fig. 17.18 Effect of moisture on SM/UF shear strength tested under reflow temperature

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to the SM/UF interface. A complete set of adhesion data should contain information of the test sample design, test condition (e.g., shear height), sample size, average and standard deviation of results, and the failure mode distribution.

17.4 Moisture/Reflow Sensitivity Test Results and Failure Analysis Flip chip daisy-chain test samples were built and tested for moisture sensitivity to investigate the impact of the underfill selection, moisture preconditioning levels, flux residue, plasma grafting treatment, overmolding, and underfill voiding.

17.4.1 Effect of the Underfill Material Selection Four different configurations of flip chip BGA test vehicles using UF-A in the first group were built and tested under JEDEC MSL3 moisture sensitivity level. These four configurations include two different ball layouts with and without molding, respectively. Table 17.5 summarizes the test results. All legs with the underfill A failed at the MSL3 level. Delaminations occurred at the interface between the underfill and the polyimide. Table 17.5 Summary of JEDEC MSL3 test with UF-A Leg ID

Configuration

# unit with this failure mode

A1 A2 A3 A4

Ball layout 1, molded Ball layout 1, not molded Ball layout 2, molded Ball layout 2, not molded

3/24 5/24 4/24 6/24

Additional experimental legs are then built using UF-C and UF-E, which have much higher saturated moisture concentration than UF-A. The test results (Table 17.6) show that the packages with underfills C and E passed the JEDEC MSL3 tests, and the packages with the underfill C passed even the MSL2 level without any delamination detected. Table 17.7 shows the results for the FCBGA with three underfill materials of the second group, tested under three levels of moisture/reflow sensitivity tests. In order Table 17.6 Summary of JEDEC MSL3 and MSL2 test results with UF-C and UF-E Underfill

Total number of failure units

UF-C UF-E

MSL3 0/24 0/18

MSL2 0/18 Not available

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Table 17.7 Results of moisture sensitivity test for the second group of underfill Package

Process

Underfill

Surface

MSL

Electrical failure

Delamination

Not molded Not molded Not molded Not molded Not molded

No flux No flux No flux No flux No flux

UF-2 UF-3 UF-1 UF-2 UF-3

Untreated Untreated Untreated Untreated Untreated

2 2 2 1 1

– – – – –

0/19 0/16 4/18 4/15 2/16

to eliminate the flux residue effect, the data reported in Table 17.7 were obtained through “no-flux” process. The MSL1 condition turned out to be too severe: none of the underfill materials could pass. For MSL2, UF-2 and UF-3 using no-flux process were able to pass the test, while UF-1 still failed.

17.4.2 Failure Mode Analysis Figure 17.19 contains X-ray images after soldering reflow. For failed units, largescale solder spread is observed due to underfill delamination. Failure analysis based on the cross-section (Fig. 17.20) shows that the critical failure site for flip chip PBGA package is the interface between the polyimide passivation layer and the underfill. Molten solder fills in the delaminated gap during the reflow process. This Solder spread

Good unit

Bad unit

Fig. 17.19 X-ray images of good and bad units after moisture sensitivity test

Electrical short caused by solder extrusion

PI Extruded solder

die

UF

solder Ni Cu

SM

Fig. 17.20 Failure analysis of FCBGA with PI/UF delamination and solder extrusion

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means that underfill adhesion with UF is critical for the selection of the underfill material.

17.4.3 Effect of Flux Residue Table 17.8 summarizes the test results in vs. normal assembly process, where noclean flux is applied. UF-2 and UF-3 cannot pass MSL2 with the presence of the flux residue. The flux residue has been found harmful, even though no-clean flux was applied. At MSL3, all the underfill materials passed the test, even with flux residue. Table 17.8 Results of moisture sensitivity test for flux residue effect Package

Process

Underfill

Surface

MSL

Electrical failure

Delamination

Not molded Not molded Not molded Not molded Not molded Not molded Not molded Not molded Not molded Not molded Not molded Not molded Not molded

Flux Flux Flux Flux No flux Flux No flux Flux No flux Flux No flux Flux No flux

UF-1 UF-2 UF-3 UF-2 UF-2 UF-3 UF-3 UF-1 UF-1 UF-2 UF-2 UF-3 UF-3

Untreated Untreated Untreated Untreated Untreated Untreated Untreated Untreated Untreated Untreated Untreated Untreated Untreated

3 3 3 2 2 2 2 2 2 1 1 1 1

0/16 0/16 0/16 2/13 – 1/11 – 6/16 – 11/11 – 4/13 –

0/16 (pass) 0/16 (pass) 0/16 (pass) 2/13 0/19 (pass) 1/11 0/16 (pass) 6/16 4/18 11/11 4/15 4/13 2/16

17.4.4 Effect of Plasma Grafting Treatment Plasma grafting treatment is performed on PI surface before assembly to enhance surface adhesion. Table 17.9 lists the test results for a normal assembly process with flux applied. It can be seen that with the grafting treatment, all the underfills can pass the MSL2 level tests. However, all the underfills still fail at the MSL1 level tests. Failure analysis was performed on failed units with surface treatment (Fig. 17.21). It shows that the delamination at the UF/PI interface is partial and may be caused by flux residue on adhesion degradation. Further, Table 17.10 provides the results of the moisture/reflow sensitivity tests at MSLI with and without flux residue effect. When the flux process is eliminated and the plasma grafting treatment is applied, MSL1 level can be achieved with the use of UF-2. Die shear test is conducted on treated samples at high temperature with moisture conditioning at 85◦ C/85%RH (21 days). The failure mode is 100% cohesive failure (Table 17.11). This means that the UF/PI interface is too strong to break. Figure 17.22 shows the cohesive failure surface for a die shear sample.

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Table 17.9 Results of moisture sensitivity test (normal process) Package

Process

Underfill

Surface

MSL

Electrical failure

Delamination

Not molded Not molded Not molded Not molded Not molded Not molded Not molded Not molded Not molded Not molded

Flux Flux Flux Flux Flux Flux Flux Flux Flux Flux

UF-2 UF-2 UF-3 UF-3 UF-1 UF-1 UF-2 UF-2 UF-3 UF-3

Untreated Treated Untreated Treated Untreated Treated Untreated Treated Untreated Treated

2 2 2 2 2 2 1 1 1 1

2/13 0/11 1/11 0/16 6/16 0/16 11/11 6/15 4/13 2/17

2/13 0/11 (pass) 1/11 0/16 (pass) 6/16 0/16 (pass) 11/11 6/15 4/13 2/17

Fig. 17.21 X-ray image for failed unit with plasma grafting

Partial Delamination

Table 17.10 Results of moisture sensitivity test for flux residue effect Package

Process

Underfill

Surface

MSL

Electrical failure

Delamination

Not molded Not molded

Flux No flux

UF-2 UF-2

Treated Treated

1 1

6/15 –

6/15 0/16

17.4.5 Effect of Overmolding Table 17.12 gives the test results for molded packages in comparison with the unmolded packages. It can be seen that molded packages fail at the MSL3 level for all the three underfills with delaminations at both the PI/UF interface and the SI/MC interface (Fig. 17.23). Overmolding causes additional thermal stresses at the PI/UF interface (to be discussed in Section 17.5).

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Table 17.11 Summary of adhesion results for treated samples

UF-2 UF/PI, 220◦ C After grafting treatment Shear speed 200 μm/s; shear height 30 μm Failure mode: 100% cohesive 85◦ C/85%RH preconditioning

(kg)

Max. Min. Ave. SD

9.49 7.31 8.28 0.84

Fig. 17.22 Failure surface image by shear test for plasma grafting treated samples

Table 17.12 Results of moisture sensitivity test for molded packages Package

Process

Underfill Surface

MSL

Delamination at SI/MC

Delamination at PI/UF

Molded Molded Molded Molded Molded Molded Not molded Not molded Not molded

Flux Flux Flux Flux Flux Flux Flux Flux Flux

UF-2 UF-3 UF-1 UF-2 UF-3 UF-1 UF-2 UF-3 UF-1

3 3 3 2 2 2 3 3 3

2/14 12/16 16/16 7/19 14/16 16/16 N/A N/A N/A

4/14 2/16 7/16 12/19 10/16 14/16 0/19 0/16 0/16

Untreated Untreated Untreated Untreated Untreated Untreated Untreated Untreated Untreated

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Underfill Selection Against Moisture in Flip Chip BGA Packages Popcorn failure detected by Thru - SCAN

Solder spread detected by X -ray

Thru-SCAN image for failed sample X-ray image at PI/UF interface

451 Die top delamination detected by X - ray

delaminationat die top

Fig. 17.23 Failure analysis for molded packages

17.4.6 Effect of Voids in Underfill UF-2 is used to investigate the effect of voids in underfill. In order to generate voids in the underfill, the substrates were not prebaked before the underfilling process. Table 17.13 shows the results of the moisture sensitivity test at the MSL2 level. It can be seen that without prebaking, failure rate increases significantly compared to the group with prebaking. Table 17.13 Results of moisture sensitivity test for voids effect Package

Process

Underfill

Substrate preheat

MSL

Electrical failure

Delamination

Not molded Not molded

Flux Flux

UF-2 UF-2

Yes No

2 2

2/13 11/12

2/13 11/12

17.5 Finite Element Modeling 17.5.1 Vapor Pressure Modeling The moisture properties (moisture diffusivity and saturated moisture concentration) of three underfill materials have been characterized as shown in Table 17.2. The moisture vaporization during reflow is a key element in understanding the failure mechanism. A theoretical model for full-field vapor pressure prediction over the entire package after moisture preconditioning, based on micromechanics approach [4, 12, 21–24], has been developed for the FCBGA. Figure 17.24 shows that the vapor pressure saturates very fast at the MSL1 moisture preconditioning level. The vapor pressure distribution is uniform and gets saturated even under MSL3 moisture preconditioning level. This implies that the vapor pressure will not increase with a

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Fig. 17.24 Transient vapor pressure distribution in FCBGA at MSL1, 220◦ C

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5h

MPa

10h

0 0.25 0.5 1 1.25 1.5 1.75 2 2.5

168h

greater moisture absorption. Such results indicate that the vapor pressure is not the only driving force for the failure. Although the vapor pressure remains at its saturated pressure with more moisture absorption, the interfacial adhesion strength may continuously deteriorate with the additional moisture. Therefore, the knowledge of the interface adhesion strength with moisture effect at high temperature condition (see Figs. 17.16, 17.17, and 17.18) is crucial in formulating the failure criteria.

17.5.2 Thermal Stress Analysis on Overmolding Effect Thermo-mechanical stress in the underfill is another driving force for a possible failure at reflow. A multi-process-induced stress finite element modeling has been carried out. As shown in Fig. 17.25, in a flip chip assembly, different stress-free

Bump/dice wafer

Flux/place die

Fig. 17.25 Stress-free conditions for multi-process in a flip chip assembly

Reflow

Stress - free: 183°C

Underfill

Stress - free: 150°C

Overmold

Stress - free: 175°C

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conditions are applied for different materials in assembly process. Conventional finite element modeling assumes only one single stress-free condition for all the materials, which is unable to capture the effect of different processes on stresses during the assembly effort. Constraint equations are applied for a sequential process modeling. Figure 17.26 shows a 2-D finite element model before molding process. Axisymmetric eight-node linear elastic element is used. Eutectic solder becomes molten at the reflow conditions and therefore the region occupied by the solder is treated as a hollow one in the model. The element size is fixed at the stress extraction point, when geometry changes. The BT material is treated as a transversely isotropic one.

Fig. 17.26 A 2-D finite element model for a flip chip assembly before overmolding

Here, thermo-mechanical stresses (Sy = normal stress, Sxy = shear stress) are extracted at several locations in the underfill region (Fig. 17.27). Table 17.14 shows the results for both the molded and not-molded packages. Both single-process and multi-process modeling results are presented. It shows that overmolding has a significant impact on the underfill stresses. However, single-process modeling cannot capture the large difference in the stresses in the underfill. Table 17.15 shows the thermal stresses with consideration of the vapor pressure-induced expansion (see Chapter 9). Again, overmolding results in larger stresses in the underfill than that in the not-molded package. Vapor pressure-induced expansion has additional contributions to the stresses, i.e., in addition to the degradation of the adhesion by moisture.

2 1

Bump Si chip Underfill

Fig. 17.27 Stress extraction location in a flip chip assembly

Substrate 4 3

1

0.44 −4.7

MPa

Sy Sxy

1.76 −7.59E–02

2

Multi-process modeling 4 −1.02 1.55

3

−6.65 −5.27 0.33 −3.09

1 1.16 −7.41E–02

2 −4.28 −3.38

3

Single stress free at 175◦ C

−0.33 0.86

4

0.31 −4.77

1

1.69 −1.70E–02

2

Not molded

Table 17.14 Thermal stresses for not-molded and molded packages (without vapor pressure effect)

−6.68 −5.28

3

3.59 −2.80

4

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Table 17.15 Thermal stresses for not-molded and molded packages (with vapor pressure effect) Multi-process modeling MPa 1 Sy Sxy

2

3

4

Single stress free at 175◦ C Single stress free at 175◦ C Not molded 1

2

3

4

1

1.41 0.82 −8.21 −2.12 1.11 0.72 −5.39 −0.44 1.11 −6.60 0.89 −6.77 2.57 −4.41 0.46 −4.42 1.04 −4.81

2

3

4

0.19 0.92

−5.89 −0.29 −4.93 1.54

17.6 Integrated Analysis of Moisture-Induced Delamination at Reflow The above results of moisture/reflow sensitivity tests demonstrate that the moisture diffusivity and the saturated moisture concentration do not correlate with the moisture performance when comparing different materials’ behaviors. For the first group of the underfills, although UF-C and UF-E absorb more moisture than UF-A, vapor pressure buildup for the three underfills is the same during reflow. The performance difference in the experiment is due to the difference in adhesion strength. However, adhesion strength at room temperature does not represent the adhesion strengths at elevated temperature. For the second group of the underfills, it is also found that the most critical parameter in moisture performance is the adhesion at high temperature with moisture. When adhesion testing is performed at high temperature with moisture, the measured value is a comprehensive parameter, which includes the effects of moisture, temperature, thermal stress, and vapor pressure. Figure 17.28 illustrates the die shear sample configuration with the flip chip assembly. It can be seen that the shear test sample is a “miniaturized” assembly. When silicon chips are employed on both sides in the die shear test, the difference between the actual assembly and the test sample is the global thermal stress effect. Moisture affects the package reliability at reflow in two ways: the generation of vapor pressure and the degradation of the interfacial adhesion. Figure 17.29 is a schematic plot showing the relative effect of moisture absorption on the interfacial adhesion and vapor pressure in the package. With more moisture absorbed, the vapor pressure will remain on the saturated vapor pressure level. However, the interfacial adhesion (at high temperature) continues to decrease with moisture. When the adhesion strength decreases to the level below the vapor pressure, delamination occurs. Thermal stress is an additional driving factor for delamination. This can be inferred from the moisture performance difference between the molded and not-molded packages. It is concluded that when selecting material for moisture performance during reflow, moisture absorption-related material properties, such as diffusivity and saturated moisture concentration, may not be critical parameters. For a particular material, even though material is able to absorb more moisture than other materials, the delamination may not be a concern, if the adhesion at the interface of

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Fig. 17.28 Adhesion test at high temperature with moisture •

• • • • •

Moisture condition same as actual package Interface adhesion strength σR Vapor pressure applied Vapor pressure induced expansion Hygro-mechanical stress Thermal stresses by local mismatch Adhesion degradation by moisture

Fig. 17.29 Schematic of relative effect of moisture absorption on interfacial adhesion and vapor pressure

Less geometry effect

Shear Test under reflow temperature with moisture

Interfacial adhesion

Vapor pressure

Level 3

Level 2

Level 1

Moisture absorption

interest after moisture absorption at high temperature is strong enough. The adhesion at room temperature may not be able to represent the interface behavior. Only the adhesion measurement at elevated temperatures with moisture effect correlates with the reflow performance. Since the interfacial adhesion strength at high temperature with moisture is a comprehensive factor, which includes the effects of moisture humidity conditions, vapor pressure, thermo-mechanical stress, and underfill material properties, it is possible that there exists an adhesion value, below which the package would fail. Such an interface adhesion value is independent of the humidity conditions and the material properties. Figure 17.30 shows that the critical adhesion value for this package is around 4.2 MPa, which can differentiate the earlier moisture sensitivity level (MSL) test results. UF-3 failed at the MSL2 level, and all the three underfills failed at the MSL1 level.

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UF/PI 220°C Shear Speed 200um/s Shear Height 30um Average Shear Strength (KG)

7 6 5 UF - 1 UF -2 UF -3

4 3 2 1 0 Dry

30°C/60RH 85°C/60RH

85°C/85RH

Fig. 17.30 Correlation of adhesion test with moisture reflow performance

17.7 Conclusions This chapter is aimed at the understanding of the moisture-induced failure mechanism for flip chip BGA package during solder reflow process. An integrated study has been carried out, including interface adhesion measurement (pull/shear), moisture sensitivity/reflow test, failure analysis, and finite element modeling. A flip chip package with 10 mm×10 mm chip size has been used for the experimental evaluation and verification with two groups of underfills. Surface plasma grafting treatment on polyimide film of bumped wafer, flux residue effect, overmolding, and voids in underfill have been also studied. The moisture vaporization during the reflow process is a key element in understanding the failure mechanism. Finite element modeling results showed that the vapor pressure was almost uniform and saturated even under the MSL3 moisture preconditioning level. This implies that the vapor pressure will not increase with an increase in the moisture absorption. Such results showed the fact that the vapor pressure is not the only driving force leading to failure. Although the vapor pressure remains at its saturated point with more moisture absorption, the interfacial adhesion strength may continuously deteriorate with an increase in the additional moisture. Therefore, the knowledge of the effect of moisture on the interfacial adhesion strength at high temperature condition is crucial for determining the failure criteria. The interface adhesion characterization, and, in particular, the measurements of the adhesive strength at high temperature with moisture, is a challenging topic. We have developed a methodology for the adhesion measurement under high temperature and humidity conditions (pull/shear) and conducted a detailed matrix study for the evaluation of the adhesion between the chip (polyimide passivation) and the underfill (PI/UF), as well as between the solder mask and the underfill (SM/UF), under different moisture and different temperature conditions. The results showed that the adhesion strength at room temperature was not sensitive to moisture. This implies that in order to correlate with moisture sensitivity performance, the adhesion test must be conducted at high temperature with moisture. At the PI/UF interface,

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the adhesion is very sensitive to moisture. At the SM/UF interface, however, the adhesion is not very sensitive to moisture. A comprehensive design of experiments for moisture sensitivity performance was conducted to investigate the role of the underfill selection, flux residue effect, voids in underfill, and overmolding effects. The results showed that the critical failure site for flip chip PBGA package is the interface between the polyimide passivation layer and the underfill. Although the adhesion data at the UF/SM interface is lower than that at the UF/PI interface, no failure was found at the interface between the solder mask and the underfill during reflow. The underfill adhesion property at high temperature with moisture was identified as the key factor to correlate with the moisture sensitivity performance. The flux residue has been found harmful, even though no-clean flux was applied. Not-molded package has better moisture performance than molded package, in terms of delamination at the PI/UF interface. The plasma grafting treatment on PI surface has been applied to improve the interface adhesion and has proved very effective. The package can pass JEDEC MSL1 moisture sensitivity test by eliminating the flux residue and applying the plasma grafting technique. Thermal stress in underfill is another driving force for the failure. A sensitivity study by using finite element modeling has been conducted on the package geometry, the underfill material, and the overmolding effect. Overall, the die size, its thickness, and the substrate thickness do not have significant effect on the stresses in the underfill. The selection of the molding compound has a minor influence on the stresses in the underfill. However, the stresses in the underfill for a molded package are larger than those for not-molded package. A sequential processing modeling technique has been developed, and it has been found that overmolding introduces additional stresses in the underfill. The study showed that the interfacial adhesion strength at high temperature with moisture was a comprehensive factor, which includes the effects of adhesion degradation by moisture, vapor pressure, thermal stress, and underfill material properties. Such a value, therefore, can represent the overall resistance of the IC package to the moisture. A failure criterion was proposed, and there exists a critical adhesion value, which may be independent of material and moisture conditions for not-molded flip chip package. Acknowledgment The authors acknowledge the contributions of their colleagues of Institute of Microelectronics (IME) and consortium members to this work.

References 1. Wang, T., Chew, T.H., Lum, C., Chew, Y.X., Miao, P., Foo, L., “Assessment of flip chip assembly and reliability via reflowable underfill”, Proceedings of 51st ECTC, 2001. 2. Tee, T.Y., Kho, C.L., Yap, D., Toh, C., Baraton, X., Zhong, Z.W., “Reliability assessment and hygroswelling modeling of FCBGA with no-flow underfill”, Microelectronics Reliability, 43(5), 741–749, 2003. 3. Joint IPC/JEDEC Standard J-STD-020D, ‘Moisture/reflow sensitivity classification for nonhermetic solid state surface mount devices”. Arlington, VA: Electronic Industries Alliance, 2004.

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4. Tee, T.Y., Fan, X.J., Lim, T.B., “Modeling of whole field vapor pressure during reflow for flip chip BGA and wire bond PBGA packages”, Proceedings of 1st EMAP Conference, Singapore, pp. 38–45, 1999. 5. Wong, E.H., Teo, Y.C., Lim, T.B.,“Moisture diffusion and vapour pressure modeling of IC packaging”, Proceedings of 48th Electronic Components and Technology Conference, ECTC, USA, pp. 1372–1378, 1998. 6. Galloway, J.E., Miles, B.M., “Moisture absorption and desorption predictions for plastic ball grid array packages”, IEEE Transactions on Components, Packaging, and Manufacturing Technology Part A, 20(3), 274–279, 1997. 7. Tay, A.O., Lin, T., “Moisture diffusion and heat transfer in plastic IC packages”, IEEE Transactions on Components, Packaging, and Manufacturing Technology Part A, 19(2), 186–193, 1996. 8. Kitano, M., Nishimura, A., Kawai, S., “Analysis of package cracking during reflow soldering process”, Proceedings of 26th International Reliability Physics Symposium, pp. 90–95, 1988. 9. Fan, X.J., “Moisture related reliability in electronic packging”, Electronic Component Technology Conference (ECTC) Professional Development Course (PDC) handout, 2005/2006/2007/2008. 10. Tee, T.Y., Ng, H.S., “Whole field vapor pressure modeling of QFN during reflow with coupled hygro-mechanical and thermo-mechanical stresses”, Proceedings of 52nd Electronic Components and Technology Conference, ECTC, San Diego, CA, USA, pp. 1552–1559, 2002. 11. Zhang, G.Q., van Driel, W.D., Fan, X.J., Mechanics of Microelectronics. New York, NY: Springer, 2006. 12. Fan, X.J., Zhou, J., Zhang, G.Q., Ernst, L.J., “A micromechanics based vapor pressure model in electronic packages”, ASME Journal of Electronic Packaging, 127(3), 262–267, 2005. 13. Fan, X.J., Zhang, G.Q., van Driel, W.D., Ernst, L.J., “Interfacial delamination mechanisms during reflow with moisture preconditioning”, IEEE Transactions on Components and Packaging Technologies, 31(2), 252–259, 2008. 14. Fan, X.J., Zhou, J., Zhang, G.Q. “Multi-physics modeling in virtual prototyping of electronic packages – combined thermal, thermo-mechanical and vapor pressure modeling”, Journal of Microelectronics Reliability, 44, 1967–1976, 2004. 15. Zhou, J., “Investigation of inner-layer dielectric (ILD) failure by hygroscopic swelling,” IEEE 55th Electronic Components and Technology Conference (ECTC), Orlando, FL, USA, May 31–June 4, 2005. 16. Fan, X.J., Lee, S.W.R., Han, Q., “Experimental investigations and model study of moisture behaviors in polymeric materials”, Microelectronics Reliability, 49, 861–871, 2009. 17. Wong, E.H., Chan, K.C., Rajoo, R., Lim, T.B., “The mechanics and impact of hygroscopic swelling of polymeric materials in electronic packaging,” Proceedings of 50th Electronic Components and Technology Conference, Las Vegas, NV, USA, pp. 576–580, 2000. 18. Fan. X.J., Zhou, J., Chandra A., “Package structural integrity analysis considering moisture”, Proceedings of Electronic Components and Technology Conference (58th ECTC), pp. 1054– 1066, 2008. 19. Shi, X.Q., Zhang, Y.L., Zhou, W., Fan, X.J., “Effect of hygrothermal aging on interfacial reliability of silicon/underfill/FR-4 assembly”, IEEE Transactions on Components and Packaging Technologies, 31(1), 94–103, 2008. 20. Cui, C.Q., Lim, T.B., “Enhancing adhesion between mold compound and substrate in BGA packaging”, Proceedings of Electronic Components and Technology Conference, May 18–21, pp. 544–549, 1997. 21. Xie, B., Fan, X.J., Shi, X.Q., Ding H., “Direct concentration approach of moisture diffusion and whole field vapor pressure modeling for reflow process: part I – theory and numerical implementation”, ASME Journal of Electronic Packaging, 131(3), 031010, 2009. 22. Xie, B., Fan, X.J., Shi, X.Q., Ding, H., “Direct concentration approach of moisture diffusion and whole field vapor pressure modeling for reflow process: part II – application to 3-D ultra-thin stacked-die chip scale packages”, ASME Journal of Electronic Packaging, 131(3), 031011, 2009.

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23. van Driel, W.D., van Gils, M.A.J, Fan, X.J., Zhang, G.Q., Ernst, L.J., “Driving mechanisms of delamination related reliability problems in exposed pad packages”, IEEE Transactions on Components and Packaging Technologies, 31(2), 260–268, 2008. 24. van Gils, M.A.J., van Driel, W.D., Zhang, G.Q., Bressers H.J.L., van Silfhout, R.B.R., Fan, X.J., Janssen, J.H.J., “Virtual qualification of moisture induced failures of advanced packages”, Journal of Microelectronics Reliability, 47(2–3), 273–279, 2007.

Chapter 18

Moisture Sensitivity Investigations of 3D Stacked-Die Chip-Scale Packages (SCSPs) X.Q. Shi, X.J. Fan, and B. Xie

18.1 Introduction The development of three-dimensional (3D) microelectronic packaging with multidie stacking technology has become essential for increasing functionality with higher memory capacity in complex and efficient architectures in smaller form factor packages. As a consequence, wafer thinning is required from the original 750 μm down to as low as 50 μm. The traditionally used die-attach paste material and the assembly method are not applicable to handle such thin dies. Wafer-level films (WLFs) for die-to-die or die-to-substrate attachment have emerged. However, a key challenge for developing ultrathin stacked-die chip-scale packages (SCSPs) is to meet the package performance requirements without delamination and cracking in the package during moisture/reflow sensitivity test. In addition, higher reflow temperature required for lead-free packaging results in the increased reliability concerns for these ultrathin plastic packages [1–4]. In this chapter, we describe the moisture/reflow sensitivity experiments that were performed on several different SCSPs, with an objective to identify new failure mechanisms involved in wafer-level die-attach films and ultrathin packages. Packages evaluated include single-die, three-die, and five-die stacking molded matrix chip-scale packages. The effects of the reflow profile and the substrate design are studied by an integrated approach of testing, failure analysis, and modeling. Different types of wafer-level die-attach films including, both high-Tg and low-Tg films were tested to detect and examine possible failure modes. Explanations to the observed phenomena are provided and the criteria for wafer-level film selection are discussed.

