Reactive Sputter Deposition (Springer Series in Materials Science)

Springer Series in materials science 109 Springer Series in materials science Editors: R. Hull R. M. Osgood, Jr. ...

Author: Diederik Depla

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Springer Series in

materials science

109

Springer Series in

materials science Editors: R. Hull

R. M. Osgood, Jr.

J. Parisi

H. Warlimont

The Springer Series in Materials Science covers the complete spectrum of materials physics, including fundamental principles, physical properties, materials theory and design. Recognizing the increasing importance of materials science in future device technologies, the book titles in this series ref lect the state-of-the-art in understanding and controlling the structure and properties of all important classes of materials. 99 Self-Organized Morphology in Nanostructured Materials Editors: K. Al-Shamery and J. Parisi

105 Dilute III-V Nitride Semiconductors and Material Systems Physics and Technology Editor: A. Erol

100 Self Healing Materials An Alternative Approach to 20 Centuries of Materials Science Editor: S. van der Zwaag

106 Into The Nano Era Moore’s Law Beyond Planar Silicon CMOS Editor: H.R. Huff

101 New Organic Nanostructures for Next Generation Devices Editors: K. Al-Shamery, H.-G. Rubahn, and H. Sitter

107 Organic Semiconductors in Sensor Applications Editors: D.A. Bernards, R.M. Ownes, and G.G. Malliaras

102 Photonic Crystal Fibers Properties and Applications By F. Poli, A. Cucinotta, and S. Selleri

108 Evolution of Thin-Film Morphology Modeling and Simulations By M. Pelliccione and T.-M. Lu

103 Polarons in Advanced Materials Editor: A.S. Alexandrov 104 Transparent Conductive Zinc Oxide Basics and Applications in Thin Film Solar Cells Editors: K. Ellmer, A. Klein, and B. Rech

109 Reactive Sputter Deposition Editors: D. Depla amd S. Mahieu 110 The Physics of Organic Superconductors and Conductors Editor: A. Lebed

Volumes 50–98 are listed at the end of the book.

D. Depla

S. Mahieu

Editors

Reactive Sputter Deposition With 341 Figures

123

Professor Dr. Diederik Depla Dr. Stijn Mahieu Gent University, Department of Solid-State Sciences 281-S1 Krijgslaan, 9000 Gent, Belgium E-mail: [email protected], [email protected]

Series Editors:

Professor Robert Hull

Professor Jürgen Parisi

University of Virginia Dept. of Materials Science and Engineering Thornton Hall Charlottesville, VA 22903-2442, USA

Universit¨at Oldenburg, Fachbereich Physik Abt. Energie- und Halbleiterforschung Carl-von-Ossietzky-Strasse 9–11 26129 Oldenburg, Germany

Professor R. M. Osgood, Jr.

Professor Hans Warlimont

Microelectronics Science Laboratory Department of Electrical Engineering Columbia University Seeley W. Mudd Building New York, NY 10027, USA

Institut f¨ur Festk¨orperund Werkstofforschung, Helmholtzstrasse 20 01069 Dresden, Germany

ISSN 0933-033X ISBN 978-3-540-76662-9 Springer Berlin Heidelberg New York Library of Congress Control Number: 2007938637 All rights reserved. No part of this book may be reproduced in any form, by photostat, microfilm, retrieval system, or any other means, without the written permission of Kodansha Ltd. (except in the case of brief quotation for criticism or review.) This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specif ically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microf ilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media. springer.com © Springer-Verlag Berlin Heidelberg 2008 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specif ic statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Data prepared by SPi using a Springer LATEX macro package Cover concept: eStudio Calamar Steinen Cover production: WMX Design GmbH, Heidelberg Printed on acid-free paper

SPIN: 12067657

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543210

Preface

The most straightforward method to change the surface properties of a material is to deposit a thin ﬁlm or coating on it. Hence, it is not surprising that an overwhelming amount of scientiﬁc and technical papers is published each year on this topic. Sputter deposition is one of the many so-called physical vapour deposition (PVD) techniques. In most cases, sputter deposition uses a magnetically enhanced glow discharge or magnetron discharge to produce the ions which bombard and sputter the cathode material. In the ﬁrst chapter of this book (Chap. 1), the details of the sputter process are discussed. Essential to sustain the discharge is the electron emission during ion bombardment. Indeed, the emitted electrons are accelerated from the target and can ionize gas atoms. The formed ions bombard again the target completing the sustaining process. A complete chapter is assigned to this process to highlight its importance (Chap. 2). Although the sustaining process can be described quite straightforward, a complete understanding of the magnetron discharge and the inﬂuence of diﬀerent parameters on the discharge characteristics is only possible by modelling (see Chap. 3). With these three chapters, the reader should be able to form an idea of the target and plasma processes occurring during a DC magnetron discharge. When a reactive gas is added to the discharge, it becomes possible to deposit compound materials. This process is called reactive sputter deposition. The changes of the deposition process as a function of the reactive gas addition are discussed in Chaps. 4 and 5. The former (Chap. 4) describes the well-known “Berg” model, which enables a better understanding of the general aspects of reactive magnetron sputtering. The next chapter (Chap. 5) summarizes several experimental results and shows the need to more detailed models to describe the reactive sputtering process. One of the major problems of the reactive sputter process is its complexity and several fundamental aspects of the process have not been elucidated yet. Only by understanding all its details, it is possible to understand the properties of the obtained thin ﬁlm as a function of the deposition conditions. In this respect, it is necessary to describe the deposition ﬂux towards

VI

Preface

the substrate. This can be achieved by modelling the transport of sputtered particles towards the substrate (Chap. 6). However, not only the metallic ﬂux but also the energy ﬂux towards the substrate is important. This latter forms the subject of the following chapter (Chap. 7). More details of the reactive magnetron sputter process can be achieved by a good knowledge of the available plasma diagnostic tools. Hence, they form the content of the next two chapters (Chaps. 8 and Chap. 9). A nice illustration of the implementation of these tools is shown in the Chap. 10 which demonstrates their use in the study of the cross-corner and cross-magnetron eﬀect (Chap. 10). Finally, the book ends with some interesting examples of materials deposited with reactive sputter deposition. Indeed, complex materials such as solid electrolytes (Chap. 11), complex oxides (Chap. 12) and electrochromic thin ﬁlms (Chap. 13). In the last chapter, the reader can learn more about the simulation of the growth of thin ﬁlm deposited by magnetron sputtering (Chap. 14). Although the technique is easy to use, it conceals enough challenges to remain scientiﬁc interesting. This explains its popularity in the academic world. Also in the industrial world, reactive magnetron sputtering remains an interesting and often used technique, due to its ﬂexibility and scalability and has gained in this way a strong position for large-area deposition of thin ﬁlms. As for most thin ﬁlm deposition techniques, sputter deposition was once considered a black art and only in the last two decades, there has been a vast increase in the range of material types which can be deposited, the complexity of thin ﬁlms which are possible, the ability to deposit precisely controlled heterostructures and the reproducibility of ﬁlm deposition. The origin of this change is the trend to analyse in more detail all relevant processes during the thin ﬁlm deposition to maximize the level of control. This forms exactly the goal of this book, i.e. to give the reader on overview of the important processes during sputter deposition and of the aim to describe them by modelling and to use them to deposit complex materials such as perovskite, solid electrolytes and electrochromic thin ﬁlms. A good understanding of the reactive sputtering process is essential when tailoring the thin ﬁlm properties. This reasoning formed also the guideline for the table of content which mimics a virtual journey from target towards substrate. Together with the authors, we hope that the diﬀerent topics discussed in the book will help the novice and experienced scientist to solve some of the problems encountered during the use of this interesting deposition technique. Gent, January 2008

Diederik Depla Stijn Mahieu www.draft.ugent.be

Contents

1 Simulation of the Sputtering Process T. Ono, T. Kenmotsu, and T. Muramoto . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Computer Simulation Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Total Sputtering Yield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.1 Incident-Energy Dependence of Sputtering Yield . . . . . . . . . . 1.3.2 Incident-Angle Dependence of Sputtering Yield . . . . . . . . . . . 1.4 Diﬀerential Sputtering Yield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.1 Energy Spectrum of Sputtered Atoms . . . . . . . . . . . . . . . . . . . . 1.4.2 Angular Distribution of Sputtered Atoms . . . . . . . . . . . . . . . . . 1.5 Sputtering from Rough Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6 Sputtering of Compound Targets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Electron Emission from Surfaces Induced by Slow Ions and Atoms R.A. Baragiola and P. Riccardi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Physical Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Excitation Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Separation of PEE and KEE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Electron Transport and Escape into Vacuum . . . . . . . . . . . . . . 2.3 Electron Yields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Dependence of the Electron Yields on Ion Velocity . . . . . . . . . 2.3.2 Electron Energy and Angular Distributions . . . . . . . . . . . . . . . 2.3.3 Electron Emission from Contaminant Surface Layers . . . . . . . 2.4 The Role of Ion-Induced Electron Emission in Glow Discharges . . . 2.4.1 Eﬀect of Electron Recapture at the Cathode . . . . . . . . . . . . . . 2.4.2 Eﬀect of Changes in the Chemical Composition of the Cathode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 2 5 5 9 16 16 21 28 30 37 39

43 43 44 44 46 46 46 47 48 48 50 53 56

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2.5 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3 Modeling of the Magnetron Discharge A. Bogaerts, I. Kolev, and G. Buyle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.1.1 The Magnetic Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.1.2 The Magnetron Discharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.1.3 The Particle–Target Interaction . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.1.4 Particle Transport in the Gas Phase . . . . . . . . . . . . . . . . . . . . . 64 3.1.5 Film Growth on the Substrate . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.2 Overview of Diﬀerent Modeling Approaches for Magnetron Discharges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.2.1 Analytical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.2.2 Fluid Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 3.2.3 The Boltzmann Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 3.2.4 Monte Carlo Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3.2.5 Hybrid Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.2.6 PIC-MCC Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.3 Challenges Related to Magnetron Modeling . . . . . . . . . . . . . . . . . . . . . 74 3.3.1 Secondary Electron Emission Yield (γ) . . . . . . . . . . . . . . . . . . . 75 3.3.2 Recapture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 3.3.3 Electron Mobility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 3.3.4 Modeling “Industrially Relevant” Magnetron Discharges . . . . 76 3.4 Two-Dimensional Semi-Analytical Model for a DC Planar Magnetron Discharge . . . . . . . . . . . . . . . . . . . . . . . . . 78 3.4.1 Description of the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 3.4.2 Examples of Calculation Results . . . . . . . . . . . . . . . . . . . . . . . . 81 3.5 PIC-MCC Model for a DC Planar Magnetron Discharge . . . . . . . . . 83 3.5.1 Particle-In-Cell Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 3.5.2 Monte Carlo Collision Method . . . . . . . . . . . . . . . . . . . . . . . . . . 95 3.5.3 Methods for Speeding Up the Calculations . . . . . . . . . . . . . . . . 99 3.5.4 Examples of Calculation Results . . . . . . . . . . . . . . . . . . . . . . . . 103 3.6 Extension of the PIC-MCC Model: To Include Sputtering and Gas Heating . . . . . . . . . . . . . . . . . . . . . . . . 115 3.6.1 Description of the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 3.6.2 Examples of Calculation Results . . . . . . . . . . . . . . . . . . . . . . . . 119 3.7 Conclusions and Outlook for Future Work . . . . . . . . . . . . . . . . . . . . . . 123 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 4 Modelling of Reactive Sputtering Processes S. Berg, T. Nyberg, and T. Kubart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 4.2 Basic Model for the Reactive Sputtering Process . . . . . . . . . . . . . . . . 133 4.3 Steady State Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

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4.4

Inﬂuence of Material Properties and Processing Conditions . . . . . . . 141 4.4.1 Reactivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 4.4.2 Sputtering Yield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 4.4.3 Pumping Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 4.4.4 Target Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 4.4.5 Mixed Targets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 4.4.6 Two Reactive Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 4.4.7 Reactive Co-Sputtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 4.4.8 Comment on Pulsed DC Reactive Sputtering . . . . . . . . . . . . . 150 4.4.9 Secondary Electron Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 4.4.10 Ion Implantation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 4.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 5 Depositing Aluminium Oxide: A Case Study of Reactive Magnetron Sputtering D. Depla, S. Mahieu, and R. De Gryse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 5.2 Some Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 5.2.1 A First Series of Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 5.2.2 A Second Series of Experiments: Oxygen Exposure and Plasma Oxidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 5.2.3 Stability Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 5.2.4 First Conclusions Based on the Experiments . . . . . . . . . . . . . . 166 5.3 An Extended Model for Reactive Magnetron Sputtering . . . . . . . . . . 167 5.3.1 The Description of Reactive Ion Implantation During Sputtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 5.3.2 The Inﬂuence of Chemisorption and Knock-On Eﬀects . . . . . 171 5.3.3 Calculation of the Reactive Gas Partial Pressure as a Function of the Reactive Gas Flow . . . . . . . . . . . . . . . . . . 173 5.4 Confrontation Between Experiment and Model . . . . . . . . . . . . . . . . . . 175 5.4.1 Simultaneous Reactive Ion Implantation and Sputtering Without Chemical Reaction . . . . . . . . . . . . . . . 175 5.4.2 Simultaneous Reactive Ion Implantation and Sputtering with Chemical Reaction . . . . . . . . . . . . . . . . . . 176 5.5 Towards a More Complete Model for Reactive Magnetron Sputtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 5.5.1 Plasma-Related Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 5.5.2 Deposition Proﬁles and Erosion Proﬁles . . . . . . . . . . . . . . . . . . 187 5.5.3 Rotating Magnetrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 5.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

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6 Transport of Sputtered Particles Through the Gas Phase S. Mahieu, K. Van Aeken, and D. Depla . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 6.2 Radial Distribution Where Sputtered Particles Leave the Target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 6.3 Energy and Angular Distribution of Sputtered Particles Leaving the Target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 6.3.1 Sigmund–Thompson Theory for the Linear Cascade Regime . . . . . . . . . . . . . . . . . . . . . . . . . . 201 6.3.2 Other Analytical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 6.3.3 Comparison to Experimental Results . . . . . . . . . . . . . . . . . . . . . 206 6.3.4 Numerical Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 6.3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 6.4 Describing the Collision with the Gas Particle . . . . . . . . . . . . . . . . . . 208 6.4.1 The Mean Free Path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 6.4.2 The Scattering Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 6.4.3 The Interaction Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 6.5 Gas Rarefaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 6.6 Typical Results of a Binary Collision Monte Carlo Code . . . . . . . . . 218 6.7 Speciﬁc Example: In-Plane Alignment of Biaxially Aligned Thin Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 6.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 7 Energy Deposition at the Substrate in a Magnetron Sputtering System S.D. Ekpe and S.K. Dew . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 7.2 Energy Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 7.3 Factors Aﬀecting Energy Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 7.3.1 Magnetron Power and Pressure . . . . . . . . . . . . . . . . . . . . . . . . . 235 7.3.2 Substrate-Target Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 7.3.3 Electrical Eﬀects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 7.4 Total Energy per Deposited Atom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 7.5 Energy Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 7.5.1 Sputtered Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 7.5.2 Reﬂected Neutrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 7.5.3 Plasma Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 7.5.4 Charge Carriers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 7.5.5 Thermal Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244 7.5.6 Model Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 7.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251

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8 Process Diagnostics J.W. Bradley and T. Welzel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 8.2 Electrical Probes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 8.2.1 Probe Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 8.2.2 Use of Electrical Probes in Pulsed Reactive Sputtering . . . . . 258 8.3 Mass Spectrometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 8.3.1 Mass Spectrometry Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 8.3.2 Application of Mass Spectrometry to Reactive Sputtering . . 271 8.4 Optical Emission Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 8.4.1 Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 8.4.2 Plasma Emission Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 8.4.3 Time-Resolved OES in Pulsed Reactive Sputtering . . . . . . . . 288 8.5 Optical Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292 8.6 Laser-Induced Fluorescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 8.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 9 Optical Plasma Diagnostics During Reactive Magnetron Sputtering S. Konstantinidis, F. Gaboriau, M. Gaillard, M. Hecq, and A. Ricard . . . 301 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301 9.2 Emission Spectroscopy of Magnetron Plasmas . . . . . . . . . . . . . . . . . . . 302 9.3 Resonant Absorption Spectroscopy of Magnetron Plasmas . . . . . . . . 311 9.4 Laser Spectroscopy of Magnetron Plasmas . . . . . . . . . . . . . . . . . . . . . . 320 9.4.1 Previous Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 9.4.2 Principle and Achievements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 9.4.3 Application to Magnetron Discharges . . . . . . . . . . . . . . . . . . . . 326 9.5 Optical Diagnostic of High-Power Impulse Magnetron Sputtering Discharges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 9.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333 10 Reactive Magnetron Sputtering of Indium Tin Oxide Thin Films: The Cross-Corner and Cross-Magnetron Eﬀect H. Kupfer and F. Richter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337 10.2 The CCE and CME as an Inhomogeneous Target Erosion . . . . . . . . 338 10.3 Evidence of the CCE and CME From In Situ Measurements . . . . . . 346 10.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346 10.3.2 The CCE and the Plasma Properties of Unipolar-Pulsed Single Magnetron Discharges . . . . . . . . . . 349 10.3.3 The CME and the Plasma Properties of Bipolar-Pulsed Dual Magnetron Discharges . . . . . . . . . . . . . 350 10.3.4 The CME and the Thermal Load of the Substrates . . . . . . . . 353

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10.4 CCE, CME and Film Property Distribution: ITO as an Example . . 354 10.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354 10.4.2 Unipolar DC-Pulsed Single Magnetron: CCE and ITO Film Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356 10.4.3 Bipolar-Pulsed Dual Magnetron: CME and ITO Film Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358 10.5 CCE, CME and the Role of the Atomic Oxygen in the Process Gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 11 Reactively Sputter-Deposited Solid Electrolytes and Their Applications P. Briois, F. Lapostolle, and A. Billard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 11.2 Crystallographic Basis of the Solid Electrolyte . . . . . . . . . . . . . . . . . . 369 11.2.1 O2− Carriers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369 11.2.2 H + Carriers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374 11.2.3 N a+ Carriers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375 11.2.4 Li+ Carriers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 11.2.5 Mixed Conductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 11.3 Application of Solid Electrolytes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 11.3.1 Solid Oxide Fuel Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 11.3.2 Microbatteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392 11.3.3 Smart Windows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399 11.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 12 Reactive Sputtered Wide-Bandgap p-Type Semiconducting Spinel AB2 O4 and Delafossite ABO2 Thin Films for “Transparent Electronics” A.N. Banerjee and K.K. Chattopadhyay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413 12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413 12.2 Spinel and Delafossite Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414 12.2.1 Spinel Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414 12.2.2 Delafossite Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416 12.3 p-Type Transparent Conducting Oxides Based on Spinel and Delafossite Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417 12.3.1 Introduction to Transparent Conducting Oxides . . . . . . . . . . . 417 12.3.2 Transparent Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418 12.3.3 p-TCO with Spinel Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 420 12.3.4 p-TCO with Delafossite Structure . . . . . . . . . . . . . . . . . . . . . . . 422 12.3.5 Other Deposition Techniques: PLD, RF Sputter Deposition, Magnetron Sputtering with RTA, and Ion Exchange Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425 12.3.6 Reactive Sputtered p-TCO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432

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12.4 Transparent Junctions Based on Spinel and Delafossite Oxides . . . . 441 12.5 Origin of p-Type Conductivity in Wide-Bandgap Spinel and Delafossite Oxide Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448 12.6 Reactive DC Sputter Deposition of Delafossite p-CuAlO2+x Thin Film . . . . . . . . . . . . . . . . . . . . . . . . . . 455 12.6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455 12.6.2 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457 12.6.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458 12.7 Conclusions and Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473 12.7.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473 12.7.2 Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477 13 Oxide-Based Electrochromic Materials and Devices Prepared by Magnetron Sputtering C.G. Granqvist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485 13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485 13.2 Energy Eﬃciency of Chromogenic Building Skins . . . . . . . . . . . . . . . . 486 13.3 Electrochromic Device Design and Materials . . . . . . . . . . . . . . . . . . . . 487 13.4 Properties and Applications of Electrochromic Foil . . . . . . . . . . . . . . 490 13.5 Conclusion and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494 14 Atomic Assembly of Magnetoresistive Multilayers H. Wadley, X. Zhou, and W.H. Butler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497 14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497 14.1.1 Giant Magnetoresistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498 14.1.2 Atomic Scale Structure Eﬀects . . . . . . . . . . . . . . . . . . . . . . . . . . 501 14.1.3 Deposition and Growth Processes . . . . . . . . . . . . . . . . . . . . . . . 504 14.2 Atomistic Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505 14.2.1 Interatomic Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505 14.2.2 MD Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515 14.3 Growth of Metal Multilayers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517 14.4 Ion-Assisted Growth of Metal Multilayers . . . . . . . . . . . . . . . . . . . . . . 532 14.5 Dielectric Layer Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545 14.6 Ion-Assisted Reactive Growth of Dielectric Layers . . . . . . . . . . . . . . . 553 14.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 561

Contributors

Arghya N. Banerjee Nevada Nanotechnology Center Department Electrical Engineering and Computer Science University Nevada Las Vegas, NV 89154, USA banerjee [email protected]

Annemie Bogaerts Research Group PLASMANT Department of Chemistry University of Antwerp Universiteitsplein 1 2610 Wilrijk-Antwerp, Belgium [email protected]

Ra´ ul A. Baragiola Laboratory for Atomic and Surface Physics University of Virginia Engineering Physics Charlottesville, VA 22904, USA [email protected]

James W. Bradley Department of Electrical Engineering and Electronics The University of Liverpool Brownlow Hill Liverpool L69 3GJ, UK [email protected]

S¨ oren Berg The ˚ Angstr¨ om Laboratory Uppsala University Box 534 751 21 Uppsala, Sweden [email protected]

Pascal Briois Laboratoire d’Etudes et de recherches sur les Mat´eriaux les Proc´ed´es et les Surfaces (LERPMS-UTBM) Site de Montb´eliard 90010 Belfort cedex, France [email protected]

Alain Billard Laboratoire d’Etudes et de recherches sur les Mat´eriaux les Proc´ed´es et les Surfaces (LERPMS-UTBM) Site de Montb´eliard 90010 Belfort cedex, France [email protected]

William H. Butler Department of Physics and Astronomy University of Alabama Tuscaloosa, Alabama, USA [email protected]

XVI

Contributors

Guy Buyle Department of Solid State Sciences Gent University Krijgslaan 281/S1 9000 Gent, Belgium [email protected] Kalyan K. Chattopadhyay Thin Film and Nanoscience Laboratory Department of Physics Jadavpur University Jadavpur, Kolkata 700032, India kalyan [email protected] Roger De Gryse Gent University Department of Solid State Sciences Krijgslaan 281 (S1) 9000 Gent, Belgium [email protected]

F. Gaboriau Laplace, University of Paul Sabatier 118 route de Narbonne 31062 Toulouse, France [email protected] M. Gaillard CAPST, SungKyunKwan University 300 Chun-Chun-Dong Jangan-gu, Suwon 440-746, Korea [email protected] C.G. Granqvist Department of Engineering Sciences The ˚ Angstr¨ om Laboratory Uppsala University Box 534 75121 Uppsala, Sweden Claes-Goran.Granqvist@ Angstrom.uu.se

Diederik Depla Gent University Department of Solid State Sciences Krijgslaan 281 (S1) 9000 Gent, Belgium [email protected]

M. Hecq Laboratoire de Chimie Inorganique et Analytique Universit´e de Mons-Hainaut Avenue Copernic 1 7000 Mons, Belgium [email protected]

Steven K. Dew Department of Electrical and Computer Engineering University of Alberta Edmonton, Alberta T6G 2V4, Canada [email protected]

Takahiro Kenmotsu Department of Environmental Risk Management Kibi International University 8 Iga-cho, Takahashi-shi Okayama 716-8508, Japan [email protected]

Samuel D. Ekpe Department of Electrical and Computer Engineering University of Alberta Edmonton, Alberta T6G 2V4, Canada [email protected]

Ivan Kolev Research Group PLASMANT Department of Chemistry University of Antwerp Universiteitsplein 1 2610 Wilrijk-Antwerp, Belgium [email protected]

Contributors

Stephanos Konstantinidis Laboratoire de Chimie Inorganique et Analytique Universit´e de Mons-Hainaut Avenue Copernic 1 7000 Mons, Belgium Stephanos.Konstantinidis@ umh.ac.be Tomas Kubart The ˚ Angstr¨ om Laboratory Uppsala University Box 534 751 21 Uppsala, Sweden [email protected] H. Kupfer University of Technology Chemnitz Institute of Physics 09107 Chemnitz, Germany [email protected] Fr´ ed´ eric Lapostolle Laboratoire d’Etudes et de recherches sur les Mat´eriaux les Proc´ed´es et les Surfaces (LERPMS-UTBM) Site de Montb´eliard 90010 Belfort cedex, France [email protected] Stijn Mahieu Department of Solid State Sciences Gent University Krijgslaan 281 (S1) 9000 Gent, Belgium [email protected] Tetsuya Muramoto Department of Computer Simulation Okayama University of Science 1-1 Ridai-cho, Okayama 700-0005, Japan [email protected]

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Tomas Nyberg The ˚ Angstr¨ om Laboratory Uppsala University Box 534 751 21 Uppsala, Sweden [email protected] Tadayoshi Ono Department of Computer Simulation Okayama University of Science 1-1 Ridai-cho, Okayama 700-0005, Japan [email protected] A. Ricard Laplace, University of Paul Sabatier 118 route de Narbonne 31062 Toulouse, France [email protected] Pierfrancesco Riccardi Laboratorio IIS INFN gruppo collegato di Cosenza Dipartimento di Fisica Universit` a della Calabria 87036 Arcavacata di Rende (CS) Italy [email protected] F. Richter University of Technology Chemnitz Institute of Physics 09107 Chemnitz, Germany [email protected] .de Koen Van Aeken Department of Solid State Sciences Ghent University Krijgslaan 281/S1 9000 Ghent, Belgium [email protected] Haydn Wadley Department of Materials Science and Engineering University of Virginia Charlottesville, Virginia, USA [email protected]

XVIII Contributors

Thomas Welzel Chemnitz University of Technology Institute of Physics 09107 Chemnitz, Germany [email protected]

Xiaowang Zhou Department of Mechanics of Materials Sandia National Laboratories Livermore, California, USA [email protected]

1 Simulation of the Sputtering Process T. Ono, T. Kenmotsu, and T. Muramoto

1.1 Introduction In this chapter, we deal with sputtering of target materials bombarded with energetic particles. In this process, target atoms are removed from the surface by collisions between a projectile and/or recoil atoms produced and the atoms in the near-surface layers of the target material. Sputtering is utilized widely and positively as a useful technique to produce thin ﬁlms, to make trace impurity analyses of materials of all sorts (e.g., Secondary Ion Mass Spectroscopy), for surface treatment and surface processing, and also for a variety of many other technological applications. However, sputtering plays an undesired role in some cases, on the other hand. The ﬁrst wall and the divertor of a thermonuclear fusion device, for example, are eroded mainly by impinging plasma ions, which causes the core plasma to be contaminated if sputtered atoms enter it, resulting in insuﬃcient heating of fuel. Therefore, quantitative knowledge on sputtering is required to be determined accurately and compiled for these scientiﬁc researches or technological development. Computer simulations of sputtering have contributed greatly to such purposes and to elucidate the pertinent processes. In what follows, we give a quantitative account of and highlight the results obtained mainly by us from computer simulations of sputtering. In Sect. 1.2 we introduce our computer codes (Monte Carlo (MC) binary code, dynamical Monte Carlo code, and molecular dynamics (MD) code) used for sputtering calculations and the outlines of the codes necessary to discuss the results are described. Section 1.3 is concerned with incident-energy dependence and angular dependence of total sputtering yield. The sputtering mechanisms of a target material bombarded with heavy and light ions are outlined. Then, semiempirical formulae for energy dependence are compared with experimental and calculated data. The sputtering mechanism for light-ion bombardment from oblique incidence is mentioned in terms of the knockout process. New semi-empirical formulae to reproduce experimental and calculated data of

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T. Ono et al.

incident-angle dependence of total sputtering yield are introduced. We also present incident-angle dependence of tungsten self-sputtering yield calculated with our computer codes for very low incident energy. The large diﬀerence found at glancing angles of incidence between the MC and the MD data is accounted for using the contour maps of deposited energy density on the surface calculated in these simulations. Section 1.4 describes diﬀerential sputtering yields with respect to energy and ejection angle of sputtered atoms. In particular, we indicate that the energy spectrum of sputtered atoms from heavy target materials with low-energy light ions can be reproduced well by semi-empirical formulae proposed recently by us. The energy spectra of sputtered atoms calculated with the MC and the MD codes are compared with each other. The components of sputtered atoms with very low energy obtained with the MD are discussed. We present typical angular distributions of sputtered atoms obtained with experiments and calculations. The diﬀerence in the angular distributions for heavy- and light-ion irradiation is described. A new semi-empirical formula that can reproduce even the heart-shaped distribution corresponding to heavy- and moderately heavy ions with very low-energy bombardment is presented. In Sect. 1.5, we mention the eﬀect of surface roughness on sputtering with low- and high-energy ions. Low-energy ions incident on a rough surface is equivalent to randomizing incident angle, and sputtering with high-energy ions is aﬀected by the averaged low-density of a rough surface. Section 1.6 goes into sputtering of compound materials. Sputtering of multicomponent targets is complex compared with that of monoatomic targets. In sputtering of multicomponent targets, compositional change near a surface is unavoidable under ion bombardment and depends on target systems. Kinetic and thermal processes occurring in a material result in the compositional change. Ion-ﬂuence dependence of the compositional change for a Cu–Ni alloy was calculated with the dynamic Monte Carlo simulation code which includes both kinetic and thermal processes.

1.2 Computer Simulation Codes Comprehensive reviews on computer simulation codes used widely for sputtering have been done [1–4]. According to how atomic collisions occurring in a solid are modeled, these codes are classiﬁed basically into two groups, i.e., MC codes which treat atomic collisions with a MC method in a binary collision approximation (BCA), and classical MD codes which assume that incident projectiles collide with a system of many atoms involved and solve time evolutionally the classical dynamics of the system from knowledge of the interaction forces between particles. Generally, MC codes are suited for simulations in much larger space- and timescales than MD ones. However, as incident energy of ions reaches a low-energy range, e.g., around 100 eV,

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the eﬀective interactive region that a moving atom feels widens. Accordingly, BCA breaks down, and MD is required, instead. Since ACAT [5] code, ACAT-DIFFUSE [6] code, DYACAT [7], and a MD code [8] have been described in detail, we describe here only the main features of these codes necessary to discuss the results obtained with these codes. The ACAT and the TRIM.SP [2, 9] codes are of the MC type. While the TRIM.SP code pursues atomic collisions by using a mean free path like many other MC codes, the ACAT code assumes an amorphous target by employing the so-called “cell model,” i.e., an amorphous target is composed of simple cubic cells, in each of which the site of a target atom is chosen stochastically with a lattice constant λ = Ω 1/3 , where the atomic volume Ω = 1/N, N the number density of the target material, and the surface is atomically rough in scale of λ/2. Moreover, one can prepare desired surface roughness by adding more cells on the original surface, as indicated in Fig. 1.1. The DYACAT code is a dynamical version of the ACAT code. In this code, the binary collision events are arranged in order of time they occur. The code can consider collisions between two moving atoms as well as a non-Markov process, which is very important for polyatomic ion bombardment on a solid. The non-Markov process is a random process whose future probabilities are determined by its most recent and all the past values. In the code, the process corresponds with collisions between a moving atom and point defects produced from a simultaneously ongoing collision cascade. Since distant collisions become important in a low-energy range as mentioned above, the code considers many-body collisions among a moving atom and several target atoms located in an eﬀective interaction range by a limited-MD calculation. Therefore, the DYACAT code can be regarded as a MD code-like unique BCA code.

Fig. 1.1. Cell model of a rough surface employed in the ACAT code. Open circles stand for atoms located randomly in cubic cells

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Fig. 1.2. Schematic diagram of the work ﬂow of the ACAT-DIFFUSE routines

The ACAT-DIFFUSE code can calculate sputtering of an amorphous monoatomic and composite materials being irradiated by ions. The code is based on the ACAT code and the DIFFUSE [10] code and its basic concept is schematically shown in Fig. 1.2. The ACAT part of the code calculates the slowing-down processes of implanted projectiles and recoil atoms produced, together with the associated vacancy and range distributions. A large total dose Φ is divided into smaller dose increment ΔΦ during which the target composition is not varied appreciably by incident ions. The bunch of ions corresponding to ΔΦ is assumed to hit the target material simultaneously and to be slowed down instantaneously. Slowdown of ions, together with the associated vacancies and range distributions are calculated in the ACAT part. Mobile atoms, not trapped in trapping sites, diﬀuse during the time interval of ΔΦ/J (J being the ion ﬂux). The DIFFUSE part copes with the thermal processes of preimplanted and currently implanted ions and recoil atoms produced by solving the diﬀusion equations numerically. The two routines are iteratively repeated n times, where n = Φ/ΔΦ. As mentioned above, MD determines the dynamics of a system of many atoms by solving Newton’s laws of motion for each particle of the system. A well-known numerical calculation method is Verlet algorithm [11]. The most important factor in MD calculations is atomic interaction force. For a fewbody system, the force can be calculated by quantum dynamics. However, for a large-scale system, the force is described by semi-empirical many-body potentials in view of calculation speed. If a constrained MD simulation on

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temperature is required, the Langevin MD (LMD) method [12] may be employed to combine the system with an external heat bath. In sputtering MD simulations, since one can prepare only a ﬁnite target, energy dissipation to the external heat bath has to be considered using a LMD method. A large number of computer codes have been developed in the ﬁelds of ionimplantation and ion-surface interactions, as discussed partly in this chapter. For convenience, those codes widely used are categorized as to atomic process and type of atomic collisions occurring in solids they employ, as depicted in Table 1.1.

1.3 Total Sputtering Yield 1.3.1 Incident-Energy Dependence of Sputtering Yield A measure of the erosion due to ion irradiation is sputtering yield, which is deﬁned as a ratio of the number of sputtered atoms to the number of incident projectiles. A large amount of experimental and calculated data on incidentenergy dependence of sputtering yield of monoatomic and multicomponent solids for normal incidence have been produced and accumulated [13–19]. The sputtering mechanism can be classiﬁed into two categories as schematically indicated in Fig. 1.3. When relatively heavy ions hit a solid surface, they deposit their energy near the surface and a collision cascade develops, resulting in the ejection of target atoms from the surface (mechanism I) [20]. On the other hand, incoming light ions such as H+ and D+ can not produce a collision cascade near the surface because the energy they transfer to target atoms in collisions is not enough to generate a collision cascade. Instead, those ions are reﬂected from inside the target material and hit near-surface atoms, causing those recoil atoms to leave from the surface if they receive suﬃcient energy to overcome the surface barrier (mechanism II) [21–23]. As the mass of incident ions becomes lighter, the sputtering mechanism shifts gradually from mechanisms I to II. For ions with intermediate mass, such as Ar+ , both mechanisms I and II contribute to the actual total sputtering yield. Considering the above sputtering mechanism, Yamamura et al. [17] revised their old semi-empirical formulae [24, 25] by interpolating them to propose a new one (hereafter called Yamamura formula) for the energy dependence of sputtering yield Y (E) of monoatomic solids for normal incidence of projectiles, as given by s Q(Z2)α∗ (M2 /M1 ) Sn (E) Eth Y (E) = 0.042 1− , (1.1) Us 1 + Γ kε0.3 E where E is projectile energy and M1 , M2 are the masses of a projectile and a −2 target atom in a.m.u., respectively, and the numerical factor in units of ˚ A . The factor Γ has the form

Slowing Down Process Thermal Process Binary Collision Approximation Molecular Dynamics Local Mixing Simple MC Dynamical MC MDACOCT24 MD-TOPS26 Model ACAT1 ACOCT5 TRIDYN10 EVOLVE12 PARASOL25 SPUT2SI29 DIFFUSE16 2 6 11 27 28 TRIM MARLOWE T-DYN dynamicMODYSEM SPUT3 PIDAT17 TRIM.SP3 Crystal-TRIM7 SASAMAL13 MOLDYCASK30 QDYN32 SASAMAL4 COSIPO8 MOLDY31 REED33 IMSIL9 DYACAT14 DYACOCT15 ACAT-DIFFUSE19 ACAT-DIFFUSE-GAS20 EDDY23 TMAP418 TRIDYN+PIDAT21 TRIDYN+DIFFUSEDC+YCEHM22 (1) Y. Yamamura and Y. Mizuno, Research report of Institute of Plasma (19) Y. Yamamura, Nucl. Instr. Meth. B 28 (1987) 17. Physics, Nagoya University IPPJ-AM-40 (1985). (20) M. Ishida, Y. Yamaguchi and Y. Yamamura, Thin Solid Films 334 (2) J.P. Biersack and L.G. Haggmark, Nucl. Instr. Meth. 174 (1980) 257. (1998) 225. (3) J.P. Biersack and W. Eckstein, Appl. Phy. A34 (1984) 73. (21) W. Eckstein, V.I. Shulga, J. Roth, Nucl. Instr. Meth. B 153 (4) Y. Miyagawa and S. Miyagawa, J. Appl. Phys. 54 (1983) 7124. (1999) 415. (5) Y. Yamamura and W. Takeuchi, Nucl. Instrum. Methods B29 (22) K. Schmid and J. Roth, J. Nucl. Mater. 313–316 (2003) 302. (1987) 461. (23) K. Ohya and R. Kawakami, Jpn. J. Appl. Phys. 40 (2001) 5424. (6) M.T. Robinson and I.M. Torrens, Phys. Rev. B9 (1974) 5008. (24) K. Yorizane, T. Muramoto and Y. Yamamura, Nucl. Instr. Meth. (7) M. Posselt, Radiat. Eﬀ. Def. Solid. 130/131 (1994) 87. B153 (1999) 292. (8) M. Hautala, Phys. Rev. B30 (1984) 5010. (25) G. Betz, R. Kirchner, W. Husinsky, F. Rudenauer and H.M. (9) G. Hobler, H. Potzl, L. Gong and H. Ryssel, in: Simulation of Urbassek, Radiation Eﬀects and Defects in Solids 130/131 (1994) 251. Semicondoctor Devices and Process, eds. W. Fichtner and D. Aemmer, (26) Javier Dom´ınguez-V´ azquez, E. Pablo Andribet, A. Mari Carmen Vol. 4 (Hartung-Gorre, Konstanz, 1991) p.389. P´ erez-Mart´ın, Jos´ e J. Jim´ enez-Rodr´ıguez, Radiation Eﬀects and (10) W. M¨ oller and W. Eckstein, Nucl. Instr. Meth. B 2 (1984) 814. Defects in Solids 142 (1997) 115. (11) J.P. Biersack, S. Berg and C. Nender, Nucl. Instr. Meth. B59–60 (27) V. Konoplev and A. Gras-marti, Philosophical magazine A71 (1995) (1991) 21. 1265. (12) M.L. Roush, T.S. Andreadis and O.F. Goktepe, Radiat. Eﬀ. 55 (28) M.H. Shapiro and T.A. Tombrello, Nucl. Instr. Meth. B84 (1994) 453. (1981) 119. (29) M.H. Shapiro, T.A. Tombrello and D.E. Harrison, Jr., Nucl. Instr. (13) Y. Miyagawa, M. Ikeyama, K. Saitoh, G. Massouras, S. Miyagawa, Meth. B30 (1988) 152. J. Appl. Phys. 70 (1991) 7289. (30) T. Diaz de la Rubia and M.W. Guinan, J. Nucl. Mater. 174 (1990) (14) Y. Yamamura, Nucl. Instrum. Methods B33 (1988) 493. 151. (15) Y. Yamamura, I. Yamada and T. Takagi, Nucl. Instr. Meth. B37–38 (31) B.L. Holian, The MOLDY program is ﬁled in mass storage at the Los (1989) 902. Alamos National Laboratory (1975). (16) K.L. Wilson and M.I. Baskes, J. Nucl. Mater. 76/77 (1978) 291. (32) D.E. Harrison, Jr. and M.M. Jakas, Radiat. Eﬀ. 99 (1986) 153. (17) W. M¨ oller, Max-Plank-Institute f¨ ur Plasmaphysik, Report IPP (33) Jeong-Won Kang, E.S. Kang, M.S. Son, and H.J. Hwang, Journal 9/44 (1983). of Vacuum Science & Technology B18 (2000) 458–461. (18) G.R. Longhurst, D.F. Holland, J.L. Jones, B.J. Merrill, TMAP4 User’s Manual, EGG-FS-10315, Idaho National Engineering and Environmental Laboratory, 1992.

Table 1.1. Computer codes used in the ﬁelds of ion-implantation and ion-surface interactions

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Fig. 1.3. Schematic diagram of the sputtering mechanisms. The case (I) indicates the mechanism for relatively heavy-ion bombardment, and the (II) that for light-ion bombardment

Γ =

W (Z2 ) . 1 + (M1 /7)3

(1.2)

The surface binding energy of a target material Us , the best-ﬁt values of the dimensionless parameters W (Z2 ), Q(Z2 ), and s are tabulated in [17]. The best-ﬁt values of α∗ are described as a function of a mass ratio M2 /M1 in the following manner: 0.249(M2/M1 )0.56 + 0.0035(M2/M1 )1.5 , M1 ≤ M2 , ∗ (1.3) α = 0.0875(M2/M1 )−0.15 + 0.165(M2/M1 ), M1 ≥ M2 . Eth is sputtering threshold energy and is expressed by the following best-ﬁt functional relation 6.7 Eth , = Us γ 1 + 5.7(M1 /M2 ) , = γ

M1 ≥ M2 , M1 ≤ M2 ,

(1.4)

where γ is energy transfer factor in an elastic collision deﬁned as γ = 4M1 M2 /(M1 + M2 )2 . ke is the Lindhard electronic stopping coeﬃcient [26], and Sn is the nuclear stopping cross section expressed by Sn (E) =

84.78Z1Z2 M1 TF 1/2 M + M sn (ε), 2/3 2/3 1 2 Z1 + Z2

(1.5)

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2 in units of eV ˚ A per atom. Note that the numerical factor of 8.478 in (21) in Ref. [17] should be corrected to 84.78 as indicated in (1.5). ε is reduced LSS energy [26], and sTF n (ε) is reduced nuclear stopping cross section and is approximated by an analytic ﬁt to the Thomas–Fermi potential [13]. Yamamura formula was applied successfully to the cases of multicomponent target materials as described below. There are other semi-empirical expressions for Y (E), called the “Bohdansky formula” [27] and the “revised Bohdansky formula”, which were used to represent a large number of experimental and calculated data [14, 15, 28]. The discrepancy of the sputtering yields calculated with the TRIM.SP and the ACAT codes is generally small. The above-mentioned revised Bohdansky and Yamamura formulae can represent experimental results within the errors of better than 30% in many cases, but more than 50% in special cases such as H+ and D+ ions onto C for low E in which chemical erosion might take place [14]. The deviations are seen in some cases for incident energies of high keV and in the threshold energy region. Sputtering yield of Cu target materials by 5 keV Ar+ impact calculated with the ACAT and the MD codes is tabulated in Table 1.2. In this MD simulation, the Cu–Cu interactions are described by TB-SMA potential [29] and the Moliere potential [30] for an equilibrium range and a short range, respectively. The Ar–Cu interaction is calculated by the Lennard– Jones [31] and Moliere potentials which are smoothly connected in a similar manner to TB-SMA + Moliere potential. We use a local electronic energy loss model based on the Firsov model [32], which is corrected by the Lindhard– Scharﬀ formula [26]. In a microscopic view, a polycrystalline target looks like a randomly oriented crystal. Therefore, in this MD simulation, we used a random surface model to reproduce the sputtering of a polycrystalline target. In this model, the target crystal is produced by a set of primitive translation vectors, which is oriented randomly for each incidence. It is shown the current simulations could reproduce almost the experimental sputtering yield [33, 34] of polycrystalline and crystal Cu target materials. The energy dependence of sputtering yield for Ar+ ions incident on Cu obtained with experiments, MD calculations and Yamamura formula (1.1) are illustrated in Fig. 1.4. It is clear from the ﬁgure that the simulation results and the formula are in good agreement with the experimental values.

Table 1.2. Calculated and experimental sputtering yield for 5 keV Ar+ → Cu at θ = 0◦ Poly. Experiment ACAT MD a Reference [33] b Reference [34]

a

5 5.2 6.8

(111) 9b 9.6

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Fig. 1.4. Energy dependence of Ar+ ions incident on Cu obtained with experiments, ACAT and MD calculations and Yamamura formula (1.1)

Yamamura formula (1.1) can represent sputtering yield data of multicomponent materials by replacing Z2 , M2 , and Us in (1.1) withtheir average values such as Z2 = ci Z2,i , M2 = ci M2,i , and Us = ci Us,i where ci is the atomic fraction of ith element [35,36]. For threshold energy, however, the maximum value of {Eth,i } is chosen except for oxygen ion bombardment for which the threshold energy is a ﬁtting parameter, where Eth,i is the threshold energy of the monoatomic solid of ith element for the projectile. The experimental and calculated sputtering yields of oxide targets displayed in Fig. 1.5 are represented well by (1.1) with the above replacements. 1.3.2 Incident-Angle Dependence of Sputtering Yield A large quantity of experimental and calculated data on incident-angle dependence of sputtering yield of monoatomic and composite solids have been produced and accumulated [14, 18, 19, 37–43]. Generally, while the incident angle, measured from the surface normal, of ions is small, the yield increases with increasing incident angle because of a cascade developed more close to the surface; after passing the maximum, it decreases with increasing incident angle for large incident angles since the screening eﬀect of neighboring surface atoms begins to prevent incident ions

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Fig. 1.5. Energy dependence of sputtering yields of Si, Ta, SiO2 , and Ta2 O5 for argon and oxygen bombardment, where solid lines correspond to (1.1), and the experimental data of monoatomic solids are from [17] and those of oxide from [36]

from entering the surface; ﬁnally it decreases sharply since incident ions are almost all reﬂected without giving energy to the solid. Taking into account the probability that incident ions can enter the surface of a solid to add a corresponding factor to a formula given by Sigmund [20], Yamamura [43] proposed a semi-empirical formula for incident-angle dependence of sputtering yield expressed by Y (E, θ) = X f exp[−Σ(X − 1)], Y (E, 0)

(1.6)

where X = 1/ cos θ, and the term X f was proposed by Sigmund [20]. Y (E, θ) is sputtering yield for incident angle θ measured from the surface normal. Σ is a physical quantity that is proportional to scattering cross section, and f and Σ are ﬁtting parameters to be determined by adjusting the formula to experimental or calculated data. It was shown that (1.6) can generally reproduce well experimental and calculated data on the incident-angle dependence of sputtering yield with light ions [14, 43]. The validity of (1.6) was checked to indicate that it is acceptable for not-too-low energies, i.e., above 1 keV, though it is not correct for self-sputtering and for heavy projectiles with energies near the threshold energy [28]. However, the second conclusion seems to be not worth special mention, since heavy projectiles with such low energies can not fulﬁll the necessary condition for developing a genuine collision

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cascade near a solid surface that (1.6) assumes as a premise for heavy-ion bombardment [43]. To account for the binding energies of incoming ions, for example, selfbombardment, where large angles of incidence cannot be reached, (1.6) has been improved, resulting in a new formula expressed as c −f c

θ π θ π , exp b 1 − 1/ cos Y (E, θ) = Y (E, 0) cos θ0 2 θ0 2 (1.7) π 1 (1.8) θ0 = π − arccos ≥ , 1 + E/Esp 2 with the ﬁt parameters f, b, c [44]. Esp , the binding energy of a projectile, has to be provided. For self-bombardment, it is equal to the surface binding energy of target atoms; for noble gas projectiles Esp = 0; for hydrogen isotopes Esp = 1 eV is assumed. With the use of large datasets [18], new ﬁts threshold energies for diﬀerent ion-target combinations and for incident angle at several mass ratios are given [18]. The angular dependence of sputtering yield obtained with the experiment and (1.6) for 1 and 8 keV H+ incident on Ni is shown in Fig. 1.6a, and that for 30 eV W+ onto W from (1.6) and (1.7) in Fig. 1.6b [44, 45]. Modeling of surfaces is a very important factor for sputtering simulations. For oblique incidence, a collision cascade tends to be developed more closely to the surface. Thus, the surface-model dependence is expected to be clearly shown up for grazing incidence. Hence, we performed simulations of low-energy ion sputtering to examine it. Again, we make a comparison of incident-angle dependence of sputtering in a low energy range calculated with both ACAT and TRIM.SP codes. Figure 1.7 shows simulation results of the TRIM.SP and the ACAT codes. The TRIM.SP result for grazing incidence approaches a ﬁnite yield. To understand this feature, let us mention the surface treatment of the TRIM.SP code. Target atoms are searched in an inner cylinder and coaxial outer ring cylinders with volume Ω and length λ along the pass of a moving atom, where the atomic volume Ω = 1/N, λ = Ω 1/3 and N is the number density of a target material. The bottom faces of the cylinders are called “target disks.” A target atom is set randomly on each target disk. A target atom found outside the surface is disregarded. If several target atoms are found, the one on the inner disk is selected. Thus, the code contains more short-range collisions than the ACAT code. Open squares in Fig. 1.7 indicate sputtering yield derived with a modiﬁed ACAT code that forces the projectiles to collide ﬁrst in the cell at an origin, and that contains more short-range collisions. For grazing incidence, the TRIM.SP result comes somewhere between the ACAT and the modiﬁed

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Fig. 1.6. Angular dependence of sputtering yield. (a) Obtained with the experiment and (1.6) for 1 and 8 keV H+ incident on Ni and (b) that for 30 eV W+ onto W from (1.6) and (1.7) [44]

ACAT results. Thus, the large energy deposited by short-range collisions increases sputtering yield in the TRIM.SP case. The knockout process of a surface target atom executed by an incident light ion becomes dominant at large angles [46, 47]. The knockout process at large angles is divided roughly into direct and indirect ones, where a “direct” one means the direct knockoﬀ of a surface atom by an incoming ion and an “indirect” one the knockoﬀ of a surface atom by an incident ion which is scattered just before near the surface by the other target atoms, as illustrated in Fig. 1.8. While only the indirect one works for the not-too-oblique incidence, the direct one plays a major role at grazing angles of incidence. Equation (1.6) does not include the contribution from the direct knockout process to the sputtering yield. Later, Yamamura et al. [47] presented a new formula for light ions where that process was also taken into account, as given by

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Fig. 1.7. Incident-angle dependence of sputtering yield for 100 eV W → W. Closed diamonds are the results of TRIM.SP [2, 9], the open squares are the results of the modiﬁed ACAT code that contains more short-range collisions

Y (E, θ) = T f exp[−Σ(X − 1)], Y (E, 0)

(1.9)

where T = (1 + A sin θ)/ cos θ, X = 1/ cos θ. The term sin θ included in T reﬂects the contribution of the direct knockout process. f, Σ, and A are parameters and estimated by adjusting the formula to experimental or calculated data. Most recently three parameters were estimated for the ACAT data of D+ ions incident obliquely on C, Fe, and W materials in the energy ranges from tens eV to 10 keV [48]. Then, the parameters were expressed as a function of incident energy. As displayed in Fig. 1.9, the dependence of normalized physical sputtering yield on incident-angle derived from (1.9) using the functions has been compared with the ACAT data for 200 eV and 1 keV D+ ions incident obliquely on C and with those from (1.9) with not using the functions and from (1.6). We found that the three formulae all agree well with the ACAT data, except for 20–40% diﬀerence between the ACAT data and (1.6) at angles of not-too-oblique incidence for 1 keV ions. Figure 1.10 indicates incident-angle dependence of tungsten self-sputtering for incident energy of 100 eV, where the solid squares, triangles, and circles represent ACAT, DYACAT, and MD results. The MD simulation assumed a random surface. The yields for normal incidence obtained with the DYACAT and MD codes are almost equal to 0.013 atoms/ion which was derived by extrapolating the experimental database of sputtering in [17] using (1.9). For grazing incidence (θ ≥ 80◦ ), the ACAT yield approaches zero since the surface normal component of the incident velocity also becomes close to zero. As a

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βout

θ β

δ α (a)

θ

B PA

PB Δθ

A

(b ) Fig. 1.8. Schematic diagram of knockout processes by light ions for oblique incidence. (a) Direct knockout process. (b) Indirect knockout process

result, impulse and deposited energy onto the surface decrease. However the DYACAT and MD yields approach a ﬁnite value (≈0.07). Figure 1.11 illustrates a density distribution of deposited energy at θ = 80◦ on the surface, where incident atoms travel from the right side to the left side, and the grid width is 5 ˚ A. A low-deposited energy density for the DYACAT and MD results is seen to expand in the left area. This is caused by complex trajectory development under many-body collisions, resulting in an increase in the deposited energy, which is given by the integration of the deposited energy density. In fact, the deposited energies are 27, 50, and 37 eV for the ACAT, DYACAT, and MD cases. Therefore, enhanced energy deposition by manybody collisions increases sputtering yield. The maximum of the deposited −2 energy density is greater than 1.6 eV ˚ A for the MD case, while it is less −2 than 1.6 eV ˚ A for the ACAT and the DYACAT cases. In the MD simulation, incident energy of a projectile temporarily changes to potential energy among the surface atoms at an impact point because the atoms behave like a cluster under cohesive potential. This is not considered in the limited-MD calculation by the DYACAT code. As a result, the deposited energy density in the MD case is higher than that in the DYACAT case. Since the highly deposited

102 D+ Æ C 200eV 101

100

10−1 ACAT Eq.(8) with functions Eq.(8) Eq.(7)

10−2

0

30 60 Incident angle θ(degree)

90

Normalized Physical Sputtering Yield

Normalized Physical Sputtering Yield

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102 D+ Æ C 1keV 101

100

10−1 ACAT Eq.(8) with functions Eq.(8) Eq.(7)

10−2

0

30 60 Incident angle θ(degree)

90

Fig. 1.9. Comparison of the normalized physical sputtering yield vs. incident angle. Left: The legend indicates the curves calculated with the three formulae. The closed circles are the data obtained with the ACAT code for 200 eV D+ onto C. Right: The caption is the same as in (left) except the incident energy is 1 keV. Refer to (right) for legend

Fig. 1.10. Incident-angle dependence of sputtering yield for 100 eV W+ → W. The solid squares, triangles, and circles indicate the results obtained with the ACAT, DYACAT, and MD codes. The curve shows (1.9) with A = 1.32, f = 3.24, and Σ = 1.87

energy density enhances sputtering yield, the MD and DYACAT results are equivalent to grazing incidence, although the deposited energy in the MD case is less than that in the DYACAT case. As indicated in the ﬁgure 1.10, this fact inﬂuences the yield for incident angles in the range 10◦ ∼ 60◦ .

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Fig. 1.11. Contour map of deposited energy density on a surface for (a) ACAT, (b) DYACAT, and (c) MD simulations of 100 eV W+ → W at θ = 80◦ . Incident atoms travel from the right side to the left side. The grid width is 5 ˚ A. The contour lines in eight colors from dark grey to light grey indicate the densities of 0.003, 0.006, 0.016, −2 0.04, 0.1, 0.3, 0.6, and 1.6 eV ˚ A

1.4 Diﬀerential Sputtering Yield While total sputtering yield is required in some cases, diﬀerential sputtering yields with respect to energy and ejection angle of sputtered atoms are of importance in other cases. We discuss diﬀerential sputtering yields below. 1.4.1 Energy Spectrum of Sputtered Atoms Quite a large quantity of experimental and calculated data on the energy spectrum of sputtered atoms from solids has been produced and summarized [2, 49–59]. It has been well established experimentally, theoretically, and by computer simulations that an energy spectrum of sputtered atoms coming from a welldeveloped collision cascade can be well reproduced by Thompson formula [60].

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Such a developed cascade is generated by high-energy medium-heavy and heavy ions. The formula is expressed in terms of diﬀerential sputtering yield Y (E) of atoms sputtered with ejected energy E for incoming ions of normal incidence as 1 − (Us + E) /γE0 dE, (1.10) Y (E)dE ∝ 3 E 2 (1 + Us /E) where E0 and E are the energies of incident ions and sputtered atoms and US is the surface binding energy of a target material, γ ≡ 4M1 M2 /(M1 + M2 )2 , where M1 and M2 are the masses of an incoming ion and a target atom. When γE0 Us , E, (1.10) is approximated by Y (E)dE ∝

E dE. (E + Us )3

(1.11)

Normalized Sputtering Yield (Arb. units / ion / eV)

As an example, we show in Fig. 1.12 an energy spectrum of sputtered Fe atoms due to 5 keV Ar+ ion bombardment of normal incidence calculated with the ACAT code, together with the Thompson formula [(1.11)]. It is clear from the ﬁgure that the formula reproduces the calculated data quite well. Falcone et al. [61] also derived a similar formula. Equation (1.11) indicates that the energy spectrum does not depend on incident energy and angle, and ejection angle. However, more rigorously, it is expected to be dependent on incident energy and angle. The dependence seems to be more prominent for a cohesive material. To be able to discuss the nature of the energy distributions quantitatively, (1.11) should be generalized to have a form,

0.08 5 keV Ar+

Fe

0.06

0.04 ACAT Thompson

0.02

0

0

10 20 30 40 Energy of sputtered atoms (eV)

50

Fig. 1.12. Energy spectrum of Fe atoms due to 5 keV Ar+ ion bombardment of normal incidence

18

T. Ono et al.

Fig. 1.13. Best-ﬁt values of k in (1.12) applied to the energy distribution of sputtered atoms from Nb irradiated normally by Ar+ ions with a variety of incident energies

Y (E)dE ∝

E dE. (E + Us )k

(1.12)

The value of k depends on the interaction potential for elastic collisions. Equation (1.12) peaks at Us /(k − 1). By computer simulations, we obtained an energy distribution at each ejection angle of sputtered atoms from cohesive Nb (Us = 7.75 eV) irradiated normally by Ar+ ions with a variety of incident energies. The best-ﬁt value of k was derived by ﬁtting (1.12) with the energy spectra, and potted in Fig. 1.13 as a function of the ejection angle. It is clear from Fig. 1.13 that a variation in k is around k = 3.0 with a width ±0.2. In addition, for less cohesive target materials like Cu, the dependence of k on ejection angle is estimated to be weaker (see for more discussion [62]). Thus, the Thompson formula can almost represent energy distributions of sputtered atoms from target materials. Deviations from the Thompson formula have been observed in measurements for incident energy below 1 keV, particularly, for light ions [52–54, 59, 62–66]. The peak of an energy spectrum tends to shift to lower energy and the width of the spectrum becomes narrower. As described in Sect. 1.3.1, the sputtering mechanism II becomes dominant in such a low energy range. To explain the energy spectrum of sputtered atoms from heavy target materials by low-energy light-ion bombardment, by assuming that sputtered atoms are only primary recoils that undergo only elastic collisions, Falcone [67] derived a formula Y (E0 , E)dE ∝ dE

E γE0 ln . 5/2 E + Us (E + Us )

(1.13)

1 Simulation of the Sputtering Process

19

Assuming likewise that light-ion sputtering is mainly due to the primary knock-on atoms, i.e., recoils, produced by ions backscattered from inside the material, Kenmotsu et al. [68] obtained a formula on the basis of the transport theory.

2 Tmax E ln , (1.14) Y (E0 , E)dE ∝ dE E + Us (E + Us )8/5 where Tmax = γ(1 − γ)E0 . It is notable that (1.10), (1.13), and (1.14) depend on incident energy of a projectile. Figure 1.14 illustrates the energy spectra of sputtered atoms calculated with the ACAT code for a Fe target material bombarded normally by 50, 100, and 500 eV D+ ions, together with (1.11), (1.13), and (1.14). Each spectrum was normalized to unity at the maximum value. Equation (1.14) predicts quite well the energy spectra for 50 and 100 eV D+ ion bombardment as compared with (1.11) and (1.13). Equation (1.14) diﬀers from the ACAT results for the 500 eV case. The reason for this diﬀerence is considered to be due to the neglect

Fig. 1.14. Energy spectra of sputtered atoms calculated with the ACAT for 50, 100, and 500 eV D+ ions incident normally on a Fe target, together with (1.11), (1.13), and (1.14)

20

T. Ono et al.

Table 1.3. Peak energies of spectra obtained by ﬁtting (1.11), (1.13) and (1.14) with the ACAT results Incident energy (eV) 50 100 500

Present work (eV)

Falcone (eV)

Thompson (eV)

0.43 1.29 2.77

0.83 1.58 2.22

2.14 2.14 2.14

of an inelastic energy loss in the model. An inelastic energy loss is dominant for 500 eV, because this energy loss increases in proportion to the projectile’s velocity. Therefore, (1.14) is valid for the incident energy of light ions below a few hundred eV. From these ﬁgures, the peak position of the ACAT results shows a slight shift toward higher energy as incident energy increases, as pointed out above. Table 1.3 lists peak energies obtained by ﬁtting (1.11), (1.13), and (1.14) with the ACAT results. Both (1.13) and (1.14) indicate that the peak position of the energy spectrum is an increasing function of incident energy. Equation (1.11) is not a function of incident energy. The peak energy of (1.13) is larger than that of (1.14) and the ACAT data for the 50 and 100 eV D+ cases. Most recently, Ono et al. [69] extended (1.14) by taking into account an inelastic and elastic energy loss while keeping the same sputtering mechanism as assumed in [68]. In addition, they assumed that primary knock-on atoms produced by backscattered ions do not lose energy while penetrating to the material up to the surface, instead of the energy loss model employed in [68]. The extended formula is expressed in terms of normalized energy-distribution function and ﬁts well with the data calculated with the ACAT code for 50 eV, 100 eV, and 1 keV D+ ions impinging on a Fe target. Figure 1.15 shows the energy spectra of sputtered particles for 5 keV Ar+ ions incident normally on a random surface. The ACAT result is plotted for comparison. The ACAT result is reproduced successfully by a Thompson distribution [60]. In the high-energy range, the MD result agrees with the ACAT result, which suggests that sputtered particles come from a collision cascade. But, sputtered particles with low-energy are considered to come from a thermal spike, and are comprised of many Cu clusters. The latter fact indicates the main diﬀerence between the MD and the ACAT results. It is well known that the ﬂux of particles sputtered from a solid surface bombarded with energetic ions is composed not only of atoms but of molecules and clusters [70]. Compared to the understanding of the properties of monomer emission in sputtering, the understanding of the formation and emission of clusters in energetic ion irradiation is much less incomplete. Both computer simulations and experiments have indicated the importance of fragmentation processes and detailed atomistic mechanism which imparts energy to an aggregation of atoms at the surface and causes its ejection [70–72].

1 Simulation of the Sputtering Process

21

Fig. 1.15. Energy spectra of particles sputtered from a Cu random surface for 5 keV Ar impact. The circles and squares are the MD and ACAT results. The open circles show the monomer yield in the MD result. The solid curve is from the approximate Thompson [60] with surface binding energy Us = 3.1 eV

1.4.2 Angular Distribution of Sputtered Atoms The collision cascade theory predicts that an isotropic distribution of recoil atoms is formed from a well-developed cascade in a target material bombarded normally by energetic projectiles, which results in a cosine-type distribution for the angular distribution of sputtered atoms [20,73]. Experimental data and simulation results indicate that the angular distribution depends on incident energy [74–79]. For low incident energy, a collision cascade is formed, but it is not well developed. As a result, the angular distribution of recoil atoms in the cascade is no longer isotropic, resulting in the angular distribution of ejected atoms being of the under-cosine or heart-shaped type [80]. For high incident energy, on the other hand, an angular distribution tends to become an over-cosine type [75], being diﬀerent from the cosine shape expected from the collision cascade theory. A qualitative explanation for the over-cosine ejection is that the contribution to sputtering from recoils produced in deeper layers that reach the surface without suﬀering collisions or that create new recoils (multigenerated) to be sputtered increases as incident energy becomes higher; in this case, the event that the recoil atoms will travel along the direction of the surface normal from the bulk to the surface is highly probable, resulting in an over-cosine distribution [80]. Figure 1.16 shows the types of angular distribution of sputtered atoms, cosine, over-cosine, under-cosine, and heart-shape. The heart-shaped type will be explained later. The angular distributions of sputtered atoms due to high-energy projectiles can be represented by cosn θ, where θ is ejection angle and n is a ﬁtting parameter [75]. Yamamura and Muraoka [78] calculated, with the ACAT code, angular distributions of sputtered recoils produced in the ﬁrst three atomic

22

T. Ono et al. cosine over - cosine under - cosine heart - shape

0o 0.15

−30o

30o

0.1

60o

0.05 0

90o Yield (atoms / ion / sterad., arb. units)

Fig. 1.16. Types of angular distribution of sputtered atom. Thick solid line, cosine type; doted line, over-cosine type; dashed-dot line, under-cosine type; thin solid line, heart-shaped type Table 1.4. Best-ﬁt values of n obtained by ﬁtting cosn θ with experimental data and the calculated angular distributions of sputtered atoms for normal incidence with the ACAT code Ion Ar Ar Ar Ar Ar Ar Ar

Target Fe Fe Fe Fe Fe Fe Fe

Energy (keV) 0.3 0.5 1.0 2.0 3.0 4.0 5.0

Beat-ﬁt n-values

Exp.