X.Q. Shi (B) e-mail: [email protected] X.J. Fan, E. Suhir (eds.), Moisture Sensitivity of Plastic Packages of IC Devices, Micro- and Opto-Electronic Materials, Structures, and Systems, C Springer Science+Business Media, LLC 2010 DOI 10.1007/978-1-4419-5719-1_18, 

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18.2 Experimental 18.2.1 Test Vehicle Description Figure 18.1 shows a schematic of the evaluated test vehicles, that comprise singledie, three-die, and five-die stacking chip-scale packages. In those packages, same type of die-attach film is applied in both die-to-die and die-to-substrate attachments. The controlled leg package is a five-die stacking CSP with four-layer (4-L) substrate. The important information regarding the package in the controlled leg is listed in Table 18.1. The package dimensions are 10 mm×14 mm×1.2 mm. Four different types of die-attach films, namely DA1, DA2, DA3, and DA4, were evaluated. In the controlled case, DA1 film was used.

Fig. 18.1 Test vehicle configurations: (a) single-die stacking CSP, (b) three-die stacking CSP, and (c) five-die stacking CSP

(a)

(b)

(c)

Table 18.1 Controlled leg package design, material, and reflow condition descriptions

Stacking number Substrate Die-attach film Reflow condition Package geometry

5 4-L DA1 Profile 1 (see Fig. 18.2) 10 mm × 14 mm × 1.2 mm

18.2.2 Reflow Profile Setting Figure 18.2 illustrates two different reflow profiles used in this study. Both profiles 1 and 2 meet J-STD-020D reflow specification. Profile 2 has a longer reflow time (about 90 s longer) compared to Profile 1. In addition, Profile 2 has a slower ramp before temperature reaches about 180◦ C. Table 18.2 shows the test matrix to study the effect of the reflow process.

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Fig. 18.2 Two reflow profiles used in the present study

Table 18.2 Text matrix for reflow profile effect

Reflow condition

Package design

Profile 1 Profile 2

Controlled leg Controlled leg

18.2.3 Substrate Design Two test matrices were designed to investigate the effect of substrate design on moisture sensitivity performance. In the first group of the experiments, 2-L and 4-L substrates were evaluated (Table 18.3). A 2-L substrate is about 30% thinner than the 4-L substrate. In the second group, 4-L substrate was used with various thicknesses of the solder mask, BT core, and the inner copper density. Table 18.4 provides the detailed information on those variables in different legs [5, 1].

Table 18.3 Text matrix for 2-L and 4-L substrates (with reflow Profile 1) Substrate design

Package description

4-L substrate (thick) 2-L substrate (thin)

five-die, DA1 five-die, DA1

Table 18.4 Text matrix for various substrate thicknesses Substrate design (4-L)

Leg 1

Leg 2

Leg 3

Leg 4

Leg 5

Solder mask BT core Total thickness

x y z

1.02x 1.1y 1.20z

1.04x 1.4y 1.47z

1.04x 1.5y 1.47z

1.4x 1.5y 1.53z

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18.2.4 Die-Attach Film Selection Four different types of die-attach films (DA1, DA2, DA3, and DA4) were selected to build both the single-die and the stacking-die CSPs. Table 18.5 shows the experimental legs with different wafer-level films. In this experiment, 4-L substrate was used for all legs. An additional objective of this study was to obtain the correlation of failure rate between a single-die stacking CSP and a multi-die stacking CSP. Table 18.5 Text matrix for wafer-level film selection study

Leg

Substrate

Stack

DA film

1 2 3 4 5 6 7 8

4-L 4-L 4-L 4-L 4-L 4-L 4-L 4-L

3 3 3 3 1 1 1 1

DA1 DA2 DA3 DA4 DA1 DA2 DA3 DA4

18.2.5 Material Properties of Die-Attach Films In order to obtain the correlation between the package moisture sensitivity performance and materials properties, digital image correlation (DIC) method and dynamic mechanical analyzer (DMA) were employed to measure the Young’s moduli of the four films at different temperatures [1]. Figure 18.3 plots the Young’s modulus of DA1 film as a function of temperature with and without the presence of moisture. The Tg of the film decreases significantly with moisture absorption. DA1 film material has a very low modulus at reflow temperature. The modulus is less than 5 MPa and is in the order of the saturated vapor pressure (4.7 MPa at 260◦ C). Table 18.6 summarizes the Young’s moduli data at 150◦ C for four different films. Since it is very difficult to obtain accurate Young’s modulus at elevated temperature, in particular, with humidity control, the values in Table 18.6 were used for comparison only. As seen in Table 18.6, DA1, DA2, and DA4 are low-Tg

Fig. 18.3 Young’s modulus of DA1 film with and without moisture

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Table 18.6 Young’s moduli of die-attach films evaluated

465

Material

Tg (◦ C)

Young’s modulus (MPa) at 150◦ C

DA1 DA2 DA3 DA4

Low Low High Low

X 0.5X Very high 0.75X

die-attach films with very low Young’s modulus (less than 5 MPa) at temperatures above 150◦ C. DA2 and DA4 have lower modulus at 150◦ C than does DA1. DA3 is a high-Tg die-attach film, and its Young’s modulus is a few orders higher than DA1. An in situ moisture absorption method was used to accurately obtain the moisture diffusivity and solubility of thin films (see Chapter 3). Figure 18.4 shows the moisture weight gain curve for a 30 μm DA1 at 30◦ C/70%RH [6]. The film reaches moisture saturation within 5 min even at room temperature. Table 18.7 lists the comparison of the saturated moisture concentrations for DA1 and DA4. Saturated moisture concentration of DA4 is twice as large as that of DA1.

Fig. 18.4 Moisture uptake as a function of time at 30◦ C/70%RH for a 30 μm DA1 film

Table 18.7 Saturated moisture concentration comparison

Material

Saturated moisture concentration at 60◦ C/60%RH

DA1 DA4

X 2X

18.2.6 Moisture/Reflow Sensitivity Test Procedures Moisture/reflow sensitivity tests were performed as shown in the flow chart in Fig. 18.5. Time-zero failure analysis was carried out for non-clean samples to identify the failure mechanisms. The assembly panels were then subjected to bake,

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Fig. 18.5 Moisture sensitivity/reflow test procedures

temperature cycling, moisture soaking, and reflow process, as specified in the JSTD-020D. Moisture preconditioning was set as 60◦ C/60%RH for 72 h, which is an accelerated moisture soaking equivalent to MSL3. The details are referred in Chapter 13. After reflow process, TSAM inspections were performed, followed by failure analysis and data analysis.

18.3 Test Results and Failure Analysis 18.3.1 Effect of Reflow Profiles Figure 18.6 is an example of TSAM images of SCSP panel after reflow test. Black regions indicate failures inside the packages. A cross-sectional view of a package confirms a large-scale cracking and voiding in the die-attach film attached to the substrate (called as bottom layer film), as shown in Fig. 18.7. Other film layers, which are sandwiched by dies, remain intact. Bottom layer film absorbs moisture through plastic substrate, while films in other layers absorb much less moisture. Therefore, no failures occur in other layers. Such a cohesive failure mode is different from the traditional interface delamination during reflow, in which adhesion reduction due to moisture is the root cause [7–10]. When reflow Profile 2 was applied, no failure was detected at all, as shown in Fig. 18.6b. This figure clearly shows the sensitivity to reflow profile setting. Residual moisture content is a key to control the failures in die-attach film. With Profile 2 subjected, sufficient time is provided to allow the residual moisture to

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Fig. 18.6 TSAM images of SCSP panel after reflow: (a) Profile 1 is applied and (b) Profile 2 is applied

(a)

(b)

Fig. 18.7 Bottom layer die-attach film cohesive failure

escape from the package before temperature reaches the peak value. A detailed analysis will be described in the subsequent section.

18.3.2 Effect of Substrate Design The above results were obtained based on the controlled leg package, in which 4-L substrate was used. As shown in Table 18.3, a test matrix was designed to evaluate the performance of the 2-L SCSP. Table 18.8 summarizes the test results between the 2-L and 4-L SCSPs. With reflow Profile 1 applied, SCSP with a 2-L substrate did not show any failure. There are two major differences between the 2-L and the 4-L Table 18.8 Failure rate comparison between 2-L and 4-L SCSP Test matrix (Table 18.3)

Leg 1

Leg 2

Substrate Failure rate

4-L substrate 32%

2-L substrate 0%

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substrates. The total thickness of the 2-L substrate is about 30% less than that of the 4-L substrate). In addition, copper trace density is different. It is believed that both factors contribute to the differences. A thicker substrate with denser copper traces will make moisture escape from the package difficult during the reflow process. To further examine the substrate thickness effect, additional design of experiment was carried out, as shown in Table 18.4. The copper density was the same, and the 4-L substrate was used for all the legs. In each experimental leg, the sample size was 240. TSAM detection and cross-sectional analysis showed that major failure mode was cohesive delamination/cracking at the bottom layer die-attach film. No delamination/cracking was observed at other interfaces and locations. Based on the TSAM detection, the delamination rates were measured and calculated for each leg. The results are summarized in Table 18.9. They show that the thicker the substrate, the higher the delamination rate. Table 18.9 Failure rate comparison for different substrate thicknesses Substrate design (Table 18.4)

Leg 1

Leg 2

Leg 3

Leg 4

Leg 5

Total thickness Failure rate (%)

z 0

1.20z 7

1.47z 32

1.47z 47

1.53z 100

18.3.3 Evaluation of Different Die-Attach Films To evaluate the performance of different die-attach films, four different die-attach films (DA1, DA2, DA3, and DA4) were selected to build both the single-die and three-die stacking CSPs, as shown in Table 18.5. The test results are summarized in Tables 18.10 and 18.11 for the three-die and single-die stacking CSPs, respectively. As expected, DA1 film exhibits a high cohesive failure rate for both the single-die and the three-die assemblies. Figure 18.8 is an example of the cross-sectional failure picture at the bottom layer film for DA1. This confirmed the film cohesive rupture failure mode. Again, other layers of the films, which are sandwiched by the dies, remain intact. No failure was observed for the packages with DA2 film and DA4 film, in both single-die and three-die assemblies. As seen in Table 18.6, DA1, DA2, and DA4 Table 18.10 Test results for the evaluation of different die-attach films (three-die stacking CSP) TSAM results Leg

Substrate Stack

DA film

Quantity

Pre-stress Post-stress

1 2 3 4

4-L 4-L 4-L 4-L

DA1 DA2 DA3 DA4

48 48 48 48

0/48 3/48 3/48 0/48

3 3 3 3

45/46 3/44 29/44 0/46

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Table 18.11 Test results for the evaluation of different die-attach films (single-die stacking CSP) TSAM results Leg

Substrate

Stack

DA film

Quantity

Pre-stress

Post-stress

5 6 7 8

4-L 4-L 4-L 4-L

1 1 1 1

DA1 DA2 DA3 DA4

45 44 45 45

0/45 0/44 0/45 0/45

30/43 0/42 41/43 0/42

Fig. 18.8 DA1 film cohesive rupture

are low-Tg die-attach films with very low Young’s moduli at elevated temperatures. Although DA2 and DA4 have lower moduli at 150◦ C than DA1, both films did not exhibit cohesive failure. DA4 absorbs the moisture in the amount twice as much as DA1 (Table 18.7). This may suggest that films with low-Tg and/or low modulus do not necessarily lead to cohesive failure during reflow. Since it is difficult to obtain accurate Young’s modulus value for a thin film at an elevated temperature, especially with humidity control, the values in Table 18.6 should be considered as references only. DA3 film showed a high failure rate. By the top-down lapping, large voids were observed at the center of the bottom layer film for both discrete and stacked packages. The cross-sectional images further captured that the failure mode was interface delamination at the bottom layer of the film/solder mask interface, as shown in Fig. 18.9. The investigation confirmed that large voids were generated by the high pressure of the pickup tool on the bottom film during the die-attach process. The new builds after modifying the process parameters demonstrated 100% clean results. From Tables 18.10 and 18.11, it is also concluded that single-die assembly performs in the same fashion as the three-die assembly if the failure occurs in the

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(a)

(b)

Fig. 18.9 Failure analysis results from the failed units with DA3 after reflow: (a) the top-down lapping shows that there were big voids captured at the center of the bottom layer film and (b) the cross section confirms that the failure mode is interface delamination between the bottom layer of the film and the substrate

bottom die-attach film. This means that the experimental evaluation can be performed on the single-die assembly for a quick assessment of moisture sensitivity performance.

18.4 Finite Element Analysis Vapor pressure buildup during reflow is presumed to be a dominant driving force for film rupture [1, 2, 11, 12]. Since the film modulus at reflow temperature is extremely low (only a few megapascals), thermal stress is by orders of magnitude lower than the modulus. When the finite deformation theory is applied, the critical void volume fraction for material to collapse is relatively small [13, 14]. This implies that thermal stress was a small fraction of the peak vapor pressure. Huang et al. [15] performed finite element analysis and showed that the thermal stress was in compressive state during the reflow process, since the film expansion was constrained by the surrounding materials with relatively high stiffness. Therefore, in the following analysis, only moisture diffusion and vapor pressure modeling are addressed. Two scenarios of vapor pressure buildup during reflow can be identified [2], as shown in Figs. 18.10 and 18.11. Before the reflow process starts, moisture condenses in nanopores or free volumes during preconditioning [16]. With temperature increasing, more and more moisture will be vaporized. At the same time, moisture concentration will decrease as more and more moisture will be diffused out of the package during reflow process. At certain temperature, the moisture may become fully vaporized. This temperature is a transition temperature for moisture from a binary state to a single vapor state. When temperature further increases, moisture is lost further. Therefore, the vapor pressure will drop (Fig. 18.10). This is referred to as Scenario I of vapor pressure buildup. Film rupture may not occur if the peak pressure is less than the critical stress of the given material. Scenario II refers to

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Fig. 18.10 Schematic diagram for Scenario I of vapor pressure buildup during reflow

Fig. 18.11 Schematic diagram for Scenario II of vapor pressure buildup during reflow

the case in which moisture in free volumes is always in a binary liquid/vapor state, as shown in Fig. 18.11. In this case, vapor pressure will remain the same as the saturated water vapor pressure. If the vapor pressure reaches the critical stress of the material, rupture will take place. Although the difference in magnitude of vapor pressure between these two scenarios is very small (less than a few megapascals), such a small difference will make a dramatic difference in the reflow performance. Finite element analysis on moisture diffusion and vapor pressure modeling were performed to correlate with the experimental results. Direct concentration approach

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(DCA) has been applied for moisture diffusion during reflow process [11, 12]. A new and simplified vapor pressure model has been used to obtain the whole field vapor pressure at reflow. The details can also be found in Chapter 4. In the present study, the package is composed of the mold compound (MC), multiple silicon dies, multiple die-attach films, solder resist (SR), and BT core, as shown in Fig. 18.12. The substrate includes two layers of SR and one layer of BT. In the following study, packages are applied to moisture preconditioning at 60◦ C/60%RH for 72 h, followed by a reflow process. Table 18.12 lists the material properties used for moisture diffusion modeling.

Fig. 18.12 Schematic structure of a 3D ultrathin stacked-die chip-scale package

18.4.1 Effect of Substrate Thickness Two substrate thicknesses of 200 and 280 μm [6] were simulated with reflow Profile 1. Results of both moisture concentration and vapor pressure in the film were obtained. Figure 18.13 shows the contours of moisture concentration at 260◦ C for packages with different substrate thicknesses. The moisture concentration of the thinner substrate in the bottom layer film is 54% less than that of the thicker substrate. It was also observed that there was virtually no difference in the moisture concentration in the MC and other films. Significant moisture in the bottom layer film was lost through the substrate during reflow. This indicates that substrate thickness plays a key role in thin package moisture performance. Figure 18.14 shows the history of the local moisture concentration in the bottom layer film for two substrate thicknesses. It can be seen that the difference in the moisture concentration becomes significant when temperature is above 150◦ C. Such a difference tends to be small again when the temperature is beyond 250◦ C, since both packages tend to be dried out eventually with time. The contours of vapor pressure are shown in Fig. 18.15 for two substrate thicknesses. For the thinner substrate, the vapor pressure is 40% less than in the thicker substrate. Figure 18.16 shows the histories of the vapor pressure evolution for these two cases. The package with the thinner substrate follows Scenario I of the vapor pressure buildup with a pressure drop, while the package with a thicker substrate follows Scenario II, in which the vapor pressure remains saturated at 260◦ C. The simulation results agree well with the experimental observations.

3.92E–4 7.83E–5 1.63E–5 5.05E–6 2.80E–6 1.67E–6

60 100 150 200 230 260 Csat

1.28E–5 4.74E–5 1.71E–4 4.72E–4 7.88E–4 1.24E–3 4.7 kg/m3

Solubility (kg/m3 Pa)

Diffusivity Temperature (◦ C) (mm2 /s)

BT substrate

2.93E–5 8.96E–5 2.70E–4 6.43E–4 9.97E–4 1.47E–3 4.5 kg/m3

Diffusivity (mm2 /s)

DA film

3.76E–4 7.52E–5 1.56E–5 4.85E–6 2.68E–6 1.60E–6

Solubility (kg/m3 Pa) 1.52E–7 5.84E–7 2.19E–6 6.21E–6 1.05E–5 1.68E–5 3 kg/m3

Diffusivity (mm2 /s) 2.50E–4 5.00E–5 1.04E–5 3.23E–6 1.79E–6 1.07E–6

Solubility (kg/m3 Pa)

Molding compound

Table 18.12 Materials properties used for the simulation of the SCSP

1.30E–6 7.52E–6 4.23E–5 1.65E–4 3.28E–4 6.02E–4 5 kg/m3

Diffusivity (mm2 /s)

Solder resist

4.17E–4 8.33E–5 1.74E–5 5.38E–6 2.98E–6 1.78E–6

Solubility (kg/m3 Pa)

18 Moisture Sensitivity Investigations of 3D SCSPs 473

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Fig. 18.13 Moisture concentration contours of a CSP at 260◦ C using the DCA approach: (a) a thinner substrate and (b) a thicker substrate

Fig. 18.14 Moisture concentration comparison between two substrate thicknesses

Fig. 18.15 Vapor pressure contours of a CSP at 250◦ C: (a) a thinner substrate and (b) a thicker substrate

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Fig. 18.16 Vapor pressure comparison between two substrate thicknesses

18.4.2 Effect of Reflow Profile Two different reflow profiles shown in Fig. 18.6 were applied. These profiles satisfy the JEDEC standard specification on temperature ramp-up as a function of time. The main difference in these two profiles is that Profile 2 has an extended time period (∼about 90 s) before temperature ramps up rapidly to the peak temperature from a temperature of 180◦ C, compared to the reflow Profile 1. Both profiles have same peak temperature of 260◦ C. The package with the substrate thickness of 280 μm was used to study the effect of the reflow profile. Figure 18.17 plots the contours of moisture concentration at 250◦ C for these two reflow profiles. The moisture concentration in the bottom layer film when the reflow Profile 2 is applied is 34% less than that when the reflow Profile 1 is applied. This is because the reflow Profile 2 has a longer exposure time at the temperature of 150◦ C to allow more moisture to be released before it ramps up. Figure 18.18 plots the contours of the vapor pressure at 250◦ C subjected to two profiles. The vapor pressure of Profile 2 in the bottom layer film is 27% less than that of Profile 1. Figure 18.19 plots the vapor pressure evolution in the bottom layer film. It can be seen that the vapor pressure buildup under Profile 2 follows Scenario I with a vapor pressure drop at the temperature of 240◦ C, while the vapor pressure buildup under

Fig. 18.17 Moisture concentration contours at 250◦ C subjected to two different reflow profiles

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Fig. 18.18 Vapor pressure contours at 250◦ C subjected to two different reflows

Fig. 18.19 Vapor pressure comparison between two substrates

Profile 1 follows Scenario II with a saturated water vapor pressure. These results are consistent with the experimental observations. From the experimental data and the vapor pressure analysis, the critical stress for film to rupture is in a very narrow range, between 2 and 6 MPa (a very rough estimate). A finite single spherical void model was introduced previously by one of the authors [13, 14] (also see Chapter 11). When hyperelastic model is applied for a rubber material, a nonlinear and non-monotonic relationship between the vapor pressure and the void volume fraction was obtained within the framework of the finite deformation theory. This defines a critical stress for the occurrence of unstable void growth. The critical stress is found to be on the same order of magnitude as the Young’s modulus of film when initial void volume fraction is between 0.01 and 0.05 [13, 14]. Although a single finite spherical void model is a simplistic approximation, it nonetheless sheds light on the mechanism of unstable void growth within the context of finite deformation. It is also observed that such a film failure is caused by a hydrostatic stress. Huang et al. [15] introduced Gent et al.’s solution [17] for a single spherical void in an infinite media to explain the cavitation phenomenon in a rubbery material. They concluded that the failure was modulated by

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the modulus and the surface energy of the material, as well as by the initial void size. Cohesive film failures at the reflow soldering conditions have not been observed previously when dispense die-attach assembly method is applied. Die-attach paste material has a much higher modulus than a wafer-level die-attach film. A reasonable estimate of the Young’s modulus for a die-attach paste material is at least 100 MPa at reflow temperature. In this case, according to the analysis from a single void model, cohesive rupture is not a concern, while the interfacial delamination is. Most of the previous studies focused on the interfacial delamination [7, 8, 10, 13, 14]. Another unique characteristic, for ultrathin CSP package, is moisture desorption during reflow process. Moisture loss at the substrate/film interface becomes significant during reflow. However, for a regular-type package, significant moisture is lost only in the exterior area of the package.

18.5 Summary Cohesive failure of die-attach film during moisture sensitivity test for stacked chipscale packages (SCSPs) becomes a particular concern due to its extremely low modulus at soldering reflow temperature. The root cause of this type of failure is difficult to discern, even with extensive root cause analysis and focused design of experiments. It has been observed that for some die-attach films, such packages are very sensitive to soldering reflow profile and substrate thickness, with massive cohesive failure within the die-attach film. Moisture escape and transport during reflow has been determined to be a significant factor for this type of failure. Further experiments based on a broad spectrum of die-attach films revealed that not all dieattach films with very low modulus are sensitive to the reflow profiles and substrate designs. If the film is not sensitive to reflow profile, even though the die-attach film has a very low modulus, the film modulus, diffusivity, and saturated moisture concentration are not critical parameters in screening die-attach films. In this case, the process control in optimizing the interfacial adhesion and minimizing the voids becomes the key modulator. Since the die-attach film is usually confined between die and substrate, therefore, the effective hydrostatic stress might be much lower than the vapor pressure. On the other hand, when cohesive failures are present, the integrated modeling approach with material characterization can be applied to provide design guidelines for key parameters including manufacturing parameters (reflow profile control), package design parameters (layout and thickness), and the material parameters (diffusivity, solubility, modulus, and porosity).

References 1. Shi, X.Q., Fan, X.J., “Wafer-level film selection for stacked-die chip scale packages,” Proceedings of 57th Electronic Components and Technology Conference, USA, pp. 1731–1736, 2007.

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2. Fan, X.J., Bekar, I., Fischer, A., He, Y., Huang, Z.Y., Prack, E., “Delamination/cracking mechanism study for ultra-thin stacked-die chip scale packages,” Intel Conference on Manufacturing Excellence (IMEC), San Diego, CA, USA, 2006. 3. Prack, E., Fan, X.J., “Root cause mechanisms for delamination/cracking in stack-die chip scale packages,” International Symposium on Semiconductor Manufacturing (ISSM), September 25–27, Tokyo, Japan, 2006. 4. Xie, B., Shi, X.Q., Fan, X.J., “Sensitivity investigation of substrate thickness and reflow profile on wafer level film failures in 3D chip scale packages by finite element modeling,” Proceedings of 57th Electronic Components and Technology Conference, USA, pp. 242–248, 2007. 5. Tang, J., et al., “4L structural full factorial DOE summary,” Unpublished internal report, Intel, 2006. 6. He, Y., Fan, X.J., “In-situ characterization of moisture absorption and desorption in a thin BT core substrate,” Proceedings of Electronic Components and Technology Conference (ECTC), pp. 1375–1383, 2007. 7. Fan, X.J., Zhou, J., Zhang, G.Q., Ernst, L.J., “A micromechanics-based vapor pressure model in electronic packages,” ASME Journal of Electronic Packaging, 127, 262–267, 2005. 8. Fan, X.J., “Moisture related reliability in electronic packaging,” ECTC Professional Development Course Handout, 2005/2006/2007/2008. 9. Zhang, G.Q., van Driel, W.D., Fan, X.J., Mechanics of Microelectronics. New York, NY: Springer, 2006. 10. Fan, X.J., Zhang, G.Q., Driel, W.D., Ernst, L.J., “Interfacial delamination mechanisms during reflow with moisture preconditioning,” IEEE Transactions on Components and Packaging Technologies, 31(2), 252–259, 2008. 11. Xie, B., Fan, X.J., Shi, X.Q., Ding, H., “Direct concentration approach of moisture diffusion and whole field vapor pressure modeling for reflow process: part I – theory and numerical implementation,” ASME Journal of Electronic Packaging, 131(3), 031011, 2009. 12. Xie, B., Fan, X.J., Shi, X.Q., Ding, H., “Direct concentration approach of moisture diffusion and whole field vapor pressure modeling for reflow process: part II – application to 3-D ultra-thin stacked-die chip scale packages,” ASME Journal of Electronic Packaging, 131(3), 031010, 2009. 13. Fan, X.J., Zhang, G.Q., Driel, W.D., Ernst, L.J., “Analytical solution for moisture-induced interface delamination in electronic packaging,” Proceedings of Electronic Components and Technology Conference, pp. 733–738, 2003. 14. Fan, X.J., Zhang, G.Q., Ernst, L.J., “A Micro-mechanics approach in polymeric material failures in microelectronic packaging,” Proceedings of 3rd International Conference on Thermal & Mechanical Simulation in Micro-Electronics (EuroSimE), pp. 154–164, 2002. 15. Huang, Z., Tang, J., Hu, C., Wang, M., Zhang, M., Liu, B., Fan, X.J., Prack, E., “Moisture induced cohesive delamination in die-attach film in ultra thin stacked chip-scale package,” Intel Assembly Technology and Text Journal, 2006. 16. Fan, X.J., Lee, S.W.R., Han, Q., “Experimental investigations and model study of moisture behaviors in polymeric materials,” Microelectronics Reliability, 49, 861–871, 2009. 17. Gent, A.N., Lindley, P.B., “Internal rupture of bonded rubber cylinders in tension”, Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences, 249(1257), 195–205.

Chapter 19

Automated Simulation System of Moisture Diffusion and Hygrothermal Stress for Microelectronic Packaging Y. Liu

19.1 Introduction Microelectronic packages are known to absorb moisture when exposed to humid ambient conditions. The presence of moisture in packages induces hygroscopic stress through differential swelling and induces vapor pressure that is responsible for the eventual popcorn cracking in reflow. Moisture induces the interfacial stresses generated between die attach and die, die and mold compound, as well as leadframe and mold compound. This may finally lead to delaminating and package cracking [1, 2]. Therefore, moisture analysis plays an important role in the integrity and reliability of microelectronic packaging. At present, more and more researches are focusing on the study of moisture and its related reliability of microelectronic packages [3–6]. Obtaining the moisture simulation results (such as hygroscopic stress and vapor pressure-induced stress) is very important to improve the IC package design and reliability for resisting failure [7]. However, most IC package development engineers and reliability engineers may not have the abilities to perform such analysis using finite element analysis (FEA). To facilitate the IC package design process and optimize solution, several simulation software programs have been developed to give R prousers convenience in modeling, meshing, or loading. For example, ICEPAK vides a fully interactive and object-based thermal management software tool. It also expands the ability to handle complex geometry and provides additional flexibility and a higher degree of automation while performing thermal analysis in today’s electronic components and systems. PakSiTM is another easy-to-use tool which is developed by Optimal Corporation. It can reduce package modeling and analysis time significantly. Despite these improvements, mistakes can still be easily made by inexperienced users. This includes misrepresenting model boundary conditions, using inappropriate element types, accepting results with an inadequate mesh, and so on. To avoid these incorrect operations and to assist semiconductor engineers to perform moisture-related simulation, it is necessary to develop a fully automated

Y. Liu (B) e-mail: [email protected] X.J. Fan, E. Suhir (eds.), Moisture Sensitivity of Plastic Packages of IC Devices, Micro- and Opto-Electronic Materials, Structures, and Systems, C Springer Science+Business Media, LLC 2010 DOI 10.1007/978-1-4419-5719-1_19, 

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simulation system that has the ability to complete the whole IC package moisture analysis automatically. ANSYS Workbench is a new-generation platform used for developing and managing FEA simulations. It not only offers highly integrated engineering simulation platform and bidirectional parametric integration with most available CAD systems but also provides multi-tiered customization tools to support a variety of development efforts [8]. ANSYS WorkbenchTM software development kit (SDK) is an open architecture platform that allows customers to develop and integrate application R spreadsheet architecture on Workbench environment. Nowadays, Microsoft Excel R  has been widely used in many fields. Especially, Visual Basic for Application (VBA) expands the capability of Excel to realize many automated and complex tasks. Zhang et al. [9] and Xia et al. [10] developed a highly efficient automated simulation system (AutoSim) for the thermal and moisture analysis in Excel spreadsheet cooperating with ANSYS Workbench. A user is only required to input the basic parameters in Excel interface. Then the JScript application, which is stored background, will drive and integrate Workbench components automatically to perform the thermal and moisture analysis on packages. The goal of this chapter is to expand the AutoSim system to have the capability of full and systematic moisture-related automated stress analysis, including moisture diffusion analysis, hygro-mechanical stress, and vapor pressure analysis. The AutoSim allows users to select the geometry models from CAD library and then perform various moisture-related analysis automatically. As an example, this customized system has been applied for moisture diffusion analysis of a Fairchild molded leadless package (MLP) family, and the results are validated using ANSYS-Multiphysics analysis.

19.2 Basic Formulations 19.2.1 Moisture Diffusion and Hygroswelling Transient moisture diffusion equation is analogous to transient heat conduction equation, and it can be described by Fick’s Law as follows:   2 ∂ C ∂ 2C ∂ 2C ∂C , =D + + ∂t ∂x2 ∂y2 ∂z2

(19.1)

where C is the local moisture concentration, x, y, and z are the spatial coordinates, and D is the diffusivity which measures the rate of diffusion. However, unlike temperature, the moisture concentration is discontinuous along bimaterial interface (see Chapter 4). Moisture concentration discontinuity across bimaterial interfaces can be overcome with the use of continuous field variables such as “wetness” [1, 2], w, as follows:

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C , 1 ≥ w ≥ 0, Csat

(19.2)

w=

where Csat is the saturated moisture concentration. The lower limit w = 0 means material is dry, and the upper limit w = 1 means it is fully saturated with moisture. Equation (19.1) can also be rewritten as   2 ∂ w ∂ 2w ∂ 2w ∂w =D + 2 + 2 . ∂t ∂x2 ∂y ∂z

(19.3)

The moisture–thermal analogy using the normalized approach is no longer valid when the saturated moisture concentration is a function of temperature [6, 11–13]. A direct concentration approach (DCA) has been developed to perform moisture diffusion analysis correctly during reflow [11]. Due to CME (coefficient of moisture expansion) mismatch among various materials, the hygroscopic stress is induced. The concept is analogous to the CTE mismatch and the thermo-mechanical stresses [3]. The hygro-mechanical problem can be solved using the same procedure as thermo-mechanical solution. It can be described by equation (19.4) as follows: εh = β · C,

(19.4)

where εh is the hygrostrain, β is the CME, and C is the moisture concentration. The representative values of CME for EMC (epoxy mold compound) and die-attach materials are given in Table 19.1. Table 19.1 Moisture absorption and hygroscopic properties of MLP 6 × 6 quarter model Material

D (mm2 /s)

Csat (mg/mm3 )

CME (mm3 /mg)

EMC Die attach

4.73e–7 1.25e–5

7.06e–3 6.20e–3

0.222 0.520

19.2.2 Vapor Pressure Model The moisture exists everywhere in polymer materials in an electronic package after preconditioning. During solder reflow in surface mounting, the temperature of the package body is raised up to 220–260◦ C. The moisture absorbed in the plastic package becomes vaporized and exerts a pressure on the internal package body. The induced vapor pressure coupled with the thermal stress and hygroscopic stress could result in a failure mechanism often referred to as “popcorn” phenomenon. It is particularly important to analyze the vapor pressure distributions and variations with temperature and moisture concentration. Most of vapor pressure models that are available in literature assume that the macroscopic delamination or voids exist in packages [6]. Since moisture stays in

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nano-voids or free volumes in polymeric materials [11], a multi-scale analysis is needed to develop vapor pressure models. In the following, a micro-mechanicsbased vapor pressure model [4–6] is introduced. The model has been validated experimentally with many case studies [14, 6]. There are three distinct cases for the vapor pressure evolution from the preconditioning temperature T0 to the current reflow temperature T [4, 5]. In case 1, the moisture in the void is in the single vapor phase at T0 ; thus the vapor pressure at T follows the ideal gas law: When

C0 pg (T0 ) T C0 ≤ ρg (T0 ) , P (T) = , f0 ρg (T0 ) fT0

(19.5)

where p is the pressure and pg is the saturated vapor pressure. In case 2, the moisture is not fully vaporized even at reflow temperature T. The moisture in the void is in the mixed liquid–vapor phase at the temperature from T0 to T. Thus the vapor pressure maintains the saturated vapor pressure during the course of the temperature rise: When

C0 ≥ ρg (T) , P (T) = pg (T) . f

(19.6)

In case 3, it is an intermediate case between case 1 and case 2, where the moisture is in the mixed liquid–vapor phase at a preconditioning temperature T0 , but in the single vapor phase at T. The moisture is fully vaporized at a temperature between preconditioning temperature T0 and the peak reflow temperature T: ⎧ C0 ⎪ ⎪ ⎨ f > ρg (T0 ) T f (T1 ) 0 When , P (T) = pg (T1 ) , ⎪ C0 T1 f ⎪ ⎩ < ρg (T) f

(19.7)

where T1 is the phase transition temperature at which the moisture can be fully vaporized.

19.2.3 Equivalent Coefficient of Thermal Expansion (CTE) Thermal conduction is much faster than moisture diffusion. When the external surface is heated to a reflow temperature, the internal package reaches a uniform temperature within a few seconds. Therefore, in the subsequent thermo-mechanical and vapor pressure models, temperature distribution during reflow can be assumed to be uniform throughout the package body. The temperature load applied is from the stress-free reference temperature (usually it selects a curing temperature or a glass transition temperature of the mold compound) to the reflow temperature. For an IC package with epoxy mold compound, after the moisture absorption, the hygroscopic strain introduces additional mismatch. The hygroscopic strain can be treated

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as additional thermal strain. The same is true for the vapor pressure which induces additional expansion and additional mismatch. The vapor pressure-induced strain can also be treated as the additional strain. Assume linear elastic analysis and in the worst case, vapor pressure and moisture are uniformly distributed. The total linear elastic strain can be written as [5, 7] εT = αT + β ∗ C + (1 − 2v)p/E,

(19.8)

where εT is the total linear strain that includes the CTE mismatch strain, the hygroscopic strain, and the vapor pressure-induced strain, α is the CTE, T is the temperature changes, v is the Poisson’s ratio, E is the modulus, and p is the average vapor pressure. The modulus of mold compound drops a few orders at the reflow temperature; thus the vapor pressure strain may become as important as thermal or hygroscopic strain in reflow. The equivalent coefficient of thermal expansion that integrated thermal CTE, hygroscopic, and vapor pressure can be further expressed as follows: CTET = α + β ∗ C/T +

1 − 2v p/E/T. E

(19.9)

19.3 Development of Automated Simulation System for Moisture Diffusion and Hygrothermal Stress 19.3.1 ANSYS Workbench Overview ANSYS Workbench includes five modules: Design SimulationTM , DesignModelerTM , CFX-MeshTM , FE ModelerTM , and DesignXplorerTM . The core of Workbench is the Design Simulation module, which is mainly used for performing structural, thermal, and electromagnetic analyses by using the ANSYS solver. DesignModeler is used for creating and modifying CAD geometry to prepare the solid model for using in Design Simulation. CFX-Mesh is a mesh generator aimed at producing high-quality meshes for using in computational fluid dynamics (CFD) simulations. FE Modeler supports data transfer from R R and ABAQUS to classic ANSYS. Finally, DesignXplorer is used NASTRAN for design optimization. The AutoSim developed in this chapter is based on Design Simulation and DesignModeler. Figure 19.1 shows a 3D molded leadless package (MLP) model used in AutoSim. ANSYS Workbench is a development platform, which allows user to carry out various developments through wide range of customization tools. For example, the Simulation Wizard Editor can be used to develop a customized wizard interface. ANSYS Workbench SDK (Software Development Kit) allows the user to develop and integrate applications compatible with the Workbench framework and architecture using application programming interfaces (APIs). One of the primary tools in the SDK architecture is the Applet Generator. The Applet Generator is an integrated

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Fig. 19.1 Package model in AutoSim

R wizard for Microsoft Visual Studio , which can produce executable applets using prebuilt Workbench source code templates. It can also automatically create the customized user interface and finish the applets installation and registration process. In addition to the compiled applications, the Workbench also supports a number of scripting languages including JScript and VBScript. JScript is recommended as the primary scripting language by ANSYS. JScript is employed to create the user interface along with HTML and XML. The user can also develop JScript applications to drive and integrate Workbench components to automate existing processes.

19.3.2 General Package Automated Simulation Platform Generally speaking, every analysis using ANSYS Workbench involves four main steps, as shown in the simulation process in Fig. 19.2. As we know, package models from the same family usually have the same or similar structure but different sizes, materials, or number of components. Therefore, a general process can be developed by performing an analysis on all package models from the same family. This general process algorithm can be stored in background and hidden from the user. This algorithm controls material assignment, meshing, loading, and postprocessing. Figure 19.3 shows the automated simulation process in AutoSim. User is only required to input the basic data in an intuitive and simple interface, and the other steps of preprocessing (meshing, loading, and boundary condition), solving, post-processing, and report will be automatically performed. As we can see, it gives the designers and inexperienced engineers much convenience in performing moisture-related analysis. In addition, it ensures the standardization of results.

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AutoSim of Moisture Diffusion and Hygrothermal Stress Preliminary Decision

Preprocessing

Solution

485 PostProcessing

Fig. 19.2 Simulation process in ANSYS Workbench

Input Basic Data

Preprocessing

Output Result

Solution

Fig. 19.3 Automated simulation process in AutoSim

To build the automated simulation process, the solid model will be developed or loaded first. Usually a user has to spend much time in building a complex package model using general FEA software during preprocessing. But a CAD model can be directly imported into Workbench because Workbench provides import and bidirectional associated capability with many CAD systems. Additionally, the names of components defined in CAD system will also be imported into Workbench along with the solid model. It is emphasized that the names of components play an important role in distinguishing the components, assigning materials to corresponding components, and applying boundary conditions to corresponding components. Based on the above idea and workbench customization tools, a general automated simulation system (i.e., AutoSim) for moisture diffusion and hygrothermal stress is developed which includes five modules: a Package Model CAD Library, an Executable Wizard System, a Package Material Library, an Environment Options (or Library), and a Report Generation System. The overall architecture of AutoSim is shown in Fig. 19.4. Fig. 19.4 Overall architecture of AutoSim

Package Material Library

Wizard System

Environment Options

Automated Simulation System

Package Model CAD Library

Report Generation System

The Package Model CAD Library is a core element of AutoSim. First, it is used for storing CAD models, which provides the user convenience to select a model for analysis. Second, The Package Model CAD Library provides a model information interface for user to manage the models’ information, shown in Fig. 19.5. The

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Fig. 19.5 Package CAD Model Information Interface

interface classifies the solid CAD models by package families and requires user to input models’ names and select corresponding materials from Package Material Library. It is noted that the inputted names should be the same as the names defined in CAD software. As we can see, it will be especially convenient when user wants to compare the results using different materials. The interface also allows user to add, delete, or modify data. All the information is saved in a database which will be used in analysis process. Wizard System is another core element of AutoSim, which contains the general procedure of moisture analysis for package models. The Wizard System has a user-friendly interface; it only requires user to input the basic parameters. An example is to input the title of simulation and user name, load the solid models from Package Model CAD Library, and input the moisture condition. Because some simulations may be performed on quarter- or half-package models, user can select the type of model. The Wizard System will collect all the information that user inputs and performs the whole moisture simulation automatically according to the predefined procedure in the background. Figure 19.6 shows the general flowchart of AutoSim which is predefined in Wizard System for automated simulation. It builds the connection with other modules and realizes the automation of simulation on package models. The selected CAD model from Package Model CAD Library is imported into DesignModeler and applied some operations, such as creating Name Selection (just as grouping geometry items into a component in classic ANSYS) and forming new part (just as gluing in classic ANSYS). In fact, all these operations are prepared for meshing and loading in Design Simulation. Then the model is imported to Design Simulation from DesignModeler. Based on the definition in Package Model Information Interface, every component of model will be assigned to corresponding materials

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Fig. 19.6 Basic flowchart of AutoSim

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Start Up Collect Input Information Import Model into DesignModeler and Apply Operations

Package Model CAD Library

Import Model into Design Simulation Assign Materials to Model

Package Material Library

Intelligent Mesh Apply Moisture Loads/BC to Model

Environment Options

Solve and Save Result Report

which come from the Package Material Library. An intelligent meshing function is implemented to generate high-quality mesh for highly accurate solutions. The boundary condition (like moisture) is automatically calculated and is applied to the package outside surface which is saved in Environment Options (or Library). Wizard System is automatically implemented for solving the model and saving the results. The results may include contours of moisture distribution, vapor pressure distribution, hygroscopic stress, and various equivalent stress-based moisture and vapor pressure. It is emphasized that the APDL commands are inserted into the Design Simulation and implementing path operations because these functions have not yet been developed by ANSYS Workbench. One of the most important steps in moisture analysis is to define appropriate material properties for package models to represent actual working conditions. There are various package materials whose parameters vary depending on manufacturing conditions. Furthermore, many material properties are temperature dependent and may require extraction from experimental inputs. For convenience to the user in creating and maintaining package material database, the Package Material Library is built based on Engineering Data Application of ANSYS Workbench. Environment Option (or Library) is the boundary condition and loads database which is transferred by Wizard System in applying loads. It provides an interface for people to modify the moisture boundary and loads of different components. It

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is especially convenient when user wants to compare the results among different thermal or moisture boundary conditions. For most engineers and designers, the documentation of analysis report is a very tedious task and time consuming. Therefore, Report Generation System of AutoSim is developed based on report function of the Design Simulation module. It has the ability to capture engineering information and automatically produce complete engineering documentation in HTML, including words, tables, and color illustrations.

19.3.3 Structure of AutoSim in Moisture-Related Analysis The above description is a general automation simulation system. Basically it can be applied to any problems, such as moisture, thermal, and stress analysis. For a highly efficient simulation automation system for moisture-related analysis, it can be further developed into three modules: a Package Moisture Model Information Library, an Executable Wizard System with Excel spreadsheet, a Package Moisture Material Library, and Moisture Environment Option. User is only required to input basic data in a Wizard interface (an Excel spreadsheet) and it will link to Workbench and automate the whole steps of moisture and vapor simulation. At last, the simulation results will also export into the Wizard interface. Figure 19.7 shows the structure of AutoSim for moisture simulation.

Moisture AutoSim

Package Model Information

Wizard System

Package Material Library

Moisture Analysis

Vapor Analysis

Integrated Analysis

Environment Options (B.C)

Fig. 19.7 Structure of AutoSim for moisture-related analysis

The Wizard System is composed of three parts, which are used for moisture analysis, vapor analysis, and integrated analysis. The Wizard System for moisture analysis performs the simulation of moisture diffusions and hygroswelling analysis. Other Wizard systems are used to perform the vapor pressure analysis and the combination analysis which includes the stress analysis of thermal–mechanical, hygro-mechanical, vapor-induced equivalent thermal mismatch, and integrated.

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19.3.3.1 Modules of Moisture-Related Automated Simulation System Figure 19.8 lists an interface window of the moisture-automated simulation system. At the main menu, there are four major functions: modeling information, wizard system, material library, and environment library. Each of the function gives the related information for thermal and mechanical, moisture, vapor pressure, and equivalent thermal stress.

Fig. 19.8 Master interfaces of AutoSim for moisture-related analysis

The Package Model Information Library plays a very important role in the whole process of the analysis automatically. It is the core element of moisture automation analysis system and provides an interface for user to store and resume CAD models easily. In Fig. 19.9, the example interface shows package model information for equivalent thermal stress analysis. It will automatically show all component names which are defined in CAD software. Then, user may select corresponding materials for every component from Package Material Library. All the information is saved in a database which will be transferred by Wizard System. Wizard System is divided into three parts: Wizard System for Moisture Diffusion and Hygroswelling analysis, Wizard System for Vapor Pressure Analysis, and Wizard System for Equivalent Thermal Stress Analysis. All the three parts have similar interfaces as the example in Fig. 19.9. The Wizard System uses Excel spreadsheet as the user interface which requires user to input the basic data. An example is to input user name, title of simulation, job name, working directory, and so on. User will also be required to select a model to be simulated and then the model

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Fig. 19.9 Package model information interface for equivalent thermal stress

Fig. 19.10 Data review example of material library

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information stored in Package Model Information Library will be exported into Wizard interface. The Wizard System will collect all the information that user inputs and performs the whole corresponding simulation automatically according to the predefined procedure in the background. Figure 19.10 shows the data review example of a group thermal coefficient of expansion (CTE) vs. temperature of the material library. Figure 19.11 shows the calculated equivalent CTE for hygroscopic swelling, vapor-induced swelling, and the integrated total CTE for a linear analysis in the environment library.

Fig. 19.11 Data review and check of equivalent CTE of environment library

19.4 Application of AutoSim 19.4.1 Moisture Diffusion Analysis for an MLP Package AutoSim has been applied for the MLP family packages from Fairchild Semiconductor. In the following study, an MLP 6 × 6 quarter model is chosen for analysis, as shown in Fig. 19.12. 19.4.1.1 Moisture Diffusion The moisture properties, i.e., diffusivity and Csat , characterized under 85◦ C/85% RH, are listed in Table 19.1 [3]. Figure 19.13 shows the comparisons of the moisture wetness distribution between ANSYS-Multiphysics and AutoSim. From Fig. 19.13, it can be seen that

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Fig. 19.12 A MLP 6 × 6 quarter model

the results agree well with each other. AutoSim is fully automatic to obtain the results. Figure 19.14 compares the hygroscopic deformation and von Mises stress between ANSYS-Multiphysics and AutoSim. Table 19.2 lists the maximum von Mises stress and the total deformation values of the two methods. From Fig. 19.14 and Table 19.2, it can be seen that the maximum values at corresponding locations obtained from AutoSim agree with those from ANSYS-Multiphysics. 19.4.1.2 Vapor Pressure Simulation Figure 19.15 shows the comparison of the vapor pressure distribution at reflow between AutoSim and ANSYS-Multiphysics. From Fig. 19.15, we can see that the results match well with each other. At reflow temperature of 220◦ C, the saturated vapor pressure is 2.32 MPa. If the moisture is not fully vaporized at reflow, the vapor pressure will maintain the saturated value, no matter how much moisture is absorbed. 19.4.1.3 Integrated Stress Modeling In the following, the package stress-free temperature is at the curing temperature of epoxy mold compound, which is 175◦ C. The temperature is raised to a reflow temperature (220◦ C) from 175◦ C. The thermo-mechanical material properties used in the modeling are given in Table 19.3 [3]. Figure 19.16 compares the integrated deformation and von Mises stress induced by hygroscopic and thermal–mechanical loads between AutoSim and ANSYSMultiphysics. Table 19.4 lists the maximum hygrothermal–mechanical von Mises stress and total deformation values of the two methods. The total strains induced by hygroscopic and thermo-mechanical loads and vapor pressure in mold compound and die attach are listed in Table 19.5. For hygroscopic strain and vapor pressure-induced strain, they are converted into the equivalent

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Moisture absorption at 48 hours

Moisture absorption at 96 hours

Moisture absorption at 168 hours Result by ANSYS-Multiphysics

Result by AutoSim

Fig. 19.13 Comparison of moisture distributions between ANSYS-Multiphysics and AutoSim

CTEs with a temperature ranging from curing temperature of 175◦ C to reflow temperature of 220◦ C so that all three modes (hygroscopic, thermal–mechanical, and vapor pressure) can be integrated into an equivalent thermo-mechanical system. The total equivalent CTE is much larger than any individual contribution. So the

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Hygroscopic deformation

Hygroscopic Von Mises stress Result in ANSYS-Multiphysics

Result in AutoSim

Fig. 19.14 Comparison of hygroscopic deformation and von Mises stress

Table 19.2 Hygroscopic stress results by ANSYS-Multiphysics and AutoSim

ANSYS-Multiphysics AutoSim

Maximum von Mises stress (MPa)

Maximum total deformation (mm)

99.402 104.65

0.02836 0.02714

thermal, hygroscopic, and vapor pressure-induced stresses are integrated to allow realistic stress analysis for prediction of damage and failure. Figure 19.17 compares the deformation and stress induced by vapor pressure only. Table 19.6 compares the corresponding maximum values based on the two methods.

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Result by ANSYS-Multiphysics

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Result by AutoSim

Fig. 19.15 Comparison of vapor pressure distribution at reflow temperature

Table 19.3 Thermo-mechanical material properties (220◦ C)

EMC Die Die attach Leadframe Pad

E (MPa)

CTE (ppm/◦ C)

v

1,100 131,000 43 127,400 127,400

34 2.8 170 17.4 17.4

0.3 0.3 0.3 0.3 0.3

Figure 19.18 compares the integrated contours of total deformation and von Mises stress under thermal, hygroscopic, and vapor pressure loads between ANSYS-Multiphysics and AutoSim. Table 19.7 compares the integrated total results between ANSYS-Multiphysics and AutoSim. Both total deformation results agree very well.

19.4.2 Material Parameter Examination One advantage of the AutoSim is that the parameter design of experiment (DoE) can be run very efficiently. Table 19.8 lists 16 legs to study the effect of epoxy mold compound properties. In addition, die size is also considered as one factor listed in Table 19.8. The purpose of the DoE study is to find out the rank of the legs. Therefore the simulation results will be used to guide the package design engineers to select the best epoxy mold compound material in early design phase. Figure 19.19 gives the integrated von Mises stress DoE results through the moisture simulation automation system. The DoE simulation has given the rank of von Mises stress level in the molding compound at reflow. In each case, the maximum stress appears at the corner interface among the molding compound, the die attach, and the die. Leg 6 with smaller Young’s modulus, higher Tg , smaller

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Integrated deformation

Integrated von Mises stress Result by ANSYS-Multiphysics

Result by AutoSim

Fig. 19.16 Comparison of integrated hygroscopic and thermal–mechanical deformation and stress

Table 19.4 Integrated hygroscopic and thermal–mechanical results in ANSYS-Multiphysics and AutoSim

ANSYS-Multiphysics AutoSim

Maximum von Mises stress (MPa)

Maximum total deformation (mm)

99.402 104.65

0.013431 0.013470

CTE, lower solubility, and smaller die size has the lowest von Mises stress, while Leg 2 with larger Young’s modulus, lower Tg , larger CTE, and larger die size gets the highest von Mises stress. This would be a helpful information for IC package designer to find the Leg 6 with best material parameters among the 16 DoE legs.

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Table 19.5 Total strain and equivalent CTE in simulation of ANSYS-Multiphysics and AutoSim EMC

Thermo-mechanical Hygroscopic Vapor pressure Integrated (total)

Die attach

Total strain

Equivalent CTE (ppm/◦ C)

Total strain

Equivalent CTE (ppm/◦ C)

1.53E–03 1.57E–03 8.44E–04 3.94E–03

34 34.8 18.7 87.5

7.65E–03 3.22E–03 2.16E–02 3.25E–02

170 71.6 480 721.6

Vapor pressure induced deformation

Vapor pressure induced von Mises stress Result by ANSYS-Multiphysics

Result by AutoSim

Fig. 19.17 Comparison of vapor pressure-induced deformation and stress

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Table 19.6 Vapor pressure-induced equivalent stress results in ANSYS-Multiphysics and AutoSim

ANSYS-Multiphysics AutoSim

Maximum von Mises stress (MPa)

Maximum total deformation (mm)

53.839 56.676

0.006949 0.006954

Integrated total deformation

Integrated total von Mises stress Result by ANSYS-Multiphysics

Result by AutoSim

Fig. 19.18 Comparison of integrated deformation and stress induced by hygroscopic, thermal– mechanical, and vapor pressure loads

19.5 Conclusion This chapter introduces the development of an automated simulation system, AutoSim, for the analysis of moisture diffusion, vapor pressure distribution, thermal stress, hygroscopic stress, vapor pressure-induced stress, and the integrated equivalent stress for microelectronic package. The automated simulation system includes

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Table 19.7 Integrated hygroscopic, thermal–mechanical, and vapor pressure results in ANSYSMultiphysics and AutoSim

ANSYS-Multiphysics AutoSim

Maximum von Mises stress (MPa)

Maximum total deformation (mm)

202.602 213.13

0.021783 0.021894

Table 19.8 Material parameter DoE arrangement EMC

Die

No.