First

Second

Third

Total

0.64 0.87 1.10 1.21 1.28 1.31 1.33

2.06 2.07 2.58 2.60 2.68 2.63 2.65

4.23 4.01 4.44 4.33 4.01 4.54 4.44

0.67 0.97 1.28 1.45 1.53 1.57 1.60

– 0.88 1.0 1.35 1.45 – –

layers of a Fe target irradiated normally by 0.3–5 keV Ar+ ions and derived best-ﬁt values of n for them, as listed in Table 1.4. The best-ﬁt values of n from the ﬁrst atomic layer derived from the ACAT results are in good agreement with those of experiments, and the degree of the over-cosine distribution, n, is an increasing function of ion energy E. This energy dependence of n is mainly due to the sputtered atoms from the ﬁrst layer. The angular distribution of sputtered recoils produced at the deeper layers has nearly the same degree of the over-cosine distribution as a function of ion energy. For E > 1 keV, the angular distribution from the ﬁrst layer shows an over-cosine distribution. Figure 1.17 shows the angular distributions of sputtered atoms for 5 keV Ar+ ions incident normally on Cu (100), (111), (110) and random surfaces. For the former ﬁrst three surfaces, the angular distribution has some characteristic peak. From Fig. 1.18, one can see that the spot pattern corresponds to the closed-pack direction of the fcc crystal. The focusing in the

1 Simulation of the Sputtering Process

23

Fig. 1.17. Angular distribution of sputtered atoms for 5 keV Ar+ impact on a Cu random surface. The circles, squares, triangles, and diamonds correspond to the results from the random, (111), (110), and (100) surfaces. The solid curve is an over-cosine ﬁt (cos θ)1.8 . The ejection angle is measured from the surface normal

Fig. 1.18. Spot patterns of sputtered Cu atoms for 5 keV Ar+ impact on Cu (100), (110), and (111) surfaces. Radial and rotational axes correspond to the polar and azimuth angles, respectively. Lines in nine colors from dark grey to light grey indicate contour lines from 10 to 90% with increment of 10%, of the maximum diﬀerential sputtering yield

closed-pack direction causes these peaks. For the random surface, on the other hand, the angular distribution has no characteristic peak and turns out to be of the over-cosine type of cos1.8 θ. This means the eﬀect of the crystal structure disappeared for a random surface. The following formula can also represent an angular distribution for normal incidence [25, 81, 82]: Y (E, θ) ∝ cos θ(1 + B cos2 θ),

(1.15)

24

T. Ono et al. Kr+

ACAT B = −0.62

0.04

−30o

0o

Cu 100 eV

30o

0.03

60o

0.02 0.01 0

90o

0.5 0.4 0.3 0.2 0.1 0

Yield (atoms / ion / sterad., arb. units) Kr+

ACAT B = 2.0

3 2

−30o

0o

Kr+

ACAT B=0

−30o

0o

Cu 500 eV

30o 60o

90o Yield (atoms / ion / sterad., arb. units)

Cu 5 keV

Kr+

ACAT B = 2.0

30o

4 60o

1

3

−30o

0o

Cu 20 keV

30o 60o

2 1

0

90o Yield (atoms / ion / sterad., arb. units)

90o

0 Yield (atoms / ion / sterad., arb. units)

Fig. 1.19. Angular distributions calculated with ACAT for 100 eV, 500 eV, 5 keV Kr+ ions incident on a Cu target. Also shown are the results of (1.15)

where B is a ﬁtting parameter. The cosine distribution corresponds to B = 0 in (1.15). B > 0 and B < 0 accord with angular distributions of over-, undercosine, and heart-shaped types, respectively. The ﬁtting function, (1.15), is useful compared with the function cosn θ, since (1.15) can describe even a heart-shaped distribution (smaller negative value of B) corresponding to very low incident energy. Figure 1.19 displays angular distributions of sputtered atoms calculated with the ACAT code for 100 eV, 500 eV, 5 keV, and 20 keV Kr+ ions incident normally on a Cu material. Also shown are the results of the ﬁtting formula [(1.15)]. The best-ﬁt values are B = −0.62 for 100 eV, B = 0 for 500 eV, B = 2.0 for 5 and 20 keV. It is quite clear from the ﬁgure that above formula [(1.15)] ﬁts very well with these calculated distributions. The value of B increases with increasing incident energy, except for 5 and 20 keV for which it is the same. Thus, it is not a linear increasing function of incident energy. The behavior of B for incident energies from 5 to 20 keV is understood as: for such high incident energy, since main cascades are formed at great depth from the surface, the recoil density created which is responsible for sputtering becomes nearly constant near the surface, resulting in tending to an isotropic distribution. The sputtering mechanism for normally incident light ions is described in Sect. 1.3.1, and that for obliquely incident light ions is also presented in Sect. 1.3.2. While an angular distribution formed by the direct knockout pro-

1 Simulation of the Sputtering Process

25

: few collison part : random part

Fig. 1.20. Schematic representation of an angular distribution of sputtered atoms due to light ions of oblique incidence

cess is expected to be narrow, that by the indirect knockout process becomes broad, because in the latter case light ions at nearly normal incidence are backscattered nearly isotropic from inside a material. This corresponds to the fact that the angular distribution due to light ions does not lead to the under-cosine type, i.e., cosine or over-cosine types [73]. Therefore, as shown in Fig. 1.20, the angular distribution by light ions of grazing incidence consists of a random and a few collision parts. Figure 1.21 illustrates the normalized angular distributions of sputtered atoms from a Ni material bombarded by 450 eV and 1 keV H+ ions at several angles of incidence [39, 75, 76]. The simulation results calculated with ACAT are in good agreement with the experiments except for the case of 450 eV H+ ions for incident angle 80◦ . This exception is considered to come from the eﬀect of the surface roughness eﬀect examined and the low incident energy. A comparison of the distribution for normal incidence with that for 60◦ indicates that, as incident angle becomes larger, a distribution tends to be sensitive to surface roughness, resulting in being broad. Figure 1.22 indicates that the angular distribution by 100 eV H+ ions incident normally on Cu is the over-cosine type (B = 0.5). In contrast, that by 100 eV Kr+ ions incident on Cu becomes the under-cosine type, as illustrated already in Fig. 1.19. Thus, it is understood that a few collision process characteristic of light-ion bombardment leads to the over-cosine type even in low incident energy. Assuming sputtering due to the direct knockout process between an incident ion with energy E and a target atom, and planar surface potential Us , the relation between a recoil angle δ and an ejection angle βout (see Fig. 1.8) is given as [83] cos2 δ sin2 (θ + δ) , (1.16) cos2 βout = cos2 δ − q 2

26

T. Ono et al.

ACAT Experiment [39, 75]

450eV

−30º

0º

−30º

30º

−60º −90º

60º

90º 1

60º

0.5

−30º

0

0.5

1

90º

−30º

0

0.5

1

90º 0

0.5

1

0

0.5

1

0º 30º 60º

90º 0.5

−30º 60º

0.5

−90º 1

30º

−90º 1

90º 0.5

−60º

0º

80º −60º

30º 60º

−30º

−90º 0.5

−90º 1

30º 60º

0º

−60º

0º

−60º

1

1keV

H→Ni

0

0.5

1

0º 30º

−60º

60º

−90º

90º 1

0.5

0

0.5

1

Fig. 1.21. Normalized angular distributions of experimental and ACAT data for 450 eV and 1 keV H+ ions incident for a Ni material for 0◦ , 60◦ , and 80◦

where θ is an angle of incidence, q = Us /γE, γ = 4M1 M2 /(M1 + M2 )2 , where M1 and M2 are the masses of a projectile and a target atom, respectively. By taking the derivative of (1.16) with respect to δ and set equal to zero, the ﬂowing transcendental equation is obtained: cos3 δ cos(δ + θ) − q 2 cos(2δ + θ) = 0.

(1.17)

In addition, preferential ejection angle βp due to the direct knockout process under q 1 is roughly given as [79, 83]

1 Simulation of the Sputtering Process

H+

ACAT B = 0.5

27

Cu

100 eV 0o

0.0006

30o

−30o

0.0004

60o

0.0002 0

90o Yield (atoms / ion / sterad., arb. units)

Fig. 1.22. Angular distributions calculated with the ACAT code for 100 eV H+ ions incident on a Ni target. Also shown are the results of (1.15) Table 1.5. Comparison with the experimental data and analytical results calculated with (1.18) on the preferential angle βp Ion Target Energy (keV)

Ar Ar Ar Ar Xe Ar Ar Ar Ar Xe H H H H H He

Cu Cu Cu Cu Cu Zr Zr Zr Zr Zr Ni Ni Ni Ni Ni Ni

500 500 150 900 200 500 500 900 150 200 0.45 1 1 4 4 4

Incident angle (degree) 80 85 85 85 85 80 85 85 85 85 80 70 80 80 80 80

βp (degree) Theory (1.18) Exp. 10.2 5.2 5.4 5.2 5.4 10.3 5.3 5.3 5.6 5.5 46.6 45.9 33.1 32.1 21.2 15.9◦

βp = cos−1 {(cos θ + q)(cos θ + 2q)}1/2 .

∼10.0 ∼5 ∼5 ∼5 ∼5 ∼11 ∼9 ∼8 ∼9 ∼5 49.3 43.0 45.0 33.7 21.0 15.0

(1.18)

Table 1.5 [79] lists the experimental data and analytical results calculated with (1.18) for βp . Equation (1.18) is in good agreement with the experimental data for the extensive energy range (0.45–500 keV). Figure 1.23 illustrates the diﬀerential sputtering yield of tungsten selfsputtering with incident energy of 100 eV and at θ = 30◦ , 60◦ , and 80◦ . Anisotropy was seen for βp , and βp increases slightly with increasing inci-

28

T. Ono et al.

Fig. 1.23. Contour map of diﬀerential sputtering yield for 100 eV W → W at θ = 30◦ , 60◦ , and 80◦ . The radial and rotational axes correspond to the polar and azimuth angle, respectively. Lines of nine colors from dark grey to light grey indicate couture lines from 10 to 90% with inclement of 10%, of the maximum diﬀerential sputtering yield

dent angle. This result corresponds qualitatively with the feature that (1.18) indicates.

1.5 Sputtering from Rough Surface It is known that the surface in the BCA code is atomically rough. The random surface in the MD code is also atomically rough. To observe the eﬀect of a surface roughness that is greater than the atomic roughness, we also performed the MD simulations using a fractal surface, which is constructed by the Fourier ﬁltering method [84]. The height z at a horizontal position r = xi+yj is given by the two-dimensional discrete inverse Fourier transform as z(r ) = {A(k ) cos(k · r ) + B(k ) sin(k · r )}, (1.19) kx =0 ky =0

where k = kx i + ky j is the wave vector, the spectral density is S(k ) = A2 (k ) + B 2 (k ) ∝ (kx 2 + ky 2 )D−4 , and D is the fractal dimension. Figure 1.24 shows the incident-angle dependence of tungsten self-sputtering yield with incident energy of 1 keV calculated with the MD code. Open circles indicate sputtering yields for the fractal surface with D = 2.15 and the RMS roughness of about 2λ, where λ is deﬁned in Sect. 1.2. We found that the rough surface reduces incident-angle dependence because the local surface normal vectors are randomized for the rough surface which is shown in Fig. 1.25a. This is equivalent to randomizing incident angle. The randomization is derived from low wave number components of (1.19) because we should consider the size of the local surface that includes a collision cascade. In Fig. 1.26, we show, with the ACAT code, the incident-angle dependence of Cu self-sputtering yield with incident energy of 1 keV. From Fig. 1.26, one can ﬁnd that ions normally incident on rough surfaces (D = 2.2, 2.5) gives

1 Simulation of the Sputtering Process

29

Fig. 1.24. Incident-angle dependence of sputtering yield for 100 eV W → W. The open circles correspond to the MD results on a rough surface

Fig. 1.25. Schemata of rough surface sputtering. (a) Low-energy ions incident on a rough surface is equivalent to randomizing incident angle. (b) High-energy ions incident on a rough surface is equivalent to a low-density surface

30

T. Ono et al.

Fig. 1.26. Incident-angle dependence of sputtering yield for 1 keV Cu → Cu with D = 2.0, 2.2, and 2.5, respectively

rise to lower sputtering yield than that on a smooth surface (D = 2.0). Since a high-energy collision cascade develops in a wide area of the surface, highenergy sputtering is aﬀected by the averaged low-density surface which is schematized in Fig. 1.25b, which reconﬁrms the results obtained by Kenmotsu et al. [85] about low-density eﬀect of the fractal surface on sputtering. This eﬀect was not found in low-energy sputtering as shown in Fig. 1.24. When a low-energy projectile collides with surface atoms, it is inﬂuenced by them, and feels the direction of the local surface normal. Thus, randomization of a surface normal is important for low-energy sputtering.

1.6 Sputtering of Compound Targets When a multicomponent material is bombarded strongly with an ion beam, near-surface compositional alteration is an unavoidable phenomenon which results from a combination of several kinetic (preferential sputtering, collision mixing, etc.) and thermal processes (radiation-induced diﬀusion, Gibbsian segregation and radiation-induced segregation, etc.). The driving forces of surface segregation are strain energy and diﬀerence in the chemical potentials between the ﬁrst and the second layers. The former is radiation-induced segregation, and the latter known as Gibbsian segregation. The relative importance of each process depends on an alloy system, the elements, energy and ﬂux of bombarding ions, and irradiation temperature [86]. To analyze the surface change of multicomponent targets under ion bombardment, Auger electron spectroscopy (AES), ion scattering spectroscopy (ISS), Rutherford backscattering spectroscopy (RBS), secondary ion mass spectroscopy (SIMS), and X-ray photoelectron spectroscopy (XPS) are used.

1 Simulation of the Sputtering Process

31

Kimura et al. [87] made an experiment of 6 keV As2 + ion implantation on Si wafers and measured the depth proﬁle up to 10 nm with high-resolution RBS. These analytical techniques are useful to estimate surface concentration and the compositional change near a surface, but the real surface concentrations of constituents are possibly diﬀerent from those measured by respective technique, because of the diﬀerent resolutions of these techniques. Therefore, it is diﬃcult to estimate the compositional change near the surface under ion bombardment for multicomponent targets experimentally. At temperatures lower than room temperature, the surface compositional change of most alloys can be explained mainly by kinetic processes, because the time constants of the processes such as the recession speed due to sputtering are much faster than those of thermal processes. At high temperatures, since the time constants of the latter processes are comparable to or longer than those of the former processes, the phenomenon becomes more complex. The ﬁrst study of bombardment-induced alterations of surface composition at high temperature was carried out on a Cu−Ni alloy by Shimizu et al. [88]. After this work, there were a lot of measurements on surface and/or surface compositional changes in binary alloys by the AES and ISS techniques [89, 90]. Lam et al. [91] measured changes on the surface and surface compositions of Ni–40 at.% Cu alloys at temperatures between 25 and 700◦C, using the ISS technique. They found that the steady-state surface composition was noticeably temperature-dependent above 400◦ C, which was interpreted in terms of the signiﬁcant contribution of the second atomic layer to the sputtering ﬂux. There are two typical theoretical approaches to understand alterations of a surface composition. One is an analytical approach which is based on a diﬀusion equation [92–95] or on a kinetic balance equation [96]. The other approach is Monte Carlo simulation [97–99]. Ho [92] introduced radiation enhanced diﬀusion into the model proposed by Patterson and Shirm [93]. Wiedersich et al. [94] presented a theory for radiation-induced segregation by introducing a concept of the preferential migration of vacancies and interstitial of a certain atom. Kelly [95] suggested that surface segregation might be important for the interpretation of compositional changes at the surface. Sigmund and his coworker [96] investigated multicomponent sputtering theoretically on the basis of the kinetic balance equation. For multiple-component targets, total sputtering yields, Y , are deﬁned with its partial sputtering yields of constituents Yi as follows [86]: Yi (1.20) Y = i

At suﬃciently low temperature, where thermal processes are not important, the ratio of sputtering yields for a binary target is expressed by Y1 c2 c1 , (1.21) = Y2 c2 c1

32

T. Ono et al.

where Y1 and Y2 are partial sputtering yields of the two constituents, and c1 , c2 , c1 and c2 are surface concentrations of each element before the ion bombardment and in the steady state. If a change in the surface concentration for a binary target due to sputtering does not occur, the ratio Y1 /Y2 is equal to unity. The ratio Y1 /Y2 for a binary target is usually determined from (1.21) by measuring the surface concentrations of constituents before the ion bombardment and in steady state. The measured sputtering yield ratio of alloys is listed in Table 1.6 [100]. A theory of sputtering on multiple component targets was proposed by Sigmund [73,96,101]. Partial sputtering yield of the i-component for a binary inﬁnite medium is given as: Yi = ci Λi FD (E, θ, 0), where Λi

= Λi

(U )i Ui

1−2mi

i = 1, 2,

(1.22)

1 Gi . ci (G)i

Table 1.6. Sputtering yield ratio of alloys. Also listed are atomic weight ratio and ratio of sublimation energies of constituent atoms of pure metals [100] System (A−B)

Mass ratio (MA /MB )−1

Sputtering yield ratio (YA /YB )

Ration of sublimation energy in eV (UA /UB )

Ion

Method and references

Al−Cu Al2 −Au Al−Au2 Si−Ni Si−Pt Si−Pt2 Au−Cr Cu−Ni Cu−Ni Ni−Pt Pd−Ni Cu−Pd Cu−Pt Cu−Au Cu3 −Au Cu3 −Au

0.42 0.14 0.14 0.48 0.14 0.14 3.3 1.1 1.1 0.3 1.7 0.63 0.32 0.32 0.32 0.32

2.1 1.9 1.3 1.6 2.1 1.6 1.4–2.0 1.7 1 1.5–1.9 1.5–1.7 1.5–1.6 1.6–3.0 1 1.1 2.3–2.8

3.36/3.52 3.36/3.80 3.36/3.80 4.70/4.46 4.70/5.86 4.70/5.86 3.80/4.12 3.52/4.46 3.52/4.46 4.46/5.86 3.91/4.46 3.52/3.91 3.52/5.86 3.52/3.80 3.52/3.80 3.52/3.80

Xe (1 keV) Ar (40 keV) Ar (40 keV) Ar (40 keV) Ar (40 keV) Ar (40 keV) Ar (0.5–2 keV) Ar (0.5–2 keV) Ar (3 keV) Ar (2 keV) Ar (0.5–2 keV) Ar (2 keV) Ar (2 keV) Ar (1 keV) Ar (40 keV) Ar (0.5–5 keV)

Ag−Pd Au−Pd Ag−Au Ag−Au Ag−Au

1.0 2.0 0.56 0.56 0.56

1.5–1.6 1.0–1.4 1.7–1.8 1.2 1

2.97/3.91 3.80/3.91 2.97/3.80 2.97/3.80 2.97/3.80

Ar (2 keV) Ar (2 keV) Ar (1 keV) Ar (40 keV) Ne (1.5 keV)

RBS [99] RBS [100] RBS [100] RBS [100] RBS [100] RBS [100] AES [101] AES [102] ISS [103] AES [104] AES [105] AES [106] AES [107] AES [107] RBS [100] Electron diﬀraction [108] AES [109] AES [109] AES [107] RBS [100] ISS [110]

1 Simulation of the Sputtering Process

33

Here ci is atomic concentration of the binary alloy. The relation between c1 and c2 is expressed by c1 + c2 = 1 for the binary alloy. The quantity F (E, θ, 0) is the deposited energy per unit depth in the alloy surface, mi exponent in the inter-atomic power law potential for an elemental the i-target, Λi a material constant for an elemental i-target, (U )i surface potential in an elemental itarget, Ui and surface potential for an i-atom of the alloy. The factor Gi /(G)i is ratio of the ﬂux functions between i-atoms in the alloy and elemental itarget. Gi and (G)i are densities of moving target atoms in a collision cascade generated by incident ions or recoil atoms for the alloy and an elemental target, respectively. For roughly equal masses M1 , M2 of the constituents, one may approximate Gi /(G)i ≈ ci . Using (1.22) and assuming m1 = m2 , the ratio of sputtering yields for the binary alloy is expressed by c1 Y1 = Y2 c2

M2 M1

2m

(U )2 (U )1

1−2m .

(1.23)

Heat of sublimation is generally taken as an approximate value for surface binding energy of elemental targets [73]. It is diﬃcult to estimate surface binding energy of each element of multiple-component targets, because the energy depends on the surface concentration of the elements and surface coordination numbers. For a random binary alloy the surface binding energy U1 is derived as a function of surface concentration of the constituents and the nearest-neighboring bond strengths [95, 102]: U1 = −Zs [c1 U11 + c2 U12 ],

(1.24)

where ZS is surface coordination number, and U11 and U12 are bond strengths. To estimate the ion-ﬂuence dependence of depth proﬁles and compositional changes during ion bombardment, there are several Monte Carlo simulation codes that are based on the BCA. The EVOLVE code was developed by Roush et al. [97]. The TRIDYN was made by M¨oller and Eckstein [98], and the ACAT-DIFFUSE was proposed by Yamamura [6]. The ACAT-DIFFUSE code calculated compositional changes near a surface and depth proﬁles in Ni–40at. % Cu alloys at various temperatures (25–500◦ C) when sputtering is taking place with normal incident-beam of 3 keV Ne+ ions [103]. The compositional change near surface calculated with the ACAT-DIFFUSE code is shown below. As Gibbsian segregation, the ACAT-DIFFUSE code uses the Darken description [104]. The application of the modiﬁed Darken equation leads to the following coupled rate equations [103–105]:

34

T. Ono et al.

⎫⎤ ⎧ φ B1 ⎨ ⎬ X 1 − X 1 1 ⎣ ΔG1 + ln ⎦, ⎩ X φ 1 − X B1 ⎭ RT 1 1 ⎫ ⎫⎤ ⎧ ⎡ ⎧ B B ⎨ X1 2 1 − X1 1 ⎬ a 2 ⎨ X1B1 1 − X1φ ⎬ 2 ⎣ln − ⎦, ln ⎩ X φ 1 − X B1 ⎭ ⎩ X B1 1 − X B2 ⎭ a1 ⎡

∂X1φ ∂t

=

Ξ1 X1B1 a21

Ξ1 X1B2 ∂X1B1 = ∂t a22

B

Ξ1 X1 i+1 ∂X1Bi = ∂t a2Bi+1

1

1

.. .

⎫ ⎧ B 2 ⎨ X1 i+1 1 − X1Bi ⎬ a Bi+1 ⎣ln − ⎩ X Bi 1 − X Bi+1 ⎭ aBi 1 1 ⎧ ⎫⎤ ⎨ X1Bi 1 − X1Bi−1 ⎬ ⎦, ln ⎩ X Bi−1 1 − X Bi ⎭ 1 1 ⎡

1

1

(1.25)

.. . where X1φ and X1Bi are fractional concentrations of species 1 in the topmost and the ith layers, respectively. In deriving above equations we use chemical potential terms for an ideal binary alloy, i.e., μ = μ0 + RT ln X, where μ0 is standard chemical potential, R universal gas constant, and T is temperature. The coeﬃcient Ξ1 corresponds to a diﬀusion constant given by Ξ1 = M1 RT . In this model segregation takes place from the bulk B to the surface Φ, because 0φ 0B 0φ 0B 0B μ0φ 1 = μ1 . Segregation energy is given by ΔG = μ1 − μ1 −2 +μ2 . Abovecoupled equations lead to the Langmuir–McLean relation in a stationary phase [91]

X1B ΔG X1φ . (1.26) = exp kT 1 − X1B 1 − X1φ Lam et al. [91] measured the surface compositional change of Ni–40 at.% Cu alloy bombarded normally with ﬂux of 3.75×1013 ions cm−2 s−1 of 3 keV Ne+ ions. The simulations were done under the same conditions as the experiments. When the specimen is heated to a high temperature, a thermodynamic driving force gives rise to Cu enrichment at the alloy surface even in the absence of sputtering. Lam et al. gave the following expression for segregation energy ΔG of a Ni–40 at.% Cu ally at high temperature (500◦ C): ΔG = −2.6kT + 0.42.

(1.27)

From (1.26) and (1.28), we have the reasonable estimation of the surface atoms fraction Cuφ and Niφ at the topmost layer before ion bombardment which is denoted by [Cux Ni1−x ] in the ensuring discussions. In the calculations with ACAT-DIFFUSE we considered only one trap site which is vacancy and the basic diﬀusion equation is for interstitial diﬀusion. The respective activation

1 Simulation of the Sputtering Process

35

Fig. 1.27. Time evolution of the Cuφ /Niφ ratio in the ﬁrst layer during 3 keV Ne+ ion sputtering of a Ni–40 at.% Cu alloy at 400◦ C, where the ion ﬂux is 3.75 × 1013 ions cm−2 s−1 . Solid symbols mean the ACAT-DIFFUSE data and open symbol Lam’s experimental data [91]. The parameters of cases A, B, C and D are listed in Table 1.7

energies of Ni and Cu are assumed to be 0.93 and 0.88 eV for the interstitial diﬀusion, and the vacancy diﬀusion is considered indirectly by solving the rate equation of trapped atoms concentration, where the trapping energies of Ni and Cu are set to be 2.03 and 1.76 eV, respectively. We use smaller detrapping energies than the diﬀusion activation energies in the material with no irradiation, because trapped atoms may be in an excited state compared with a lattice atom. This leads to the radiation-induced diﬀusion. Figure 1.27 shows the calculated Cuφ /Niφ ratio in the topmost layer at 400◦ C as a function of bombarding time. We made simulations for four cases in which the physical parameters used are listed in Table 1.7, where ΔG0 is the segregation energy before bombardment. Since (1.28) can not be applied to T < 500◦C, both ΔG0 and [Cux Ni1−x ] are determined from the extrapolation of the experimental data [91]. The ion-ﬂuence dependence of Cuφ /Niφ ratio of case A is in agreement with the experimental data only at the early stage (t < 10 s), and the parameters of case A give the large steady-state Cuφ /Niφ ratio compared with the experiment. The segregation speed of case B is very small and it gives good agreement with the experimental steady-state Cuφ /Niφ ratio, but the ratio drops more rapidly than the experiment. There are experimental evidences [106, 107] that segregation energy under irradiation is smaller than that before bombardment. Referring to ion-ﬂuence dependence of the calculated Cuφ /Niφ ratios for case A and B, we adopt the

36

T. Ono et al.

Table 1.7. Initial surface atoms fractions Ξ, ΔG0 , ΔGS and decay constant τ for cases A, B, C and D Parameters Initial surface atoms fractions Ξ (cm2 s) ΔG0 (eV) ΔGst (eV) τ (ions cm−2 )

Case A

Case B

Case C

Case D

[Cu0.99 Ni0.01 ]

[Cu0.99 Ni0.01 ]

[Cu0.99 Ni0.01 ]

[Cu0.4 Ni0.6 ]

1.0 × 10−15 0.175 0.175 –

3.5 × 10−17 0.175 0.175 –

1.0 × 10−15 0.175 0.050 2.0 × 1016

1.0 × 10−15 0.175 0.050 2.0 × 1016

Fig. 1.28. Time evolution of the Cuφ /Niφ ratio at ﬁrst layer during 3 keV Ne+ ion sputtering of a Ni–40 at.% Cu alloy at various temperatures, where the ion ﬂux is 3.75 × 1013 ions cm−2 s−1 . Solid symbols denote the ACAT-DIFFUSE data and open symbols denote Lam’s experimental data [91]. The parameters used in the calculation are listed in Table 1.7. The cross marks denote the ACAT-DIFFUSE simulation of T = 100◦ C with the initial atom fraction [Cu1.0 Ni0.0 ]

following ansatz: ΔG = max[ΔG0 exp(−Φ/τ ), ΔGst ],

(1.28)

where ΔGst is segregation energy in a steady state. As shown in Fig. 1.27, the ion-ﬂuence dependence of the calculated Cuφ /Niφ ratio for case C is in good agreement with the experiment in the whole range considered. To show the dependence of the initial surface atoms fraction on Cuφ /Niφ ratio, we use the bulk atoms fraction as an initial surface atoms fraction in case D. Before 50 s, Cuφ /Niφ ratio is strongly dependent on the initial surface atoms fraction, but, after 50 s, the Cuφ /Niφ ratio shows the same dependence as that of case C.

1 Simulation of the Sputtering Process

37

Table 1.8. Best-ﬁt parameters of the initial surface atoms fractions Ξ, ΔG0 , ΔGS and decay constant τ for various temperatures Parameters

Temperature 100◦ C

200◦ C

300◦ C

400◦ C

550◦ C

Initial sur- [Cu0.4 Ni0.6 ] [Cu0.79 Ni0.21 ] [Cu0.89 Ni0.11 ] [Cu0.99 Ni0.01 ] [Cu0.92 Ni0.08 ] face atoms fractions −1 6.0 × 10−16 1.0 × 10−15 1.0 × 10−14 Ξ (cm2 s ) 2.0 × 10−17 1.0 × 10−16 ΔG0 (eV) 0.003 0.006 0.120 0.175 0.200 0.003 0.006 0.045 0.050 0.080 ΔGst (eV) 2.0 × 1016 8.0 × 1016 τ (ions – – 2.0 × 1016 −2 cm )

The Cuφ /Niφ ratio calculated with the ACAT-DIFFUSE code at various temperatures is displayed in Fig. 1.28, where solid symbols mean the ACAT-DIFFUSE data and open symbols Lam’s experimental data [91]. The parameters used in the calculation are listed in Table 1.8, where ΔG0 and the initial surface atoms fraction [Cux Ni1−x ] are also determined from the extrapolation of experimental data. In low temperature (<300◦ C), the time constant of kinetic process or the recession speed due to sputtering is faster than the segregation speed, and so we can reproduce the experimental data without using the ansatz (1.28). While the time constant of kinetic process is independent of temperature, the segregation speed Ξ is an increasing function of temperature. If we employ the ansatz (1.28), as is presented in Fig. 1.28, we can choose the best-ﬁt parameters which give good agreement with the experimental ionﬂuence dependence of the Cuφ /Niφ ratio. As a comparison, we calculated the Cuφ /Niφ ratio at 100◦ C, assuming that only Cu atoms are present in the ﬁrst layer before bombardment. These ACAT-DIFFUSE data are plotted by cross marks in Fig. 1.28. For 3 keV Ne+ ion bombardment we need more than 2.0 × 1015 ions cm−2 s−1 before the initial surface conditions do not aﬀect the Cuφ /Niφ ratio. This is consistent with the case D result shown in Fig. 1.27. Figure 1.29 illustrates the ﬂux dependence of Cuφ /Niφ ratio during sputtering at 300◦ C, where the parameters in Table 1.8 were used in the calculation and solid and open symbols mean the ACAT-DIFFUSE data and Lam’s experiment data, respectively. The ACAT-DIFFUSE data are in good agreement with the experiment for three ﬂuxes. The steady-state Cuφ /Niφ ratio of high ﬂux (1.88 × 1014 ions cm−2 s−1 ) indicates a slightly small value, because the kinetic process is strong compared with the other two ﬂuxes.

1.7 Conclusion We have given a quantitative account of and highlighted the results on sputtering obtained mainly with our computer codes, together with semi-empirical formulas that well reproduce the results.

38

T. Ono et al.

Fig. 1.29. Flux-dependence of the Cuφ /Niφ ratio during 3 keV Ne+ ion sputtering of a Ni–40 at.% Cu alloy at 300◦ C, where the ion ﬂux is 3.75 × 1013 ions cm−2 s−1 . Solid symbols indicate the ACAT-DIFFUSE data and open symbols indicate Lam’s experimental data [91], and the used parameters are listed in Table 1.4

After having described a brief outline of our computer codes in Sect. 1.2, we have mentioned in Sect. 1.1.3 dependences on incident energy and incident angle of total sputtering yield, together with corresponding semi-empirical formulas. The large diﬀerence found at glancing angles of incidence between the MC and the MD data was accounted for using the contour maps of deposited energy density on the surface calculated in these simulations. We have described diﬀerential sputtering yield in sputtered energy and ejection angle in Sect. 1.1.4. We have shown that the semi-empirical formulas agree well with the energy spectrum of sputtered atoms from heavy target materials with low-energy light ions. The diﬀerence in the angular distributions for heavy- and light-ion bombardment was described. We have also introduced a new semi-empirical formula that represents even the heartshaped angular distribution due to very low-energy heavy- and moderately heavy-atom bombardment. In Sect. 1.1.5, we have mentioned the eﬀect of surface roughness on sputtering with low- and high-energy ions. Low-energy ions incident on a rough surface is equivalent to randomizing incident angle, and sputtering with highenergy ions is aﬀected by the averaged eﬀective low-density of a rough surface. In Sect. 1.1.6, we have treated sputtering of compound materials. We have pointed out that kinetic and thermal processes occurring in a material result in the compositional change. Ion-ﬂuence dependence of the compositional change for a Cu−Ni alloy was calculated with the ACAT-DIFFUSE code where both kinetic and thermal processes are taken into account.

1 Simulation of the Sputtering Process

39

Acknowledgments. The authors are greatly indebted to the theoretical work and computer simulations done by late Prof. Y. Yamamura. They would like to thank Emeritus Prof. T. Kawamura for suggesting valuable comments and encouraging them to complete this work. This work was partly supported by a Grant-in-Aid of the Academic Frontier Project and KAKENHI (19055005) by the Ministry of Education, Culture, Sports, Science, and Technology of Japan.

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2 Electron Emission from Surfaces Induced by Slow Ions and Atoms R.A. Baragiola and P. Riccardi

2.1 Introduction Electron emission from surfaces is of crucial importance in determining the properties of electrical discharges, where it is caused by the impact of ions, atoms, electrons, and photons. At the microscopic level, the physics of electron emission from solid targets is usually described by a three-step model: electron excitation, electron transport to the surface, and its escape through the surface. This division serves a heuristic purpose and it must be borne in mind that, in purely surface events, actually only one step is involved. What distinguishes electron emission by diﬀerent incoming particles is the excitation step [1], which depends strongly on the momentum of the particle. This is because there is a minimum energy needed to extract an electron from the solid (work function for metals, band gap plus electron aﬃnity for nonmetals) and this energy transfer implies a momentum transfer from the projectile. This chapter is concerned with heavy particle collisions (ions and atoms) at low energies (below a few keV) and will discuss ﬁrst the physical mechanisms and then applications to electrical discharges in gases. The overall picture of electron emission induced by heavy particles is the following. Electrons are excited from the target or the projectile as a result of Coulomb interactions involving the nuclei and electrons through mechanisms that are grouped in two categories, potential and kinetic, depending on the source of the excitation energy. Such excitations occur mostly in binary collisions at the surface or very shallow depths, since the penetration depth of low-energy atomic projectiles is usually very shallow, tens of nm or less. The excited electrons can be ejected directly into vacuum or undergo a series of collisions in the target solid (electron transport) on their way to the surface. The collisions are either elastic scattering with atomic cores, which cause large deﬂections in trajectories, or energy loss collisions by scattering with other electrons, contingent on the availability of electronic states. As a result of such inelastic scattering, the electrons which succeed in escaping the solid come from a shallow depth, of the order of 2 nm for metals and semiconductors and up to a few tens of

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nm for insulators. In the latter case, the depth of origin of electrons is limited, at low primary energies, by the slowing down of the projectile mainly as a result of ion–atom collisions. Electron escape involves energy loss through the surface barrier and change of momentum perpendicular to the surface. The main observable in electron emission is the average electron yield γ (number of electrons ejected per primary particle), either as an integral quantity or in the form of distributions of electrons according to their energies, angles of emission, and spin state. Emission events are statistically distributed; i.e., the yield ﬂuctuates around the mean value γ and is described by probanPn = γ). bilities Pn of emission of n electrons per projectile ( Pn = 1; At the low impact velocities of interest, only low n (0, 1, 2) are important [2]. Experiments show that γ is at most ∼2–3 and depends critically on the electronic structure of the surface. Large increases in γ are detected when going from clean metals to gas-covered surfaces. The energy of emitted electrons is less than 20 eV, typically peaking at a few eV, while the distribution of emission angles with respect to the surface normal is cosine or below cosine. For single crystals, the angular distribution is strongly aﬀected by diﬀraction.

2.2 Physical Mechanisms The fundamental physics of electron emission in slow ion–surface interactions has been reviewed in detail, with emphasis on atomically clean surfaces. See reviews in books [3–7] and speciﬁc articles on kinetic [8,9] and potential [10,11] electron emission. Here, the focus will be on slow singly charged ions mostly impacting gas-covered surfaces, typical of electrical discharges. 2.2.1 Excitation Mechanisms In the impact energy range of interest, two main electron excitation mechanisms can be broadly distinguished, kinetic and potential, depending on whether the excitation energy is provided by the motion of the projectile or its potential energy. The potential and kinetic emission mechanisms are not exclusive of collisions at surfaces but also happen in two-body gas-phase collisions. Both mechanisms can only occur above an energy threshold related to U , the minimum energy required to free an electron. It is typically assumed that the electron comes from the surface and has a binding energy that is not much aﬀected by the incoming particle. This is a good approximation for metals, where U is equal to the work function and falls in the approximate range 1.5–6 eV. In nonmetals (semiconductors and dielectrics), U is often approximated by the minimum binding energy of a valence electron, as usually it costs less energy to remove an electron from the solid than from the incoming atomic particle (its ionization potential). In this case, U is equal to the surface band gap plus the electron aﬃnity. Values range approximately from 4 to 11 eV.

2 Electron Emission from Surfaces Induced by Slow Ions and Atoms

45

In potential electron emission (PEE), electron excitation results from the conversion of internal energy ε brought by an ion or an excited atom, through a two-electron Auger process. Such process can be Auger capture where an electron from the solid is captured by the ion and another electron is excited or Auger deexcitation where an excited projectile relaxes to a lower state transferring the energy to another electron. For electron emission to occur, the energy released in the Auger process, ε− U , has to exceed U (i.e., emission requires ε > 2U ). For most singly charged ions, PEE does not occur at surfaces that have been exposed to the atmosphere, since the relation ε > 2U is not generally satisﬁed for adsorbed molecules. In kinetic electron emission (KEE), electrons are excited as a consequence of time-varying Coulomb interactions between the nuclei and electrons of the incident particle and the surface, within the constraints of the Pauli exclusion. Here, several mechanisms are possible, depending on the type of surface. In metals, projectiles can interact with loosely bound (“conduction”) electrons and shallow core levels (such as the d-band in light transition metals). Deeper core levels are not accessible at the energies of interest. Binary collisions of “free” valence electrons of the targets with the screened Coulomb ﬁeld of the projectile are the dominant excitation mechanism for light projectiles (H, He, Li) on metals. A collision with a nearly free electron cannot result in a large energy transfer because the mass mismatch between the heavy particle and the electron prevents transferring suﬃcient momentum. The maximum energy transfer to an electron by a much heavier atomic particle occurs in head on collisions, where the electron gains twice the projectile velocity after a single scattering. The resulting energy transfer is T = 2mv(v + ve ), where v and ve are the velocity of the projectile and the target electron before the collision, respectively, and m the electron mass. Therefore, there is a minimum impact velocity that will result in a free electron excited to a state with energy above the vacuum level, when T = W , given by [12] vF 2W vth = 1+ −1 , (2.1) 2 mvF2 where W is the work function, vF the Fermi velocity, and m the electron mass. This corresponds to 1.5–3 × 107 cm s−1 (117–470 eV amu−1 ) for most metals, consistent with extrapolation of the experimental results for light projectiles [12]. Deviations from (2.1) contain information on the velocity distribution of electrons at the surface [13]. For heavy projectiles, the observed threshold velocities are an order of magnitude lower than (2.1). This is due to an additional electron excitation mechanism. This is the electron–electron interactions during the interpenetration of the electron clouds of the projectile and one of the target atoms which promote electronic levels directly into the ionization continuum or through autoionizing states [14].

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A direct demonstration of the importance of excitations in such binary atom–atom collisions below the free electron threshold of (2.1) was made by Rabalais et al. [15] who studied the impact parameter dependence of KEE in collisions of 4 keV Ar+ with Ni(110) and found that electron emission required a minimum impact parameter in a collision below 0.3 ˚ A. In binary collisions between projectile and a target atom, the minimum possible threshold for KEE allowed by energy conservation is when the center-of-mass energy equals U . However, quite above this threshold the electron yield is usually undetectable above the background of other secondary processes. 2.2.2 Separation of PEE and KEE PEE and KEE are separable in two limiting cases. When Ecm < U , and ε > 2U , only PEE can occur. If, on the other hand, ε < 2U and Ecm > U , electrons can only be ejected by the kinetic mechanism. In KEE, the threshold condition is when the maximum energy transfer is equal to U . Energy transfer center-of-mass energy Ecm has to exceed U . PEE does not require the motion of the projectile but can be aﬀected by it, whereas KEE can be aﬀected by the degree of excitation of the projectile. Electron emission statistics have been used to separate PEE and KEE for singly charged ions, based on the fact that PEE generally results in at most one electron being emitted [16]. 2.2.3 Electron Transport and Escape into Vacuum At low projectile impact energies, many of the electrons are emitted from the surface layer and it is diﬃcult or incorrect to separate scattering inside the solid and transmission through the surface barrier. Inside the solid, excited electrons undergo a cascade of collisions until their energy is degraded into heat or stored in long-lived excited states. Those excited electrons which are directed outward may cross the surface of the solid and escape before being thermalized, giving rise to electron emission. Therefore, the energy distribution of emitted electrons does not represent an equilibrium situation. An important characteristic of the low-energy ion impact case discussed here is that the vast majority of the initially excited electrons have very small kinetic energies, insuﬃcient to excite additional electrons above the vacuum level. That is, electron multiplication [17] is typically unimportant.

2.3 Electron Yields Experiments involve measuring the dependence of electron emission on different factors. These include the projectile and target properties and the bombardment geometry. Important properties of the projectile are its excitation and ionization state, its mass, and whether it comes as a single atom,

2 Electron Emission from Surfaces Induced by Slow Ions and Atoms

47

a molecule, or a cluster of atoms. Relevant target properties are the elemental composition and atomic and electronic structure in the surface region, the magnitude of surface electric ﬁelds, the temperature, and, for magnetic materials, the degree of magnetization. The relevant geometrical factors in experiments include the angle of incidence with respect to the surface and to the possible preferred crystallographic planes. Electrons can absorb a much larger energy transfer (even a substantial fraction of the center-of-mass energy in the collision) if they are not free, but bound to atoms. In this case, the treatment of the collision is similar to that of ionization in gas-phase collisions, where electronic excitations occur due to electron–electron interactions which promote electronic levels directly into the ionization continuum or through autoionizing states [5]. Atom–atom collisions can excite electrons from the projectile or the target and are thought to be the main mechanism ejecting electrons during impacts on gas-covered surfaces [18]. The atomic collisions considered here can occur between a projectile atom and a target atom, between fast target recoils and other atoms, or even between atoms in the projectile in the collision spike formed on impact.

2.3.1 Dependence of the Electron Yields on Ion Velocity Early measurements using atomic ions have shown that, at low velocities, the KEE yields have the velocity dependence γ = γo (v − vth ),

(2.2)

for ν not too close to νth . The extrapolated value of νth is ∼4.5 × 106 cm s−1 (10.6 eV amu−1 ) for gas-covered surfaces [19, 20], roughly independent of the type of bombarding ions. The implicit acceptance of (2.2) has inﬂuenced the way data have been plotted in the literature. One can ask whether the extrapolated value νth is aﬀected by a limited experimental sensitivity or the way the data are plotted. KEE yields induced by Xe+ ions on atomically clean gold [21, 22] depart from the linear behavior of (2.2) and do not have a deﬁnite threshold down to ν = 1.2 × 106 cm s−1 (100 eV). KEE down to 1.5 × 106 cm s−1 (160 eV) has previously been observed by Waters [23] for Cs on W who also found that gas adsorption increases the electron yields by three orders of magnitude at these low velocities. We will return to this last point later, because of its signiﬁcance for discharges. The model of KEE resulting from binary low velocity atomic collisions suggests that the projectile velocity be measured in terms of the characteristic velocity aΔE vc = , (2.3) which follows from Massey’s [24] adiabatic criterion, where a is the range of the interaction causing the transition with energy defect ΔE. At low velocities,

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this suggests a similar dependence that has been proposed for ionization collisions in the gas phase, using a straight-path approximation [25, 26], γ = γo exp(−vc /v),

(2.4)

or a sum of exponentials if several processes are present with diﬀerent values of νc . Breaks in the plot of log γ vs. 1/ν could then be used to identify diﬀerent excitation channels. In the limit of very low velocities, (2.4) should break down for at least two reasons (1) the inability to reach interatomic distances where the coupling to the continuum is suﬃciently strong and (2) the existence of an absolute binary threshold when the center-of-mass energy equals U . Situations close to this absolute binary threshold have been identiﬁed in the impact of relatively light ions on gas-covered surfaces [18], from comparisons with gas-phase ionization cross sections. Beyond the binary collision approximation, the minimum possible threshold results from energy conservation, when the projectile energy equals U . For this to occur, the lattice has to absorb all the momentum of the projectile and all the available energy has to go into the excitation of a single electron. This is very unlikely for heavy particle impact, since there is a large number of alternative pathways for the dissipation of the incident energy. 2.3.2 Electron Energy and Angular Distributions Ferr´on et al. [27] have measured electron energy distributions for 4 keV Ar+ on clean and oxidized Al and Mo surfaces. The peak of the distributions occurs at a few eV and there are relatively fewer high-energy electrons from oxidized surfaces. Other collision systems are characterized by electron energy distributions with sharp or broad peaks characteristic of speciﬁc processes, such as autoionization, plasmon decay, or the decay of shallow core levels [5]. Recently, the method of factor analysis of energy distribution curves has been used to identify diﬀerent mechanisms of ion-induced electron emission [28]. The angular distribution of ejected electrons has, in general, a cosine dependence on angle with respect to the surface normal. Structure is superimposed on this dependence in the case of experiments on single crystals, due to the diﬀraction of the electrons [29]. 2.3.3 Electron Emission from Contaminant Surface Layers Figure 2.1 depicts the results of analytical expressions given by Phelps and Petrovic [30] for electron yields γi (γa ) from metal surfaces under the impact of Ar+ ions (Ar neutrals) both for clean and contaminated (dirty) surfaces, based on a compilation of experimental data. This graph serves to illustrate several points. For Ar+ on clean surfaces, the electron yields are constant at very low energies, indicating the predominance of PEE. In contrast, Ar neutrals,

2 Electron Emission from Surfaces Induced by Slow Ions and Atoms

49

Electron emission yields

101

100

10−1

Ar+ 10−2

Ar0 10−3 10

100

1000

10000

Ion Energy (eV)

Fig. 2.1. Electron emission yields for argon ion and atom bombardment for clean (dashed curves) and dirty (continuous curves) metal surfaces (adapted from [30])

which carry no potential energy, do not produce PEE. The electron yields for neutrals are exclusively due to KEE and increase rapidly with energy above a threshold which is below 40 eV. The KEE component of Ar+ is essentially the same as that of Ar, due to the spatial separation of the PEE and KEE mechanisms. PEE occurs outside the surface by Auger neutralization producing neutral Ar which then enters the solid producing KEE. For dirty surfaces, the PEE yield by Ar+ is suppressed, a general property of PEE caused by the stronger bonding of electrons in adsorbates compared to metals. Strikingly, the KEE yield, seen clearly for neutral Ar, is much larger for dirty than for clean surfaces and the ratio decreases with increasing projectile energy, as reported earlier [31]. This behavior of dirty surfaces is similar to that of insulators which also have larger KEE yields than for clean metals or semiconductors. In most of the literature, this is attributed to a larger mean electron escape depth due to the reduced electron scattering for electron energies below the band gap. However, this eﬀect is not important at the low energies appropriate to electron discharges, where ion penetration is very shallow. A more important factor is the easier electron escape from insulators due to a reduced surface barrier. Comparative experiments on the adsorption of oxygen on clean Al and Mo surfaces showed very large eﬀects on the yields [27] with γ increasing for Al and decreasing for Mo. Since one can expect a similar electronic conﬁguration in the oxygen in both cases, the reason for the large diﬀerences in the two materials is not likely to result from diﬀerences in direct excitation. Rather, it was argued that yields were mainly aﬀected by the change in the surface barrier but not necessarily related to changes in the work function.

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2.4 The Role of Ion-Induced Electron Emission in Glow Discharges The pivotal role of electron emission yields in electrical discharges has become better understood in the last decades. Recent complex numerical models [32–39], categorized as ﬂuid, kinetic (Monte Carlo), and hybrid (combination), have shown that the modeled discharge characteristics are seriously inﬂuenced by the accuracy of the input data. Models require realistic cross sections for electron, ion, atom and photon collisions with the gas, as well as realistic probabilities for electron, ion, atom and photon interactions with electrode surfaces. Whereas the data for modeling the relevant gas-phase processes are relatively well known [30, 39, 40], those describing electrode processes are often uncertain, such as the electron emission yields from cathode materials under actual gas discharge conditions. Therefore, there has been signiﬁcant eﬀort spent lately in understanding issues associated with secondary electron emission processes in modeling the characteristics of gas discharges [30,40–45]. A comparison with measured voltage–current characteristics is generally the ﬁrst way to check the results of model calculations. An important parameter is the ratio of the electron to ion current densities at the cathode surface, γ = Je,tot /Ji,tot , called the apparent or eﬀective secondary electron emission yield per ion. The derivation of this quantity is not trivial, since several particles (positive ions, metastable atoms, fast neutrals, and photons) contribute to electron emission from the cathode and their relative importance changes with the operating parameters and conditions of the discharge. Furthermore, as compared with ion beam measurements of electron emission yields of heavily sputtered samples in ultrahigh vacuum, cathode materials operated under discharge conditions can have signiﬁcantly diﬀerent secondary emission yields [30]. Nevertheless, until recently, it was common practice to assume a value of γ independent of discharge conditions. An example of the eﬀect of the choice of γ is shown in Fig. 2.2, taken from [39], depicting the voltage–current density curve of the helium discharge for pL = 3 Torr cm, where p is the pressure and L the electrode separation. The simulation is based on a 1D hybrid model, using diﬀerent values of γ . As can be seen from Fig. 2.2, the particular choice of the value of γ results in pronounced diﬀerences in the calculated curves, none of which are consistent with experimental data. We note that the curve obtained assuming γ = 0.3, a value that corresponds to typical electron yields for He+ on clean metal surfaces, disagrees strongly with the experimental data. Figure 2.2 reports also the characteristic obtained from a ﬂuid model calculation, using γ = 0.16. It agrees quite well with experiment, suggesting that cathode was not cleaned by the low-sputtering yield of He since contaminated surfaces have low PEE yields. However, as discussed in [39], the ﬂuid model fails to reproduce other characteristics of the discharge, such as the spatial distributions of ion and electron densities.

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51

Fig. 2.2. Electrical characteristics of helium glow discharges. The 1D hybrid modeling results (ﬁlled symbols) obtained for pL = 3 Torr cm are shown for apparent secondary electron yield values γ = 0.1, 0.13, 0.16, and 0.3. kTe = 0.3 eV is assumed in the model. The dashed line is the result of a ﬂuid calculation with γ = 0.16 and kTe = 1 eV, while asterisk denotes experimental data obtained at pL = 3.38 Torr cm (from [39])

Phelps and Petrovic [30] reviewed the processes responsible for the production of the initial secondary electrons required for the growth of current at electrical breakdown and for the maintenance of cold-cathode discharge in argon, a commonly used as a benchmark gas for discharge studies. These electrons are produced in collisions of Ar ions, fast Ar atoms, metastable atoms, or photons with the cathode or in ionizing collisions of fast atoms or ions with the neutral Ar atoms in the gas phase. Since electron emission yields for ions, fast atoms, metastable atoms, and photons vary greatly with particle energy, surface conditions and discharge conditions, the eﬀective yield γ has to include the eﬀect of all the relevant mechanisms as accurately as possible. The authors assembled a large amount of data for photoelectric yields and secondary electron emission yields by argon ions and fast argon atoms, as a function of ion and atom energy, for a large number of diﬀerent metal surfaces, both clean and dirty. Since data for diﬀerent metal surfaces are rather close to each other, they made analytical ﬁts [30, 46] for electron emission yields as a function of impact energy for both clean and dirty surfaces, as shown in Fig. 2.1. The ﬁts should be best for KEE yields from contaminated surfaces

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because of the insensitivity to the target material. For clean surfaces, it is better to use the PEE yield from the ﬁt to a large number of materials [47] γp = 0.032(0.78Ei − 2φ).

(2.5)

Here Ei is the neutralization energy of the ion and φ the work function of the surface. For contaminated surfaces, the PEE is quite smaller, as shown in Fig. 2.1 for Ar+ (Ar0 only produces KEE). In this case, there is no equivalent expression to (2.5) since yields depend not only on φ but also on the type of contaminant. The analytical expressions provided by Phelps and Petrovic stimulated several studies that improved the description of discharge processes in argon [30, 39, 41–45]. Given the energy-dependent electron yields for each relevant process, the apparent yield can be calculated self-consistently from the simulation. As an example of the procedure, we mention here the work by Bogaerts and Gijbels [41] who developed a hybrid model to describe the discharge conditions typically used for analytical glow discharge mass spectrometry. In this technique, the material under analysis is used as the cathode of the glow discharge, and the particles sputtered by energetic plasma species are identiﬁed by mass analysis. Under the typical conditions of such a discharge, only Ar+ and fast Ar play a signiﬁcant role in electron emission from the cathode. Hence the apparent yield can be calculated from the simulation as γ =

Je,tot = Ji,tot

Ei,max 0

Fi (E)γi (E)dE + Ei,max 0

Ea,max 0

Fa (E)γa (E)dE

,

(2.6)

Fi (E)dE

where γi (E) and γa (E) are the yields induced by ions and atoms shown in Fig. 2.1 while Fi (E) and Fa (E) are the calculated ion and atom ﬂux energy distribution at the cathode. The energy distributions Fi (E) and Fa (E) depend on discharge conditions and may signiﬁcantly aﬀect the value of the eﬀective yield. For example, the model of Phelps and Petrovic calculates the eﬀective yield describing the ﬂuxes of electrons, ions, atoms, and photons in a spatially uniform electric ﬁeld. Attempts have been made to use this eﬀective electron yield, calculated for a uniform electric ﬁeld, to model also the cathode fall of abnormal glow discharge [40, 46]. The failure of these attempts led to intense debate [39, 40, 44, 46, 48], recently clariﬁed by Donk´ o and coworkers [39, 44]. Using a hybrid model, they showed that the diﬀerent electric ﬁeld distributions result in dissimilar energy distributions of species bombarding the cathode, thereby modifying the eﬀective electron yield. This points to the important fact that the electron emission yields induced by ions and neutrals (γi (E) and γa (E)) can be used in the simulations, but the eﬀective yield γ has to be calculated under the actual discharge conditions. The analytical expressions for γi [30, 46] were recently used in modeling the breakdown behavior in radiofrequency argon discharges [49]. The dependence of γi on the incidence angle θ was included and taken to be ∝ 1/ cos θ.

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53

It was found that, at low gas pressures, the breakdown voltage is a multivalued function of pressure, i.e., a single pressure corresponds to several breakdown voltages [50]. The multivalued branch of the breakdown curve could be reproduced only by taking into account the energy dependence of the ion-induced secondary electron emission yield. The inclusion of the angular dependence of the yield improved the agreement with experimental data. It is important to remark that many of the above-mentioned studies used the yields γi and γa for “dirty” metal surfaces. However, it is known that, for untreated metal surfaces, the KEE yields decrease with successive sputtering cycles as contaminants are removed [47] while, at energies below a few hundred eV, the PEE yields increase upon sputter cleaning. Furthermore, changes in the electron emission yields, due to spatial and temporal modiﬁcation of the surfaces of electrodes during the discharge, can produce plasma nonuniformities and instabilities in discharge parameters [51], which are major concerns in plasma-based processing of materials, such as ﬁlm growth and etching. We now consider the magnetically assisted magnetron glow discharges, where secondary electrons are trapped in the region near the cathode by an external magnetic ﬁeld. The electron conﬁnement allows operation at low pressures of a few millitorrs with typical applied voltages between 200 and 500 V, making the magnetron discharge very convenient for sputter deposition. The magnetic ﬁeld strength is adjusted to avoid aﬀecting the ions, which are extracted from the plasma and hit the cathode, where they give rise to sputtering and electron emission. Models of the magnetron discharge [35, 42], discussed in the following section of the book, show that sputtering is predominantly determined by ions of the buﬀer gas, with a much smaller contribution of fast neutral and a marginal contribution of sputtered target particles. Therefore, electron emission from the cathode is primarily determined by ion impact. The dependence of the magnetron discharge characteristics on secondary electron yields has been investigated by self-consistent calculations. As an example, Kondo and Nanbu [52] found with a Monte Carlo model a substantial decrease in both the electron density and ionization rate when decreasing γ from 0.15 to 0.12. Shidoji et al. [53] discussed the inﬂuence of the electron yield on the current–voltage characteristic of the Ar discharge using a hybrid model, with γ = 0.0005 Va, where Va is the applied voltage (in the range 240–400 V). The authors found that the Va in the simulated J–V characteristic was lower than the experimental value obtained with a Cu cathode, and an agreement required halving the value of γ, which they state would make it too small compared to experimental values. The authors attributed the discrepancy to diﬀusion loss of electrons. 2.4.1 Eﬀect of Electron Recapture at the Cathode Inelastic collisions and a fraction of elastic collisions prevent the ejected electrons from returning to the cathode. However, since the electron mean free

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R.A. Baragiola and P. Riccardi

path is inversely proportional to pressure, at the low gas pressures of a magnetron discharge [42,54,55], a signiﬁcant number of these electrons can return to the cathode and be recaptured without producing ionizations. The eﬀect of electron recapture on the argon discharge characteristics has been discussed in a simpliﬁed [54] and a detailed model of the dc planar magnetron [42]. Since electron emission from the cathode is primarily determined by ion impact, the eﬀective electron emission yield is given by [42] γ =

Nej − Nrec Nrec = γion − , Nion Nion

(2.7)

where Nej is the rate of electrons produced by ion impact, Nrec the rate of electrons recaptured at the cathode, and Nion the rate of ion impacts on the cathode. The eﬀective electron yield without recapture, i.e., only due to ion = Nej /Nion . The authors calculated impact at the cathode, is given by γion γion using the energy-dependent expression for γi given for clean metal surfaces [30]. For these types of surfaces, Fig. 2.1 shows that at the Ar+ energies typical of a magnetron discharge electron emission is determined by PEE with a nearly constant yield. The eﬀective yield γ is a function of the pressure and the electron reﬂection coeﬃcient RC, which in turn depends on the cathode material, including contaminant layers. Kolev and Bogaerts [42] calculated that γ is signiﬁcantly reduced by electron recapture and exactly one half of γ for the intermediate value of RC = 0.5. The inﬂuence of diﬀerent discharge parameters on the discharge voltage during magnetron sputtering has been recently discussed by Depla et al. [55] who compiled a list of electron emission yields for several metals from experimental data and empirical formulas found in literature [47, 56, 57]. As seen in Fig. 2.3, the discharge voltage for constant current operation of the magnetron resulted inversely proportional to the PEE yield of the target material [58]. This ﬁnding can be understood on the basis of the well-known equation proposed by Thornton [59] for Vmin , the minimum discharge voltage to sustain a magnetron discharge, W0 Vmin = , (2.8) γ εi εe where W0 is the eﬀective ionization energy (≈30 eV for Ar+ ), εi the ion collection eﬃciency, and εe the fraction of the maximum number of ions Vmin /W0 that can be made on average by a primary electron before it is lost from the system. Expressing the eﬀective yield γ as the product of the ion-induced electron emission yield of the target material γi and the eﬀective gas ionization probability E(p) [56], we get Vmin =

W0 . E(p)γi εi εe

(2.9)

Assuming a material-independent recapture probability and a constant pressure leads to the inverse proportionality between the discharge voltage and γi , reported in Fig. 2.3.

Inverse of the discharge voltage (x10−31 / V)

2 Electron Emission from Surfaces Induced by Slow Ions and Atoms

55

Ag Al Au Ce Cr Cu Mg Nb Pt Re Ta Ti Y Zr

4.0

3.5

3.0

2.5

2.0

1.5 0.00

0.05

0.10

0.15

0.20

ISEE coefficient Fig. 2.3. The inverse of the measured discharge voltage VAr as a function of the electron emission yields shown in the horizontal axis, for diﬀerent metallic targets, measured at a constant current of 0.3 A and argon pressure of 0.3 Pa. The error bars are based on the minimum and maximum values reported in the literature (from [55]) 60

β(x105V/A2)

50

Al Ag Au Cu Cr Mg Nb Re Ta Ti Y

40 30 20 10 0 0.05

0.10

0.15

0.20

Fig. 2.4. The inﬂuence of the electron emission yields (horizontal axis) on the coeﬃcient β (from [56])

The electron emission properties of the cathode material inﬂuence also the I–V characteristics of the discharge. The measured I–V curves [56] have been reproduced by the equation I = β(V − Vmin )2 [60], where β is a constant. As shown in Fig. 2.4, the value of β increases with increasing γi . As discussed

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R.A. Baragiola and P. Riccardi

in [56] this is because, for a ﬁxed discharge voltage, a higher γi produces a higher plasma density [52], which means a lower plasma impedance and, therefore, a higher value of β. 2.4.2 Eﬀect of Changes in the Chemical Composition of the Cathode It is noteworthy that, for some target materials (Al, Cr, Mg, Nb, Re, Ti) at low discharge current, the discharge voltage decreases with increasing current [55], possibly due to target contamination by residual gases during sputtering. Indeed, since water is the main species in the residual gas, its chemisorption on target surfaces cannot be ruled out, especially at low discharge current. Chemisorption is critical in reactive magnetron sputtering of a metallic target, where a reactive gas is added to the discharge to deposit a compound material. The addition of the reactive gas results in the formation of a compound material not only on the substrate (anode) but also on the target (cathode) where its formation is balanced by the sputtering process. This changes the electron emission properties of the cathode which, together with the modiﬁcation of the plasma composition, changes the plasma impedance. At a constant discharge current, this change of the plasma impedance results in a change of the discharge voltage. Whether the voltage increases or decreases with respect to the discharge voltage with metallic targets depends on the target material [61–63]. It has been found [60] that the discharge voltage during reactive sputtering of aluminum decreases when adding oxygen or nitrogen, in contrast to the case of other metallic targets. The diﬃculty in the understanding of these contrasting behaviors is that both the target condition and the plasma composition change when adding the reactive gas. A series of interesting experiments [58, 64] have been recently performed to study the behavior of the discharge voltage, at constant current, during reactive sputtering of oxides. In these experiments, the metal target is ﬁrst sputtered in pure Ar until a constant discharge voltage, VAr , is established. Then Ar was replaced by pure oxygen and the new discharge voltage, VO2 , was measured. In a third step, O2 was replaced with Ar and the discharge voltage with the oxidized target, Vox,Ar , was measured. In this way Vox,Ar can be directly compared to VAr , since both are measured under identical experimental conditions and plasma composition. As shown in Fig. 2.3, the measured discharge voltage for metallic targets VAr is inversely proportional to the ion-induced electron emission yield γi of the target. A straight line can be ﬁtted to the data in Fig. 2.3 1 = A + Bγi . VAr

(2.10)

Given the ﬁtting coeﬃcient A and B, which are only valid for a given series of experiments because they depend on the experimental conditions (discharge

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current, pressure, and magnetic ﬁeld), the authors attempted to extract the electron emission yield of the oxidized target as 1 1 −A . (2.11) γi,ox = B Vox,Ar The literature data for ion-induced emission yield of oxides are scarce. For magnesium oxide, the authors found a value of 0.4, which is of the same order magnitude of the value of 0.2, measured by ion beam experiments [65,66]. We note here that the yield obtained by this procedure should be more properly as deﬁned in (2.7), compared with the eﬀective yield without recapture, γion and may not be directly compared with ion beam-induced emission yields γi . In fact, (2.9) and (2.10) are based on a compilation of PEE yields for clean metal surfaces, i.e., constant yield γi in the ion energy range of interest for magnetron discharge for which γion = γi (see, e.g., (2.6)). For dirty or oxidized , surfaces and in general for KEE, there will be diﬀerences between γi and γion this last being determined by the dependence of γi on ion energy and by the ion energy distribution at the applied discharge voltage. The extent of this diﬀerence will depend on the narrowness of the ion energy distribution, but it should be carefully taken into account as it can be a source of discrepancy when comparing electron emission yields obtained by diﬀerent experimental techniques and procedures. Another source of discrepancy may be the assumption of a constant probability of recapture of electrons at the cathode. Chemisorption aﬀects the electron recapture at the cathode and hence the eﬀective ionization probability. As shown by Babout et al. [67] for copper, the electron reﬂection coeﬃcient decreases with oxygen exposure, i.e., recapture becomes more important. A remarkable ﬁnding of these experiments is that two groups of materials could be distinguished from the analysis discussed above: one where the electron yield increases on oxidation (Al, Ce, Li, Mg, Y) and one where it decreases (Cr, Nb, Re, Ta, Ti). This ﬁnding is in apparent contrast with the generally accepted idea that oxide materials have larger yields than metals, although it is not inconsistent with the diﬀerent behavior of Al and Mo upon oxidation [27], mentioned above. A suggestion for the uneven behavior of diﬀerent materials upon oxidation has been proposed based on a study by Wittmaack [68] of electron emission from n-type silicon bombarded with O+ and O+ 2 ions. A conclusion of this work is that the enhanced electron yield generated by oxygen implantation in silicon is directly proportional to the fractional coverage of the surface with SiO2 islands growing at the bombarded surface. Isolated oxygen atoms embedded in Si or suboxides (SiOx , x < 2) apparently produce only a negligible change in the electron yield. This interpretation, however, has not been accompanied by arguments based on electron excitation, transport, and escape mechanisms. Based on Wittmaack’s work, Depla et al. [58] concluded that the discharge voltage behavior during reactive sputtering of metal oxides originates in the formation of an oxide layer of the order of 1–2 nm, as estimated from the sum of the ion range and the straggle

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of the oxygen implanted during the plasma oxidation. The formation of this oxide layer changes the electron yield of the target; depending on the type of oxide formed during plasma oxidation and subsequent sputtering in argon, the yield is high (oxides) or low (suboxides). The low yield of suboxides is a very interesting feature that has not yet been elucidated and deserves further investigations with the use of in situ surface analysis techniques.

2.5 Outlook The description of the understanding of physical mechanism and its application to some types of gaseous discharges points to directions for research. The most important variable in electron emission seems to be the state of the surface, which changes dynamically during the operation of the electric discharge. This is because of the competition of sputtering which removes native surface contamination and chemical alterations due to ion implantation (in reactive discharges) and recondensation of impurities from surfaces in the vacuum system. Possibly the most promising ﬁrst step would be the study of electron emission yields using reactive gas ions over a range of targets, incident energies, and accumulated ion ﬂuences. Fundamental studies need to relate observed changes in electron yields to measured changes in surface composition, as determined, e.g., by X-ray photoelectron spectroscopy. This is particularly important to understand the materials dependence of the changes of electron yield upon oxidation.

References 1. J. Schou, in Physical Processes of the Interaction of Fusion Plasmas with Solids, Chap. 5, ed. by W.O. Hofer and J. Roth (Academic, New York, 1996) 2. K. T¨ oglhofer, F. Aumayr, H.P. Winter, Surf. Sci. 281, 1430 (1993) 3. D. Hasselkamp, H. Rothard, K.-O. Groeneveld, J. Kemmler, P. Varga, H. Winter, Particle Induced Electron Emission II (Springer, Berlin Heidelberg New York, 1992) 4. R.A. Baragiola (ed.), Ionization of Solids by Heavy Particles (Plenum, New York, 1993) 5. R.A. Baragiola, in Low Energy Ion-Surface Interactions, Chap. 4, ed. by J.W. Rabalais (Wiley, New York, 1994) 6. H. Kudo, Ion-Induced Electron Emission from Crystalline Solids (Springer, Berlin Heidelberg New York, 2001) 7. H. Winter, H. Burgd¨ orfer (eds.), Slow Heavy-Particle Induced Electron Emission from Solid Surfaces (Springer, Berlin Heidelberg New York, 2007) 8. B.A. Brusilovsky, Appl. Phys. A 50, 111 (1990) 9. S. Valeri, Surf. Sci. Rep. 17, 85 (1993) 10. R.A. Baragiola, Radiat. Eﬀ. 61, 47 (1982) 11. H.D. Hagstrum, in Chemistry and Physics of Solid Surfaces VII, ed. by R. Vanselow, R.F. Howe (Springer, Berlin Heidelberg New York, 1988), p. 341

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R.A. Baragiola and P. Riccardi E.V. Barnat, G.A. Hebner, J. Appl. Phys. 98, 013305 (2005) S. Kondo, K. Nanbu, J. Phys. D: Appl. Phys. 32, 1142 (1999) E. Shidoji, K. Ness, T. Makabe, Vacuum 60, 299 (2001) G. Buyle, W. De Bosscher, D. Depla, K. Euﬁnger, J. Haemers, R. De Gryse, Vacuum 70, 29 (2003) G. Buyle, D. Depla, K. Euﬁnger, R. De Gryse, J. Phys. D: Appl. Phys. 37, 1639 (2004) D. Depla, G. Buyle, J. Haemers, R. De Gryse, Surf. Coat. Technol. 200, 4329 (2006) L.M. Kishnevskiy, Radiat. Eﬀ. 19, 23 (1973) D. Depla, S. Heirweigh, S. Mahieu, J. Haemers, R. De Gryse, J. Appl. Phys. 101, 013301 (2007) J.A. Thornton, J. Vac. Sci. Technol. 15(2), 171 (1978) W.D. Westwood, S. Maniv, P.J. Scanlon, J. Appl. Phys. 54, 6841 (1983) R. Mientus, K. Ellmer, Surf. Coat. Technol. 116–119, 1093 (1999) D. Depla, R. De Gryse, Plasma Sources Sci. Technol. 10, 547 (2001) D. Depla, J. Haemers, R. De Gryse, Plasma Sources Sci. Technol. 11, 91 (2002) D. Depla, J. Haemers, R. De Gryse, Thin Solid Films 515, 468 (2006) P. Riccardi, M. Ishimoto, P. Barone, R.A. Baragiola, Surf. Sci. 571, L305 (2004) W.S. Vogan, R.L. Champion, V.A. Esaulov, Surf. Sci. 538, 211 (2003) M. Babout et al., J. Phys. D: Appl. Phys. 10, 2331 (1977) K. Wittmaack, Surf. Sci. 419, 249 (1999)

3 Modeling of the Magnetron Discharge A. Bogaerts, I. Kolev, and G. Buyle

3.1 Introduction Because of the industrial importance of sputter deposition magnetrons, there is a strong drive to simulate the entire magnetron deposition process, to replace trial-and-error experiments. This can lead to serious cost reduction, both for the manufacturers and the users of magnetron sputter equipment. The reasons are straightforward. For a typical coating plant, one of the main costs is the installation cost. Hence, it is a major advantage to have equipment that can realize a large throughput which ﬁts speciﬁcations like required deposition speed, uniformity, reproducibility, or target lifetime. This means that magnetron manufacturers strive to a minimum “setup time,” which requires from them the ability to predict whether the proposed design will work or not before the machine is actually built. This could be achieved by simulating the machines’ characteristics. Of course, also the possibility of optimizing the deposition parameters without actually performing any real world experiment is attractive. The ideal magnetron sputter deposition simulation would use as input the desired coating characteristics (e.g., electrical resistance, adhesion, refractive index, etc.) and process requirements (e.g., deposition speed, price per square meter, etc.). It would yield as output the necessary process parameters, e.g., sputter mode (DC, RF, pulsed, etc.), gas pressure, magnetic ﬁeld strength, electrical power input, etc. In reality, we are still far away from such a model. The model becomes more realistic when the input and output are switched (see Fig. 3.1). In this way, the parameters deﬁning the deposition process are the input; the deposited ﬁlm properties form the output. Such model is referred to as a “virtual sputter magnetron.” Eﬀorts are made to develop such a simulation tool, e.g., [1–4]. Now, we will consider the virtual sputter magnetron of Fig. 3.1 in more detail. Basically, it consists of the following modules: – Magnetic ﬁeld modeling – Magnetron discharge modeling

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System: geometry, B - field, electrical power,…

Magnetic field

Magnetron discharge

Particle Target interaction

Film properties: Physical: adhesion, conductance, hardness,… Economical: cost per m2,…

Transport in gas phase

Film growth

Fig. 3.1. Sketch of a virtual sputter magnetron, a simulation tool that would allow simulating the entire magnetron sputter-deposition process. The basic parts needed in such a tool are also shown

– Particle–target interaction, sputtering – Transport of the sputtered particles through the gas phase – Deposition and ﬁlm growth at the substrate From a scientiﬁc view-point, these modules cover a wide range of disciplines (plasma physics, surface physics, materials science, etc.). Some of the modules can be considered as known physics, others as challenging research topics. An example of the latter is the relation between the particles arriving at the substrate and the properties of the deposited ﬁlm. An accurate self-consistent virtual sputter magnetron that can operate over a wide range of parameters requires careful treatment of each of these modules. Like in a chain, the weakest link will determine the total strength: no matter how good the other modules, if there is one in the global model that is not accurate, the outcome of the whole model will be aﬀected. In the following, the diﬀerent parts will be very brieﬂy discussed and references to some relevant literature will be given. 3.1.1 The Magnetic Field Essential for a magnetron discharge is of course the magnetic ﬁeld. Hence, it is necessary for any simulation to have accurate values for the magnetic ﬁeld. This can be achieved for the most complex magnetic conﬁgurations with high accuracy by using ﬁnite element models that are available as commercial packages or as free- or shareware. Packages reported in the literature regarding magnetron sputtering simulation are, e.g., POISSON [5, 6], OPERA [7], FEMME [8] or ELF/MAGIC [9]. A disadvantage of this method is that a high accuracy is only reached for a very dense mesh, which makes the magnetic ﬁeld calculation time consuming. Very high accuracy is needed, however. Indeed, the length scale over which the electrons move during a time step when retracing their orbits is very small, in the order of 0.1 mm or less. For an accurate

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simulation of the electron orbits, the magnetic ﬁeld must vary smoothly over this scale length. Another possibility is to calculate the magnetic ﬁeld analytically. This has the major advantage that the ﬁeld strength can be determined almost instantaneously at any point in space, which guarantees the smooth variation of the magnetic ﬁeld along an electron orbit. Drawback is that only relatively simple magnetic conﬁgurations can be modeled and that the eﬀect of magnetic shunts or complex magnet shapes cannot be dealt with. The last possibility is to start from a measured magnetic ﬁeld and interpolating or ﬁtting it by an analytical expression. This also leads to a smooth spatial variation of the magnetic ﬁeld. Of course, in such an approach the principle of virtual coater is violated: it does not allow simulating diﬀerent magnetic ﬁeld conﬁgurations, unless they are built in reality and measured accurately. 3.1.2 The Magnetron Discharge The simulation of the magnetron discharge, based on the magnetic ﬁeld, the gas pressure, and the electrical power input, is the next step. The underlying basic physics is at microscopic level “only” the motion of charged particles in a region subjected to an electric and magnetic ﬁeld. This, combined with the necessary cross sections and electron yields, is in principle suﬃcient to describe the magnetron discharge. However, the emerging behavior of the plasma as a whole can be very complicated and turns this module of the virtual coater into one of the most diﬃcult hurdles to take. Indeed, the small timescales required for the electron motion (10−11 –10−12 s) combined with the large timescales required for reaching equilibrium (10−5 s) make the computational load of numerical modeling extremely, and for certain conﬁgurations even unrealistically, high (see also Sect. 3.2 below). As the magnetron discharge is in principle the heart of the process, it is surprising that the more advanced simulation of the sputter process presented in [2] can completely bypass this and the previous module. Instead, the simulation starts with a proﬁle characterizing the sputtered particles. This module of the virtual sputter magnetron will be dealt with more extensively in Sect 3.2, where the diﬀerent modeling approaches and their speciﬁc (dis)advantages will be discussed. Also the rest of the chapter will be devoted speciﬁcally to the magnetron discharge modeling. 3.1.3 The Particle–Target Interaction The sputtering process is based on the removal of target atoms by ion bombardment. The simulation of ion bombardment on a solid is well developed. These packages do not only allow determination of the sputter yield, i.e., the average number of atoms removed per incoming ion, but are also able to reproduce the angular and energy distribution of the atoms that leave the

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surface. Very well known are Monte Carlo (MC) codes, such as TRIM [10,11], SRIM [12], and packages based on these. These packages have as main shortcoming that they are not dynamical, i.e., changes in the solid because of the incoming ion ﬂux are not taken into account. Packages that take this into account are for instance TRIDYN [13, 14] and KALYPSO [15]. Another MC simulation package on sputtering is ACAT [16]. All the mentioned packages are numerical simulations, implying that the computational load is heavy. This is especially true for the dynamical codes. Hence, eﬀorts are made to determine properties like the sputter yield and the angular and energy distributions of the sputtered particles by analytical expressions. These analytical expressions can be purely empirical or can be based on a simpliﬁed model. For the sputter yield, an example of an empirical expression is the well-known formula of Matsunami [17], whereas an example of a simpliﬁed model is the work reported in [18]. Also for the energy and angular distribution of the sputtered particles analytical models exist. A nice overview of this issue can be found in [19]. 3.1.4 Particle Transport in the Gas Phase Once the particles are sputtered from the target, they start spreading out through the vacuum chamber. The collision dynamics of these rather low energy (typically some tens of eV or below) particles are known. However, discussion exists about which interatomic potential is to be used [20]. This is not an academic discussion as the choice of the interatomic potential inﬂuences the simulated energy and angular distribution of the sputtered particles at the substrate [21]. As such, the exact potential is required for realistic thin ﬁlm growth models. Ideally, the sputtered particle transport is described by combining a MC based model (for nonthermalized particles) and a diﬀusion model (for thermalized particles) [22]. In [23] the transport is described by a MC approach (SIMSPUD) and by a diﬀusion approach. Also in [24] a MC model is described. In [25] the ﬁlm thickness distribution is simulated using a MC model for diﬀerent target materials and for diﬀerent target-substrate distances at diﬀerent pressures. The results agree well with the experimental results, even for conditions where the ratio of the substrate and target diameter is large. Of course, also for this aspect of the magnetron sputter process simpliﬁed models have been developed, e.g., [26]. More information on simulations for particle–target interaction and particle transport in the gas phase can be found in the chapter “Transport of sputtered particles through the gas phase” by S. Mahieu et al. 3.1.5 Film Growth on the Substrate For this part, the input consists of the energy and angular distribution of the particles arriving at the substrate and their arrival rate. With “particles” is not only meant the sputtered particles but also the electrons and discharge

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gas particles (neutrals and ions) as they also contribute to the energy deposition at the substrate. The relation between this input and the resulting ﬁlm properties is one of the more diﬃcult parts when modeling the magnetron sputter process. A ﬁrst step is the simulation of the ﬁlm thickness distribution and/or its deposition rate, as this follows rather straightforwardly from the information about the incoming particles and the sticking coeﬃcients. In practice, in a lot of cases only this aspect is considered. A more advanced form of this is “feature scale modeling.” In microelectronics, the deposited coating might be required to ﬁll structures like a thin trench or via. Feature modeling tries to simulate the exact coating thickness on all surfaces of such a feature [27–31]. One step further is to actually simulate the microstructure of the deposited material. The most accurate simulations are based on molecular dynamics, but this is extremely computationally intensive. Consequently, (empirical) approximations are needed. A sound discussion of this problem together with some examples of predicted structures can be found in [32]. In [33] the deposition on grain boundaries was simulated for Ti. Examples of the microstructural evolution during ﬁlm growth (and the kinetic MC simulation thereof) can be found in [34]. Of course, also simpliﬁed models are developed, e.g., for the biaxial alignment in yttria-stabilized zirconia layers [35].

3.2 Overview of Diﬀerent Modeling Approaches for Magnetron Discharges The term numerical modeling refers to the process of ﬁnding approximate numerical solutions to a system of proper physical equations that adequately describe the system of interest. In a slightly broader aspect, also analytical models fall in this category. The latter are based on simpliﬁcations of globally valid, but complicated physical equations, rather than on numerical solutions of these globally valid equations. The choice of the proper set of equations is normally based on the given operating conditions. In other words, certain physical approximations are assumed already prior to the process of numerical solving, which in its turn introduces mathematical (numerical) approximations. The overall goal is always to obtain the most useful results at the lowest possible computational price. A complete model of a magnetron discharge must include the magnetron plasma and its interactions with (some of) the solid surfaces that surround it. There are two surfaces that cannot be omitted in a model. These are the cathode (also known as target) and the substrate where the ﬁlm is deposited. In many cases, the substrate is grounded, and therefore, acts as an anode. An intrinsic part of the operation of the magnetron is the eﬀective electric ﬁeld that results from the external power source and the movement of the plasma charged particles. Therefore, a procedure that calculates this ﬁeld

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should also be a part of the model. When the calculation of the resulting electric ﬁeld is included in the model, the model is called self-consistent. It should be mentioned that for real self-consistency, some external electrical circuit should be coupled to the magnetron plasma [36–39]. However in the literature, it is common to use the term self-consistent even when no external circuit is included. The existing models of magnetrons can be classiﬁed in several ways. The ﬁrst division is between analytical and numerical models. The numerical models can further be split into ﬂuid or kinetic models. The latter (i.e., kinetic) models can be based on numerical solutions of the Boltzmann equation, or on Monte Carlo (MC) simulations, also called particle simulations. These models are, however, not self-consistent, and need to be combined with a solution of the Poisson equation, resulting in either hybrid models or PIC-MCC simulations. In following sections, a literature overview of these diﬀerent modeling approaches will be given. 3.2.1 Analytical Models Analytical models (e.g., [40–57]) usually approximate the magnetron chamber with a one-dimensional (or sometimes even zero-dimensional) domain in the coordinate space, where the electric and magnetic forces are perpendicular to each other and the electron transport is considered in the direction parallel to the electric ﬁeld and perpendicular to the magnetic ﬁeld. In addition, the magnetic ﬁeld is considered constant. Such a picture results, however, in a particularly simple form of the electron transport coeﬃcients. Indeed, only the diagonal elements of the tensors of mobility and diﬀusion are nonzero and can be regarded as permutations of the mobility and diﬀusion referring to the nonmagnetized case [58]. In such an approach, classical diﬀusion is considered. Lieberman and coworkers [5, 41–43] have done many eﬀorts for developing analytical models for magnetron discharges. Wendt and Lieberman [5, 42, 43] developed a two-dimensional analytical model. The discharge area was split up into arch-shaped areas, with the shape determined by the magnetic ﬁeld lines. In this way, the authors were able to relate the width of the sputter erosion proﬁle to the discharge voltage and current, and the magnetic ﬁeld strength, through the Larmor radius [5]. Also the light emission could be described with this model [41]. In [43], two diﬀerent models for the movement of the electrons in a cylindrical postmagnetron have been proposed and compared with experimental data. In [46–48], a particularly interesting result has been the prediction of the appearance of a negative space charge region due to the highly restricted electron mobility at strong magnetic ﬁelds and low pressures. This result has been later on validated by more realistic particle simulations for both cylindrical [36] and planar magnetrons [37]. Recently, an analytical model has also been proposed for an RF sputtering system [49].

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Analytical models have also been used intensively by Bradley and coworkers. In a series of papers, they have investigated diﬀerent parts of the magnetron discharge, such as the cathode fall [50], the presheath [51], and the bulk plasma [52]. All these studies are based on an earlier work by the same author [59], which is a one-dimensional ﬂuid description. In [50, 51] the classical diﬀusion has been replaced by Bohm diﬀusion and the results have indicated that the later is a more realistic mechanism for the electron transport across the magnetic force lines. Recently, M¨ oller [53] proposed an analytical model for a reactive magnetron plasma (argon – nitrogen gas mixture), based on a balance between ion generation and transport. Ar+ , as well as N2 + and N+ , ions were considered in this model, and it was assumed that all ions, created in the plasma by electron-impact ionization, arrive at the target in a free-fall transport regime. Beside the diﬀerent ion ﬂuxes, also the ﬂuxes of reactive N atoms and N2 molecules to the target were estimated. These data formed the input for surface processes, such as sputtering and implantation for the various ions, and adsorption for the neutral species [53]. Finally, Buyle et al. have recently developed a self-consistent two-dimensional semi-analytical model for a DC planar magnetron, to reproduce the magnetron dependence on external parameters over a wide range [54–57]. This model will be explained in more detail in Sect. 3.4 below. A general disadvantage of analytical models is that they are unable to describe quantitatively the complex electron motion in the multidimensional electric and magnetic ﬁelds crossed at arbitrary angles, which is the situation in real sputter magnetrons, especially in the planar ones. However, analytical models have proven to be an important step in the understanding of magnetron discharges, with several advantages compared to complicated numerical simulations. Their main advantages are the relative simplicity, the ability to produce fast results, and the fact that the results are intuitively easy for understanding. They are particularly suitable in situations where the main purpose of the model is to deﬁne whether a given phenomenon is important or negligible. Such example is the electron recapture at the cathode, which has been studied by the semi-analytical model described by Buyle et al. (see also Sect. 3.4 below) [54–57]. The model has shown unambiguously the major importance of electron recapture at the cathode, and these results have later been conﬁrmed by particle simulations [37]. 3.2.2 Fluid Models Fluid models are based on the continuity, the momentum and mean energy conservation equations of the plasma species. By coupling these equations to the Poisson equation, the electric ﬁeld distribution can be calculated in a self-consistent way. Fluid methods ﬁnd extensive use, for instance, in the ﬁeld of aerodynamics. However, they are not so commonly used to describe magnetron

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discharges [48, 59–64]. Indeed, magnetron discharges cannot be so easily considered as a ﬂuid. The main reason is that they are operated at relatively low pressure (typically several millitorr). At such low pressure, the main assumptions of the ﬂuid theory are not necessarily valid. An additional diﬃculty arises from the complicated forms of the equations of the magnetohydrodynamics, which describe a magnetized ﬂuid. If these equations are applied to arbitrary magnetic and electric ﬁelds, they require elaborated discretization, resulting in long computation times. Another issue is the validity of the classical diﬀusion at high ratios of the magnetic ﬁeld and the gas pressure. At relatively weak magnetic ﬁelds and relatively high gas pressure, ﬂuid models with simpliﬁed transport coeﬃcients can be employed. This has been done in [61], where the bulk plasma in an RF cylindrical postmagnetron has been simulated and the results have been compared to a particle simulation. A ﬂuid description has been used also to develop a theory of the cathode sheath in magnetrons [62]. A two-dimensional ﬂuid model using the drift-diﬀusion theory has been reported in [63]. It is, however, applied to conditions, which are diﬀerent from typical sputtered magnetron conditions, i.e., a pressure of several torr and a magnetic ﬁeld weaker than 100 G. An attempt to overcome the complexity of the full magnetohydrodynamics equations of the electron transport [65] was recently proposed in [64]. In this paper, the presence of the magnetic ﬁeld is included as a perturbation to the ﬂux equations describing the nonmagnetized case and assuming a classical transport. However, it can be argued that the electrons are so strongly magnetized that this aspect cannot be represented in their transport by a perturbation. Hence, the condition for applying the perturbation formalism is thus violated.

3.2.3 The Boltzmann Equation The maximum information with minimum assumptions about the discharge can be obtained by kinetic models. As mentioned above, they can be divided into two groups: either solutions of the Boltzmann equation or particle simulations. The direct solution of the Boltzmann equation has been a popular tool for plasma modeling for many years. For magnetron discharges, the Lorentz force needs to be included. Adding the Lorentz force term, however, complicates signiﬁcantly the solver and makes it impractical in two and three dimensions and for arbitrary magnetic ﬁelds. There is one situation where it can, and has been, successfully used in magnetrons. This is the simulation of cylindrical postmagnetrons, where in a large part of the discharge the magnetic ﬁeld is one-dimensional and constant, which simpliﬁes the Boltzmann equation. This is illustrated by the work of Porokhova et al. [66–73]. To ﬁnd a self-consistent solution for a given input of magnetic ﬁeld strength, gas pressure and discharge current, the Boltzmann equation was

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supplemented by some other requirements. In [67], self-consistency was reached by adding an equation, describing the ion motion in the collisional regime (i.e., a ﬂuid model for the ions) and the Poisson equation. In [69] the radial distribution of the electric ﬁeld was determined by ﬁxing the discharge voltage to the experimentally measured one and by demanding that the radial potential distribution provides a radial electron density distribution that is similar to the experimentally measured one. This latter approach seems “less self-consistent” because both the discharge current and voltage are used as input parameters. In [67] the model was one-dimensional, whereas in [69] the model was extended to two dimensions, so that also the axial inhomogeneities generated by the shields at the ends of the cylindrical postmagnetron can be modeled. A major advantage of the method is the small computational load: a typical calculation requires about 2–10 min, depending on the number of grid points [74]. The presented results in the above-mentioned references show a very good agreement with experimental data. However, the results were obtained at relatively high gas pressure (above 3 Pa) and relatively weak magnetic ﬁeld strengths (maximum 400 G). It would be interesting to see whether this modeling approach can deal with low pressures and strong magnetic ﬁelds, as these are the working conditions where anomalous electron transport can be expected. Furthermore, it is also not evident to adapt this technique to a twodimensional model for the planar magnetron discharge, due to the nonuniform magnetic ﬁeld [74].

3.2.4 Monte Carlo Simulations In MC simulations, computational test particles that represent a large number of real plasma particles are followed. Their movement is subject to the applied forces and the collisions of the particles are included by using probabilities and random numbers. This technique is very easy to implement and fast to compute. Its main disadvantage is that the forces must be an input, i.e., the simulation is not self-consistent. There are many MC simulations, often called direct Monte Carlo simulations (DMCS), of diﬀerent types of magnetrons reported in the literature. Among them are [75–83], which have contributed largely to the understanding of the transport and collision properties of the charged particles in magnetron discharges. The group of Sheridan–Goree et al., e.g., [75–79], was able to simulate the ionization distribution using a two-dimensional MC model and compared it with optical emission measurements. The basis of their model was a simple retracing of the high energy electron orbits by numerically integrating the Lorentz equation and combining this with a MC approach for the collision events. Similar work is reported in [84,85]. The group Sheridan–Goree also simulated the ion motion [78] and the inﬂuence of the magnetic ﬁeld [79] using the same Monte Carlo model.

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Ido et al. used a MC model to simulate the erosion proﬁle in planar magnetrons. First, the erosion proﬁle in a cylindrical and a rectangular magnetron was simulated for various pressures and magnetic ﬁeld conﬁgurations [85–87]. Then, the erosion proﬁle using ferromagnetic targets was simulated. They report how the eroded region can be inﬂuenced by placing a ferromagnetic ring on top of the target [88] and by the outer part of the yoke [89]. For a ferromagnetic target, the eroded region strongly inﬂuences the magnetic ﬁeld strength. In [90] it is reported how this eﬀect is taken into account, which leads to a very accurate erosion proﬁle simulation. The main advantages of the MC method are that it is easy to implement, it can handle the low gas pressures encountered in magnetron discharges, and it is much faster than self-consistent methods, such as PIC-MCC models. Therefore, it can be used on (large) three-dimensional geometries, see e.g., [91– 96]. In all these references the MC model is basically used to investigate the cross corner eﬀect. This term is used to denote the enhanced ionization and erosion that occurs at opposite sides of a (long) rectangular target, and which is attributed to a disturbed E × B drift of the electrons after they drifted through the end region of the racetrack. Here, the MC method has an advantage over the PIC-MCC method: In [97] a three-dimensional magnetron was simulated but the variation of the ionization along the racetrack was too large to notice the cross corner eﬀect. Although the PIC-MCC method should undoubtedly be able to reproduce this eﬀect, it would cost an enormous computational eﬀort. Another example illustrating the beneﬁcial use of a MC model is the explanation of the so-called plasma emission redistribution (PER) eﬀect [98]. This eﬀect occurs during pulsed magnetron sputtering. When the plasma emission of a single pulse is observed, it was noticed that at the very beginning of a pulse the emission came predominantly from the turnaround regions of the racetrack, whereas in steady state, the emission came predominantly from the central straight sections of the racetrack. Using a MC model and adapting the settings for the situation at the very beginning of a single pulse, this eﬀect could be reproduced and the origin of the eﬀect could be retraced, as explained in [98]. Finally, the last application mentioned here for MC simulations of magnetron discharges is the simulation of the sputtered atoms transport, as was also brieﬂy discussed in Sect. 3.1.4. These are normally non-self-consistent trajectory calculations of the sputtered particles with included collisions with the background gas atoms [23, 24, 89, 91, 99–105]. In this way the spatial distribution of the sputtered atoms and their energy and angular distribution at the substrate are calculated. This allows accurate predictions for the quality of the deposited ﬁlm. Possible eﬀects of the spatial location of the target and the substrate can be easily studied. Input is needed for the starting positions of the sputtered atoms at the cathode. This is usually taken either from an experimentally measured erosion proﬁle or from a calculated erosion proﬁle by a particle model.

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3.2.5 Hybrid Models While electrons are heavily magnetized, as discussed above, the ions can be considered practically nonmagnetized, due to their large masses. Therefore, in contrast to the electrons, they can be well described by a classical ﬂuid approximation. This assumption forms the foundation of the so-called hybrid models. Hybrid models are usually a combination of ﬂuid and particle models. In the simulations of nonmagnetized glow discharges (e.g., [106]), the ions and the bulk electrons are regarded as a ﬂuid, while the energetic (beam-like) electrons, emitted from the cathode or generated in the sheath, are simulated as particles, i.e., fully kinetically. This approach combines the precision of the kinetic models with the relatively higher speed of the ﬂuid codes and successfully overcomes the low pressure restrictions. Magnetron simulations based on the hybrid model are explained in [9, 107–115]. Shidoji et al. were able to simulate the magnetron discharge and its dependence on external parameters, such as the gas pressure, the electrical power [92], and the magnetic ﬁeld strength [114]. Also the inﬂuence of balancing the magnetic ﬁeld [111] and of depositing an insulating layer [109] were investigated. Vyas and Kushner [31] used a modiﬁcation of their twodimensional hybrid plasma equipment model [115] to simulate a hollow cathode magnetron discharge. The eﬀect of power and pressure was investigated, as well as the inﬂuence of magnitude and orientation of the applied magnetic ﬁelds. The limits of validity of hybrid modeling for magnetron discharges are discussed in [112]. It is reported that the application of the hybrid model becomes problematic for strong magnetic ﬁelds and/or low gas pressures. Indeed, in such cases the results appear unrealistic: a large amount of ionization occurs at rather large distance from the cathode. The reason is that at high magnetic ﬁeld strengths the electrons hardly diﬀuse across the magnetic ﬁeld lines anymore when using the classical theory. Consequently, an electric ﬁeld is formed between the sheath region and the anode. Because of this electric ﬁeld, ionizations occur in that region. Also the simulation results reported in [114] express this behavior: The ionization in the region from 10 to 40 mm above the target is stronger for a magnetic ﬁeld strength of 360 G than for 180 G but the peak ionization is lower. This is opposite to the behavior reported in [116]: there the simulated peak ionization rate increases with increasing magnetic ﬁeld. The latter result appears more realistic, as the magnetic ﬁeld is applied to the discharge to intensify the magnetron discharge, not to spread it out. The problem of the hybrid model to deal with strong magnetic ﬁelds is probably due to the fact that it does not account for the anomalous electron transport. Indeed, as mentioned, the slow electron transport is typically treated using a ﬂuid model. This requires the electron diﬀusion coeﬃcients

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for the transport perpendicular to the magnetic ﬁeld lines. This coeﬃcient is obtained using the classical theory, i.e. D⊥ =

DB=0 1+

ω2 ν2

,

with D⊥ the diﬀusion coeﬃcient in the direction perpendicular to the magnetic ﬁeld lines and DB=0 the one without magnetic ﬁeld. However, according to experimental evidence (e.g., [117]), the diﬀusion across the magnetic ﬁeld lines is larger than predicted by D⊥ . This problem of uncertainties in the electron transport coeﬃcients has been partially overcome by using the data provided by a parametric study performed by numerical solution of the Boltzmann equation for given sets of reduced electric and magnetic ﬁelds [113]. Similarly, Vyas and Kushner [31] derived the transport coeﬃcients, for use in the ﬂuid equations, from a kinetic simulation, to enable the ﬂuid algorithm to represent more accurately the low pressure operation. The second limitation of a hybrid model is the fact that the ions are not at all characterized by a Maxwellian distribution, which questions their description as a ﬂuid. The third problem is related to the criterion of selecting which electron can be considered slow. In the nonmagnetized situation [106] the discharge is in a positive space charge mode. Hence, once the electron has traversed the sheath and has an energy below some threshold, it can be transferred to the slow group. In magnetrons, depending on the reduced magnetic ﬁeld, there can be a negative space charge mode. This means that even if the electron energy is below the threshold at a given moment, the electron can still become fast. This is deﬁnitely the situation at high reduced magnetic ﬁelds. This situation has led to a modiﬁcation of the classical hybrid scheme, where all the electrons are treated kinetically, while only the ions are described as a continuum [114]. In this way, the ﬁrst and the third drawbacks are eliminated, but the computational cost, however, approaches that of a particle model. In conclusion, the main advantage of the hybrid model is that it is faster than the PIC-MCC models discussed below (a solution can be obtained in 2–3 days). The payoﬀ for this advantage is that assumptions need to be made about the slow electron motion in crossed electric and magnetic ﬁelds. Because of the latter, this technique seems to fail to describe the anomalous electron transport that occurs for strong magnetic ﬁelds and/or low gas pressures. 3.2.6 PIC-MCC Simulations When the calculation of the electric ﬁeld produced by the external power source and the spatial distribution of the plasma charged particles is added to a MC simulation, the whole simulation becomes self-consistent. It is commonly referred to as PIC-MCC simulations [118]. PIC-MCC simulations are the most powerful numerical tool for the investigation of magnetron discharges. They

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can cope with the low operating pressures and the strongly inhomogeneous ﬁeld and density distributions. In addition, they are capable of providing a full picture about the processes occurring in the discharge chamber. The drawback of the PIC-MCC simulations is their extensive computational load. This is especially true when two- and three-dimensional simulations are needed, especially for simulating magnetron discharges. The latter is related to the long characteristic times (typically longer than 10−5 s) for achieving a steady state. Simulations of cylindrical postmagnetrons have been performed in one dimension [36,119]. Planar magnetrons can, however, not be simulated with a one-dimensional code. A full three-dimensional PIC-MCC model of a planar magnetron has been reported [97,120]. It has shown the lack of angular dependence in axisymmetrical planar magnetrons. This result has opened the way for simulating this type of magnetrons by a two-dimensional model in cylindrical coordinates. The ﬁrst very thorough work of that kind has been [116] followed by [121]. The PIC-MCC method has also been successfully applied to RF sputter magnetrons [122]. Moreover, quite some work reports planar magnetron simulations using the OOPIC code [4,6–8]. This OOPIC code was developed by Verboncoeur et al. [123] and can be downloaded freely [124]. Another software package that is used for magnetron discharges is PEGASUS, which combines PIC-MCC simulations with Gaussian ﬁtting, to investigate the erosion [125]. The software itself is described in more detail in [126, 127] and is based on NEPTUNE. The latter is used in [1] to simulate copper deposition by magnetron sputtering. Furthermore, the inﬂuence of the dielectric target in an RF sputtered magnetron has been investigated in [128]. Recently, a hybrid PIC-MCC – ion relaxation model has been reported [129]. Here, the electrons are resolved in a standard PIC-MCC algorithm, whereas the ionic distribution is calculated by a continuum relaxation model. In [4] and [6] it is reported that no steady state is found in the PIC-MCC simulations, but the number of particles was continuously increasing. In both cases, however, the time during which the plasma is simulated was very short (5 and 3 μs, respectively). Following the discharge for a longer time period apparently leads to a steady state, e.g., [8, 97, 116]. However, it can be argued that a reliable steady state, i.e., a steady state where the discharge evolves to the correct region of the current–voltage characteristic, can only be reached by including an external electric circuit [37]. The required time for reaching convergence is then typically about 20 μs [37], whereas the results of [8] suggest that convergence was reached after roughly 10 μs. We have developed our own PIC-MCC model for a planar magnetron discharge, which includes the external circuit [37] and accounts for the gas heating and the sputtered atom transport and collisions [38]. This model will be discussed in detail further in this chapter. It is clear that PIC-MCC simulations produce a wealth of data. However, care has to be taken when interpreting the results. Here we mention some shortcomings of the results reported by the group of Nanbu et al. [97,116,121]. First, the time step Δt used for the electron orbits is rather large: in [116]

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it is mentioned that Δt ≈ 0.2 ns. The examined magnetrons have Bmax in the range of 325–650 G. With these Bmax correspond Larmor frequencies of 6–11 GHz, which means that Δt varies from 0.18 to 0.36 times the inverse of the Larmor frequency. In [130] it is argued that such large time steps result in an inaccurate orbit calculation and in a serious artiﬁcial electron energy loss. These inaccuracies compromise both the position and the amount of ionization simulated, which seriously questions the reliability of the presented results. This might be the origin of the second shortcoming of these simulations: the simulated cathode sheath thicknesses are very large, in [116] sheath thicknesses vary from 4.5 to 5.8 mm. In reality, a sheath thickness of at most 3 mm is observed (e.g., [91, 130, 131]). Third, the current densities are extremely low for magnetron discharges. From the sketch of the magnetron conﬁguration in [116] we can infer a racetrack surface of roughly 24 cm2 (racetrack length ≈24 cm and width ≈1 cm). The total currents listed in the article are between 35 and 50 mA, which means current densities around 1.5–2.1 mA cm−2 . These values are at least a factor 10 lower than the current densities typically encountered in magnetron sputtering. This discrepancy can again be attributed to the necessity of including an external electric circuit [37]. The fourth remark concerns the simulated current–voltage characteristics: With increasing discharge voltage the discharge current and the electron density are found to decrease, the cathode sheath thickness is found to increase [121]. These simulated dependences are opposite to experimental observations (e.g., [130, 132]). On the other hand, a very interesting result of the PIC-MCC simulations is the magnetic ﬁeld dependence: in [116] the magnetic ﬁeld strength Bmax is varied from 325 to 650 G at constant discharge voltage (Vd = 500 V) and gas pressure (0.67 Pa). The simulations show an increase in the plasma density and in the ionization rate. Moreover, the discharge intensiﬁes and the cathode sheath thickness is found to decrease. This is in agreement with common sense: with increasing magnetic ﬁeld strength, the magnetron intensiﬁes and is better conﬁned. This result seems to indicate that the anomalous electron transport is, at least qualitatively, correctly simulated (see also the discussion about the hybrid model above). In spite of the mentioned shortcomings, the PIC-MCC technique is in principle a very viable method. Hence, we may conclude that PIC-MCC simulations are the most powerful tool to tackle the problem with the full description of the planar magnetrons at all operational conditions. The price for that, however, is the very long computation time.

3.3 Challenges Related to Magnetron Modeling No matter how sophisticated a simulation model is, there are some limitations to what can be expected from the calculation results. The origin of this might be due to inadequate experimental input data or to the speciﬁc geometry or

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operating conditions of the process. As such, these situations can be called problem cases or, more positive, challenges related to magnetron modeling. Here, we give a list of the most important ones of these challenges. 3.3.1 Secondary Electron Emission Yield (γ) The secondary electron emission yield γ denotes the number of secondary electrons emitted per incoming ion. The magnetron characteristics depend very strongly on the exact value of the secondary electron emission yield. Unfortunately, these yields are extremely diﬃcult to measure. Consequently, for most materials this yield is not accurately known. This is probably the most fundamental factor limiting the output of magnetron simulations: whatever model used for the magnetron simulation, it can only give accurate results when the applied secondary electron emission yield is correct. In Shidoji et al. it is mentioned that reducing the secondary electron emission yield by 50% can decrease the currents with a factor four to ﬁve [9]. In [116] an increase of the secondary electron emission yield from 0.12 to 0.15 leads to a substantial increase in the plasma density (from 1.1 to 1.7 × 1010 cm−3 ) and in the discharge current (from 34.9 to 49.5 mA). Given this situation, the values for the secondary electron emission yield used in magnetron simulations strongly vary. Usually, γ is taken to be independent of the discharge voltage (e.g., in [97,120]). On the other hand, Shidoji et al. use a secondary electron emission yield that depends on the discharge voltage [9]. Sometimes, quite unrealistic values for the secondary electron emission yield are used, e.g., in [133] where for certain conditions a secondary electron emission yield of 5 is assumed for a metal surface. Also in [125] γ is used as a tuning parameter: the authors mention that it is set to 0.03 as a larger value sometimes leads to the unbounded increase of superparticles, i.e., the simulation does not reach a steady state but the plasma density continues to increase. The challenge here is to make the magnetron simulations so reliable that, once the model is calibrated using a material with a relatively well-known secondary electron emission yield, comparison of the experimental and simulation results can be used to determine the secondary electron emission yield of the investigated target material. This is, however, a very ambitious goal, due to the many other uncertainties in the models. Therefore, eﬀorts should also be made for accurate measurements of the secondary electron emission yield. In this respect, Depla et al. recently determined ion induced secondary electron emission yields for several oxides [134]. 3.3.2 Recapture The orbit of a secondary electron emitted from the target follows the magnetic ﬁeld lines. When the electron does not interact with the discharge gas, this will lead to an electron–target interaction. This event is characterized by

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the reﬂection coeﬃcient R, which gives the probability that the electron is reﬂected. If the electron is not reﬂected, it is recaptured by the target (see also Sect. 3.4 below). To simulate this eﬀect accurately, the initial electron energy may not be neglected, the orbit calculation should be performed very accurately and the reﬂection coeﬃcient R needs to be known. The required accuracy has important consequences as it can only be reached by reducing the time step used for retracing the electron orbits, which seriously increases the computational eﬀort. In [130] it is shown that the time step needs to be at least a factor of two smaller than currently encountered in magnetron simulations. Second, experimental values of R, needed as input for the simulation, are very scarce. This is highly inconvenient because the process of recapture is quite sensitive to this reﬂection coeﬃcient [37, 135]. 3.3.3 Electron Mobility The problem of the anomalous electron transport was already mentioned above in Sect. 3.2.5. Indeed, the electron transport in the direction perpendicular to the magnetic ﬁeld lines is larger than expected from classical diﬀusion theory. The enhanced mobility is probably due to oscillations in the electric ﬁeld. This eﬀect has its consequences for magnetron modeling. Obviously, all methods that rely on the classical theory are aﬀected. This is especially true for the models that rely on the ﬂuid theory, as this requires diﬀusion coeﬃcients (see also the discussion about the hybrid model in Sect. 3.2.5). In principle, the PIC-MCC method should be able to deal with this problem as it uses no assumptions about the particles. However, a culprit here might be the timescale at which the phenomena occur. A broad range of oscillation frequencies have been observed in plasmas, but the typical frequency range is of the order of some 100 kHz, corresponding with a period of 10 μs. Logically, it can be assumed that the discharge only reaches a steady regime after some oscillation periods. This means that the discharge should be followed during a time span of at least 50 μs. Usually, PIC-MCC simulations are not performed for such a long time, implying that they will not accurately describe the eﬀect. A possible way to model the enhanced electron mobility is by adding an extra type of collisions, the so-called Bohm diﬀusion collisions. The contribution of Bohm diﬀusion can then be tuned until the simulations correspond with the experimental measurements. This will be brieﬂy explained for the analytical model in Sect. 3.4. For the modeling of Hall thrusters, a similar technique has been used, see e.g., [135, 136]. 3.3.4 Modeling “Industrially Relevant” Magnetron Discharges Of course, the magnetron discharges used for industrial sputter deposition purposes are not fundamentally diﬀerent from the ones used in laboratories.

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Nevertheless, there are some aspects that make them extremely challenging to simulate. In principle, including these characteristic features in the models is not a fundamental problem, but it will make the simulations much more computational intensive. Given that the computational load is already high (order of several days for both the PIC-MCC and hybrid models), it is clear that an industrially relevant virtual sputter magnetron is not for the immediate future, even taking into account Moore’s law, which states that the computation power doubles, on average, every 18 months. In the following, a few of these challenges will be outlined. Geometry Although it is not a fundamental limit, the geometry of the magnetron considered can make certain models useless. In the glass coating industry, magnetrons with cathodes up to 4 m long are used. For such dimensions, the PIC-MCC technique becomes useless because of the unrealistically high computational eﬀort. Hence, less computational intensive methods are needed. An example is the simulation of the eﬀect of the turnaround region on the uniformity. For this type of simulations the MC method is currently used (see Sect. 3.2.4 above). Although the latter model has the disadvantage that the inﬂuence of the anode cannot be modeled self-consistently, it is still the preferred method for such large-scale magnetrons, as the computational load of the PIC-MCC would be forbiddingly high. (High Power) Pulsed Sputtering For industrial applications, pulsed sputtering is frequently used. The typical frequency range is in the order of 10–100 kHz. To simulate such processes, the magnetron needs to be followed for several periods, i.e., several times 100 − 10 μs. At this moment, this cannot be achieved by PIC-MCC modeling. A good candidate for this type of problems would be a hybrid model. Currently, high power pulsed sputtering is gaining interest because of its potential to deposit coatings with unique properties. In such discharges extremely high electrical powers are applied during short intervals. Because of the high plasma density, typical approximations made in magnetron modeling are not valid anymore. First, the magnetic ﬁeld strength in the magnetic trap region changes because of the large Hall currents induced during the high power on-pulse [137]. In all simulation models known to us, this inﬂuence is not accounted for. Second, because of the high ionization degree in these high power discharges, it will not be possible anymore to neglect the interactions between charged particles (Coulomb collisions). Again, most simulation models for planar magnetrons neglect this type of interactions. In [138] a cylindrical postmagnetron is simulated with a PIC-MCC model, taking into account electron–electron interactions, albeit in a simpliﬁed way. We have included

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these interactions in our PIC-MCC model [38, 39], based on the method described by Nanbu [139–141]. Third, the gas density reduction or gas rarefaction: in Sect. 3.6, it is discussed how the energetic plasma particles can heat the discharge gas, which leads to a gas density reduction. For standard operating conditions, this eﬀect can be neglected. However, in high power pulsed sputtering this will not be the case. This eﬀect is usually not accounted for in magnetron models. To our knowledge, only the PIC-MCC model described in this chapter (Sect. 3.6) is able to deal with this eﬀect [38, 39]. Accuracy The speciﬁcations for sputter-deposited coatings can be very strict. A typical example is the required coating uniformity. Even for large area coating of glass (with cathode lengths of almost 4 m) the required uniformity is usually better than ±0.2%. It is not evident for a numerical technique to reach this level of accuracy. For an MC technique, the only way to reach this is by following a suﬃciently large number of particles, i.e., the accuracy comes at the cost of computational load. Apart from this, several other eﬀects inﬂuence the accuracy at this scale. Some examples are the gas heating due to sputtered particles and the resulting gas density reduction, a nonuniform gas inlet, the inﬂuence of the erosion groove formation on the process, redeposition on the target, heating of the target, the inﬂuence of the sputtered particles, etc. Again, all of these examples form no fundamental problem, but they might seriously increase the computational eﬀort. Basically, the mentioned eﬀects are all examples of “extended self-consistency.” Usually, in magnetron modeling the term self-consistency is used with respect to the electric ﬁeld. However, because of the on-going sputtering and deposition during the process, the environment of the magnetron changes. For a very accurate magnetron simulation, also these changes have to be taken self-consistently into account.

3.4 Two-Dimensional Semi-Analytical Model for a DC Planar Magnetron Discharge In this section, the self-consistent two-dimensional semi-analytical model developed by Buyle et al. for a DC planar magnetron [54–57, 130] will be explained in more detail, because it is very powerful, in spite of its simplicity. Also some characteristic results will be presented.

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3.4.1 Description of the Model Ionization Model First of all, an ionization model was developed, to calculate the ionization rate due to the high energy electrons, i.e., deﬁned as the electrons with energy above the threshold for ionization. For this purpose, the discharge area was split into arch-shaped regions. This can be justiﬁed, because the collisionless motion of these high energy electrons is limited to such arch-shaped regions. The eﬀect of electron collisions with the background gas was analytically modeled as a probability for the electrons to hop from one arch to another. Output of this model was the spatial distribution of ions, generated by a single electron emitted from the target. It was found that the ionization distribution is not directly inﬂuenced by the gas pressure. This characteristic could be used by future models for magnetron discharges, to reduce the computational load. Another important result was that a substantial amount of ionization occurs in the cathode sheath of the magnetron. This so-called sheath ionization is important because the electrons generated in this way can be further accelerated and give rise to more ionization. This eﬀect was characterized by a multiplication factor, which is deﬁned as the ratio between the total number of ions generated due to the emission of a single electron, and the theoretical number of ions that can be generated without sheath ionization. The multiplication factor was found to be close to one for electrons emitted at the edge of the racetrack, but it can rise to values of 3–5 for electrons emitted close to the racetrack center. Therefore, an average multiplication factor, m, was introduced. Eﬀect of Electron Recapture Furthermore, the process of electron recapture at the cathode was taken into account by introducing the eﬀective gas interaction probability (EGIP), deﬁned as: s EGIP = f = 1 − exp − , (3.1) l where s is the average distance traveled by the electron before it is recaptured at the cathode and λ is the mean free path length of the electron. For typical magnetron operating conditions (300 V discharge voltage, 600 G maximum magnetic ﬁeld strength, and 0.5 Pa gas pressure) the EGIP was typically found to be around 1/3, i.e., about 2/3 of the electrons appears to be captured. Self-Consistent Model The model was made self-consistent by considering the ionization distribution from a large number of electrons emitted from the cathode, taking into

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account the multiplication factor and EGIP for each electron. Indeed, from the ionization distribution, obtained in this way, the ion bombardment at the target can easily be deduced. This determines the average number of emitted electrons, based on the ion-induced secondary electron emission yield (γ). In this way, the model is made self-consistent, by iterating through this process, and demanding that the original and the new secondary electron emission proﬁles should be identical. With this model, the Thornton relation [142] for determining the minimum discharge voltage at which the magnetron can be maintained is extended to a general relation: W , (3.2) Vd = γ < f m > εe ε i where W is the eﬀective ionization energy (∼30 eV for argon), εi is the ion collection eﬃciency, and εe stands for the theoretical number of ions that the electron eﬃciently generates before it is lost from the discharge. Both εi and εe can be assumed equal to one for typical magnetron conditions. Note that in the original Thornton relation, sheath ionization is not considered (m = 1) and the EGIP (f ) was assumed equal to 0.5. Because the model developed by Buyle et al. is two dimensional and includes the magnetron conﬁguration (geometry and magnetic ﬁeld strength), f and m can be calculated more accurately. This extended Thornton relation illustrates that the pressure and magnetic ﬁeld inﬂuence the magnetron discharge through f and m, as all the other quantities in the formula are constant for a given target material and typical magnetron conditions. Calculation of the Discharge Current Furthermore, to deduce the discharge current (Id ) from the obtained magnetron properties, the line current density, jm , was introduced, which is related through the racetrack length, Lrt as: Id = jm Lrt . To determine jm , the Child-Langmuir law had to be extended, leading to the following relation for jm : ! jm = jd A||,t A||,s

B(x)dx,

(3.3)

where jd is the surface current density, the factors A,t and A,s account for the fraction of ions generated within the sheath (typically between 1/4 and 1/2), and for the ions that are generated scattered over the racetrack length, respectively. Finally, the integration is needed to convert the surface current density, jd , into the line current density, jm , and accounts for the nonuniformity across the racetrack (x is the direction across the width of the racetrack). Using this relation, the discharge current could be calculated. The model was able to reproduce the behavior of the magnetron discharge with decreasing pressure and constant current. Also typical current–voltage characteristics

3 Modeling of the Magnetron Discharge

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could be simulated. However, it appeared that the extreme steepness of the current–voltage characteristics was missing, and that the inﬂuence of the magnetic ﬁeld on the gas pressure dependence was not retrieved. This example clearly illustrates the possibilities and limitations of analytical modeling. Eﬀect of Coulomb Collisions and Anomalous (or Bohm) Transport Finally, to resolve the discrepancy between the simulated and experimental results, two processes not included in the model so far were examined, i.e., Coulomb collisions and Bohm (or anomalous) diﬀusion. The ﬁrst process could explain the magnetic ﬁeld dependence of the pressure eﬀect in cylindrical (or post) magnetron discharges, but it can be ruled out for planar magnetrons, because the high energy electrons are too energetic. The latter process was added to the model in an empirical way, by introducing an artiﬁcial type of interactions, the Bohm diﬀusion collisions. The idea comes from Hall thruster simulations, where a similar approach is followed [135, 136]. The Bohm diﬀusion collisions represent the electron interactions with the electric ﬁeld oscillations, which are supposed to generate anomalous diﬀusion. The “amount” of Bohm diﬀusion is deﬁned as the occurrence of the Bohm diﬀusion collisions relative to the standard collisions (ionization, excitation, and elastic collisions), and it is proportional to the magnetic ﬁeld and inversely proportional to the gas pressure, indicating that anomalous electron transport is especially important at strong magnetic ﬁelds and low pressures. The inﬂuence of increasing the “amount” of Bohm diﬀusion on the magnetron properties was simulated. These changes could be related to the increased electron mobility in the direction perpendicular to the magnetic ﬁeld lines. The main advantage of including Bohm diﬀusion is that it enables to reproduce the extremely steep current–voltage relations, which are characteristic for a magnetron discharge. 3.4.2 Examples of Calculation Results The results of this analytical model were compared with experimental results, using two input values, i.e., the electron reﬂection coeﬃcient and the relative occurrence of Bohm diﬀusion collisions, as tuning parameters. Two examples will be discussed in the sections below. In both cases the experimental results were obtained using a commercially available planar circular magnetron (Von Ardenne PPS50, see also Sect. 3.5). Calculated Ionization Distribution vs. Measured Plasma Emission Distribution Figure 3.2 shows the plasma emission recorded as a function of distance perpendicular to the target. The experiment and, hence, the results are very

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plasma emission (a.u.)

1.2

120

z' - axis (pixels) 80 60 40

100

20

0

0.12Pa 0.23Pa 0.40Pa 0.55Pa 1.0Pa 2.2Pa

1 0.8 0.6 0.4 0.2 0

(a)

−1

0

1

2 3 4 z - axis (mm)

5

ionisation distribution (a.u.)

82

1.2

0.10Pa 0.20Pa 0.40Pa 0.60Pa 1.2Pa 2.0Pa

1 0.8 0.6 0.4 0.2

6

(b)

0

−1

0

1

2 3 4 z - axis (mm)

5

6

Fig. 3.2. The inﬂuence of the gas pressure on the optical emission of the magnetron at 50 W, as measured (a) and as simulated (b). Note that the emission has been normalized to the maximum emission at 2.2 Pa (2.0 Pa) for the experiments (simulations). The dashed vertical line (part a) indicates the position of the target. The dotted line (part a) suggests the “true” emission, i.e., without target reﬂection, for the case of 0.40 Pa

similar to what was measured by Lan Gu and Lieberman [41]. The z -axis represents the distance along the direction perpendicular to the target (expressed in pixels). The vertical line at z = 107 indicates the position of a small peak that is due to the light that reaches the camera after reﬂection on the target. According to [41] the exact position of the target surface is probably at slightly lower z -values. The z -axis in pixel-scale could be converted into the z-axis in mm-scale. In the analytical model the light emission of the plasma is not simulated. However, the excitations and ionizations generated by the high energy electrons occur practically at the same positions. Hence, the ionization rate distribution can be used for comparison with the experimentally measured emission intensity and is plotted in Fig. 3.2b. As one can see, the shift of the peak and the decreased intensity with decreasing pressure are reproduced very well. Current–Voltage Characteristics For a second example of the analytical model, the discharge voltage is calculated as a function of the electrical current for diﬀerent secondary electron emission yields (γ) at constant pressure (0.3 Pa). The variation in γ was experimentally achieved by using diﬀerent target materials under otherwise identical experimental conditions. Figure 3.3 shows that the increasing steepness of the current–voltage characteristic with increasing γ is reproduced nicely. The relative spacing between the curves is also reproduced very well for γ = 0.06 through 0.14. For γ = 0.18 the experimental curve lies much closer to γ = 0.14 than the simulated one. A possible explanation might be that the choice of yttrium (Y) as material for obtaining the experimental curve corresponding

3 Modeling of the Magnetron Discharge 0.6

0.5

Y

Mg

Al Au

0.4 0.3 0.2 0.1

(a)

0 250 300 350 400 450 500 550 600 discharge voltage Vd (V)

discharge current Id (A)

discharge current Id (A)

0.6

γ = 0.18

γ = 0.14

83

γ = 0.10

0.5 0.4 0.3

γ = 0.06

0.2 0.1

(b)

0 250 300 350 400 450 500 550 600 discharge voltage Vd (V)

Fig. 3.3. Inﬂuence of the secondary electron emission yield γ on the current–voltage characteristics at 0.3 Pa, as measured (a) and as simulated (b). The experimental curves are obtained with diﬀerent target materials: Au, Al, Mg, and Y. The corresponding γ-values used in the simulation for these materials are 0.06, 0.10, 0.14, and 0.18, respectively, as described in [143]

with γ = 0.18, is based on a calculated value of γ and not on experimental data, see [143]. In view of the relative simplicity of this analytical model, and the fact that certain aspects are completely neglected (such as the eﬀect of bulk electrons), the agreement between the simulations and experimental data is very satisfactory. Therefore, it can be concluded that this analytical model is able to reproduce self-consistently the inﬂuence of the main three external parameters (i.e., magnetic ﬁeld strength, gas pressure, and electrical power) over a wide range. Also the eﬀect of the secondary electron emission yield, γ, could be correctly simulated. This indicates that the model captures the most important processes occurring in the magnetron discharge, and is therefore a valuable “virtual” tool to gain insight in the generic magnetron behavior.

3.5 PIC-MCC Model for a DC Planar Magnetron Discharge This section will give a detailed description of the PIC-MCC model developed by Kolev and Bogaerts for a DC planar magnetron [37–39, 144]. Some characteristic results will also be illustrated. 3.5.1 Particle-In-Cell Model The PIC model is a numerical model describing an ensemble of collisionless charged particles, which can be, but not necessarily, under the inﬂuence of an external electromagnetic force. The constituents of the ensemble are not real physical subjects. They are artiﬁcial objects, representing the main physical

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properties of the real particles, such as charge, mass, and momentum. These computational particles are referred to as superparticles (SPs). Each SP represents a large number of real particles. This number is called weight and is in the order 106 –109 . Thus, the ﬁrst approximation of PIC is the replacement of the real particles in a physical system with artiﬁcial superparticles. The second approximation is the discretization of time. This means that the simulated system jumps from one temporary state to another, in contrast to the real system, where the time evolution is continuous. The third approximation is the space discretization. Indeed, a mathematical spatial grid is imposed. The electrostatic ﬁeld that results from the position of all simulated particles at a given moment of time is calculated on the grid only. The external (electric and magnetic) ﬁeld, if any, is calculated on the same grid. The particles advance is then made by interpolating the forces resulting from these ﬁelds from the grid to the particle locations. The trajectory of the SPs is simulated during a large number of time steps. A schematic diagram of a PIC computational cycle, over a time period Δt equal to the discretization pace in time, for the case of an external magnetic ﬁeld, B and electrostatic ﬁeld E, is presented in Fig. 3.4. Before the ﬁrst execution of the cycle, the initial state of the system needs to be speciﬁed. This includes the initial distributions of the particles in the coordinate and the velocity spaces. In fact, this is the main guess in a PIC simulation, so it must be a physical one. In following sections, the diﬀerent steps of the computational cycle will be explained in detail. Integration of equations of motion, moving particles Fi ⎯→ vi’ ⎯→ xi

Weighting (E, B)k ⎯→ Fi

Particle loss / gain at the boundaries (emission, absorption)

Conver gence

Δt

No Integration of Poisson’s equation on the grid (ρ)k ⎯→ (E)k

Yes

End

Weighting (x, v)i ⎯→ (ρ)k

Fig. 3.4. A scheme of a PIC cycle for the case of electrostatic ﬁeld, E, and an external magnetic ﬁeld, B. Here v represent the velocity of the SPs, x their coordinate, F the force acting upon them, and ρ is the charge density. The index k refers to the grid and the index i to the SPs. The time step of the cycle is Δt

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Integration of the Equation of Motion In a DC magnetron, the force acting on a charged particle has two components: electric and magnetic. The gravitational force is ignored because its magnitude is very low in comparison to the electric and magnetic forces, due to the small masses of the electrons and ions. Further, the magnetic force can be considered external, because the magnetic ﬁeld that results from the motion of the charges inside the magnetron is only a small perturbation to the magnetic ﬁeld created by the magnets. The electric force, on the other hand, is a combination of the applied (external) electric ﬁeld and the electric ﬁeld induced by the charged particles. Thus the force is given by: F = F electric + F magnetic = qE + q(v × B),

(3.4)

leading to the equations of motion m

dv = q(E + v × B) dt dx =v dt

where x denotes the coordinate. This is a system of ordinary diﬀerential equations. It is discretized by the method of ﬁnite diﬀerences [145] using central diﬀerences for maximum stability and accuracy at low computational cost. A standard way to achieve this is to use the leapfrog algorithm, which is explained in Fig. 3.5.

velocity v-Δt /2

vt-Δt/ 2

vt+Δt / 2

time

coordinate xt Ft - Δt / 2

0

t - Δt /2

t

xt+Δt Ft+Δt

time

t + Δt /2 t + Δt

Fig. 3.5. A sketch of the leapfrog algorithm. The position of a particle is advanced from a moment t to a moment t + Δt, even though the velocity is not known in neither of the two moments, but in between. This represents the time centering. In time t = 0, the initial conditions are speciﬁed at the same time. That is why the velocity is initially returned half a time step back in time

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The time centering is clearly seen. The application of the leapfrog algorithm leads to the following system of ﬁnite diﬀerence equations

v t+Δt/2 − v t−Δt/2 v t+Δt/2 − v t−Δt/2 q = Et + ×B Δt m Δt x t+Δt − x t = v t+Δt/2 . (3.5) Δt The magnetic ﬁeld is not indexed, because it is constant with time. The system (3.5) is in vector form. When written in components, it produces in general six scalar equations. Those of them that originate from the ﬁrst equation are heavily coupled because of the rotation term. This makes the direct solution very complicated and computationally ineﬀective, because a solution is needed for every particle per each time step. The problem can be surmounted by noticing that the ﬁrst term in the right-hand side of (3.5) is acceleration along the electric ﬁeld and changes the magnitude of the velocity, while the second term is a rotation of the velocity vector, which does not alter the velocity magnitude. Then the force can be split into pure acceleration and pure rotation. To stick with the time centering, the acceleration can be performed in two stages, each with the half of the time step, while the rotation is performed at once, in between the two half-accelerations. In terms of velocities this can be expressed as half acceleration

f ull rotation

half acceleration

Δt/2

Δt

Δt/2

v t−Δt/2 −−−−−−−−−−−→ v −−−−−−−−−−−→ v −−−−−−−−−−−→ v t+Δt/2 , where v and v are some dummy velocities. Half-accelerations are trivial for handling since there is no coupling there. The rotation can be handled geometrically, as ﬁrst suggested by Boris [146] and explained in detail in [144]. Charge Assignment Once the particles’ positions are calculated, the charge density, ρ, at the grid must be obtained. This procedure is called charge assignment. It is done, by ascribing fractions of each point charge to the neighboring grid points. To account for the charge conservation, the sum of all fractions must be equal to the point charge. The resulting charge, assigned to a given grid point is the sum of all fractions assigned to that grid point. The charge density then is the grid charge divided by some speciﬁed volume around it. The function, which determines what fraction of the point charge is assigned to a given grid point, is called weighting function or shape factor, S. The latter term arises from the way the grid sees the particles. There are diﬀerent ways to construct the weighting function. The choice is always a compromise between more accurate physics incorporated and higher computational costs. The simplest scheme for charge assignment is the so-called nearest grid point (NGP) scheme. The NGP scheme assigns the whole point charge to the

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NGP. It is computationally very attractive, but is seldom used, because of its coarseness that can introduce fatal numerical instabilities. The NGP scheme is of zeroth order. The ﬁrst-order scheme is the so-called cloud-in-cell (CIS) scheme, ﬁrst introduced by Birdsall and Fuss [147] for one-dimensional plasma simulations. The CIS scheme uses linear interpolation to assign the charge to the NGPs. It is much more accurate and also smoother than the NGP scheme. When still more smoothness or accuracy is desired, higher order schemes can be used. Then a point charge is assigned not only to the closest grid points, but also to one or several distant grid points. The interpolation function is then of second or higher order. The fact that it is not linear anymore leads to often unacceptable computational intensiﬁcation. That is why the CIS scheme is the most commonly used scheme. In two dimensions, the linear weighting may be performed in two ways. The ﬁrst one is the complete analogue of the CIS scheme. The second one is area weighting, also known as bilinear weighting. When axisymmetric systems are modeled, the usual choice of coordinate system is cylindrical (r–z). Although formally two-dimensional, it in fact describes a volume. To represent this correctly in the charge assignment, the weighting is to be volumetric (r2 , z), rather than area weighting. The way it is done is shown and explained in Fig. 3.6. Integration of Poisson’s Equation on the Grid The charge distribution, characterized by the charge density, ρ, creates an electrical potential, V , given by Poisson’s equation, which in cylindrical (r, z) coordinates reads ∂ ∂V (r, z) ρ(r, z) 1 ∂ ∂V (r, z) r + =− r ∂r dr ∂z ∂z ε0 ρ(r, z) = q(ni (r, z) − ne (r, z))

(3.6)

where ni and ne represent the ion and electron number density, respectively. The discretized form of (3.6) is obtained by applying the Gauss’ law, for the dashed volume, centered on a grid node (ri , zj ) (see Fig. 3.7): qi,j = 2πri+1/2 ΔzEr i+1/2,j − 2πri−1/2 ΔzEr i−1/2,j ε0 2 2 (Ezi,j+1/2 − Ezj, i−1/2 ), + π ri+1/2 − ri−1/2 where the geometric factors are deﬁned as follows Δri+1/2 ≡ ri+1 − ri " 2# 2 2 Δr i ≡ ri+1/2 − ri−1/2 " 2# 2 Δr 0 ≡ r1/2 .

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z Δr A

B qk

Δz C

zj+1 zk

D

zj

ri

θ

r

rk ri+1

Fig. 3.6. Illustration of the charge assignment in cylindrical (r, z) coordinates, according to the volumetric weighting CIS scheme. The charge qk , located at point (rk , zk ), is distributed among the four grid nodes A, B, C, and D of the grid cell it is located in. The fraction of qk that is assigned to A, for example, is equal to the product of qk and the ratio of the volumes: (1) obtained by full rotation of the shaded area of the grid cell ABCD around the z-axis and (2) obtained by full rotation of the whole grid cell ABCD around the z-axis. Δr and Δz are the grid sizes in r- and z-direction, respectively

z

Δr Ez Er

zj

q, V Δz 0

ri

r

Fig. 3.7. A sketch of the computational grid with grid separations Δr and Δz. The dashed line centered on the grid point (ri , zj ) represents the surface on which the Gauss’ theorem is applied. The discrete values of the charge, q, and the potential, V , are known in the grid nodes, whereas the components of the electric ﬁeld, Er and Ez , are deﬁned on the Gauss’ surface. The surfaces allocated at the origin, r = 0, (left-dashed box) are half the size of those located in the volume

3 Modeling of the Magnetron Discharge

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Employing single cell ﬁnite diﬀerencing Er i+1/2,j =

Vi+1,j − Vi,j Δrj+1/2

Ez i,j+1/2 =

Vi,j+1 − Vi,j Δz

and using a standard ﬁve-point stencil [146], the discretized form of (3.6) becomes 2ri−1/2 2ri+1/2 (Vi+1,j − Vi,j ) − (Vi,j − Vi−1,j ) (Δr2 )i Δri+1/2 (Δr2 )i Δri−1/2 1 1 + (Vi,j+1 − 2Vi,j + Vi,j−1 ) = ρi,j i > 0 Δz 2 ε0 2r1/2 1 1 (V1,j − V0,j ) + (V0,j+1 − 2V0,j + V0,j−1 ) = ρ0,j 2 2 (Δr )0 Δr1/2 Δz ε0

i=0 (3.7)

The charge density ρi,j is obtained from ρi,j = qi,j /voli,j , where voli,j ≡ π(Δr2 )i Δz.

(3.8)

In the second of (3.7), an implicit boundary condition is implied representing the symmetry around the axis r = 0 $ ∂V $$ = 0. ∂r $r=0 The other boundary conditions are discussed in the next section. Equation (3.6) is an elliptic partial diﬀerential equation with separable coeﬃcients. This favors the use of some of the so-called rapid elliptic solvers [148], which are much more eﬃcient than the more frequently used mesh-relaxation methods (MRM’s) [149]. Since there is no periodicity in either of the directions, fast Fourier transform techniques [150] are inapplicable. Instead, the cyclic reduction method (CRM) can be employed. The CRM is more complicated from programmer’s viewpoint, but it is the most eﬃcient numerical method for the case of interest. The description of the general CRM and a possible algorithm for its implementation is given in [151]. If an equidistant grid in the z-direction is used, the CRM algorithm is even faster. An additional advantage of the CRM is that as a direct method, it is presumably more accurate than any of the MRM’s, which are iterative. External Circuit In modeling of magnetron discharges, an external circuit needs to be incorporated, to ensure that the model describes the magnetron discharge in the correct current–voltage regime [37,144]. Figure 3.8 gives a schematic diagram of a simple external circuit, consisting of a constant voltage source, Vext , and

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Cathode

Rball

Vext

Fig. 3.8. An external circuit consisting of a constant voltage source, Vext , and a ballast resistor, Rball , in series with the cathode. The dot-dashed line represents the symmetry axis, r = 0

a ballast resistor, Rball in series with the cathode, together with a sketch of the planar magnetron considered in the present study. The presence of an external circuit leads to the necessity of simultaneous advance in time of the circuit and the discharge. This problem is known as modeling of bounded plasmas with external circuits [152]. Its numerical application in 1D has been given in detail in [152–154]. A comprehensive procedure for the case of 2D Cartesian coordinates can be found in [155]. For 2D cylindrical (r, z) coordinates, certain modiﬁcations in the procedure of [155] are necessary. This is explained in detail in [144]. In the following, a brief description is presented. The coupling between the circuit and the discharge is maintained through satisfying the charge conservation at the cathode A

dσ = Iext (t) + Qdisch dt

(3.9)

where σ is the total surface charge density at the cathode, Iext is the external circuit current, A is the cathode surface, and Qdisch is the charge deposited from the discharge on the cathode during a period dt, due to the bombarding ﬂuxes of the charged plasma species. The total surface charge can be determined independently of (3.9) applying the Gauss’s theorem on a number of boxes, closely surrounding the cathode. This is done in the following manner. The cathode surface is divided into nr1 boxes, as shown in Fig. 3.9.

3 Modeling of the Magnetron Discharge

91

z Ez ½, 0 i-1

0

Ez ½, nr1

Ez ½, i i

i+1

nr1 E r r 0, nr1+½

Fig. 3.9. The cathode surface (z = 0, r ∈ [0; rnr1 ]) is enclosed by nr1 boxes. For each of them, the Gauss’ law is applied. For all boxes, except the one centered on r = nr1 , the ﬂux of the electric ﬁeld through the boxes’ surfaces is nonzero only in +z-direction. For the box centered on r = rnr1 , there is also a nonzero ﬂux in r-direction

For the ith box the Gauss’ law is % ε0 E · ds = Qi , Si

where Si is the surface of the ith box, ds is the surface element, and Qi is the total charge inside the box. The total charge, Qi , is a sum of the surface charge, caused by the charging of the cathode by the discharge and the external circuit, and the volume charge that comes from the charged plasma particles. Then the Gauss’ law takes the form % % ! ε0 E · ds = Qi = σi ds + ρi dV , Si

Si

V oli

where σi is the surface charge density at point i, ρi is the charge density in the same point, and V oli is the volume of the box. This is equivalent to εEz i,1/2 =

1 ρi Vol i + σi 2

(3.10)

By use of ﬁnite diﬀerences, Ez i,1/2 can be expressed as (Φ0 − Vi,1 )/Δz, where Φ0 is the cathode potential. Rearranging (3.10) for σi and summation over all boxes i, yields an expression of the total surface charge density on the cathode (σT ) as a function of the cathode potential (Φ0 ), the potential values at the ﬁrst grid point in the discharge, for all the boxes, i.e., radial positions (Vi,1 ), and the corresponding volume charge densities in these boxes [144]. Furthermore, (3.9) can be discretized with backward ﬁnite diﬀerences " # A σTt − σTt−1 = [Iext (t) + Idish ] Δt (3.11)

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Then according to Kirchhoﬀ’s voltage loop law, the cathode potential, Φ0 = Vext − Rext Iext . Expressing from there Iext and introducing it to (3.11) produces

1 Δt σTt = (Vext − Φ0 ) + Qtdish + σTt−1 (3.12) A Rext Equation (3.12) can be combined with the equation for σT (obtained by rearranging (3.10); see above and [144]) in a single equation for Φ0 as a function of the potentials, Vi,1 and charge densities, ρi,0 both taken in time t, and the total surface charge density at time (t − 1). The problem here is that such an equation is at the same time a boundary condition for the Poisson’s equation (3.7) (see above). This leads to the necessity that (3.7) must be solved iteratively until the boundary condition is fulﬁlled, which is extremely ineﬃcient in computational sense. Alternatively, the potential at any grid point, Vi,j , can be expressed as a superposition of two other potentials P L Vi,j = Vi,j + Φ0 Vi,j .

(3.13)

P , is a result solely of the presence of charges inside the The potential, Vi,j P magnetron. Thus, it is a solution of (3.7) with boundary conditions vi.0 = P P Vi,nz = Vnr,j = 0, where nr and nz represent the grid nodes located at the L walls of the magnetron. The dimensionless potential, Vi,j , accounts for the inﬂuence of the cathode potential and is a solution of the Laplace equation L L ΔVi,j = 0 with boundary conditions Vi≤nr = 1 and V L = 0 at the walls. 1 ,0 Replacing Vi,j with (3.13) ﬁnally yields an expression for Φ0 as a function of the potentials and charge densities in the plasma, in front of the cathode, at time t, the external (applied) potential, and the total surface charge density at time (t − 1).