Leg

Tg

CTE

E (MPa)

Solubility

Die size

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

−−−+− −++−+ −+−++ +++++ −+++− +−−−− −−+−− −−−−+ +−++− ++−+− −+−−− −−+++ +++−− ++−−+ +−−++ +−+−+

110 110 110 150 110 150 110 110 150 150 110 110 150 150 150 150

40 60 60 60 60 40 40 40 40 60 60 40 60 60 40 40

500 800 500 800 800 500 800 500 800 500 500 800 800 500 500 800

0.0085 0.0045 0.0085 0.0085 0.0085 0.0045 0.0045 0.0045 0.0085 0.0085 0.0045 0.0085 0.0045 0.0045 0.0085 0.0045

3×3×0.152 4×4×0.152 4×4×0.152 4×4×0.152 3×3×0.152 3×3×0.152 3×3×0.152 4×4×0.152 3×3×0.152 3×3×0.152 3×3×0.152 4×4×0.152 3×3×0.152 4×4×0.152 4×4×0.152 4×4×0.152

five modules: a Package Model CAD Library, an Executable Wizard System, a Package Material Library, an Environment Options (or Library), and a Report Generation System. This allows users to select the geometry models from CAD library and then perform various moisture-related analysis automatically. It is especially helpful for engineers who do not know FEA and moisture theories to run the simulation easily by using this system for co-design simulation automation. The automated simulation system has been applied for moisture diffusion and related stress analysis of an MLP package. A design of experiment (DoE) simulation for epoxy mold compound material examination has been carried out and discussed by using AutoSim. The simulated results from AutoSim agree well with the results from ANSYS-Multiphysics. It should be noted that in some stress simulation case, there is small difference (within 5%) between ANSYS-Multiphysics and AutoSim due to the possible different meshes, solvers, and current limitation of workbench tool itself. However, the methodology developed in this chapter provides a highefficiency solution for package designers and reliability and test engineers who do not have modeling and moisture physics background to find the optimized result

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Fig. 19.19 DoE simulation results of integrated von Mises stress

much faster than does regular method. This may extremely save the design cycle time and the cost for new package product development. Acknowledgments The author thanks the support from the package development and automation development of Fairchild Semiconductor Corporation and the collaboration with Fairchild-ZJUT Joint Lab at Zhejiang University of Technology in China.

References 1. Wong, E.H., Teo, Y.C., Lim, T.B., “Moisture diffusion and vapor pressure modeling of IC packaging,” Proceedings of 48th Electronic Components and Technology Conference, Seattle, Washington, USA, pp. 1372–1378, 1998. 2. Wong, E.H., Chan, K.C., Tee, T.Y., Rajoo, R. “Comprehensive treatment of moisture induced failure in IC packaging„” Proceedings of the 3rd IEMT/IMC, Tokyo, Japan, pp. 176–181, 1999. 3. Tee, T.Y., Zhong, Z., “Integrated vapor pressure, hygroswelling, and thermo-mechanical stress modeling of QFN package during reflow with interfacial fracture mechanics analysis,” Microelectronics Reliability, 44, 105–111, 2004. 4. Fan, X.J., Zhou, J., Zhang, G.Q., Ernst, L.J., “A micromechanics-based vapor pressure model in electronic packages,” ASME Journal of Electronic Packaging, 127, 262–267, 2005. 5. Zhang, G.Q., van Driel, W.D., Fan, X.J., Mechanics of Microelectronics. New York, NY: Springer, pp. 281–374, 2006.

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6. Fan, X.J., Zhang, G.Q., van Driel, W.D., Ernst, L.J., “Interfacial delamination mechanisms during soldering reflow with moisture preconditioning,” IEEE Transactions on Components and Packaging Technologies, 31(2), 252–259, 2008. 7. Fan, X.J., “Moisture related reliability in electronic package,” Professional Development Short Course, 58th Electronic Components and Technology Conference, Lake Buena Vista, Florida, USA, 2008. 8. ANSYS, Documentation for ANSYS Workbench, 12. Canonsburg, PA: ANSYS, 2008. 9. Zhang, Y.X., Liang, L.H., Liu, Y., et al., “Modeling automation system for electronic package thermal analysis using Excel spreadsheet,” ICEPT , Shanghai, China, pp. 147–150, 2007. 10. Xia, Y.J., Zhang, Y.X., Liu, Y., et al., “Development of moisture automation analysis system for microelectronic packaging structures,” ICEPT, Shanghai, China, pp. 66–70, 2008. 11. Fan, X.J., Lee, S.W.R., Han, Q., “Experimental investigations and model study of moisture behaviors in polymeric materials,” Microelectronics Reliability, 49, 861–871, 2009. 12. Xie, B., Fan, X.J, Shi, X.Q., Ding, H., “Direct concentration approach of moisture diffusion and whole field vapor pressure modeling for reflow process: part I – theory and numerical implementation,” ASME Journal of Electronic Packaging, 131(3), 031010, 2009. 13. Xie, B., Fan, X.J., Shi, X.Q., Ding, H., “Direct concentration approach of moisture diffusion and whole field vapor pressure modeling for reflow process: part II – application to 3-D ultra-thin stacked-die chip scale packages,” ASME Journal of Electronic Packaging, 131(3), 031011, 2009. 14. van Driel, W.D., van Gils, M.A.J., Zhang, G.Q., Ernst, L.J., “Driving mechanisms of delamination related reliability problems in exposed pad packages,” IEEE Transactions on Components and Packaging Technologies, 31(2), 260–268, 2008.

Chapter 20

Moisture-Driven Electromigrative Degradation in Microelectronic Packages L.F. Siah

20.1 Introduction Electromigration is a migration phenomenon that involves the transport of a metal under the influence of an applied field. Two types of electromigration that are known to contribute to failure in microelectronic devices have been identified. The first is a solid state migration that occurs typically at high temperatures (>150◦ C), involves high current densities (>104 A cm−2 ), and is manifested physically in the formation of vacancies, voids, and hillocks at the affected regions. The second is electrochemical (sometimes called ionic or electrolytic) by nature in which metal is transported, usually through or across a nonmetallic medium, between two oppositely biased conductors under ambient temperatures (<100◦ C) at low current densities (<1mA cm−2 ) [1]. In the latter mode, the low local temperatures and current densities allow sufficient moisture to collect at the dielectric, thereby enabling electrolytic conduction when an electric potential is applied. The signature metallic dendrites, conductive anodic filament (CAF), and colloidal staining are all manifestations of electrochemical migration that have been observed in microelectronic devices. Although similar in their manifestations, electrochemical migration is fundamentally different from corrosion in that the former involves the transport of metal ions under the influence of an applied electric field, whereas an electrical bias is not an absolute necessity for corrosion to occur. This chapter will focus on the aspect of electrochemical migration (ECM), primarily manifested as bridging metallic dendrites, that results in electrical failures of microelectronic devices.

20.2 Electrochemical Migration (ECM) Since its early stages, the microelectronics industry has constantly been under the shadow of electrochemical migration-induced failures of the metal conductor lines L.F. Siah (B) e-mail: [email protected] X.J. Fan, E. Suhir (eds.), Moisture Sensitivity of Plastic Packages of IC Devices, Micro- and Opto-Electronic Materials, Structures, and Systems, C Springer Science+Business Media, LLC 2010 DOI 10.1007/978-1-4419-5719-1_20, 

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in devices. With the unrelenting demand for device miniaturization and higher conductor line density, this threat is not likely to diminish in the near future either. Intensive research from both the theoretical and experimental aspects for the past 30 years, i.e., since the mid-1970s [2–5], is a testimony to the importance of this failure mechanism to the microelectronics industry. This is because, in a system comprising two oppositely biased electrodes, such as the conductor lines found in microelectronic devices, an electrochemical cell can be formed in the presence of a continuous moisture path. A number of electrode reactions then become possible [6]. Electrode reactions resulting in the formation of metallic bridges that short-circuit two adjacent electrodes will induce leakage failures in the microelectronic device. Reactions that result in electrode depletion (broken conductor line) or passivation will give rise to resistance failures of the devices. Not surprisingly, one of the most important qualification tests for microelectronic packages is an evaluation of the reliability of these, typically, non-hermetic, polymeric materials against ECM-induced failure. Conditions of humidity, temperature, and bias are used to accelerate the penetration of moisture through the polymeric protective material and/or along interfaces of these materials and the metallic conductors which they enclose. Two JEDEC standards are available for this purpose, namely the (i) highly accelerated temperature and humidity stress test (HAST) (JESD22-A110-B) and the (ii) steady-state temperature humidity bias life test (THB) (EIA/JESD22-A101-B). In biased HAST, conditions such as 110◦ C/85% RH and 130◦ C/85% RH are typically used in conjunction with a suitable bias voltage specific to the application voltage peculiar to the device being evaluated. Under the THB condition, the evaluation is typically carried out at 85◦ C/85% RH together with a bias voltage suitable for the device under evaluation. The JEDEC standards specified a generic reliability requirement of 96 h at 130◦ C/85% RH HAST, 264 h at 110◦ C/85% RH HAST, and 1,000 h at 85◦ C/85% RH THB conditions.

20.3 ECM Mechanism The ECM mechanism involves the dissolution of a metal at the anode (positive electrode) and the transportation of the metal ions or conductive metal complexes formed along the moisture path to the cathode (negative electrode). At the cathode, these metal ions are reduced and deposited as pure metal, which then grows back toward the anode in the form of dendrites. A short circuit resulting in leakage failure occurs when these metallic dendrites bridge the two electrodes. This phenomenon arises because electrolysis of water at the anode causes the region around it to become acidic from the H+ ions produced, thereby setting up an environment conducive for metal dissolution and ion formation as explained below. Conversely, at the cathode, water hydrolysis releases OH− ions, resulting in an alkaline condition in the vicinity of the electrode that is suitable for precipitation [7].

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(I) At the anode: oxidation and metal loss/dissolution a) Production of hydronium ion:  H2 O → 1 2O2 ↑ +2H+ + 2e−

(20.1)

b) Electrolytic dissolution of metal conductor: M → Mn+ + ne−

(20.2)

For copper conductors: Cu → Cun+ + ne− (n = 1,2). (II) At the cathode: reduction and protective passivation a) Production of hydroxyl ion: 2H2 O + 2e− → H2 ↑ +2OH−

(20.3)

b) Reduction of metal ion: Mn+ + ne− → M

(20.4)

For copper conductors: Cun+ + ne− → Cu (n = 1, 2) The production of H+ at the anode and OH− ions at the cathode creates a pH gradient between the two electrodes. From the simplified Pourbaix (pH–potential) diagram for copper (Fig. 20.1), in the pH range between 7 and 11, copper is passivated and no corrosion will occur. Below pH 7, copper dissolution is expected to happen at potentials greater than 0.2 V. Above pH 5, however, the solubility of copper ions declines rapidly, becoming nearly insoluble at ∼ pH 8.6. In summary, H+ generation at the anode causes a drop in the local pH, thereby releasing soluble Cun+ that migrates under the influence of an applied voltage toward the cathode where the alkaline environment causes the copper ions to become insoluble and precipitate out as metallic copper. Electrical failure in the device occurs as a result of either (i) an “open” circuit due to the dissolution of the copper anode resulting in a broken conductor or (ii) a “short” circuit arising from the cathode-to-anode bridging of metallic dendrites. Many metals and metal alloy systems have been reported in the literature to be susceptible to ECM [8–12]. In assessing the ECM susceptibility of some pure metals, Takemoto et al. found that the ECM susceptibility of metals in pure water (i.e., neutral pH) appears to be related to their pH–potential diagram; metals having passivation regions at the neutral pH range would be immune to ECM. They also noted that, in certain cases, susceptibility was observed, even though immunity was expected. They concluded that the pH–potential diagram offers valuable information on immunity to ECM, even though it cannot predict susceptibility to ECM with complete accuracy [11].

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Fig. 20.1 Simplified Pourbaix diagram for copper

Harsanyi et al. reported that the migration propensity of pure metals is in the order: Ag+ >Pb2+ >Cu2+ >Sn2+ [13] and, from this, showed a better correspondence between migration rates and the solubility products of the metal hydroxides than with, the commonly referenced, standard electrode potential of the metal ion (Table 20.1). For a given system in equilibrium, Aa Bb ↔ aAn+ + bBm− .

(20.5)

The solubility product constant (Ksp ) of the system, which reflects the solubility of the substance in water, is given by the following equation: Ksp = [An+ ]a [Bm− ]b .

(20.6)

Table 20.1 Electrochemical and solubility data of metal ions and their hydroxides Metal ion [Mn+ ]

Standard electrode potential (V)

Solubility product of hydroxides M(OH)n at 20/25◦ C, Ksp

Ionic solubility, S (M)

Ag+ Pb2+ Cu+ Cu2+ Sn2+

+0.779 −0.126 +0.520 +0.337 −0.136

1.52 × 10−8 1.43 × 10−20 1.00 × 10−14 4.80 × 10−20 5.45 × 10−27

1.23 × 10−4 1.53 × 10−7 1.00 × 10−7 2.29 × 10−7 1.11 × 10−9

The smaller the solubility product (Ksp ), the lower is the solubility of the metal hydroxide.

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If S is the solubility of Aa Bb , then [An+ ] = aS and [Bm− ] = bS. ∴ Ksp = [An+ ]a [Bm− ]b = (aS)a × (bS)b . And, the solubility of the metal ions (S) is given by the following equation:  S=

a+b

Ksp . × bb

aa

(20.7)

Therefore, the more soluble the metal hydroxide, the higher will be the metal ion concentration available for transport to the cathode for reduction and, consequently, faster metallic dendrite growth [12, 13].

20.4 ECM: Contributing Factors The microelectronics device is assembled from a complex combination of materials and manufacturing processes and is used in a wide variety of environmental conditions. Naturally, device failure can then be expected to be associated with the interaction of a host of such variables. However, as shown in equations (20.1), (20.2), (20.3), and (20.4), for ECM to initiate, a basic set of ingredients must first be present in order to complete the electrochemical cell between the two electrodes. These are (1) a percolative moisture path, (2) a supply of migrating ions, and (3) a bias voltage as a driving force for the ions; this being a transport phenomenon, the ECM process may be expected to be also accelerated by temperature.

20.4.1 Moisture (Humidity) Factor From equations (20.1), (20.2), (20.3), and (20.4) above, it is conceivable that the existence of a comparatively low-resistance electrolytic path between the electrodes is a fundamental criterion for ECM. Besides being the transport medium, it also provides, through water electrolysis, the requisite pH conditions for metal dissolution and precipitation at the respective electrodes as explained above. This moisture path need not necessarily be a permanent one, i.e., it can be broken (dried up), regenerated, or reformed as a different path, depending on the ambient conditions. However, the duration of a percolative moisture path is a key factor in determining the mean time to failure (MTTF) of microelectronic devices. Earlier studies have shown that, under the same conditions of humidity (RH) and temperature (T), the MTTF remains somewhat similar and is independent of the onset of the bias voltage, i.e., regardless of whether the bias voltage was applied at the beginning or later after a short time lapse following a period of exposure to only RH and T. This reinforces the observation that a conductive path must first be available for the onset of ECM [4].

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20.4.2 Voltage Factor Without a bias voltage, the driving force for ion migration is governed by the electrochemical potentials of the participating electrodes. The role of an applied voltage is to overcome the barrier of the electrochemical potentials, thereby resulting in a greater propensity for ECM in biased systems. Since the minimum voltage required for water hydrolysis is 1.2 V, it is conceivable that below 1.2 V, little or no ECM activity may be expected. However, the standard electrode potential for copper dissolution is +0.337 V for Cu2+ and +0.520 V for Cu+ with respect to the standard hydrogen electrode (SHE). Thus, copper ion elution does occur, albeit slowly, even below the minimum theoretical voltage for water hydrolysis. At higher voltage, however, more ions are made available as the pH drop due to water hydrolysis becomes conducive for metal dissolution [14]. As the bias voltage used in most microelectronic devices easily exceeds this minimum, ECM failure remains a persistent reliability issue that must be addressed [15]. In a series of studies by researchers at Bell Laboratories [3–5], a two-step model was proposed for ECM failure in printed circuit boards (PCBs) involving an initial voltage-independent degradation of the epoxy resin/glass fiber interface and a subsequent voltage-dependent electrochemical reaction for CAF growth in the PCBs. In other words, the epoxy–glass fiber reinforcement interface in the PCB must first be compromised and a moisture path made available before the effect of voltage is fully realized. In the case of CAF, the metal-ion complexes formed at the anode proceeds along the separated fiber/epoxy interface toward the cathode, resulting in an electrical failure when the anode and the cathode are bridged. It has also been observed that when differently spaced conductor lines are biased together, there is a preferential propensity for dendrite/filament growth in regions of the narrowest spacings. This appears to suggest that the critical electrical variable may be the voltage gradient (electric field) across the spacing and not the voltage per se. However, quantifying the electric field acting on the migrating ion is non-trivial due, in part, to the time dependency of the variables involved in the equation, i.e., branching and tortuosity of the electrolytic paths in the insulator and a constantly changing path length, ionic concentration, and conductivity.

20.4.3 Temperature Factor Higher temperature increases the susceptibility to ECM, especially when coupled with high RH. The main effect of temperature is to increase conductivity, probably due to an increase in ion mobility with temperature and/or a decrease in the viscosity of surface solution [1]. Thus, an Arrhenius relationship is commonly used to model the temperature dependency of this failure mechanism:  MTTFECM ∝ exp

−

Ea kT

 ,

(20.8)

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where Ea is the activation energy, k = 1.38×10−23 J K−1 is the Boltzmann constant, and T is the absolute temperature. Apart from these basic ingredients, a host of processes, materials, and usage variables may influence the predisposition to ECM in microelectronic devices. These include any variables that enhance moisture ingression and promote metal dissolution (even of the “noble” metals) and their transport.

20.4.4 Material Factor Polymeric insulator materials (epoxies, phenolics, or silicones) used to protect microelectronic devices are non-hermetic and highly susceptible to moisture penetration. At any RH, the moisture absorption tendency of the microelectronics package is dependent on both the type and the surface condition of the insulator material [16, 17]. ECM susceptibility of hydrophilic materials is conceivably higher than that of hydrophobic materials. Clean, smooth hydrophobic surfaces are not anticipated to acquire more than a few molecular layers of water until ∼100% RH, at which point condensation of bulk liquid (droplets) occurs. On the other hand, in insulating materials with polar groups, adsorption of water as invisible films occurs at much lower RH values, with the extent of adsorption increasing with rising RH. Likewise, the ECM susceptibility of a smooth surface is relatively less than that of a cracked or scratched surface. Surface impairment gives rise to high-energy surfaces conducive for capillary condensation, thereby lowering the minimum ambient RH required for moisture adsorption, even on otherwise water-repellent materials. The main effects of absorbed moisture are moisture-induced plasticization and/or micromechanical degradation. The mechanical and chemical integrity of the epoxy is altered and deteriorates as a result of (i) microcrack formation from hygromechanical stresses, (ii) polymeric bond degradation due to chain scission, (iii) reduction of the glass transition temperature (Tg ) due to plasticization, and (iv) degradation of polymer interfaces resulting in de-adhesion (delamination). As interfacial voids or delaminations are potential nucleation sites for capillary condensation, these can then provide an easy path for moisture ingression, i.e., a path of least resistance, to any available ambient moisture. Two states of water have been identified in absorbed moisture in epoxy systems, namely (a) mobile, unbonded, “free” water residing in nanovoids in the epoxy system and (b) bound water hydrogen bonded to the polymeric backbone [17, 18]. Zhou and Lucas [19, 20] further classified the bound water into type I and type II depending on the number of hydrogen bonds formed with the epoxy network and the temperature and duration of moisture exposure. It has been suggested that the unbonded water does not cause any significant swelling, whereas the hydrogen-bonded water results in polymer swelling that will lead, subsequently, to hygromechanical stresses and delaminations. Apart from the polymeric materials, the nature of the metal conductor surface also plays a role in determining the device susceptibility to ECM failure. Rough

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surfaces possess high-energy points that are ready targets for the migrating metal cations. In addition, metals that form tenacious metal oxides (e.g., Al2 O3 and CuO) are certainly more protected against ECM than those having more soluble metal oxides (e.g., AgO).

20.4.5 Effect of Ionic Contaminants: Complexation and Metal-Ion Liberation Much confusion surrounds the role of ionic impurities in the electrochemical migration process. Generally, the presence of ionic impurities is not a prerequisite for the onset of electrochemical migration as testified in documented evidence of dendritic growth from water drop (WD) tests using deionized water [21]. However, for certain corrosion-resistant metals (e.g., Au, Pd, and Pt), the presence of ionic impurities, especially chlorides (Cl− ), allows a series of complexation reactions to happen that will liberate the metal or metal–complex cations. In this manner, an otherwise corrosion-resistant metal can also be rendered susceptible to, an impurity-induced, electrochemical migration process. For example, the discovery of gold dendrites inside ceramic packages leads to simulation experiments to induce their growth (Fig. 20.2). It was found that the gold dendrites would grow only in the presence of all three factors, namely (i) bias, (ii) hygroscopic

Fig. 20.2 Gold dendrites grown in dilute KAu(CN)2 + nonylphenol (Fig. 2 in Ref. [10]). Reproduced with permission, © 2004 IEEE

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nonylphenol (as the moisture trap or vehicle), and (iii) KAu(CN)2 (the complexation agent in the gold plating bath). The key factor, however, was the availability of the nonylphenol moisture trap, which was subsequently traced to the insufficient bake schedule [10], again underlying the importance of moisture in the ECM equation. Harsanyi presented an impurity-induced ECM model [21], in which the following reactions provide the migrating metallic species to complete the electrochemical cell: (a) Formation of a primary negative complex ion from an impurity-induced anodic corrosion: − Au + 4Cl− → AuCl− 4 + 3e

(b) A multistep chemical process liberating metal cations or metal–complex cations: −

AuCl4 + H+ → H[AuCl4 ] → HCl + AuCl3 → H+ + 4Cl− + Au3+ (c) Cation (Au3+ ) migration toward the cathode under an electric field influence (d) Reduction and deposition at the cathode in the form of metallic (Au) dendrites The influence of ionic impurity is rather complex and involves various counteracting effects that change depending on the nature of the conductor and the concentration of the impurity ions. Experiments with deionized water (DIW) and various concentrations of NaCl showed, qualitatively, different acceleration/retardation effects of chloride on the ECM process and different types of deposit morphologies depending on the impurity concentration [14, 21, 22]. In the case of metals like Ag, Pd, Cu, Sn, and their alloys, thin filamentary dendrites were observed after an incubation period in samples exposed to DIW alone. Dendritic growths were observed to occur earlier at low NaCl concentration (1– 10 mM) than with DIW and were more robust in form. Both resulted in short circuits when the dendrites bridge the electrodes. At intermediate concentration (100 mM), dendritic growth was not evident, probably as a result of formation of a corrosion barrier film, presumably chloride salts, on the anode. At very high NaCl concentration (1 M), a thicker and denser deposit was observed instead of dendrites, which also resulted in a short circuit (vide infra). In metals like Au, Pd, and Pt, the ECM activity is directly proportional to the concentration of the impurity ion. The higher the NaCl concentration, the more the metal-ion complexes formed and the faster these metals succumb to dendritic growth and short circuit; the qualitative results agree well with their THB data [21]. Harsanyi provided an explanation for the apparent anomalous behavior of Ni ECM, in which Ni dendrites are formed at the anode instead of at the usual cathodic site [23]. The following steps were proposed:

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(1) Formation of the primary cation by the usual anodic corrosion: Ni → Ni2 + + 2e−

(20.11)

Ni2+ + 2OH− ⇔ Ni(OH)2 (green precipitate)

(20.12)

(2) Chemical reactions that result in secondary anionic complexes: + Ni2+ + 2H2 O → HNiO− 2 + 3H

(20.13)

The solution in the vicinity of the cathode (alkaline pH) is conducive for this process which proceeds at pH > 10.1. The result is a reversal in the direction of nickel migration. (3) Migration of the anionic Ni complex through the electrolyte, under an electric field, toward the anode (4) Electrochemical–chemical processes at the anode resulting in the deposition of metal oxides or metallic dendrites: + − 3HNiO− 2 + H → Ni3 O4 (black) + 2H2 O + 2e

(20.14)

2+ 4HNiO− → Ni + NiO2 + Ni3 O4 + 2H2 O + 2e− 2 + Ni

(20.15)

or HNiO− 2

+ OH− → Ni + O2 + H2 O + 2e−

(20.16)

It is plausible that other metal species may also show a similar, seemingly, anomalous behavior if the local pH condition is conducive for the formation of anionic metal-ion complexes, thereby resulting in a reversal of the migration direction.

20.4.6 Effect of Contaminants on Water Uptake The presence of contaminants, primarily from assembly process residue and airborne particles deposited later, can shift the ECM dependence on RH to lower RH values. These residues and hygroscopic particles provide sites for moisture adsorption, thereby allowing condensation to occur at RH levels lower than saturation. One of most deleterious process contaminants is the flux residue from the various assembly processes. These residues act either by modifying the epoxy surface and altering their moisture absorption propensity or, through a degradation process, becoming the source of moisture itself.

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From gas analysis carried out on a hybrid package after a burn-in step at 125◦ C, Benson et al. detected water and carbon dioxide that is consistent with the decomposition of flux residue in the package. Their results indicate that degradation of flux residues (organics) can result in surprisingly excessive moisture levels (∼ 1%) in the package tested [24]. Flux formulation has been shown to greatly affect ECM rates [25, 26]. Certain flux constituents, like the strongly hygroscopic polyglycols, greatly enhance the hydrophilicity of the epoxy. Polyglycol rapidly diffuses into the epoxy polymeric network at the assembly temperatures used and is retained within after the cleaning step. These become sites for water condensation and a significant amount of moisture absorption can result if the critical humidity level is exceeded. Apart from flux residues, other hygroscopic contaminants are also known to affect the manner of moisture adsorption on epoxy surfaces. Warren et al. reported that contamination of α-alumina substrates with small amounts of CuCl2 showed an enormous effect on water uptake [15]. Two stages in the moisture adsorption process – two “critical” RH regimes – were proposed: 1. First, critical RH (CRH1): hydration of CuCl2 to CuCl2 ·2H2 O 2. Second critical RH (CRH2): RH in equilibrium with a saturated solution of CuCl2 , reported to be at ∼69% RH This showed that the amount of solution adsorbed on the substrate surface is dependent on the total mass of the contaminants present and can be several orders of magnitude larger than the amount of water which would be adsorbed in the absence of such a contaminant. Depending on the wetting characteristics of the solution on the substrate, this surface film may be either continuous or discontinuous (patchy) [15]. In view of the significant role that these contaminants play in accelerating moisture absorption and, consequently, ECM failure, efforts have been made to suppress or control their occurrence. This have included, among others, steps like washing with hot deionized water to leach out ionic impurities and addition of ionic complements to bind such ionic impurities [27].