−a2 Φ0 =

nr 1 −1 i=0

P P Vi,1 − a3 Vnr − a4 1 ,1

nr 1 −1

ρi,0 − a5 ρnr1 ,0 +

i=0

a1

Qtdisch A

t−1 + a6 Vext + σT

, (3.14)

where a1 −a6 are coeﬃcients, dependent on geometrical factors and on L [144]. Vi,j In this way, Φ0 at time t can be calculated only from known quantities at the same time. Then the overall procedure for simultaneous advance of the circuit and the discharge in time is as follows. In the beginning of the simuL lation, the Laplace equation is solved to determine Vi,j . Next, the coeﬃcients a1 through a6 are calculated. These two steps are performed only once. Then P at each time step, (3.7) is solved with zero boundary conditions to obtain Vi,j . L P With Vi,j and Vi,j known, (3.14) is solved for Φ0 . Afterward, (3.13) is used to produce the discrete potential distribution in the discharge Vi,j . Finally,

3 Modeling of the Magnetron Discharge

93

t (3.12) is solved to get σT , which is going to be used in (3.14) during the next time step. Finally, once the potential, Vi,j , is known, the electric ﬁeld E is calculated from E = −∇V.

Force Interpolation and Smoothing With E i,j calculated above, the force F i,j needs to be interpolated to the particle locations. This operation is known as force interpolation and is inversely identical to the charge assignment (see the section above). What is important is that the same shape factor must be used in both charge assignment and force interpolation. Not doing so usually results in a nonphysical self-force, i.e., a particle experiences a “force” caused by the particle itself [148, 153]. Using the same shape factor secures the total momentum conservation of the simulated system. The procedure of weighting (charge assignment and force interpolation) introduces naturally ﬂuctuations of the grid quantities. The amplitude and the density of the ﬂuctuations are reversely proportional to the number of SPs per grid cell. In magnetrons, the charge distribution is very inhomogeneous (see Sect. 3.5.4 below). This results in a situation where in some grid cells the number of SPs is very small, which can cause strong ﬂuctuations. These ﬂuctuations can evolve in instabilities that can terminate the simulation or bring it to a nonphysical solution. To prevent that from happening, digital ﬁltering or smoothing is needed. The smoothing can be described as the substitution of the grid quantities at every grid node with some-averaged (smoothed) values received by averaging the grid quantities at the adjacent grid nodes. Diﬀerent methods exist for that. In the current simulation, after the charge assignment is ﬁnished the charge density is smoothed before being used for calculation of the potential. There are many digital ﬁlters that in principle can be used [156, 157]. However, the ﬁlter must be isotropic to represent correctly the physical reality. Additionally, it must be computationally eﬃcient because the ﬁltering is performed at each time step. The ﬁlter, adopted in our work, uses the unﬁltered values of the closest neighboring grid points (9-point ﬁltering) [153]. It can be represented by the following transformation ρﬁltered i,j ←

" raw # raw raw raw raw raw raw raw 4ρraw i,j +2 ρi−1,j +ρi+1,j +ρi,j−1 +ρi,j+1 +ρi−1,j−1 +ρi−1,j+1 +ρi+1,j+1 +ρi+1,j−1 . 16

Stability and Accuracy of the PIC Model The PIC model is a discrete approximation of a continuous physical picture. As such, it always introduces a numerical noise. The magnitude of this noise reaches zero only when the number of SPs per grid cell approaches the number

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of real particles in the same grid cell. Therefore, all kinds of particle simulations are by deﬁnition noisy in contrast to ﬂuid models. The noise, however, should be kept under a certain maximum level to have meaningful results. More importantly, the error introduced by the noise must not be allowed to grow with the simulation. Several factors directly inﬂuence the noise. These include the time step, the number of SPs per grid cell, the shape factor, and the grid size. The speciﬁc mechanism through which this inﬂuence is manifested depends on the type of the numerical integrator of the equation of motion. In our model, the leapfrog integrator is implemented. A quantitative analysis for the error introduced by this method is given in [144]. It is found that the standard leapfrog algorithm has a quadratic error term for ω0 Δt 1, where ω0 is the characteristic frequency in the simulated system. In DC magnetrons, the two highest frequencies are the electron plasma frequency ωpe = ne qe2 /ε0 me and the electron gyro frequency, ωce , given by ωc ≡ |q|B/m. Hence, ω0 = max{ωpe , ωce}. It should be emphasized that the error is cumulative with the number of time steps. This means that the longer the simulation is run, the bigger the overall error is. Consequently, the following paradox exists. Setting the tolerable error too small limits the number of time steps. Allowing a large number of time steps increases the error as the cube of the time step [153]. In the literature, a common compromise has been set ω0 Δt ≈ 0.2.

(3.15)

In magnetrons, the standard leapfrog algorithm is expanded to deal with the magnetic ﬁeld and the rotation caused by that ﬁeld. Thus, it is important to keep the calculated rotational angle reasonably close to the real one. An analysis of this problem can be found in [148]. It shows that for magnetic ﬁeld strengths of interest the condition (3.15) secures that the rotation term of the equation of motion (see section “Integration of the Equation of Motion”) is calculated with an error not exceeding that of the general leapfrog algorithm. The exact condition is ω0 Δt < 0.35. (3.16) Generally, in two and three dimensions, the discussion for the stability and accuracy is much more complex. However, when one of the dimensions is dominant and the stability is achieved for it, it can be accepted that the whole simulation is stable. Typically, the dominant dimension is in the direction of the strongest gradient of the electric ﬁeld. For our magnetron simulations, it is the z-direction. In line with that, the Courant criterion [158] is vk Δtk /Δz ≤ 1,

(3.17)

where vk is the characteristic velocity of the kth type of SPs and Δtk is its time step. The meaning is that, if (3.17) is violated, too many SPs are jumping

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over ﬁeld variations, which leads to numerical heating. Thus for a given Δt, deﬁned by (3.16), the formula (3.17) sets a bottom limit for the grid size, Δz. At the same time, the grid must be ﬁne enough to resolve the sheath. This leads to the upper limit for Δz Δz ≤ λD ,

(3.18)

where λD is the Debye length. Relations (3.15), (3.17) and (3.18) deﬁne the stability and accuracy domain in terms of time step and grid size for the standard PIC simulation. Adding to that the MCC method (see below) will bring some additional conditions. More details about that are given at the end of Sect. 3.5.2. Modiﬁcations of the stability criteria with respect to speeding up the procedure are presented in Sect. 3.5.3. 3.5.2 Monte Carlo Collision Method The PIC method has been originally designed to model collisionless plasmas. In magnetrons, as in other types of glow discharges, collisions sustain the discharge. Therefore, a numerical model must be able to incorporate them. This can be achieved by coupling the PIC model with a Monte Carlo collision (MCC) model. This means that at a certain moment of the time step the SPs should be checked for collisions. The coupling is not just a numerical trick made to account somehow for the collisions. It has sound physical grounds, which follow from the Boltzmann equation [144]. The collision probability for all individual SPs needs to be calculated during every time step. Let us consider here the electrons as example of the SPs. It can be proven [159] that the probability, Pi , for the ith electron to collide binary with any of the particles of type g (gas atom, for example) during time Δt agrees with the probability received from the elementary free-path theory [160]. That is Pi = vΔt, where ν is the collision rate given by v = ng g¯σT with ng being the target density, g¯ the average relative speed between the ith electron and the target particles, and σT is the total cross section. In case of big disparity between the speed of the colliding particle, vi , and the mean speed of the target particles, a common approximation is g¯ ≈ vi . The cross section and therefore the collision rate are generally energy dependent. Since the velocities of the particles change with time, the collision rate is also time dependent. The probability, Q, that an electron, starting at time t = 0, does not collide in the interval (0, t + Δt) is Q(t + Δt) = Q(t)[1 − v(tΔt)],

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where the term in the square brackets is the probability for no collision in the interval (t, t + Δt). When Δt → 0, this equation becomes dQ = −v(t)Q(t) dt with a solution

! t

Q(t) = exp − v(t)dt .

(3.19)

0

Consequently, the probability that a collision takes place within a time t = tc , is given by: Prob{tc } = 1 − Q(tc ). This probability is calculated by generating a uniformly distributed random number (U ) in the interval [0,1] [161] 1 − Q(tc ) = U.

(3.20)

Hence, once U is generated, the time tc , which deﬁnes when a collision takes place, can be calculated from (3.19) and (3.20). This constitutes the general Monte Carlo procedure for determining whether a collision takes place. However, it is impractical, unless the collision rate is constant. Instead, the null-collision method, ﬁrst introduced by Scullerud [162], can be used. Its main feature is the introduction of a constant maximum collision frequency, vmax , that is always higher than v(t) for any t. Hence, when (3.19) and (3.20) are solved with νmax instead of v, the solution is −1 tc = −vmax ln U.

(3.21)

To ﬁnd a relation between tc and tc , the same U should be used. Then according to (3.20), tc < tc . The collision probabilities for v and vmax , respectively, at time, t = tc , are ! tc

Pc = 1 − exp −

v(t)dt , 0

(Pc )max = 1 − exp(−vmax tc ).

(3.22)

Consequently, the probability that a collision is regarded real, i.e., it really happens in the model, is equal to Pc /(Pc )max . Note that the condition, Pc < (Pc )max , is always fulﬁlled. The eﬃciency of the method arises from the fact that there is no need to calculate the actual collision time tc in (3.20). If tc is small enough, which is always true if the time step of PIC is used, the collision rate can be

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approximated with a quadratic polynomial. Then the integral in the ﬁrst of (3.22) becomes [139] !

tc

v(t)dt = 0

tc [v(0) + 4v(tc /2) + v(tc )] . 6

(3.23)

Equation (3.23) can be used to determine the probability for collision from (3.22). So far, the total probability of collision, PT has been discussed. When there are m types of collision, all possible in the time interval of interest, the probability for the kth type of collision (0 < k ≤ m), characterized by a collision rate vk is given by ! tc

Pk = 1 − exp −

vk (t)dt 0

and PT =

m

Pk .

(3.24)

k=1

Then the sampling of the kth collisional event is made with a probability of Pk /PT . The drawbacks of the null-collision method are connected to the implicit condition that the particles in the ensemble have the same collision rates. Or, what is equivalent, that their mean collision path is the same. Such situation is easily realized in a uniform electric ﬁeld, for instance. That is why the method is especially eﬃcient in swarm calculations. Its application to PIC simulations has been introduced by Vahedi and Surendra [163]. However, no theoretical analysis has been carried out to determine what strengths of the electric ﬁeld gradients are allowed for the stability domain of the null-collision method. In magnetrons, strong gradients in both electric and magnetic ﬁelds exist, and as it has already been pointed out, the whole magnetron plasma is very inhomogeneous. The amplitude of the electric ﬁeld gradients is proportional to the strength and geometry of the magnetic ﬁeld. All this makes the use of the null-collision method in magnetron modeling highly questionable, especially at strong magnetic ﬁelds. An additional problem may appear from the selection of the particles (especially the electrons) which are considered for collision in each time step. The procedure of Vahedi and Surendra [163] requires the determination of some maximum number of particles eligible for collision. It is intuitively clear that when the particles are with small dispersion in their velocity distribution they can be selected randomly. Unfortunately, the latter is not the case in magnetrons, where a relatively small number of electrons are responsible for the main processes that sustain the discharge. Consequently, if the colliding electrons are selected purely on random basis it can lead to underestimation of the collisions of the “important” group of electrons.

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The above discussion motivates the introduction of a collision sampling procedure, both capable of dealing with strongly inhomogeneous velocity and spatial distributions and which is computationally eﬀective. Such a procedure has been developed by Nanbu [164]. It makes it possible by use of a single random number to determine not only whether a collision occurs, but also what type of collision takes place. In this way, the computational eﬃciency is signiﬁcantly improved. The checking is done on per particle basis, which ensures the equal treatment of all particles. For the case of electron-neutral collisions, where the speed of the neutrals is neglected and they are considered homogeneously distributed in space with a density, ng , the procedure is as follows. The total probability for collision is given by (3.24), where Pk = ng vσk Δt.

(3.25)

Here, v is the electron speed. Equation (3.24) can be rewritten as m

1 − Pk , Pk + 1 = PT + (1 − PT ) = m k=1

which is visualized in Fig. 3.10. The unit length is divided into m equal intervals, where m stands for the number of diﬀerent collision types. Each interval has two parts. In the kth interval, e.g., the left part has a length equal to 1/m − Pk and the right side is Pk . The sum of the right parts of all m intervals equals the total collision probability, PT and the sum of the left parts gives the probability of no collision, 1 − PT . The procedure is to generate a uniformly distributed random number U ∈ [0, 1]. The integral part of mU +1 speciﬁes the kth interval corresponding to the kth collisional event, i.e., k = int[mU + 1]. Then only Pk needs to be calculated, which is a signiﬁcant speed-up in case of big m. Finally, the same U is checked to see in which part of the kth interval it falls. If U>

k − Pk m

holds, the kth collisional event occurs. If not, no collision takes place. P1 0

1 m

P2

Pk

2 m

m−k−1 m

m−k m

Pm

m− 1 m

1

Fig. 3.10. Visualization of the Nanbu’s method [162] for sampling a collisional event. The right-hand side of the kth interval (drawn with thicker lines) represents the probability of the kth type of collision. The sum of the left-hand sides of all intervals (represented by thinner lines) is equal to the probability of no collision. The sum of the right-hand sides equals the total collision probability, PT

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In all MCC algorithms, the collisional time step, Δtc , must be small enough in order not to miss a real collision. This condition stems from the fact that for one time step, the colliding particle is allowed to undergo at maximum one collision. For the Nanbu’s method, this condition is Pk < 1/m for all m, for all electron energies. The electron energies in DC magnetrons are restricted approximately to the energy equivalent of the applied voltage. Then some Pmax can be estimated, that corresponds to the biggest cross section, σmax , of all the included processes for all the possible energies. Then the maximum allowed Δtc can be obtained from (3.25) with σk replaced by σmax and Pk = 1/m. This is practically not a limitation at all, when the method is used in PIC simulations, because the general time step limitation of PIC is more restrictive (see above (3.16)). The coupling of the collision check with the PIC cycle can be done in diﬀerent moments inside the time step. Our choice is to check for a collision in the middle of the time step. This choice has been dictated by the time centering of the leapfrog integrator (see section “Integration of the Equation of Motion”, and especially Fig. 3.5). At this moment, the positions of the particles are exactly known. At the same time, only half of the acceleration is applied. The rotation may or may not be calculated. It does not matter, because the rotation does not change the speed and hence the energy of the colliding particle. Therefore, the energy is also known at the middle of the time step, though the velocity is unknown. The inclusion of the MCC module to the PIC method is shown schematically in Fig. 3.11. In case of collisions, the precollision velocity of the colliding particle is replaced by its postcollision velocity, which is determined based on the fundamental laws of conservation of energy and momentum during collision, plus geometrical considerations related to the particle’s orientation before the collision, as is explained in detail in [144], for the diﬀerent types of collisions (electron-neutral, ion-neutral, neutral-neutral, and Coulomb collisions). 3.5.3 Methods for Speeding Up the Calculations As already mentioned before, PIC-MCC simulations of DC magnetrons are very time-consuming. This is caused by two main factors. The ﬁrst one is the relatively high plasma density leading to a large number of SPs that need to be simulated. The second one is the time needed for convergence to be achieved. The simulation should be run for at least 10−5 s, which is the relaxation time in a DC glow discharge [165]. The high plasma density limits the allowed time step, which results in a large number of time steps (computational cycles) that should be performed to reach the 10−5 s limit. All this motivates the incorporation of computational techniques and physical approximations that can alleviate the computational load. Here, an overview of the methods, used to achieve this goal, is given.

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Integration of equations of motion, moving particles: Fi ⎯→ vi

MCC Yes

Weighting (E, B)k ⎯→ Fi

Integration of Poisson’s equation on the grid (ρ)k ⎯→ (E)k

Post-collision velocities vi ⎯→ vi’

Δt

Weighting (x, v)i ⎯→ (ρ)k

No

No

Convergence Yes End

Fig. 3.11. Scheme of a PIC-MCC cycle. The collision check is performed at time t + (1/2)Δt. The notation vi refers to the postcollision velocity of the ith particle. All other symbols are as in Fig. 3.4

Subcycling Subcycling [158] is the partial advance of the simulated system. This means that diﬀerent parts of the system are advanced with diﬀerent time steps. The fast evolving components are normally advanced a ﬁxed number of times per one evolution of the slow components. If the system time step, and therefore the main cycle, is those of the slower components, then the fast ones are moved several times within the main cycle. Or in other words, they are subcycled. The fast particles that require the smallest time step (see section “Stability and Accuracy of the PIC Model”) are the electrons. Ions are roughly 2,000 times heavier than electrons and hardly move during an electron time step. This allows, according to the stability and accuracy criteria of the PIC method, that they can be advanced safely once per 20–50 electron time steps. The electric ﬁeld, however, is recalculated after each electron time step. In this sense, the term subcycling is to some extent a misnomer in the present study. Variable Time Step The initial density, loaded in the beginning of the simulation, is much lower than the density in a steady state. The time step restriction [(3.16)] must be obeyed at any time. Since the plasma density changes, so can the time step. The classical approach is to ﬁx the time step to obey (3.16) for the maximum expected density. This is a simple and safe decision from a programmer’s

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Time step, [s]

6x10-11

4x10-11

2x10-11

4x10-12 2x10-6

4x10-6

6x10-6

8x10-6

10-5

Time, [s]

Fig. 3.12. Adapting of the time step throughout a typical simulation

point of view, but is computationally ineﬀective, because unnecessary small time steps are used in the initial stage of the simulation when the discharge is being built up and the plasma density is low. Alternatively, we choose to use a variable time step. This is done in the following way. At the beginning, the time step is set to satisfy (3.16) for the initial electron density. Afterward, at every 5,000 time steps the maximum electron density in the discharge is found and if (3.16) does not hold anymore, the time step is increased by 25%. This is illustrated in Fig. 3.12, where the time evolution of the time step in a typical simulation is shown. As it is seen, during a signiﬁcant part of the simulation, the time step is larger than the steady state time step. This allows decreasing the necessary number of computational cycles, and hence the overall computation time, by 30–40%. Optimization of the Weighting The weighting has been discussed in previous sections “Charge Assignment” and “Force Interpolation and Smoothing”. Each particle should be assigned to the four NGPs at every time step. If the coordinates of the particles are stored in physical units for distance, a ﬂoating-point division should be performed to determine to which cell the particle belongs. This is computationally very costly. Instead, the coordinates of the particles are stored in terms of grid cells. For example, if the ith particle has a coordinate, r = 3.356 expressed in cell units, rather than in meters, the determination of the cell in which the particle is located is done by simply taking the integer part of the coordinate.

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The remaining part speciﬁes the location of the particle inside the cell. When the real coordinate of the particle is needed, a multiplication is performed, which is computationally more eﬀective than a division. Sorting In the classical form of the PIC method, the simulated particles of a given type are indistinguishable. Each particle is just an element of an array. The position of the particle in this array, i.e., its number, is arbitrary and does not provide any speciﬁc information for the particle. This means that there is no correlation between the position of the particle in the array, and the particle’s location in the coordinate space. This organization is somehow natural to understand and straightforward to program. The addition of the MCC technique ﬁts into this scheme if the collisions are only between the given type of particles and the background gas, which is homogeneously distributed in the velocity and coordinate space. Examples for such collisions are the electronargon atom collisions. In any other type of collisions (e.g., Coulomb collisions), a collision partner must be found, based on its spatial location. One way to do that is to perform a search among all the particles and to ﬁnd all collision candidates that are in the vicinity of the incident particle. The usual method here is to approximate this vicinity to the cell in which the incident particle is located. Such procedure is, however, computationally very ineﬃcient. Alternatively, if the array of the particles is not randomly formed, but ordered in such a way that the number in the array is in direct relation to the cell where the particle is located, ﬁnding a collision partner will be much faster. The ordering of the particles in such a way is called sorting. It not only facilitates the calculation of collisions, but also has a strong, positive side eﬀect. It speeds up the entire PIC-MCC simulation. This acceleration is in relation with the architecture of the modern computers, as is explained in [144]. It has been reported [166] that for a 2d3v PIC simulation the calculation time decreases with 40–70% when sorting is implemented. Algorithms for ordering of data can be found in text books of numerical methods [167, 168]. However, common sorting techniques are very slow at sorting large arrays of particles, which is the case in a PIC-MCC simulation of a DC magnetron. For example, a quicksort, which is an “in place sort algorithm” [168], needs to pass through the particles approximately log2 N times, where N is the number of particles. This leads to the impressive 8kN log2 N ﬂoating point memory loads and stores for the case of a 2d3v PIC-MCC simulation with k types of particles. This ineﬃciency is a result of the fact that most of the well-known sorting algorithms originate from the past, when the amount of memory has been the main restriction. Contemporary workstations oﬀer suﬃcient amount of memory and thus there is no need for in place algorithms (algorithms that order an array without using auxiliary arrays). Therefore, we used the “out of place sorting algorithm” [166], as is explained in detail in [144].

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Diﬀerent Weights for Diﬀerent Types of Particles Depending on the aim of the particular magnetron simulation, diﬀerent plasma species can be included that can have rather diﬀerent number densities. For example, while the electrons and argon ions have always similar densities, the density of the sputtered atoms and fast argon atoms is typically one to three orders of magnitude higher. In this case, it is not feasible to use the same weight for the neutrals and for the charged particles. The condition that the minimum number of followed particles must be such that there are at least several SPs per Debye sphere, combined with the demand for maximal speed of the calculations, determines the weight of the SPs representing the real type of particles with the lowest density. The weight of the SPs representing the real particles with higher density is chosen also higher. How much higher is determined from the practical consideration that the number of SPs from each type must be similar. Using diﬀerent weights allows obtaining the necessary statistical representation, without paying the price of following an unnecessary large number of SPs. The implementation of diﬀerent weights is trivial in a PIC code. When a MCC method is added, however, there are two cases. The ﬁrst one is when plasma species collide with the uniformly distributed background gas, or when they collide with other plasma species with the same weight. In this case, the procedure is the same as when all SPs are equally weighted, because the weight is anyway included in the charge assignment and force interpolation. The second case includes collisions between SPs with diﬀerent weight. This requires an additional treatment, as explained in detail in [144]. The guiding principle here is that the SPs represent real particles, and all physical relations between the physical particles must be correctly represented by the SPs. 3.5.4 Examples of Calculation Results Operating Conditions and Simulation Data In this section, the PIC-MCC model described in Sect. 3.5, will be applied to a laboratory magnetron, Von Ardenne PPS 50 (see below), operated in argon with a copper cathode, to illustrate the type of results calculated with this model. This includes, among others, the distribution of the electric ﬁeld and potential, the densities of the plasma species and their energy distribution functions, and the erosion proﬁle as a result of cathode sputtering. The calculation results will be quantitatively compared with existing experimental and numerical data. The scheme of the planar magnetron used for the calculations is shown in Fig. 3.13. It is a Von Ardenne PPS 50 magnetron (commercially available), used with plasma shield (the sidewall on the scheme in Fig. 3.13). The axisymmetric magnetic ﬁeld is created by two concentric magnets located under the powered electrode, i.e., the cathode. The magnetron is balanced, which means

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30 Substrate 20

z (mm)

10

0

Cathode

-10

S

N

N

S Yoke

-20 0

10

20 r (mm)

30

Fig. 3.13. Scheme of the magnetron Von Ardenne PPS 50 with the spatial distribution of the (measured) magnetic ﬁeld. The scheme is axisymmetrical relative to the axis, r = 0

that the majority of the magnetic ﬂux lines originates at and returns to the cathode surface without crossing the anode. All walls, except the cathode, are grounded and act as an anode. The smallest separation between the electrodes is equal to 2 mm and the distance between the cathode and the opposite anode plate, where the substrate is mounted, is 24 mm. The cathode is a copper disk with a thickness of 3 mm and a diameter of 58 mm. The discharge is maintained by a DC power supply, which can be run in a constant current or in a constant voltage mode. The magnetic ﬁeld used in the simulation has been experimentally measured when the discharge has been not operational. In the simulation, the external circuit shown in Fig. 3.8 above, is connected to the cathode. In this numerical study, the magnetron plasma consists of argon atoms, singly charged argon ions and electrons only. All other plasma species are excluded from the analysis. In addition, the argon atoms are considered homogeneously distributed at room temperature (300 K). The choice of these plasma species is dictated from the fact that they are the dominant ingredients and play the main role for the formation and maintenance of the discharge.

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The inﬂuence of the sputtered atoms and the presence of the nonequilibrium argon atoms will be discussed in Sect. 3.6 below. The collisions that are taken into consideration are electron elastic scattering from the argon atoms, electron- and ion-induced excitation and single ionization of the argon atoms, and elastic scattering of argon ions from their parent atoms. The last process includes isotropic scattering and charge transfer. The excited argon atoms are not followed in this simulation. The process of their formation, however, is important for a correct representation of the energy balance. In the case of electrons, it also contributes to the conductivity of the discharge, since the electrons cross the magnetic ﬁeld lines due to collisions. Because the main excitation levels of the argon atom are very closely located in terms of energy [169], all electron-impact excitation processes are grouped into a single collision with an energy loss for the electrons of 11.55 eV. This is done to limit the computational time. The cross sections of the abovementioned collisions have been adopted from the literature [169–173], and can be found back, plotted as a function of energy, in [144]. At the walls, besides sputtering and secondary electron emission, also recapture of electrons at the cathode is included (see also the previous section). The maximum number of the SPs in this simulation is two millions, i.e., one million electrons and one million argon ions. In the beginning of the simulation, they are loaded with uniform density in the coordinate space and with a Maxwellian distribution in the velocity space. The initial density equals 3 × 1014 m−3 . The external circuit is set with a resistor of 1,200 kΩ and with a constant voltage source of −800 V. This corresponds to typical experimental values of this type of magnetron. The maximum magnetic ﬁeld is 0.045 T. The computational grid has 241 nodes in z-direction and 129 nodes in r-direction. The initial time step is set to 3×10−10 s. The number of electron subcycles per ion cycle is 25. The simulation is run until convergence is obtained in terms of cathode potential and particles’ densities. This is illustrated in Fig. 3.14, where the time evolution of the cathode potential, Φ0 , is shown. Note that, although the external applied voltage is equal to −800 V, the voltage drop across the magnetron discharge is only about −330 V. The gas pressure for this example of simulation results is kept ﬁxed at 0.67 Pa. Calculated Potential and Electric Field Distribution The calculated potential distribution is shown in Fig. 3.15. It has a clearly expressed radial dependence, which follows the pattern of the magnetic ﬁeld. The gradient in the potential is steepest near the cathode (i.e., in the sheath, see below), and at about r = 18.2 mm, where the radial component, Br , of the magnetic ﬁeld has a maximum. Above the center of the cathode, where the magnetic ﬁeld lines are perpendicular to the cathode surface (see Fig. 3.13), the potential shape is identical to that of a nonmagnetized discharge. As a whole, the plasma potential is negative almost in the entire discharge, i.e., the discharge operates in a negative space charge mode. This

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Cathode potential, Φ0 (V)

0

-100

-200

-300

-400 0x100

10-5

2x10-5 Time (s)

3x10-5

4x10-5

Fig. 3.14. Relaxation of the calculated cathode potential, Φ0 , with the physical time of the simulated system. The convergence occurs at time, t ∼ 12 μs

Fig. 3.15. Calculated potential distribution

is in accordance with analytical models [46, 62], a 1d PIC-MCC simulation of a cylindrical postmagnetron [36], and experimental measurements at similar operating conditions [174]. The sheath architecture can also be seen in Fig. 3.15. The sheath itself should be redeﬁned in the case of magnetrons. In nonmagnetized glow discharges, the sheath boundary is frequently deﬁned at the line, which separates the negative from the positive values of the potential. This deﬁnition works well in discharges operated in positive space charge mode. In mag-

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netrons, however, the sheath border should be deﬁned as a line where the potential has a well-pronounced inﬂexion. After the sheath, the next part of the potential can be deﬁned as a presheath. This region is still characterized by a negative space charge and a relatively small electric ﬁeld (in comparison to the sheath). This presheath is totally absent in discharges with positive space charge. The reason for appearance of the negative space charge and the presheath is in the restricted mobility of the electrons, due to the magnetic conﬁnement. The potential distribution from Fig. 3.15 creates an electrical ﬁeld, which axial and radial components are shown in Figs. 3.16 and 3.17, respectively.

Fig. 3.16. Axial component, Ez , of the electric ﬁeld. The white line corresponds to Ez = 10 kV m−1 and may be considered as the end of the sheath

Fig. 3.17. Radial component, Er , of the electric ﬁeld

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Fig. 3.18. Radial component of the electric ﬁeld, Er , in the region r ≤ 25 mm

The magnitude of the axial ﬁeld, Ez , is approximately ten times stronger than the magnitude of the radial ﬁeld, except in the proximity of the gap between the cathode and the sidewall. In the sheath region above the racetrack, Ez approaches 500 kV m−1 . The sheath border with its strong radial dependence is represented by the white line in Fig. 3.16. Along it, the magnitude of the ﬁeld is approximately 10 kV m−1 . The sheath thickness is only 1.6 mm above the racetrack, whereas at r = 0 it is about 13 mm. The sheath is thinnest and Ez strongest exactly in the middle between the magnetic poles (r = 18.2 mm). The radial ﬁeld, Er , changes in the sheath. The ﬁeld is strongest near r = rmax , where the gap between the cathode and the grounded side wall is located. The structure of Er is such that the region where Er > 0 repels the electrons outward, whereas the region Er < 0 accelerates the electrons outward. This has an eﬀect of electrostatic trap, which enhances the magnetic conﬁnement. The “valley-mountain” structure of Er is more clearly seen in Fig. 3.18, where the region of the discharge away from the sidewall is shown. Calculated Electron and Ar+ Ion Densities Figure 3.19 shows the calculated electron density proﬁle. Most electrons are strongly conﬁned between the magnetic poles. The calculated density proﬁle reproduces satisfactorily the experimental data obtained by Langmuir probe measurements. For example, the calculated peak value at p = 5 mTorr is 1.6 × 1017 m−3 , whereas in [174] it is 9 × 1016 m−3 at p = 2 mTorr. The plasma decay with the distance from the cathode, as well as the radial variation of the electron density, agree very well with the data reported in [172] for p = 5 mTorr. The plasma distribution has a distinctive maximum at z = 1.2 mm. Except in the sheath, the Ar+ ion density proﬁle is identical to the electron density proﬁle. This is so, because although the ions are not magnetized, and therefore not magnetically trapped, they are electrostatically bound to the electrons. The Ar+ ion density proﬁle has a maximum at the same spot as

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Fig. 3.19. Calculated electron density

Fig. 3.20. Calculated proﬁle of the electron-impact ionization rate

the maximum of the electron density. In the sheath, the Ar+ ion density is nonzero, in contrast to the electron density. This gives rise to a positive space charge, and hence strong gradients in the potential distribution and axial electric ﬁeld distribution. Calculated Collision Rates For the sustainment of the discharge, ionization of the argon atoms is crucial. In the present model, ionization is carried out by electrons and Ar+ ions. The calculated electron-impact ionization rate is illustrated in Fig. 3.20. The Ar+ impact ionization rate is not shown, because it is of minor importance at the operating conditions investigated. It is present only in the sheath where the ions can gain enough energy from the electric ﬁeld to ionize the atoms [144]. Its peak (5×1021 m−3 s−1 ) is about 1.5 order of magnitude lower than the peak of the electron-impact ionization (1.2 × 1023 m−3 s−1 ). Integrated over the whole computational domain, electron-impact ionization is about 800 times more

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Electron-impact ionization (m-3s-1)

1.2x1023

8.0x1022

4.0x1022

0.0x100 0

5

10 15 z (mm)

20

25

Fig. 3.21. Calculated electron-impact ionization rate, as a function of distance from the cathode, above the racetrack at r = 18.2 mm

important than Ar+ -impact ionization. Therefore, with reasonable accuracy, the Ar+ -impact ionization can be omitted in models and estimates for the current operating conditions. This is like expected, in view of the low voltage across the magnetron. In DC nonmagnetized glow discharges, where the applied voltage is in the order of 1 kV, this process cannot be neglected for an accurate description of the discharge behavior [175]. The axial proﬁle of the electron-impact ionization rate above the racetrack at r = 18.2 mm is shown in Fig. 3.21. It has a maximum at z = 1 mm, i.e., inside the sheath. Its closeness to the cathode can be explained with the magnetic conﬁnement. The Larmor radius for electrons with a speed of 107 m s−1 in a magnetic ﬁeld of 450 G is 1.26 mm. This means that the electrons, ejected from the cathode, stay long enough in a hemisphere, which center is on the cathode and with a diameter equal to the Larmor radius. The electrons have an energy, which is optimal for ionization, before reaching the surface of the hemisphere. The shape of the ionization proﬁle shows that most of the ionization is carried out by the primary electrons, originating at the cathode, rather than by secondary electrons, created in ionization collisions. There is nevertheless a signiﬁcant amount of ionization taking place in the presheath and even in the bulk plasma. The borders of the two regions are reﬂected in the two inﬂexion points of the ionization proﬁle at z ≈ 4 mm and z ≈ 14 mm. The rates of electron elastic collisions and electron-impact excitation are characterized by a similar proﬁle as the electron-impact ionization rate, but a second maximum is observed at about z = 2–3 mm. This can be explained, because the mean electron energy in this region is around 10 eV, which gives

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Fig. 3.22. Calculated mean energy of the electrons. Note that the z-axis is now reversed with respect to the previous ﬁgures, for the sake of clarity of the presented results. The cathode is still located at z = 0. The white line in the bulk corresponds to an energy of 10 eV

rise to a lot of elastic collisions and excitation, but which is a bit too low for eﬃcient ionization. Calculated Mean Energy and Energy Probability Function The collision rates, together with the distribution of the electric and magnetic ﬁeld determine the spatial distribution of the mean electron and ion energy and the corresponding energy probability functions. The calculated mean energy of the electrons is presented in Fig. 3.22. Note that the z-axis is reversed now, so that the energy spatial distribution is more clearly visible. Above the racetrack, where the electrons are strongly magnetized, their mean energy is about 40 eV. With radial displacement from the racetrack, the mean energy increases to 180 eV above the edges of the cathode. This increase is proportional to the weakening of the radial component of the magnetic ﬁeld away from the centers of the magnets. Those electrons that enter the bulk are mostly with low energies, i.e., below the inelastic threshold. This fact, as well as the sharp transition of the mean energy proﬁle to a plateau, immediately after the sheath, illustrates the eﬀectiveness of the magnetron: the primary electrons are almost entirely utilized in ionization and excitation events before being lost. The region along the symmetry axis is strongly depleted from electrons, which is reﬂected by the “valley” in the mean electron energy proﬁle. The distribution of the Ar+ ion mean energy (Fig. 3.23) follows the potential distribution. As it can be expected, the mean energy is high only in the sheath, with a maximum on the cathode surface. In the bulk, it is low, i.e., between 0.2 and 0.6 eV. The mean ion energy in the region between the

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Fig. 3.23. Calculated mean Ar+ ion energy. The cathode is located at z = 0

poles of the magnet is about 225 eV, which is approximately 70% of the cathode voltage. This ratio is slightly higher than the ratio of 60%, calculated in [116]. The diﬀerence can be explained from the broader sheath in [116], which allows the ions to spend more time in the sheath and consequently increases the probability for symmetric charge transfer collisions. These collisions are one of the two factors preventing the ions from obtaining energy values equal to the full cathode potential. The second factor is related to the location of the maximum of the ionization (see Fig. 3.20 above); it is between the sheath and the presheath. Thus, most of the produced ions accelerate in a potential diﬀerence that is less than the full interelectrode potential. All this shows that the common assumption of “freely falling ions” is not very accurate. Finally, in contrast to the electron mean energy, the ion mean energy does not have a radial minimum above the racetrack. This is a direct result from the fact that the ions are not magnetized. The mean energy does not provide information about the population in the energy spectrum. Such information is given by the energy probability function (EPF), f (ε)(= F (ε)ε−1/2 ), where F (ε) is the energy distribution function and ε is the energy. The normalization of the EPF is: f (ε)ε1/2 dε = 1. The knowledge of the EPF also allows us to determine what the distribution of the velocities is and therefore to deﬁne a temperature, which allows simulated data to be compared with data received from probe measurements. As it has been already discussed, probe measurements are normally devoted to study the bulk plasma, because the sheath region compromises the accuracy of the probe readings [176]. For this reason, to compare our calculation results with experimental data, the quasilocal EPF has been sampled in the bulk in the present example. The sampling spot is a volume given by 14 mm < z < 16 mm and 16 mm < r < 20 mm. The calculated electron energy probability function (EEPF) is shown in Fig. 3.24. It represents practically a Maxwellian distribution with a temperature of 6.7 eV. Such a value is in good agreement with the spatial survey of magnetron plasma by means of a Langmuir probe [177]. In

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1012

EEPF (eV-3/2m-3)

1011 1010 109 108 107 106 0

20

40 Energy (eV)

60

80

Fig. 3.24. Calculated electron energy probability function (EEPF) in the bulk (14 mm < z < 16 mm, 16 mm < r < 20 mm)

the latter experiments, for p = 5 mTorr, the electron temperature at z = 3 cm is found to be 5 eV and decreases with increase of z(Te = 2.5 eV at z = 5 cm). Therefore, our calculated Te of 6.7 eV at z = 1.5 cm appears to be consistent with the experiment. The Maxwellian distribution at such low pressure is a result of the magnetic conﬁnement of the electrons, which secures enough collisions with the argon atoms before the electrons diﬀuse into the bulk. There are reports in the literature for existence of two electron populations with diﬀerent temperatures, which produces a Bi-Maxwellian distribution [178, 179]. More recent work [177], however, fails to conﬁrm such phenomenon. The calculated results in the present example also do not indicate the existence of two electron populations with diﬀerent temperatures. The Ar+ ions behave in a very diﬀerent way than the electrons. Being practically not magnetized, the ions cannot stay for a long enough time in the discharge. This means they cannot suﬀer enough collisions for bringing them in equilibrium with the background gas. This is reﬂected in their EPF, shown in Fig. 3.25. As it is clear from this ﬁgure, the energy distribution is far from Maxwellian or other equilibrium distributions. In this case, the use of the temperature as a characteristic of the velocity distribution makes no sense. This result indicates that the use of ﬂuid description for the plasma in DC magnetron discharges operated at standard conditions will not be correct. The same refers to hybrid models [110], where a Maxwellian distribution for the ions is normally assumed and they are treated as a continuum. The IEPF in Fig. 3.25 also questions the idea of measuring the ion temperature

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Ar+ IEPF (eV-3/2m-3)

1013

1012

1011

1010

0

4

8 12 Energy (eV)

16

20

Fig. 3.25. Calculated Ar+ ion energy probability function (IEPF) in the bulk (14 mm < z < 16 mm, 16 mm < r < 20 mm)

in DC magnetrons by probe experiments. In a more global aspect, the ion temperature does not bring any valuable information for the state of the plasma in DC magnetrons. It can only be used as mean ion energy, without providing any further insight for the velocity distribution. Calculated Ion Flux Bombarding the Cathode The Ar+ ions that reach the sheath region or are created inside the sheath, accelerate toward the cathode, which they can bombard. This bombarding ﬂux is responsible for the generation of primary electrons that sustain the discharge and for the sputtering. The rate of sputtering is proportional to the energy density of the bombarding ﬂux. The spatial distribution of this ﬂux at the cathode surface determines the sputtering region, i.e., the racetrack. Therefore, the knowledge of the ﬂux is important, to predict the utilization of the target at given operating conditions. The calculated Ar+ ion ﬂux at the cathode is therefore presented in Fig. 3.26. The ﬂux is more or less limited to the region between the magnetic poles. This is in accordance with all experimental data, for instance for the erosion rate due to sputtering (see also Sect. 3.6). Its amplitude is proportional to the Ar+ ion density. The localization of the ﬂux, which follows the localization of the ion density in the radial direction, is a conﬁrmation of the fact that the ions are practically not magnetized. Therefore, their movement in the sheath can be approximated as being directed toward the target, only disturbed by the collisions in the sheath.

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Ar+ flux at the cathode (m-2s-1)

0.0x100

-4.0x1020

-8.0x1020

-1.2x1021

-1.6x1021 0

10

20

30

r (mm)

Fig. 3.26. Calculated Ar+ ion ﬂux at the cathode

As mentioned before, this Ar+ ion ﬂux gives rise to sputtering at the cathode (target). The behavior of sputtered atoms and corresponding ions, as well as of the Ar metastable atoms (which are important for the ionization of the sputtered atoms), will be described in Sect. 3.6.

3.6 Extension of the PIC-MCC Model: To Include Sputtering and Gas Heating In Sect. 3.5, a detailed description has been given about the PIC-MCC model for an argon DC magnetron with copper cathode. The behavior of the sputtered copper atoms and corresponding ions was, however, not yet taken into account, because the Ar+ ions and electrons are the dominant plasma species, determining the magnetron discharge behavior. However, to improve the application of sputter deposition, it is of course important to have a better insight in the behavior of the sputtered atoms. Therefore, the present section deals with an extension of the previously described PIC-MCC model to include the sputtered atoms and ions. Moreover, it should be realized that the region in front of the cathode in a sputter magnetron is a highly dynamic region. Except the charged particles and equilibrium gas atoms, there exist additional energetic species such as reﬂected, neutralized gas atoms, atoms born in charge exchange collisions, and nonthermal sputtered atoms. All of them can participate in momentum transfer collisions with the background, cold atoms. These collisions are expected to be highly eﬀective, due to the similar masses of the colliding partners. In this way, signiﬁcant energy and momentum can be deposited from the energetic species to the background gas, giving rise to gas heating, and thereby

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creating density inhomogeneity. These processes will also be treated in the present section. 3.6.1 Description of the Model Species Included in the Model and Their Collision Processes The present model is based on the general PIC-MCC algorithm, presented in the previous section, but some additional species are included, i.e., the fast argon atoms (Arf ), sputtered copper atoms (Cu), singly ionized copper ions (Cu+ ) and argon metastable atoms (Ar∗m ). The latter species are included, because they play an important role in ionization of the sputtered atoms. In addition, several new collision processes are added, such as electron-impact excitation to the Ar∗m levels, and excitation and ionization from these Ar∗m levels, quenching of the Ar∗m levels by collisions with electrons or Ar atoms, electron–ion recombination, ionization of the sputtered Cu atoms by electronimpact, Penning ionization and asymmetric charge transfer. Details can be found in [144]. Besides these collision processes in the plasma, also some additional surface interactions are taken into account, such as sputtering and secondary electron emission caused by fast atoms and copper ions (Cu+ ). Furthermore, deexcitation of the metastable argon atoms and recombination of the argon ions takes place at the walls. The energetic argon atoms are reﬂected and possibly thermalized at the walls. The coeﬃcient of thermal accommodation, which is a measure for the energy exchange between energetic plasma species and the walls, has been chosen equal to 0.5. Numerical Procedure As it has been explained in the previous section, the PIC-MCC simulation needs to be run until a convergence is obtained. This numerical convergence must be correlated to the attainment of steady state by the real physical system that is the subject of the simulation. The time necessary for the physical system to reach a steady state is determined by the slowest processes in the system. When the heating of the gas is taken into consideration, the characteristic time, τH for thermal equilibrium (i.e., bringing the heat conduction to a steady state) is the longest: τH ∼ 10−2 s. This estimate is based upon the relation [180] L cp ρL2 . = τH = VH k Here, L (0.1 m [101]) is the characteristic diﬀusion length, VH (= k/(ρcp L)) is the characteristic speed of heat transfer, cp is the speciﬁc heat per unit mass at constant pressure, ρ (= 7.97 × 10−5 kg m−3 [181]) is the argon mass density, k (= 0.018 W m−1 K−1 [181]) is the thermal conductivity of argon.

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At the same time, the characteristic time for bringing electrons and ions to steady state does not exceed 10−5 s. All other important processes, such as the relaxation time for thermalization of the energetic neutrals and pressure equalization, are situated in between these two limits. Because of this big diﬀerence in the characteristic time steps of the electrons, ions, fast neutrals, and thermal conduction, some modiﬁcations in the general PIC-MCC algorithm are necessary to cope with this disparity. Not doing so would result in a huge amount of computational time. This is so, because of the general restriction for the time step (3.16) (see section “Stability and Accuracy of the PIC Model”). The procedure used here [182] is to advance the diﬀerent sorts of particles with diﬀerent time steps. The hierarchy being Δte Δti Δtn (with e = electron, i = ion, and n = neutral). This diﬀerence in the time steps is accounted for by the weight, W of the produced energetic, charge-exchange neutrals and sputtered atoms, i.e., Wn = Ws = Wi

Δtn , Δti

(3.26)

where s refers to the sputtered atoms. Electrons are subcycled inside the ion time step (see section “Subcycling”) and have We = Wi . In this way, it is assured that the production and loss rates of the real plasma particles are correctly represented, i.e., the global mass conservation is obeyed. The procedure separates the particles into two groups, i.e., fast and slow. The upper size of the SPs from each group can be controlled independently from the corresponding value of the other group. When the upper limit is reached, only the members of the corresponding group are reduced twice, and their weight is doubled. The weight and number of the SPs from the other group are not changed. However, a change in the time step is needed, to maintain (3.26) to be valid. Because Δti is coherent with the stability criterion, the time step that always changes is Δtn (= Δts ). The overall cycle consists of one ion time step. At the end of this time step, the power, P , transferred to and from the feeding gas is accumulated mg Wn v l 2 − vl 2 vl2 v l 2 − + , P = Vcell Δtn 2 2 2 l

l

l

where vl is the post- and vl the precollision velocity of the lth gas atom, mg is the gas mass, Vcell is the volume of the computational grid cell. The ﬁrst sum is the contribution from all collisions between the feeding gas atoms from one side and the ions, fast atoms, metastable atoms, and sputtered atoms from the other side. Only collisions, in which the postcollision energy of the gas atoms is less than some threshold, are counted. This threshold is chosen to be [182] (3.27) Eth = 9 × 3/2kb Tg , where kb is the Boltzmann constant.

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The other collisions result in creation of fast gas atoms, which are incorporated by the second sum. The third sum is the contribution of the thermalized fast gas atoms. This calculated power is used as a source term in the heat conduction equation ∂Tg P 1∂ ∂ 2 Tg r =− , (3.28) + ∂z 2 r∂ ∂r k which is solved once per 10−8 s (actually, after each number of time steps divisible exactly by 100 and which sum is greater than or equal to 10−8 s) to calculate the gas temperature, Tg . In the above equation, k is the thermal conductivity of the gas. It should be mentioned that Tg is a dynamic quantity dependent on the coordinates. Consequently the threshold energy given by (3.27) is also dynamic (changes with time) and is a function of the coordinates. The sputtered atoms are followed as particles until being thermalized. Once that happens, they cannot anymore contribute to the gas heating directly; collisions between fast argon atoms and sputtered atoms are disregarded in the model, because of the statistical insigniﬁcance of the process. The overall copper density, however, is an important quantity for ﬁlm deposition purposes. Therefore, a compromise between accuracy of the algorithm and its computational eﬃciency is to treat the thermalized copper atoms as a ﬂuid. Thus, the overall copper density is a sum of the density of the fast copper atoms and the slow copper atoms. The density of the slow (thermalized) copper atoms, nsl Cu , can be obtained by solving the diﬀusion equation, which in (r, z) cylindrical coordinates reads DCu Δnsl Cu (r, z) = rloss (r, z) − rprod (r, z),

(3.29)

where DCu is the diﬀusion coeﬃcient of copper atoms in argon, rloss is the rate of loss of the slow copper atoms, and rprod is their production rate. The −1 diﬀusion coeﬃcient is taken to be, DCu = 1.44 × 10−2 cm2 s [183]. This value is based on the rigid-sphere collision model and refers to a pressure of 1 Torr and temperature of 300 K in argon. The loss rate of the copper atoms, rloss (r, z), is equal to the rate of ionization of the copper atoms, caused by electron-impact, Penning ionization, and asymmetric charge transfer. The production rate of the copper atoms, rprod (r, z), is equal to the rate of thermalization of the sputtered atoms. Equation (3.29), as well as (3.28), is mathematically the same as the Poisson equation for the potential. Therefore, the same numerical technique, i.e., cyclic reduction [154], is used for their & sl solution. ' The boundary conditions of (3.29) are Δnsl Cu |wall = 0 and ∇r nCu (0, z) = 0. The latter represents simply the cylindrical symmetry of the system. The procedure described above can be represented by the ﬂowchart in Fig. 3.27.

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Initial density and velocity distribution

PIC / MCC for e−, Ar+, Cu+ Production of neutrals Arf, Arm* , Cu with statistical weight Wn = Wi Δtn / Δti Advancing the external circuit

DMCS for Arf, Arm* , Cu, Production of e−, Ar+, Cu+ with statistical weight Wi = Wn Δti / Δtn

Heat Transfer Temperature calculation New gas density

Diffusion transport of Cusl New total Cu density

tn+1 = tn + Δt

No

Convergence

Output

Yes

Fig. 3.27. Flowchart of the simulation procedure for calculation of the gas heating and the behavior of the sputtered (copper) species. The abbreviation DMCS stands for “Direct Monte Carlo simulation”

3.6.2 Examples of Calculation Results The simulation procedure shown in Fig. 3.27 is applied to the magnetron discharge presented in Fig. 3.13. Simulations performed for pressures of 0.13, 0.53, 1.3, 3.3, 6.7, and 13 Pa, and for a maximum radial magnetic ﬁeld above the cathode of 1,300 G, will be illustrated here. To verify the expected pressure dependence of the gas heating, the parameters of the external circuit (see section “External Circuit”) have been readjusted in the course of the runs to maintain a constant power of 70 W.

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z (mm)

20 15 10 5 0

-30

-20

-10

0 10 r (mm)

20

30

Fig. 3.28. Contour plot of the calculated gas temperature distribution at p = 6.7 Pa

Gas temperature (K)

1000

800

600

400

200 0

2

4

6 8 10 Pressure (Pa)

12

14

Fig. 3.29. Calculated maximum gas temperature as a function of the gas pressure at constant electric power of 70 W

Temperature Distribution Figure 3.28 illustrates the calculated gas temperature distribution for the case of 6.7 Pa. The temperature reaches its maximum in the center of the discharge (both in axial and radial direction. The eﬀect of gas pressure on the maximum gas temperature is plotted in Fig. 3.29. At 0.13 and 0.53 Pa, there is practically no heating of the gas. The rise of the gas temperature is about 1 K, which is within the limit of the expected calculation error. With the increase of the pressure, the gas begins to heat up. For p = 1.3 Pa, the temperature increases to 316 K, at 6.7 Pa, the maximum gas temperature is about 600 K (cf. also Fig. 3.28), and it reaching almost 1,000 K at 13 Pa.

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Hence, it can be concluded that for the given operating conditions (argon gas, copper cathode, input power of 70 W), the gas heating is not signiﬁcant for pressures of up to 1.3 Pa. These are typical conditions for laboratory magnetrons. Commercial sputtering magnetrons may be up to ten times bigger and with power supplies of several kW. These operating conditions, however, are outside the scope of this study. Indeed, PIC-MCC simulations would become too time-consuming for such large magnetron discharges (see also Sect. 3.3 above). It is interesting to compare the obtained results with other data from the literature. The results for p = 6.7 Pa can be compared to [182], where the gas heating in a sputtering glow discharge is calculated for p = 5.6 Pa and 40 mm electrode separation. The temperature proﬁle obtained there for a copper cathode and three times higher cathode voltage agrees very well with the gas temperature proﬁle illustrated here. The lower voltage in the present case can be easily explained by the magnetic trap leading to much higher discharge eﬃciency, and to some extent with the smaller volume of the gas. Another comparison can be made with [184], which is the most often cited work in the literature about the gas heating in sputter magnetrons. The author reports a density reduction of about 37% for a pressure of 4 Pa and a current of 300 mA. This corresponds reasonably well with our calculation results, in spite of the larger reactor geometry. Indeed, it can be deduced from Fig. 3.29 that the gas temperature at 4 Pa would be around 440 K, which is about 47% higher than 300 K. More substantial is the diﬀerence with the calculations reported in the recent work of Epke and Dew [185]. The maximum temperature is on average a factor of two higher than the values presented here. In addition, the axial temperature proﬁle is with a diﬀerent shape. The values of the gas temperature in [185] are also higher than those in [184]. The shape of the proﬁle in [185] resembles those obtained for analytical glow discharges in [186]. The common issue between these two models is that they are entirely or partially ﬂuid. In addition, [185] is not a self-consistent simulation, but based on several assumptions, each of which brings uncertainties. The close correspondence of the absolute calculation values presented here, with the kinetic simulation [182] and the early experimental work [184] indicate that a kinetic self-consistent simulation represents more accurately the considered eﬀect of gas heating in sputter magnetrons at typical operating conditions. Density Proﬁles of the Other Plasma Species The 2D density proﬁle of the electrons (and Ar+ ions) was already presented in section “Calculated Electron and Ar+ Ion Densities” (Fig. 3.19). However, with the extended model, also the density proﬁles of the sputtered copper atoms, and the corresponding Cu+ ions can be calculated, as well as the density proﬁle of the Ar metastable atoms. Figure 3.30 presents the sputtered Cu atom density distribution at a pressure of 0.67 Pa. It shows a maximum at

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Fig. 3.30. Calculated sputtered Cu atom density

Fig. 3.31. Calculated Cu+ ion density

r = 18 mm, where also the electron (and Ar+ ion) density, the electron-impact ionization rate and hence the ion ﬂuxes toward the cathode reached their maximum. Indeed, the ion ﬂux gives rise to sputtering, hence most sputtering takes place at r = 18 mm, which explains the maximum in the sputtered Cu atom density. However, the peaks in the Cu atom density proﬁle are deﬁnitely not so pronounced as in the electron density proﬁle. This is because the Cu atom density proﬁle is much more spread out by diﬀusion. It was found that at 0.67 Pa, a nonnegligible fraction of Cu atoms with energies of a few eV can reach the opposite wall of this magnetron discharge, where normally a substrate is mounted for deposition purposes. At higher pressures, however, the majority of the fast Cu atoms thermalize before reaching the anode [39]. The density proﬁle of the corresponding Cu+ ions is illustrated in Fig. 3.31. It is characterized by a very similar proﬁle as the electrons and Ar+ ions, but its density is clearly lower, so the main positive charge in the plasma is attributed to the Ar+ ions. Erosion Proﬁle Due to Sputtering Finally, the last calculation result shown here is the calculated erosion proﬁle at the cathode, as a result of sputtering (see Fig. 3.32). Only one half of the axisymmetric target is shown. The erosion rate reaches its maximum at

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Normalised erosion profile

0.4

0

- 0.4

- 0.8 Calculated Measured -1.2 0

10

20

30

r [mm]

Fig. 3.32. Comparison of calculated (solid line) and measured (dashed line) normalized erosion proﬁle

r = 18 mm, as expected. To verify the model, the calculated erosion proﬁle is compared to a measured one at approximately the same operating conditions after 4 h of sputtering. The agreement is very satisfactory. This demonstrates that the model captures the major physical processes of magnetron sputtering, including two-dimensional eﬀects. Therefore, it can in principle be used to support experimental research, for instance for predicting how the target sputtering can be made more uniform and hence the target material can be consumed in a more eﬃcient way.

3.7 Conclusions and Outlook for Future Work In this chapter, we have given an overview of diﬀerent modeling approaches developed for magnetron discharges, emphasizing their beneﬁts and weaknesses. Furthermore, a two-dimensional self-consistent semi-analytical model and a two-dimensional PIC-MCC model are described in detail, and some examples of calculation results are presented. It was concluded that analytical approaches can give a very rapid prediction of certain discharge characteristics, but they are of course only valid under well-speciﬁed conditions. For a full description of the magnetron discharge, the PIC-MCC model is most appropriate, but it requires a very long computation time, which is acceptable for academic research, but unsuitable for industrial applications of sputter magnetrons. Nevertheless, the PIC-MCC simulations can give very useful insights,

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to assist experimental work, and to provide a benchmark for the development of analytical models. There is, however, still room for improvements and further developments of both models. The analytical model can be further improved by taking into account some processes which are neglected up to now, such as the self-consistent calculation of the electron temperature and the presheath, the electron contribution to the discharge current, and the eﬀect of gas density reduction. Furthermore, by making minor, nonfundamental changes to the model, it could also be used to investigate aspects of the magnetron discharge, like the eﬀect of the erosion groove formation on the target, or switching to another (nonreactive) discharge gas. The PIC-MCC model, developed up to now, will also form a basis for further numerical studies. Indeed, the model is now only applicable to DC magnetrons in argon, but for the deposition of metal oxides and nitrides, reactive gas mixtures (argon–oxygen or argon–nitrogen) need to be used. Therefore, we plan to extend the PIC-MCC model, as presented here, to reactive gas mixtures, to predict the discharge behavior for reactive sputterdeposition purposes. Moreover, DC magnetrons often encounter problems when reactive gas mixtures are used, due to the deposition of nonconductive oxides or nitrides onto the cathode surface, and the subsequent charging issues of the cathode, leading to discharge failure. Therefore, we would also like to extend the current PIC-MCC model, developed for a DC magnetron, to pulsed magnetron discharges, so that the model will become more widely applicable to a range of operating conditions.

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4 Modelling of Reactive Sputtering Processes S. Berg, T. Nyberg, and T. Kubart

4.1 Introduction Sputtering is a widely used technique to fabricate thin ﬁlm coatings. Equipment for large area coatings is easy to set up and ﬁlm uniformity may be satisfactory controlled over large processing areas. Sputtering is normally carried out in an argon ambient. Not only elemental pure single metal targets may be used, but also metal alloys can be sputtered which oﬀers the possibility to deposit also complex coatings. Common for all inert argon sputtering processes is that the simplicity of the process only requires rather rudimentary process control. These properties make sputtering an attractive and competitive coating process. By adding a reactive gas to the sputtering process, it is possible to form a compound between sputtered metal atoms and reactive gas molecules. In this way, it is possible to form oxides, nitrides, borides, carbides, etc. To distinguish inert argon sputtering from the process where reactive gases are added, the latter process is commonly referred to as a reactive sputtering process. At ﬁrst glance, one may believe that reactive sputtering processes may be as easy to carry out as the simple and straightforward inert sputtering processes. Unfortunately this is not the case. The addition of the reactive gas signiﬁcantly changes the behaviour of the sputtering process. Both deposition rate as well as the composition of the ﬁlm will be heavily inﬂuenced by the ﬂow of the reactive gas [1–3]. Typical processing curves are shown in Figs. 4.1 and 4.2. Figure 4.1 illustrates a schematic of a typical processing curve for ﬁlm deposition rate vs. ﬂow of the reactive gas. Note that the curve takes diﬀerent pathways for increasing the reactive gas ﬂow than for decreasing this ﬂow. This is indicated by the arrows in the ﬁgure. As can be seen, this curve shows a hysteresis behaviour. Increasing the reactive gas ﬂow slightly beyond the processing point A in the ﬁgure will result in an avalanche-like transition down to point B. Decreasing the reactive gas ﬂow from high values down to just below point C will result in an avalanche-like transition from C up to D

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Fig. 4.1. Typical experimental curve for a reactive sputtering process (rate indicated by means of optical emission spectroscopy)

Fig. 4.2. The partial pressure of the reactive gas corresponding to the curve in Fig. 4.1

in the ﬁgure. It is these avalanche-like transitions that primarily make process control rather complicated for reactive sputtering processes. Figure 4.2 illustrates a typical dependency of reactive gas partial pressure vs. ﬂow of the reactive gas. The processing positions A–B–C–D from Fig. 4.1 are indicated also in this ﬁgure. Note that also the partial pressure of the reactive gas will change dramatically at positions A and C and that this curve also exhibits a hysteresis at the same values of the ﬂow of the reactive gas as the curve in Fig. 4.1. Figures 4.1 and 4.2 may illustrate the processing curves for reactive sputter deposition of AlN from an elemental Al target in a mixture of Ar + N2 . It is known that the sputtering yield of Al is signiﬁcantly higher than the sputtering yield of AlN. This is one of the reasons for the complex behaviour of the processing curves. Originally (with zero ﬂow of nitrogen) the sputter erosion rate from the target is determined by the sputtering yield of the pure Al metal. A slight increase of the ﬂow of nitrogen will not signiﬁcantly change the composition of the target surface. Therefore the deposition rate does not

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change markedly. Sputtered atoms, however, will be deposited at a far larger substrate surface than the eroded target surface area. This results in a higher fraction of compound at the deposited substrate areas. From Fig. 4.2, it can be seen that, despite that the ﬂow of reactive gas increases (small values of the reactive gas ﬂow), almost no partial pressure is generated in the processing chamber. This illustrates that almost all nitrogen is used up to form AlN at the substrate. From zero and up to position A, the target is said to operate in metallic mode. AlN is formed also at the target but, due to the sputter erosion, less compound will be formed at the target than at the substrate. This explains the slow decrease of the deposition rate up to position A. At this position, conditions are generated that force the partial pressure to increase dramatically to position B. This new nitrogen partial pressure is high enough to completely form AlN also at the whole target surface. From this position, the target is said to be in the poisoned mode. It has been “poisoned” by the nitrogen and a layer of AlN has been formed on the target surface. As a consequence, the deposition rate will be determined by the low sputtering yield value for AlN instead of the much larger sputtering yield value for pure Al. This explains the drastic drop in deposition rate at position A. The nitrogen that is not used up to form AlN will contribute to building up of the partial pressure of nitrogen. Since less Al is sputter eroded after passing the transition A–B, excess nitrogen will show up as an additional nitrogen partial pressure. Consequently, the partial pressure of nitrogen will be higher during decrease of the nitrogen ﬂow. This will be valid until the nitrogen partial pressure will not be large enough to completely form AlN on the target. From this position (C), the target converts to being substantially metallic again (position D) and sputter erosion will be determined by the Al sputter yield.

4.2 Basic Model for the Reactive Sputtering Process As shown in the previous paragraph, the processing curves for the reactive sputtering process do exhibit hysteresis eﬀects. In addition, avalanche-like transitions occur at the edges of the hysteresis region. It is not easy to judge how diﬀerent processing parameters aﬀect the overall processing behaviour. This calls for a model capable of predicting the inﬂuence of diﬀerent parameters on the process. It should be understood, however, that a model taking into consideration all aspects of this process would be very complex and therefore not so useful for the common user. However, a model has been suggested that has successfully reduced the number of necessary parameters but still enables the users to predict the general behaviour of the outcome of deﬁned reactive sputtering processes. This model is commonly referred to in the literature as the “Berg’s model” [2–9]. Despite the simplicity of this model, it is frequently used as the base for more detailed treatments of reactive sputtering processes. The starting point for developing a model is to try to deﬁne the processing conditions as correct as possible. Simpliﬁcations must be made to keep the

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complexity down without loosing contact with reality. We start with showing a schematic of a simpliﬁed reactive sputtering processing chamber. This is shown in Fig. 4.3. We suggest that, for a mathematical treatment, Figs. 4.4 and 4.5 below may replace Fig. 4.3 to describe the reactive sputtering process. Figure 4.4 illustrates the ﬂux of sputtered particles from the target as well as the ﬂux of reactive gas molecules arriving to the substrate. A fraction (Θt ) of the target area (At ) has reacted with the reactive gas and formed a compound layer at the target surface. This is illustrated so that a fraction Θt of the target surface area consists of the compound. A similar situation will exist at the collecting (= substrate) area (Ac ) but the reacted fraction (Θc ) of this area will not be the same as at the target. During sputtering of the target, an outcoming ﬂux of sputtered metal atoms Fm will be generated. For simplicity we assume that this ﬂux

Fig. 4.3. A simple reactive sputtering system

Fig. 4.4. Particle ﬂuxes to the substrate area Ac

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Fig. 4.5. Flows of reactive gas in the system

originates from the metal fraction (1 − Θt ) of the target area. We also make the simpliﬁcation that sputtering from the compound area Θt at the target will result in sputter erosion of the compound molecules [10]. During sputtering of the target, a ﬂux of sputtered metal-compound molecules Fc will be generated. In the mathematical description of Figs. 4.4 and 4.5, the ﬂux Fc will originate from the Θt fraction of the target area. The argon ion current density causing sputtering from the target surface is denoted J. The argon ion current is assumed to be evenly distributed over the target surface. Note, however, that sputtering from the Θt fraction of the target will generate a ﬂux of compound molecules, while sputtering from the (1 − Θt ) fraction will result in sputtering of metal atoms. In addition to the sputtered particles, also reactive gas molecules will arrive at the target and the collecting areas. Figure 4.5 illustrates the three possible pathways Qc , Qt , and Qp for the total ﬂow Qtot of reactive gas to the processing chamber. The consumption of reactive gas molecules at the substrate is denoted Qc in the ﬁgures, Qt is the consumption at the target, and Qp is the throughput to the vacuum pump. We will use the notations from Figs. 4.4 and 4.5 in the following treatment. Solving for the behaviour of the reactive gas forms the basis of this treatment. The key parameter is the partial pressure P of the reactive gas. There exists a simple gas kinetic equation for the relation between ﬂux of molecules F at all surfaces and the partial pressure [11]. This relation is given by the expression P F = √ , (4.1) 2kT πm where k is a Boltzmann’s constant, T the absolute temperature, and m the mass of the gas molecule.

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4.3 Steady State Equations In the following treatment, it is assumed that the process has reached steady state condition. Thus there are no time-dependent variations in the process. This will make it fairly easy to ﬁnd balance equations for the target and collecting areas At and Ac . Furthermore, we assume that the partial pressure of argon is much higher than the partial pressure of the reactive gas. Based on this, we assume that the sputtering contribution from ionized reactive gas can be neglected. Sputtering is assumed to be carried out by the argon ions. To avoid introducing confusing constants, we also assume that one reactive gas atom forms a compound molecule with one target metal atom and one gas atom (AlN, TiN, etc.). The reader may adjust for this in the case of forming other compounds (like TiO2 , Al2 O3 , etc.). The target area will be evenly sputter bombarded by the argon ion current density J(A m−2 ). At steady state, a balance must exist between sputter removal of compound material from the poisoned part Θt of the target and formation of compound due to poisoning of the (1−Θt ) metal part by reactive gas. This condition is described by (4.2) J Yc Θt = α2F (1 − Θt ), q

(4.2)

where q is the electron charge. The left-hand side determines the sputter removal of compound molecules, where Yc denotes the sputtering yield of compound molecules from the target by energetic ions hitting the poisoned fraction Θt of the target. The right-hand side deﬁnes the formation of compound molecules at the (1 − Θt ) metal part of the target. Here 2F deﬁnes the ﬂux of reactive gas atoms (assuming two atoms per gas molecule) at the partial pressure P and α denotes the sticking coeﬃcient, the probability that an arriving gas molecule will react with the target metal and form a metal-compound molecule at the target surface (poisoning). From (4.2) it is easy to solve Θt as a function of F . The steady state condition for the substrate area Ac can be derived by corresponding arguments. At steady state, the sum of the sputtered material (metal atoms and compound molecules) and the reactions with deposited ﬁlm metal atoms balances so that the substrate surface concentration Θc does not change. The total rate of outsputtered compound molecules Fc from the target will be J Fc = Yc Θt At . (4.3) q A fraction Θc of these molecules will arrive at the compound part Θc Ac of the substrate area. However, depositing compound on compound does not alter the chemical condition of this part of Ac . Depositing compound on the metal fraction (1 − Θc )Ac of the substrate area, however, will convert a metal

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surface to a compound surface. Thus, the rate of converting the metal part of the substrate surface to compound by deposition of outsputtered compound molecules can be described by the expression Fc (1 − Θc ). In addition to this, compound molecules may also be formed by reactions with the reactive gas and the non-reacted metal atoms at the (1 − Θc )Ac fraction of the substrate surface. This will also convert some of the metal fraction to compound. The total conversion rate for formation of these compound molecules is 2Qc , where Qc = αF (1 − Θc )Ac .

(4.4)

The total rate of forming compound molecules at the substrate surface will be the sum of the terms Fc (1 − Θc ) and 2Qc . The factor 2 corresponds to the fact that one reactive gas molecule forms two molecules of compound. Sputtered unreacted metal atoms will also arrive to the substrate surface. The total rate of erosion Fm from the target for these metal atoms will be Fm =

J Ym (1 − Θt )At , q

(4.5)

where Ym denotes the sputtering yield of metal atoms. The fraction Θc of the substrate surface consists of compound and the remaining fraction (1 − Θc) consists of pure unreacted metal atoms. Sputtered metal atoms arriving at the metal-compound fraction of the substrate will convert some metal-compound area to metal area in a corresponding way as described for the arriving metal molecules above. At steady state, the rate of compound formation due to sputtering of compound and gettering of reactive gas onto metal parts of the substrate equals the elimination of compound due to deposition of metal onto compound parts of the substrate. This deﬁnes the balance equation of the substrate surface Fc (1 − Θc ) + 2Qc = Fm Θc .