20.5 Mechanism of Ion Transport in ECM For ECM failure due to bridging dendrites, the metal ions liberated at the anode must be transported to the cathode where it can be reduced and grow back toward the anode as metal dendrites. Ion transport in an electrochemical cell can arise from the following mechanisms: 1. Diffusion – due to concentration or chemical potential gradient from metal dissolution 2. Migration – action of an electric field force on the metal ion 3. Convection – driven by coulombic forces

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The Nernst–Planck flux equation is commonly used to represent the flux (J) of an ionic species (i) in a dilute electrolytic solution: Ji = Ci V − Di (∇Ci ) − (Di Zi F/RT)Ci (∇φ),

(20.17)

where i = 1, 2, 3, . . . , n; Ji is the flux vector of the ith species (mol cm−2 s−1 ); Ci is the concentration (mol cm−3 ); Zi is the electrical charge (mol equiv mol−1 , positive for cations, negative for anions); V is the fluid velocity vector (cm s−1 ); F is the Faraday constant (9.65 × 104 C[mol equiv]−1 ); R is the universal gas constant (8.3143 J K−1 mol−1 ); T is the absolute temperature (K); φ is the electrical potential (V); Di is the ionic diffusion coefficient of the ith species (cm2 s−1 ) which is equal to RTμi ; and μi is the electrical mobility of the ith species (cm2 mol J−1 s−1 ). The first, second, and third terms in equation (20.17) refer to the convective, diffusive, and electromigrative contributions to the flux, respectively. Convection is mostly driven by coulombic forces due to local electric charges and by buoyancy forces due to concentration gradients that lead to density gradients. It is generally agreed that in cells <50 μm thick, convection is strongly damped, with diffusion and, mainly, migration as the dominant modes of ion transport; in thicker cells, convection dominates. In the context of the ECM problem in microelectronic devices, it is reasonable to assume that only the diffusion and migration modes should prevail. In view of the complex physicochemical, hydrodynamic, ion transport processes involved, many studies have been conducted and are still being actively pursued to understand the mode of transport and its role in the growth and morphology of metallic dendrites. Questions on the respective roles of each transport mode in the resultant metallic deposit continue to intrigue researchers in the field. Chazalviel [28] introduced a 1D numerical model for ion transport in electrochemical deposition with only diffusion and migration as the transport modes. The assumptions were a growthless regime (fixed boundaries), potentiostatic conditions (constant anode–cathode potential), and low concentrations (numerical constraints). The model predicted the existence and behavior of a depletion layer next to the cathode. The Chazalviel 1D model, though giving great insight, is limited to steady-state regimes. Following this, Fluery et al. described a model for electrochemical deposition (ECD) and ionic motion in which the growth speed of the metallic deposit equals the speed of anions withdrawing from the zone invaded by the metallic filaments. At every moment during growth, both cations and anions drift in the electric field in opposite directions; the cations meet the growing front and add on to it, while the anions pile up near the anode [29]. In other words, the front of the metallic dendrites is always rushing and remaining just behind the withdrawing anions (Fig. 20.3). The zone enclosed between the filaments is completely depleted of ions of any kind. Fluery et al. also proposed that the Hecker effect, i.e., striking morphological changes during the growth of the metallic deposits, is produced by changes in the solution due to positively charged “impurities” from the anode or encounters with zones of different pH. Initially, the impurities are on the edge of the anode but as the deposit grows, the impurities leave the anode, drift in the bulk, and move toward

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Fig. 20.3 Model for ECD (Fig. 2 in Ref. [29]): (a) schematic view of cation and anion concentration evolution during growth; (b) equivalent resistors, R1 , R2 , and R3 are resistances of each part; (c) concentration profiles of anions and cations during growth in a parallel geometry. The concentrations are almost zero between the filaments because of the deposition of copper and the migration out of the anions; the concentrations are almost constant between the tips and the anode because of the drift motion of the two kinds of ions in opposite directions; the concentrations get larger and larger near the anode because of the production of cations by the anode and the piling up of anions on a narrow layer. Reproduced with permission, © 1991 The American Physical Society

the deposit. The first “impurities” that reach and hit the growing dendritic front will induce a change in the morphology of the growing filaments (Fig. 20.4). In the context of water, these “impurities” are the protons and hydroxyl ions – thereby providing evidence of a protonic drift involved; other impurities may exist too. Thus, controlling the pH and the impurities would enable a control of the dendritic morphology [29] and, consequently, mitigate the threat from ECM as filamentary-type dendrites are more dangerous than dense, compact dendrites. Marshall et al. presented a simplified macroscopic 1D model [30] for ECD with two concentration fronts advancing in opposite directions, namely the following: 1. Deposit front advancing from cathode toward the anode with a velocity proportional to the anion mobility times the electric field

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Fig. 20.4 Sequence of pictures showing the Hecker Effect in the growth of a deposit in a needle-square geometry. The transition line appears to reproduce the shape of the square anode (Fig. 7 in Ref. [29]). Reproduced with permission, © 1991 The American Physical Society

2. pH front emanating from the anode toward the cathode with a velocity proportional to the proton mobility. Here, the electrolytic cell is visualized, from an electrical standpoint, as a resistance which is a function of the deposit front-anode length (i.e., the cathode-anode length originally), that decreases with time as the deposit grows. The metal cations released due to anode dissolution, which is expected to be much faster than the transport processes, result in a local acidification due to the following reaction: Cu2+ + H2 O → CuOH+ + H+ .

(20.18)

The liberated proton, i.e., the “impurities” in the Fluery model above [29], migrates toward the cathode.

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20.6 Dendritic Morphology Different forms of dendrites have been identified, namely (i) trunk-type dendrites: a single dendrite growing within a fluid bridge from cathode to anode, (ii) lace-/treetype dendrites: growth along a film or damp surface between the electrodes, and (iii) sludge: burnt-out dendrites due to high current flow from bridging of electrode gap. For successful dendritic growth, first, there must be a sufficient ionic concentration to initiate the process and a continuous supply thereafter to sustain the growth. Not surprisingly, there is an associated incubation period (for ion buildup) that is dependent on the chemical environment of the system. Copper dendritic growth rate was observed to increase with decreasing pH, which is attributed to an increase in the concentration of dissolved copper resulting from anodic dissolution. Increased pH has been shown to inhibit the formation of dendrites and slow down their rate of growth due to the decreased solubility of copper in higher pH solutions. For example, acidic solutions (pH ∼1–3) enhance the tendency for microcrystalline dendritic growth. At higher pH (∼5.6), polycrystalline deposits are preferred. At higher pH (∼8.3), no dendrites were observed; instead, solid corrosion products were collected in the space between the anodic and cathodic stripes [15]. In summary, the characteristic phenomena involved in copper dendritic growth during the electrochemical migration process are as follows [31]: 1. An incubation stage that involves the dissolution of the anode, releasing copper ions that are then transported to the cathode: migration controlled 2. Stable copper deposition at the cathode surface: diffusion controlled 3. Dendritic growth triggered by instability related to the depletion of copper ions close to the cathode Thus, in a closed circuit, the Cu2+ front propagates from the anode to the cathode during the incubation period, determined by the transport of metal cations, which ends when the electrodeposition process starts [30]. Gabrielli et al. showed that the activation energy, defined as the current necessary to build the dendrite (stable and unstable growth), increased with the potential difference up to a limit which was related to the limitation of the current by diffusion (Fig. 20.5), suggesting that dendritic growth is limited by the diffusion of copper ions coming from the anode [31]. Furthermore, the short-circuit time was observed to be proportional to the inverse of the square of the activation current in agreement with the Chazalviel model which describes dendritic nucleation by a depletion of copper ions at the cathode surface and dendritic growth as limited by diffusion. In another set of experiments, Gabrielli et al. showed that, under the same potential (V) condition, the short-circuit time is proportional to the separation distance (S) of the two microelectrodes. This indicates that the growth rate of the dendrites is the same and further supports diffusion as the rate-limiting factor (Fig. 20.6). For very narrow spacing, the incubation period where the copper ions are transported from the anode to the cathode is not readily discernible.

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(A)

(a)

(b)

(c) (B)

Fig. 20.5 (a) Current transients measured on 3-μm-diameter disks separated by a distance of 3 μm under the application of various V between the two disk microelectrodes in a 10–4 M oxalic acid solution (Figs. 2 and 3 in Ref. [31]); (b) SEM images after current transient measurements of (a) at (a) 1, (b) 0.6, and (c) 0.4 V. Bottom electrode is the cathode (Fig. 3 in Ref. [31]). Reproduced by permission of ECS – The Electrochemical Society (2007)

The amplitude of the electric field (V/S) had a strong influence on the dendritic morphology. A high electric field results in a filamentary and thin morphology (time-independent activation current), whereas a low electric field results in a more compact morphology (time-dependent activation current) (Fig. 20.7). For example, for the same microelectrode spacing, dendritic growth was observed even at 0.4 V but, as a result of the lower electric field, the morphology is more compact, favoring denser dendrites distributed more homogeneously around the peripheral of the cathode; no short circuiting results although the anode is totally consumed in this case (Fig. 20.5). In contrast, higher and less uniform electric field at higher potential probably accounted for the growth to be located just in front of the anode. Indeed, the filamentary morphology is the more dangerous as only a small quantity of copper is sufficient to quickly result in a short-circuit event [31].

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(A)

(a)

(c)

(b)

(d) (B)

Fig. 20.6 (a) Current transients measured on disks of various diameter separated by a distance equal to their diameter in a 10–4 M oxalic acid solution, under 1.2 V (Fig. 5 in Ref. [31]); (b) SEM images corresponding to the current transients measured in (a) (Fig. 6 in Ref. [31]). Reproduced by permission of ECS – The Electrochemical Society (2007)

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(A)

(B) Fig. 20.7 (a) Current transients on 3 μm × 30 μm bar and 3 μm × 3 μm square at various separation distances in a 10–4 M oxalic acid and 5× 10−4 M copper sulfate solution, under 1.2 V. The current transient measured at the start of the experiment is identical and the short-circuit time is about seven times shorter with a 3 μm distance compared to the 10 μm gap (Ref: Fig. 11 in [31]); (b) SEM images corresponding to the current transients measured in (a) (Fig. 12 in Ref. [31]). Reproduced by permission of ECS – The Electrochemical Society (2007)

20.7 Summary The microelectronic devices comprise complicated multi-material systems and their interactions. As such, the ECM threat to failure in microelectronic devices affects more than conductor lines at both the die and package levels; any metal-containing component is, in principle, potentially susceptible to ECM failure, e.g., capacitors,

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solder (BGA), and bond wire in WB devices. The availability of moisture appears to be the most critical factor for this failure mechanism. Suppressing or controlling moisture availability would buy some margin for the active lifetime of the devices. Much work has been published recently on the fundamentals of moisture absorption in polymeric dielectric systems and dendritic growth models. Such work continues to fascinate researchers and deepens the understanding on this important issue.

References 1. Krumbein, S.J., “Tutorial: Electrolytic models for metallic electromigration failure mechanisms,” IEEE Transactions on Reliability, 44, 539–549, 1995. 2. Lahti, J.N., Delaney, R.H., Hines, J.N., “The characteristic wearout process in epoxy-glass printed circuits for high density electronic packaging,” IEEE Proceedings of International Reliability Physics Symposium, pp. 39–43, 1979. 3. Lando, D.J., Mitchell, J.P., Welsher, T.L., “Conductive anodic filaments in reinforced polymeric dielectrics: formation and prevention,” IEEE Proceedings of International Reliability Physics Symposium, pp. 51–63, 1979. 4. Welsher, T.L., Mitchell, J.P., Lando, D.J., “CAF in composite printed circuit substrates: characterization, modeling and a resistant material,” IEEE Proceedings of International Reliability Physics Symposium, pp. 235–237, 1980. 5. Mitchell, J.P., Welsher, T.L., “Conductive anodic filament growth in printed circuit materials,” Proceedings of the Printed Circuit World Convention II, pp. 80–93, 1981. 6. Osenbach, J.W., “Corrosion-induced degradation of microelectronic devices,” Semiconductor Science and Technology, 11, 155–162, 1996. 7. Katayanagi, H., Tanaka, H., Aoki Y., Yamamoto, S., “The effects of adsorbed water on printed circuit boards and the process of ionic migration,” ESPEC Technology Report, 9, 15–20, 2000. 8. Manepalli, R., Stepniak, F., Bidstrup-Allen, S.A., Kohl, P., “Silver metallization for advanced interconnects,” IEEE Transactions on Advanced Packaging. 22, 4–8, 1999. 9. Harsanyi, G., “Copper may destroy chip-level reliability: handle with care – mechanism and conditions for copper migrated resistive short formation,” IEEE Electron Device Letters, 20, 5–8, 1999. 10. Kersey, J.L., Blish, II, R.C., “Gold dendrite simulation: root cause determination,” IEEE Transactions on Device and Materials Reliability. 4, 189–191, 2004. 11. Takemoto, T., Latanision, R.M., Eagar, T.W., Matsunawa, A., “Electrochemical migration tests of solder alloys in pure water,” Corrosion Science, 39, 1415–1430, 1997. 12. Yu, D.Q., Jillek, W., Schmitt, E., “Electrochemical migration of Sn–Pb and lead free solder alloys under distilled water,” Journal of Materials Science: Materials in Electronics, 17, 219–227, 2006. 13. Harsanyi, G., Inzelt, G., “Comparing migratory resistive short formation abilities of conductor systems applied in advanced interconnection systems,” Microelectronics Reliability, 41, 229–237, 2001. 14. Reid, M., Punch, J., Rodgers, B., Pomeroy, M.J., Galkin, T., Stenberg, T., et al., “Factors that influence ionic migration on printed wiring boards,” IEEE Proceedings of International Reliability Physics Symposium, pp. 300–304, 2005. 15. Warren, G.W., Wynblatt, P., Zamanzadeh, M., “The role of electrochemical migration and moisture adsorption on the reliability of metallized ceramic substrates,” Journal of Electronic Materials, 18, 339–353, 1989. 16. Apicella, A., Tessieri, R., De Cataldis, C., “Sorption modes of water in glassy epoxies,” Journal of Membrane Science, 18, 211–225, 1984.

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17. Luo, S., Wong, C.P., Leisen, J., “Fundamental study on moisture absorption in epoxy for electronic applications,” International Symposium on Advanced Packaging Materials, pp. 293–298, 2001 18. Musto, P., Ragosta G., Mascia, L., “Vibrational spectroscopy evidence for the dual nature of water sorbed into epoxy resins,” Chemistry of Materials, 12, 1331–1341, 2000. 19. Zhou, J., Lucas, J.P., “Hygrothermal effects of epoxy resin. Part I: the nature of water in epoxy,” Polymer, 40, 5505–5512, 1999. 20. Zhou, J., Lucas, J.P., “Hygrothermal effects of epoxy resin. Part II: variations of glass transition temperature,” Polymer, 40, 5513–5522, 1999. 21. Harsanyi, G., “Irregular effect of chloride impurities on migration failure reliability: contradictions or understandable?”, Microelectronics Reliability, 39, 1407–1411, 1999. 22. Nieman, D.A., “Effect of contamination on copper migration in TAB tape structures,” IEEE International Reliability Physics Symposium, pp. 87–92, 1994. 23. Harsanyi, G., “Electrochemical processes resulting in migrated short failures in microcircuits,” IEEE Transactions on Components, Packaging, and Manufacturing Technology A, 18, 602–610, 1995. 24. Benson, R.C., Romenesko, B.M., Weiner, J.A., Nall, B.H., Charles, Jr., H.K., “Metal electromigration induced by solder flux residue in hybrid microcircuits,” IEEE Transactions on Components, Hybrids, and Manufacturing Technology, 11, 363–370, 1988. 25. Ready, W.J., Turbini, L.J., “The effect of flux chemistry, applied voltage, conductor spacing and temperature on conductive anodic filament formation,” Journal of Electronic Materials, 31, 1208–1224, 2002. 26. Canumalla, S., Ludwig, K., Pedigo, R., Fitzgerald, T., “A study on ranking of commercial fluxes for electrochemical migration (ECM) propensity for Cu, Sn and Ag surface finishes,” IEEE Electronic Components and Technology Conference, pp. 625–632, 2006. 27. Yamamoto, S., “How impurities affect ionic migration and how to counter their impact,” ESPEC Technology Report, 12, 10–16, 2001. 28. Chazalviel, J.N., “Electrochemical aspects of the generation of ramified metallic electrodeposits,” Physical Review A, 42, 7355–7367, 1990. 29. Fleury, V., Rosso, M., Chazalviel, J.N., “Geometrical aspect of electrodeposition: the Hecker effect,” Physical Review A, 43, 6908–6916, 1991. 30. Marshall, G., Molina, F.V., Soba, A., “Ion transport in thin cell electrodeposition: modelling three-ion electrolytes in dense branched morphology under constant voltage and current conditions,” Electrochimica Acta, 50, 3436–3445, 2005. 31. Gabrielli, C., Beitone, L., Mace, C., Ostermann E., Perrot, H., “Copper dendrite growth on a microcircuit in oxalic acid,” Journal of the Electrochemical Society, 154, H393–H399, 2007.

Chapter 21

Interfacial Moisture Diffusion: Molecular Dynamics Simulation and Experimental Evaluation H. Fan, E.K.L. Chan, and M.M.F. Yuen

21.1 Introduction Moisture-induced reliability has been extensively investigated; moisture diffusion in plastic-encapsulated packages adversely affects the interfacial adhesion between epoxy molding compound (EMC) and copper substrate and significantly reduces the reliability of the package. It is known that moisture is transported to EMC/Cu interface via diffusion in the bulk epoxy resin as well as via seepage along the interface. Distinguishing these two mechanisms of moisture transport to the interface is rather important for the understanding of moisture effect on package reliability. Obviously, a traditional method like finite element analysis widely used in electronic packages is not suitable for modeling the moisture diffusion at a nanoscale level. Molecular dynamics (MD) simulation is now one of the fastest growing research areas and can reproduce material behavior at atomic level. Therefore, investigation of moisture diffusion using MD simulation in electronic packaging is both necessary and attractive. The knowledge of the moisture properties of packaging materials is essential for reliability modeling of moisture-induced damage in electronic packages, thus providing insights into the mechanics of failure and the roles of materials in the failures. Interfacial moisture diffusion as one of the important mechanisms of moisture transport plays an important role in the interfacial delamination and failure in the package. Therefore, experimental determination of interfacial moisture diffusion is becoming necessary for investigation of delamination in electronic packages.

M.M.F. Yuen (B) e-mail: [email protected]

X.J. Fan, E. Suhir (eds.), Moisture Sensitivity of Plastic Packages of IC Devices, Micro- and Opto-Electronic Materials, Structures, and Systems, C Springer Science+Business Media, LLC 2010 DOI 10.1007/978-1-4419-5719-1_21, 

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21.2 Molecular Dynamics Simulation of Moisture Diffusion 21.2.1 Molecular Dynamics Simulation Molecular modeling is one of the fastest growing fields in the science of simulating their behavior with the equations of quantum and classical physics. The molecular dynamics (MD) simulation was first introduced by Alder and Wainwright to study the interactions of hard spheres in the late 1950s [1, 2]. The method is now a well-established and important tool that endeavors to provide information on an atomistic scale for understanding the basic origins of material performance [3–8] in a wide variety of topics including modulus, adhesion, thermal conductivity, solubility, diffusion, and reactivity. The basic theories of MD simulation can be found in many handbooks [9–11]. Here we give a brief introduction on the MD simulation. Two kinds of methods, quantum mechanics (QM) and molecular mechanics (MM), are used in MD simulations. The QM method solves the Schrödinger equation from first principles, which accounts for the positions of nuclei and electrons and provides structural, electronic, and dynamic properties of the system with high accuracy. It can also simulate the process of a chemical reaction involving bond forming, bond breaking, charge transfer, etc. However, QM is restricted by long calculation times and costly calculations, thus it is only suitable for simulating small systems consisting of up to several hundreds of atoms. Electronic effects are averaged out in the MM method, so it cannot describe the evolution of electrons in a chemical reaction. However, it can be used to describe the performance of large and complex organic, inorganic, and solid-state systems due to its inexpensive and fast calculation. Compared with QM, MM is more applicable for the investigation of material performance in the multi-interface systems commonly found in electronic packages. Normally, atoms in MD simulations are modeled as point masses interacting through potentials. The accuracy of the MD simulation is directly related to these potentials, which are usually characterized experimentally. The potential energy of the system provides the forces on each atom, which can be used to determine the acceleration, velocity, and positions of each atom. In the classical molecular dynamics method, Newton’s equations are used to describe the equations of atom motions as follows: Fi = mi

d 2 ri ; Fi = −∇i , dt2

(21.1)

where Fi , mi and ri are, the force vector, mass, and position vector of molecule i, respectively.  is the potential energy function of the system. The total potential in MM is represented by the superposition of valence and nonbond interactions. The valence terms consist of bond stretch, bond angle bending, and dihedral angle torsion terms, while non-bond interactions consist of van der Waals and electrostatic terms. Most of the force fields have been characterized as an energy function only of the atomic positions with some constants. For example, a

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simple generic force field [12] is given here: E = Ebond + Eangle + Etorsion + Eelec + Evdw .

(21.2)

The valence terms are given as follows: Ebond = kb (rij − r0 )2 ; Eangle = ka (θijk − θ0 )2 ; Etorsion = kt (1 + cos (3ϕijkl )), (21.3) where Ebond and Eangle are the energy due to bond stretching or compression and angle bending, respectively. Etorsion is the energy due to torsion alternations. kb ,ka ,kt are force constants; rij ,r0 are the bond distance and the equilibrium bond distance for bond ij, respectively. θijk ,θ0 are the angle and the equilibrium angle between bond ij and bond jk, respectively. ϕijkl is the angle between bond ijk and bond jkl planes. Non-bond terms include the electrostatic force and the van der Waals force: Eelec =

qi qj ; Evdw = α 4π ε0 rij



R0 rij

12

 −β

R0 rij

6 ,

(21.4)

where Eelec and Evdw are energy terms due to electrostatic and van der Waals interactions, respectively. qi ,qj are charges in electron unit, ε0 is the dielectric constant, and rij is the bond distance for bond ij.R0 is the van der Walls bond length; α, β are the constants. Some commonly used force fields in MD simulation, such as AMBER, CHARMM, CVFF/PCFF, and COMPASS, have been widely used for description of organic, inorganic, and biomaterial systems. Parameters in these potentials are derived from experimental data or ab initio and semi-empirical quantum mechanical theory. Considering the structural constraints, the forces on the atoms can be calculated from the potentials. Accelerations of atoms can be derived based on Newton’s second law and the corresponding velocities and new positions of the atoms will be obtained. Based on statistical mechanics, macroscopic properties of a thermal equilibrium system can be obtained from motion of atoms and molecules of the system. The Monte Carlo (MC) method is another simulation method used for modeling low- or medium-density systems but not high-density systems. It only considers configuration space without the momentum part of the phase space. Compared with MD simulation, the MC method cannot be used to simulate dynamic processes of the system. MD simulation is a very useful tool to provide fundamental information on the structure and dynamics of the system in electronic packages. It can predict material performance of new materials in synthesis for optimization of the structure before experimental trials, such as Young’s modulus, thermal expansion coefficients, glass transition temperature, interfacial adhesion, and thermal conductivity. It can also study crack generation, moisture-induced failure, and interfacial adhesion commonly occurring in packaging design. However, few research efforts have been

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dedicated to the investigation of the performance of materials in electronic packaging until recently [13–33]. Iwamoto has applied MD simulation to the investigation of property trend analysis, surface energy modulus, and the adhesive formulation effect in the microelectronics packaging industry [13–22]. We have focused our research on the study of reliability, moisture diffusion, epoxy resin properties, and thermal conductivity in electronic packaging [23–33].

21.2.2 Molecular Dynamics Models of Moisture Diffusion Some researchers had used MD simulations in the investigation of the diffusion of water molecules in some kinds of polymers [34–38], but little attention was paid to the moisture diffusion in a cross-linked epoxy resin and its interface in electronic packaging. Fan et al. [24] conducted MD simulations to investigate moisture diffusion into the epoxy molding compound (EMC) and the EMC/Cu interface. The MD results showed that the seepage along the EMC/Cu interface was more prevalent than moisture diffusion in the bulk EMC, thus rendering it a dominant mechanism causing moisture-induced interfacial delamination in plastic packages. MD simulations were conducted using Materials Studio (Accelrys, Inc.) software. The condensed-phase optimized molecular potential for atomistic simulation studies (COMPASS) force field was used in the MD simulations. COMPASS force field enables accurate prediction of material properties for a broad range of materials under different conditions. The COMPASS force field can be accurately applied on the systems of polymers, metals, and their interfaces. In typical EMC formulations, the core chemical structure of the EMC governing the adhesion properties of the EMC material was formed by the reaction of epoxy resin with curing agents. EMC modeled in this study consists of epoxy resin and curing agent. The model did not include filler and pigments, which need large-scale models that are beyond the current MD simulation scope. In this study, diglycidyl ether of bisphenol A (DGEBA) epoxy and methylene diamine dianiline (MDA) curing agent were selected as the basic components of the EMC formulation due to their wide usage. During the curing reaction, the hydrogen atoms in the amine groups of the curing agent molecules react with the epoxide group of epoxy resin. The reaction opens the end structure of the epoxy group allowing four epoxied molecular groups to react with a curing agent molecule at its NH2 sites at the ends, as shown in Fig. 21.1. As the reaction continues, the epoxy resin and curing agent molecules generate more cross-links. The cross-linking activity expands in all directions and forms a network of macromolecules. Two kinds of models were built to investigate the moisture diffusion in the bulk epoxy as well as the interfacial moisture diffusion along the EMC/Cu interface. The bulk MD models composed of a fragment of fully cured epoxy resin network and different amounts of water molecules were built using the amorphous module in Accelrys. All the bulk models were built with a rectangular simulation cell 1.97 nm × 1.97 nm × 1.97 nm in all directions. To avoid surface effect, periodic

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Fig. 21.1 Process of the curing agent and epoxy resin reaction

boundary conditions in all directions were used. The interface models with different amounts of water molecules at the interface were built with a rectangular simulation cell 1.81 nm × 1.81 nm in the x- and y-directions, and periodic in the plane perpendicular to the EMC/Cu interface. The total height of the interface model was 12.4 nm and the thickness of copper in the model used was 1.43 nm. The height of the MD model in this study was sufficient to prevent any size effect in the z-direction on the mobility of water molecules. The dimensions of the MD models in this study are chosen by using the smallest core structure which governs material performance. Therefore, not only the properties of the molecular level systems can be essentially the same as those of the macroscopic system but also computational requirement can be reduced. The mass ratio of water molecules to the EMC in both kinds of MD models varied from 1.1 to 2.2%. The mobility of water molecules in the two models is governed by the non-bonded interactions between atoms. All the atoms in these models except for the copper atoms in the interface model were allowed to move freely in all simulations. Energy minimization was performed to find the equilibrated structure of the two systems at 85◦ C. Figure 21.2 shows the morphological configurations of the two kinds of MD moisture model.

EMC chains

EMC chains

z y x

Water molecules

Water molecules

Cu atoms (a)

(b)

Fig. 21.2 Morphological configurations of (a) the bulk EMC and (b) the EMC/Cu interface system

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All the simulations were then performed with a presumed moisture concentration value using the NPT ensembles at a temperature of 85◦ C. MD simulations were conducted to equilibrate the whole system for about 80 ps under a pressure of 0.1 MPa at 85◦ C. The velocity Verlet algorithm [39] was used for integration with the non-bonded interactions including van der Waals and electrostatic forces in all MD simulations. The Ewald summation was used for the non-bonded interactions. The moisture diffusion constants can be obtained in principle from diffusion trajectories r(t) of water molecules from an MD simulation. From the Einstein relation, the diffusion coefficients for the water molecules were calculated from the meansquared displacements, s(t) =< |r(t) − r(0)|2 >, of the water molecules averaged over time as follow [24]: N d  1 lim < [ri (t) − ri (0)]2 , D= 6 N t→∞ dt

(21.5)

i=1

where D is the moisture diffusion coefficient, ri (t) is the coordinate of the center of the mass of the ith water molecule, and N is the number of water molecules in the system. Figure 21.3 shows the mean-squared displacements of water molecules against time for both the bulk EMC and the EMC/Cu interface models. All the data in each graph were fitted using the straight line with the slope of a. Since the value of the mean-squared displacement is already averaged over the number of water molecules N, equation (21.5) can be simplified as follows [24]: D = a/6.

(21.6)

The slope of the fitted line for different mass ratios of water molecules to the EMC was used to calculate the moisture coefficients for different cases by equation (21.6), and the calculated values are listed in Table 21.1.

(a)

(b)

Fig. 21.3 Mean-squared displacement of water molecules against the simulation time (a) in the bulk EMC and (b) at the EMC/Cu interface and the fitted lines for different mass ratios of water molecules to the EMC

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Table 21.1 Predicted moisture diffusion coefficients both in the bulk EMC material and at the EMC/Cu interface under different conditions Mass ratio of water molecules to the EMC

Moisture diffusion coefficient in the bulk EMC material (mm2 /s) Moisture diffusion coefficient at the EMC/Cu interface (mm2 /s)

1.1%

1.7%

2.2%

7.12e–5

5.58e–5

4.87e–5

7.29e–4

4.71e–4

3.79e–4

MD simulation results showed that the predicted moisture diffusion coefficient decreased with the increase in the mass ratio of water molecules to the EMC. The moisture diffusion coefficient was dependent on the moisture concentration in the system at a given temperature and relative humidity (RH). A high amount of moisture absorbed in the system results in a low moisture diffusion coefficient. However, increase in moisture concentration resulted in a lower moisture diffusion coefficient. Moreover, more water molecules present in the EMC materials or at the EMC/Cu interface may form water clusters, which can lower the mobility of water molecules resulting in low moisture diffusion coefficient. This phenomenon was also proved experimentally and numerically by other researchers [35, 40]. At the same environmental condition, the moisture diffusion coefficient for the EMC/Cu interface was higher (almost one order of magnitude) than that for the bulk EMC material. This may be attributed to the larger pore sizes at the EMC/Cu interface than those within the EMC material, which caters for higher water molecule mobility at the EMC/Cu interface. Comyn et al. [41] and Zanni-Deffarges and Shanahan [42] found that the amount of water diffusion at the interface was higher in magnitude than that in the bulk epoxy. They concluded that capillary diffusion along the interface exacerbated water ingress, and surface tension effects near the polymer–metal interface increased the effective driving force for water penetration. These experimental results are all consistent with the results from MD simulations in this study, stipulating that moisture could more readily penetrate into the package along the EMC/Cu interface than in the bulk EMC. On the other hand, cracks always exist at the EMC/Cu interface after encapsulation, which is another potential factor for enhancing moisture diffusion along the EMC/Cu interface. Therefore, we concluded that the seepage along the interface was the dominant mechanism for moisture diffusion into the EMC/Cu interface in plastic packages. The conventionally studied mechanism of moisture diffusion into the interface via the bulk EMC material is only a secondary moisture penetration path to the interface [24]. From MD simulation results, it is concluded that the seepage of moisture along the EMC/Cu interface is an important factor in the design against moisture-related failures in plastic packages. Fan et al. [43–45] developed a multiscale micromechanics-based vapor pressure model to estimate the vapor pressure evolution at reflow. They also suggested that the package moisture sensitivity performance at the interface is the only parameter to control adhesion at elevated

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temperature [46]. The present MD simulation approach provides only a qualitative prediction of the moisture diffusion coefficient, but it would be a useful tool to investigate the performance of epoxy molding compounds and their interfaces under different moisture conditions.

21.2.3 Effect of Interfacial Adhesion of Copper/Epoxy Under Different Moisture Levels Moisture-induced reliability concerns have been extensively studied in a package design. Popcorning in plastic-encapsulated IC packages is a defect frequently occurring during solder reflow due to moisture penetration into the packages. Moisture absorption has a detrimental effect on the EMC/Cu interfacial adhesion and drastically reduces the reliability of the encapsulated package. Factors governing the interfacial delamination are mainly the moisture content and the adhesion strength of the epoxy/copper interface at the target temperature. The loss of interfacial adhesion due to moisture is governed by the moisture diffusion rate combined with vapor pressure generated at the interface. Understanding interfacial adhesion subjected to different levels of moisture content is of significant interest to the electronic packaging industry. Although the moisture absorption in electronic package has been widely studied [43–46], investigations at the molecular level are becoming increasingly important and necessary. In order to investigate the effect of moisture content at the EMC/Cu interface on the adhesion, a series of MD models containing different amounts of water molecules were inserted at the interface between the epoxy chains and the copper substrate. The EMC modeled in this study consisted of epoxy resin and curing agent, which is the same structure as shown in Fig. 21.1. As shown in the previous section, the MD models were built with a rectangular simulation box 1.81 nm × 1.81 nm in the x- and y-directions and periodic in the plane perpendicular to the EMC/Cu interface. The mass ratio of water molecules to epoxy varies from 0 to 6.7%. All the copper atoms were held rigid, while the epoxy chain and water molecules could move freely in all directions. The non-bond interactions include van der Waals and electronic static forces. The Ewald simulation technique was used for the dispersion interactions. Energy minimization was then conducted to obtain an equilibrated structure of the bimaterial system. The whole structure of the epoxy was equilibrated at a temperature of 85◦ C, using the ensembles of the constant number of particles, constant volume, and constant temperature (NVT), and the whole system achieved the strongest bonding between the epoxy and copper. The total potential energy was represented by the superposition of valence and non-bond interactions. The valence terms consist of bond stretch, bond angle bending, and dihedral angle torsion terms, while non-bond interactions consist of van der Waals and electrostatic terms. Since the interaction between the epoxy and the copper substrate is a non-bond interaction, the interfacial bonding energy comes from

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the electrostatic and van der Waals forces in the molecular system. Generally, the interaction energy was estimated from the energy difference E between the total energy of the whole system and the sum of the energies of individual molecules as follows: E = Etotal − (Eepoxy + ECu ),

(21.7)

where Etotal is the total energy of the whole system, Eepoxy is the energy of the epoxy without the copper substrate, and ECu is the energy of the copper substrate. The interfacial bonding energy γ was evaluated using the interfacial energy E and the contact area A between the copper substrate and the epoxy: γ = E/A.

(21.8)

Based on equations (21.7) and (21.8), the bonding energy between the epoxy and the copper substrate for different amounts of water penetrated at the epoxy/Cu interface was calculated and plotted against the moisture content, as shown in Fig. 21.4. The higher the interfacial bonding energy, the higher the force needed to separate the EMC from the Cu substrate. The interfacial bonding energy generally decreased with the increase of the moisture content at the EMC/Cu interface. The higher the content of moisture on the copper substrate, the lower the adhesion strength between EMC and copper substrate. These MD results indicate that the adhesion strength between the EMC and the Cu substrate is affected by the moisture content absorbed at the EMC/Cu interface. More water molecules present at the EMC/Cu interface may form water clusters, which can increase the gap between the EMC and the Cu substrate resulting in

Fig. 21.4 Interfacial bonding energy as a function of mass ratio of water molecules to epoxy resin

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lower van der Waals force. Therefore, the adhesion strength between the EMC and the Cu substrate dominated by the van der Waals force in this study was generally decreased by moisture content absorbed at the EMC/Cu interface. Comyn et al. [41] and Bowditch [47] studied humidity effect on adhesive joints and they concluded that weakening of the interfacial adhesion could result from van der Waals force being gradually reduced when water penetrated the EMC/Cu interface. These experimental results are all consistent with the results from MD simulations in this study confirming that moisture drastically affects interfacial adhesion and is one of the key reliability concerns in package designs.

21.3 Experimental Methods on Detecting Interfacial Moisture Diffusion 21.3.1 Background Numerous research efforts have been focused on the different parameters controlling the kinetics or ultimate moisture uptake inside plastic packages [48–50]. However, they are mostly concerned with the bulk moisture diffusion of the epoxy compound. There is a need to understand interfacial moisture diffusion at a fundamental level. Few efforts have been made on interfacial moisture diffusion modeling due to the limited availability of measurement tools. Zanni-Deffarges and Shanahan [42] observed that the diffusion coefficient of a torsional adhesive joint was higher than that of simple bulk adhesive sample. The water ingress was estimated from changes in overall elastic behavior of the polymer. Chan et al. [31] and Fan et al. [24] used molecular dynamics to show that the value of the moisture diffusion coefficient at the epoxy molding EMC/Cu interface was almost one order higher than that in the bulk EMC material. On the other hand, many experimental techniques have been employed to study water adsorption at material interfaces [51–53]. Proton nuclear magnetic resonance (NMR) spectroscopy and solid-state NMR spectroscopy have been used to map the presence of moisture and its influence on relaxation within the interface region by Hoh et al. [54]. The distribution of water was successfully imaged at around 50 μm resolution. However, this resolution is too low to reflect the moisture content in the interfacial region. Dielectric relaxation spectroscopy can detect water in the interfacial region while distinguishing it from water in the bulk resin, and bound water can be distinguished from mobile water [55]. However, neither the detailed concentration profile of water can be obtained nor the specific location and nature of the bound water can be determined. Neutron reflectivity (NR) is capable of obtaining a concentration profile of adsorbed water and probing the structure of the interface. Neutron reflectivity has been used to characterize moisture at interfaces in thin films [56]. In these cases, an excess of water, dependent on the substrate hydrophilicity, was observed at the

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polymer/substrate interface [56, 57]. However, a neutron reflectometer is expensive and not widely available. Hence, alternative measurement methodology is needed for the study. Nguyen et al. [58, 60] developed an in situ measurement method for water content within a few micrometers from the coating/metal interface by Fourier transform infrared– multiple internal reflection (FTIR–MIR) measurement. In FTIR–MIR measurement, the infrared radiation penetrates the sample only to a depth of less than 2 μm making it generally insensitive to sample thickness. The intensity of the wave decays exponentially with distance from the surface. The evanescent wave penetration also depends on its incidence angle. This technique has excellent sensitivity to low levels of water within the penetration depth of the evanescent wave (∼200–400 nm), and the measurement can be performed in situ. Another important advantage of this technique is that the OH bonding state of water can be determined, allowing one to distinguish between physically adsorbed and chemisorbed water. However, its depth resolution is limited due to the fairly large penetration depth of the evanescent wave. Nguyen and colleagues [58, 60] have extensively analyzed the problem of water diffusion into a polymer/substrate interface using the high-energy surface of an internal reflection element (IRE) as the substrate (germanium, KRS-5, and silicon). When an epoxy-coated copper specimen is exposed to water, water will eventually enter the epoxy/Cu substrate interfacial region, interact with the evanescent wave, and be detected. The moisture content at the epoxy/Cu interface can then be quantified by the FTIR–MIR technique. The substrate in Nguyen’s case was a ZnSe attenuated total reflection (ATR) crystal having a refractive index greater than that of organic films and water. The depth to which the radiation penetrates the sample is proportional to the wavelength. The problem was treated as a two-layered model as shown in Fig. 21.5. The first layer contained the water uptake in the epoxy sample within the penetration depth of the evanescent wave dp : dp =

γ 2π n1 [sin θ − (n2 /n1 )2 ]1/2 2

,

(21.9)

where γ is the wavelength of the infrared radiation in vacuum, n1 and n2 are the refractive indices of the epoxy sample and the substrate, respectively, and θ is the

Water absorbed in polymer within IR penetration depth Water layer Substrate

Fig. 21.5 Illustration of the model used for quantifying water at the polymer/substrate interface

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incident angle. dp is defined as the point at which the amplitude of the evanescent field decays to 1/e of the value at the epoxy/substrate interface. For any MIR measurement, the refractive index of the sample should include the ATR correction. The refractive index of the epoxy sample was measured by a variable angle ellipsometry system. The penetration depth of the evanescent wave on the DGEBA/DICY system, plotted in accordance with equation (21.9), is shown in Fig. 21.6. Water is indicated by the absorbance at 3,400 cm–1 . The FTIR–MIR shows a penetration depth of 0.4485 μm at this wave number and therefore the interfacial moisture absorption can be measured up to a depth of 0.4485 μm for this DGEBA/DICY epoxy system.

5 n = 1.554

Penetration Depth (μm)

4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 500

1000 1500 2000 2500 3000 3500 4000 Wavenumber (cm–1)

Fig. 21.6 Penetration depth of infrared in the DGEBA/DICY epoxy sample inside FTIR-MIR spectrometer

Using the equations quoted by Nguyen and coworkers [58, 60], Chan and Yuen [59] evaluated the thickness and weight of the water layer at the EMC/Cu substrate interface. The total amount of water was obtained by combining the data of an FTIR–MIR measurement on specimens exposed to water and an FTIR– MIR intensity–concentration calibration curve of water in D2 O solution. However, using different H2 O concentrations in D2 O solutions to establish an FTIR–MIR intensity–concentration curve for water may not totally reflect the water content at the EMC/Cu interface due to different experimental setup. Chan and Yuen [59] measured the water content on the top exposed surface of the sample which should have a more direct correlation with the bulk sample weight gain. Actual moisture content can be estimated by obtaining the FTIR–MIR signal from the exposed surface. Hence, water content was directly calibrated by the FTIR–MIR absorbance signal from the exposed surface of the epoxy sample, assuming that the exposed surface reached saturation value during the moisture absorption test.

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21.3.2 Interfacial Moisture Diffusion Measurement Example 21.3.2.1 Sample Preparation The thin circular epoxy test slabs for such measurements were fabricated by molding the epoxy compound made up of bisphenol A epoxy resin (DGEBA) and dicyandiamide (DICY) hardener with a catalyst on top of a commercial-grade copper leadframe C194 substrate according to methodology presented by Chan and Yuen [59]. After curing the epoxy at 145◦ C for 1 h, the test slabs were baked at 125◦ C for 24 h in a conventional oven to remove moisture; they were then placed in a humidity chamber at 85◦ C/85% RH at 1 atm. The initial weight of each test slab before moisture absorption was then measured by an electronic balance. The percentage weight gain was used to monitor the level of moisture absorption with respect to time. This method assumes that the diffusion process was controlled by a constant diffusion coefficient and that samples were initially dried before exposure to moisture. After moisture diffusion, a diametrical strip of the circular epoxy test slab was sectioned and the moisture content in the interfacial layer of each section was measured using an FTIR spectrometer. The sectioning methodology was according to Chan and Yuen [59]. Figure 21.7 shows the numbering of samples for the sectioning. Sample location 1 is the outermost sample of the epoxy diametrical strip, while sample location 5 is the innermost sample close to the center of the test slab.

Fig. 21.7 Illustration of sample preparation for FTIR–MIR measurements and numbering of samples

21.3.2.2 FTIR–MIR Measurement After sectioning, the sample was placed on top of a 80 mm × 10 mm × 5 mm, 45◦ parallelogram, spectroscopic-grade ZnSe internal reflection element (IRE) crystal to detect the OH bonding related to moisture absorption. At a 45◦ incidence angle, the element produces nine reflections inside the sample. The crystal was stored in a dry box at room temperature with 30% relative humidity. The FTIR–MIR measurements were taken from samples within 1 h of pre-conditioning. The background signal (specimen-free spectrum) was subtracted from the measured data to obtain the spectrum. FTIR–MIR measurements were conducted at 4 cm−1 resolution with unpolarized IR radiation at 45◦ incidence angle, and absorbance was obtained by averaging results from 32 measurements. The absorbance value at 3,400 cm−1 was used in the subsequent quantitative analysis. A typical moisture absorption measurement is shown in Fig. 21.8.

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20

x 10–3 Sample with moisture penetration Dry Sample

Absorbance (a.u.)

15

10 Shake-up Peaks

5

0

–5 500

1000

1740 2000

2500

3000 3350

4000

Wavenumber (cm–1)

Fig. 21.8 Typical FTIR–MIR spectrum after moisture diffusion into epoxy system (DGEBA/DICY)

The intensity of the signal gathered in the FTIR–MIR measurement is dependent on the effective area of the epoxy sample in the measurement, which is a function of contact area of sample with IRE crystal, roughness of sample, and background noise. Since all samples have similar roughness, the FTIR–MIR measurement signal depends only on the sample area. The signal should, therefore, be normalized against the sample cross-sectional area. For this material system, the saturation moisture weight gain is about 6% at 700 h. The diffusivity D can now be experimentally determined using absorption data with the Fickian model [equation (21.10)] of one-dimensional diffusion and it is found to be 9.98 × 10−13 m2 /s:

D=

π 16



Mt /M∞ √ t/h

2 ,

(21.10)

where Mt is the total mass of the diffusing substance absorbed by the sample at time t, M∞ is the equilibrium mass of the absorbed substance, and h is the thickness of the sample. The Fickian model is normally applied to bulk diffusion and the deviation of theoretical Fickian model from the experimental data is likely due to the presence of the copper substrate in the measurement sample.

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21.3.2.3 FTIR–MIR Signal Calibration To correlate the FTIR–MIR signal with the actual moisture absorbed in the interfacial region, Nguyen et al. [61] developed an FTIR–MIR analysis by using different H2 O concentrations in D2 O solutions to establish an FTIR–MIR intensity– concentration curve for water. In this study, however, the bulk water absorption in percentage weight gain of the sample was used to calibrate the FTIR–MIR measurement from the top exposed surface of the bulk absorption sample. Assuming a uniform moisture distribution in the bulk absorption sample, the water content on the top exposed surface should have a direct correlation with the gravimetric measurement of the sample. Since the absorbance signal depends on the contact area of sample with the IRE crystal, the area of the exposed samples was evaluated in a similar fashion as that of interfacial samples. Figure 21.9 shows the calibration curve of the absorbance and corresponding moisture concentration. The calibrated FTIR–MIR measurement was then used to calculate the interfacial moisture content. 6

x 10–5

Concentration (g/mm3)

5 4 3 2 1 Experimental results Fit

0

0

0.2

0.4

1.2 1.4 0.6 0.8 1 Normalized Absorbance

1.6

1.8 2 x 10–5

Fig. 21.9 Calibration curve of moisture concentration against normalized absorbance (“fit” – linear fitting of experimental results)

21.3.2.4 Results of FTIR–MIR Measurement Figures 21.10 and 21.11 show the FTIR–MIR measurement results in the interfacial and the top exposed regions. The “sample location” shown on the abscissa is the location of the sample on the diametrical strip of the test slab shown in Fig. 21.7. Sample location 1 denotes the outermost sample, while the sample location 5 indicates the central region of the circular epoxy test slab with copper substrate.

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Concentration (g/mm3)

1.5

x 10–4 700hours 650hours 505hours 403hours 301hours 207hours 98hours

1

0.5

0

1

2

3 Sample Location

4

5

Fig. 21.10 Moisture concentration against time in the interfacial region of epoxy samples

Concentration (g/mm3)

1.5

x 10–4 700hours 650hours 505hours 403hours 301hours 207hours 98hours

1

0.5

0

1

2

3 4 Sample Location

5

Fig. 21.11 Moisture concentration against time on the exposed surface of epoxy samples

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For the interfacial moisture absorption measurement, the spectral peak around 3,400 cm−1 for all samples confirms the presence of OH bond in the interfacial region. The abscissa indicates different sample locations in the diametrical strip of the FTIR–MIR measurement sample. The ordinate indicates the contact areanormalized absorbance value which is obtained from averaging the results from diametrically symmetric sample locations (with the same sample location as shown in Fig. 21.7) on either side of the diametrical strip. Using the calibration curve from the bulk samples depicted in Fig. 21.9, the absorbance results are used to calculate the moisture concentration over time at individual positions and the results are presented in Figs. 21.10 and 21.11, respectively. The DGEBA/DICY samples follow the Fickian law with a bulk diffusion coefficient of 9.98 × 10−13 m2 /s. From the absorbance results, the absorbance in the EMC/Cu interface is found to be around 2.2 times that of the corresponding top exposed region of the epoxy. The higher value in the interface is likely to originate from moisture seepage into the interfacial region. The absorbance at the edge sample (Sample Location 1) was found to be higher than that in the interior. This implies that the moisture absorbed at the edge blocks the moisture from diffusing into the interior region. This is reflected in Figs. 21.10 and 21.11 when comparing the moisture concentration. An important observation is that the maximum moisture concentration in the interfacial region is higher than the corresponding value at the top exposed region which represents a saturation state. This implies that the interfacial region has the capacity to hold more water molecules than does the top surface which exemplifies the bulk epoxy material. This suggests that the interfacial region, which is between the epoxy molecule chain and copper molecules, is likely to have larger pores as compared with the bulk epoxy material and thus have a larger capacity to hold water molecules in the interfacial region. This is consistent with the results obtained by the MD modeling of Fan et al. [24] and Xiao and Shanahan [62]. Fan et al. [24] also suggested that the higher moisture content in the interfacial region originated from the seepage at the epoxy/Cu interface and water molecules were locked in the pores at the epoxy/Cu interface, causing degradation. In addition, Xiao and Shanahan [62] claimed that the epoxy system undergoes irreversible trapping of water initially.

21.3.3 Effect of Copper Oxide Content Under Interfacial Moisture Diffusion on Adhesion 21.3.3.1 Work of Adhesion Delamination at the EMC/Cu interface adversely affects the reliability of IC packages and this is a common failure mode during the qualification process [63, 64]. One of the factors governing the interfacial delamination is the moisture absorption property of the polymer material, primarily epoxy compound used in the package.

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Normally, there are four primary mechanisms for adhesion which have been proposed. They include mechanical interlocking, diffusion theory, electronic theory, and adsorption theory [65]. For the EMC/Cu interface, the contributions of interfacial diffusion and electrostatic forces between the adhesive and the substrate causing adhesion are far lower than the effects of mechanical interlocking and absorption [65]. For the case of absorption-governed adhesion with only secondary forces acting across an interface, the stability of an adhesive/substrate interface in the presence of moisture can be ascertained from thermodynamic arguments. The thermodynamic work of adhesion WA in an inert medium is given by Kinloch [65]: WA = γa + γs + γas ,

(21.11)

where γa is the surface free energy of the adhesive, γs is the surface free energy of the substrate, and γas is the interfacial free energy. In the presence of a liquid, the thermodynamic work of adhesion WAd is given as follows: WAd = γal + γsl + γas ,

(21.12)

where γal and γsl are the interfacial free energies between the adhesive/liquid and substrate/liquid interfaces, respectively. Typically, the thermodynamic work of adhesion of an adhesive/substrate interface in an inert medium Wa is positive, which indicates the amount of energy required to separate a unit area of the interface. However, the thermodynamic work of adhesion in the presence of a liquid WAd can be negative, which indicates that the interface is unstable and will separate when it meets the liquid. Thus, the calculation of WA and WAd can indicate the environmental stability of the adhesive/substrate interface. Kinloch [65] has shown that WA and WAd may be calculated from the following expressions:   WA = 2 γaD γsD + 2 γaP γsP ,

(21.13)        D P D P D P D P D D P P = 2 γlv − γa γlv − γa γlv − γs γlv − γs γlv + γa γs + γa γs , 

WAd

(21.14) where γD is the dispersion component of surface free energy, γP is the polar component of surface free energy, and γlv is the surface free energy of the liquid. Table 21.2 gives the polar and dispersion surface free energies of epoxy, copper, and water. Table 21.2 Polar and dispersion surface free energies of epoxy, copper, and water [65] Substance

γ (mJ/m2 )

γD (mJ/m2 )

γP (mJ/m2 )

Epoxy Copper Water

46.2 1,360.0 72.2

41.2 60.0 22.0

5.0 1,300.0 50.2

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Using the values given in Table 21.2 and substituting into equation (21.13), the thermodynamic work of adhesion of the epoxy/Cu interface is 260.7 mJ/m2 . If water is present at the EMC/Cu interface, the thermodynamic work of adhesion given by equation (21.14) is –270.4 mJ/m2 . Therefore, since the work of adhesion is positive before exposure to moisture and negative after exposure, all adhesions of the epoxy/Cu interface are lost if water is exposed to the interface. Investigation of moisture-induced adhesion degradation and surface analysis was conducted using button shear tests. Button samples were prepared to investigate the effect of moisture on the adhesion at the epoxy/Cu interface. Figure 21.12 shows the experimental setup for the button shear test. Epoxy buttons were molded onto the copper substrate and they were then put in humidity chamber at 85◦ C/85% RH at 1 atm. For each certain time of moisture adsorption, some samples were taken out and were sheared off by a Dage micro-tester. After shearing off the epoxy button, surface analysis was conducted on the delaminated copper substrate surface by X-ray photoelectron spectroscopy (XPS). Fig. 21.12 Experimental illustration for button shear test

An earlier study by Cho and Cho [63] and Chung et al. [66] showed that under continuous thermal oxidation, there was a change from the mixture of metal copper and cuprous oxide to only cuprous oxide and from cuprous oxide to cupric oxide (Cu/Cu2 O → Cu2 O → CuO). It was claimed that this change improved the adhesion strength at the interface. Nevertheless, delamination was found if cupric oxide appeared at the edge of the sample. In addition, the previous studies [67, 68] could not fully explain the improved adhesion by cuprous oxide growth. Fan et al. [23] also showed that cuprous oxide was the key to the adhesion improvement. To verify the effect of cuprous oxide on adhesion due to interfacial moisture diffusion, XPS was conducted on button shear test samples. 21.3.3.2 X-Ray Photoelectron Spectroscopy XPS was used to examine the chemical composition of the surface of the copper substrates after the button shear test. Since oxides were removed from the copper surface before bonding with epoxy, it is possible that oxide growth from moisture pre-conditioning would have an effect on the interfacial fracture toughness results. An X-ray photoelectron spectrometer (Surface Science, model PHI 5600, USA) was used to determine the type and level of copper oxide present on the fracture surface after moisture pre-conditioning at 85◦ C/85% RH for up to 168 h, as well as after thermal aging at 85◦ C for 168 h. All the measurements were performed using aluminum anode that provided the Kα (1,486.6 eV) radiation with a pass energy of 59 eV. The instrument was equipped with concentric hemispherical analyzers. All

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XPS measurements were made at a takeoff angle of 45◦ , with respect to the sample surface. The inspected area was 800 μm in diameter and sampling depth was about 5 nm. To eliminate error from contamination or material degradation, copper surface of the sheared sample was tested by XPS within 1 h of conducting the shear test. The three different areas shown in Fig. 21.13 were analyzed. Exposed area is the region of the copper substrate without epoxy sample molded on top. Outer adhesion area is the ring-shaped outer region where the epoxy sample is molded on top, while inner adhesion area is the center region where the epoxy sample is molded on top. Usually the outer adhesion area is a circular ring region. Before analyzing the atomic concentrations, the surface elemental identification was necessary. In the wide scan, there were two kinds of copper oxides – cuprous and cupric oxides. To determine their individual contents, the composition of the copper (Cu2p3 ) peak was inspected.