(4.6)

From (4.2) and (4.6), it is relatively simple to solve for Θc as a function of F . In addition to solve for Θt and Θc , we also want to obtain an expression for the deposition rate D. This can be obtained by ﬁrst calculating the sputter erosion rate from the target. We have assumed that every compound molecule contains one metal atom and one atom from the reactive gas. Thus, the total number of outsputtered metal atoms from the target Rm must be Rm =

J [Ym (1 − Θt ) + Yc Θt ]At . q

(4.7)

A fraction Θc of these metal atoms has reacted with the reactive gas and formed compound molecules at the substrate. The remaining (1 − Θc ) fraction is still unreacted metal atoms. Assuming that Rm will be evenly distributed over the area Ac and taking into consideration the speciﬁc densities of the

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Normalized rate, Rm, D (a.u.)

1.2 1.0 0.8 D 0.6 0.4 Rm 0.2 0.0 0.00

0.05

0.10

0.15

0.20

0.25

0.30

Reactive gas pressure (Pa) Fig. 4.6. Sputter erosion rate Rm and substrate deposition rate D vs. the pressure of reactive gas

elemental metal and the formed compound, the deposition rate D may be written as (4.8) D = Rm [c1 (1 − Θc ) + c2 Θc ], where c1 and c2 are the material-speciﬁc related constants to obtain the desired unit for D. Typical results for calculated values for D and Rm as a function of the partial pressure P are shown in Fig. 4.6. Note that D initially may increase somewhat for a small ﬂow of the reactive gas before slowly decreasing due to the decrease in Rm . This maximum is caused by outsputtered metal atoms taking up reactive gas atoms thus forming compound molecules at the substrate surface. At this stage, it must be pointed out that D and Rm do not show any hysteresis behaviour when plotted as a function of the reactive gas partial pressure. This was not the case for the deposition rate vs. reactive gas ﬂow as previously shown in Fig. 4.1, where the curve has a pronounced hysteresis. To be able to plot D and Rm as a function of the reactive gas ﬂow Qtot , we must ﬁnd a relation between Qtot and P . From Fig. 4.5, we may conclude Qtot = Qt + Qc + Qp ,

(4.9)

where Qc , Qt , and Qp as indicated by the arrows represent the reactive gas consumptions at the substrate and target surfaces and throughput to the external vacuum pump Qt = αF (1 − Θt )At ,

(4.10)

Qc = αF (1 − Θc )Ac , Qp = SP,

(4.11) (4.12)

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where S is the pumping speed of the vacuum pump. For simplicity, we choose the same sticking coeﬃcient α at the target and substrate areas. These additional mass ﬂow equations unambiguously deﬁne the relation between Qtot and P . From what has been derived so far, it is possible to plot Θc , Θt , P, D, and Rm vs. the Qtot . Typical results from such calculations are shown in Figs. 4.7–4.9.

1.0 B

C

Fractions Θt, Θc

0.8

0.6

0.4

A

Θc

Θt

0.2 D 0.0

0

1

2

3

4

5

Reactive gas flow (sccm) Fig. 4.7. Calculated compound fractions Θt and Θc at the target and substrate, respectively, as a function of the ﬂow of reactive gas

Normalized rate, Rm, D (a.u.)

1.2 1.0 D

0.8

A 0.6 0.4

D C

B

0.2 0.0

Rm 0

1

2

3

4

5

Reactive gas flow (sccm) Fig. 4.8. Calculated sputtering Rm and deposition D rate vs. the ﬂow of reactive gas

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Pressure, P (a.u.)

0.4

0.3

B

0.2

0.1

0.0

C A

D 0

1

2

3

4

5

Reactive gas flow (sccm) Fig. 4.9. Calculated pressure vs. the ﬂow of reactive gas

Processing points corresponding to the positions A, B, C, and D in Figs. 4.1 and 4.2 are inserted in all the calculated curves. A continuous increase or decrease of the reactive gas ﬂow Qtot will directly cause an avalanche from A to B (increasing Qtot ) or from C to D (decreasing Qtot ). By only varying Qtot , it will not be possible to operate the process on the A–C part of the curve. The width of the S shape of the curves represents the hysteresis width. This region is marked by the shadowed region in the ﬁgures. It should be pointed out that a practical optimum operation point frequently appears to be as close to the left of point A as possible. Due to small processing ﬂuctuations, however, it is diﬃcult to obtain a stable operation at this position. A small increase in reactive gas ﬂow will cause a dramatic change (decrease) in deposition rate. To return to the high deposition rate close to the left of A, one has to pass through the whole hysteresis loop. This is not a satisfactory solution for a process control system. From Fig. 4.6, it was shown that selecting the reactive gas partial pressure P as the control parameter results in single-valued erosion and deposition rates for all values of P . Due to this, a feedback control system setting a desired value for the partial pressure is the preferred way of carrying out process control for reactive sputtering processes. With the partial pressure control, it is possible to follow the curves in Figs. 4.7–4.9 without avalanching at A and C. Thus, it is possible to operate at any working point. The width and shape of the hysteresis depend on diﬀerent processing parameters. In the following, it will be illustrated how some material properties and processing conditions aﬀect the hysteresis.

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4.4 Inﬂuence of Material Properties and Processing Conditions 4.4.1 Reactivity The value of the sticking coeﬃcient α indicates the reactivity between the gas and the target metal. In Fig. 4.10, the calculated sputter erosion rate Rm vs. Qtot for three reactive sputtering processes diﬀering only in their values of α is shown. The results illustrate clearly that the hysteresis will be less pronounced for low reactivity processes [12]. For some gas/target material combinations, the hysteresis eﬀect may not even occur. 4.4.2 Sputtering Yield The sputtering yield value for the metal (Ym ) is typically signiﬁcantly higher than the sputtering yield value for the corresponding compound (Yc ). The hysteresis is very sensitive to the ratio Yc /Ym . Figure 4.11 shows the calculated sputter erosion rate Rm vs. Qtot for three reactive sputtering processes diﬀering only in their values of the ratio Yc /Ym . The results illustrate that the hysteresis will be less pronounced for materials where Yc does not deviate too much from Ym [13]. Due to this eﬀect, some target materials may exhibit small or almost no detectable hysteresis. It must be understood that reactivity α and the ratio Yc /Ym are fundamental material properties. It is therefore not possible to freely choose these values in a speciﬁc processing condition.

Sputter erosion rate, Rm (a.u.)

1.0

0.8

0.6

0.4 0.3 0.2

0.0

0.1

α=1

0

1

2

3

4

5

Reactive gas flow (sccm) Fig. 4.10. Inﬂuence of the sticking coeﬃcient α on the reactive process. The sputtering rate is calculated for three diﬀerent values of α

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Sputter erosion rate, Rm (a.u.)

1.0

0.7

0.8 0.5 0.6

0.4

0.2

Yc / Ym=0.3

0

1

2

3

4

5

6

Reactive gas flow (sccm) Fig. 4.11. Sputtering rates calculated for three diﬀerent ratios of the compound (Yc ) and metal (Ym ) sputtering yield

Sputter erosion rate, Rm (a.u.)

1.0

0.8

0.6

800 l/s

0.4 400 l/s 0.2

0.0

S=80 l/s

0

1

2

3

4

5

Reactive gas flow (sccm) Fig. 4.12. Sputtering rate vs. the ﬂow of reactive gas calculated for three values of pumping speed

4.4.3 Pumping Speed In contradiction to α and the ratio Yc /Ym , the pumping speed S of the vacuum system may be controlled externally and set to a desired value. In Fig. 4.12, the calculated sputter erosion rate Rm vs. Qtot for three reactive sputtering processes diﬀering only in their values of the pumping speed S is shown. The results illustrate that the higher the value of S the hysteresis will be less pronounced. For S high enough, the hysteresis disappears [14]. This is often used in smaller lab systems where suﬃcient pumping speed may be

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Sputter erosion rate, Rm (a.u.)

1.0

0.8 3 cm2

0.6

12 cm2

0.4

0.2

0.0

At=150 cm2 0

1

2

3

4

5

6

7

8

Reactive gas flow (sccm) Fig. 4.13. Inﬂuence of the target area calculated for three diﬀerent areas of the target

achieved. In large-sized industrial systems, however, the required pumping speed value for hysteresis-free operation is often unattainable high. 4.4.4 Target Size In a speciﬁc system it may be possible to select the size of the target. Figure 4.13 shows the calculated sputter erosion rate Rm vs. Qtot for three reactive sputtering processes diﬀering only in their values of the target size At . The results illustrate that the hysteresis will be less pronounced for small target areas. When At is small enough, the hysteresis is predicted to disappear [15]. This behaviour is generally valid and is not caused by the fact that a smaller target will be exposed to a higher argon sputtering ﬂux for identical total target current. Altering the target current for the small target does not change the shape of the processing curve. 4.4.5 Mixed Targets It has been found that some target mixtures may aﬀect the reactive sputtering process in such a way that no hysteresis will appear [16]. It has been suggested to fabricate a mixture of a metal and its corresponding metal compound. The metal compound is the one expected to be formed by the metal and the reactive gas in the process. Having diﬀerent concentrations of compound in such a target may strongly aﬀect the processing curves. Figure 4.14 shows the calculated sputter erosion rate Rm vs. Qtot for three reactive sputtering processes diﬀering only in the fraction of compound in the target.

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Sputter erosion rate, Rm (a.u.)

0.7 0.6

Θb=0%

0.5 0.4 20%

0.3 50%

0.2 0.1 0.0 0

1

2

3

4

5

6

7

Flow of reactive gas (sccm) Fig. 4.14. Sputtering rate vs. the ﬂow of reactive gas calculated for three mixed targets diﬀering in the fraction of compound in the target

Fig. 4.15. Target conditions for a mixed target

The results show that the hysteresis is reduced for increasing fraction of compound in the target. Above a certain compound concentration, the hysteresis disappears. This type of target design oﬀers the possibility to obtain a stable and non-critical process without a need for feedback control of reactive gas partial pressure. The deposition rate depends on the actual composition of the target, but it is always higher than from the corresponding pure metal target operated in compound mode. The results for the mixed target were obtained by introducing a slight modiﬁcation of the target conditions as originally described in (4.2). The target erosion must correspond to the mixed target composition deﬁned by fraction Θb of the compound in the target bulk. Preferential sputtering of the high sputtering yield material Ym takes place, so the concentration of compound at the target surface would be always higher than Θb . The conditions at the target are schematically shown in Fig. 4.15.

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The term Θt denotes the fraction of compound at the target surface. This fraction is diﬀerent from the bulk concentration even when sputtering in pure argon. At the remaining part of the target, there is a similar competition between formation of compound and sputter removal of compound as described in the previous sections. Sputter erosion of surface material (compound or metal) will expose a subsurface having Θb compound concentration. Unlike the original basic balance equations, the conditions here may expose, with a probability Θb , a compound after sputter erosion. The compound fraction at the surface may increase due to sputtering of metal with the rate equal to Jq Ym (1 − Θt )Θb and in a corresponding way, the metal fraction at the surface can be increased by sputtering of compound at a rate equal to Jq Yc Θt (1 − Θb ). This gives the following balance equation for the target surface 2αF (1 − Θt ) +

J J Ym (1 − Θt )Θb = Yc Θt (1 − Θb ). q q

(4.13)

The balance equations at the substrate may be treated in the same way as for the simple one metal target one gas system shown in the beginning of this chapter. 4.4.6 Two Reactive Gases When two reactive gases are supplied to the processing chamber, a modiﬁcation of the original equations has to be done. This is the situation when oxygen and nitrogen may be added to form an oxy-nitride of some target material. It is likely that one of the gases may be more reactive than the other. Normally oxides are formed more easily than nitrides. Due to this diﬀerence in reactivity, an additional reaction must be considered. With a certain probability, the most reactive gas may break up the metal compound formed by the less reactive gas and replace this by a metal compound based on the more reactive gas atoms. In Fig. 4.16, a schematic illustration for a mathematical model for the target is shown. Here F1 and F2 represent the ﬂuxes of the two diﬀerent reactive gases “1” and “2” at their respective partial pressures. Θt1 and Θt2 represent the frac-

Fig. 4.16. Target treatment for the model of reactive sputtering with two reactive gasses “1” and “2”

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tions of the target covered by compound “1” and compound “2”, respectively. We assume that there exists no chemical mixture of the two compounds. Two equations for the target surface are then required, one for each reactive gas. Assuming that gas “1” can replace gas “2” in compound “2” and form compound “1”, the ﬁrst balance equation will be 2α1 F1 (1 − Θt1 − Θt2 ) + 2α12 F1 Θt2 =

J Yc1 Θt1 , e

(4.14)

where α12 is the replacement coeﬃcient expressing the probability that the incoming reactive gas “1” replaces the existing gas atom in its metal compound thus converting it into the other compound. The ﬁrst term in the left-hand side in the equation represents the gettering of gas “1” onto the free metal surface fraction (1 − Θt1 − Θt2 ). The second term represents the replacement of gas “2” atoms by gas “1” atoms in the metal compound at the target surface. The right-hand side of the equation represents the sputter erosion of metal-compound “1” from the Θt1 fraction of the target surface. The balance equation for gas “2” will be almost identical with the exception that the fraction area Θt2 of compound “2” will be reduced due to the replacement eﬀect. This will result in the following balance equation: 2α2 F2 (1 − Θt1 − Θt2 ) − 2α12 F1 Θt2 =

J Yc2 Θt2 . e

(4.15)

The balance equations at the substrate may be treated in analogous way to what was outlined for the target including the replacement eﬀect. Results from the calculations may be divided into two groups: 1. Zero replacement probability between the gases The 3D graph in Fig. 4.17 indicates that the two-gas processing system may result in a trapping eﬀect, for a constant ﬂow of gas “2” equal to 4 sccm (dashed curve in graph) and increasing gas “1” to enter the poisoned region. For these processing conditions, it will not be possible to return to the metallic mode (high deposition rate) only by decreasing the ﬂow of gas “1”. Even for zero ﬂow of gas “1”, the system will remain in the poisoned mode caused by gas 2 [17–20]. In this way the process may be trapped in the poisoned mode. 2. A ﬁnite replacement probability between the two gases Assuming that gas “1” may react both with the target metal as well as with the compound formed from gas “2” requires non-zero value of replacement coeﬃcient α12 in (4.14) and (4.15). In this treatment, we assume that this reaction will generate the same compound as from reactions between metal and gas 1. Results from calculations based on these assumptions are shown in Fig. 4.18 for diﬀerent constant supplies of gas “2” and in Fig 4.19 for 5 sccm of gas “2”. Note that the hysteresis may disappear for a gas ﬂow of gas “2” having values above a critical value. Moreover, when approaching high ﬂow levels for gas

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Sputter erosion rate, Rm (a.u.)

Fig. 4.17. Sputter erosion rates vs. ﬂow of reactive gas “1” calculated for diﬀerent ﬂows of gas “2”. No replacement between gases is assumed

0.6 q2 = 0 sccm 5

0.4

2

10 0.2

0.0 0

1

2

3

4

5

6

7

Flow rate of gas "1" (sccm) Fig. 4.18. Sputter erosion rate vs. ﬂow of gas “1” for diﬀerent ﬂows of gas “2”

“1”, remarkable small amounts of compound “2” are present in the deposited ﬁlm (indicated by low Θc2 and high Θc1 values). This eﬀect points out a further way of obtaining hysteresis-free reactive sputtering operation [21]. This technique, however, will only be attractive when a small fraction of the extra compound may be accepted in the deposited ﬁlms. 4.4.7 Reactive Co-Sputtering In certain applications, it may be favourable to use two separate targets as sputtering sources. This is convenient when studying properties of ﬁlms with diﬀerent compositions of two materials. Carrying out reactive sputtering from two metal targets, however, increases signiﬁcantly the complexity of

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Fractions, Θc1, Θc2

1.0 0.8

Θc1 Θc2

0.6 0.4 0.2 0.0 0

1

2

3

4

5

6

7

Flow rate of gas "1" (sccm) Fig. 4.19. Fractions of compounds “1” and “2” at the substrate for 5 sccm of reactive gas “2”

Fig. 4.20. Fluxes of sputtered material in the model with two separate targets

the process [22]. The main reason for this is that both target surfaces will be exposed to identical partial pressure of the reactive gas. This implies that two metals having quite diﬀerent reactivity to the reactive gas will not form the stoichiometric compound at the same partial pressure value. A mathematical treatment of a basic reactive co-sputtering process may be carried out in the following way. Assume that the system may be represented by the schematic shown in Fig. 4.20. Here Θc1 and Θc2 represent the fraction of metal compound formed at the metal “1” (= y) and metal “2” (= 1 − y) fractions, respectively, of the substrate surface and Θt1 and Θt2 represent the corresponding compound formations at the two separate targets. The balance equations for the two targets can be treated as two separate balances having identical partial pressure P of the reactive gas. This treatment will be identical to what has been described previously. “y” is deﬁned as the fraction of material from atoms originating from target “1” and consequently (1 − y) is the fraction of material from atoms

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originating from target “2”. The total number T1 of sputtered metal atoms from target “1” is given by T1 =

J1 [Ym1 (1 − Θt1 ) + Yc1 Θt1 ]At1 . q

(4.16)

Assuming one metal atom and one gas atom in the compound molecule, corresponding number T2 sputtered from target “2” will be T2 =

J2 [Ym2 (1 − Θt2 ) + Yc2 Θt2 ]At2 . q

(4.17)

The fraction y of material “1” in the deposited ﬁlm will be deﬁned as y=

T1 . T1 + T2

(4.18)

With this deﬁnition of y, it is possible to treat the surface fraction yAc as the collecting area for all metal “1”-based material and (1 − y)Ac as the collecting area for all metal “2”-based material. In this way, the treatment of reactive co-sputtering has been reduced to solving two single target processes joined by the partial pressure of the reactive gas. Note that y will be strongly dependent on the partial pressure P . From the above, it is possible to generate calculated curves for y, Θc1 , Θt1 , Θc2 , Θt2 , and P as a function of Qtot . To illustrate that reactive co-sputtering may cause quite complicated relations, we choose to show a curve for y vs. Qtot (Fig. 4.21). As can be understood from this ﬁgure, it may be quite complicated to fabricate a mixed ﬁlm of two metals with arbitrary composition if the desired composition must be generated by carrying out the process inside the hysteresis region.

Fig. 4.21. Calculated fraction y of the material “1” in co-sputtered ﬁlm vs. the ﬂow of reactive gas

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4.4.8 Comment on Pulsed DC Reactive Sputtering Pulsed DC reactive sputtering has become a popular biasing technique to avoid arcing at insulating spots at target surfaces. Operation frequencies use to be in the 20–300 kHz region. Applying a short negative DC pulse to a sputtering target gives rise to a burst of sputtered material. At ﬁrst sight, one may believe that these bursts of sputtered material will arrive to the substrate at a rate corresponding to the applied pulse frequency. At these frequencies, however, the transit time for a sputtered atom to reach the substrate will be in the millisecond range (see Chap. 6). Scattering by argon atoms slows down the initial speed and causes additional travelling distance. Due to this eﬀect, the bursts will be spread in time upon arrival to the substrate. The overall result will be that consecutive bursts will overlap and cause an almost continuous ﬂow of sputtered material to arrive to the substrate [23]. Due to the behaviour described above, a pulsed DC reactive sputtering process may be mathematically treated as a continuous DC sputtering process. This is of course only valid for the steady state conditions as have been presented in this chapter. More details of the pulsed DC processes can be found in Chap. 8. 4.4.9 Secondary Electron Emission In the treatment above, we have assumed a constant argon ion current for all levels of reactive gas ﬂow. This is of course quite a simpliﬁcation. A detailed treatment has to consider that the electron emission eﬃciency diﬀers between a clean metal surface and a partially oxidized/nitrided target surface. The eﬀect of variation of secondary electron emission will be treated in more detail in Chap. 5 and elsewhere [24, 25]. 4.4.10 Ion Implantation In a self-sustained sputtering plasma, argon ions are generated by electron impact ionization. Upon arrival at the target, a 500 eV argon ion may be implanted some 30–50 ˚ A. The eﬀect of this implantation, however, is assumed not to inﬂuence the target material at the penetration depth. In reactive sputtering, however, also the reactive gas may be ionized. These ions may also be accelerated by the electric ﬁeld and implanted into the target. These implanted reactive gas ions will easily react with the target metal atoms and form compound molecules. Due to this eﬀect, there will always be some compound formation in the whole surface region reaching into the ion penetration depth. This eﬀect will increase the response time for a reactive sputtering process when shifting from one processing point to another. In our treatment so far, we have not included this eﬀect. To correctly carry out a treatment of the dynamic response of a reactive sputtering process, this eﬀect must be included. In the following chapter(s), it will be shown how this eﬀect may inﬂuence the reactive sputtering process.

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4.5 Concluding Remarks It must be understood that the assumptions made for the calculations in this chapter are quite crude simpliﬁcations. Experience has shown, however, that the general shapes of the predicted curves remarkably well mirror what has been found from a large variety of experimental conditions. This encourages us to assume that we correctly have treated the major parameters that determine the processing behaviour. In this chapter, we have chosen simplicity to observe and point out the major inﬂuence of diﬀerent processing parameters. We believe that this may serve as a good ﬁrst approximation until the need arises for a more detailed analysis.

References 1. I. Saﬁ, Surf. Coat. Technol. 127, 203 (2000) 2. S. Berg, T. Nyberg, H.-O. Blom, C. Nender, Handbook of Thin Film Process Technology (Institute of Physics Publishing, Bristol, UK, 1998) 3. S. Berg, T. Nyberg, Thin Solid Films 476, 215 (2005) 4. S. Berg, H.-O. Blom, T. Larsson, C. Nender, J. Vac. Sci Technol. A 5, 202 (1987) 5. S. Berg, T. Larsson, C. Nender, H.-O. Blom, J. Appl. Phys. 63, 887 (1988) 6. H. Bartzsch, P. Frach, Surf. Coat. Technol. 142–144, 192 (2001) 7. V.A. Koss, and J.L. Vossen, J. Vac. Sci. Technol. A: Vac. Surf. Films 8, 3791 (1990) 8. H. Ofner, R. Zarwasch, E. Rille, H.K. Pulker, J. Vac. Sci. Technol. A: Vac. Surf. Films 9, 2795 (1991) 9. H. Sekiguchi, T. Murakami, A. Kanzawa, T. Imai, T. Honda, J. Vac. Sci. Technol. A: Vac. Surf. Films 14, 2231 (1996) 10. A.J. Stirling, W.D. Westwood, Thin Solid Films 7, 1 (1971) 11. J.F. O’Hanlon, A User’s Guide to Vacuum Technology (Wiley, New York, 1980) 12. J. Schulte, G. Sobe, Thin Solid Films 324, 19 (1998) 13. S. Zhu, F. Wang, W. Wu, L. Xin, C. Hu, S. Yang, S. Geng, M. Li, Y. Xiong, K. Chen, International Journal of Materials & Product Technology (Inderscience Enterprises, Guilin, China, 2001), p. 101 14. S. Kadlec, J. Musil, J. Vyskocil, Vacuum 37, 729 (1987) 15. T. Nyberg, S. Berg, U. Helmersson, K. Hartig, Appl. Phys. Lett. 86, 164106 (2005) 16. Y. Hoshi, T. Takahashi, IEICE Trans. Electron. E87-C, 227 (2004) 17. W.D. Sproul, D.J. Christie, D.C. Carter, S. Berg, T. Nyberg, in Proceedings of the 46th Annual SVC Technical Conference, Society of Vacuum Coaters, San Francisco, CA, 2003, p. 98 18. N. Martin, C. Rousselot, J. Vac. Sci. Technol. A: Vac. Surf. Films 17, 2869 (1999) 19. P. Carlsson, C. Nender, H. Barankova, S. Berg, J. Vac. Sci. Technol. A: Vac. Surf. Films 11, 1534 (1993) 20. H. Barankova, S. Berg, P. Carlsson, C. Nender, Thin Solid Films 260, 181 (1995) 21. D. Severin, O. Kappertz, T. Kubart, T. Nyberg, S. Berg, A. Pﬂug, M. Siemers, M. Wuttig, Appl. Phys. Lett. 88, 161504 (2006)

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22. N. Martin, C. Rousselot, Surf. Coat. Technol. 114, 235 (1999) 23. L.B. Jonsson, T. Nyberg, I. Katardjiev, S. Berg, Thin Solid Films 365, 43 (2000) 24. A. Pﬂug, B. Szyszka, V. Sittinger, J. Niemann, in Proceedings of the 46th Annual SVC Technical Conference, Society of Vacuum Coaters, San Francisco, CA, 2003, p. 241 25. Y. Matsuda, K. Otomo, H. Fujiyama, Thin Solid Films 390, 59 (2001)

5 Depositing Aluminium Oxide: A Case Study of Reactive Magnetron Sputtering D. Depla, S. Mahieu, and R. De Gryse

5.1 Introduction The deposition of aluminium oxide from an aluminium target in DC mode is used in this chapter to illustrate the diﬀerent aspects of the reactive magnetron sputter process. The choice for this combination of target material and reactive gas is given by the fact that the well-known hysteresis behaviour, described in the previous chapter, is clearly demonstrated for this combination. Two key aspects of the process are responsible for this behaviour. The strong difference in the molecular sputter yield and density for Al and Al2 O3 results in a dramatic decrease of the deposition rate when the target is poisoned [1]. Similarly the ion induced secondary electron emission coeﬃcient of aluminium changes strongly when reacting with oxygen to form aluminium oxide. Hence, the absolute discharge voltage drops in the order of 100 V when the target becomes poisoned [2]. The previous chapter describes the “Berg” model for reactive magnetron sputtering. Several experimental trends can be explained using this model. The model includes most important processes accounting for its success. In short the model describes the gettering of the reactive gas by the target material which inﬂuences the reactive gas partial pressure. At low reactive gas ﬂow, the reactive gas is almost completely gettered and hence the target condition remains metallic. When on increasing the reactive gas ﬂow the maximum amount of reactive gas which can be gettered is reached, the reactive gas partial pressure increases and the target becomes completely poisoned. Depending on the experimental conditions this change from metallic to poisoned mode can occur abruptly. Although the model described in the previous chapter explains quite well the hysteresis behaviour some experiments described in this chapter are diﬃcult to understand from this model. This ﬁnds its origin to the opinion of the authors in the description of the poisoning mechanism of the target. Indeed, in the “Berg” model, the reaction between the target material and the reactive gas is described by chemisorption. This is in ﬁrst order a correct approach for the reaction on the substrate but is not a complete description for the target process. Indeed, during magnetron

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sputtering the target is bombarded by ions from the plasma, including reactive gas ions. The ion energy is deﬁned by the discharge voltage and is in the order of 400 eV. Hence, the ions become implanted in the target at a depth in the order of a few nanometers. Two major conclusions can be drawn. First, when reacting with the target material, the reactive ion implantation results in a much thicker layer than modelled in the “Berg” model. Secondly, the reaction mechanism becomes more complicated and hence this could inﬂuence the description of the dynamics of reactive magnetron sputtering. These two major conclusions will be addressed in the ﬁnal part of this chapter where an model is presented describing the reactive ion implantation in an analytical way.

5.2 Some Experiments 5.2.1 A First Series of Experiments The simplest experiment to study the reactive sputtering process is the socalled hysteresis experiment: the discharge is ignited in pure argon, at a given pressure by introducing a certain argon ﬂow to vacuum chamber. The ratio between the argon ﬂow and the argon pressure deﬁnes the argon pumping speed. Keeping the discharge current constant, the oxygen ﬂow is stepwise increased. Between each step the process parameters are logged until the process is in steady state. When the target is completely poisoned the measuring procedure is reversed, i.e. the oxygen ﬂow is stepwise decreased until the discharge is again in pure argon. One easy to measure process parameter is the discharge voltage. Although the discharge voltage has a negative value, one generally plots and discusses its absolute value. The tradition will be followed in the remainder of the text. Figure 5.1 (top) shows the result of a hysteresis experiment for the system aluminium/oxygen. We refer to the ﬁgure caption for the experimental details. With a suﬃcient sensitive gas independent pressure gauge the total pressure change can also be measured. Here, a capacitance pressure gauge was used and the result of this measurement is shown also shown in Fig. 5.1 (bottom). Figure 5.1 shows the well-known hysteresis eﬀect which can be explained using the basic model. Hence, when the target is poisoned the discharge voltage drastically decreases. It is also noticed that, when still in metallic mode, the discharge voltage slightly increases as indicated by the dotted line in the ﬁgure. Several eﬀects can cause a discharge voltage change. This can be understood from the following equation for the discharge. More details on the derivation of (5.1) can be found in [3]: Vdischarge =

W0 , γISEE εe εi Em

(5.1)

discharge voltage (V)

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0.65 0.60 0.55 0.50 0.45 0.40

flow (sccm)

2.0 increasing flow decreasing flow

Fig. 5.1. Discharge voltage (top) and total pressure (bottom) as a function of the oxygen ﬂow during reactive sputtering of an aluminium target mounted in a planar 2 in. magnetron at constant current (0.4 A) and constant argon pressure (0.4 Pa). The pump speed was 16 L s−1 . The oxygen ﬂow was stepwise increased after 2 min

with W0 the eﬀective ionisation energy (in eV), εi the ion collection eﬃciency, εe the fraction of the theoretical amount of ions that the electron eﬀectively generates before it is lost from the discharge, γISEE the ion induced electron emission (ISEE) coeﬃcient (see chapter Baragiola), E the eﬀective gas ion probability and m the multiplication factor. For a magnetron discharge the electrons are trapped in close vicinity of the target. Escape from this trap is only possible through several interactions with the sputter gas. Consequently, εe can be considered close to unity. Because of the trapping of the electrons, most ionisation takes place close to the target surface. Hence, the vast majority of the ions reaches the cathode, which implies εi practically equal to unity. The eﬀective ionisation energy W0 varies only slightly for diﬀerent magnetron discharge conditions and has a typical value of 30 eV for argon. However, W0 depends on the gas composition of the discharge. Adding a diﬀerent gas, say a reactive gas, will change its value and hence the discharge voltage. E depends mainly on the gas pressure, and it accounts for the fact that some of the electrons do not interact with the gas but are recaptured by the target. The ionisation caused by electrons that are generated in the cathode sheath is characterised by the multiplication factor. The multiplication factor depends strongly on sheath thickness which is deﬁned by the magnetic ﬁeld, pressure

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and the discharge power. Finally, the ISEE coeﬃcient γISEE gives the number of electrons emitted per incoming ion on the target. The ISEE coeﬃcient depends strongly on the target condition. Under the experimental conditions, the magnetic ﬁeld strength is not changed and the work of Buyle [3] shows that the change in the power is too small to strongly aﬀect the sheath thickness. So, in the given context, essentially three parameters inﬂuence the discharge voltage, i.e. the gas composition, gas pressure and the target condition. These could explain the measured discharge voltage. However, one must take care since the gas composition and pressure change simultaneously. Hence, other experiments are needed to explain the discharge voltage behaviour. The experiment described in Fig. 5.1 has been repeated under the same conditions but the pumping speed has been changed by opening the throttle valve between the vacuum chamber and the turbomolecular pump. Changing the pumping speed strongly inﬂuences the hysteresis behaviour as can be understood from the “Berg” model described in the previous chapter. This experiment shows some interesting features. Using the discharge voltage measured in pure argon as a reference, the discharge voltage diﬀerence between a metallic target and a fully poisoned target remains remarkable constant although the pressure change depends strongly on the pumping speed. At low pumping speed (16 L s−1 ) the gas pressure increases on poisoning with 50% and the oxygen gas fraction is approximately 30% while at high pumping speed (130 L s−1 ) the gas pressure increase is only 14% and the oxygen gas fraction is approximately 12%. Hence, one can conclude that the discharge voltage under these experimental conditions is hardly aﬀected by the reactive gas pressure and the plasma composition. This also means that the slight increase of the discharge voltage on addition of oxygen (see Fig. 5.1) is diﬃcult to explain based on gas related eﬀects. The gas pressure and plasma composition before the critical point hardly changes. Although diﬃcult to see in Fig. 5.2, there is clear trend: the discharge voltage increase before the critical point becomes larger with the pumping speed (see also further, Fig. 5.19). To explain the eﬀect of the discharge voltage increase a second set of experiments was performed which is discussed in the next paragraph. 5.2.2 A Second Series of Experiments: Oxygen Exposure and Plasma Oxidation Aluminium [2] As the discharge voltage seems only be aﬀected by the target condition, the discharge voltage was measured under identical conditions except for the target condition. This type of experiments can be obtained by ﬁrst exposing the aluminium target for a given period to a certain oxygen ﬂow without sputtering the target. Generally an exposure to a gas ambient is expressed in a

pressure difference (ΔPa)

voltage difference (ΔV)

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S = 16 L /s S = 32 L /s S = 65 L /s S = 130 L /s

0 −40 −80 −120 −160 0.25 0.20 0.15 0.10 0.05 0.00 0

1

2 3 flow (sccm)

4

5

Fig. 5.2. Discharge voltage change (top) and pressure change (bottom) as a function of the oxygen ﬂow during reactive sputtering of an aluminium target mounted in a planar 2 in. magnetron at constant current (0.4 A) and constant argon pressure (0.4 Pa) for diﬀerent argon pumping speeds. The oxygen ﬂow was stepwise increased after 2 min

number of Langmuirs (L), for which 1 L equals 1 × 10−6 Torr s. After the oxygen exposure the oxygen ﬂow is switched oﬀ and the discharge ignited in pure argon at constant power (50 W). The discharge voltage is registered during the target sputter cleaning. Using this measuring procedure the discharge voltage is measured under identical conditions and hence its change can be directly related to the target condition. Especially the ﬁrst measured and stable discharge voltage V30 ms , i.e. 30 ms after the discharge ignition is strongly related to the target condition as the target condition is hardly aﬀected by the sputtering processes. Figure 5.3 (left) shows the discharge voltage behaviour during sputter cleaning after a given exposure. Figure 5.3 (right) shows the discharge voltage diﬀerence between V30 ms and VAr , i.e. between the ﬁrst stable discharge voltage and the discharge voltage measured during sputtering aluminium in pure Ar. This experiment has been repeated under diﬀerent experimental conditions but the general trend is that V30 ms ﬁrst increases on oxygen exposure up to an exposure of 300 L and then starts to decrease. This behaviour can be understood as follows. At high oxygen exposure an oxide layer is formed on the target prior to sputtering. The formation of the oxide layer, in the case aluminium, results in an increase of the ISEE coeﬃcient. Hence the discharge voltage decreases. However, for small exposures, no oxide is formed. Indeed, the general mechanism for the oxidation of aluminium at room temperature, for which

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360 340 320

constant time (15 s) −3 constante pressure (3.7 10 Pa) −2 constante pressure (1.7 10 Pa)

25 15 5 −5 −15 −25

oxidation

exposure time 5s 10s 20s 40s 80s 160s 320s 640s 1280s 2560s 4260s

(V30ms − VAr) (V)

target voltage (V)

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chemisorption

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−35 −45

300 0.1

0.2 0.3 sputter time (s)

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102

103 104 105 oxygen exposure (L)

Fig. 5.3. Discharge voltage behaviour during sputter cleaning of an aluminium target which was exposed to a given time (see legend) at a constant pressure of 3.7 × 10−3 Pa (left) and the discharge voltage diﬀerence between the discharge voltage measured 30 ms after discharge ignition and the discharge voltage measured during sputtering aluminium in pure argon (right). During the sputtering the argon pressure was constant (6 × 10−1 Pa) and the power was kept constant at 50 W. The experiment has been performed by exposing the target for a constant time at diﬀerent pressures and for diﬀerent period at two constant pressures

good agreement in the existing literature [4–10] is found, is the following. Before oxide formation a chemisorbed layer is formed. The onset of oxidation begins only after the surface is completely covered by a chemisorbed oxygen monolayer. When this happens, the aluminium surface becomes comparatively non-reactive as judged by weight gain and resistivity changes. Depending on the method of production, cleaning and (or) pre-treatment of the aluminium, the onset of oxide formation as given by literature [4–10] varies from 50–70 L exposure, over 130–180 L exposure, up to about 200–300 L. Hence, it seems from this experiment that the formation of the chemisorbed layer results in a decrease of the ISEE coeﬃcient of the target. The mechanism for this is not completely clear. Important in the context of this chapter is that (1) the sticking coeﬃcient of oxygen on aluminium target is in the order of 1/100 which is a very low value and that the oxidation of the aluminium target by oxygen exposure is a slow process. Indeed as Fig. 5.3 (right) shows, the discharge voltage diﬀerence changes logarithmic with the oxygen exposure. To reach the discharge voltage diﬀerence between a metallic target and a poisoned target (see Fig. 5.2) one should expose the target to very high pressures (or for a very long time) before this value can be reached. Of course, one can reason that the sticking coeﬃcient for oxygen during magnetron sputtering is higher than the value derived here. Indeed, in the plasma highly active oxygen, i.e. oxygen radicals, is also present. These radicals have a much higher sticking coeﬃcient on metals in the order 1. Pekker [11, 12] estimates before the critical point the dissociation degree in the order of a few percent while the dissociation can increase in the order of 10–30%, depending on the experimental conditions. In the case of aluminium this would result in average sticking coeﬃcient in the

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discharge voltage (V)

order of 0.1. However, with the given experimental parameters for Fig. 5.2, no hysteresis can be modelled with the basic model. Hence, chemisorption can not be solely responsible for the target oxidation during reactive sputtering. This is an important conclusion which led to the hypothesis that the target poisoning mechanism is also aﬀected by implantation of reactive gas (here oxygen) ions which are formed in the plasma by ionisation of the neutral reactive gas molecules. At this moment this hypothesis has been conﬁrmed in several ways. The most direct proof has been given by G¨ uttler et al. [13]. These latter authors have studied in situ the nitrogen concentration in a titanium target which was sputtered in a mixture of nitrogen and argon. It was clearly shown that the nitrogen concentration stems with several monolayers of TiN at the target surface. They have shown that the thickness of the formed TiN layer on a poisoned target agrees with the ion range of the N2+ ions which are accelerated over the cathode sheath. This latter can also be proven indirectly by using a similar measuring scheme as described above [14]. Before measuring the discharge voltage during sputter cleaning in pure argon, the target is ﬁrst sputtered in pure oxygen until a constant discharge voltage is measured. As Fig. 5.4 shows, the discharge voltage measured 30 ms after discharge ignition in pure argon has a low value, comparable with the discharge voltage measured in poisoned mode (see Fig. 5.1). After approximately 0.35 s the discharge voltage starts to increase to reach ﬁnally the value typically for aluminium sputtered in pure argon. Assuming that during the plasma oxidation the reactive ions become implanted with an energy related to the discharge voltage measured during plasma oxidation, one can calculate the ion range and straggle using SRIM. Following Todorov and Fossum [15], the oxide thickness formed during plasma oxidation can be estimated from the sum of the ion range and straggle and should therefore be in the order of 1.5 nm. Based on the experimental current density (0.03 A cm−2 )

360 340 320 300 280 0.001

0.01

0.1

1

10

time (s) Fig. 5.4. Discharge voltage behaviour during sputter cleaning of an aluminium target which was ﬁrst plasma oxidized in pure oxygen (0.4 Pa, 0.4 A). The sputter cleaning procedure was performed in pure Ar (0.4 Pa, 0.4 A)

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and the oxide thickness, and the onset of the discharge voltage change, one can calculate a total sputter yield. Repeating the experiments under diﬀerent experimental conditions results in a value of the sputter yield of 0.231 (error: 0.028), which agrees quite well with published values (0.25 [16]). For sake of completeness let us compare this latter value with the calculated sputter yield of the chemisorbed oxygen on the target [17]. This value can be retrieved from the experiments described in Fig. 5.3 on the assumption that the ISEE coeﬃcient during sputter cleaning of a target covered by a chemisorbed layer changes in the following way γT = γm (1 − θsc ) + γmc θsc ,

(5.2)

with γm the ISEE coeﬃcient of the clean aluminium target, γmc the ISEE coeﬃcient of a covered aluminium target and θsc the fraction of the target covered with oxygen. During the experiment the discharge voltage changes and therefore the ion energy of the impinging ions will change, inﬂuencing the ISEE coeﬃcient. However, the discharge voltage change is small, so this inﬂuence can be easily neglected. Also, due to the small change in discharge voltage one can also assume that, except for the ISEE coeﬃcient, the parameters in (5.1) remain constant during the sputter cleaning. In this way, by normalizing the discharge voltage as V − VAr x= , (5.3) V30ms − VAr one can easily proof that x equals θsc because the ISEE coeﬃcients hardly change. Following Dawson [18] an exponential change is expected for the removal kinetic with the rate of removal given by dθsc = −Ic+ θsc Q, dt

(5.4)

with Ic+ the ion current density and Q the removal cross section. This results in an exponential decrease of x from which the removal cross section can be calculated. In Fig. 5.5 x is given as a function of the ion ﬂuence (calculated based on the assumption that the ion current density is equal to the current density). An experimental value of 4.95 × 10−17 (error 1.16 × 10−17 ) cm2 is found. This is of the same order of magnitude as the cross section published by others [19]. As the oxygen surface density for a fully covered aluminium surface Nox equals 1.15×1015 atoms cm−2 , the sputter yield Y = (Q Nox ), has a value between 0.03 and 0.06. Compared to the oxygen sputter yield from a plasmaoxidized target this value is much lower. This is somewhat surprising as the binding energy between oxygen and aluminium is in both cases similar and the chemisorbed layer is a surface layer. Indeed, SRIM simulations [20] show a higher yield for oxygen sputtered from a chemisorbed layer (simulation performed with SRIM 2006.02, 0.3 nm O layer on 300 nm Al layer with 0.35 keV Ar bombardment) than from the oxide. A possible reason for this diﬀerence

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1.0 0.8

x

0.6 0.4 0.2 0.0 0.0

0.4

ion fluence

0.8

1.2x1017

(ion/cm2.s)

Fig. 5.5. Relative discharge voltage x as a function of the ion ﬂuence (calculated from the current density) during the sputter cleaning of a chemisorbed oxygen layer on an aluminium target. The full represent the exponential ﬁt from which the removal cross section is calculated

can be found in the knock-on of the chemisorbed oxygen into the aluminium target. SRIM shows that this is quite important eﬀect which redistributes the oxygen over a depth of 4 nm (simulation performed with SRIM 2006.02, 0.3 nm O layer on 300 nm Al layer with 0.35 keV Ar bombardment). The same simulation gives a ratio between the sputter atoms to recoil implanted atoms of .1551/.2605 or 1.65. Although this is a strong eﬀect which could result in a slower decrease of the discharge voltage, its inﬂuence of the calculation of the sputter yield is not understood yet. Indeed, one would expect that the knock-on implanted atoms would form aluminium oxide resulting in a faster decrease of the discharge voltage. Based on the experiments described in this paragraph, several aspects of the reactive sputtering process can be understood. First, one notices that several mechanisms play a role in the poisoning of the target, i.e. chemisorption, knock-on implantation and direct reactive ion implantation. Second, the poisoning of the target results in a drastic decrease of the erosion rate of the target and as such in drastic decrease of the deposition rate. Indeed, at the same ion energy the calculated sputter yield for aluminium is in the order 0.6 (0.5475 for 380 eV, using SRIM) while the measured total sputter of aluminium oxide is in the order of 0.23. Taking into account the density change, the ratio between the deposition rate in metallic mode and poisoned mode is in the order 10/1, which is conﬁrmed by most authors [1]. Finally, as third conclusion, it noticed that the ISEE coeﬃcient, and as such the discharge voltage, can depend on the interaction mechanism of the oxygen molecules. Chemisorbed oxygen seems to lower the ISEE coeﬃcient while the formation of oxide (subsurface oxygen) increases the ISEE coeﬃcient. However, a word of caution is necessary. One may not generalize this latter conclusion. Indeed, not all oxides have a high ISEE coeﬃcient. Replacing the target by

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another material can lead to diﬀerent conclusions. To stress this point some experiments, similar as described in Fig. 5.4, are in the next paragraph. Plasma Oxidation of Other Materials [21]

inverse of the discharge voltage (x10−3 1/V)

The performed experiments are similar to the experiment described in Fig. 5.4, i.e. a target is sputtered in pure argon until a constant discharge voltage is noticed. Then argon is replaced by oxygen and again the target is sputtered until a constant discharge voltage is registered. Finally, the oxygen is again replaced by argon and the target is sputter cleaned and the discharge voltage is registered. This experiment was performed for Ag, Al, Au, Ce, Cr, Cu, Li, Mg, Nb, Pt, Re, Ta, Ti, Y and Zr. The discharge voltage measured in pure argon is related to ISEE coeﬃcient of the metal, as given by (5.1). Within a small region of ISEE coeﬃcient, a linear relationship between the ISEE coeﬃcient and the inverse of the measured discharge voltage can be expected. This is exactly what the experiment shows (see Fig. 5.6). Based on this relationship between the ISEE coeﬃcient and the discharge voltage, one can calculate the ISEE coeﬃcient from a discharge voltage measured under identical experimental conditions. Hence, the discharge voltage measured 30 ms after starting up the sputter cleaning procedure of the plasmaoxidized target can give information about its ISEE coeﬃcient. Performing the above described experiment, it is found that the group of studied metals splits up in two groups. For the ﬁrst group (Al, Ce, Li, Mg and Y) the

Ag Al Au Ce Cr Cu Mg Nb Pt Re Ta Ti Y Zr

4.0

3.5

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2.0

1.5 0.00

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0.10

0.15

0.20

ISEE coefficient Fig. 5.6. The measured (inverse) discharge voltage in pure argon as a function of the ISEE coeﬃcient of the metallic target material (Argon pressure: 0.3 Pa, discharge current 0.3 A)

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ISEE coeﬃcient increases on oxidation of the target. This corresponds with the generally accepted idea that the ISEE coeﬃcient for oxides is larger than for the corresponding metal. However, for the second group (Ag, Au, Cr, Cu, Nb, Pt, Re, Ta, Ti, Zr) the ISEE coeﬃcient after plasma oxidation is smaller than the ISEE coeﬃcient of the corresponding metal. For some materials (Ag, Au, Cu and Pt) it is questionable if the oxidation procedure actually modiﬁes the target surface composition drastically but for the other materials of this group the low ISEE coeﬃcient is surprising. The origin, but not the complete explanation, for this low ISEE coeﬃcient, is the reduction of the oxide under ion bombardment. Indeed, after plasma oxidation, the metals of the ﬁrst group form an oxide which sputters congruently, meaning that no reduction occurs on ion bombardment. Hence, their behaviour agrees with the fact that oxides have a higher ISEE coeﬃcient than the corresponding metal. However, for the second group, the oxide reduces under ion bombardment. The eﬀect of the sputter reduction was found after studying TiO2−x target (with x ranging from 2 to 0.25, i.e. from pure Ti towards TiO1.75 ). These targets were manufactured by sintering mixtures of Ti and TiO2 [22]. These compound targets are all reduced titania targets, having an ISEE coeﬃcient lower than Ti. It also shows that the ISEE coeﬃcient is related with the bulk oxygen to metal ratio of the oxide. Figure 5.7 shows this relationship for the two discussed groups.

0.6

Cr2O3 Nb2O5 ReO3 Ta2O 5 TiO2 reduced TiO2-x Al2O3 CeO2 Li2O MgO Y2O3 ZrO2

ISEEox coefficient

0.5 0.4 0.3 0.2

0.12 0.08 0.04 0.00 0.0

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1.0 1.5 2.0 bulk oxygen-to-metal ratio

2.5

3.0

Fig. 5.7. ISEE coeﬃcient of oxidized targets and component targets as a function of the bulk oxygen-to-metal ratio. Filled symbols are used for the oxides with a high ISEE coeﬃcient (no sputter reduction), Open symbols are used for oxides with low ISEE coeﬃcient and grey stars are used for the component targets. The ISEE coefﬁcients were determined by the empirical relationship between the ISEE coeﬃcient and the discharge voltage as shown in Fig. 5.6

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ln [γO-/ N(O)](a.u.)

17

Al Ce Cr Cu Li Mg Nb Pt Re Ta Ti Y

15 13 11 9 7 5 −4

−3

−2 ln [γe]

−1

0

Fig. 5.8. Relationship with the measured ISEE coeﬃcient of the oxide (see Fig. 5.7) and the intensity of the high energy O− peak measured by energy resolved mass spectrometry during reactive sputtering of the targets in an oxygen/argon mixture

The bottom line of this paragraph is that the discharge voltage change during reactive sputtering is material dependent. For aluminium chemisorption results in a discharge voltage increase, while oxidation results in discharge voltage decrease. As shown above, depending on the material, oxidation can also result in a discharge voltage increase. Based on this work, it is possible to predict the direction/magnitude of the change. Knowing this eﬀect is important as the change target in condition during reactive magnetron sputtering also aﬀect the deposited thin ﬁlm properties. Indeed, the ISEE coeﬃcient of oxides is also related to the emission of negative oxygen ions, which bombard the growing thin ﬁlm with an energy in the order of the discharge voltage, i.e. several hundred electronvolts [23]. Figure 5.8 shows this relationship and as shown by Ngaruiya et al. [24] the thin ﬁlm properties are strongly related to this negative oxygen bombardment. 5.2.3 Stability Experiments The experiments have learned that target poisoning during reactive sputtering is inﬂuenced by chemisorption, knock-on implantation and direct reactive ion implantation. In these latter two processes, the reactive atoms are distributed in the target over 2 nm in the case of magnetron sputtering. Plasma immersion implantation experiments and ion beam experiments show the importance of the reaction kinetics and diﬀusion of these implanted ions in the formed oxide layer. To show that the implanted reactive atoms do not react immediately with the target material, one can introduce a waiting period between the oxidation of the target and its subsequent sputter cleaning to check the “stability” of the measured discharge voltage 30 ms after igniting the discharge. Hence, a typical stability experiment was performed as follows. After sputtering the aluminium target in pure Ar until a constant discharge voltage was registered, oxygen was introduced into the chamber. After stabilisation of the discharge

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V30ms-VAr (V)

−30 −32 −34 −36 −38 −40 0

500

1000 1500 2000 waiting period (s)

2500

3000

Fig. 5.9. Change of the discharge voltage diﬀerence between the discharge voltage measured at discharge ignition and in pure argon as a function of the waiting period between switching oﬀ the discharge (and oxygen ﬂow interruption) and the igniting the discharge in pure Ar (measured at constant power 50 W, argon pressure 0.6 Pa (60 sccm) and 1.7 sccm oxygen). Under the given condition the target was not completely poisoned

voltage, the oxygen ﬂow was interrupted. Simultaneously the magnetron discharge was switched oﬀ. After a given waiting period the magnetron was switched on again in pure Ar. During the waiting period the gas atmosphere was pure Ar. Figure 5.9 shows the change of the discharge voltage on discharge ignition (V30 ms ) as a function of the waiting period. Under the used conditions (see ﬁgure caption) the target is not fully poisoned. A small but signiﬁcant decrease of the discharge voltage is noticed which becomes constant after approximately 40 s. This eﬀect is not induced by the residual gasses in the vacuum chamber as an exposure of the same period hardly aﬀects the discharge voltage on discharge ignition [25]. A more provoked eﬀect has been measured by introducing a waiting period between the sputter cleaning of the target and interruption of the reactive gas ﬂow during reactive sputtering of Si in a mixture of nitrogen and argon [26]. Figure 5.10 shows discharge voltage behaviour during sputter cleaning a polycrystalline silicon target which was ﬁrst sputtered in a 50/50 mixture of argon and nitrogen. After reaching a constant discharge voltage the magnetron was switched oﬀ simultaneously with the nitrogen ﬂow. After a given waiting period the discharge voltage was measured in pure Ar. Again one notices that the discharge voltage behaviour changes as a function of the introduced waiting period. In this experiment, the desorption of nitrogen gas from the target could be registered using a mass spectrometer. Both the aluminium and silicon experiments give evidence that the reaction between the reactive gas and the target material can be quite slow, and clearly show that implanted atoms can further react with the target

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target voltage (V)

500 waiting period 0s 1s 12 s 120 s 1200 s 2430 s

480 460 440 420 0

200

400 time (s)

600

800

Fig. 5.10. Discharge voltage behaviour during sputter cleaning a polycrystalline Si target in pure argon (50 W, 0.3 Pa) which was ﬁrst sputtered in a 50/50 mixture of nitrogen and argon (in reactive mode)

material and/or diﬀuse out of the target after the magnetron discharge has been switched oﬀ. 5.2.4 First Conclusions Based on the Experiments The above-discussed experiments are all based on the discharge voltage behaviour as a function of the experimental conditions. These studies are only valid if one only compares the discharge voltage (behaviour) after carefully controlling the experimental conditions. Indeed, discharge voltages are only interesting when comparing their values or behaviour when measured under identical conditions. It must be stressed that this mistake is often noticed in literature where discharge voltage measured in pure argon is compared with the discharge voltage measured in a mixture of both argon and the reactive gas. This has no use because, as (5.1) shows, the discharge voltage depends not only on the target condition but also on the plasma composition. Nevertheless, the chemisorption experiments (see section “Aluminium”) show the sensitivity of the discharge voltage on discharge voltage ignition, and this eﬀect is due to the sensitivity of the ISEE coeﬃcient of the target. These experiments also show that a more complete model for reactive magnetron sputtering must include reactive ion implantation and knock-on implantation. Moreover, the stability experiments show that the reaction kinetics describing the reaction between the implanted reactive atoms and the target atoms is also an important point of the reactive sputter model. Based on this conclusion, the next part of this chapter describes a ﬁrst try to extend the model described in the previous model to account for the described experiments.

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5.3 An Extended Model for Reactive Magnetron Sputtering Several models have been developed to describe the reactive sputtering process. Most of these are based on the basic model discussed in the previous chapter. Indeed, these models add speciﬁc topics to this model, such as plasma chemistry, the discharge voltage dependence of the target material sputter yield, the chemisorption reaction and many others. However, none of these models can explain the experiments shown in Sect. 5.2. The reason is extremely simple: the basic model includes only chemisorption as a reaction between the target material and the reactive gas. This is in ﬁrst order a correct approach for the reaction on the substrate but is not a complete description for the target process. However, the approach presented by Berg and Nyberg can still be used but the target processes should be reconsidered. To implement reactive ion implantation in an analytical way, it is advisable to ﬁrst derive a model that includes only implantation and compares its results with experiments where chemisorption does not aﬀect the target condition. During reactive magnetron sputtering this is diﬃcult to achieve because not only reactive ions but also neutral species are present which can chemisorb on the target surface. However, during reactive ion beam experiments such results can be obtained. Indeed, the compound formation during this type of experiments is studied by change the angle of incidence between the ion beam and the surface. Typically in such experiments the compound is formed at normal incidence (0◦ ) and at small impact angles but above a critical angle no complete oxidation of the target occurs. In this chapter a model is presented which can describe these experiments. It is based on the work of Schulz and Witmaack [27], who described ion implantation in the presence of sputtering. Building further on this model, the inﬂuence of chemisorption is included. This results in a more complete model to describe the target processes during reactive magnetron sputtering. The processes which take place on the substrate, i.e. deposition and reaction, are described in the same way as proposed in the previous chapter. Also the approach suggested in the previous chapter, i.e. the calculation of the ﬂow balance is considered. This enables to describe the process parameters as a function of the reaction gas ﬂow. 5.3.1 The Description of Reactive Ion Implantation During Sputtering Simultaneous Reactive Ion Implantation and Sputtering Without Chemical Reaction A classical problem is to calculate the concentration of implanted ions during sputtering. An interesting zero-order approximation has been proposed by Schulz and Wittmaack [27]. Although the model has been described in detail

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by these authors, the derivation is repeated here to make this chapter as complete as possible. The probability that a particle will come at rest in the target at a distance from the surface between x and x + dx is p(x)dx, where p(x) is the normalized distribution, ! D p(x)dx = 1 − B, (5.5) 0

with D the implantation depth and B the back scattering coeﬃcient that accounts for the reﬂected ions. The depth in the target is represented by x. If I is the ion current density (ion cm−2 s−1 ) and f is the mole fraction of the reactive gas in the plasma or beam, then the number of reactive ions that bombard the target per area and time unit is 2f I. Hence, only molecular ions (R2+ ) are taken into account, and it is assumed in the case of reactive magnetron sputtering that the ionisation probability of the reactive gas and the argon gas in the plasma is equal to each other. It is also assumed that the ion energy is much larger than the binding energy of the molecular ions. Therefore, each molecular ion will dissociate into two reactive atoms, each having approximately half the energy of the original ion. The implantation of the argon atoms is neglected. A similar approach is followed by other models (e.g. TRIDYN [28]) based on the argument that the argon atoms will quickly diﬀuse from the target. The reactive atoms become implanted following the implantation proﬁle (see (5.5)). So, in a given slab of the target at position x in the target, 2f Ip(x) reactive atoms are implanted or ∂nr (x, t) = 2fIp(x, t)∂t,

(5.6)

with nr the concentration of the non-reacted implanted reactive atoms in the target. In the following x ˆ represents a coordinate with its origin ﬁxed in space. Due to the ion bombardment the surface will recede with a speed deﬁned by the erosion rate vs (t) which is deﬁned as vs (t) =

IYs (t) dˆ xs = , dt n0

(5.7)

with x ˆs (t) the instantaneous position of the surface and n0 the atomic density of the target (atoms cm−3 ). Strictly speaking the atomic density of the target is also a function of time. However, in this ﬁrst approach the change of the atomic density of the target is neglected. This assumption is made based on the fact that the atomic target density ratio between the compound and metals is on average in the order of 2. As (5.7) shows, the erosion rate depends on the ratio between the sputter yield and the atomic density of the target. Hence by keeping the atomic density of the target constant, the inﬂuence of the sputter yield of the model will be too large. However, knowing the large errors on the sputter yields of compounds at small energy (see paragraph A.2.1.1 and Sputtering by Ono in Chap. 1), this approach seems reasonable.

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The coordinate x with its origin in the instantaneous surface is then related to the stationary coordinate x ˆ by x = xˆ − xˆs (t).

(5.8)

Due to erosion, the implanted ions are shifted towards the surface. Simultaneously, additional ions are implanted. Assuming that the implantation proﬁle is not aﬀected by the implantation of reactive ions in the target, i.e. p(ˆ x, t) = p(x) and the range distributions are shifted by the amount x ˆs (t), i.e. p(ˆ x, t) = p(ˆ x−x ˆs (t)). (5.9) The resulting time-dependent concentration of the implanted atoms becomes then ! t nr (ˆ x, t) = 2fI p (ˆ x − xˆs (t ))∂t . (5.10) 0

However, one is not interested in this solution because one needs to know the time-dependent concentration of the implanted atoms nr (x, t). This latter distribution can be derived from (5.10) by realizing that ﬁnal position of the surface x ˆs (t) is given by ! t I Y (t )dt . (5.11) x ˆs (t) = XS = n0 0 This makes it possible to write the coordinate x as x = xˆ − XS

(5.12)

and the distribution nr (x, t) as !

t

nr (x, t) = 2fI

p (x + XS − x ˆs (t )) ∂t ,

(5.13)

0

with x ˆs (t ) the surface position at time t . It is important to realize that during reactive magnetron sputtering and ion beam experiments, the sputter yield Ys changes as a function of the time, which makes a step-by-step deduction of the accumulated implantation distribution necessary. When the implanted atoms do not react with the target material, the sputter yield remains constant during the experiment. In that speciﬁc case, the ﬁnal surface position XS (see (5.11)) becomes x ˆs (t) = XS =

IY Δt n0

and using (5.7), (5.13) can be rewritten as nr (x, t) =

2fI vs

!

S

p (x + y) dy. 0

(5.14)

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The concentration at the surface (x = 0) equals then with (5.5) nr (0, t) =

2fI 2f (1 − B) = n0 (1 − B). vs Ys

(5.15)

This latter result has been derived by several authors [27, 29, 30]. Simultaneous Reactive Ion Implantation and Sputtering with Chemical Reaction Evidently, in most cases the implanted reactive atoms can react with the target material to form compound molecules. This will inﬂuence the target composition and also the sputter yield of the target. Hence, to calculate the time-dependent concentration, the time dependence of the erosion rate must be known. As the latter depends on the surface concentration, (5.13) can only be solved numerically. As shown below, it will be necessary to subdivide the target into two regions, i.e. s, the surface region from which sputtering occurs with a thickness in the order of a monolayer, and b, the subsurface region in which the reactive ions become implanted and react with the target material at a given rate. The thickness of this layer is deﬁned by the implantation depth D. As proposed by Herbots et al. [31] the reaction rate R will be given by R = −kznr(x, t)nm (x, t),

(5.16)

with nm (x, t) the concentration of the non-reacted target material and k the reaction rate constant. The stoichiometry of the formed compound molecules deﬁnes z, i.e. MRz . Hence, the change in the concentration of the non-reacted implanted atoms with time can be written by combining (5.6) and (5.16) or ∂nr (x, t) = 2fI p(x) − kznr (x, t)nm (x, t). ∂t

(5.17)

A similar equation can be derived for the change in the concentration of the non-reacted target material with time, i.e. ∂nm (x, t) = −knr (x, t)nm (x, t). ∂t

(5.18)

Based on the deﬁnition of the erosion speed, one can rewrite the last two equations as vs (t)

∂nr (x, t) = 2fI p(x) − kznr (x, t)nm (x, t), ∂x

∂nm (x, t) vs (t) = −knr (x, t)nm (x, t). ∂x

(5.19)

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The reaction of the target material will result in a change in the target sputter yield and also in a change of the erosion rate. The sputter yield of the target can be deﬁned as θrs Yr + θms Ym = Ys ,

(5.20)

with θrs and θms the fraction of reacted and non-reacted target atoms at the surface of the target; evidently θrs + θms = 1. Yr and Ym represent, respectively, the sputter yield of the formed compound molecules and the target atoms. Hence, it is assumed that the non-reacted implanted atoms are not sputtered. We assume that these atoms diﬀuse from the surface into vacuum, just as the implanted argon atoms. Diﬀusion of non-reacted implanted atoms from the target has been discussed in the previous section. As the sputter yield of the compound and the target material are not equal, preferential sputtering should be taken into account. To describe this eﬀect the fraction of compound molecules at the interface between the surface zone s and the subsurface zone b, i.e. θrb is introduced. This fraction can be calculated from the concentration of non-reacted target atoms nm (s) at the position x = s, with s the thickness of the surface zone: θrb = 1 −

nm (s) . n0

(5.21)

As it is assumed that the non-reacted implanted atoms diﬀuse from the surface zone, there is no chemical reaction in the surface zone. Based on this assumption the following continuity equation can be derived [32] vs (t)θrb n0 = Iθrs Yr .

(5.22)

This relates the fraction of compound molecules at the interface to their fraction in the surface zone. Indeed, the left-hand side (LHS) of (5.22) describes the transport of compound material from the subsurface zone b to the surface zone s by the movement of the target surface under ion bombardment. The right-hand side (RHS) of the same equation describes the sputtering of the compound from the surface zone. As will be discussed in Sect. 5.4.2, these equations can be solved numerically, which enables to describe the target condition under diﬀerent experimental conditions. In the case of the ion beam experiments (see further) the target condition can be described as a function of the impact angle between the beam and the surface. In the case reactive magnetron sputtering the target condition can be described as a function of the reactive gas mole fraction or pressure. 5.3.2 The Inﬂuence of Chemisorption and Knock-On Eﬀects During reactive magnetron sputtering the target is also exposed to neutral gas species. Hence, chemisorption of these species cannot be neglected. Moreover,

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as discussed by Rosen et al. [28] the chemisorbed atoms can be knocked into the target by ions bombarding the target, resulting in compound formation not only at the surface but also at subsurface region of the target. Indeed, as shown in section “Aluminium” (see Fig. 5.5), knock-on implantation seems to be an important eﬀect. To account for this latter eﬀect and for chemisorption, the model must be further extended. Therefore, the fraction θcs is introduced which is deﬁned as the fraction of compound formed by chemisorption at the target surface. Hence, the surface layer s is now characterized by three fractions, i.e. θcs , θrs and θms for which the sum is by deﬁnition equal to 1. θcs , θrs and θms represent, respectively, the surface fraction of compound formed by chemisorption, the fraction of compound formed by reaction between implanted reactive atoms and the target atoms and ﬁnally the non-reacted target atoms. Hence it is assumed that no chemisorption occurs on the formed compound. Consequently, the target sputter yield Ys must be redeﬁned as compared with (5.20): θrs Yr + θms Ym + θcs Yc = Ys ,

(5.23)

with Yc the sputter yield of the compound formed by chemisorption. The other sputter yields have been deﬁned before. In this simpliﬁed model it is assumed that the compound formed by chemisorption and reactive ion implantation is identical. Hence, the sputter yield Yc = Yr . To modify the model for chemisorption and knock-on implantation, the set of (5.19) should be altered. The knock-on of chemisorbed atoms into the target will modify the amount of reactive atoms which become implanted into the target. Hence, (5.19) should be rewritten as vs (t)

∂nr (x, t) = 2fI p(x) − kznr (x, t)nm (x, t) + Iθcs βpc (x), ∂x ∂nm (x, t) vs (t) = −knr (x, t)nm (x, t), ∂x

(5.24)

with pc (x) the implantation proﬁle of the knock-on atoms. In a ﬁrst approach it is assumed that this implantation proﬁle does not diﬀer from the reactive ion implantation proﬁle p(x). β is the knock-on yield which is the number of chemisorbed atoms that are knock-on implanted per incoming ion. The fraction of compound formed by chemisorption at the target is deﬁned by three processes: (1) Formation by chemisorption of neutral molecules on the non-reacted target material (2) The removal by sputtering (3) Knock-on of the chemisorbed reactive atoms into the target This results in the following equation which balances the formation and removal by sputtering and knock-on no,s

2F I dθcs = αθms − Yc θcs I − βθcs , dt z z

(5.25)

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with no,s the atomic surface density. F represents the ﬂux of neutral molecules on the target surface given by F =√

fP tot , 2πmkT

(5.26)

with Ptot the total pressure, m the molecular mass, k the Boltzmann constant and T the absolute temperature. The sticking coeﬃcient of the reactive gas on the target surface is deﬁned by α. At steady state (5.25) reduces to I 2F αθms = Yc θcs I + βθcs . z z

(5.25 )

A similar balance equation can be written down for the steady-state fraction of the target material in the surface layer I 2F βθcs + IYs θmb = Ym θms I + αθms . z z

(5.27)

Indeed, on the LHS of (5.27) the ﬁrst term accounts for the removal of a chemisorbed atom from a compound molecule, while the second term accounts for the transport between the subsurface region and the surface region. On the RHS of (5.27) the sputtering of the target material and the loss of non-reacted target material due to the reaction with the neutral reactive gas molecules by chemisorption is described. For the compound formed by reactive ion implantation only the transport from the subsurface region to the surface region must be taken into account. Hence, (5.22) remains valid. Again this equation can be solved numerically and enables to describe the target condition as a function of the reactive gas mole fraction in the case of magnetron sputtering. However, generally the experiments are performed as function of the reactive gas ﬂow (see Figs. 5.1 and 5.2). Hence, it will be necessary to derive the relationship between the reactive gas partial pressure and the reactive gas ﬂow. 5.3.3 Calculation of the Reactive Gas Partial Pressure as a Function of the Reactive Gas Flow During magnetron sputtering the partial pressure of the reactive gas is controlled by gettering of the reactive gas by the target material. A good approach to this problem has been proposed by Berg and Nyberg in the previous chapter. However, as the description of the target condition has been altered, not all the equations described in the previous chapter can be used. To help the reader, some of the equations are repeated in this chapter. The reactive gas ﬂow qo into the vacuum chamber must be equal to the sum of the reactive gas

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ﬂow into the pump, the ﬂow towards the target (target consumption) and the ﬂow towards the substrate (substrate composition), i.e. qo = qp + qt + qc .