Fig. 21.13 Different areas on the fracture copper surface where XPS measurements were conducted

Exposed area

Inner adhesion area Outer adhesion area

A narrow scan with peak pass energy of 59 eV was conducted on the same specimen to obtain C1s , O1s , Cu2p3 , Si2p , N1s , and F1s . The purpose was to ascertain the intensity of Cu2p3 and O1s peaks in order to determine the cuprous oxide content. The Cu2p3 peak having a sharp shake-up sub-peak, as shown in Fig. 21.14, shows that Cu2+ is present, which indicates that cupric oxide was present on the examined surface, and not Cu0 and Cu1+ . If no Cu2+ shake-up peak is found, as in the case of Fig. 21.15, the cuprous oxide content can be obtained from O1s peak. Narrow scan results of oxygen peak were used to separate the cuprous oxide (Cu2 O) content and the metallic copper (Cu0 ) content by curve fitting. A typical oxygen peak, from the metal oxide, is shown in Fig. 21.16. 21.3.3.3 Moisture and Copper Oxide-Related Adhesion From the Cu2p3 , three different kinds of copper states were found – metallic copper (Cu0 ), copper (I) (Cu1+ ), and copper (II) (Cu2+ ). Both Cu0 and Cu1+ coexist on the inner adhesion area and all three kinds of copper appear only on the outer adhesion area and the exposed area. The XPS results show that cuprous oxide was the only

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Fig. 21.14 A typical XPS spectrum in the Cu2p3 region of the outer adhesion area on the copper surface

Fig. 21.15 A typical XPS spectrum in the Cu2p3 region of the inner adhesion area on the copper surface

Fig. 21.16 A typical XPS spectrum in the O1s region of the inner adhesion area on the copper surface

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oxide type found on the inner adhesion area regardless of experiment duration, while both cuprous and cupric oxides were observed in the other areas. Since the adhesion force was only due to the inner adhesion area, the oxide contents on the other two areas were not considered. The cuprous oxide content on the inner adhesion area was measured from its XPS narrow scan oxygen peak, O1s , in the XPS spectrum. There were three different oxide types found on the sheared sample: metal oxide at 530.3 eV peak and organic oxides at the 531.5 and 532.5 eV peaks. As copper is the only metal found in the entire series of examined samples, the metal oxide is copper oxide by default. Since there was no cupric oxide found on the inner adhesion area for all specimens, the copper oxide should be Cu2 O. Curve fitting was performed using Multipak version 6.0 (Physical Electronics) to obtain the relative percentage of oxide content. In accordance with the different oxide percentages obtained in peak fitting and the overall oxygen content, the cuprous oxide content is defined as follows: Cu2 Ocontent = Kmetal O,

(21.15)

where Kmetal is the percentage of metal oxide from the O1s narrow scan and O is the oxygen percentage of the total atomic concentration of all elements found on the surface. After calculating the Cu2 O content on the sheared surface, correlation of shear force with percentage of cuprous oxide content is plotted in Fig. 21.17. For increasing moisture content, the shear force shows a similar trend as the percentage

Fig. 21.17 Shear force and cuprous oxide content in the interfacial region against moisture content (weight gain)

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of cuprous oxide. In short, interfacial adhesion had a direct relationship with the cuprous oxide content in the interfacial region. The formation of cuprous oxide was due to the interfacial moisture diffusion. While the adhesion increased by cuprous oxide growth at low moisture content, continuous moisture ingress led to degradation of interfacial adhesion at 1.5% weight gain. This concentration is far lower than the bulk moisture diffusion saturation value obtained in the above section. The drop in adhesion at this low moisture concentration is suspected to occur from faster moisture diffusion rate in the interfacial region, and cuprous oxide is further transformed into cupric oxide, which reduces adhesion strength at the interface.

21.4 Summary With proper formulation of the MD model and appropriate use of boundary conditions, potential functions, and simulation procedure, MD simulation can provide good understanding of the moisture diffusion at the fundamental level. It can distinguish bulk moisture diffusion and interfacial moisture diffusion and investigate individual moisture effect on package reliability. By contrast, traditional continuum models depending on bulk moisture diffusion coefficient of the material cannot represent moisture transport in channels of the material and effects of functional groups on moisture transport. The MD results showed that the seepage along the EMC/Cu interface is more prevalent when compared to moisture diffusion into the bulk EMC, thus rendering it a dominant mechanism causing moisture-induced interfacial delamination in plastic packages. It was also shown that the interfacial bonding energy dominated by the van der Waals force in this study was generally decreased by moisture content absorbed at the EMC/Cu interface. Experimental investigation by FTIR– MIR measurements with the new calibration method also showed higher moisture content at the interfacial surface than at the exposed surface. It can be concluded that the interface has an absorption mechanism differing from that of the bulk epoxy and that it requires a new model to describe the phenomenon rather than Fickian law. Therefore, the fundamental knowledge obtained from MD simulation can contribute toward the development of a methodology that can provide detailed moisture diffusion mechanism at interfaces in electronic packages. MD simulations are capable of generating an in-depth insight into the local molecular interactions; a consistent approach to relate the MD results to the results in an equivalent continuum model is needed to provide a full understanding of moisture diffusion across the scale range. By studying the adhesion change under moisture diffusion and analyzing the fracture surface in button shear tests by XPS, the effect of interfacial moisture diffusion on adhesion can be explained by the moisture-induced cuprous oxide growth and cupric oxide transformation under thermal loading at the epoxy/Cu interface.

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About the Editors

Dr. X.J. Fan (Xuejun Fan) is currently an associate professor in the Department of Mechanical Engineering at Lamar University, Beaumont, TX, USA. He was a senior staff engineer at Intel Cooperation, Chandler, AZ, USA, from 2004 to 2007, a senior member research staff with Philips Research Lab at Briarcliff Manor, NY, USA, from 2001 to 2004, and a member technical staff and group leader at the Institute of Microelectronics (IME), Singapore, from 1997 to 2000. Dr. Fan received his Ph.D. in engineering mechanics from Tsinghua University, Beijing, China, in 1989. He earned his master’s degree and bachelor’s degree in applied mechanics from Tianjin University, Tianjin, China, in 1986 and 1984, respectively. In his earlier career he held a faculty position at Taiyuan University of Technology, Shanxi, China, from 1989 to 1997. He received the Young Scientist Fellowship from Japan Society of Promotion of Science (JSPS) to work at the University of Tokyo, Tokyo, Japan, from 1993 to 1994. He was a visiting professor at the University of British Columbia, Vancouver, Canada, from 1996 to 1997. Dr. Fan’s interests and expertise lie in the areas of design, modeling, material characterization, and reliability in micro-/nano-electronic packaging and microsystems. He has published more than 100 scientific papers and filed 5 patents in worldwide patent offices. During his tenure with Intel, he received several awards including Divisional Recognition Awards (2005, 2006), Excellent Technical Contribution Award (2005), Outstanding Team Contribution Awards (2005, 2006), and Best Presentation Award (2005). In 2008, he was elected as IEEE distinguished lecturer. In 2009 he received the 2008 Best Paper Award of IEEE Transactions on Components and Packaging Technologies. He also received the Outstanding Contribution Award from EuroSimE and Significant Contribution Award from ICEPT-HDP in 2009. Dr. Fan was promoted to a full professor at Taiyuan University of Technology, Taiyuan, Shanxi, China, in 1991 and became one of the youngest professors in China at the age of 27. He was a nominee for the title of “1991 Ten

X.J. Fan, E. Suhir (eds.), Moisture Sensitivity of Plastic Packages of IC Devices, Micro- and Opto-Electronic Materials, Structures, and Systems, C Springer Science+Business Media, LLC 2010 DOI 10.1007/978-1-4419-5719-1, 

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About the Editors

Outstanding Youth of China,” and received the Young Faculty Award in 1994 from Fok Ying-Tung Education Foundation. Dr. Fan is a senior member of IEEE, an associate editor of the IEEE Transactions on Components and Packaging Technologies, and a visiting chair professor at South China University of Technology (Guangzhou, China). He is the member, advisory member, and co-chair of ECTC, EuroSimE, EPTC, ICEPT-HDP, ESTC, and micro/nano-reliability conferences. Dr. E. Suhir is distinguished member of technical staff (ret), Physical Sciences and Engineering Research Division, Bell Labs, Murray Hill, NJ, USA. Currently he is on the faculty of the Electrical Engineering Department, University of California, Santa Cruz, CA, USA, where he teaches a course “Basics of Electronic Reliability.” He is also visiting professor, Department of Mechanical Engineering, University of Maryland, College Park, MD, USA, and is guest professor, Key Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi’an, China. Dr. Suhir is fellow of the Institute of Electrical and Electronics Engineers (IEEE), the American Physical Society (APS), the Institute of Physics (IoP), UK, the American Society of Mechanical Engineers (ASME), and the Society of Plastics Engineers (SPE). He is a co-founder of the ASME Journal of Electronic Packaging and served as its technical editor for 8 years (1993–2001). Dr. Suhir has authored about 300 technical publications (patents, papers, book chapters, books), including monographs “Structural Analysis in Microelectronics and Fiber Optics,” VanNostrand, 1991; “Applied Probability for Engineers and Scientists,” McGraw-Hill, 1997; and recent Springer publication E. Suhir, CP Wong, YC Lee, eds. “Micro- and Opto-Electronic Materials and Structures: Physics, Mechanics, Design, Packaging, Reliability,” Springer, 2007. He is editor of the Springer book series on physics, mechanics, design-for-reliability, and packaging of microelectronic and photonic systems. Dr. Suhir is member of the board of governors and distinguished lecturer of the IEEE CPMT (components, packaging and manufacturing technology) Society and is associate editor of the IEEE CPMT Transactions on Advanced Packaging. Dr. Suhir received many distinguished service and professional awards, including 2004 ASME Worcester Read Warner Medal for outstanding contributions to the permanent literature of engineering through a series of papers in mechanical, microelectronic, and optoelectronic engineering, which established a new discipline known as the structural analysis of microelectronic and photonic systems; 2001 IMAPS John A. Wagnon Technical Achievement Award for outstanding contributions to the technical knowledge of the microelectronics, optoelectronics, and packaging industry; 2000 IEEE-CPMT Outstanding Sustained Technical Contribution Award for outstanding, sustained, and continuing contributions to the technologies in fields encompassed by the CPMT Society; 2000 SPE International

About the Editors

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Engineering/Technology (Fred O. Conley) Award for outstanding pioneering and continuing contributions to plastics engineering; 1999 ASME and Pi-Tau-Sigma Charles Russ Richards Memorial Award for outstanding contributions to mechanical engineering; and 1996 Bell Laboratories Distinguished Member of Technical Staff Award for developing extremely accurate and robust engineering mechanics methods for predicting the reliability, performance, and mechanical behavior of complex structures used in manufacturing Lucent Technologies products.

Subject Index

A ABAQUS software, 99, 174, 199–200, 206, 215 Acceleration factor (AF), 339 Adhesion degradation of EMCs, impact of moisture on, 58 capillary action, water absorption by, 59 effect of moisture absorption and desorption, 63 EMC/Cu interface, fracture mechanics approach, 59–63 ENF test for interfacial fracture toughness measurement, 59–60 finite element analysis of ENF model, 61 inter-chain hydrogen bonds, breaking of, 59 interfacial fracture toughness, calculation of, 61 load–displacement curve of fracture test, 60–61 mechanisms of, 59 permanent degradation in adhesion, 64 reversibility of adhesion loss for OSG film, 64 VCCT, use of, 61 wicking, water absorption by, 59 Adhesion test, 444 moisture high temperature, 444 reflow, correlation, 444 Adhesive thickness effects, in interfacial fracture toughness, 314 See also Integrated circuit (IC) packages Anomalous moisture uptake, 5, 39 ANSYS-Multiphysics, 499 ANSYS tool, 41, 61, 174, 198, 202–203, 210–213, 216 ANSYS Workbench, 487 simulation process, 485

integrated hygroscopic, thermal–mechanical, 496 simulation of, 497 vapor pressure-induced equivalent stress, 498 Application programming interfaces (APIs), 483 Archimedes principle, CHS characterization by, 56–57, 154 Arrhenius equation, 75, 82–83, 182 and Arrhenius relationship, 508 diffusivity, 400 Aspect ratio, 162 Attenuated total reflection (ATR), 533 Automated simulation system, 479–480, 485 advantage of, 495 architecture of, 485 basic flowchart of, 487 moisture-related analysis master interfaces of, 489 structure of, 488 package model, 491 process, 489 AutoSim system, 480 See also Automated simulation system B Ball grid array (BGA) packages, 435 alpha radiation compound, 435 configuration, 436 moisture-induced wire bond failures, 413 polymer materials, 415 wire bond reliability carrier description, 414–415 finite element modeling, 416–417 material characterization, 415–416 polymer materials, 415 results, 417–418

555

556 Ball-spacer technology, 426 BGA packages, see Ball grid array (BGA) packages Bias voltage, 504, 507 Biharmonic equation, role, 262 See also Integrated circuit (IC) devices, moisture-sensitive plastic packages BiHAST, see Highly accelerated stress test with bias (BiHAST) Bi-material model, analysis of moisture desorption moisture concentration, 102 over-saturation, 104 problem, 102–103 substrate/die-attach film structure in stacked-die chip scale package, 102 two-step loading, 103 Bismaleimide–triazine (BT) material, 72, 338 Bump structure layout of silicon chip, 436 Button shear test, 392, 541 C CAD software library, 480 systems, 480, 485 CAF, see Conductive anodic filament (CAF) Capillary diffusion, 35 CFD, see Computational fluid dynamics (CFD) Chip scale package (CSP), 347, 472 moisture concentration contours of, 474 vapor pressure contours of, 474 See also Single-die stacking Chromatic sensor, 51 CME, see Coefficient of moisture expansion (CME) C-Mode surface acoustic microscopy (C-SAM), 412, 437–438 inspections, 398 MSLs, 412 Package 1, 404 Coefficient of hygroscopic swelling (CHS), 52, 121, 155, 186 See also Hygroscopic swelling characterization process Coefficient of moisture expansion (CME), 223, 231, 234, 230, 241, 401, 481 Coefficient of thermal expansion (CTE), 126, 133, 229, 241, 247, 304, 346, 359, 443 Compound/substrate interface, 414 moisture concentration, 418 Computational fluid dynamics (CFD), 483 Conductive anodic filament (CAF), 2, 503, 508

Subject Index Continuum theory, in encapsulated IC devices, 279–283 See also Encapsulated IC devices, continuum theory Copper corrosion, 517 dendritic growth, 517 Corrosion, in electronic packages, 2 Crack-tip opening displacements (CTODs), 133 CTE, see Coefficient of thermal expansion (CTE) CTODs, see Crack-tip opening displacements (CTODs) Cup test, 183 Curing agent process, 541 Current transients measurements, 518–520 D DCA, see Direct concentration approach (DCA) DCB, see Double cantilever beam (DCB) Deionized water (DIW), 511 Dendritic morphology dendrites growth, 2 electric field amplitude of, 518 Design of experiment (DoE), 495 material parameter, 496 simulation, 477 DGEBA/DICY epoxy, 534 infrared, penetration depth, 534 samples, 539 DIC method, see Digital image correlation (DIC) method Die-attach (DA) film, 75, 83 DA3 film, 469 DA1 film cohesive rupture, 469 voiding, 281–282 See also Encapsulated IC devices, continuum theory Dielectric relaxation spectroscopy, 532 Dies attach films cohesive failure, bottom layer, 468 evaluation of, 468–470 residual moisture, 466 types of, 464 Young’s moduli, 464 compound interface, 425 die-to-pad ratios, 423 pad-to-body, 3D responses, 422

Subject Index mold compound interface delamination, progression of, 412–413 shear tests, 20–21, 392, 445 preparation process, 442 schematic of, 442 setup, 443 stacking concepts, 429 Diffusion law, general, see Fick’s second law of diffusion Digital image correlation (DIC) method, 139, 148, 464 DIP, see Dual-in-line (DIP) Direct concentration approach (DCA), 12, 30, 84, 92, 132, 222, 348, 399, 472, 481 bi-material model, analysis of moisture desorption for, 102–104 implementation procedures, 100 PBGA package, application to, 104 theory, 97–99 verification, 100–102 See also Moisture diffusion analysis DMA, see Dynamic mechanical analyzer (DMA) DMC approach, see Direct concentration approach (DCA) Double cantilever beam (DCB), 18 D2 Pak package, report, 378 Dual-in-line (DIP), 419 Dynamic mechanical analyzer (DMA), 464 E Electrochemical deposition (ECD), 514 model for, 514 Electrochemical impedance spectroscopy, 35 Electrochemical migration (ECM), 503–504, 517 electrical failure, 505 susceptibility, hydrophilic materials, 509 Electromigration, 503 Electronic package, 481 EMC/Cu interface models, 523, 534, 541, 545 dispersion surface free energies, 540 EMC/Cu interface system morphological configurations, 527 predicted moisture diffusion coefficients, 528 EMCs, see Epoxy molding compounds (EMCs) Encapsulated IC devices, continuum theory, 279–296 gurson model and void evolution rate, extension, 289–291 moisture-induced damage, 292

557 rigid-plastic model, 291–292 single void growth elasto-plastic model, 283–286 hyperelastic model, 286–287 void behavior, 287–288 End-notched flexure (ENF), 392 test, 60 load–displacement curve of, 60 Energy minimization, 530 Environment library, CTE, 491 Epoxy cresol novolac (ECN), 29 Epoxy molding compounds (EMCs), 30, 65–66, 359, 492, 523, 532 adhesion degradation, impact of moisture on, 72 capillary action, water absorption by, 59 effect of moisture absorption and desorption, 63 EMC/Cu interface, fracture mechanics approach, 61–66 ENF test for interfacial fracture toughness measurement, 59–60 finite element analysis of ENF model, 61 inter-chain hydrogen bonds, breaking of, 59 interfacial fracture toughness, calculation of, 61 load–displacement curve of ENF fracture test, 60–61 mechanisms of, 58 permanent degradation in adhesion, 64 reversibility of adhesion loss for OSG film, 64 VCCT, use of, 61 wicking, water absorption by, 59 hygroscopic swelling, impact of, 50 Archimedes principle, for volume measurements, 56 hygroscopic strain, amount of, 52 TMA/TGA approach, for CHS estimation, 54–56 topography of top surface of TQFP-epad package, 51 warpage direction of package, change in, 51 warpage measurement of bi-material beams, 52–54 moisture behavior of, 30 moisture desorption behavior of, 42–43 Arrhenius-like diffusion coefficient of QFP package, 48 desorption coefficient, estimation of, 47

558 Epoxy molding compounds (cont.) desorption curves, analysis of, 45–46 experiment on packages various temperatures, 42 Fickian and non-Fickian desorption parameters, 47 Fickian model, failure of, 45 non-Fickian moisture desorption model, 46 residual moisture content, formation of, 44, 65 source of error in experiment, 46 temperature-dependent desorption results, 43–44 moisture diffusion in, 33 dry weight of package, 31 effect of sample geometry on non-Fickian behavior, 38 Fickian and non-Fickian absorption parameters, 42 Fickian moisture diffusion, 36–37 interfacial, 35 mass of moisture and square root of exposed time, 32–33 materials and moisture content, diffusion coefficients of, 40 moisture accommodation at interfaces, 35–36 moisture diffusion in package and in bulk EMC, 33 moisture uptake curve of package in bulk EMC, 33 non-Fickian behavior, effect of sorption conditions on, 39 non-Fickian dual-stage moisture diffusion, 37 one-dimensional Fickian diffusion in plate, 37 types of plastic packages for study of, 29 second run of moisture absorption, 48, 65 baking, effect of, 50–51 expansion of free volumes in polymeric materials, 49 re-sorption experiment of bulk samples, 49 See also Moir´e interferometry Epoxy resins moisture diffusion in, 31 reaction, process of, 535 Epoxy systems, 509 FTIR–MIR spectrum, 536 moisture concentration, 538–539

Subject Index Equivalent coefficient of thermal expansion, 168 Executable Wizard System, 499 F Failure criterion factors calculation of, 405 Failure rate determination, 351 See also IPC/JEDEC moisture sensitivity level Faraday constant, 514 FCBGA, see Flip-chip ball-grid-array (FCBGA) FCOB, see Flip-chip-on-board (FCOB) FEA, see Finite element analysis (FEA) FEM model, 422, 430 Fiber/epoxy interface, 508 Fickian and non-Fickian moisture diffusion absorption–desorption cycles, 7 curve fit for homogeneous underfill material, 6 desorption curves, 8 Fickian moisture absorption, example of, 5 Fickian transport of moisture, equation for Boltzmann–Arrhenius type, 3 in humid environment, 4 initial and boundary conditions, 4 temporal and spatial moisture concentration, 4 total moisture mass, 4 gain curve for thick BT core sample, 8 least-squares fitting technique, 6 linear superposition, 9 non-Fickian diffusion, 8 normalized moisture uptake, 9 temperature dependence of diffusion constant, equation for, 3 “two-stage” sorption, 9 Fickian model, 536 Fick’s law, 3, 40, 73, 480 Filler loading, importance, 373, 380 See also Moisture sensitivity level (MSL) of plastic-encapsulated packages Film/solder mask interface, 469 Film/substrate interface delamination, 466 Finite deformation theory application, 284 Finite difference method (FDM), 191 Finite element analysis (FEA), 61, 73, 83, 132, 394, 479 modeling, objective, 347 software packages, 194, 198 Flame Retardant 4 (FR-4) resin, 72 Flip chip assembly

Subject Index 2-D finite element model, 453 stress extraction, 457 stress-free conditions, 453 Flip-chip ball-grid-array (FCBGA) packages, 109, 222, 279, 435 experiments, design of fluxless assembly process, 437 plasma grafting surface treatment, 437 test vehicles, 436–437 underfilling process, 438 failure analysis of, 451 finite element modeling thermal stress analysis, on overmolding effect, 452–455 vapor pressure modeling, 451–452 ILD/UBM structures, 435 material characterization moisture diffusivity concentration, 440–441 pull/shear adhesion test, 441–446 saturated moisture concentration, 440–441 thermo-mechanical properties, 439–440 moisture-induced delamination, integrated analysis of, 455–457 moisture/reflow sensitivity test, 446 moisture sensitivity/reflow test results failure mode analysis, 447–448 flux residue, effect of, 446 overmolding, effect of, 449–450 plasma grafting treatment, 448–449 underfill material selection effect, 446–447 voids effect, in underfill, 451 transient vapor pressure distribution, 452 Flip chip BGA configurations, 436 Flip chip daisy-chain test, 446 Flip-chip-on-board (FCOB), 305 designs, 131 Fluery model, 516 Flux formulation, 513 Flux process, 437, 447 Fourier’s law of heat conduction, 187 Fourier transform infrared–multiple internal reflection measurement, 533 Fourier transform infrared spectroscopy (FTIR-MIR), 35 measurements, 535 spectrometer infrared, penetration depth of, 533 FPA, see Fully porous adhesive (FPA) Fracture copper surface different areas on, 542

559 Fracture mechanics, 407 Fracture toughness/adhesion strength moisture effect die shear test DAGE Series 4000 with hot plate, 20 for underfills, 20 fracture toughness measurement crack growth, 19 DCB silicon/underfill/silicon (Si/UF/Si) specimen, 18 environmental conditions, 19 load–displacement plots, 18 loading–unloading curve, 18 Free volume fraction of polymers estimation, 13 Fully porous adhesive (FPA), 305 Fused silica (FS), 30 G Gold dendrites, 510 Gurson flow potential, 303–304 Gurson model and void evolution rate, extension, 289–291 See also Encapsulated IC devices, continuum theory H HAST, see Highly accelerated stress test (HAST) Heat conduction, 187 thermal stress analysis, 403 Hecker effect, 514, 516 Henry’s law, 10, 182 Highly accelerated stress test (HAST), 2, 412, 416, 418 stitch bond, 418 stitch failure, 414 Highly accelerated stress test with bias (BiHAST), 2 Humidity control, 469 Humidity stress test, 504 Hydrophobic polymer film, and water vapor transmission, 13 Hydrophobic resin system, usage, 363 See also Moisture sensitivity level (MSL) of plastic-encapsulated packages Hygro-mechanical modeling, of IC packages, 230–231 See also Integrated circuit (IC) packages Hygro-mechanical stress analysis, 398–402 Hygroscopic deformation, 494 von Mises stress, comparison of, 494 Hygroscopic properties of MLP, 481

560 Hygroscopic stress, 2, 55, 113, 153, 487 ANSYS-Multiphysics and AutoSim, 494 Hygroscopic stress modeling ABAQUS, use of, 199–200 ANSYS input template for hygro-thermal loading, 216 input templates for advance analogy, 210–213 use of, 202–203 FDM schemes, for mass diffusion equations anisothermal 1-D problem, 208–209 isothermal axisymmetric problem, 209–210 hygro-thermo-mechanical stress analysis, 197–199 templates for combined analysis program to change record key, 213–215 UEXPAN, example program for, 215 verification of, 200–202 Hygroscopic swelling, 1, 153–154, 186 Archimedes principle, for volume measurements, 56–58 EMCs, impact of, 51–52 equivalent CTE for, 491 hygroscopic strain, amount of, 52 measurement moir´e interferometry (MI) technique, 16 silicon/underfill/FR-4 assembly for, 16 swelling-induced strains by using superposition method, 16 thermoelectric heating and cooling technique, 16 strain, formula, 400 TMA/TGA approach, for CHS estimation, 54–56 topography of top surface of TQFP-epad package, 51 total moisture volume and volume expansion coefficient of, 23 total volume, 22 warpage direction of package, change in, 51 warpage measurement of bi-material beams, 53 See also Moir´e interferometry Hygroscopic swelling characterization process coefficient, calculation procedure for, 172 TMA/TGA method and moir´e interferometry, comparison between, 173