(5.28)

The reactive gas ﬂow towards the pump is deﬁned by the pumping speed S and the reactive gas partial pressure in the vacuum chamber which is at constant total pressure equal to fPtot . Hence, the ﬂow to the pump equals qp = SfPtot .

(5.29)

Similarly to the “Berg” model it assumed that the deposited target material reacts with the reactive gas only by chemisorption. In this way the ﬂow towards the substrate is given by qc = αc F (1 − θc )Ac ,

(5.30)

with F the ﬂux of the reactive gas molecules towards the substrate, αc the sticking coeﬃcient of the reactive gas molecules on the substrate, Ac the substrate area and θc the fraction of compound on the substrate. This latter fraction can be calculated as described in the previous chapter by writing down the following balance equation At At 2αc F (1 − θc ) + I(Yc θsc + Yr θsr )(1 − θc ) = IYm θsm θc , z Ac Ac

(5.31)

where it is assumed that the compound formed by chemisorption and by reactive ion implantation has the same stoichiometry. The reader can ﬁnd more details in the previous chapter to understand this balance equation. The calculation of the ﬂow towards the target is more complicated. Indeed, besides the chemisorption, reactive ions become implanted in the target by direct implantation and knock-on implantation where they can react with the target atoms. Hence, the total amount of reactive atoms in the target at a given time per unit area can be calculated by integration of the distribution of the implanted reactive atoms and the compound molecules in the subsurface region of the target, i.e. ! D [nr (x, t) + z (no − nm (x, t))] dx. (5.32) N (t) = S

In this way, the ﬂow towards the target can be calculated as z Iβθsc 1 dN + F αθsm − + Ys θrb At . qt = 2 dt 2 2

(5.33)

The ﬁrst term accounts for the change in the total concentration of reactive atoms in the subsurface region of the target. The second term describes the amount consumed by chemisorption. This part is similar to the equation

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proposed in the previous chapter. The third term of (5.33) describes the atoms which become implanted by knock-on into the target. One must subtract their contribution from the amount which is chemisorbed as the model already accounts for these atoms in the integral given in (5.32). The last term of this equation accounts for the compound molecules present in the surface region. As the non-reacted atoms in the surface region diﬀuse out of the target, they are not consumed by the target. In steady state, (5.33) simpliﬁes to z Iβθsc + Ys θrb At , qt = F αθsm − (5.33 ) 2 2 as the distribution of the implanted atoms and the formed compound molecules in the subsurface region does not change anymore. Based on (5.28) and the following the same, one can calculate the ﬂow needed to reach a certain mole fraction in the vacuum chamber. In this way, one can plot the target condition and the partial pressure of the reactive gas as a function of the ﬂow, similar to experimental results (see Figs. 5.1 and 5.2).

5.4 Confrontation Between Experiment and Model In Sect. 5.3 a complete description of a reactive sputtering model is given which takes into account several target reactions, i.e. chemisorption, knockon implantation and direct reactive ion implantation. In this section several aspects of the model will be confronted with the experimental results described in Sect. 5.2 together with some speciﬁc experiments. In this way, the reader can judge the value of the proposed model. The description of the model has been build up stepwise, taking more processes into account in each step. This approach has been chosen to make the evaluation of the model more transparent by confronting certain facets of the model with the experiment. 5.4.1 Simultaneous Reactive Ion Implantation and Sputtering Without Chemical Reaction Magnetron sputtering of silver (Ag) in a mixture of nitrogen/argon is an example where reactive ions become implanted in the target but do not react with the target material [33]. Moreover, nitrogen does not react on the substrate to form silver nitride. Therefore, this example is interesting to look in a little more detail. Figure 5.11 (top) shows the discharge voltage behaviour during sputter cleaning a silver target which was ﬁrst exposed to given dose of nitrogen ions. These latter ions were implanted in the target using an ion gun at 5 keV. The discharge voltage is clearly a function of the implantation dose. Figure 5.11 (bottom) shows the discharge voltage behaviour during sputter cleaning a silver target. In this case the target was exposed to the same dose of nitrogen ions but prior to the sputter cleaning procedure a waiting period was introduced. One notices that the eﬀect on the discharge voltage fades away

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46

345

23 12 x1016 ions / cm2 5.8 2.9 1.4

discharge voltage (V)

340 335 330

20 s 25 s 30 s 40 s 50 s 100 s

334 333 332 331 0

20

40 60 time (s)

80

100

Fig. 5.11. Discharge voltage behaviour during sputtering cleaning of a silver target in pure argon (0.4 Pa, 50 W). Using an ion gun the target was bombarded with nitrogen ions prior to the sputter cleaning procedure. In the top ﬁgure the total dose was increased. In the bottom ﬁgure the same dose (1.4 × 1016 ion cm−2 ) was used but before sputter cleaning a given waiting period was introduced

with an elongation of the waiting period. This example shows that implantation of reactive ions in a target during reactive magnetron sputtering can inﬂuence the discharge voltage, even without chemical reaction between the target material and the target atoms. 5.4.2 Simultaneous Reactive Ion Implantation and Sputtering with Chemical Reaction The Target Condition During Oblique Reactive Ion Implantation During this type of experiments, the target is only bombarded by reactive ions. So, the mole fraction f can be set equal to 1. By changing the angle between the reactive ion beam and the surface normal the sputter yield of both the target material and the formed compound will change. This will inﬂuence the oxidation level of the target surface. Figure 5.12 shows the results of such an experiment performed by Alay and Vandervorst [34]. The ﬁgure shows the oxidation of a Si target by 5 keV O+ 2 implantation as a function of the ion beam angle. In this experiment the target oxidation level has been experimentally measured by following the Si2p line in X-ray photoelectron spectroscopy (XPS) from which the oxidation level can be calculated. Based

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oxidation level

1.0 0.8 0.6 0.4 experimental data (taken from Alay et al.)

0.2

θrb θrs

0

20

40 60 angle of incidence(°)

80

Fig. 5.12. Oxidation level dependence on the angle of incidence of 5 keV O+ 2 ion beam on silicon. Simulation parameters were taken from De Witte (sputter yield ratio of silicon to silicon oxide) or simulated using SRIM (ion range and ion range straggle, sputter yield Si, backscattering coeﬃcient). The reaction rate constant k was used as a ﬁtting parameter between the experimental data and the calculated oxidation levels of the subsurface and surface region (k = 1×10−22 cm3 atom−1 s−1 ) (correlation coeﬃcient 0.9584). The obtained results are independent of the used ion beam current density

on the attenuation length of the photoelectrons the sample depth of XPS is in the order of 5 nm. At normal incidence (0◦ ) the target is completely oxidized (oxidation level 1). At beam angles larger than a critical angle of approximately 22◦ the oxidation level decreases with increasing beam angle. Figure 5.12 shows also the calculation values for θrs and θrb . The values were derived by numerically solving the set of (5.19) and following the same. The sputter yield ratio of Si and SiO2 as a function of the angle of incidence at this energy was taken from the work of De Witte [35]. Changing the angle of the ion beam also modiﬁes the implantation proﬁle. A Gaussian implantation proﬁle was deﬁned. Hence ⎡ 2 ⎤ 1 x − Rp ⎦. p(x) = √ exp⎣− √ (5.34) 2πΔRp 2ΔRp The projected ion range Rp and the ion straggle ΔRp were calculated using SRIM. No value of the ion current density (I) was reported in the work of Alay and Vandervorst [34]. However, Wittmaack [36] reported similar results as the former authors using an ion current density in the order of 1 × 1015 ion (cm−2 s−1 ). The same author also reported that increasing the ion current density to 1×1016 ion cm−2 s−1 has no inﬂuence on the oxidation level of the target. The independence of the obtained results for the ion current density was checked. The following solution scheme was used. Initial values of θrb and the beam angle were chosen. The chosen beam angle deﬁnes the sputter yields Ym and Yr . The erosion rate corresponding with the initial value of θrb was calculated

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based on (5.21) and (5.23). Solving numerically the set of (5.19) using the trivial boundary condition nm (0) = no and nr (0) = 0, a value of nm (s) can be calculated, which deﬁnes a certain value of θrb . In steady state the initial value of θrb should correspond to this latter value. Hence, the beam angle is change iteratively until this condition is reached. In the way, a plot of θrb and θrs can be made and compared with the experiment. The reaction rate constant k was used as a ﬁtting parameter to obtain a good correlation between the experiment and the model. The obtained result indicates that the reactive ion implantation is capable of describing this type of experiments. The Target Condition During Reactive Magnetron Sputtering as a Function of the Reactive Gas Mole Fraction Without Chemisorption/Knock-On Implantation During reactive magnetron sputtering the mole fraction of the reactive gas can be modiﬁed by changing the reactive gas ﬂow. Of course, the gettering of the reactive gas by the sputtered target material will inﬂuence the actual reactive gas mole fraction in the vacuum chamber. So f in the model represents the actual reactive gas mole fraction in the vacuum chamber. With the model described in Sect. 5.3.1, one calculates the mole fraction for a given target condition. Of course, in Sect. 5.3.1 the eﬀect of chemisorption of the reactive gas on the target is not taken into account. Nevertheless, it is instructive to see the inﬂuence of the reactive ion implantation on the target condition without taking into account chemisorption. Using the same value for the reaction rate constant k as obtained in the previous section, one can calculate the silicon target condition in a reactive magnetron sputtering experiment as a function of the oxygen gas mole fraction in a mixture of argon and oxygen using the following solution scheme. Again an initial value of θrb is chosen and the erosion rate calculated. In contrast to the ion beam experiments, during reactive magnetron sputtering low energy ions (typically 400 eV) bombard the target always at normal incidence. The sputter yield of Si was calculated with SRIM and set equal to 0.4. The sputter yield of the oxide was set equal to 0.04. The implantation proﬁle of O+ 2 was calculated using SRIM (Rp = 1.7 nm and ΔRp = 1 nm). By numerically solving the set of equations (5.18) using the trivial initial boundary conditions nm (0) = no and nr (0) = 0, a value of nm (s) can be calculated, which deﬁnes a certain value of θrb . In steady state the initial value of θrb should correspond to this latter value. Hence, the mole fraction f is changed iteratively until this condition is reached. In the way, a plot of θrb and θrs versus the mole fraction is obtained. Figure 5.13 shows the results. As expected the target becomes oxidized with increasing oxygen gas mole fraction. For reason which will be clear further in text, the inﬂuence of the nitrogen mole fraction on the target condition during reactive magnetron sputtering

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degree of oxidation

1.0 0.8 0.6 0.4 θrb θrs

0.2 0.0 0.00

0.01

0.02 0.03 0.04 0.05 mole fraction oxygen

0.06

0.07

Fig. 5.13. Calculated dependence of degree of oxidation of a Si target as function of the mole fraction in the plasma during reactive magnetron sputtering. The used current density was set to a value typical for reactive magnetron sputtering, i.e. 1 × 1017 ions cm−2 s−1 . The other used parameters are discussed in the text

of Si3 N4 will now be discussed. The sputter yield ratio between Si3 N4 (z = 4/3) and Si was experimentally found to be 1/7. The implantation proﬁle of nitrogen ions was again assumed to be Gaussian with the ion range 1.8 nm and the ion range straggle 1.1 nm (SRIM simulation for 400 eV N2 + on Si). Based on an almost linear relationship between the nitrogen ﬂow and the nitrogen partial pressure, it was argued that chemisorption was negligible during this experiment. Further, it was also argued that the chemical reactivity of nitrogen is much lower as compared with oxygen. This eﬀect can be simulated by lowering the value of the reaction rate constant k. Figure 5.14 (top) shows the simulated degree of nitridation of the Si target using the discussed parameters and for diﬀerent values of k. Figure 5.14 (bottom) shows the discharge voltage behaviour during reactive sputtering of Si as a function on the nitrogen mole fraction. As the experiment shows, the discharge voltage changes abruptly as a function of the nitrogen mole fraction. The same feature is noticed at low values of k in the model. In this speciﬁc case, the model can only compare the qualitative behaviour of the target condition as a function of the nitrogen mole fraction and not the quantitative behaviour. Indeed, at these large mole fractions the diﬀerence between the sputter yield of the reactive ions and the argon atoms should be taken into account. However, the abrupt change of the target condition as a function of the mole fraction is clearly represented. This strange eﬀect needs some extra explanation to be understood. The interested reader can read Appendix for more details. With Chemisorption/Knock-On Implantation The inﬂuence of chemisorption without knock-on implantation (β = 0) has been studied using the same settings as for Fig. 5.14, setting k = 1×10−23 cm3 atom−1 s−1 and by modifying the inﬂuence of the sticking coeﬃcient on the

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1.0 0.8 k=100 k=10

0.6

k=3.2

θb

k=1

0.4

θs

0.2

discharge voltage difference (V)

0.0 0.0

0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.8

1.0

40 30 20 10 0 −10 −20 −30 0.4 0.6 mole fraction nitrogen

Fig. 5.14. Top: The inﬂuence of the reaction rate constant k on the degree of target nitridation as a function of the nitrogen mole fraction. The simulation parameters are described in the text. Bottom: Discharge voltage diﬀerence measured between the discharge voltage measured after nitrogen addition and the discharge voltage measured in pure argon for a polycrystalline silicon target. The target was sputtered at constant power (50 W) [26]

abrupt behaviour. Figure 5.16 shows the result. As the sticking coeﬃcient increases, the S-shape behaviour of the target condition θrb as a function of the reactive gas behaviour disappears, i.e. no abrupt change in the target condition will occur when the sticking coeﬃcient is quite high. This can be understood as follows. As the sticking coeﬃcient increases, the target surface condition becomes more and more deﬁned by the chemisorption, which decreases the erosion rate. Hence, the sputter time increases, and the reactive atoms get more time to react which is similar to a situation with a higher reaction rate constant. Hence a similar situation develops as shown in Fig. 5.14 (left). Figure 5.15 shows also the target surface condition behaviour using the “Berg” model (for the same pressure and a sticking coeﬃcient equal to one). As one notices, the behaviour is quite similar to the described model. This explains the success of the basic model presented by Berg and Nyberg. Indeed,

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1.0 α=0 α=0.001 α=0.01 α=0.05 α=0.1 α=0.5 α=1.0 basic model

fraction metal θms

0.8 0.6 0.4 0.2 0.0 0.00

0.05

0.10 0.15 0.20 mole fraction reactive gas

0.25

0.30

Fig. 5.15. Target surface condition (metal fraction) as a function of the reactive gas mole fraction for diﬀerent sticking coeﬃcients. Except for the sticking coeﬃcient, the same conditions were used as in Fig. 5.14. The total pressure was set at 0.2 Pa

degree of oxidation

1.0 0.8

sticking coefficient α=0.1 β=0 β=0.001 β=0.01 β=0.05 β=0.1 β=0.5 β=1

0.6 0.4 0.2 0.0 0.0

0.2

0.4 0.6 mole fraction reactive gas

0.8

1.0

Fig. 5.16. Subsurface condition (θrb ) as a function of the reactive gas mole fraction for diﬀerent knock-on yields β, keeping the sticking coeﬃcient constant at 0.1. All other parameters where identical as in the previous ﬁgure

when the reactive gas has a suﬃcient high sticking coeﬃcient, the target surface condition described by both models is similar. Hence, the well-known hysteresis behaviour will be similar. This latter eﬀect will be discussed in more details in the following section. The diﬀerence between both models is that at a mole fraction of 0.15, the target is completely poisoned over a depth of approximately 3 nm in the presented model, while the latter is of course not the case in the basic model. Using the same conditions, the eﬀect of knock-on can be studied, by using a sticking coeﬃcient equal to α = 0.1 and by modifying the knock-on yield β. As shown in Fig. 5.16, increasing the knock-on yield has the opposite eﬀect than chemisorption. At a constant oxidation level, the corresponding reactive mole fraction shifts towards higher values. The same behaviour is noticed for lower sticking coeﬃcients. At low sticking coeﬃcients, one notices that

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an abrupt change in the target becomes possible again with an increasing knock-on yield. The Target Condition During Reactive Magnetron Sputtering as a Function of the Reactive Gas Flow In the previous section, some features of the model were discussed, and it was shown that some experiments can be understood from the model. The aim of this chapter is to discuss the details of the reactive sputtering of aluminium in a mixture of oxygen and argon. Figures 5.1, 5.2 and 5.9 summarize the most important results. Although, some of the details have been already discussed, the model can help the reader to understand this reactive sputtering process in more detail. However, in this ﬁrst discussion not all details of the reactive sputter process are implemented. These aspects, such as the inﬂuence of the deposition and erosion proﬁle, plasma-related topics and the target design, are discussed in Sect. 5.5. The reason for this subdivision is that the model needs further development to describe these aspects also. To model a set of hysteresis experiments as depicted in Fig. 5.2, several parameters, such as the pumping speed, target size, total current and current density, discharge voltage, can be taken from the experimental conditions. Based on this latter parameter, the implantation parameters, and the sputter yield of the target material can be calculated based on SRIM. Of course, some important parameters are diﬃcult to retrieve from the experiments. Although the sticking coeﬃcient of the reactive gas on the target has been determined, this value can only be used as a lower limit because the presence of oxygen radicals can increase the average sticking coeﬃcient. Although the knock yield can also be estimated from simulations (e.g. SRIM, TRIDYN, . . .) its value is diﬃcult to estimate because these models are very sensitive to the input parameters such as surface binding energy. A similar, but slightly more complex problem is the sticking coeﬃcient on the deposited target material. Indeed, as shown by Passeggi et al. [41], the sticking coeﬃcient of the reactive gas during deposition is generally larger than for chemisorption of the reactive gas on an already formed metal layer. The reason for this diﬀerence lays in the fact that the chemisorption process during deposition is better described as co-deposition of the reactive gas molecules and the target materials. Another “free” parameter is the substrate area. In (5.31) it is assumed that the target material is deposited uniformly over the substrate (and chamber walls) with a given area. Of course, this is generally not true. A deposition proﬁle should be taken into account. This problem is tackled in the next section but it complicates the model description. However, with (5.31) one actually implements an average ﬂux of the deposited target material on the substrate. The value of this ﬂux is changed by modifying the substrate area in the model. In this way, one accounts for the inﬂuence of the ﬂux. This approach will be followed in this section. In the next section, a more detailed discussion will be held on this topic.

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To compare the model results with the experimental results, the sum of the squared diﬀerences between the calculated critical points and the experimental critical points, i.e. χ2 , was calculated for diﬀerent combinations of the sticking coeﬃcient on the target and substrate, the knock-on yield, the reaction rate constant and the substrate area. As a critical point is deﬁned by the oxygen ﬂow and the oxygen pressure at the critical point, two values of χ2 can be calculated, one for the ﬂow and one for the pressure. Figure 5.17 shows the inﬂuence of the used parameters on the ratio between χ2 calculated for the ﬂow and the experimental error. Although the parameters were varied over a large interval, only 2.5% of the calculations resulted in a lower χ2 than the experimental error. This sets some restrictions to the value

1000

100

10

1 1

24 579 10 13 15 16 18 sticking coefficient on the target α

1000

100

10

1 1

2

0 0.02 0.03 0.04 0.05 0.06 0.08 0.09 0.1 0.12 0.13 0.2 0.22 0.3 0.33 0.5 0.66 1.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14

0 0.1 0.11 0.15 0.2 0.22 0.3 0.33 0.45 0.5 0.6 0.66 0.99 1

3 5 6 8 912 1314 knock on yield β

1000

100

10

1 1 2 3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

58 912 13 16 18 reaction rate constant k

1000 1 2 3 4 5 6 7 8 9 10 11 12 13 14

100

10

1

1 24 56 8 11 12 14 sticking coefficient on the substrate Ac 1000 1 2 3 4 5 6 7 8 9 10 11 12

100

10

1 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

0.05 0.053 0.075 0.1 0.15 0.225 0.25 0.273 0.3 0.493 0.5 0.55 0.75 1

256 300 512 600 603.97 900 951.94 1000 1024 2048 4096 16384

2 468 9 101112 substrate area Ac

5 10 14.7 15 17.3 18.5 19.9 20 21.5 24.5 30 40 45 50 60 80 90 500

Fig. 5.17. The ratio of the calculated χ2 and the experimental error. The χ2 is based on the diﬀerence between the modelled and experimental critical ﬂows for the experiment depicted in Fig. 5.2. The ratio is plotted as a function of the modiﬁed parameters in the model. The numbers on the X-axis refer to the value of the parameter given in the legend. Between two numbers the value of the modiﬁed parameter is kept constant while the other parameters are modiﬁed. The substrate area is given in cm2 , while the reaction rate constants are given in 10−24 cm3 atom−1 s−1

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Table 5.1. Average value and standard deviation (between brackets) for the modiﬁed parameters in the model for which the ratio between the χ2 and the experimental error is smaller than one for both χ2 calculated based on the critical ﬂows and the oxygen pressure at the critical point Sticking coeﬃcient target

Sticking coeﬃcient substrate

Knock-on yield

Reaction Substrate area rate constant (cm2 ) 3 −1 −1 (cm atom s )

0.17 (0.034)

0.35 (0.13)

0.22 (0.093)

2.0 × 10−23 (4.9 × 10−26 )

380 (150)

of the modiﬁed parameters. The sticking coeﬃcient on the target should be lower than 0.33. The sticking coeﬃcient on the substrate is lower than 0.75. The limit of the knock-on yield is around 0.33. No good ﬁts are obtained with a substrate area larger than 1, 024 cm2 . The reaction rate constant layers between 14.5 × 10−24 and 24.5 × 10−2 cm3 atom−1 s−1 . Combining this result with the χ2 for the critical pressures, an even more sever reduction of the number of combinations (six out of 3,087 combinations) which results in a good ﬁt is achieved. Table 5.1 shows the average value of the used parameters together with the standard deviation. Although no experimental quantiﬁcation of these values have been made, the values seem reasonable. The sticking coeﬃcient of oxygen on the aluminium target is much higher than the one measured but as reasoned before the dissociation and excitation of oxygen molecules can explain this higher sticking coeﬃcient. Indeed, it was expected from the work of Pekker [11, 12] that the sticking coeﬃcient should be in the order of 0.1. The higher sticking coeﬃcient for oxygen on the substrate has been discussed before. The ratio between the knock-on yield and the sputtering yield was calculated with SRIM (see above) to be 1.65. As the total sputter yield for the chemisorbed oxygen was set equal to the sputter yield of aluminium oxide, i.e. 0.23, the oxygen sputter yield is 0.14 and hence a value of 1.62 is found for the ratio. A substrate area of 380 cm2 agrees with a circular substrate with a diameter of 11 cm, which seems an acceptable value for deposition from a 2 in. magnetron. The reaction rate constant is may be surprising low but estimated from the small standard deviation its value is a key parameter in the model and can only be changed within a limited interval. Some other experimental trends can be understood from the model. Before the abrupt decrease of the discharge voltage a small increase of the discharge voltage (see Fig. 5.1) is noticed, which was attributed to chemisorption of oxygen on the target. The maximum value of the target coverage by chemisorption θsc is shown in Fig. 5.18 for diﬀerent pumping speeds. The target coverage by chemisorption increases a function of the pumping speed. Also shown in Fig. 5.18 is the voltage diﬀerence between the maximum registered voltage

5 Depositing Aluminium Oxide

20 θcs,max

0.12 15 0.10 10 0.08 5 16

32

65 pumping speed (L /s)

discharge voltage differerence (V)

25 0.14

185

130

θrb,20s-θrb,steady state

Fig. 5.18. On the left-hand side, the maximum value for the target coverage θsc for diﬀerent pumping speed calculated by the model using the parameters discussed in the text and given in Table 5.1. On the right-hand side the diﬀerence in the maximum discharge voltage registered and the discharge voltage measured in pure Ar

0.15 0.10 0.05 0.00 0.00

0.05

0.10 0.15 0.20 mole fraction oxygen

0.25

Fig. 5.19. Change of the subsurface compound fraction due to waiting without sputtering. θrb,steady state refers to the steady-state compound fraction during reactive sputtering while θrb,20 s refers to the compound fraction calculated 20 s after switching oﬀ the discharge, i.e. without sputtering

and the discharge voltage measured in pure Ar for diﬀerent pumping speed. A similar eﬀect is noticed. It was shown in Sect. 5.2 that the discharge voltage of an aluminium target ﬁrst sputtered in a mixture of argon and oxygen, can depend on the waiting period before the sputter cleaning in pure Ar. The eﬀect of a waiting period is simulated with the model using the same parameters as used for Fig. 5.19. Figure 5.19 shows the diﬀerence between the subsurface θrb compound fraction reached after steady state and the subsurface compound fraction θrb after 20 s waiting without sputtering for diﬀerent oxygen mole fractions in the plasma. Clearly the non-reacted implanted reactive atoms continue to form compound

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even without sputtering. This could explain the changes in discharge voltage as shown in Fig. 5.9.

5.5 Towards a More Complete Model for Reactive Magnetron Sputtering Of course the model for reactive magnetron sputtering is far too simple to describe all facets of this complex deposition technique. When carefully analysing the assumptions made in the model, it is clear that still quite some progress can be made resulting in more complete model. Some of the needed modiﬁcations are quite straightforward and can be easily implemented in the model. 5.5.1 Plasma-Related Topics In the discussion related to Table 5.1, the much higher sticking coeﬃcient of the oxygen molecules on the target as compared to the measured and literature values was attributed to the dissociation of the oxygen molecules into oxygen radicals with a much higher sticking coeﬃcient than the molecular oxygen. Hence, it is important to implement the plasma chemistry. A ﬁrst attempt to include the plasma chemistry in reactive sputtering modelling was performed by Pekker et al. [11, 12]. To reach this goal a space average model was purposed. The needed reaction rate constants for the plasma reactions have been derived by developing a simple model for the DC magnetron discharge. Once these reaction rate constants are known, the concentration of all species in the plasma should be known, and in this way the equations derived in Sect. 5.3 can be improved by including more species. In this way, the diﬀerence in the ionisation probability of argon and the reactive gas can be included which is a better approach than the assumption made in the proposed model. Indeed, in the model it was assumed that the fraction of reactive ions bombarding the cathode is equal to the fraction of reactive gas in the vacuum chamber. Taking into account other species such as reactive gas radicals will inﬂuence the importance of for example chemisorption as these species have generally a higher sticking coeﬃcient. The inﬂuence of the deposition parameters on the plasma chemistry can be included in the model. Improving the DC magnetron discharge model will be necessary for a better description of the plasma chemistry. Indeed, it is well known that the ISEE coeﬃcient strongly inﬂuence the plasma parameters and in this way also the plasma chemistry. As also the target condition changes as a function of the reactive gas ﬂow, a complete model of reactive magnetron sputtering will only be possible when the magnetron discharge is modelled in all its details. We refer to Chap. 3 for more details.

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5.5.2 Deposition Proﬁles and Erosion Proﬁles Inﬂuence of the Deposition Proﬁle To calculate the substrate condition during reaction magnetron sputtering, i.e. θc , the deposition of the compound molecules and the target atoms which are sputtered from the target should be taken into account. This is given in (5.31). Indeed, the second term of the LHS of this equation describes the sputtering of the compound from the target and the deposition on the substrate. The RHS of (5.31) describes in the same way the sputtering of the metal atoms and their deposition on the substrate. As can be revealed from this equation the sputtered material is deposited uniformly on a substrate with a given dimension. Of course, it is well known that this latter is not valid. In a more realistic approach, a deposition proﬁle can be measured. As the material ﬂux towards a surface element of the substrate is not equal, the composition will not be uniform. Hence, (5.30) and (5.31) should be rewritten. In most cases the deposition proﬁle is radial symmetric and therefore these equations will be modiﬁed as an example for this speciﬁc situation. The substrate can be subdivided in a series of concentric rings with Δr as width, ! r 2 Ac = 2πr dr 2πn(Δr) . (5.35) 0

n

One can attribute to each ring a θc , and the reactive gas ﬂow towards this ring is, using (5.30) qc,n = αc F (1 − θc,n )Ac,n = 2πn(Δr)2 αc F (1 − θc,n ), qc,n . qc =

(5.36)

n

The substrate condition can be calculated using (5.31) as 2αc At wn At wn F (1 − θc,n) + I(Yc θsc + Yr θsr )(1 − θc,n ) = IYm θsm θc,n , (5.37) z Ac,n Ac,n with wn a weighting factor which depends on the deposition proﬁle (see further). It is assumed that the weighting factor is not dependent of the deposited material, i.e. oxide or metal. Using a quartz balance the deposition proﬁle of aluminium sputtered from a 2 in. magnetron (see caption for more experimental details) was measured and is shown in Fig. 5.20. Based on this measured deposition proﬁle it is possible to calculate a deposition rate on a planar substrate. The data can be ﬁtted with a sigmoid curve ψ(r). This function must be normalized as ! ∞ ψ(r)2πr dr = 1. (5.38) 0

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15 30 45 60

−15

1

−30

0.8 0.6 0.4

75

−45 −60 −75

0.2 90

0

−90

Fig. 5.20. Normalized deposition rate for the aluminium from a 2-in. magnetron. Experimental conditions: 0.4 Pa Ar, current 0.4 A. The deposition rate was measured with a quartz balance positioned on a circle with a radius of 10 cm, i.e. the balance/target distance was 10 cm and constant

The weighting factors are then calculated as wn = ψ(r)2π(Δr)2 .

(5.39)

Performing this procedure, weighting factors have been calculated for a planar substrate located 6 cm from the target and with a diameter of 32 cm. These conditions have been chosen as the average material ﬂux on the substrate is equal to the homogeneous material ﬂux on a substrate with an area of 380 cm2 (see Table 5.1). Interesting, this results in the same hysteresis behaviour of the pressure as a function of the oxygen ﬂow is simulated in Sect. 5.4. From this analysis one learns that it is the average material ﬂux on the substrate which also inﬂuences the critical point. It is also clear that to reach a suﬃcient degree of oxidation at a high deposition speed one must be able to work between two critical points, or where the hysteresis curve has a negative slope. This can be achieved by using some kind of feedback control of the oxygen ﬂow as shown for the ﬁrst time by Sproul. An excellent review by this author on this topic is given in [37]. Comparing the top squares in Fig. 5.21, it is clear that to fully oxidize (95%) the deposited material the working point when taking into account the deposition proﬁle shifts even further to higher oxygen pressures and hence to lower deposition rates. Hence, it is important to simulate the deposition proﬁles which can be done by using the knowledge described in chapter 6 of this book. Inﬂuence of the Erosion Proﬁle Similar to the material ﬂux, the ion ﬂux to the target, i.e. the ion current density, is not homogeneous during magnetron sputtering. This is clearly noticed during planar magnetron sputtering by the formation of the erosion track. From the erosion proﬁle (see Fig. 5.22) one can estimate the ion current density distribution on the target. However, this is a crude approximation as the deepening of the race track results in a strong modiﬁcation of the

5 Depositing Aluminium Oxide θc

Profile 0.9 0.7 0.5 0.3 0.1 0.9 0.7 0.5 0.3 0.1 0.9 0.7 0.5 0.3 0.1 0.9 0.7 0.5 0.3 0.1

oxygen pressure (Pa)

0.2

0.4

0.6

189

Homogeneous

0.8

1.0

0.08 0.06 0.04 0.02 0.00 0.6 0.8 1.0 1.2 1.4 1.6 1.8 flow (sccm)

Fig. 5.21. Simulated hysteresis behaviour using the parameters described in Table 5.1 of the oxygen pressure as a function of the reactive gas ﬂow for a pumping speed of 16 L s−1 . On the RHS the substrate condition is given for four diﬀerent points on the curve when a homogeneous material ﬂux is used and a substrate area of 380 cm2 . The top square corresponds with on oxide fraction of 95%. On the LHS the substrate condition is given for the same points of the hysteresis curve but now the deposition proﬁle as shown in this ﬁgure is taken into account. The full line is the oxidate state for the central line along the substrate. The substrate was at 6 cm from the target and a diameter of 32 cm

0.0

depth (mm)

−0.2 −0.4 −0.6 −0.8 −1.0 −25

−15 −5 5 15 position on the target (mm)

25

Fig. 5.22. Erosion proﬁle measured after 60 h sputtering of an aluminium target at constant current (0.4 A) and constant argon pressure (0.4 Pa) (markers). The simulated target condition (value of θsr ) on the ﬁrst critical point (see Fig. 5.23) is also shown

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actual magnetic ﬁeld. Hence, at this moment the presented results are only qualitatively correct. In the model presented in Sect. 5.3, this inﬂuence was not implemented as only the measured area of the proﬁle was used to calculate the average ion current density. In this section a method is suggested to include this feature of the deposition process. To account for the non-homogeneous current density, the target (5 cm diameter) is subdivided in ten concentric rings with a width of 2.5 mm and based on the measured erosion proﬁle a current density is attributed to each ring. Then the model is applied for each of these rings to calculate the target condition as a function of the reactive gas pressure or fraction. To calculate the substrate condition and the total ﬂow, the material ﬂux towards the substrate must be calculated. Neglecting at this point the deposition proﬁle (see previous section), (5.30) and (5.31) can again be used. The values of θsc , θsm and θsr needed to solve (5.30) are calculated by averaging over the diﬀerent target parts using the ion current density as weighting factor. As the model actually calculates the reactive gas mole fraction from the target condition, it is necessary to interpolate to have the target condition of each target part at the same mole fraction. Figure 5.23 shows a calculated pressure/ﬂow hysteresis together for some speciﬁc points on this curve the target condition (value of θsr ). As expected the target is ﬁrst poisoned in the regions where the current density is low. θsr

0.16

0.0

0.2

0.4

0.6

0.8

1.0

oxygen pressure (Pa)

0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 0.9

1.1

1.3 1.5 flow (sccm)

1.7

Fig. 5.23. Simulated hysteresis behaviour using the parameters described in Table 5.1 of the oxygen pressure as a function of the reactive gas ﬂow for a pumping speed of 16 L s−1 . To calculate the current density on the target the erosion proﬁle shown in the ﬁgure is used. The target condition is represent by the surface fraction of compound formed by reaction between the implanted (direct and knock-on) reactive atoms, i.e. θsr . The larger markers refer to a point on the hysteresis curve for which the target condition is shown. Due to the low resolution of the target subdivision the curve shows some non-realistic jumps

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At the ﬁrst critical points (at approximately 1.7 sccm) only the region within the highest current density remains more or less metallic. 5.5.3 Rotating Magnetrons To use magnetron sputtering on a large, industrial scale it is necessary to cope with some of the disadvantages inherent to the technique. Particularly, in the case of standard planar magnetrons, the presence of the race track often limits the target consumption to 25 up to 30% and increases the cost of ownership. A sputter source which is able to largely eliminate this problem is the rotating cylindrical magnetron. In this concept, the target is a cylindrical tube, which rotates around a stationary magnet conﬁguration pointing in the direction of the substrate. Although a stationary race track is present during the sputtering process, no groove is formed in the rotating target and a very high target consumption may be achieved [38]. The simulation of this magnetron type during reactive magnetron sputtering is quite challenging because the time dependency is very important. This ﬁnds its origin in the fact that a given surface element of the target remains only for a limited time in the race track. Outside the race track the reactive gas can be chemisorbed on the target. Hence, it is not surprising that the rotation speed inﬂuences the hysteresis behaviour. Figure 5.24 shows the shift of the hysteresis towards lower oxygen ﬂow as a function of the rotation speed. The simulation of this eﬀect will not be discussed in this chapter as the implementation becomes quite complicated. However, in this context it is

discharge voltage (V)

360

340 0 rpm 2.4 rpm 8.9 rpm 64.1 rpm

320

300

280

0.0

0.5

1.0 1.5 oxygen flow (sccm)

2.0

2.5

Fig. 5.24. Discharge voltage behaviour during reactive sputtering of aluminium with the rotating cylindrical magnetron for diﬀerent rotation speeds. The arrows indicate the shift of the hysteresis when increasing the rotation speed. Experimental conditions: constant Ar pressure, 0.4 Pa and constant discharge current, 0.3 A [39]

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important to mention that maybe the most important diﬀerence between the “Berg” model and the model described in this chapter is the time dependency. To proof this point, a hysteresis is simulated with both models. The simulation conditions of both models have been chosen to reach approximately the same hysteresis curve, explaining the diﬀerences between the used sticking coeﬃcients. So, from this point of view, i.e. steady-state conditions, the results are comparable. However, more important is the diﬀerence in the kinetics which is introduced by implementing reactive ion implantation. To illustrate this diﬀerence, the following experiment is simulated. During partial pressure control, the ﬂow is regulated to maintain a given partial pressure of the reactive gas. When the experiment is started both target and substrate are in metallic mode. So, in the beginning the reactive gas ﬂow must be high because most of the reactive gas is consumed by the target material. The reaction of the gas with the target material will cover both target and substrate with compound and progressively less reactive gas is needed. Hence, as a function of time the reactive gas ﬂow will decrease. This situation is simulated using the “Berg” model and with the presented model. Figure 5.25 shows the results. In agreement with the expectations, implementing ion implantation and knock-on results in more reactive gas consumption during the target oxidation. For the “Berg” model: sticking coeﬃcient reactive gas on the target: αt = 0.7, sticking coeﬃcient reactive gas on the substrate αc = 0.7. For the implantation model: Rp = 2 nm, ΔRp = 1 nm, β = 1, reaction rate −1 constant k = 1 × 10−22 cm3 atom s−1 : αt = 0.03 and αc = 0.35. There is also only a small diﬀerence in steady state as the contribution of the target to the total ﬂow is small. However, an important diﬀerence is noticed in the path to reach this steady state. From practical point of view

flow (sccm)

100

Berg model presented model

10

1

0.1 0.01

0.1 time (s)

1

10

Fig. 5.25. Reactive gas ﬂow as a function of time during partial pressure control (0.06 Pa) simulated using the “Berg” model and the implantation model. Simulation conditions: current 0.167 A, target surface 10 cm2 , substrate + chamber walls surface 1,000 cm2 , pumping speed 10 L s−1

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this discussion may look not relevant. However, as the thickness of formed compound layer on the target is not just the assumed monolayer in the “Berg” model, one should realize that the process kinetics can not be described accurately, which could inﬂuence the understanding of reactive sputtering process using rotating cylindrical magnetron (and/or partial pressure control) where the “Berg” model fails.

5.6 Conclusion In this chapter a model for reactive magnetron sputtering is presented. The main diﬀerence between the presented model and the “Berg” model is the implementation of the reactive ion implantation into the target during this process. Taking this eﬀect into account makes it possible to explain in more detail some experimental results during the reactive magnetron sputter deposition of aluminium oxide from an aluminium target. However, this is not the “end” of the modelling work. More work has to be done to make this model more complete. Especially the implementation of the plasma chemistry is important. Also, further experiments are needed to reduce the number of “free” parameters. Acknowledgements. The authors wish to thank the following persons for their contribution to this paper: J. Haemers, A. Segers, K. Euﬁnger S. Mahieu, S. Heirwegh. X.Y. Li, A. Colpaert and G. Buyle. The authors also wish to express the gratitude to the IWT-Vlaanderen and N.V. Bekaert for the ﬁnancial support.

Appendix To facilitate the discussion the model described in Sect. 5.3.1 will be simpliﬁed. Instead of assuming a Gaussian implantation proﬁle, one can assume that the ions are implanted in a slab with thickness w located at x = D in the target. Outside this slab no ions are implanted. Hence, p(x) = (1 − B)/w, because ! D p(x)dx = 1 − B. (5.40) D−w

If the reaction rate is slow enough, the implantation and the reaction can be decoupled in time, i.e. one can ﬁrst describe the implantation/sputtering process and follow the reaction of the implanted ions as the slab moves towards the surface of the target. So, the concentration of the ions in the slab before the reaction starts can be calculated as follows. With (5.40) the concentration of the ions in the slab will change as ∂nr =

2fI (1 − B) ∂t. w

(5.41)

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However, as no ions are implanted outside the slab, the implantation period in the slab is deﬁned by the erosion rate of the target Δti = w/vs . Hence, ! ! nr 2fI (1 − B) Δti 2fI (1 − B) w 2fI 2f n0 ∂nr = ∂t = = (1 − B) = (1 − B). w w vs vs Ys 0 0 (5.42) This is not a surprising result as it has already derived before (see (5.14)). Due to the simultaneous sputtering, the surface moves towards this slab. Stated otherwise, with the initial concentration of the reactive atoms described by (5.42), the slab starts to move towards the surface while the reactive atoms react with the target atoms with an initial concentration given by no . Under this assumption the reaction kinetics is given by ∂nr (x, t) = −kznr(x, t)nm (x, t), ∂t ∂nm (x, t) = −knr (x, t)nm (x, t). ∂t

(5.43)

In contrast to (5.23) this latter equation can be solved analytically which 2f results in − zθ rb 1 = kn0 Δtr , (5.44) ln 2fYs 2f − z Ys Ys (1 − θrb ) with Δtr the reaction time. In steady state this reaction time is equal to the time for the slab to reach the surface or equal to D/vs . Hence, one can write 2f Ys D Ys − zθrb = kn20 = C ste , (5.45) ln 2f 2f I Ys − z Ys (1 − θrb )

0.2

−0.6 −0.2

0.6

1.6

1

1.3

0.6 0.5

0

0.4 0.3

-0.3

-0.1 0.1

0.4

0.8

−0.4

0.0 0.00

0.6

0.2

1

-0.2

1.2

b

−1 −0.8

-1.4 -1.2 -1 -1.1 -0.9 -0.7 -0.8 -0.6 -0.4 -0.5

1.8

0.4

0.8 1.4

θ

0.4

1.0

−1.4 −1.2

*

θ

b

0.6

−1.6 0.2

0.8

1.6

1.0

-1.7 -1.3 -1.5

which makes it possible to solve (iteratively) this equation and to plot the target condition as a function of the mole fraction f . The behaviour of the target condition as a function k is similar to the one shown in Fig. 5.26

B

0.2 A

0

0.02

0.04 0.06 mole fraction reactive gas

0.08

0.10 −23

k=1x10

sputter time > reaction time sputter time < reaction time θb implanted concentration too low form amount of compound implanted concentration = amount of formed compound amount of non reacted reactive atoms

−3

(cm /at.s)

0.0 0.00

0.02

0.04 0.06 mole fraction reactive gas

0.08

0.10

k=3x10−23 (cm−3/at.s) sputter time > reaction time sputter time < reaction time θb implanted concentration too low form amount of compound implanted concentration = amount of formed compound amount of non reacted reactive atoms

Fig. 5.26. Ratio between reaction time and sputter time for two diﬀerent values of k. The used values for the sputter yield were Ym = 0.5 and Yr = 0.05. The current density was set equal to 2 × 1017 ions cm−2 s−1 and the implantation depth D 3 nm. The stoichiometry was set z = 2

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(right). The simplicity of (5.45) makes it possible to understand the abrupt target behaviour as function of the mole fraction for low k values. Indeed, one can calculate, for a given target surface condition, the reaction time needed to reach a certain value of θb . This reaction time can be compared to the time needed to reach the slab located at a depth D in the target. The value of the sputter time Δts can be calculated based on the target surface condition, given by Ys . The ratio Δts /Δtr is shown as a function of θb and the mole −1 −1 fraction for a larger value of k (3 × 10−23 cm3 atom s ) and for a low −1 value of k (1 × 10−23 cm3 atom s−1 ). On both plots the solution of (C.7), i.e. the steady-state value of θb as a function of the mole fraction is also plotted which agrees with the ratio Δts /Δtr = 1. This curve separates the plot into two regions. On the left-hand side (low fractions) the reaction time is longer than the sputter time. On the right-hand side the opposite is true. Also plotted on the same ﬁgure is the amount of non-reacted reactive atoms in the target. As one can notice in both situations a certain amount of these atoms is present. This can be understood as follows. When the surface reaches the implantation slab, the reaction must stop, even if not all reactive atoms have reacted with the target material to form compound material. Of course, for the low k value example this amount of non-reacted reactive atoms is much higher than for the higher k value example. So, when increasing the mole fraction, one deviates from the steady state to a situation that the reaction time is shorter than the sputter time (see Fig. 5.26 arrow A). Hence, the reactive atoms have more time to react resulting in more compound formation (see Fig. 5.26 arrow B), which further increases the sputter time. Hence more compound formation becomes possible, on the condition that enough reactive atoms are present. Here the diﬀerence between the low and high k value example becomes clear. In the higher k value example the amount of non-reacted reactive atoms is quite small but in the low k value example this amount is much high. Hence, at the critical point (see Fig. 5.26 asterisk) the following situation develops. The deviation from the steady state results in more compound formation as the reaction time is shorter than the sputter time. However, due to large amount of non-reactive atoms present in the target, this results in a strong increase of the compound formation, which lowers the erosion rate, i.e. increases the sputter time with even more compound formation as a result. However, to form more compound more time is needed. Hence, this avalanche ends when the reaction time becomes again equal to the sputter time. This analysis shows another important point. Some simulation codes (e.g. TRIDYN) are used to describe the oxidation of the target by implantation of reactive atoms. These simulations show that the target condition behaviour does not change abruptly. This can be understood from the presented model as these simulation codes do not take the reaction rate into account, i.e. the reaction between the implanted species and the target is immediate or stated diﬀerently a very high value for k. From the given analysis

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it is understandable that no abrupt changes can be calculated with these models. Using an inﬁnitive reaction rate in (5.45) shows that 2f /Ys = zθrb . Or stated diﬀerently, using (5.22), each implanted atom reacts with the target material to form compound material: Ys I 2f I = Iθrs Yr . θrb n0 = n0 z

(5.46)

Hence, there are no non-reacted reactive atoms present and an avalanche situation can never develop. As a ﬁnal remark it can be shown that (5.45) is almost similar to a previously published equation. Indeed, in a previous model, the concentration of the implanted reactive ions was calculated in the same way as above. However, as no time dependence was taken into account, the amount of implanted of reactive atoms was generally much larger than the amount needed to form the compound, i.e. z. Hence for 2f /Ys z (5.45) becomes −

Ys2 ln(1 − θrb ) = f. 2C ste

(5.47)

In the previous model the inﬂuence of preferential sputtering was not taken into account, and the following equation was derived [40] −

Yb ln(1 − θrb ) = f, 2C ste

(5.48)

with Yb = (Yc − Ym )θrb + Ym . Both (5.47) and (5.48) give a similar S-shaped curve.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

K. Koski, J. H¨ ols¨ a, P. Juliet, Surf. Coat. Technol. 116–119, 716 (1999) D. Depla, R. De Gryse, Plasma Sources Sci. Technol. 10, 547 (2001) G. Buyle, PhD Thesis, Ghent University, 2005 T. Do, N.S. McIntyre, Surf. Sci. 440, 438 (1999) V. Zhukov, I. Popova, V. Fomenko, J.T. Yates Jr., Surf. Sci. 441, 240 (1999) V. Zhukov, I. Popova, J.T. Yates Jr., J. Vac. Sci. Technol. A 17, 1727 (1999) V. Zhukov, I. Popova, J.T. Yates Jr., Surf. Sci. 441, 251 (1999) W.H. Krueger, S.R. Pollack, Surf. Sci. 30, 263 (1972) B.C. Mitrovic, D.J. O’Connor, Surf. Sci. 405, 261 (1998) A. Arranz, C. Palacio, Surf. Sci. 355, 203 (1996) L. Pekker, Thin Solid Films 312, 341 (1998) E. Ershov, L. Pekker, Thin Solid Films 289, 140 (1996) D. Guttler, B. Abendroth, R. Grotzschel, W. Moller, D. Depla, Appl. Phys. Lett. 85, 6134 (2004) 14. D. Depla, J. Haemers, R. De Gryse, Thin Solid Films 515, 468 (2006)

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15. S.S. Todorov, E.R. Fossum, Appl. Phys. Lett. 52, 48 (1988) 16. R. Behrish (ed.), Sputtering by Particle Bombardment II, (Springer, Berlin Heidelberg New York, 1981) 17. D. Depla, R. De Gryse, J. Vac. Sci. Technol, A 20, 521 (2002) 18. P.H. Dawson, Surf. Sci. 57, 229 (1976) 19. E. Taglauer, W. Heiland, U. Beitat, Surf. Sci. 89, 710 (1979) 20. The Stopping and Range of Ions in Matter (SRIM) can be downloaded from www.srim.org 21. D. Depla, S. Heirwegh, S. Mahieu, J. Haemers, R. De Gryse, J. Appl. Phys. 101, 013301/1 (2007) 22. D. Depla, H. Tomaszewski, G. Buyle, R. De Gryse, Surf. Coat. Technol. 201, 848 (2006) 23. S. Mahieu, D. Depla, Appl. Phys. Lett. 90, 121117/1 (2007) 24. J.M. Ngaruiya, O. Kappertz, S.H. Mohamed, M. Wuttig, Appl. Phys. Lett. 85, 748 (2004) 25. D. Depla, R. De Gryse, Plasma Sources Sci. Technol. 10, 547 (2001) 26. D. Depla, A. Colpaert, K. Euﬁnger, A. Segers, J. Haemers, R. De Gryse, Vacuum 66, 9 (2002) 27. F. Schulz, K. Wittmaack, Radiat. Eﬀ. 29, 31 (1976) 28. D. Rosen, I. Katardjlev, S. Berg, W. Moller, Nucl. Instrum. Meth. B 228, 193 (2005) 29. J.C.C. Tsai, J.M. Morabito, Surf. Sci. 44, 247 (1974) 30. Y. Kudriavtsev, R. Asomoza, Appl. Surf. Sci. 167, 12 (2000) 31. N. Herbots, C. Hellman, O. Vancauwenberghe, in Low Energy ion-surface interactions, ed. by J.W. Rabalais (Wiley, New York, 1994), ISBN 0471938912 32. W. Patterson, G. Shirn, J. Vac. Sci. Technol. 4, 343 (1967) 33. D. Depla, R. De Gryse, Vacuum 69, 529 (2003) 34. J.L. Alay, W. Vandervorst, Phys. Rev. B 50, 15015 (1994) 35. H. De Witte, Ph.D. University of Antwerp, Belgium 36. K. Wittmaack, Surf. Sci. 419, 249 (1999) 37. W.D. Sproul, D.J. Christie, D.C. Carter, Thin Solid Films 491, 1 (2005) 38. J. Musschoot, D. Depla, G. Buyle, J. Haemers, R. De Gryse, J Phys. D. Appl. Phys. 39, 3989 (2006) 39. D. Depla, J. Haemers, G. Buyle, R. De Gryse, J. Vacuum Sci. Technol. A 24, 934 (2006) 40. D. Depla, R. De Gryse, Surf. Coat. Technol. 183, 184 (2004) 41. M.C.G. Passeggi, L.I. Vergara, S.M. Mendoza, J. Ferron, Surface Science 50`e– 510, 825 (2002)

6 Transport of Sputtered Particles Through the Gas Phase S. Mahieu, K. Van Aeken, and D. Depla

6.1 Introduction Knowledge of the transport of sputtered particles through the gas phase is not only a fundamental research topic, but also of main interest to know the properties of the arriving metal ﬂux at the substrate or chamber walls as a function of the deposition geometry and deposition conditions. Characterisation or modelling of this metal ﬂux is, e.g. of interest when a high thickness uniformity is needed [1], when complex substrates are to be deposited [2], or when the thin ﬁlm composition has to be controlled [3]. However, not only the amount of arriving metallic particles has to be controlled, but also their direction and impact energy are inﬂuencing the ﬁnal properties of the deposited thin ﬁlms. Although some attempts have been done, characterisation of the incoming direction [4] or the energy [5] of metal particles experimentally is diﬃcult to carry out. A better attempt is to simulate the transport of the sputtered particles, and to verify the simulation code by the experimental much more accessible deposition proﬁle [6]. An overview of the simulation of the transport of the sputtered particles through the gas phase is given in this article. Section 6.2 describes the place wherefrom the sputtered particles leave the target. Section 6.3 discusses the diﬀerent ways to describe the initial energy and direction of the sputtered particles, when leaving the target. In Sect. 6.4, the mean free path, and thus the distance to a collision with the background gas, is discussed. Also the collision and the interaction potential needed to describe the collision are treated in Sect. 6.4. Section 6.5 brieﬂy discusses the possible ways to include the eﬀect of gas rarefaction. Finally, in Sect. 6.6 a concrete simulation model is described and some typical results are shown.

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6.2 Radial Distribution Where Sputtered Particles Leave the Target Magnetron sputtering is based on the generation of a magnetically enhanced glow discharge. As discussed in detail by A. Bogaerts et al. in Chap. 3 [7], positive discharge gas ions are accelerated towards the target, which is kept at negative voltage. This ion bombardment results in the emission of secondary electrons from the cathode, which are conﬁned in the vicinity of the target due to the electric and magnetic ﬁelds. This conﬁnement of the electrons by a non-uniform electric and magnetic ﬁeld causes a locally enlarged ionisation degree of the sputter gas. Since the ionized gas particles are nearly not inﬂuenced by the magnetic ﬁeld, they are accelerated perpendicular to the target surface by the electrical ﬁeld. Hence, the locally enlarged ionisation degree results in a locally enlarged ion bombardment of the target and thus a non-uniform erosion of the target resulting in a racetrack [8]. However, one should take into account that this racetrack is not a direct reproduction of the radial distribution wherefrom sputtered particles leave the target. The racetrack is formed by the local erosion of the target, counteracted by the redeposition of some sputtered particles onto the target. Hence, the resulting racetrack is a combination of sputtering and redeposition. The radial distribution wherefrom the sputtered particles leave the target, used for simulating the metal ﬂux towards the substrate can be deduced following two approaches. After sputtering a target, one can measure experimentally the proﬁle of the resulting racetrack, e.g. by proﬁlometry. The inverted proﬁle could be taken as the radial distribution wherefrom sputtered particles leave the target [9–16]. However, following this approach during a simulation, one should take care that redeposited particles are already taken into account. Hence, simulated particles leaving the target, but which ﬁnally seems to be redeposited onto the target, should be omitted during the simulation. In another approach, one can simulate the ionisation distribution of the sputter gas and a perpendicular projecting of it onto the target gives the place where ions strike the target [17–25]. This distribution where ions strike the target can also be measured experimentally by measuring the local current into the target region [26, 27]. Because sputtered atoms leave the target in the near vicinity of the ion impact, the distribution where ions bombarded the target corresponds with the distribution where sputtered particles leave the target. In case that the projection of the ionisation distribution is used as input for the radial distribution of leaving particles, redeposited particles onto the target should be taken into account during the simulation.

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6.3 Energy and Angular Distribution of Sputtered Particles Leaving the Target Together with a description of the total sputter yield, Sigmund [28] and Thompson [29] also provided a description of the energy and the angular distribution of the sputtered atoms, respectively. Because nearly all other analytical models of the sputter process are based on the Sigmund–Thompson theory, this theory will be discussed in Sect. 6.3.1. The results of other analytical models, based on the Sigmund–Thompson theory will be summarized in Sect. 6.3.2. Examining experimentally measured energy and/or angular distributions of sputtered atoms indicate that the analytical models not perfectly match with the experiment (see Sect. 6.3.3). A better ﬁt with the experimental energy and angular distribution could be obtained by simulating the sputtering process, or by studying this process by solving the master equations for the linear collision cascade generated by ion impact (see Sect. 6.3.4). 6.3.1 Sigmund–Thompson Theory for the Linear Cascade Regime According to Sigmund, it is convenient to distinguish the collision cascade into three regimes: the single-knock-on regime, the linear cascade regime and the spike regime [28]. In the single-knock-on regime, the bombarding particle transfers energy to target atoms which, possibly after having undergone a small number of one-to-one collisions, are ejected from the surface. In the linear and the spike regime, the recoiled target atoms are energetic enough to generate secondary and higher generation recoils. In this way, a cascade of recoils is generated, and again some atoms at the surface may by ejected from the solid. In the linear regime, the density of recoils is suﬃciently low to ensure that most collisions involve one moving and one stationary particle. This regime is called linear since the sputter yield is found to be proportional to the ﬁrst power of the projectile energy. In the spike regime, the density of recoils is so high that collisions between two moving atoms are frequently occurring. Quantitatively, the single-knock-on regime falls into the lower and medium incident energy region, except for light ions where, because of ineﬃcient energy transfer, it extends up to the lower keV region. The linear cascade regime is characteristic for bombarding particles with an energy from several hundreds eV to some keV and MeV, except for the heavier ions, which tend to cause the spike regime. In case of magnetron sputtering, the lower energy part of the linear cascade regime is of main interest since the bombarding particles have an energy in the range of several hundreds eV. The sputter yield Y is deﬁned as the number of sputtered atoms per bombarding particle. To calculate the sputter yield in function of the energy of the bombarding particle, the number of atoms which suﬀer recoil and the

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fraction of these recoiled atoms that are able to escape from the surface, should be known. Let n(E, E0 ) be the mean number of atoms set in motion with an initial energy larger than some value E0 in a cascade initiated by a primary particle of initial energy E(> E0 ). Allowing only for elastic collisions and ignoring all binding forces between target atoms, one ﬁnds the expression [30]: n(E, E0 ) = Γm

E for large E, E0

(6.1)

with Γm a parameter depending only on the index m, which is a parameter depending on the energy E and which characterizes the scattering cross section. However, a particle bombarding a solid will not only dissipate its energy by elastic nuclear collisions, but also by exciting the electrons. This energy delivered to the electrons will not provide a chance to the atoms to recoil, since this energy will be immediately shared with all other electrons. Therefore, the total number of atoms set in motion after the impact of a primary particle with energy E will not be n(E, E0 ) but n(E, E0 )

FD (E, Ω, r ) , E

(6.2)

where FD (E, Ω, r ) is the density of deposited energy for a particle of energy E impinging under direction Ω at the solid surface at position r , slowed down due to the continuous drain of energy to the electrons. Therefore, the mean number of atoms moving at any time with an energy (E0 , dE0 ) is given by n(E, E0 )

FD (E, Ω, r ) FD (E, Ω, r ) dE0 dt0 = n(E, E0 ) , E E v0 |dE0 /dx|

(6.3)

where dt0 is the mean time needed by a recoil atom to slow down from E0 + dE0 to E0 , v0 is the velocity of a target atom with energy E0 . Hence, the impact of an energetic particle generates a stationary distribution of moving target atoms. Assuming that the direction in which these target atoms move is isotropic, and thus assuming a complete collision cascade, it can be calculated how much of these target atoms are able to reach the surface under a speciﬁc direction Ω 0 . This, together with (6.1) gives an expression for the mean number of atoms moving with an energy (E0 , dE0 ) in the direction (Ω 0 , d2 Ω 0 ) in the volume (r , d3 r ): Γm

FD (E, Ω, r ) dE0 d2 Ω 0 Ω0 . E0 v0 |dE0 /dx| 4π

(6.4)

Multiplication with v0 ﬁnally yields the current density of atoms reaching the target surface. If these particles can overcome the potential barrier existing at

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the surface, they are considered as sputtered. The simplest model for surface binding is based on a planar surface barrier Us . Finally, an expression for the sputter yield of a particle impinging with an energy E and angle θ at the surface in function of the energy E0 of the sputtered target atoms (r = 0) and their angular direction θ0 is given: d3 Y = Γm

FD (E, θ, 0) dE0 d2 Ω 0 cos θ0 . E0 |dE0 /dx| 4π

(6.5)

Nice about the analytical theory is that the energy and angular distribution of the sputtered atoms can be deduced from (6.5). Assuming a planar surface barrier Us that the recoiled target atoms have to overcome before being sputtered and taking into account the conservation of momentum, the following equations must be fulﬁlled: E1 cos2 θ1 = E0 cos2 θ0 − Us , 2

2

E1 sin θ1 = E0 sin θ0 ,

(6.6a) (6.6b)

in which the subscript 0 indicates the situation before the target atom reaches the surface and the subscript 1 indicates the situation after the atom leaves the target, as also shown in Fig. 6.1. The energy is indicated by E, v indicates the velocity and θ is the direction with respect to the surface normal. It results from (6.6a) that E1 cos θ1 d2 Ω1 = E0 cos θ0 d2 Ω 0 and hence, (6.5) yields: FD (E, θ, 0) E1 dE1 d2 Ω 1 (6.7) cos θ d3 Y = Γm 1 (E1 + Us )2 |dE0 /dx|E0 =E1 +Us 4π The factor dE0 /dx expresses the loss in energy when a target atom moves through a medium. Hence dE0 /dx is given by NS n (E) in which N is the density of the medium and Sn (E) is the nuclear stopping cross section. According to Sigmund [30] the nuclear stopping cross section is proportional to E 1−2m . The parameter m depends on the energy E and is 0 for E = Us , 0.2–0.3 for E = 1 keV and reaches unity when E is very high. Hence (6.7) gives an

Fig. 6.1. Eﬀect when an atom passes the planar surface barrier Us (left) or is reﬂected at the target surface (right). The indices 0 and 1 indicate the situation just before and just after the ejection respectively

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expression for the energy and angular distribution of the sputtered atoms: N (θ1 , E1 ) =

d3 Y E1 ≈ cos θ1 . dE1 d2 Ω 1 (E1 + Us )3−2m

(6.8)

The energy distribution has its maximum at Nmax = Us /(2(1 − m)). The angular distribution of the sputtered particles is a cosine function. Thompson [29] derived this expression in case for very low energetic bombardment (m = 0), leading to the well-known energy distribution function: N (θ1 , E1 ) ≈

E1 cos θ1 (E1 + Us )3

and Nmax =

Us . 2

(6.9)

It should be remarked that (6.6) only takes into account that an atom is refracted upon passing through the planar surface barrier. However, it was not taken into account that some atoms (those with E0,x < Us ) are really hindered to be sputtered from the target due to the existence of the surface barrier. Secondly, it is noticed in (6.8) that this analytical model suggests that the energy distribution and the angular distribution are independent of each other. One of the main assumptions of the Sigmund–Thompson theory is that of a complete collision cascade, and thus the assumption of a complete isotropic recoil distribution. However, in case of magnetron sputtering, the energy of the bombarding ions E is often below 400 eV. Hence, the collision cascade generated by the ion impact is often not complete. To make sure that the sputter model is also applicable for magnetron sputtering, some authors have extended or adapted the Sigmund–Thompson theory for the case of low energetic (and/or light) ions, bombarding (heavy) targets. 6.3.2 Other Analytical Models Falcone developed a theory for collisional sputtering, equivalent to the Sigmund–Thompson theory, but that can be extended to other collisional regimes [31]. More explicitly, the Falcone theory should also be applicable in the single knock-on regime. Falcone assumed that a target atom, after having undergone a recoil, arrives at the target surface (and thus can be sputtered) without having undergone elastic collisions. The recoiled target atom only loses energy by inelastic collisions. This is in contradiction to the Sigmund–Thompson theory which assumed that recoiled target atoms only undergo elastic collisions and lose energy by a continuous eﬀect of electronic stopping. In case of bombarding heavy targets by low energy ions, Falcone’s theory resulted in an expression for the energy and angular distribution of sputtered atoms:

6 Transport of Sputtered Particles Through the Gas Phase

N (θ1 , E1 ) ≈

E1 log (E1 + Us )5/2

γE E1 + Us

205

cos θ1 .

(6.10)

Here γE is the maximum transferable in a collision energy between an incident ion of energy E and mass M1 and a target atom of mass M2 : γ=

4M1 M2 . (M1 + M2 )2

(6.11)

However, Kenmotsu argued that inelastic energy loss cannot be dominant for low energy (few hundred eV) ion sputtering [32]. He mentioned that for light ion sputtering, the dominant sputter mechanism is that, after entering the target, an ion is backscattered ﬁrst by a target atom and then knocks oﬀ a target atom near the surface on its way out. Based on this mechanism, and neglecting the inelastic energy loss by electronic stopping, he derived a new expression for the energy and angular distribution of sputtered atoms:

2 E1 γ(1 − γ)E N (θ1 , E1 ) ≈ log cos θ1 . (6.12) E1 + Us (E1 + Us )8/5 Finally, Ono adapted the theory of Kenmotsu by taking into account the inelastic energy loss by electron stopping, which was neglected by Kenmotsu [33]. However, Ono also assumed that primary knock-on atoms produced by ions backscattered at large angles do not lose energy while penetrating the material up to the surface (similar to Falcone). He obtained the following expression for the energy and angular distribution of sputtered atoms due to light ion bombardment: ⎛ ⎞ 1/2 E1 B + E ⎠ cos θ1 , N (θ1 , E1 ) ≈ log ⎝ 1/2 (E1 + Us )5/2 B + (E1 + Us )1/2 / (γ(1 − γ)) (6.13) with B = 2C(γ(1 − γ))1/2 /K, in which 1/2 π 2Z1 Z2 e2 2 M1 C = 0.276a 2 M2 a and

1.216 × 10−2 Z1 Z2 1/2 2 3/2 eV nm , 1/2 2/3 2/3 Z1 + Z2 M1 7/6

K=

where Z1 and Z2 are the atomic numbers of the incident ion and the target atom, respectively, and a is the Thomas–Fermi screening length. All above analytical models assume that the momentum density of the sputtered particles is isotropic. However, Sanders and Roosendaal have shown that due to the conservation of momentum, the momentum density in a collision cascade is not isotropic [34, 35]. Taking into account the conservation

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of momentum, Roosendaal and Sanders developed an analytical model to describe the energy and angular distribution of sputtered atoms [36]. This model provides an analytical solution for three diﬀerent sputter scenarios. In scenario I, the incident ion causes a primary recoil. This primary recoil is energetic enough to induce further recoils and thus a complete collision cascade. In scenario II, the incident, light ion is backscattered by a target atom. In its way out of the target, the backscattered ion causes a primary recoil and thus also a collision cascade. Finally in scenario III, the energy of the incident ion is so low that it dissipates all its energy in the vicinity of the target surface. 1/2 E1 E1 cos2 θ1 + Us 1 − 3C cos θ1 , (6.14) N (θ1 , E1 ) ≈ E (E1 + Us )3/2 √ with C = 1/ γ (scenario I),

M1 M1 + M2 M2 M1 − M2 if M1 < M2 (scenario II), or C = M1 /M2 (scenario III). This model shows that the energy distribution of the sputtered atoms depends on their emission angle θ1 . C≈

6.3.3 Comparison to Experimental Results The above-described analytical models give an expression for the energy and angular distribution of the sputtered particles. It can be noticed for all models, except for the Roosendaal model, that the energy and angular distribution are independent of each other. Moreover, these energy-independent angular distributions are always a cosine distribution and do not depend on the energy of the ion E. For the Sigmund–Thompson theory, even the energy distribution of the sputtered atoms does not depend on the energy of the ion E. However, experimentally measured energy and angular distributions reported in literature are in contradiction to these observations. It was observed by Goelich [37] and Chernysh [38] that the angular distribution of the sputtered atoms, due to the impact of low-energy ions, deviates from the cosine distribution. This deviation from the cosine distribution was also reported by Stepanova [39] and Zhou [40]. It was also observed [37, 41] and reported [39, 42, 43] that the angular distribution of the sputtered particles depends on the energy of those particles. This means that, in contradiction to most of the analytical models, the energy and angular distribution are not independent of each other. As a general trend, it was experimentally observed that the most probable energy of sputtered particles emitted closely the normal on the target is lower than the most probable energy of particles leaving the target at high angles.

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To overcome the discrepancies between the analytical models and the experiments, several simulation models have been developed. Such codes simulate the collision cascade generated by ion impact by a Monte Carlo binary collision approximation, e.g. TRIDYN [44], SRIM/TRIM [45], ACAT [46], MARLOWE [47] or by molecular dynamics, e.g. the work by Zhou [40] and Harrison [48]. In literature, the results of these simulation codes have been extensively compared to the experimentally measured data such as sputter yields as well as energy and angular distributions. The simulation codes seemed to be able to reproduce satisfactory the dependency of the energy distribution on the energy of the primary ion E [49, 50]. Also a deviation from the cosine distribution could be simulated [37, 50] as well as the dependency of the angular distribution on the energy of the sputtered particles [37, 50, 51]. It can be concluded that these simulation codes can be used to create an input for the simulation of transport of sputtered particles. However, the use of these codes has the drawback that it increases the computing time, and that for each situation (target material, ion material and ion energy) the energy and angular distribution of the nascent sputter ﬂux has to be simulated. 6.3.4 Numerical Method Stepanova and Dew also studied the energy distribution of sputtered atoms by low energy Ar+ ions [39]. They studied this process by numerically solving the master equations describing the linear collision cascade generated by ion impact. They included only elastic binary collisions. However, beside a planar surface barrier, they also took into account a focusing eﬀect. They calculated the angle-resolved energy distribution of the atoms sputtered by normal impact of low energy Ar+ ions on 26 diﬀerent target materials. Fitting those results, they could obtain a semi-empirical expression for the angular and energy distributions: q E1 M1 (E1 cosq1 θ1 + Us ) 2 exp −A N (θ1 , E1 ) ≈ (E1 + Us )3−2m M2 E E1 + Us χ(θ1 ), (6.15) 1− Emax + Us with Emax the maximal emission energy and χ(θ1 ) the angular distribution. Although Stepanova mentioned for some conditions that this angular distribution is almost a cosine distribution, they did not discuss it in more detail. A reasonable overall agreement between their numerical calculations and the suggested semi-empirical expression was obtained for: A = 13,

q1 = 2 − M2 /4M1 ,

and q2 = 0.55.

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An expression for the maximal emission energy was given by Moussel et al. [49]: 6 M1 + 2M2 Emax = γE (6.16a) 2M1 + 2M2 while the maximal energy is also sometimes taken from Emax + Us = γE (6.16b) [11, 14]. It should be remarked that the parameter m is the same parameter as in the Sigmund–Thompson theory and thus should have a value between 0 and 0.2 for ion energies E of some hundreds of eV. 6.3.5 Conclusions It was experimentally observed that low energy ion bombardment (E ≈ 200–400 eV) results in the ejection of sputtered target atoms. The angular distribution of these sputtered atoms is ion energy E dependent, and deviates from the simple cosine distribution. Also the energy distribution of the sputtered distribution seems to deviate from the simple Sigmund–Thompson formula and is also observed to depend on the emission angle θ1 of the sputtered atoms. Although there are many variations and adaptations to the Sigmund– Thompson model by various researchers (see Sect. 6.3.2), it continued to be hard to ﬁt all experimental observations with an analytical model. These experimental observations can be reasonably reproduced by the simulation codes based on Monte Carlo binary collision method as well as by the codes based on molecular dynamics. In an attempt to avoid the use of theses simulation codes, Stepanova developed a semi-empirical model. In Fig. 6.2, the energy distributions of atoms sputtered by 200 eV normal impact of Ar+ ions on an Al target are shown. Those energy distributions were calculated from above-mentioned analytical models. However, the results of Kenmotsu, Ono and Roosendaal (scenario II) are not shown, since these models are only valid for light ion bombardment, i.e. M1 < M2 . Also the experimental values, as measured by Goelich are shown for comparison [37]. It can be observed that only the Roosendaal model and the semi-empirical model of Stepanova indicate an angular dependent energy distribution. The Stepanova model can reproduce the experimental values, at least if the parameter m is taken as a ﬁtting parameter and if Emax was calculated from (6.16b). Here m was taken as 0.5, what is high compared to the predictions of Sigmund [30].

6.4 Describing the Collision with the Gas Particle Knowing the place where the sputtered particles leave the target (Sect. 2) and their initial energy and direction (Sect. 3), one can start describing their motion through the gas phase.

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209

a

b

Fig. 6.2. Energy distributions of Al atoms sputtered by Ar+ 200 eV ion impact, and emitted in a direction of 0◦ (a) or 60◦ (b) which respect to the target normal

Generally, some assumptions are made when describing the collisional transport through the gas phase. Often, only interactions between sputtered particles and the sputter gas are considered. This assumption is justiﬁed because the concentration of sputtered particles (ns ) is very small compared to the concentration of the background gas (ng ) at typical magnetron sputter conditions (ns /ng is 10−2 –10−3 ). Secondly, the presence of charged particles (ions, electrons) and the occurrence of non-elastic interactions is neglected because ion and electron concentrations are small in comparison with the neutral atom quantity (typical ionization degree is 10−3 –10−4 ) [52]. Thirdly, for similar reasons only sputtered atoms and no multi-atomic particles are considered. In some cases, it is assumed that the distribution of the background gas is constant in time and space. This latter assumption ignores the pressure variations which may occur during sputtering at higher pressures and sputtering power due to gas heating or gas rarefaction. This eﬀect of gas rarefaction will be treated in more detail in section 6.5.

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6.4.1 The Mean Free Path The collisions between the sputtered particle and the background gas are assumed to be a random process described by a Poisson distribution. Therefore, the distance to the ﬁrst collision or the length of the free path between two succeeding collisions, λ∗ , is generally determined stochastically from the Poisson distribution according to a standard Monte Carlo procedure: λ∗ = λ ln (1/1 − x), where x is a random number from the interval (0,1) and λ is the mean free path of a sputtered atom [53–57]. Although there is only one physical correct mean free path, there are several mathematical ways to approximate this mean free path. The mean free path λ is related to the collision cross section σ by λ=

kB T 1 = , ng σ pσ

(6.17)

with ng the density, T the temperature, p the pressure of the background gas and kB the Boltzmann constant. In case of the hard sphere approximation σ is calculated from σ = π(rs + rg )2 ,

(6.18)

with rs and rg the atomic radius of the sputtered particle and the background gas, respectively. Taking into account the motion of the background gas, and assuming a Maxwellian gas, the collision cross section as calculated from the kinetic gas theory is given by [59] 1/2 ms , σ = π(rs + rg ) 1 + mg 2

(6.19)

with ms and mg the molecular mass of the sputtered atom and the background gas, respectively. Sometimes, this additional mass factor was simpliﬁed resulting in [15, 21]: σ = π(rs + rg )2 (2)1/2 . (6.20) These collision cross sections are independent of the energy or the relative velocity of the colliding atoms, although it has been shown that σ is energy dependent [54, 60]. Robinson showed that this energy dependency can be approximated by an empirical power law: σ(E) = σ(E0 )

E E0

−0.29

σ(E) = σ(E0 ) if E < E0 , where E0 = 1 eV.

if E > E0 ,

(6.20a) (6.20b)

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211

In stead of multiplying σ with the empirical power law, the energy dependency of the collision cross section can also be approximated by using energy dependent atomic radii, as suggested in the variable hard sphere (VHS) model [12, 61, 62]. In this VHS model, the collision cross section is given by σ = πd2VHS ,

(6.21)

where dVHS , the velocity dependent diameter is given by 1 (ds,VHS + dg,VHS ), 2 ω −1/2 1 2kTref i , = dref i,VHS 2 mr vr Γ (5/2 − ωi ) 15 mi kTref /π i = s, = 2(5 − 2ωi )(7 − 2ωi )μi (Tref )

dVHS = di,VHS ref

di,VHS

(6.22) (6.23) (6.24)

with subscript s standing for the sputtered atoms and subscript g for the background gas. μi (Tref ) is the viscosity at the reference temperature Tref , ωi is a temperature exponent describing the velocity dependence of the cross sections and mr is the reduced mass: ms mg /(ms + mg ). In another, but more computation time consuming approach, the collision cross section can be taken as σ = πb2max ,

(6.25)

in which bmax is the value of the impact parameter for which still a small deviation of the sputtered atom trajectory is calculated. The method to calculate this maximal impact parameter bmax is described in Sect. 6.4.2. 6.4.2 The Scattering Angle After a collision between the sputtered atom and the background gas, the sputtered particle is scattered and thus changes its direction of motion. The geometry of this scattering interaction in the centre of mass frame is shown in Fig. 6.3. In case of the hard sphere approximation, the scattering angle θcom is given by (6.26) θcom = 2Arccos(z), with z a random number in the interval (0,1). The polar scattering angle in the laboratory frame θlab is calculated by (6.27), while the azimuthal scattering angle φlab is random between 0 and 2π. sin θcom . (6.27) θlab = Arctg cos θcom + ms /mg

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(a)

(b)

Fig. 6.3. The geometry of the scattering process in the centre of mass frame (a) and the special case for the hard sphere approximation (b)

After collision with the background gas, the sputtered atom has lost energy, and the remaining energy in the laboratory frame Elab is calculated by: 2(1 − cos θcom )mg ms . (6.28) Elab = Elabold 1 − (ms + mg )2 However, this hard sphere approximation is too crude, since the sputtered atom and the background gas interact with each other during the collision process by repulsive and attractive forces. These forces can be described by a spherically symmetric atom–atom interaction potential V (r). Then the scattering angle is given by: ! ∞ dr 2θcom = π − 2b , (6.29) 2 {1 − [V (r)/E 2 2 1/2 r com ] − (b /r )} r0 in which r0 is implicitly determined by V (r0 ) 2 2 , b = r0 1 − Ecom

(6.30)

with b the impact parameter between 0 and bmax , r the inter-atomic distance, V (r) the interaction potential and Ecom the energy of the sputtered particle in the centre of mass frame. Ecom and Elab are related by: Ecom = Elab

mg /ms . (1 + mg /ms )

(6.31)

The maximal impact parameter bmax is then determined as the maximal value of b for which still a deﬂection is calculated: θcom > θmin where the θmin is an arbitrary value usually taking between 0.2◦ and 2◦ [6, 16, 50]. Sielanko [63] derived an analytic expression for the polar scattering angle θcom using the Lindhard’s diﬀerential cross section [64, 65]. sin2

θcom 2

−n P 2 ε2/n = 1+ , (K 2 B)1/n

(6.32)

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213

with B = (8n − 1)/n2 , and P = b/a with a the screening length and b the impact parameter. ε is given by: Ecom . (6.33) ε = 6.9456 × 106 a Zs Zg By ﬁtting this analytical scattering angle to the numerical evaluation of the scattering integral (6.29) for the screened Coulomb potential with Moliere screening function and Firsov screening length (see Sect. 6.4.3), Sielanko obtained the following expressions for n and K: n = 1 + 4 exp(−1.9ε0.1 ), K = A − DP − C,

(6.34) (6.35)

with

n2.8 √ , A = 0.224[1 + 0.52 ln(1 + ε1.2 )]n1.206 sin 13.8 + 0.12 ε

0.00034 2 B = 0.0283 exp , (6.36) + 0.75 (n − 2.9) 0.001 + ε0.0227n3.8 0.001 C= . 0.0156 + P (ε0.11 +3.962P 0.82 ) To know the new direction of the sputtered atom, the scattering direction (θlab and φlab ) should be added to the original direction (θ and φ) as schematically shown in Fig. 6.4 what ﬁnally results in the new direction of the sputtered particle (θnew and φnew ). This addition of two directions is done by the following matrix multiplication [55, 66]: ⎤ ⎡ ⎤ ⎡ cos(θ) cos(φ) − sin(φ) sin(θ) cos(φ) sin(θnew ) cos(φnew ) ⎣ sin(θnew ) sin(φnew ) ⎦ = ⎣ cos(θ) sin(φ) cos(φ) sin(θ) sin(φ) ⎦ cos(θnew ) − sin(θ) 0 cos(θ) ⎤ ⎡ sin(θlab ) cos(φlab ) × ⎣ sin(θlab ) sin(φlab ) ⎦ . cos(θlab ) In this way, the new direction in which the sputtered particle moves is known. 6.4.3 The Interaction Potential The interaction between two atoms is described by an interaction potential V (r). A large number of interaction potentials can be found on literature, and a good overview is given by Eckstein [67]. To describe the interaction between a thermalized background gas atom and a sputtered atom with an energy ranging from thermal up to a few tens of eV, not only the short range repulsive forces, but also the long range attractive forces should be taken into account. However, most of the available interaction potentials only count for one of both forces.

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Fig. 6.4. Deﬁnition of the original (θ and φ) and the additional direction (θlab and φlab ) which has to be added to obtain the new direction of the sputtered atom

Attractive Potentials An often applied attractive potential was proposed by Morse: V (r) = D[exp(−2α(r − r0 )) − 2 exp(−α(r − r0 ))].

(6.37)

A list of all available parameters D, α and r0 for homonuclear interactions is given in [67]. Also the Lennard–Jones potential, in most cases the 6–12 potential, describes the attractive forces and is given as: V (r) = λ6 r−6 − λ12 r−12 .

(6.38)

Repulsive Potentials Most of the potentials describing the repulsive forces are of the group of screened Coulomb potentials. These potentials can be written as: V (r) =

Z1 Z2 e2 Φ(r/a), r

(6.39)

with Φ(r/a) the screening function and a the screening length. This screening function is often approximated by r Φ(r/a) = ci exp −di , a i=1 n

with

n i=1

ci = 1.

(6.40)

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215

Table 6.1. Parameters for the diﬀerent screening functions [67]

n c1 c2 c3 c4 d1 d2 d3 d4

Bohr

Moli`ere

Kr-C

Ziegler– Biersack– Littmatk

Lenz–Jensen

1 1

3 0.35 0.55 0.1

3 0.1909 0.4737 0.3354

3 0.0102 0.2433 0.7466

1

0.3 1.2 6

0.2785 0.6372 1.9192

4 0.0282 0.2802 0.5099 0.1818 0.2016 0.4029 0.9423 3.1998

0.206 0.3876 1.038

Table 6.1 shows the used constants for diﬀerent screening functions. The Bohr, Moli´ere, Kr-C and Lenz–Jensen screening function can be used with several screening lengths: – The Firsov screening length [68]: 2 1/3 −2/3 9π 1/2 1/2 aB Z 1 + Z 2 aF = 128 – The Lindhard–Scharﬀ screening length [69]: 2 1/3 −1/2 9π 2/3 2/3 aB Z 1 + Z 2 . aLS = 128

(6.41)

(6.42)

In case of the homonuclear case (Z1 = Z2 ), Robinson suggested to use the “universal” value [67]: A. (6.43) aF = 0.0750 ˚ The Ziegler–Biersack–Littmark screening function should be used with their own screening length [70]: 2 1/3 " #−1 9π aB Z10.23 + Z20.23 , (6.44) aZBL = 128 with aB is the Bohr radius. There is no strong justiﬁcation why to use the Firsov screening length or the Lindhard–Scharﬀ screening length. So, the screening length can be seen as a ﬁtting parameter. Lenz and Jensen proposed another screening function, to be used with the Lindhard–Scharﬀ screening length [67]: ΦLJ (r/a) = (1 + y + 0.344y 2 + 0.485y 3 + 0.002647y 4)e−y with y = 9.67r/aLS .

(6.45)

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Also Nakagawa and Yamamura suggested a screening function [71]: ΦNY (r) = exp(−Ar + Br3/2 − Cr2 ).

(6.46)

The parameters A, B and C where calculated for all individual elements [71] and include the screening length. Applying the geometric mean rule for heteronuclear collisions lead to the following constants:

2/3 1 1 3/2 3/2 A12 = A11 + A22 (B11 + B22 ) , , B12 = 2 2

4/3 1 3/4 3/4 C11 + C22 . (6.47) C12 = 2 Beside these individual potentials, Nakagawa and Yamamura also provided an average screening function [71]: ' & (6.48) Φaverage (r/as ) = exp −α(r/as ) + β(r/as )1.5 − γ(r/as )2 , with

as =

and

9π2 128

1/3 aB (6.49)

2/3

(Z10.307 + Z20.307 )

Z10.169 + Z10.169 , β = 0.763 Z10.307 + Z20.307

4/3 Z10.0418 + Z20.0418 γ = 0.191 α = 1.51, . Z10.307 + Z20.307 (6.50) Another, widely used [72, 73] repulsive potential, but not a member of the screened Coulomb family, is the Born–Mayer potential which is given by:

r

V (r) = ABM e−BBM .

(6.51)

In which ABM is an energy parameter and BBM is a screening length. Abrahamson [74] calculated the parameters ABM and BBM for 104 homonuclear interactions, by ﬁtting the Born–Mayer potential with the Thomas– Fermi–Dirac interaction potential. Based on the combining rule, the parameters for heteronuclear interactions can be calculated: (6.52) V12 (r) = V11 (r)V 22 (r) and thus:

A11 A22

B11 + B22 . (6.53) 2 Nice about the Born–Mayer potential is that the collision cross section can be approximated by A12 =

σ = π(rsg )2 ,

and B12 =

with rsg =

−2 Ecom ln , Bs Bg As Ag

(6.54)

with Bs , As and Bg , Ag the homonuclear Born–Mayer constants for the sputtered atom and the background gas, respectively [5, 55].

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Combined Potentials Some potentials combine as well as the attractive as the repulsive potentials. These combined potentials are usually a combination of a standard repulsive potential and a standard attractive potential, ﬁtted by an intermediate potential. The procedure to obtain this intermediate potential is described by Eckstein [67]. Myers et al. [51] developed a combined potential by ﬁtting the Born–Mayer potential with the attractive part of the Lennard–Jones potential: V (r) = A exp(−Br) + (C/r)D − (E/r)6 ,

(6.55)

with (C/r)D a term used to produce a smooth transition between the repulsive part and the attractive part. Yamamura [50] provided a combined potential by adding the Morse potential to the screened Coulomb potential, without using an intermediate potential. In stead of using an attractive potential, combined with a repulsive potential, Kuwata et al. [75] calculated a quantum-chemical interaction potential for Argon–Copper and Argon–Aluminium using the Kohn–Sham density functional theory, utilizing the PW91 potentials. These quantum-chemical interaction potential describe as well as the attractive as the repulsive part nicely.

6.5 Gas Rarefaction In the introduction of the previous section, it was stated that the distribution of the background gas is often assumed to be constant in time and space. However, the interaction between energetic particles and the background gas results in a dynamic behaviour of the volume in front of the magnetron. This dynamic behaviour was ﬁrst measured by Hoﬀman [76], who called this a “sputter wind” and attributed it to the pressure variations into a vacuum chamber resulting from collisions between the sputtered particles and the background gas. Later on, Rossnagel [77] and Dr¨ usedau [78] suggested that the pressure inside the vacuum chamber remains unaltered, but claimed that the density of the background gas reduces and called this gas rarefaction or gas heating. They experimentally measured the reduction of the gas density as a function of system pressure, discharge power, target material, by means of a local pressure probe. As shown in(6.17), the mean free path of a sputtered particle depends on the density of the background gas. Also the interatomic interaction and the scattering angle depend on the energy of the background gas ((6.29), remark that Ecom is used). Hence, this gas heating or gas rarefaction in front of the target should be taken into account, when describing the collisional transport of sputtered particles through the gas phase.

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Rossnagel [77], Dr¨ usedau [78] and Palmero [79, 80] proposed an analytical model to describe the gas rarefaction. Although (1) they assumed that only sputtered atoms transfer energy to the background gas, (2) they made other simplifying assumptions and (3) the uncertainty in several of the input parameters, their calculated gas densities behave similar to the measured gas densities. Several authors developed a Monte Carlo (or particle-in-cell Monte Carlo) model to simulate self-consistently the DC magnetron discharge, paying attention to the gas heating or gas rarefaction [81–86]. By taking into account that the background gas can not only be heated by collision with sputtered particles, but also by collisions with ions, or reﬂected neutrals, and even thermal radiation from hot bodies or optical emission from the plasma, they revealed the inﬂuence of several deposition parameters on the eﬀect of gas rarefaction. It was, e.g. generally concluded that the gas temperature (and thus also the mean free path) increases with increasing discharge power, system pressure or target sputter yield. The same tendencies were observed by Ekpe and Dew, who simulated the gas heating eﬀects by numerical modelling [87]. Like they also discuss in another chapter of this book, they mentioned that the gas heating eﬀect not only inﬂuences the transport of the sputter particles, but also signiﬁcantly inﬂuences the global energy ﬂux towards the substrate and thus inﬂuences the thin ﬁlm growth in general [88].

6.6 Typical Results of a Binary Collision Monte Carlo Code Based on the above-mentioned theories and ideas, a binary collision Monte Carlo simulation program has been developed by our research group. The radial distribution wherefrom sputtered particles leave the target was deduced from an experimentally measured racetrack in case that a circular, planar 2 in. magnetron is used as sputter source. In case that a rotating, cylindrical magnetron is used as sputter source, the radial distribution wherefrom sputtered particles leave the target was obtained by a perpendicular projection of the simulated ionisation distribution in front of the target [89]. The initial energy and angular direction of the nascent sputter ﬂux were simulated by SRIM. The mean free path was calculated from (6.25), and the scattering angle in the centre of mass frame from (6.29). The code allows the user to choose between several screened Coulomb potentials (Moliere, Kr-C, Ziegler–Biersack– Littmark = ZBL) with Firsov screening length and, in case of the Ar−Al and Ar−Cu combination, the combined potential as calculated by Kuwata (see Sect. 6.4.3). No gas rarefaction was taken into account, i.e. the background gas distribution was assumed to be constant in space and time. The motion of the

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b

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d

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Fig. 6.5. Comparison of the simulated and experimentally measured deposition proﬁles, of a circular, planar c2 inch Cu target, sputtered by Ar ions. The simulated data were obtained by using the ZBL (a), the Kr-C (b), the Moli`ere (c) and the Kuwata (d) potential

background gas was taken into account, assuming that the background gas is a Maxwellian gas of 400 K. When the energy of the sputtered particles decreased below an arbitrary value, it was assumed to be thermalised, and the further collision process was taken as a random motion. Figure 6.5 shows the simulated and experimentally measured deposition proﬁles for a circular, planar 2 in. Cu target, sputtered in Ar, at 0.55 Pa. An ion energy of 400 eV was taken to carry out the simulations. The inﬂuence of the chosen interaction potential is investigated. For each interaction potential (Moli`ere, Kr-C, ZBL or Kuwata), one calibration factor has been introduced to be able comparing the experimental and simulated results. This because the experimental data represent a deposition rate (a thickness divided by the deposition time), while the simulations are time independent and only give a thickness proﬁle. More precisely, the simulated data have been multiplied by a factor, in such a way that the simulated and experimental deposition rate at a target-substrate distance of 16 cm and at radial distance R of 0 m are nearly the same. This calibration factor is only necessary to overcome the time independence of the simulation, and does not have to be changed in function of the pressure, T-S distance or vertical height.

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The full lines represent the simulated data, while the experimental data are shown by the dotted lines and open symbols. It is observed that all of the used interaction potentials can nicely reproduce the experimental deposition proﬁles as a function of the target-substrate distance. Moreover, no real diﬀerence between the several simulated proﬁles can be observed. Nevertheless, the choice of a speciﬁc interaction potential inﬂuences the description of the collision process, and thus the properties of the simulated arriving metal ﬂux. These properties of the metallic particles arriving at the central place of the substrate (R ≤ 0.01 m) are shown in the Figs. 6.6–6.9. The total amount of arriving particles (in arbitrary units) and their average energy is given as a function of the target-substrate distance for the several interaction potentials. Also the number of collisions that the non-thermalised particles suﬀered is shown. It is observed that the average energy of the arriving particles is higher when using the Kuwata potential, although these particles suﬀer more collisions. This indicates that the Kuwata potential, which not only takes into account the repulsive forces but also the attractive forces, is softer than the screened Coulomb potentials. As already mentioned, also the material ﬂux during rotating, cylindrical cathode magnetron sputtering can be simulated by the developed code. A scheme of the setup of the rotating, cylindrical magnetron and where the deposition proﬁles were measured is shown in Fig. 6.9. The material ﬂux was measured at a radial distance of 114 mm from the central axis of the

Fig. 6.6. Total number of particles arriving at the central place of the substrate (R ≤ 0.01 m) as a function of the target-substrate distance and the used interaction potential

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Fig. 6.7. The average energy of the particles arriving at the central place of the substrate (R ≤ 0.01 m) as a function of the target-substrate distance and the used interaction potential

Fig. 6.8. The number of collisions that the non-thermalised particles arriving at the central place of the substrate (R ≤ 0.01 m) suﬀered as a function of the targetsubstrate distance and the used interaction potential

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Fig. 6.9. Front and side view of the rotating cylindrical magnetron and the place where the material ﬂux was registered by a quartz crystal oscillator

Fig. 6.10. Experimental and simulated deposition proﬁles during rotating, cylindrical magnetron sputtering of a Cu cathode in Ar (400 eV) at 0.3 Pa

cylindrical target. These ﬂuxes were measured at a lateral distance of 96, 132 and 190 mm away from the left side of the target. Figure 6.10 shows the simulated and the experimental deposition proﬁles, for a Cu cathode, sputtered in Ar at 0.3 Pa. The simulations were carried out with the Kuwata potential. Again, the simulated data have been multiplied by a factor, in such a way that the simulated and experimental data at the

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largest deposition rate are more or less the same. A good correlation between both curves is observed.

6.7 Speciﬁc Example: In-Plane Alignment of Biaxially Aligned Thin Films Biaxially aligned thin ﬁlms are polycrystalline thin ﬁlms with not only a preferential crystallographic out-of-plane orientation, but also with alignment along a certain reference direction parallel to the substrate plane. This type of ﬁlms has been obtained by unbalanced reactive magnetron sputter deposition on both amorphous glass and randomly textured polycrystalline substrates tilted with respect to the incoming material ﬂux [90–93]. The quality of the in-plane alignment can be evaluated from X-ray diﬀraction pole ﬁgures, and is usually expressed by the full width at half maximum (FWHM) of the diﬀraction pole. The inﬂuence of several deposition parameters (target-substrate distance, target-substrate angle, deposition pressure and substrate bias) on the degree of in-plane alignment has been discussed [93]. It was shown that the inﬂuence of these parameters can be traced to the inﬂuence of two main properties, i.e. the mobility of the adatoms at the growing surface and the angular spread of the incoming material ﬂux. This angular spread of the incoming material ﬂux, as a function of the deposition parameters could be simulated by the above-described binary collision Monte Carlo model. The Moli´ere screening function with Firsov screening length was used. Figure 6.11 shows the inﬂuence of an increasing target-substrate angle α on the simulated angular spread of the incoming ﬂux and the resulting inplane alignment for YSZ thin ﬁlms, as measured from the XRD pole ﬁgures. It is observed that the tendency of both curves are similar, indicating that the improvement of the in-plane alignment with increasing target-substrate angle α is caused by a decreasing angular spread of the incoming material ﬂux.

Fig. 6.11. Inﬂuence of the target-substrate angle α on the degree of in-plane alignment for 1.3 μm thick YSZ ﬁlms deposited by unbalanced magnetron sputtering on positively biased polycrystalline stainless steel (Vs = +15 V) at a pressure of 0.425 Pa, a T-S distance of 13 cm, ﬂoating temperature, and an Ar/O2 ratio of 60/2.5

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Fig. 6.12. Inﬂuence of the pressure on the degree of in-plane alignment for 1.3 μm thick YSZ ﬁlms deposited by unbalanced magnetron sputtering on positively biased (+15 V) polycrystalline stainless steel at a target-substrate angle of 55◦ , a T-S distance of 13 cm, ﬂoating temperature and an Ar/O2 ratio of 60/2.5

The inﬂuence of the deposition pressure on the simulated and experimentally measured angular spread is shown in Fig. 6.12. The angular spread of the incoming material ﬂux decreases with decreasing pressure because the sputtered particles undergo fewer collisions with Ar and are thus less scattered. The diﬀerence between the simulated angular spread and the experimentally measured in-plane alignment at low pressure is caused by a too strong variation in total energy ﬂux towards the substrate [93]. This inﬂuence of the deposition parameters on the energy ﬂux towards the substrate is discussed in Chap. 7 of this book.

6.8 Conclusions The several steps and approaches to simulate the collisional transport of sputtered particles through the gas phase by a binary collision Monte Carlo method have been treated. The nascent sputter ﬂux, and thus the initial energy and angular distribution of sputtered atoms leaving the target have been discussed in detail. It could be concluded that the analytical models can not fully describe the experimentally observed energy and angular distribution of sputtered particles, in case of low energy (E < 400 eV) ion bombardment. The use of a numerical model and even better a simulation code such as ACAT, SRIM, TRYDIN. . . is believed to approach better the reality. The collision between the sputtered particles and the background gas is described in detail. Also the use of several kinds of interaction potentials was summarized. It could be suggested that the use of a combined potential, taking into account the attractive as well as the repulsive forces, is recommended. The mean free path can be deduced from the used interaction potential, by calculating the maximal impact parameter.

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In the ideal case, a global model, simulating the magnetron discharge, together with the transport process would allow the user to take into account the eﬀect of gas heating on both processes. Although the gas heating eﬀect was not yet included in the described model, general results about the transport of sputtered particles are shown. Finally, a clear correlation between the properties of the incoming material ﬂux, in speciﬁc the angular spread on the incoming ﬂux, and the in-plane alignment of biaxially aligned thin ﬁlms has been shown.

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7 Energy Deposition at the Substrate in a Magnetron Sputtering System S.D. Ekpe and S.K. Dew

7.1 Introduction In any deposition process, the eﬀective energy deposited onto a surface of a substrate material by the depositing and reactive particles is essential to understanding the mechanism of ﬁlm growth on the surface [1–4]. For low-pressure plasmas, such as with the magnetron sputtering process, these particles include electrons, ions, neutrals, etc. [2,5–9], which interact with the surfaces and each other through collisions and or chemical reactions. It should be evident therefore that the energy ﬂux onto a substrate depends on the process conditions, such as magnetron power, pressure, geometry, etc. [2, 5, 8]. The deposited energy causes the eﬀective temperature of the growing ﬁlm to rise [10]. As the particles arrive at the substrate, they transfer momentum, and increase the mobility of the particles at the surface of the growing ﬁlm [3, 4]. They also cause peening, increasing density and comprehensive stress [11–17]. Apart from surface mobility, the reaction rates/pathways are greatly inﬂuenced by this incident energy, and hence the micro- and nanostructure and the properties of the growing ﬁlm depend strongly on the energy management [18–24]. The relationship between substrate temperature and ﬁlm properties, such as columnar structure, grain size, etc., has been well established [25–31]. The density and temperature of the plasma species at the substrate region have been shown to also aﬀect the properties of the deposited ﬁlm [32–34]. Gas pressure, as a process parameter, aﬀects the kinetic energy of the deposited species as well as the characteristics of the plasma [7, 8, 35, 36], hence it may be said to have an important indirect eﬀect on the micro- and nanostructural evolution of the ﬁlm. Since these eﬀects determine the eﬀective energy deposited [36], then, energy ﬂux onto the substrate is one of the important parameters in many high performance thin ﬁlms. Several factors contribute to integral energy ﬂux to the substrate. Some of these include the energy of the sputtered atoms – kinetic and potential (heats

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of condensation and reaction), plasma radiation, energy transfer from gas collision and heating eﬀect, reﬂected gas neutrals, and the kinetic and potential (recombination) energies of ions and electrons at the substrate [2, 5–8, 37]. Recombination energy of the charged particles (electrons and ions) is greatly determined by the substrate potential, and the surface electrical conductivity [38, 39]. At potentials diﬀerent from the ﬂoating potential, where the number densities of ions and electrons are signiﬁcantly diﬀerent, the recombination energy becomes insigniﬁcant compared with the other energies. Wendt et al. [37] showed that the kinetic energy of ions accelerated in the potential drop in front of the substrate is not the main contribution to the thermal power at the ﬂoating potential. The reﬂected neutrals have been considered to depend on the mass of gas ion relative to that of the target material [2, 5]. The velocity of the incident ion relative to the target material, vrel may be expressed as: Mi − Mt vi , vrel = (7.1) Mi + Mt where vi is the ion velocity just before striking the target, Mi and Mt are, respectively, the masses of the gas ion and the target material. If the mass of the incident ion is less than that of the target material, it is likely that the ion will be reﬂected backward in a single collision, and the energy of the reﬂected ion may be a signiﬁcant fraction of its initial energy [40]. If the mass of incident ion is greater than that of the target material, the ion can be reﬂected backward only as a result of more than one collision, and of course with a reduced energy. Thus for argon on aluminum, the reﬂected neutrals would contribute a negligible eﬀect to the integral energy at the substrate. However, for Ar/N2 atmosphere, the reﬂected neutralized nitrogen may contribute a signiﬁcant factor to the energy ﬂux. Energy exchange within the reactor may be said to be determined by two sets of parameters: external and internal. The external parameters are the controllable experimental factors, such as power, voltage, current, DC or RF excitation, the geometry, and the composition/pressure of the background gas. The internal parameters are factors, such as the degree of ionization, potential drop in the plasma sheath, masses of the component particles, and the free paths of the various diﬀerent particles. These internal parameters inﬂuence the ﬂux of particles as well as the energy ﬂux toward the substrate. These two sets of parameters interact in a complicated manner that determines the total energy ﬂux to the substrate. Figure 7.1 shows the schematic representation of the interaction of the parameters resulting in the diﬀerent sources of energy ﬂux in the sputter reactor. The determination of the energy ﬂux can be used as a tool to infer the relationship between the parameters. The following sections discuss the measurement of energy in a typical deposition system, process factors aﬀecting the deposited energy, the interpretation of the measured energy in terms of energy per deposited atom, and a model for the estimation of the energy per deposited atom.

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Etc Ec Ea

Substrate Etr Ee

Eiz Ep

Etr Er Etc

Plasma Ei Target

Fig. 7.1. The sources of energy ﬂux in a sputter deposition system. E is the energy ﬂux and the subscripts i, a, r, c, p, e, iz, tr, and tc represent incident ion, sputtered particle, reﬂected neutral, condensation, plasma radiation, electron, positively ionized gas atom, thermal radiation, and thermal conduction through the substrate holder and probably to the gas

7.2 Energy Measurement When energy is deposited onto a surface, the temperature of the surface rises. Thus, by measuring the change in temperature, the deposited energy can be inferred. The measurement of the increase of the in situ substrate temperature has been a well-established method for the determination of the integral energy ﬂux to the substrate [2, 5, 41–43]. Another method for the determination of the thermal ﬂux at the substrate is the steady-state determination of the temperature gradient along the sample holder [6] although this does not account for the front-side heat losses due to, for example, radiation or gas transport. Many techniques for determining temperature have been developed over the years. These are signiﬁcantly complicated by the vacuum system, reducing thermal contact, and uniformity. Some require physical contact between the measuring device and the specimen, and others employ noncontact methods such as radiometry and luminescence. For the contact methods, thermocouples have been widely used [2, 10]. This has a major advantage of making low temperature measurements (<700 K) using a simple set-up. A potential problem associated with the use of this type of discrete sensors is that of the thermal contact. Unfortunately, in many cases this contact is not ideal, and may lead to the formation of a temperature diﬀerence between the specimen and the thermocouple [44,45]. The temperature jump that exists between the surface of a wall and the surrounding gas at low pressure [46] may also be a problem in using such discrete devices. Noncontact methods include the radiometric method, which measures the radiation emitted from a heated body. In

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some radiometers, the total emission, I = εσT 4 , is measured (ε and σ being, respectively, the surface emissivity and Stefan–Boltzmann constant), in others, the emission is in limited spectral ranges [47]. In both cases, the radiation from the target is determined by its temperature and emissivity. This method is applicable mostly at higher temperatures (>900 K) and requires corrections for the surface emissivity [48] and other factors. A solution to the above issues would be the use of the temperaturedependent resistance of homogeneously heated thin ﬁlms or other sensors embedded in the substrate surface [6, 7, 49, 50]. The main advantage of this technique is that the sensing element is buried inside the absorber, and hence does not require attachment of the thermal sensor to the specimen. Selfheating eﬀects [51, 52] by the sensing current can be minimized by applying a low-bias voltage [6] across the terminals of the thermistor, and by the use of a high resistance material. Silicon thermistors appear to be nearly ideally suited as thermometers for high-resolution microcalorimeters [51]. A polysilicon thin ﬁlm thermistor created using a modiﬁed complementary metal-oxide semiconductor (CMOS) process is reported in [7, 36, 49]. It consists of a four point serpentine polysilicon structure suspended on a membrane for reduced thermal capacity. A thin silicon dioxide (SiO2 ) layer covers to act as an absorber and to prevent electrical shorting when depositing metals ﬁlms. The factors of interest are the temperature sensitivity of the sensor, thermal capacity of the absorber, and the thermal conductance linking the substrate to the ambient. The temperature-dependent resistance of the sensor is given by the power series [7]: & ' R(T ) = R0 1 + α(T − T0 ) + β(T − T0 )2 + γ(T − T0 )3 + · · · . (7.2) Figure 7.2 shows the temperature dependent resistance of two iterations of the sensor designs. As reported [7, 36, 49], it was found that for low temperature measurements (∼250◦ C), second and higher orders can be neglected, and a linear dependence assumed. Figure 7.3 is a photo of one of the cells of the second iteration of the sensor design (details can be found in [36]).

7.3 Factors Aﬀecting Energy Flux The integral energy deposited onto the substrate depends on several factors, which can be controlled through the process conditions, such as magnetron power (DC/RF), gas (inert/reactive) pressure, substrate-target distance and substrate bias. The diﬀerent individual contributions to the total deposited energy respond/react diﬀerently to changes in the process conditions. For instance, at constant power mode, increase in pressure of the process gas may result in a decrease in voltage. The eﬀect of this would be an increase in the plasma densities, including negative ions (where electronegative materials are used), increase in the reﬂection probability of gas neutrals, decrease in the

Relative change in resistance of sensor

7 Energy Deposition at the Substrate in a Magnetron Sputtering System

233

0.25 polyfit (sensor 1)

0.2

expt (sensor 1) polyfit (sensor 2)

0.15

expt (sensor 2)

0.1 0.05 0

0

25

50 75 100 Temperature (oC)

125

150

Fig. 7.2. Dependence of the resistance of sensor on temperature. The solid line and dashes are the polynomial ﬁt to the experimental data for sensors 1 and 2, respectively

Fig. 7.3. Photo of one of the cells of the second iteration sensor showing the arrangement of the sensing elements and the etched silicon underneath the SiO2 covered polysilicon

kinetic energy of the particles (sputtered, reﬂected neutrals, charge carriers), and of course increase scattering eﬀects. Increased scattering leads to greater gas heating – higher temperature gradient [53–57], and hence increase heat transfer through conduction. The eﬀect on the transport of the particles is, however, complicated by the inhomogeneous rarefaction of the process gas. Figure 7.4 shows a simulated inhomogeneous rarefaction of the process gas for the sputtering of Al at a pressure of 1.33 Pa and magnetron power of 300 W from a 7.6 cm circular planar target [57]. The theoretical and experimental impact on the energy ﬂux of several such factors will be explored below.

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Fig. 7.4. Rarefaction of the process gas for the sputtering of Al in (a) Ne, (b) Ar, and (c) Kr at a pressure of 1.33 Pa and magnetron power of 300 W. The data were taken along a vertical plane through the center of the chamber with the substrate located at a distance of 10 cm in front of the target [57]

7 Energy Deposition at the Substrate in a Magnetron Sputtering System 0.025 Total energy flux (W/cm2)

0.05 Total energy flux (W/cm2)

235

(a) 0.04 0.03 0.02

0.67 Pa 1.33 Pa

0.01

(b) 0.67 Pa 1.33 Pa

0.02 0.015 0.01 0.005

0

0 0

100 200 300 Magnetron power (W)

400

0

100 200 300 Magnetron power (W)

400

Fig. 7.5. On-axis steady-state energy ﬂux at the substrate region as a function of magnetron power at a substrate-target distance of (a) 10.8 and (b) 21 cm for two diﬀerent pressures during the deposition of Al

7.3.1 Magnetron Power and Pressure Not surprisingly, the total energy deposited at the substrate generally increases with magnetron power [5–7] for both DC and RF operation modes. It has been shown that increasing pressure results in reduction of the total energy at the substrate due to energy losses from increase interactions of the particles in transport to the substrate region [7, 8]. Figure 7.5a shows the variation in the total energy ﬂux at a distance of 10.8 cm from a 76 mm target during the deposition of Al, with power and pressure. For the range of process conditions considered in that study, energy ﬂux increases linearly in direct proportion to power. The power transfer eﬃciency to an area at the substrate was determined as 1.6 × 10−4 and 1.4 × 10−4 cm−2 for pressures of 0.67 and 1.33 Pa, respectively [36]. This value varies with pressure probably because of changes in the ionization eﬃciency in the plasma and in the energy absorption rate of the gas for the energetic particles from the target. In a related study using Cu [49], it was observed that the variation in energy ﬂux with power indicates a nonlinear dependence. The deviation was attributed to the eﬀect of increased reﬂected neutrals, sputtering yield, gas heating eﬀect, and the thermalization of energetic particles. Cu shows a reduced thermalization compared with Al at the same process conditions [57–59], hence is associated with higher power transfer eﬃciency than Al is. In a study with molybdenum [60], total energy deposited onto the substrate was measured experimentally, and shown to reduce with pressure. It was further shown that while some factors vary appreciably, some vary minimally or remain constant with pressure. 7.3.2 Substrate-Target Distance Figure 7.5b shows the variation in the total energy ﬂux with power for pressures of 0.67 and 1.33 Pa at a substrate-target distance of 21 cm (long throw) for the sputtering of Al. The energy in this case is lower than that at a

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distance of 10.8 cm. Similarly, the power transfer eﬃciency reduces greatly to 7.0 × 10−5 and 5.2 × 10−5 cm−2 for the respective pressures. Experimental results presented in [6] show a similar trend for the deposition of Al at magnetron powers of 38 and 65 W. Initial increase in distance results in a rapid decrease in energy, however, at greater distances, further increase in distance results in a minimal decrease in energy. The greater separation between pressures at longer throw distances indicates the greater importance of the kinetic energy and scattering under these conditions. Since at these distances, most of the particles are thermalized. Such particles would contribute negligible further kinetic energy to the total deposited energy. 7.3.3 Electrical Eﬀects Biasing of the substrate can be used in studying the eﬀect of charge carriers (electrons and ions) on the total energy deposited onto the substrate [61, 62]. The contribution of these charge carriers depend on their densities and temperatures and the electric ﬁeld in the substrate region. The electric ﬁeld in the sheath at the substrate region may be inferred from the potential diﬀerence, Vb = Vpr − Vpl , where Vpr and Vpl are, respectively, the probe and plasma potentials. The probe potential at which the probe current is zero deﬁnes the ﬂoating potential. The plasma characteristics – plasma and ﬂoating potentials, charge carrier densities, and temperatures – can be determined using a Langmuir probe [6,63–66], and are essential in the estimation of the deposited energy due to the charge carriers. Where electronegative species are present, negative ions may exist. Given the masses of these negative ions, while the electrons are conﬁned by the magnetic ﬁeld in front of the target, the negative ions are accelerated away from the target. Given the distance of ﬂight toward the substrate and the accelerated energy of the negative ions, these ions can reach the substrate with signiﬁcant energy. The density of these ions depends strongly on the partial pressure of the electronegative specie(s), and the total pressure of the system. The energy ﬂux at the probe for probe potentials greater than the plasma potential is given approximately by [7, 37, 67]: p = po + je Vb ,

(7.3)

where po is the energy ﬂux at a probe potential equal to the plasma potential and je is the saturation current density at the probe for a given bias. Figure 7.6 shows the estimated energy ﬂux at the substrate at a distance of 10.8 cm from the target for Al sputtered from a 7.6 cm target at 200 W and 0.67 Pa. Also presented are the directly measured energy ﬂuxes at lower potentials. Higher biases tended to damage the sensor (ﬁrst iteration). This ﬁgure clearly indicates a very strong sensitivity of energy ﬂux to probe voltage, and hence the important role electrons can play in heating the growing ﬁlm and the substrate during deposition. On the other hand, ions are clearly not as

7 Energy Deposition at the Substrate in a Magnetron Sputtering System

237

Total energy flux (mW/cm2)

250

200 estimated measured

150

100

50

0

-15

-10

-5 0 5 Probe potential (V)

10

15

Fig. 7.6. Total energy ﬂux at the substrate as a function of probe potential for a magnetron power of 200 W, substrate-target distance of 10.8 cm and gas pressure of 0.67 Pa

important to the energy ﬂux. However, for probe potentials much lower than the ﬂoating potential, the sensitivity of the energy to ions becomes apparent [67]. Substrate biasing therefore oﬀers an important tool in the control of energy ﬂux to the growing ﬁlm.

7.4 Total Energy per Deposited Atom To fully understand the eﬀect of energy on the mechanism of ﬁlm growth, it is useful to interpret the energy at the substrate on a per deposited atom basis. As already noted, several factors contribute to the total energy ﬂux. Those factors of course depend on the process conditions. The total energy per deposited atom Etot may be evaluated by normalizing the total energy ﬂux at the substrate to the atomic deposition rate φat . Thus, Etot = qtr /φat ,

(7.4)

where φat = (dr NA ρ)/M , and dr is the average deposition rate determined from the ﬁlm thickness, NA is Avogadro’s constant, ρ is the density, which is usually less than the bulk density and M is the molar mass. The dependence of the total energy per deposited atom on magnetron power for two diﬀerent gas pressures for Al deposition is shown in Fig. 7.7. Values of the determined total energy per deposited atom depend strongly on the magnetron power and gas pressure regimes. The results show that, for

S.D. Ekpe and S.K. Dew Energy per deposited atom (eV)

238

60 55 50

0.67 Pa

45

1.33 Pa

40 35 30 25 20

0

100 200 300 Magnetron power (W)

400

Fig. 7.7. Total energy per deposited aluminum atom as a function of magnetron power at gas pressures of 0.67 and 1.33 Pa using a substrate-target distance of 10.8 cm

both 0.67 and 1.33 Pa, the energy per atom decreases with increasing magnetron power. Of course, both the energy ﬂux and deposition rate increase with power. However, the deposition rate increases more quickly than the energy ﬂux, hence the downward trend observed in Fig. 7.7. In part, this is due to the gas rarefaction eﬀect as higher powers result in signiﬁcant gas heating that reduces particle scattering and hence increases the ﬂux of sputtered particles to the substrate. However, the rarefaction of the ﬁlling gas adjacent to the cathode [53, 56] increases the impedance of the plasma, aﬀects the current– voltage characteristics of the discharge [68], and reduces the contribution of charge carriers to the total energy. Dickson et al. [69] noted that a possible eﬀect of gas heating is a decrease in electron density in ionized physical vapor deposition (IPVD). Thus, increased gas heating with magnetron power limits the increase in the electron contribution to the total energy. Also, gas density reduction aﬀects the ionization of the gas through reduced electron collisions, as well as a reduction in the contribution to the energy ﬂux due to plasma radiation. Figure 7.7 also shows that by increasing the gas pressure from 0.67 to 1.33 Pa, the energy per deposited atom increases. However, as the magnetron power is increased, the diﬀerence in the energy per deposited atom between the two pressures decreases such that at higher magnetron powers it trends toward being constant irrespective of both power and pressure [7, 8]. Thornton [2] suggested that, for a given metal, the energy per atom deposited is independent of the deposition rate and gas pressure. However, in a related study [5], it was shown that the deposited energy per atom decreases with increasing magnetron power, but with decreasing process gas pressure. Results for the sputter deposition of AlN in a RF discharge [70] also shows that the energy per deposited particle increases with decreasing discharge power, but also with increasing sputtering pressure. In comparison with that

7 Energy Deposition at the Substrate in a Magnetron Sputtering System

239

of a DC discharge, it was noted that energy per deposited particle in a RF discharge was signiﬁcantly higher [2, 70]. The observed trend shows that the plasma eﬀects are more important, at least at lower power levels. The above shows the dependence of energy ﬂux toward the substrate on the process conditions. Individual contributing factors respond diﬀerently and in a complicated manner with changes in the process conditions. As the deposited energy aﬀects the mechanism of ﬁlm growth, it is essential to model the eﬀects of the process conditions on the energy ﬂux. This would provide the tool for understanding of the ﬁlm growth mechanism, as well as controlling the ﬁlm growth for desired properties.

7.5 Energy Model Thornton [2] proposed that the total energy per incorporated atom may be estimated from the following model: Etot = U + Ek + Eo

RE + EP . Y

(7.5)

The ﬁrst and second terms are the contributions of the heat of condensation (and, by extension, reaction) and the average kinetic energy of the deposited atoms, respectively. The third term represents the contribution of the reﬂected gas neutrals, Er (determined per sputtered atom in terms of the sputtering yield, Y ) as a function of the incident ion energy, Eo and energy reﬂection coeﬃcient, RE (which depends on the energy of the incident ion [5, 40]). This contribution depends greatly on the masses of the sputtered atom and that of the process gas. The fourth term represents the contribution due to radiation within the plasma. As already shown, the contribution of the charge carriers must not be ignored. Thus, to the above model, we would add contributions due to electrons and ions bombardment Ech and thermal radiation Et from hot bodies within the reactor (both in terms of per incorporated atom). Etot = U + Ek + Eo

RE + EP + Ech + Et . Y

(7.6)

The nature of Ech depends strongly on the substrate bias. At ﬂoating and higher potentials, it would be reasonable to assume that it is mainly from electrons [7, 37, 60], and probably negative ions [71]. Since the last terms in (7.6) can be determined from the bulk plasma properties and the power input, respectively, it may be necessary to rewrite (7.5) in the form of the total transferred energy qtr to the substrate: qtr = φat (U + Ek + Er + EP ) + qch + qt ,

(7.7)

where qch and qt are, respectively, the total contributions of the charge carriers and the thermal radiation.

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7.5.1 Sputtered Particles The contribution of the sputtered particles to the total deposited energy is mainly from their potential energy (condensation/reaction) and kinetic energy. The condensation energy, U per atom of aluminum, copper, and tungsten are, respectively, 3.33, 3.5, and 8.9 eV [2, 72]. For the reactive sputter deposition process, energy of reaction must be considered. The average kinetic energy of the ejected atoms may be determined using the modiﬁed Thompson model (with a correction factor as detailed in [73]). The modiﬁcation takes care of the high-energy tail observed with high ion energies which is usually found to drop oﬀ sharply with the relatively low ion energies associated with magnetron sputtering. The ﬁnal expression for the energy distribution which combines the Thompson distribution [74], modiﬁed anisotropy correction, and cut oﬀ factor (which sets the distribution to vanish at E = Emax ) is as follows [73]: q

Mg (E cosq11 ϑ + Ub ) 2 f (E)dE ∝ E(E + Ub )−3+2m exp −A Mt Ei E + Ub dE, (7.8) × 1− γEi where ϑ is the emission angle, Ub is the surface-binding energy, A = 13, q2 = 0.55, and q1 ≈ 2 − Mt /4Mg . Emax is the maximum emission energy, which is related to the sputtering threshold, Eth , by: Emax = (E0 Ub )/Eth . The maximum recoil energy γEi is sometimes taken to be equal to (Emax + Ub ). The parameter m, which depends on the species, was found to be generally between 0.20 and 0.23 [73]. The average initial energy Eki determined using the semi-empirical relation of (7.8), for sputtered Al and Cu atoms as a function of the ion energy are shown in Fig. 7.8. In transport toward the substrate, this energy is degraded due to collisions with the gas to Ekf , and may be expressed in the form: μd μηP d = Eki exp − , (7.9) Ekf = Eki exp − λ kT where η is the collision cross section for momentum exchange between the sputtered particles and gas molecules, λ is the mean free path and μ is related to mass ratio of the gas to the particle, and is given by [75]: (1 − M )2 (1 + M ) μ=1− ln for M < 1, 2M (1 − M ) (1 + M ) (M − 1)2 ln for M > 1, μ=1− 2M (M − 1) with M = Mg /Mt .

7 Energy Deposition at the Substrate in a Magnetron Sputtering System

241

Fig. 7.8. Average kinetic energy of Al and Cu atoms sputtered normally to the surface as a function of the argon ion energy obtained from the semi-empirical model of (7.7)

Clearly, the contribution per sputtered particle to the total energy ﬂux increases with ion energy (power), but decreases with pressure due to scattering, and of course is aﬀected by the changes in the local temperature [53, 56]. 7.5.2 Reﬂected Neutrals The contribution of the reﬂected neutrals to the total deposited energy depends on the mass ratio of the target material to that of the incident ion. For a given gas, both the energy and particle reﬂection coeﬃcients have been shown to increase with the mass of the target material [5]. In [5], it was reported that the reﬂection coeﬃcients decrease monotonically with increase in the incident energy, since the probability for backscattering decreases with the penetration depth. However, above 400 eV, the diﬀerences in values for diﬀerent energies are small, and the coeﬃcients may be assumed constant with energy. The functional dependence of the energy reﬂection coeﬃcient on the target voltage, VT , within the range of study [5] is then given by: ε VT , (7.10) RE = 1 − VE where VE is a ﬁtting parameter, which was found to be around 20,000 V for the heavy elements, but lower for the lighter ones. The power ε was found to be around 0.006 for germanium and to increase to about 0.037 for tungsten. The initial energy of the reﬂected neutral is equal to the product of the ion energy

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and the reﬂection coeﬃcient. Because of collisions with the gas, the deposited energy of the reﬂected neutrals decays exponentially with pressure–distance product as: ηr P d RE E0 exp − , (7.11) Er = Y kT where ηr is the cross section for momentum transfer between the reﬂected neutral and the gas. Since this energy contribution is scaled with the ejected atoms at the target, and the interest is in terms of the deposited atoms at the substrate, it would be necessary to factor (7.11) by the deposition eﬃciency, which is deﬁned as the ratio of the deposited particle ﬂux at the substrate to the emitted ﬂux at the target. 7.5.3 Plasma Radiation The contribution of the plasma radiation is due to the radiation emitted as a result of ionization and excitation events. These events are said to be caused by electrons with energies above the inelastic collision cross section threshold [2]. The average energy spent by an electron in making an ion is about 26.4 eV for argon [76]. The diﬀerence between this energy and the ionization energy of the gas (15.8 eV for argon) is radiated from the plasma. For an event involving an electron and argon atom, this energy is roughly estimated to be emitted in either the forward or reverse direction at about 5.33 eV [2]. In terms of the energy per sputtered atom, this energy is normalized to the sputtering yield as EPS = 5.33 eV/Y, (7.12) which assumes every ion is collected at the cathode. However, the interest is in terms of the energy per deposited atom; therefore, EPS is further normalized to the deposition eﬃciency [7] as: EP = EPS /χde ,

(7.13)

where χde is the deposition eﬃciency. It depends on scattering events, and is determined by pressure and the distance of the substrate from the target. Since the spatial proﬁle of depositing ﬂux depends on the process conditions and system geometry [58], then the deposition eﬃciency would also be determined by the process conditions and system geometry. Gas heating eﬀects would result in improvement in the deposition eﬃciency through reduced scattering of the sputtered particles [53, 56, 57]. In the low power regime of operation, this eﬃciency reduces greatly with pressure, and hence a large increase in the contribution of the plasma radiation to the total deposited energy per atom. This contribution to the total energy per deposited atom decreases with power, but at high power densities, it tends toward being constant. This may be attributed to the gas heating eﬀects, especially at high power densities [53, 54, 57, 77].

7 Energy Deposition at the Substrate in a Magnetron Sputtering System

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7.5.4 Charge Carriers Substrate bias is a signiﬁcant factor in determining the contribution of ions and electrons to the total energy deposited onto the growing ﬁlm [6, 78–82]. For instance, when the substrate is negatively biased, positive ions (essentially from the process gas) are accelerated to the substrate, on the other, when it is biased positively, electrons and negative ions are accelerated to the substrate. In either case, the charged particles transfer their energy or a part to the growing ﬁlm [72, 80, 81]. If the ion energy is high, it may also result in resputtering of the deposited ﬁlm, leading to a loss in energy [83]. At a substrate bias potential equal to or greater than the ﬂoating potential, the primary positive ions contribute an insigniﬁcant energy to the growing ﬁlm, whereas electrons contribute signiﬁcantly to the total energy [5, 7, 37]. Positive ions have been shown to be signiﬁcant only at potentials lower than the ﬂoating potentials [67, 78, 81]. The energy contribution of the charge carriers depends on their temperatures, kT , and densities, n, as well as the potential, Vbias , i.e., the substrate potential Vsub relative to the plasma potential, VP . Apart from their kinetic energies, recombination energy of the carriers at the substrate also contributes to the total deposited energy. This energy, however, is signiﬁcant mostly at ﬂoating potentials (in which case the net current of the electrons and ions is zero). This energy is determined by the ﬂux of the ions ji , ionization potential Eion of the process gas (which is about 15.8 eV for Ar), and work function Φ of the substrate. It may be expressed as [67] qrec = ji (Eion − Φ). (7.14) For a Maxwellian energy distribution, the energy ﬂux of electrons, and ions are, respectively, given by [6, 43, 67, 84]:

0.5 e(VP − Vsub ) kTe Eee = 2kTe ne , exp − 2πme kTe 0.5 kTe Eei = 0.61neVbias , mi

(7.15) (7.16)

where mi and me are, respectively, the mass of the ions and electrons. The sum of these contributions gives the contribution from the charged carriers Ee . The electron density in the substrate region is proportional to the discharge power [78], and for a given power depends on the pressure. The spatial distribution of electron density is highly inﬂuenced by the pattern of the magnetic ﬁeld in a magnetron system, as shown in Fig. 7.9 [66]. The electron density is signiﬁcantly higher above the target etch tracks than along the central axis at those regions close to the target. However, at large target-substrate distances the distribution tends to ﬂatten out. That of the ions is similar, though of a lower density at some distances from the edge of the sheath. For a balanced magnetron system, the shape proﬁle of the spatial distribution of electrons

244

S.D. Ekpe and S.K. Dew 7.00E+10

Density, ne (cm-3)

6.00E+10

40 mtorr 3cm

5 mtorr 3 cm

40 mtorr 5 cm

5 mtorr 5 cm

40 mtorr 10 cm

5 mtorr 10 cm

5.00E+10 4.00E+10 3.00E+10 2.00E+10 1.00E+10 0.00E+00 0

2

4

6

8

10

12

14

16

Lateral displacement (cm) Fig. 7.9. Langmuir probe lateral scan of the proﬁle of electron density for diﬀerent pressures and diﬀerent distances from the target [66]

seems to be similar to that of the deposition rate. The densities increase with pressure and power. Electron temperature depends on the gas-target combinations and discharge voltage. For a given experimental system, the dependence of electron temperature on the discharge voltage Vd is given by [68]: kTe = υVd2 ,

(7.17)

where υ is constant for a given gas-target combination, magnetic ﬁeld and system geometry. The spatial proﬁle of the electron temperature was also shown to follow that of the electron density, being higher in regions of high electron density than at regions of low density. However, it was also observed that the spatial electron temperatures decrease with pressure [66], probably as a result of more frequent collision and excitation of the process gas. The dependence of these plasma properties on the deposition properties can generally be estimated from Langmuir probe measurements. 7.5.5 Thermal Radiation Usually, the target in a magnetron sputtering system is water cooled. However, a weak thermal link has been observed between the target shield and the water-cooling system. Thus, during operation, the shield heats up and results in a signiﬁcant heat transfer to the substrate by thermal radiation [8]. There is also evidence of signiﬁcant temperature gradient between the target surface and the cooling surface, when the target material is nonconducting or has low thermal conductivity [46]. These and other hot surfaces could certainly

7 Energy Deposition at the Substrate in a Magnetron Sputtering System

245

contribute signiﬁcant energy to the substrate in a low temperature deposition. The main source of heating in this case is from the system input power. The steady-state temperature of these surfaces is therefore expected to increase with magnetron power. The net radiation Qtr between the two grey bodies separated by nonabsorbing medium is given as [85] Qtr = F12 σ(ε1 A1 T14 − ε2 A2 T24 ),

(7.18)

where ε and σ are, respectively, the surface emissivity and Stefan–Boltzmann constant, F12 is the view factor of body 2 relative to that of 1, and T is the surface temperature. In the sputter deposition system, the target and the shield around the target may be treated as a small grey body in a grey enclosure [86], if the diﬀerence in temperature between the substrate and the chamber walls is small. The grey enclosure behaves as a black body through the opportunities for ultimate absorption oﬀered by repeated reﬂection from its walls [86]. All the emission from the target q12 will ultimately be absorbed by the enclosure. However, only a fraction of the emission from the walls will be absorbed by the target, depending on the view factor, F12 , of the wall with respect to the target and the emissivity of the target. Bayley et al. [86] showed that the net radiation ﬂux qtr from the heating source to the walls of the enclosure is given by: qtr = ε1 σ(T14 − T24 ),

(7.19)

where ε1 is the emissivity of the hot body whose surface temperature is T1 . For a typical case study [7, 36], T2 was assumed at room temperature, while the shield temperature, T1 was estimated by considering that almost all the incident energy is converted into heat and the main sources of heat lost from the shield are by thermal conduction through the gas as well as through the shield material to the cooling surface and radiation. As already stated, the energy source to the shield is mainly from the system input power. The emissivity used was found to be diﬀerent from the bulk emissivity for steel. A value of 0.79 was used, which is higher than the bulk value. This value is close to the value for oxidized steel [87]. There has been evidence that the surface emissivity of material does change with temperature and surface roughness [48,88–90]. For example, Love [89], cites an increase in emissivity for chromium steel from about 0.2 at 600◦ C to over 0.7 at 900◦C. Simonsen [90] gave values for the emissivity of steel at 100◦C ranging from 0.066 to 0.97, depending on whether the surface is polished or rough. Figure 7.10 shows the comparison of the modeled shield temperature with the measured values. In the magnetron sputtering system, the ground shield around the target and the surface of the target are always subjected to bombardment by energetic particles, and hence their surfaces are rough. At a magnetron power of 200 W, the contribution of thermal radiation to the deposited energy during the sputter deposition of Al was estimated to be about 11% of the total

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Fig. 7.10. Comparison of the model with the measured temperature of the shield around a 76 mm planar target located in the magnetron sputter chamber of radius 24 cm during the sputtering of Al at a magnetron power of 200 W and gas pressure of 0.67 Pa

energy [7]. This is signiﬁcant. For the deposition of reactive materials such as AlN, where the target surface might be coated with the reactive material (which in some cases may not result in a conducting surface) during the operation, the contribution is expected to be higher. 7.5.6 Model Results The following presents the results of the model, which shows good agreement with experimentally determined values for diﬀerent process conditions. The spatial proﬁle of energy per deposited particle is also presented. Total Energy Flux at the Substrate The steady-state total energy deposited as a function of the magnetron discharge powers for gas pressures of 0.67 and 1.33 Pa at substrate-target distances of 10.8 and 21 cm along the central axis of the target are shown in Fig. 7.11. A similar trend was obtained for Cu [36]. As expected, the total deposited energy increases with power, but reduces with pressure and distance. The trends seem to suggest a nonlinear dependence on power, probably due to gas heating eﬀects. Figure 7.12 shows the variation in the on-axis total energy with distance for Al at 0.67 Pa sputtered from a 7.6 cm target at three diﬀerent powers [36]. The deposited energy follows the pattern of particle deposition [58], especially at distances not too far oﬀ from the target. This suggests that a major contribution to the total energy at such distances may be from sputtered particles.

7 Energy Deposition at the Substrate in a Magnetron Sputtering System 0.04

0.1 (a) 0.08

0.67 Pa (model)

Total energy flux (W/cm2)

Total energy flux (W/cm2)

247

1.33 Pa (model) 0.67 Pa (expt) 1.33 Pa (expt)

0.06 0.04 0.02 0

0.67 Pa (model)

(b)

1.33 Pa (model)

0.03

0.67 Pa (expt) 1.33 Pa (expt)

0.02

0.01

0 0

100 200 300 400 Magnetron power (W)

500

0

100 200 300 400 Magnetron power (W)

500

Fig. 7.11. Steady-state energy as a function of magnetron power at substrate-target distances of (a) 10.8 and (b) 21 cm during the sputter deposition of Al at 0.67 and 1.33 Pa

Total energy flux (W/cm2)

1 0.8 0.6

100 W

0.4

300 W

200 W

0.2 0

0

5

10 15 z (cm)

20

Fig. 7.12. Variation in the total energy ﬂux at the substrate with substrate-target distance, z as a function of magnetron power at a gas pressure of 0.67 Pa during the sputter deposition of Al

The on-axis deposited energy initially increases with distance to a maximum at some point close to the target, then, thereafter falls oﬀ. The trend of the fall is steep initially, then leveling oﬀ afterward. This behavior is attributed to the erosion proﬁle of the magnetron target, as it is consistent with the proﬁles of sputtered and plasma particles [58, 66]. The trend of the modeled result at some distances oﬀ the target is consistent with experimental results of [43]. At long distances, most of the sputtered atoms are thermalized after involving several collisions with the background gas. Thus the energy contribution of the sputtered atoms to the total deposited energy is greatly reduced to just about their condensation energy. In addition to the reduction in the energy of the sputtered atom, the ﬂux of the sputtered atoms is also reduced due to scattering and spreading.

S.D. Ekpe and S.K. Dew Energy per deposited atom (eV)

248

90 80 0.67 Pa (model)

70

1.33 Pa (model)

60

0.67 Pa (expt)

50

1.33 Pa (expt)

40 30 20

0

100 200 300 400 Magnetron power (W)

500

Fig. 7.13. Total energy per deposited Al atom as a function of power at distance of 10.8 cm for diﬀerent pressures

Total Energy per Deposited Atom Variation in the total energy per deposited atom with power and pressure for Al is shown in Fig. 7.13 [36]. Although the model may overestimate the energies at very low powers or very high pressures by underestimating the deposition ﬂux [36,58], the trend suggests that the total energy per deposited atom decreases strongly with power, but increases with pressure. However, at high power densities, it remains constant with power and pressure. The power threshold of this saturation depends on the spatial location of the substrate relative to the target. It should be expected that the power threshold would increase with spatial distance. The size of the target is also a determining factor in the spatial proﬁle of the total energy per deposited atom. Figure 7.14 compares the eﬀect of circular target size on the simulated spatial proﬁle of the total energy per deposited atom, for the same power density (9.5 W cm−2 ) and pressure (0.67 Pa) for Al deposition [36]. Increase in the size of the inner radius of the etch track as well as the overall target size results in a shift in the regions of uniform ﬁlm away from the target. As can be noticed in (b), this shift results in a lower energy per deposited atom compared with those of the smaller target (a) over the same area. However, the simulated energy per deposited atom at regions of uniform ﬁlm is about the same for both cases under the same power density and other operating conditions. For Al and Cu, this energy is about 28 and 25 eV atom−1 , respectively, given the DC planar magnetron considered in that study [36] and limits of uncertainty. The atomic weight of the sputtering gas has been shown to have a strong inﬂuence on the energy per deposited atom [91]. This energy decreases with atomic weight of the process gas. For instance, for the deposition of molybdenum using cylindrical-post magnetron sputtering source with the sensor located at a radius of 14.2 cm from the cathode axis, values of the energy per deposited atom has been shown to decrease from about 85 to below

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Energy per deposited atom (eV) (a) 120 100 80 60 40 20 0

10 5 5

0 10 z (cm)

15

20

25 −10

−5

R (cm)

Energy per deposited atom (eV) (b) 120 100 80 60 10

40 20 0

5 5

0 10 z (cm)

15

20

25 −10

−5

R (cm)

Fig. 7.14. The eﬀect of the size of target and etch track on the energy per deposited atom, for targets with erosion tracks of radii between (a) 0.9 and 3.32 cm and (b) 3.15 and 7.0 cm

30 eV atom−1 when the process gas was changed from neon to xenon [91]. Apart from the eﬀect of reduced sputtering yield when using gases of lower atomic weight, the high energy per deposited atom measured with the use of neon is attributed to the eﬀect of reﬂected neutrals. The energy per deposited atom in the case of reactive deposition has been shown to be generally higher than that of elemental deposition [70, 91]. This is attributed to, among others, the atom reﬂection at the cathode, a reduced sputtering yield (reduced deposition rate) [92–94] due to compound formation on the surface of target by adsorbed working gas species [95, 96], a reduced ion component in the discharge current because of higher secondary electron emission coeﬃcient at the target [91], and the eﬀect of negative ions accelerated from the sheath in front of the target toward the substrate. However, the eﬀects of induced secondary electron emission (ISSE) coeﬃcient and negative

250

S.D. Ekpe and S.K. Dew 35

30

(a)

25

Contributions to the energy per deposited atom (eV)

Contributions to the energy per deposited atom (eV)

35 sputtered atom reflected neutral plasma radiation

20

electrons

15

thermal radiation

10 5 0

(b)

30

sputtered atom reflected neutral

25

plasma radiation

20

electrons

15

thermal radiation

10 5 0

0

100 200 300 400 Magnetron power (W)

500

0

100 200 300 400 Magnetron power (W)

500

Fig. 7.15. Contributions by mechanism to the total energy per deposited Cu atom as a function of magnetron power at a substrate-target distance of 10.8 cm and gas pressure of (a) 0.67 and (b) 1.33 Pa

ions may not generally hold in all cases. For instance, it has been shown that the ISSE coeﬃcient decreases with oxygen content in cases where there may be reduction behavior of the oxides under ion bombardment [96]. Thornton and Lamb [91] reported values of 230 and 100 eV atom−1 , respectively, for Al2 O3 and Cr2 O3 , which are several times higher than values reported for the elemental metals at similar process conditions. To control the deposition process for a desired ﬁlm property, it is necessary to understand the eﬀects of process conditions on the individual energy contributions. Figure 7.15 shows the estimated contributions to the on-axis total energy per deposited atom as a function of power and pressure, using Cu as a case study, at a substrate-target distance of about 10.8 cm. The trend of the results suggests that the plasma eﬀects (electrons and plasma irradiation) are more important at lower power levels. The contribution of the sputtered atom increases with power but decreases with pressure as would be expected. In the low power regime, the contribution of electrons decreases rapidly with power, but at high powers, it is nearly constant with power. That of the plasma irradiation has a similar trend to that of the electron, though the initial decrease is not as rapid as that of the electron. Both contributions increase with pressure. At about 300 W and 0.67 Pa, both electrons and plasma irradiation contribute about 30% each to the total energy per deposited Al atom [36]. This percentage contribution changes with pressure and power. In obtaining the above, it was assumed that all incident energy at the substrate is absorbed. However, in practical context, some of the radiant energy may be reﬂected away from the surface, though some through multiple reﬂections may be deposited back onto the substrate [97]. It should also be noted that the reﬂection coeﬃcient decreases with energy [87], and since we are dealing with low energy here, the associated error in the estimation, of course reduces. The contribution of the reﬂected neutrals decreases marginally with power, but increases marginally with pressure. This is consistent with the results reported in [60]. Though the energy and particle reﬂection coeﬃcients

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251

increase with pressure through reduced discharge voltage for a constant power mode of operation, the eﬀect is limited by the decrease in the incident ion energy.