Subject Index and traditional slope method, 172 effect of non-uniform moisture distribution averaged approach I, 159–160 averaged approach II, 160 hygroscopic swelling-induced deformation, 158–159 moisture distribution, 157–158 result of approaches, 161–166 point-measurement method, use of, 154–157 averaged hygroscopic strain, 155 averaged moisture concentration, 155 average strain/average moisture content plot, 155 coefficient of hygroscopic swelling, computation of, 156 combined TMA/TGA method, use of, 154 moisture and hygroswelling material properties, 157 TMA/TGA data set for no-flow underfill, 155 TMA/TGA hygroscopic swelling measurement setup, 154 stress effect, 166–171 averaged total strain/hygroscopic strain and averaged moisture content, 171 elastic strain and hygroscopic strain distribution, 169–170 FEA results of elastic and hygroscopic strain, 169 sequentially coupled field transient analysis, 167–169 specimen configuration, 167 total and displacement by hygroscopic swelling, plot of, 170 total displacement calculation, 170–171 Hygroscopic von Mises stress, 494 Hygrothermal aging and fracture toughness of assembly, 144–146 fringe patterns during, 140 strain gradients at leftward of silicon/ underfill interface, 142 I Ideal gas law, 106 Instron Model 5566 test system, role, 366 Integrated circuit (IC) devices, moisture-sensitive plastic packages, 245–276 analysis, 247–268 boundary conditions, 250–251

Subject Index constitutive equations, 247–250 elongated package, 257–267 initial curvature and initial stresses, 253–256 stresses, 251–252 von Mises stress, 267 data calculation, 270 Integrated circuit (IC) packages, 221–222, 479 definition, 301 design, 419, 479 hygro-mechanical modeling, 230–231 integrated stress modeling, 232–234 hygro-mechanical stress, 239–240 hygromechanical stress and thermo-mechanical stress, 240–241 modeling methods, 234–236 moisture diffusion, 238–239 interfacial fracture mechanics modeling, 234–237 moisture diffusion modeling, 222–225 nonlinear viscosity and pressure sensitivity effects, 323–328 pressure sensitivity and plastic dilatancy role, 317–323 extended damage zone formation, 321–323 void growth and coalescence, 319–321 residual stress effects and vapor pressure, 304–317 adhesive failure mechanisms, 305–310 full-field analysis, 315–317 interfacial fracture toughness, 310–315 thermal modeling, 225–227 thermo-mechanical modeling, 232 vapor pressure modeling, 227–230, 303–304 Integrated hygroscopic thermal–mechanical deformation, comparison of, 496 Integrated interfacial stress distribution, 404 Integrated stress analysis, 402 Integrated stress modeling of IC packages, 232–234 in package stress estimation, 232–234 in PCT hygro-mechanical stress, 239–240 hygromechanical stress and thermo-mechanical stress, 240–241 modeling methods, 237–238 moisture diffusion, 238–239 See also Integrated circuit (IC) packages; Pressure cooker test (PCT)

561 Integrated von Mises stress, DoE simulation, 500 Interfaces adhesion characterization, 441 measurement, 457 mechanical tests for, 391 moisture absorption, effect of, 456 strength, 452 delamination, 303–304, 359, 389, 469 (see also Integrated circuit (IC) packages) fracture morphology of, 148 water accumulation at, 35 Interfacial bonding energy water molecules, mass ratio of, 531 Interfacial fracture mechanics approach, 133 effective stress intensity factor, 134 effective Young’s modulus, 133 interface crack problem, 133 interfacial stress intensity factor, 134 phase angle, 134 relative crack displacement, 133 Interfacial fracture mechanics modeling of IC packages, 234–236 in package stress estimation, 234–236 See also Integrated circuit (IC) packages Interfacial fracture tests, 139 Interfacial fracture toughness, 310–315 See also Integrated circuit (IC) packages Interfacial hydrothermal strength experimental procedures for characterization of, 137 critical interfacial fracture toughness, determination of, 139 specimen preparation, 137–138 thermal and hygrothermal deformation, measurement of, 138 of sandwiched assembly critical interfacial fracture toughness, 146–147 fracture toughness under hygrothermal aging, 144–146 hygrothermal displacement, 139–141 reliability of silicon/underfill interface, 147–148 thermal deformation, 141–143 Interfacial moisture diffusion adhesion, effect of, 530 copper oxide content, effect of moisture, 539–545 work of adhesion, 539–541

562 Interfacial moisture diffusion (cont.) X-ray photoelectron spectrometer, 541–542 EMC/Cu interfacial adhesion, 530–532 experimental methods background, 532–534 copper oxide content, effect of, 539–545 measurement example, 535–539 measurement examples FTIR–MIR measurement, 535–536 sample preparation, 535 FTIR–MIR signal calibration, 537 moisture-induced reliability, 523 molecular dynamics (MD) simulation, 524–526 models, 526–530 Interfacial shear strength, 392–393 Interfacial stress distribution, 396 from hygro-mechanical stress analysis, 398 from thermo-mechanical stress analysis, 394 Inter-layer dielectric, 435 Internal reflection element, 533, 535 IPC/JEDEC industry standard J-STD-020D, joint, 334–337 IPC/JEDEC moisture sensitivity level, 333, 345–346 experimental support, 341–344 finite element modeling, 347–350 local moisture concentration equivalency method experimental support, 341–344 theory, 337–341 methods, 346–347 J Joint Electron Device Engineering Counil (JEDEC) JEDEC MSL3 test UF-A, summary of, 446 underfill, 447 standards, 411, 475 importance, 221 J-STD-020D specification, in moisture sensitivity rating, 334–335 See also IPC/JEDEC industry standard J-STD-020D, joint L Leadframe-based packages die/compound interface, 3D responses, 425

Subject Index Leadframe-based wire bond packages, 412 Leadframe/substrate-based package family examples of, 420 Lead-free reflow, peak temperature for, 395 Linear elastic material properties, 395 Local moisture concentration interfacial adhesion strength determination, 225 in IPC/JEDEC moisture sensitivity levels experimental support, 341–344 theory, 337–341 local vapor pressure determination, 345 package cracking, 221 prediction, 241 role, 346 in soaking time determination, 347 vapor pressure calculation, 227 See also IPC/JEDEC moisture sensitivity level M Manufacturing exposure time (MET), 335 Material library data review example of, 490 Material properties thermal/mechanical, 440 MD simulation, 524 Mean time to failure, 507 data, 511 MEMS package, hermeticity of, 193 Mercury intrusion method, 3 Mercury intrusion porosimetry, 13 Metal hydroxides solubility products of, 506 Metal ions electrochemical and solubility data of, 506 Microelectronic devices mean time to failure, 507 popcorn failure, 411 Microelectronic packages, 479 AutoSim, application of integrated stress modeling, 492–495 moisture diffusion, 491–492 vapor pressure simulation, 492 conductive anodic filament, 503 dendritic morphology, 517–520 ECM mechanism, 504–507 ionic contaminants, effect of, 510–512 ion transport, mechanism of, 513–516 material factor, 509–510 moisture factor, 507 temperature factor, 508–509 voltage factor, 508

Subject Index water uptake, contaminants effect, 512–513 electrochemical migration, 503–504 hygrothermal stress, automated simulation system, 483–484 ANSYS workbench overview, 483–484 package models, 484–488 material parameter examination, 495–498 moisture diffusion, automated simulation system, 483–484 ANSYS workbench overview, 483–484 package models, 484–488 moisture-related analysis, AutoSim structure modules, 488 moisture-related automated simulation system, modules of, 489–491 Wizard System, 488 moisture sensitivity, 479 thermal expansion, equivalent coefficient of, 482–483 vapor pressure model, 481–482 Microelectronic packages, failures in, 1 tests for, package reliability highly accelerated stress test (HAST), 2 moisture/reflow sensitivity test, 2 temperature/humidity (TH) test, 2 types of, 1 MLP package, 480 MLP 6 × 6 quarter model, 491–492 MOCON test, 183 Modified solubility, 190 Moir´e interferometry, 16, 113, 135, 154 experimental procedure grating replication procedure, 118 hygroscopic deformation, measurement of, 118–119 initial preparation, 116–117 moisture content measurement, 118 reference sample, 117 test sample, 118 hygroscopic swelling measurement, of mold compounds CHS measurement, accuracy of, 124–125 CHS of mold compounds, 120–123 CHS, value of, 122 effect of grating on sorption and desorption characteristics, 123–124 experimental results, 122–123 hygroscopic and thermal deformations, comparison between, 123

563 hygroscopic strain and moisture content, 122 hygroscopic strain, determination of, 121 material properties of mold samples tested, 120 V -field fringe patterns of mold compounds, 121 for measurement of hygroscopic swelling, 113 plastic quad flat package, analysis of, 125 bending displacement, induced by swelling, 128 fringe patterns of package, 125–126 PQFP package for moir´e experiments, 125 sorption curve, 127 stress-induced strains, calculation of, 127 swelling and moisture content, 127 total deformation of package, 127 total strain of package, 127 real-time observation and testing apparatus, 115 computer-controlled environmental chamber, 115 moir´e interferometer, 115 tuning and measurement, 115–116 warped wavefronts from deformation of sample, 114 Moisture analysis material properties for, 400 concentration, 481 calibration curve of, 537 reflow profiles, 475 substrate thicknesses, comparison, 474–475 concentration, calculation, 422 content predicted and measured, 421 in substrate-based package, 423 desorption, 400 diffusivity, 451 factor, 507 induced reliability, 530 preconditioning, 407 properties, 428 sorption, 12–13 swelling, 430 uptake, 465 vaporization, 451

564 Moisture absorption, 401, 430 ANSYS-Multiphysics and AutoSim, 499 calculation, 370 definition, 367 of MLP, 491 See also Moisture sensitivity level (MSL) of plastic-encapsulated packages Moisture diffusion, 182–183 analytical solutions of diffusion equation, 184 moisture weight gain data and curve fit, 185 transient moisture transmission rate, 185–186 modeling of, 186–185 effective-volume scheme, 193–197 Moisture diffusion analysis, 91 direct concentration approach (DCA) bi-material model, analysis of moisture desorption for, 102–104 implementation procedures, 102 PBGA package, application to, 104–105 theory, 106 verification, 100–102 finite element analysis, 479 integrated stress modeling, 492–495 moisture diffusion, 498 normalization method for, 92 PBGA package, application to, 96–97 theory, 92–94 thermal-moisture analogy, 95–96 vapor pressure simulation, 492 Moisture diffusion coefficient calculation, 367 See also Moisture sensitivity level (MSL) of plastic-encapsulated packages Moisture diffusion/hygro-stress analysis, 401 Moisture diffusion in EMCs, 36 dry weight of package, 31 effect of sample geometry on non-Fickian behavior, 38 Fickian and non-Fickian absorption parameters, 42 Fickian and non-Fickian simulations of moisture absorption, 42 Fickian moisture diffusion, 36–37 interfacial moisture diffusion, 33 mass of moisture and square root of exposed time, 32 materials and moisture content, diffusion coefficients of, 42 moisture accommodation at interfaces, 35–36

Subject Index moisture diffusion in package and in bulk EMC, 33–35 moisture uptake curve of package in bulk EMC, 33 non-Fickian behavior, effect of sorption conditions on, 39 non-Fickian dual-stage moisture diffusion, 37–41 one-dimensional Fickian diffusion in plate, 37 types of plastic packages for study of, 31 Moisture diffusion modeling, 472 of IC packages, 222–225 See also Integrated circuit (IC) packages Moisture-induced delamination integrated analysis of, 455–457 Moisture-induced failures, encapsulated IC devices, 279–283 See also Encapsulated IC devices, continuum theory Moisture/reflow sensitivity tests, 2, 92, 435, 446, 465 Moisture-related failure modes in packages, 413 Moisture-related reliability, 411 Moisture-related structural similarity rules carrier description, 419–420 finite element modeling, 421–422 material characterization, 420–421 reliability testing, 419 results, 422–424 Moisture-sensitive plastic packages of IC devices, 245–247, 270–271 analysis, 247–250, 268 boundary conditions, 250–251 constitutive equations, 247–250 elongated package, 257–267 initial curvature and initial stresses, 253–256 stresses, 251–252 von Mises stress, 267 data calculation, 270 Moisture sensitivity level (MSL), 437, 456 assessment, 411–412 C-SAM images, 412 JEDEC standards, 411 package type, 421 substrate-based packages, 421 tests, flowchart of, 393 Moisture sensitivity level (MSL) of plastic-encapsulated packages, 359–362 experimental data and analysis, 369–369

Subject Index adhesion and moisture absorption correlation, 371–374 moisture absorption, 370–371 mold cap thickness effect, 379 mold compound compaction effect, 379–385 pull tab adhesion data, 369–362 second series, 375–378 experimental procedures and setup D2 Pak package report, 368 moisture absorption samples, 367 moisture sensitivity testing, 367 mold compound chemistry, 363 QFN package report, 367 tensile pull sample report, 366–367 Moisture sensitivity/reflow tests, 411 Moisture sensitivity test (MST), 315, 434, 450 classifications, 334–337 for flux residue effect, 448–449 importance, 333 for molded packages, 450 objective, 279 of underfill, 447 for voids effect, 451 X-ray images of, 447 Moisture weight gain measurement, 5 curves, 440 data, 441 dry weight, measurement of, 6 Fickian fit for moisture uptake for underfill sample, 6 least-squares fitting technique, use of, 6 moisture absorption–desorption experiment for thin BT core, 6–7 moisture absorption for molding compound, 8–9 moisture diffusion, reduction in rate of, 8 moisture weight gain curve for thick BT core, 8 non-Fickian effect, consideration for, 9–10 specimen geometries and humidity conditions, 5 test, 400 two-stage moisture absorption process, 8 two-stage sorption, features of, 9 Mold cap thickness and QFN packages, 379 Mold compound compaction, effect, 379–385 See also Moisture sensitivity level (MSL) of plastic-encapsulated packages 3D Molded leadless package model, 483 Molded packages failure analysis, 451 Molding compounds, 391

565 behaviors, 414–415 leadframe, interfacial strength of, 392 moisture absorption of, 400 moisture concentration, 417 principal stress, 430 prony coefficients, 416 relaxation times, 416 Molecular dynamics simulation, 524 Monte Carlo method, 525 MSL, see Moisture sensitivity level (MCL) MTTF, see Mean time to failure Multi-functional micro-moir´e interferometry (M3 I) system, 135, 138 Multiple damage zone mechanism, definition, 306 See also Integrated circuit (IC) packages N Nernst distribution law, 182 Neutron reflectivity, 532 Non-Fickian diffusion, 38–40 Normalized concentration, 188 Novalac A and B, molding compound diffusivity, 338 O Organosilicate glass (OSG), 64 Over-saturation, 12, 104 P Package body fractures, 427 CAD model information interface, 486 cracking, types, 305 families, optimization technique, 424 materials, moisture properties of, 526 model information interface, 486 for equivalent thermal stress, 489 popcorning testing, stages, 278–295 reliability, moisture affects, 426 stress estimation, integrated stress modeling, 173–177 See also Integrated circuit (IC) packages Pad-to-body ratio, 423 Palladium pre-plated lead-frame, 391 Partially porous adhesive (PPA), 307 PBGA, see Plastic ball grid array (PBGA) package PCT, see Pressure cooker test (PCT) Peak package body temperature, determination, 335 See also IPC/JEDEC industry standard J-STD-020D, joint Permeability of polymer, 182

566 Phenolic novolac (PN), 30 Photomechanics measurement techniques digital image correlation (DIC), 136–137 moir´e interferometry, 115 Physical Electronics 670A Scanning Auger Nanoprobe, usage, 366 PI/UF interface, 444 adhesion strength, 444 delamination, 446 pull strength, 444 shear strength moisture effect, 444 Plasma grafting, 448 shear test, failure surface image, 392 and surface roughness, 438 Plastic ball grid array (PBGA) package, 92, 304–305, 315–316 Plastic dilatancy, in IC packages, 317–319 extended damage zone formation, 321–323 void growth and coalescence, 319–321 See also Integrated circuit (IC) packages Plastic encapsulated microcircuits (PEMs), 29 disadvantage of, 29, 113 hygroscopic swelling behavior of, study of (see Moir´e interferometry) See also Epoxy molding compounds (EMCs) Plastic-encapsulated packages, MSL, 359–362 experimental data and analysis, 369–385 adhesion and moisture absorption correlation, 371–374 moisture absorption, 371–374 mold cap thickness effect, 379 mold compound compaction effect, 379–384 pull tab adhesion data, 369–370 second series, 378–379 experimental procedures and setup D2 Pak package report, 368 moisture absorption samples, 367 moisture sensitivity testing, 367 mold compound chemistry, 363–366 QFN package report, 367–368 tensile pull sample report, 364 Plasticity theory, 283 See also Encapsulated IC devices, continuum theory Plastic packages, of IC devices, 279–283 See also Integrated circuit (IC) devices, moisture-sensitive plastic packages Poisson’s ratio, 483

Subject Index Polyimide passivation, 438 Polyimide surface, 438 Polymer bi-material strip, hygro-thermomechanical behavior bi-material specimen, 203–205 experimental procedure, 205 FE model, validation of, 206–207 simulation procedure, 205–206 temperature-induced deformation, 206 thermal contraction and moisture-induced swelling, combined effects of, 207 Polymeric insulator materials, 509 Polymeric materials in electronic packaging effect of fillers, 23–24 fracture toughness/adhesion strength moisture effect die shear test, 19–21 fracture toughness measurement, 17–19 moisture diffusion duration local moisture concentration, 24 one-dimensional moisture diffusion problem, 24 temperature change, 25 types of boundary conditions, 24 moisture in polymers, state of, 21–22 swelling behaviors of, 16–17 total moisture and volume change due to hygroscopic swelling, 22–23 Polymeric seals, 193 Polymer/substrate interface, 533 Polymer volume, 13 Popcorn cracking phenomenon, 359 See also Moisture sensitivity level (MSL) of plastic-encapsulated packages Popcorn failure, 1, 132 Pore size distribution, 14 Positron annihilation lifetime spectroscopy (PALS), 15 Post-curing process, 390 Post-mold cure (PMC), 359, 366–367, 377 PPF leadframe, see Palladium pre-plated leadframe Pressure cooker test (PCT), 2, 221 integrated stress modeling hygro-mechanical stress, 239–240 modeling methods, 237–238 moisture diffusion, 182–183 and thermo-mechanical stress, 240–241 Pressure-sensitivity index, determination, 325 See also Integrated circuit (IC) packages Printed circuit board (PCB), 1, 245, 280, 508

Subject Index Prony series, parameters of, 204 Pull/die shear tests, 441 Pull tab fabrication process, 364 See also Moisture sensitivity level (MSL) of plastic-encapsulated packages Pull test sample configurations, 442 setup, 443 shear test, 444 Q Quad flat non-lead (QFN) packages, 222, 279 compound crack, response surface, 432 daughter die crack, response surface, 432 features, 389 FE models of, 421–422 finite element model, 347–350, 394 hygro-mechanical stress analysis, 398–402 hygrothermal delamination, 389 integrated stress analysis, 402–407 interfacial strength, mechanical tests for, 391–393 manufacturing process of, 390 moisture sensitivity tests, 393 and mold cap thickness, 379 (see also Moisture sensitivity level (MSL) of plastic-encapsulated packages) report, 366 schematic of, 391 Si spacer, warpage of, 429 stacking concepts, 429 strength ratio, 373 thermo-mechanical stress analysis, 394–398 two-dimensional half model of, 394 See also Moisture sensitivity level (MSL) of plastic-encapsulated packages Quad flat package (QFP), 279, 419 Qualification program, 419 Quantum mechanics, 524 R Reflow process, 470 profile, 463 setting, 466 text matrix, effect, 463 types, 2 Relative humidity (RH), 6, 529 Representative elementary volume (REV), 106, 293 Representative volume element (RVE), 227 RSM models, 422 Rubbery material, 476

567 S SAM inspections, 398, 404 of Package 1, 406 of Package 2, 406, 407 SAM images, 412 SAT, see Scanning acoustic tomography Saturated moisture concentration, 10, 182, 451, 465 content of, 12 DCA approach, 12 effect, 341 as function of temperature, 11 for die-attach film, 12 glass transition temperature and, 11 Henry’s law, 10 over-saturation phenomenon, 12 at reflow soldering temperatures, 12 and relative humidity and absolute temperature, 10 linear relationship between, 121 Scanning acoustic microscopy, role, 376 See also Moisture sensitivity level (MSL) of plastic-encapsulated packages Scanning acoustic tomography, 60, 376 Semiconductor and MEMS packages, moisture-induced deformations in, 181 Shear force, 544 Shear stress in molding compound, 404 Shear tests failure modes of, 392 sample configurations, 442 Shift function, 204 Short-circuit, 518, 520 Shrink small outline packages (SSOPs), 389 Silicon die fractures, 427 Silicon-spacer concept, 426–427 interface stress plot, 430 moisture concentration, 440 stress response, 432 Silicon/underfill/FR-4-sandwiched assemblies, 137 SI/MC interface, 449 Single-die stacking, 468 SM/UF interface, 446 SM/UF shear strength moisture effect, 445 Soft die-attach film microstructures, 15 Software development kit, 483

568 Solder mask, 442 thicknesses of, 472–475 and underfill, 451 Solder resist, 472 material properties, 352 Solubility, 93–96 product constant, 506 SSOPs, see Shrink small outline packages (SSOPs) Stacked-die chip-scale package (SDCSP) 3D applications, die-attach films selection development of, 461 evaluation of, 468–470 material properties of, 464–466, 495 moisture/reflow sensitivity tests, 455–457 reflow process, vapor pressure, 475–476 3D ultrathin, schematic structure, 472 materials properties, simulation of, 464 reflow profiles effect of, 466–467, 475–477 setting, 466 substrate design, 463 effect of, 467–468 substrate thickness, effect of, 472–475 test vehicle descriptions, 462 TSAM images of, 466 Stitch bond predicted forces, 417 Strain energy release rate (SERR), 61 Stress distribution, 429 Stress intensity factors (SIFs), 133–134 Subsequent thermo-mechanical moisture simulations, 413 Substrate-based BGA packages, 412 Substrate design, 463 failure rate comparison, 468 Substrate design, view, 467–468 Substrate thickness effect, 472 Superposition method, 16, 143, 173 Surface acoustic tomography, 362, 369 Surface mount devices (SMDs), 333 Surface mount process, 1 Surface-mount (SM), 279 Swelling-induced strains by using superposition method, 16 System-in-packages, 424 moisture sensitivity of carrier description, 426 finite element modeling, 427–428 microelectronics, 424 results, 428–433 silicon-spacer technology, 426

Subject Index T Temperature cycling (TMCL), 412 Temperature, humidity, bias (THB) test, 2 Temperature/humidity (TH) test, 2 Test vehicle configurations, 462 THB test, see Temperature, humidity, bias (THB) test Thermal aging test, 138 Thermal analysis material properties for, 395 Thermal and hygroscopic nonlinear stress analysis, 174 bump region structure and local finite element mesh patterns, 175 ILD/UBM opening failure, 176 maximum normal and shear stress at UBM/ILD region, 176 modeling approach, 175 moir´e measurement and finite element analysis, comparison between, 175 moisture diffusion and package deformation history during HAST, 175 multi-step temperature/humidity loading profile, 174 Thermal coefficient of expansion, 491 Thermal gravimetric analyzer (TGA), 43, 55, 73, 154 Thermal mechanical analyzer (TMA), 55, 154 Thermal mismatch strain, 123 Thermal modeling, of IC packages, 225–226 See also Integrated circuit (IC) packages Thermal–moisture analogy, 30, 95–96, 187–188 and multi-material problems advanced analogy, 189–191 interfacial discontinuity, 188–189 normalized analogy, 189 validation of analogies, 196–197 and single material problems, 187 Thermal stresses, 390 analysis, 395 molded packages, 450–451 for not-molded packages, 453–455 Thermo-gravimetric analyzer (TGA), 230 Thermo-hygroscopic stress analysis, modeling hierarchy for, 198 Thermo-mechanical analyzer (TMA), 230 Thermo-mechanical material properties, 428, 497–498 Thermo-mechanical modeling, of IC packages, 232 See also Integrated circuit (IC) packages

Subject Index Thermo-mechanical simulations characteristics of, 416 Thermo-mechanical stress, 394 distribution, 396 material properties, 395 Thin BT core, moisture absorption–desorption behavior of change in sample weight, 74 diffusion equation for thin samples, 74 experiment on, 73 and comparison with literature data, 82–83 instrumentation used, 76 material used, 75 moisture diffusivity, 77–78 saturated moisture content, 78–80 temperature dependence of diffusivity, 81 initial and boundary conditions, 74 saturated moisture concentration in material, 79 temperature dependence of diffusion constant, 67 traditional measuring techniques, errors in, 73 Thin leadframe-based packages, 423 Thin small outline packages (TSOPs), 265 Through-scanning acoustic microscope (TSAM), 351 Time-zero failure analysis, 465 TMCL, see Temperature cycling (TMCL) Traction–separation law, 302 Two-stage or dual-uptake diffusion, 5 Two-stage sorption theory, 26 U UF/PI interface, 448 Ultrathin stacked chip scale packages (UT SCSP), 83 moisture diffusion and vapor pressure modeling for failure rate of DA film, 83 impact of substrate thickness on failure rate, study of, 83 moisture diffusivity of BT core materials, and FEA evaluations, 81 moisture preconditioning and reflow process, 84 residual moisture sensitivity to substrate thickness, 85 role of diffusivity in thin substrate, 81 use of DA films, 83 UT SCSP, structure of, 83

569 vapor pressure in DA film for diffusivities data, 87 technology, 83 Under bump metallurgy, 435 Under-bump metallurgy (UBM), 175 V van der Waals forces, 531 Vapor-induced swelling, 491 Vapor pressure distribution, comparison of, 498 evolution in bottom layer film, 466 induced deformation stress, comparison of, 504 induced expansion, 453 induced stress, 494 model, 108 analysis during reflow process for bi-material model, 108–109 FCBGA package, application to, 109 numerical data, 107–108 PBGA package, application to, 110 theory, 106–107 modeling finite element analysis, 479 IC packages, 221–222 models, 484 reflows, 495 scenarios of, 489 schematic diagram, 471 substrates, 476 Verlet algorithm, 528 Virtual crack closure (VCC), 235 virtual crack closure technique (VCCT), 61 Virtual prototyping techniques, 419, 421 Virtual saturation, 118 Void behavior, in interface, 287–289 See also Encapsulated IC devices, continuum theory Void density, effect, 382–384 See also Moisture sensitivity level (MSL) of plastic-encapsulated packages Void formation, 439 Void volume fraction, classification, 284 See also Encapsulated IC devices, continuum theory von Mises stress, 500 calculation, 265 definition, 294 See also Integrated circuit (IC) devices, moisture-sensitive plastic packages

570 W Wafer-level films, 461 die-attach film, 477 selection text matrix, 464 Washburn’s equation, 14 Water drop tests, 510 Water forming reduction of, 504 Water molecules mean-squared displacement of, 528 in polymeric materials type I or type II bonding, 21 Water sorption and moisture sorption, 12 effect of hydrophobic membrane on, 13 for hydrophobic coating film, 14 surface diffusion mechanism, 13

Subject Index Wetness, 97, 190 distribution, 401 Wet weight, 122 Wizard System, 486 interface, 483 WLFs, see Wafer-level films X XPS analysis, 438 on grafted PI surface, 439 spectrum in O1s region, 543 X-ray photoelectron spectroscopy, 541 Y Young’s modulus, 464, 468, 525 of DA1 film, 464 of die-attach films, 464 role in IC devices, 265–266