7.6 Conclusions The eﬀective energy deposited onto the surface of a growing ﬁlm plays an important role in determining the property and structural formation of the ﬁlm. The diﬀerent sources of the deposited energy in a magnetron sputter deposition system are reviewed. Embedded sensors, such as microfabricated polysilicon thin ﬁlm thermistor, oﬀer a useful tool to measuring the energy ﬂux at the substrate. This eliminates the problems associated with discrete sensors, such as thermocouples. Experimentally determined values of energy ﬂux are also presented for typical case studies. A theoretical model for estimating the energy ﬂux at the substrate is also reviewed and results compared with reported experimental data. The model takes into consideration the eﬀects of process conditions on the various contributions to the total deposited energy. The total deposited energy has been shown to vary with the process conditions. At large distances from the target (long throw), sputtered particles contribute negligibly to the total deposited energy. Estimated total energy per deposited atom is found to decrease with power, but increase with pressure at low power regimes. This energy trends toward being independent of power and pressure for given spatial location relative to the target. It is generally shown that, the energy per deposited atom is highly dependent on the spatial location. The energy per deposited atom is greater in RF systems than in DC systems. For the reactive deposition process, the energy per deposited atom is generally higher than that of elemental deposition. This is attributed to the reduced deposition rate as a result of formation of compound on the target surface, among others.

References 1. B.A. Movchan, A.V. Demshishin, Phys. Met. Metallogr. 28, 83 (1969) 2. J.A. Thornton, Thin Solid Films 54, 23 (1978) 3. J. Greene, in Handbook of Deposition Technologies for Films and Coatings: Science and Technology, Applications, 2nd edn., ed. by R.F. Bunshah (Noyes Publications, Park Ridge, 1994), p. 681 4. S. Mahieu, P. Ghekiere, D. Depla, R. De Gryse, Thin Solid Films 515, 1229 (2006) 5. T.P. Drusedau, T. Bock, T.-M. John, F. Klabunde, J. Vac. Sci. Technol. A 17(5), 2896 (1999) 6. H. Kersten, H. Deutsch, H. Steﬀen, G.M.W. Kroesen, R. Hippler, Vacuum 63, 385 (2001)

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S.D. Ekpe and S.K. Dew S.D. Ekpe, S.K. Dew, J. Vac. Sci. Technol. A 20, 1877 (2002) S.D. Ekpe, S.K. Dew, J. Vac. Sci. Technol. A 21, 476 (2003) L.G. Jacobson, F.L. Freire Jr., J. Vac. Sci. Technol. A 17, 2841 (1999) S.S. Lau, R.H. Mills, D.G. Muth, J. Vac. Sci. Technol. 9, 1196 (1972) H. Windischmann, Crit. Rev. Solid State Mat. Sci. 17, 547 (1992) S.D. Bernstein, T.Y. Wong, R.W. Tustison, J. Vac. Sci. Technol. B 12, 606 (1994) M. Chinmulgund, R.B. Inturi, J.A. Barndard, Thin Solid Films 270, 260 (1995) D. Liu, S.K. Dew, M.J. Brett, T. Janacek, T. Smy, Thin Solid Films 236, 267 (1993) C.-T. Wei, H.-P. Shieh, Jpn. J. Appl. Phys. 45, 6405 (2006) T. Takahashi, H. Nakabayashi, T. Terasawa, K. Masugata, J. Vac. Sci. Technol. A 20, 1205 (2002) C.-H. Lee, H.-Y. Lee, K.S. Liang, T.-B. Wu, Physica B 248, 109 (1998) S. Mahieu, G. Buyle, D. Depla, S. Heirwegh, P. Ghekiere, R. De Gryse, Nucl. Instrum. Methods Phys. Res. B Beam Interact. Mater. Atoms 243, 313 (2006) J. Bretagne, C.B. Laporte, G. Gousset, O. Leroy, T.M. Minea, D. Pagnon, L. De Poucques, M. Touzeau, Plasma Sources Sci. Technol. 12, S33 (2003) A. Subrahmanyam, K. Valleti, S. Joshi, G. Sundararajan, J. Vac. Sci. Technol. A 25, 378 (2007) Y. Jung, J. Seo, D.W. Lee, D. Jeon, Thin Solid Films 445, 63 (2003) J. Kikuchi, S. Fujimura, R. Kurosaki, H. Yano, J. Vac. Sci. Technol. A 15(4), 2035 (1997) R.R. Chromik, W.K. Neils, E.J. Cotts, J. Appl. Phys. 86, 4273 (1999) T.T. Lay, Y. Yoshitake, B. Mebarki, J. Vac. Sci. Technol. A 20, 2027 (2002) J.A. Thornton, J. Vac. Sci. Technol. 11, 666 (1974) J.A. Thornton, J. Tabock, W. Hoﬀman, Thin Solid Films 11, 111 (1979) D.W. Hoﬀman, J.A. Thornton, J. Vac. Sci. Technol. 20, 355 (1982) J.A. Thornton, D.W. Hoﬀman, J. Vac. Sci. Technol. A 3, 576 (1985) K.-H. Muller, J. Appl. Phys. 62, 1796 (1987) H. Windischmann, J. Vac. Sci. Technol. 9, 2431 (1991) D.W. Hoﬀman, Thin Solid Films 107, 353 (1983) S.M. Rossnagel, M.A. Russak, J.J. Cuomo, J. Vac. Sci. Technol A 5, 2150 (1987) S. Hosokawa, A. Konishi, K. Hiratsuka, K. Annoh, Thin Solid Films 73, 115 (1980) C. Wyon, R. Gillet, L. Lombard, Thin Solid Films 122, 203 (1984) S.K. Dew, T. Smy, M. Brett, Jpn. J. Appl. Phys. 33(Part 1), 1140 (1994) S.D. Ekpe, PhD Thesis, University of Alberta, Edmonton, 2005 R. Wendt, K. Ellmer, K. Wiesemann, J. Appl. Phys. 82, 2115 (1997) J.E. Daugherty, D.B. Graves, J. Vac. Sci. Technol. A 11, 1126 (1993) J.F. Behnke, T. Bindemann, H. Deutsch, K. Becker, Contib. Plasma Phys. 37, 345 (1997) H.F. Winters, H.J. Coufai, W. Eckstein, J. Vac. Sci. Technol. 11, 657 (1993) D.H. Zhang, D.E. Drodie, Thin Solid Films 251, 151 (1994) R.P. Howson, H.A. J’afer, A.G. Spencer, Thin Solid Films 193/194, 127 (1990) H. Kersten, G.M.W. Kroesen, H. Hippler, Thin Solid Films 332, 282 (1998) Z. Dohnalek, S. Mezhenny, I. Lyubinetsky, W.J. Choyke, J.T. Yates Jr., J. Vac. Sci. Technol. A 15(5), 2766 (1997) H. Nishino, W, Yang, Z. Dohnalek, V.A. Ukraintsev, W.J. Choyke, J.T. Yates Jr., J. Vac. Sci. Technol. A 15(1), 182 (1997)

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52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83.

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84. J.W. Lee, J.J. Cuomo, J. Vac. Sci. Technol. A 22, 260 (2004) 85. A.J. Chapman, Heat Transfer, 2nd edn. (Macmillan Company, New York, 1967) 86. F.J. Bayley, J.M. Owen, A.B. Turner, Heat Transfer, (Nelson, Great Britain, 1972) 87. D. R. Lide (Editor-in-Chief), Handbook of Chemistry and Physics, (CRC Press, Boca Raton, 1991) 88. A. Matthews, Vacuum 32, 311 (1982) 89. T.J. Love, Radiative Heat Transfer, (Merrill, New York, 1968) 90. J.R. Simonsen, An Introduction to Engineering Heat Transfer, (McGraw-Hill, New York, 1967) 91. J.A. Thornton, J.L. Lamb, Thin Solid Films 119, 87 (1984) 92. J.A. Thornton, Thin Solid Films 80, 1 (1981) 93. A. Cortona, W. Husinsky, G. Betz, Phys. Rev. B 59, 15496 (1999) 94. G. Este, W.D. Westwood, J. Vac. Sci. Technol. A 2, 1238 (1984) 95. S. Berg, T. Nyberg, Thin Solid Films 476, 215 (2005) 96. D. Depla, S. Heirwegh, S. Mahieu, J. Haemers, R. De Gryse, J. Appl. Phys. 101, 013301 (2007) 97. S.A. Nikitov, Y.V. Gulyaev, A.D. Boardman, Wave. Random Media 6, 61 (1996)

8 Process Diagnostics J.W. Bradley and T. Welzel

8.1 Introduction Reactive sputtering of materials can be carried out using a number of diﬀerent types of plasma excitation methods including DC, RF, Pulsed DC and AC, with the power applied to a sputter cathode. The usual conﬁguration adopted in industry is the magnetron, operated typically in the so-called unbalanced mode. Although DC and RF excitation are often employed in non-reactive plasmas, with each technique having its own particular advantages (e.g. DC is high rate, RF can sputter many types of targets), it has become common when introducing reactive gases like oxygen or nitrogen to modulate the discharge power by pulsing the driving voltage waveform. Modulating the applied power in the form of pulses in the frequency range 5–350 kHz was introduced in reactive magnetron sputtering as a solution to the problem of arcing of insulating material at the target. This sputtering system has been used for almost 20 years as a method for the rapid deposition of various dielectric thin ﬁlms for a variety of technological applications. In both industrial and academic research, two pulsing conﬁgurations are typically utilised: unipolar and bipolar modes [1]. The latter may be asymmetrical or symmetrical. The asymmetrical bipolar mode diﬀers from the unipolar mode in that a positive voltage (typically +30 to +50 V) at the cathode is introduced instead of grounding the target within ‘oﬀ’ phase. The technique is widely used, for instance, for a preparation of high quality insulating dielectric ﬁlms [2–4]. A typical representation of the target voltage and current traces for this pulse mode is shown in Fig. 8.1. It is now well recognised that asymmetrical bipolar pulsing is more eﬃcient than the symmetrical conﬁguration in its ability to discharge insulating spots on the target by plasma electron bombardment when the polarity of the magnetron target is reversed [3]. This chapter reviews most of the recent investigations of reactive sputter deposition processes using plasma diagnostic techniques. Special emphasis is placed on the increasingly popular method of mid-frequency pulsed magnetron sputtering. Despite being closely related, the relatively new technique

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Fig. 8.1. Typical pulsed magnetron discharge waveforms: (a) voltage and (b) current. After the large positive transient at t = 5 μs (duration 200 ns) the remainder of the ‘oﬀ’ phase is known as the reverse time (from [77])

of high-power pulsed ionised magnetron sputtering (HPPMS or HIPIMS, see, e.g. [5, 6]) with extremely short voltage pulses compared to pulse repetition time, is not covered in much detail here. The chapter is subdivided into different plasma diagnostic methods such as electric probes, mass spectrometry, optical emission spectroscopy (OES) and laser-induced ﬂuorescence (LIF). Each method is brieﬂy described and its application to particular aspects of reactive sputtering is presented.

8.2 Electrical Probes Since their introduction by Langmuir and Mott-Smith [7, 8] electrical probes have developed to be one of the most frequently used techniques to characterise plasma-processing discharges, including sputtering discharges. This is due to the fact that, experimentally, probe techniques are comparatively easy

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to apply and that current-voltage data can be readily obtained. However, correct interpretation of probe characteristics is not so simple. 8.2.1 Probe Techniques A typical electrical single probe, as introduced by Langmuir and Mott-Smith, is a small conducting electrode of well-deﬁned geometry – mostly in the form of a cylindrical wire – which is variably biased with respect to a ﬁxed potential, e.g. the grounded wall of the processing chamber. If its potential is positive relative to the plasma potential Vp , then the probe draws an electron current, from which the electron density can be determined. If its bias is slightly negative with respect to Vp electrons begin to be repelled, and from the attenuation of electron current with increasing negative bias in this retardation region, the electron energy distribution function (EEDF) or under the assumption of an approximately Maxwellian distribution the electron temperature Te can be calculated [9]. Biasing the probe potential more negatively, still leads to the point where the diminishing current is compensated by the positive ion current at the ﬂoating potential Vf , which is consequently determined from the zero current value of the probe characteristics. Finally, if the probe is biased even more negatively, the ion saturation current is reached from which in principle, the ion density can be obtained. The general problem with electrical probes is that they are physically in contact with the plasma. This may lead to signiﬁcant disturbances of the plasma environment and therefore it is an usual requirement that probes have very small dimensions. Adjacent to a biased probe surface, a space-charge sheath will form, through which the charged particles have to pass to be collected. For this reason, in most cases, there is no simple relationship between the measured current and the density of the charged species in the plasma bulk, particularly true when cold ions move through the positive space-charge region. This necessitates complex theories for diﬀerent probe geometries when considering the ion collection part of the characteristics (see, e.g. [10–12] and references therein). Another form of electrical probes applied to reactive discharges is the double probe. In this case, the probe consists of two – normally identical – electrodes and the voltage is applied between both probe tips instead against a ﬁxed reference [13]. The complete system is insulated which has the advantage that no reference is needed and that the probe “ﬂoats” with any ﬂuctuations in the potential of the surrounding plasma. This makes double probes advantageous for measurements in pulsed or strongly ﬂuctuating discharges, allowing average values to be gleaned. However, as the probe has no reference, no values of the plasma or ﬂoating potentials (Vp , Vf ) can be obtained, and due to the isolated set-up, the current is always limited by the ion saturation current. It has therefore to be assumed that the density of the electrons equals that of the positive ions, which must be calculated from the ion saturation current. An experimental approach to do this without complex calculations has been

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given by Sonin [14]. Another drawback of the method is that only a small part of the EEDF can be probed and from this it has to be extrapolated to a Maxwellian distribution. Under this assumption, an electron temperature can be determined [15, 16]. A single probe can also be built as a so-called emissive probe. This method is based on the fact that, once the probe is heated enough, it starts not only to emit photons but also electrons. To achieve this heating, the probe wire is mostly formed into a loop, which carries a separate conduction current. If the probe is above the plasma potential, the thermal electrons cannot overcome the potential barrier to the plasma and the emission is prevented. From a probe below the plasma potential, the electrons can leave the surface and upon moving away from the probe form a virtual additional ion current [17, 18]. If this current is of the order of the electron saturation current the probe characteristic is strongly modiﬁed: At the plasma potential a sharp kink occurs and the apparent ion current forces the ﬂoating potential to move close to the plasma potential [18]. The kink in the characteristics gives a very precise measurement of the plasma potential with a theoretical error of the order of kTW /e (k – Boltzmann constant, e – elementary charge, TW – wire temperature) compared to the single probe evaluation. If the wire temperature is chosen appropriately, the apparent ﬂoating potential may be used as a direct measure of the plasma potential. This gives a convenient method to access time-varying plasma potentials as the ﬂoating potential is quite easily measured with a high-impedance oscilloscope. All probe methods have the advantage that they measure the plasma at one particular point, i.e. they give three-dimensionally resolved results. The measurement position can be chosen simply by an appropriate positioning of the probe. On the other hand, special care has to be taken with respect to surface modiﬁcation of the probe surfaces in reactive sputtering. As a probe material, mostly wires of tungsten, platinum or gold are used that withstand the reactive gas component. Special constructions of ceramics or glass prevent contact with conductive surfaces when conducting layers are deposited. To avoid insulating layer formation on the probe, the tips are heated or frequently cleaned by sputtering, i.e. the application of a high negative potential. An advantage of the double probe technique for reactive sputtering is that the characteristic is symmetric, any falsiﬁcation of the probe due to contamination can be immediately observed by deviations from the symmetry. This is signiﬁcantly more diﬃcult with asymmetric single probe characteristics. 8.2.2 Use of Electrical Probes in Pulsed Reactive Sputtering Recently, pulsed magnetron discharges have been widely used for reactive sputtering of thin ﬁlms. Apart from discharges which are aimed at the achievement of a highly ionised ﬂux of sputtered material in a quite short time (high-power pulse magnetron sputtering, see, e.g. [5, 6]) such discharges are typically operated with frequencies between about 1 and 500 kHz and a duty

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cycle (i.e. the duration of the sputter pulse to the total period) of several 10’s of %. Such discharges have been characterised by time-averaged single Langmuir probes which average the plasma parameters over many periods [19–21]. Glocker [21] reports that the average electron density is elevated by a factor of 4 and the electron temperature by a factor of 1.3 compared to a DC discharge accompanied by an increase in the energy inﬂux to the substrate. Lee et al. [22] found that with increasing pulse frequency from 75 to 250 kHz the ion density is increased as well as the electron temperature. The results are hard to compare because Glocker ran the magnetron discharge in constant power mode but Lee et al. with constant current. Due to the probably varying plasma potential as reference these measurements are uncertain and it is necessary to measure the quantities with a single probe time resolved. The ﬁrst such measurements to be reported were by Mahoney et al. [23] who found an increase in the electron temperature compared to DC and with increasing frequency but no signiﬁcant increase in the density when they afterwards averaged their time-resolved values. A similar result was published by Seo et al. [24] who observed a signiﬁcant increase in Te with decreasing duty cycle, but only a weak dependence of ne at constant power. Bradley et al. [25,26] have investigated an asymmetric bipolar-pulsed magnetron with a time-resolved single probe on the discharge axis and found an increase in Te and ne compared to the DC case by about 30% and 20%, respectively (see Fig. 8.2). Moreover, they observed very high-electron temperature values just at the beginning of the pulse ‘on’ phase after the target voltage was switched to negative values. Though these values were probably not due to a Maxwellian distribution, they indicate the presence of a ‘burst’ of high-energy electrons during the ﬁrst μs of the ‘on’ phase. Even in the following quiescent part of the ‘on’ phase Te has values above that of the DC case as shown in Fig. 8.2. For a similar magnetron sputtering system with the same power supply Belkind et al. [27] and with a diﬀerent pulse power supply Bradley et al. [28,29] and B¨ acker et al. [30] observed a similar ‘burst’ with the eﬀective electron temperature reaching values sometimes as high as 38 eV (see Figs. 8.3 and 8.4). The phenomenon is explained by the rapidly advancing sheath in front of the negatively biased target, which accelerates electrons into the bulk plasma causing this ‘burst’. Through inelastic collisions this results in a developing electron density on the scale of some μs (cf. Figs. 8.2 and 8.4) with the electrons still keeping energies slightly higher than in a DC discharge. Initially, high electron temperatures in the ‘on’ phase were also observed in discharges with longer timescales and longer ‘on’ phases [24,31–36]. In some cases, where the EEDF was thoroughly studied with a single probe [24, 31, 33, 34], it has been shown that Te,eﬀ actually consists of a high-temperature electron group and a cold-temperature electron group with the hot group containing this signiﬁcant temperature peak [31] (see Figs. 8.5 and 8.6).

260

J.W. Bradley and T. Welzel 25

15

(a) 50 kHz 12 Ne/1015m−3

Teff / eV

20 15 10 5

9 6 3

0 0

2

4

6

(a) 50 kHz

0

8 10 12 14 16 18 20

0

2

4

6

Time / μs 8

12 10 Ne/1015m−3

6 Teff / eV

8 10 12 14 16 18 20 Time / μs

4 2

(b) 100 kHz 0 0

1

2

3

4

5

6

Time / μs

7

8

9 10

8 6 4 2

(b) 100 kHz

0 0

1

2

3

4 5 6 Time / μs

7

8

9 10

Fig. 8.2. Eﬀective electron temperature (left) and electron density (right) for two diﬀerent pulse frequencies at the same duty cycle of 80%. The average value is given by the horizontal lines in the ﬁgures and compared to the values obtained for a DC discharge at the same power of 200 W (the lower horizontal lines). The ﬁgures start with the ‘oﬀ’ phase at 0 μs (from [50])

Fig. 8.3. Eﬀective electron temperature during one pulse (f = 100 kHz) for diﬀerent axial positions of the probe along the axis of symmetry. The duty cycle is 50% with the ‘oﬀ’ phase starting at 0 μs and the ‘on’ phase starting at 5 μs (from [28])

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Fig. 8.4. Plasma density and eﬀective electron temperature in a pulsed-DC discharge at 20 kHz with a duty cycle of 80% in metal and reactive mode. The target material used was Al, the pulse ‘on’ phase starts at 10 μs (after [27])

In all these cases, after the temperature peak, a rise of in the electron density is observed. The timescale for this strongly depends on the pulse parameters but is always longer than for the temperature rise (cf. Figs. 8.2 and 8.4). Time-resolved double probe measurements in a discharge comparable to that of Bradley et al. [28] but in reactive mode and with a diﬀerent target material (Mg) reproducibly revealed two peaks in the charge carrier density at the beginning of the ‘on’ phase [37–42] for diﬀerent conditions (see Fig. 8.7). They do not show, however, signiﬁcant temporal changes in Te . This is not surprising as double probes are rather insensitive to the EEDF as discussed above. The argumentation for the formation of the two peaks in the density is basically the same as discussed for the temperature peaks. The fast advancing cathode sheath rapidly accelerates electrons, which are ‘left over’ from the previous pulse. Subsequent ionisation collisions lead to the ﬁrst density peak. Afterwards, the heavy ions move to the cathode, release secondary electrons which are accelerated and upon collisions start to form a stationary discharge with a high density in form of the second maximum.

262

J.W. Bradley and T. Welzel

(a)

1011 1 ms 3 ms 5 ms 7 ms 9 ms 11 ms 15 ms 25 ms

EEPF (eV-3/2 cm-3)

After pulse-on 1010 25 ms 109

108

107 1 ms 106

0

5

10

15

20

25

Kinetic energy (eV)

EEPF (eV-3/2 cm-3)

(b)

1011 26 ms 28 ms 29 ms 31 ms 32 ms 34 ms 38 ms 50 ms

After pulse-off 1010

26 ms

109

108

107

106

50 ms

0

5

10

15

20

25

Kinetic energy (eV) Fig. 8.5. Electron energy distribution functions for diﬀerent times within a pulse in (a) the ‘on’ phase and (b) the ‘oﬀ’ phase for a 20 kHz discharge with 50% duty cycle. Times refer to the beginning of the ‘on’ phase at 0 μs (from [34])

The subsequent drop in the density before the stationary state is a consequence of the power supply behaviour which is diﬀerent to that of Bradley et al. [26, 28]: the target voltage waveform exhibits a strong initial overshoot (see Fig. 8.8a) whereas the one used by Bradley et al. has an almost rectangular form (see Fig. 8.8b). The relaxation of the target voltage also leads to much reduced ionisation in the discharge volume. A two-dimensional survey of the discharge cross section has conﬁrmed this picture [43]. The ﬁrst maximum was found primarily in the middle of the discharge (see Fig. 8.9) because in the initial stage of the ‘on’ phase electrons can

8 Process Diagnostics

263

12

z = 2 cm z = 4 cm z = 6 cm z = 8 cm z = 10 cm z = 12 cm

10

Te (eV)

8

6

4

2

0 0

100

200

300

400

500

Time (μs)

Fig. 8.6. Electron temperatures at diﬀerent heights above the racetrack in a 2 kHz discharge with 50% duty cycle. The ﬁgure starts with the ‘oﬀ’ phase at 0 μs and shows two groups of diﬀerently hot electrons during the whole ‘on’ phase with especially the hot group peaking at the start of the ‘on’ phase (from [31])

Charge Carrier Density [1010 cm-3]

10

on

off

8 6

C

A

D

E

B

4 2 0 10 8 6 4 2 0 0

1

2

3 Time [µs]

4

5

Fig. 8.7. Temporal evolution of the charge carrier density in a reactive 200 kHz discharge for diﬀerent Ar/O2 mixtures and a duty cycle of 60%. The timescale starts with the ‘oﬀ’ phase. The traces show two density peaks (A, C) at the beginning of the ‘on’ phase (2 μs) with their intensity depending on the gas mixture F(O2 )/(F(Ar) + F(O2 )) of (top) 44% and (bottom) 9% (from [38])

Ud / V

264

J.W. Bradley and T. Welzel 200 100 0

−100

V ~ 110 V V ~ 21 V

time / µs

0 1 2 3 4 5 6 7 8 9 10 11

−200

V ~ −175 V

−300 −400 −500

V ~ −540 V

−600

Fig. 8.8. Target voltage waveforms for a pulsed magnetron discharge driven by a standard Pinnacle Plus (left) and a modiﬁed Pinnacle Plus (right) (both Advanced Energy Inc.) unit. The rectangular one was obtained for a Ti target in argon, the overshooting one with a Mg target in Ar/O2 but the waveforms are rather due to the power supply than due to the operating conditions. The marks given by Bradley et al. (right) are ‘A’ for the ‘on’ phase, ‘B’ for the stable ‘oﬀ’ phase and ‘C’ for the overshoot in the ‘oﬀ’ phase (after [26])

10

Axial Position z [mm]

n [10 40

>12 10 8 6 4 2 <1

30 20 10 −60

−40

−20 0 20 40 Radial Position x [mm]

60

n [1010 cm−3]

50

cm−3] Axial Position z [mm]

50

>60 50 40 35 30 20 10 <5

40 30 20 10 −60

−40

−20 0 20 40 Radial Position x [mm]

60

Fig. 8.9. Spatial distribution of the charge carrier density measured with a double probe. The ﬁrst density maximum (left, 0.4 μs after the start of the ‘on’ phase) is dominant in the discharge centre, the second (right, 1.0 μs after the start of the ‘on’ phase) in the torus but spreading out due to collisions. Axial distance of 0 mm corresponds to the target. Note the diﬀerent scale to display the maximum intensity (from [43])

not gain enough energy close to the cathode to ionise the working gas because the target voltage is still too low. The secondary electrons start directly from the cathode and gain most of their energy within the developed sheath with increase target voltage. Thus, the ionisation resulting in the second density maximum is more concentrated to the target and the magnetic trap. Electrons escaping the trap by collisions cause further ionisation outside it yielding a generally higher density than for the ﬁrst maximum. At ﬁxed geometry and pulse parameters but altered varying gas mixtures and gas pressure in reactive mode, double probe investigations have also

4

C

n I750.4 nm

16

3

12 2

A

8

D

1

4

0 0 −1 −2

0

0 −300 −600 0

1

2

3 4 Time t' [µs]

5

Intensity [104 cts.]

20

265

Discharge Current [A]

Target Voltage [ V ]

Charge Carrier Density [1010 cm−3]

8 Process Diagnostics

6

Fig. 8.10. Temporal development of the charge carrier density measured with a double probe and the emission intensity of the 750.4 nm argon line in reactive mode. The discharge was operated at 150 kHz with 60% duty cycle using an Mg target in 10 sccm O2 + 50 sccm Ar (from [42])

been performed. It has turned out that both external parameters have significant inﬂuence on the plasma density development during the ‘on’ phase. The build-up of the discharge is accelerated for higher pressures due to enhanced collisions [40]. Changing the gas from pure argon to an argon/oxygen mixture with an Mg target this is even more pronounced with a sudden change between two discharge modes [42] (see Figs. 8.10 and 8.11). MgO has a very high secondary electron emission coeﬃcient γ, much higher than that of Mg, as reported by Depla et al. [44] for magnetron sputtering in Ar and Ar/O2 gas. Consequently, in reactive mode, the electron emission resulting in the second density maximum described above is strongly enhanced and the discharge develops faster. The changes are not as pronounced when a Ti target is used as the γ coeﬃcients of Ti and TiOx are much closer. Changes between reactive and metal mode with an Al target have also been attributed to the γ coeﬃcient [27] while no signiﬁcant changes in the speed of the development were observed (see Fig. 8.4). As it has turned out the changes in the plasma impedance also aﬀect the output of the power supply resulting in a very complex behaviour of such pulsed magnetron discharges [40, 42]. It seems therefore likely that changes in the discharge geometry or the wall conditions may have a similar inﬂuence. This has been shown by Swindells et al. [45] who used a single probe, changed the position and potential of the substrate holder, and observed about a doubling of ne in the ‘on’ phase for a ﬂoating substrate holder compared to a grounded one.

J.W. Bradley and T. Welzel 2.0

C

n I750.4 nm

9

1.5

6

1.0 B

A

3

0.5 0.0

0

0 −1 0 −300 −600 0

1

2

3 4 Time t⬘ [µs]

5

6

Intensity [104 cts.]

12

Discharge Current [A]

Target Voltage [V]

Charge Carrier Density [1010 cm−3]

266

7

Fig. 8.11. Temporal development of the charge carrier density measured with a double probe and the emission intensity of the 750.4 nm argon line in metal mode. The discharge was operated at 150 kHz with 60% duty cycle using an Mg target in 50 sccm Ar (from [42])

Single probes have been frequently applied to study the ‘decay’ of the plasma in the pulse ‘oﬀ’ or ‘reverse’ phase. These studies show that it would be too simple to just describe the behaviour by a passive switch-oﬀ in many cases. This has been shown by Bradley et al. [28] who found – additional to the peak in Te in the ‘on’ phase described above – a second peak of very high electron temperatures up to 30 eV just after the target voltage was reversed to positive values, i.e. the discharge was switched ‘oﬀ’. At the same moment the electron density starts to drop. Swindells et al. [45] have shown that this Te peak is strongly dependent on the substrate position and potential (see Fig. 8.12). Karkari et al. [46] could correlate it by time-resolved mass spectrometry (see Sect. 8.3) to the occurrence of high-energetic ions. Plasma potential measurements (see below) could ﬁnally prove that this Te peak results from a second burst of high-energetic electrons, which at the ‘on’-‘oﬀ’ transition originate from an advancing substrate sheath [45]. In the rest of the ‘oﬀ’ phase, ne and Te decay, however, not modelled by a single exponential but with a more complex behaviour. Due to a variety of diﬀerent experimental set-ups it is diﬃcult to obtain a consistent picture. Nevertheless, several groups report an exponential decay of the plasma density or the target current with typical decay times of several 10 μs [3, 27, 28, 31, 33, 47–49]. In addition, very rapid density or current decays were observed with time constants of about 1 μs [3, 25, 27, 33, 41, 42, 47].

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267

9 8 7

Teff [eV]

6 5 4 3 2 1 0

0

2

4

6

8

10

Time [μs]

Fig. 8.12. Temporal development of the eﬀective electron temperature in a 100 kHz discharge with 60% duty cycle for diﬀerent positions and diﬀerent potentials of the substrate holder: without substrate (squares), with ﬂoating substrate (circles), with grounded substrate (triangles). The position of the substrate holder and the single probe were 125 and 90 mm, respectively (from [45])

Bradley and B¨acker studied pulsed discharges with comparatively long ‘oﬀ’ times and were able to detect additional long decay times of more than 100 μs [31, 50]. As mentioned above, two-temperature EEDFs were observed during the ‘on’ phase. The initial very fast decay of about 1 μs is therefore attributed to the loss of the high-temperature part of the electron population due to the sudden disappearance of the accelerating cathode voltage sheath when the target voltage is switched ‘oﬀ’ or reversed [3, 33, 47]. The cold electrons subsequently decay on a longer timescale of several 10 μs which thought to be given by ambipolar diﬀusion and the ion transport through the sheaths at the electrodes and walls [31, 33, 47, 50]. Finally, the very long decay is believed to be a consequence of the complex magnetic ﬁeld in a magnetron discharge which traps slow electrons and results in a signiﬁcant charge carrier density at re-ignition even for long ‘oﬀ’ phases [31, 50, 51]. Spatially resolved investigations revealed that the decay is faster close to the cathode and quite slow in the discharge centre close to the magnetic null where electrons are conﬁned eﬀectively. In this region, the decay rate was about 300 μs and prior decay times of a few 10 μs were not observed at all [31, 51]. Additionally, within the ﬁrst ∼70 μs of the ‘oﬀ’ phase a weak density peak has been observed moving away from the cathode with about the ion acoustic speed which is attributed to a damped ion acoustic wave [31, 51].

268

J.W. Bradley and T. Welzel 'overshoot' 400 300

stable 'reverse' time

200

stable 'on' time

Potential (V)

100 0 −100 −550

−600 −650 −700

discharge voltage

−750 −0.5 0.0 0.5 1.0 1.5 4 5 Time (μs)

6

7

8

9

10

Fig. 8.13. Target potential (solid line) and plasma potential (dotted line) and plasma potential distribution in dependence on the time within one pulse in an asymmetric bipolar 100 kHz discharge with 50% duty cycle. The plasma potential follows closely the positive target potential in the ‘oﬀ’ phase and stays close to ground in the ‘on’ phase (from [54, 55])

The temporal evolution of the plasma potential in pulsed magnetron discharges has been studied by means of emissive probes using the ﬂoating-point method [52–55]. This technique allowed a direct and precise determination with a better energy- and time resolution. The latter is determined by the sheath impedance and the stray capacitance to ground. Karkari et al. [53] give an estimate of the time resolution of 20 ns or better. The potential resolution is in the range of 1 V for quiescent voltage phases and kTe /e in transient phases [52, 55]. All reported measurements were done in an asymmetric bipolar-pulsed magnetron discharge where the target voltage in the ‘oﬀ’ phase is slightly positive (about 10% that of the ‘on’ phase). A particular characteristic of the power supply used is a sharp and high (up to several 100 V) positive overshoot just when the target voltage is switched from negative to positive values (‘on’ to ‘oﬀ’, see Fig. 8.1). The emissive probe measurements show that the plasma potential reacts immediately to changes in the target voltage [52, 54, 55] (see Fig. 8.13). As soon as the target voltage starts going negative at the beginning of the ‘on’ phase, the plasma potential decreases to values close to ground and is only marginally inﬂuenced by subsequent temporal changes in the highly negative target potential [53]. Close to the substrate, the plasma potential was found to be a few volts above ground, but negative in the target region. Across the discharge, there is a signiﬁcant potential drop between the bulk plasma and the cathode sheath. Karkari et al. [54] give a value of the resulting electric ﬁeld pointing towards the target of about 400 V m−1 . The situation in the stable ‘on’ phase is observed to be the same as for a DC magnetron discharge. As soon as the target voltage is reversed to positive values, the plasma potential is lifted within less than the probe resolution of 20 ns to positive values. During the quiescent part of the pulse ‘oﬀ’ phase it remains a few

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volts above the potential of the most positive electrode, which in this case is the target. The variation of the plasma potential along the axis is weak in this phase and the electric ﬁeld collapses in the reverse phase. Consequently, the E × B drift along the magnetron torus is interrupted. Interestingly, the plasma potential also follows the very high positive target potential directly at the beginning of the ‘oﬀ’ phase. Bradley et al. [55] and Vetushka et al. [54] report values of Vp over +376 V at a distance of 10 mm from the target while the target voltage itself is only about +250 V during the ‘overshoot’ [55]. Even close to the substrate values of +290 V for Vp were measured. The electric ﬁeld will therefore be reversed during the short period of the ‘overshoot’ before it collapses in the quiescent ‘oﬀ’ phase. The high potentials have signiﬁcant consequences on the understanding of the origin of the high-electron temperature measured during this time as well as for ﬁlm deposition. Especially when the substrate is held at a ﬁxed potential (e.g. ground), a positive space-charge sheath will be formed in front of the substrate and electrons are accelerated away from it into the bulk plasma. Considering a plasma potential of about +300 V and a grounded substrate holder, these electrons may exhibit initial energies of up to 300 eV. The Te peak (cf. Figs. 8.3 and 8.12) observed by Bradley [28] and Swindells [45] in such an asymmetric bipolar discharge is therefore not unlikely. It also explains why Te is raised more signiﬁcantly with the substrate holder at ground potential than in the ﬂoating case. With the grounded substrate, electrons with as much as 300 eV may be produced whereas the ﬂoating substrate holder will more or less follow the rapid changes in the plasma potential and the electron energies will be much lower. On the other hand, ions created during the phase of the high plasma potential in the substrate region will be accelerated towards any surface at ﬁxed potential. Surfaces at ground potential, e.g. the walls surrounding the discharge will thus be subject to an ion bombardment with ion energies reaching 300 eV which causes sputtering of the surface and may lead to impurities in the process. A two-dimensional study of the plasma potential by emissive probes in the same discharge published by Vetushka et al. [52, 54] conﬁrmed the results and showed good agreement with the values obtained with a single probe. Throughout the whole discharge volume, the plasma potential is lifted to values above the target potential during the overshoot and the stable ‘oﬀ’ phase, most positive values during the overshoot are reached above the racetrack. During the ‘on’ phase, most negative values were found close to the racetrack with the electric ﬁeld being opposite to that during the ‘overshoot’. Within the bulk plasma the plasma potential is lifted to more positive values than the most positive electrode in the system at any time. Signiﬁcant radial ﬁeld components are observed in both stages in the magnetron torus.

270

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8.3 Mass Spectrometry In reactive magnetron sputtering, DC conditions can in some cases be used, however when in pulsed mode, the nature of the driving voltage waveform will dictate the nature of the time-evolution of the plasma potential throughout the plasma bulk, and therefore the potential at which ions are created [53]. In general, it has been established that the plasma potential remains close to or a few volts above the most positive surface in the system, irrespective of the nature of the waveform, i.e. unipolar or bipolar asymmetric or symmetric. The plasma potential, which may have a spatial structure, follows the driving waveform, keeping up with it, since the plasma potential can vary on a timescale of the electron plasma frequency (∼100 MHz) [53]. Ions will be accelerated out of the plasma through the sheaths to surfaces gaining energy equal to the diﬀerence between the plasma and the surface potentials. Therefore as the plasma potential varies in time, this energy may also vary. Ions can bombard such surfaces with energy up to the maximum sheath voltage drop provided the ions have enough time to cross the sheath, before the plasma potential changes again. An electrically ﬂoating surface will also follow the plasma potential, with the sheath voltage typically several electron temperatures (kTe /e – measured in eV) below the plasma potential. The potential drop between the substrate and plasma through which ions can gain the maximum energy eVs is given by Vs = Vp − Vsub ,

(8.1)

where Vp is the local plasma potential and Vsub is the substrate (ﬁlm) potential. In the bipolar mode where Vp may attain high positive values for periods long enough for ions to cross the sheath, then for ﬁxed bias substrates with conducting ﬁlms Vs may be substantial. However, for electrically isolated ﬁlms and substrates kTe Meﬀ 1 + ln Vp − Vsub = , (8.2) 2e 2πme where Te is the instantaneous eﬀective electron temperature and Meﬀ is the eﬀective ionic mass. This relationship is slightly altered (down) if a high proportion of negative ions are in the plasma. For an idealised argon plasma, Vp − Vsub ≈ 5.2kTe/e, which is typically 15–20 V in the magnetron at the substrate position and the ﬁlm bias and plasma potential ride together maintaining a small potential diﬀerence. Plasma mass spectrometry has been used to good eﬀect in a number of reactive magnetron systems to determine the arriving ion energies both time averaged and time resolved through the pulse cycle. 8.3.1 Mass Spectrometry Technique Plasma mass spectrometry is a well-developed technique that provides information on the identity of the neutral and charged species present in a

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discharge, and an indication of their relative ﬂux to a material surface or substrate. There are many excellent and detailed reviews of this technique as applied to plasma discharges, for instance Zeuner [56] and Jarvis et al. [57]. Here we highlight how mass spectrometry is used in the areas of reactive sputtering to gain information on neutral and ionic plasma species. In particular, energy and time-resolved measurements of the particles at the substrate are discussed. This information can be valuable in terms of understanding the plasma physical and chemical processes. The instrument commonly used in many plasma research laboratories and in some industrial situations to examine processing plasma environments is the quadrupole type mass spectrometer [58]. In basic terms mass spectrometry provides information on the types of species that exist in a plasma that are capable of reaching the instrument and the relative ﬂuxes of those species. The spectrometer is used to sample ions or neutral species from the plasma process chamber and allows them to ﬂow in to several analysis stages (i.e. energy and mass discrimination). However, to guide and accelerate the particles through the system must they be charged, i.e. ionic. This means neutral species entering the spectrometer need to be ionised before the analysis stage. This is done in an ionisation source, usually an electron impact ionisation source (see, e.g. [59]) situated close to the sampling oriﬁce. However, to analyse only plasma in the absence of neutrals the ionisation source is switched oﬀ. The ionised particles are then extracted from this source by an ion optical system consisting of electrically biased lenses and then mass analysed. A typical mass ﬁlter is the quadrupole mass ﬁlter (ﬁrst employed by Paul and Steinwedel [60]). The analysis is usually done by correlating the ﬁltered masses (mass-to-charge ratio, M/z) to the intensity of the ion counts recorded at a suitable detector. The mass-selected ions are detected typically using a Faraday cup or a Channeltron multiplier. In some cases, there will be an energy analyser situated between the quadrupole and the ionisation source, and the instrument therefore provides both energy and mass discrimination. 8.3.2 Application of Mass Spectrometry to Reactive Sputtering The typical laboratory set-up for reactive magnetron sputtering experiments is shown in Fig. 8.14, with mass spectrometer facing the target and sometimes being part of the substrate either electrically ﬂoating or grounded. Reactive sputtering can take place with many types of excitation, e.g. DC, RF, Pulsed DC and AC. Some examples of the use of DC sputtering with mass spectroscopic diagnostics are given in the work of Synders et al. [61] who found a correlation between the discharge composition and the binding energy of the bond M−O in the compound MOx . Snyders et al. [62] also studied three reactive systems: Sn−Ar/O2 , Ti−Ar/O2 and Ag−Ar/O2 in DC sputtering and used an RF coil to inﬂuence the chemical composition of both the discharge and the ﬁlms. Using the RF coil, the fully oxidised ﬁlms are reached at lower reactive gas ﬂow and consequently at higher deposition rate.

J.W. Bradley and T. Welzel

I-V

Computer

U/I/T

Energy Spectra

272

Pulsed DC Supply U

Oscilloscope I Acquisition Unit

TD

Trigger/ Time Delay

T

EQP

Center Line End Cap with Grid Probe Tip

Fig. 8.14. Diagram of the experimental rig, showing the relative positions of the magnetron, mass spectrometer barrel and end cap and Langmuir probe stem (from [29])

In a rather diﬀerent application, but using energy-resolved mass spectroscopic techniques, N2 /Ar gas mixtures, were used in an unbalanced DC magnetron with a graphite target to obtain the IEDFs of C+ , CN+ and C2 N+ 2. Since the energies of C2 N2 were low (no tail), it was assumed that they were not sputtered. Besides C and N atoms and ions, other species, like preformed Cx Ny particles, play an important role during growth of fullerene-like carbon nitride (CNx ) thin ﬁlms [63]. Titanium oxynitride thin ﬁlms were deposited by DC reactive magnetron sputtering from titanium metallic target and from oxygen and nitrogen as reactive gases. It was shown that mass spectrometry used to help control the technique [64]. In other DC reactive magnetron sputtering applications, energy-resolved mass spectrometry was used to get the energy distributions of positive and negative ions impinging on the surface of a growing TiO2 ﬁlm as a function of the total pressure [65]. It has been shown by Petrov et al. [66] using in situ double-modulation mass spectrometry during deposition of TiN by DC reactive magnetron sputtering from a Ti target in mixed Ar + N2 discharges that incident Ar+ and N+ 2 ion ﬂuxes are highly monoenergetic with energies corresponding to the applied negative substrate bias with respect to the plasma potential. However, the energy distributions of incident Ti+ and N+ ions are extended due to the high-energy tails in their sputter-ejection energy distributions. The primary sputter-ejected particles are Ti and N atoms. TiN, TiN+ and Ti+ do not contribute signiﬁcantly to ﬁlm growth kinetics. (DC and RF) reactive magnetron sputtering from an Fe target in Ar− H2 S atmospheres was used to deposit thin pyrite (FeS2 ) ﬁlms for solar cells

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applications [67]. A quadrupole mass spectrometer in combination with an electrostatic energy analyser was used to measure the species arriving at the substrate and their respective energies. The sulphur chemistry produces a large variety of sulphur–hydrogen species Sx Hy with x up to 11 and y = 0–5. From the energy distributions the plasma potential was determined for diﬀerent discharge powers, total pressures and H2 S to Ar ratios. The addition of H2 S to the discharge atmosphere reduces the eﬀective ion energy by about a factor of 2. The metal ions which originate from sputtered atoms from the Fe target display a high energy shoulder at pressures below 1 × 10−2 mbar, at higher pressures the thermalisation of the sputter metal ions is visible from the strong decrease in this shoulder. Energy-resolved mass spectrometry in conjunction with probe measurements has also been used in RF sputtering and deposition of carbon nitride. Ionic species and their ﬂuxes on the substrate for various discharge conditions were determined. With increasing energy ﬂux of the ion bombardment, the overall [N]/[C] ratio of the ﬁlms decreases [68, 69]. As well as RF sputtering, other, novel sputter techniques have also been utilised to generate reactive plasmas for ﬁlm deposition: for instance, by electron beam generation in the synthesis of TiN ﬁlms [70], with the plasma diagnosed by mass spectrometry. From the IEDFs we can gain knowledge of the sputtering process and particle–sheath interactions at the target. Detailed investigations into the form of the IEDFs in reactive sputtering have been carried out by Misina and co-workers [71, 72] in the DC magnetron for TiN and TiWN ﬁlm deposition. It was found that the energy spectra of ions at low pressures were characterised by extended high-energy tails. The high energy of sputtered metal atoms follows from their distribution at the cathode after being sputtered. The high-energy gas ions Ar+ , N2 + , N+ (see Fig. 8.15) stem from two 2 sources; transfer of energy in the collisions with the sputtered metal atoms and the

p=0.1 Pa, Ud =450 V

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Ion energy (eV)

Fig. 8.15. Ion energy distribution of the gaseous species during sputtering of WTi target in a mixture of argon and nitrogen at the total pressure of (a) 0.1 Pa and (b) 1 Pa (from [71])

274

J.W. Bradley and T. Welzel 107

Integral Intensity (arb. units)

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4

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CH4 flow (sccm) Fig. 8.16. Integrated intensity of positive ions as a function of methane ﬂow for total pressure of 0.1 Pa (from [72])

reﬂection of the energetic ions from heavy elements in the target. A strong reduction of the ion energy at the substrate was found when the pressure was increased from 0.5 to 10 Pa. The work was backed up by TRIM Monte Carlo simulations. As well as the IEDFs the relative contributions of various species are important to understand the reactive process. This is shown in [72] where Ti–C:H ﬁlms were deposited at various methane ﬂows (see Fig. 8.16) as the methane ﬂow rate is varied. It has been common in recent years to use the pulse technique to reduce target arcing events in reactive deposition of materials, and mass spectrometry has been applied to these pulsed systems. Muratore et al. [73] used a quadrupole plasma mass spectrometer to measure the time-averaged ion energy distribution functions (IEDFs) of argon, oxygen and titanium species at electrodes immersed in a 60 kHz pulsed magnetron discharge, during the deposition of titanium oxide thin ﬁlms. The substrate was electrically grounded. It was found that the time-averaged IEDFs correlate well to the time-resolved target voltage waveforms. That is ions can be seen in the IEDF at energies corresponding to the high positive potentials in the reverse time of the pulse (see Fig. 8.17). This trend can be seen also in the oxygen ions with 6 μs reverse time (see Fig. 8.18). It should be noted as explained above, with instruments such as the 45◦ energy analyser on the quadrupole instrument the energy in the IEDF is actually an eﬀective stopping potential and not the absolute ion energy. It tells us approximately the potential at which the ion was created given collision-less conditions between creation and detection points. For this reason it may be possible to detect ions at negative apparent energies.

8 Process Diagnostics (c) (b) 200

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Fig. 8.17. Target voltage waveforms and argon IEDFs are shown for the (b) 60 kHz pulsed discharge with 6 μs reverse time and (c) 60 kHz pulsed discharge with 1 μs reverse time (from [73]) (a)

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Fig. 8.18. IEDFs measured with an EQP in a 60 kHz pulsed discharge with a 6 μs reverse time for singly charged (a) argon ions, (b) titanium ions, (c) atomic oxygen ions and (d) molecular oxygen ions (from [73])

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It was found that at a ﬂoating surface the diﬀerence between the ﬂoating potential and the plasma potential was a few volts giving an eﬀective electron temperature of approximately 2.5–3.0 eV, even at the ‘positive spike’ on the cathode voltage waveform observed during pulsing. If the substrate is electrically grounded, then the ions created at high positive potentials in the reverse time are detected with energy given by the plasma potential. This may be many hundreds of volts, depending on the magnitude of the positive overshoot in the driving waveform. For unipolar driving this may be close to zero, a few volts above zero. This is described in detail in [29] where in an asymmetric bipolar-pulsed DC magnetron time-averaged IEDFs of Ar+ and Ti+ were measured. In agreement with Muratore et al. [73], low-energy ions are generated in the ‘on’ phase when the plasma potential is typically a few volts above ground. The Ti+ energy spectra show a remnant of the original sputter-neutral energy distribution function. The mid-range ions are produced in the quiescent region of the voltage reverse phase, when the plasma potential is raised globally a few volts above the cathode potential, typically 10–30 V. The high-energy ions are generated in a period of 0.3 μs, during the discharge voltage overshoot, when the target potential rises to typically over +140 V (see Fig. 8.19). It was found from quantitative studies using ion ﬂuxes from time–resolved Langmuir probes that at the higher pulse frequencies, e.g. 350 kHz, these ‘fast’ ions make up to about a quarter of the total ion ﬂux at the substrate and an upper bound transient power ﬂux of about 2.5 times the maximum delivered in the ‘on’ phase [29]. The total power ﬂux to a substrate in the sustained phase of the discharge is found to increase with frequency and reverse time. A study of the eﬀect of pulse frequency on IEDFs (of N+ , N2 + , Ar+ , Ti+ ) in a TiN deposition process by reactive pulsed magnetron sputtering has been undertaken using quadrupole mass spectrometry by Kim et al. [74]. The

DC 100 kHz, 0.4 μs 100 kHz, 2.0 μs 100 kHz, 4.5 μs 350 kHz, 1.4 μs

counts per second

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104 C 103

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40 60 energy/V

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Fig. 8.19. Ar+ energy spectra (IEDF) for the cases: 100 kHz at 0.4, 2.0 and 4.5 μs reverse time and 350 kHz at 1.4 μs reverse time (left) and Ti+ energy spectra (IEDF) for the cases: 100 kHz at 0.4, 2.0 and 4.5 μs reverse time and 350 kHz at 1.4 μs reverse time (right) (from [29])

8 Process Diagnostics (a)

(b) 107

7

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106

Intensity (cts / s)

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Intensity (cts / s)

277

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N N2+ Ar+ Ti+

6

Intensity (cts/s)

10

105 104 103 102 −20 −15 −10 −5

0

5

10 15 20 25 30

lon energy / eV

Fig. 8.20. Ion energy distribution functions (IEDFs) as a function of pulse frequency; pAr = 3 mTorr; pN2 = 0.2 mTorr; Id = 600 mA, and pulse frequency (a) 10 kHz; (b) 30 kHz; (c) 50 kHz at a duty cycle 50% (from [74])

magnetron was unipolar pulsed with zero reverse voltage. This has a major eﬀect on the IEDFs as can be seen in Fig. 8.20 which have no tail extending to high energy. Ions at negative energies in Fig. 8.20 reﬂect the potential at which they were created in the system. The IEDF of Ti diﬀers from that of the gas species in that it extends to high energies reﬂecting the fact that the neutral titanium from which it was created has a sputter energy distribution. Detailed time-averaged studies of the form of the IEDF have been made by Moiseev et al. [75, 76] in an opposed target (Penning type) magnetron with B ﬁeld running parallel to E. The source was operated at 50 kHz, pulse widths between 496 and 8,016 ns, and constant current run of 2 A, at 0.4 Pa Ar gas pressure. The energy and ﬂux of the ions arriving at the substrate are measured at diﬀerent times during the pulse cycle. As the pulse ‘oﬀ’ period is extended, there are large increases in ion energy and ion ﬂux (see Fig. 8.21). The current and voltage pulse characteristics are shown in Fig. 8.22. The

278

J.W. Bradley and T. Welzel Pulse of period 8016 ns 6016 ns 4016 ns 3056 ns 2056 ns 1056 ns

1.E+07

Ar lon flux (s−1)

1.E+06

1.E+05

1.E+04

1.E+03

1.E+02 0

20

40

60

80

100

lon energy (eV)

Fig. 8.21. Total Ar+ ion counts in mass spectrometer as a function of energy. Frequency = 50 kHz, pressure = 53 × 10−3 mbar, target current = 2 A (from [76])

Fig. 8.22. Current and voltage pulse characteristics. Frequency = 50 kHz, average current = 2 A, pulse ‘oﬀ’ time = 2, 016 ns, pressure = 53 × 10−3 mbar (from [76])

initial overshoots in the target voltage cause a rapid expansion of the plasma sheath at the analyser extractor oriﬁce and wide variations in plasma potential leading to an initial pulse of high-energy ions during the ﬁrst 500 ns. Time-resolved measurements of the IEDFs in the pulsed magnetron both operating in reactive and non-reactive mode have been carried out by the team of Bradley in Liverpool. This was done using a method of ion gating

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Fig. 8.23. The experimental set-up: (a) grid assembly inside of the end cap of the mass spectrometer, (b) the signal diagram showing schematically the cathode potential (Uc ), the grid potential (Ug ) and the detector voltage (Ude ) (from [77])

Fig. 8.24. The time-resolved IEDFs obtained with 1 μs time resolution on the pulsed magnetron at diﬀerent parts of the pulse cycle (from [77])

in a specially made end cap ﬁtted to the spectrometer barrel [55]. A time resolution of 4 μs could be achieved. It was seen that the high-energy peaks correlate with the target voltage overshoot as well as the medium energy with the reverse phase and low energy with the ‘on’ time. The ‘on’ phase IEDF is indistinguishable from that in a DC plasma for both Ar and sputtered material (Ti). Recently, an improved version of the measurement technique with a much better time resolution was developed [77]: Fig. 8.23a shows the set-up and Fig. 8.23b a potential schematic of the gating system. The corresponding real waveform of the target voltage is the same as in Fig. 8.1. The obtained waveforms of the measured time-resolved IEDFs are shown in Fig. 8.24. Time-resolved IEDFs were obtained with 1 μs time resolution, and these revealed large variations in the form and width of the ion energy spectra at diﬀerent times during the discharge cycle, governed by the temporal evolution of the plasma potential.

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Voltage Delay (μs) 10

Intensity (104 count / s)

20

9 8

15

7 6

10

5 4 3

5

2 5x

1 5x

0 20

40

60 80 100 Energy (eV)

120

0 140

Fig. 8.25. Ar+ ion energy distribution for the gating delays from 0 to 10 μs and the eﬀective gating width of 1 μs. The distributions were obtained by diﬀerentiation of the subsequent measurements with the gating width of 20 μs and the delay incremented by 1 μs (from [78])

The results conﬁrm and improve upon time-resolved IEDF measurements made in the same system previously [78] (20–100 kHz) operated in argon, argon/oxygen and argon/helium mixtures. These results showed that a significant fraction of the ions (both gas and sputtered-ionised atoms) have energies >150 eV and are generated at the beginning of the ‘oﬀ’ phase in a duration of typically <1 μs. However, time resolution was obtained using a gating delay of the detector (with time resolution 20 μs) rather than the ions entering the instrument and a mathematical process was subsequently employed to produce IEDFs every 1 μs. These results are shown in Fig. 8.25. The results discussed so far have been focussed on positive ions. However, in reactive plasmas containing electronegative gases such as oxygen, ﬂuorine or hydrocarbons, negative ion concentrations may also become considerable. However, despite some interesting studies using mass spectrometry there is to date little data on their densities. Misina et al. [78] measured the energy distribution of O− and O2 − negative ions (time averaged) in reactive magnetron sputtering, and demonstrated that the surface oxygen concentration at the target is decreasing during the ‘on’ period in the metal mode while it is constant in the oxide mode. Importantly O− and O2 − ions were detected with energies up to nearly the cathode fall potential equivalent value, that is, over 450 eV. These have been created at the cathode in the form of TiO2 which is dissociated and accelerated across the cathode fall to the mass spectrometer, however details of the IEDFs showed that there is about 25 V drop of the voltage on the oxide layer in the oxide mode. This can be seen in Fig. 8.26. The features in the IEDFs at intermediate

8 Process Diagnostics

281

Intensity (count / s)

104

P2 103

P1 O−

102 O2−

101 0

100

200 300 Energy (eV)

400

500

Fig. 8.26. Energy distribution of O− (m/q = 16 amu) and O2 − (32 amu) negative ions for an oxygen ﬂow of 2 sccm in the oxide mode. The pressure was 4 mTorr, Pdc = 300 W, frequency = 20 kHz, trev = 10 μs (from [78])

energy can be correlated directly with the form of the driving bipolar discharge voltage. These ﬁndings are important for understanding plasma energetics and growth involving electronegative species. Low-, medium- and high-energy O− ion populations were experimentally detected by Mr´ az and Schneider [79] in some very good work, during magnetron sputtering of Al in an Ar/O2 atmosphere, where the target was covered with an oxide layer. In Fig. 8.27 the distribution of O− ions is shown together with theoretical predictions based on collisionless plasma dynamics. In agreement with [78] and based on model calculations, the authors propose that non-sputtered O− ions originating from the target surface are accelerated in the cathode fall. The authors argue that high-energy O− ions are not sputtered but may be generated at the cathode surface through desorption of O− or O followed by electron attachment and subsequent acceleration over the cathode fall. Medium-energy O− ions on the other hand may be formed through sputtering of AlO and AlO2 clusters, with acceleration over the cathode fall and subsequent dissociation. Since these ions can bombard the growing ﬁlm with high energy even to electrically ﬂoating substrates (unlike positive ions which only strike the substrate with high energy if the surface has a ﬁxed bias and is not ﬂoating), the negative ions may have a key role in the amount of energy/power that is deposited into the ﬁlm and hence the growth processes. This was investigated by Mr´az and Schneider in the reactive sputtering for the growth of transition metal oxide thin ﬁlms [80] where the energy distributions of O− ions of magnetron sputtered Nb, Ta, Zr and Hf in an Ar/O2

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Fig. 8.27. (a) Measured IEDF of O− ions (solid line) and target potential distribution (open square). The distribution ﬁts the measured high-energy O− ions well. (b) Measured IEDF of O− ions (solid line) and theoretical distribution function for medium-energy O− ions (ﬁlled square) (from [79])

atmosphere were measured as a function of the oxygen partial pressure. Again as in [78] three ion populations were detected in the plasma: high-, mediumand low-energy ions, with energies corresponding to the target potential, half of the target potential, and 150 eV, respectively. It was deduced that large ﬂuxes of medium- and high-energy O− ions comparable to the ﬂuxes of the low-energy O− ions enable formation of crystalline transition metal oxide thin ﬁlms during low temperature growth. Similar results were obtained in a recent work by Mahieu and Depla [81] who investigated the IEDFs of O− ions in reactive sputtering of 13 diﬀerent metals. As Mr´ az and Schneider they found the two high-energy peaks being equivalent to the target potential and half its value and a low contribution for the materials investigated. The results further revealed that the production of O− at the target scales with the secondary electron emission coeﬃcient γ [81]. Energetic negative ions of O2 − and O− were also observed using timeof-ﬂight mass spectrometry during indium tin oxide (ITO) preparation by sputtering an ITO target in Ar in a DC magnetron [82]. The authors also detected reﬂected Ar atoms and O3 − however at less relative ﬂux than O− and O atoms. It has been noted that negative ions may greatly aﬀect the ion-assisted deposition process of oxides at the substrate. For instance, in the magnetron, energetic re-sputtering of the ﬁlm by high-energy negative ions from the cathode can occur and this phenomenon is highlighted as being particularly important in ITO [82] and transparent conductive oxide (TCO) fabrication [83].

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Intensity (arb units)

1500

1000

500

0 0

200

400 600 Energy (eV)

800

Fig. 8.28. The IEDF of O− in DC conditions. Two peaks in the IEDF of O− were observed in spectra at ∼40 and 430 eV

In recent work at Liverpool negative ion spectra have been obtained in the sputtering of a titanium target in mixtures of argon and oxygen for both DC and bipolar pulsing. Only O− was observed, with no other negative species recorded (i.e. no O2 − ). In DC mode two peaks in the IEDF of O− were observed in spectra at ∼40 and 430 eV (see Fig. 8.28). The maximum ion energy recorded was at 500 eV. The high-energy group is from the cathode, while the low is from ions created in the plasma bulk. When the system is pulsed with 200 kHz and 50% duty cycle, the characteristic three peaks are again detected. The IEDF has a low-energy peak at ∼26 eV, a broad “hump” at ∼400 eV and a high-energy tail extending to ∼840 eV (see Fig. 8.29). The two peaks above 300 eV can be related to the cathode voltage waveform, which contains a negative overshoot of −760 V and reaches a potential of −414 V at the end of pulse ‘on’ phase. Both the DC and 200 kHz O− IEDFs contain ions with energies greater than that that could be provided by the cathode potential alone. This difference was also observed by Mr´ az et al. [80]. They attribute the additional energy to the sputtered energy distribution of O− as it leaves the cathode. This ﬁts with the observation of fast sputtered species generated even in DC conditions in the tail of the IEDF in the works of Misina et al. [71, 72]. In DC reactive magnetron sputtering energy-resolved mass spectrometry was used to get the energy distributions of positive and negative ions impinging on the surface of a growing TiO2 ﬁlm as a function of the total pressure. The low-energy peak (close to 1 eV) of thermalised particles and the highenergy tail (higher than 2–3 eV) of the energy distribution of species like + + Ar+ , O+ , O+ 2 , as well as Ti and TiO , depend strongly on the variation of the total pressure (see Fig. 8.30). The mean energy and relative ﬂux of positive

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Intensity (arb units)

800

600

400

200

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400 600 Energy (eV)

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Fig. 8.29. O− IEDF recorded whilst operating in pulsed mode at 200 kHz 50% duty (from [79])

Fig. 8.30. Energy distribution of Ar+ , O+ , TiO+ and O− ions impinging on the surface of titanium oxide growing ﬁlm (from [65]). The eﬀect of the total pressure on the slope of the high-energy tail and on the maximum intensity of the distribution of positive and negative species is clearly shown

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and negative ions (determined from their energy distributions), showed a correlation between the characteristics of the species bombarding the growing ﬁlms and the resulting ﬁlm properties [65]. The mean energy E and relative ﬂux of O− ions calculated from the energy distribution are inversely inﬂuenced by the total pressure with regard to the positive species. Reactive sputtering has also been carried out with RF excitation as well as DC. Both positive and negative ion IEDFs have been recorded by Andersson et al. [84] for reactive magnetron sputtering of an Al target in Ar/O2 gas mixtures. The positive ions of ﬁlm-forming species exhibited bimodal energy distributions, both for direct current and radio frequency discharges, with the higher energy ions most likely originating from sputtered neutrals. For the negative oxygen ions a high-energy peak was observed, corresponding to ions formed at the target surface and accelerated towards the substrate over the sheath potential. As the total pressure was increased the high-energy peaks diminished due to gas-phase scattering (see Fig. 3.31). Figure 8.31 shows recorded O− energy distributions for diﬀerent O2 partial pressures at a total pressure of 0.33 Pa. There are two distinct peaks in the distributions corresponding to O− ions that have been accelerated over the target sheath voltage and reached the mass spectrometer without collisions. One important ﬁnding was that the amount of energetic oxygen increases strongly in the transition region between the metallic and oxidised mode of the target and then levels but as the target becomes oxidised. This can be seen in Fig. 8.32 where the height of these peaks is compared to the target voltage, as a function of the O2 partial pressure. In [85] the deposition ﬂux of molecular species such as AlO+ obtained during reactive radio frequency magnetron sputtering of an Al target in Ar/O2 gas mixtures was investigated using mass spectrometry. The amount of neutral AlO in the deposition ﬂux is at least an order higher than the amount of Al.

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Fig. 8.31. Energy distributions of O− for seven O2 partial pressures ranging from 13 to 227 μPa, with the arrow indicating increasing O2 pressure (from [84]). The total pressure was 0.33 Pa

J.W. Bradley and T. Welzel 500 Al+ DC bias

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300 0

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Fig. 8.32. Target self-bias voltage compared to peak heights of the O− high-energy peaks as functions of O2 partial pressure (from [84]). The total pressure was 0.33 Pa

8.4 Optical Emission Spectroscopy 8.4.1 Technique OES provides an experimentally simple tool for process characterisation of reactive sputter processes. The radiation emitted from the plasma is coupled out of the sputter chamber by a window or an optical ﬁbre and spectrally dispersed in a monochromator. As the gaseous species emit a characteristic wavelength pattern, information on particular species along a line of sight in the plasma is obtained. With the help of modern CCD or intensiﬁed charge coupled device (ICCD) detectors, fast and even time-resolved measurements with a resolution in the nanosecond range are possible. The most important advantage of the OES is the fact that it is a passive method, which – in contrast to any electrical probe – does not interfere with the plasma. The most critical diﬃculty with OES is the relation of the measured emission to the separated plasma parameters of interest. Plasmas applied to sputtering applications are generally not in equilibrium. Therefore, each individual emitting state and its population has to be treated separately. This often necessitates extensive collision-radiative models. A simpliﬁcation, which is appropriate in many cases, is the corona model [86, 87]. Here, the processes that determine the population of an excited, emitting state (i) of a particle are reduced to excitation by inelastic electron impact from the ground state (g) of the particle and de-excitation by spontaneous emission only. In this case, the density of this emitting level, which is – in optically thin plasma – directly proportional to the intensity measured, can be written from a simple balance of excitation and de-excitation in the stationary state as ni = ng ne kgi / Aik , (8.3) k

with ni is the density of (particles in) excited state i, ng is the density of the ground state, ne is the electron density and Aik is the eﬀective transition

8 Process Diagnostics

287

probability for raidative processes from level i to any lower level k. The factor kgi is the rate coeﬃcient which is given by [88] ! ∞ √ 2 kgi = · σgi (ε) · ε · f (ε) · dε, (8.4) me εi where me is the electron mass, σgi is the cross section for electron impact excitation from the ground to the particular excited state, f is the electron energy distribution function normalised to one, ε is the electron energy, εi is the excitation energy (onset energy) of state i. Equations (8.3) and (8.4) clearly show that – even in this simple case – the emission is governed by a combination of three plasma-dependent factors: the density of the particles, the electron density, and the energy distribution of the electrons. If the dependence of two of the quantities is known, information about the third can be obtained, e.g. when using the working gas of known pressure as particles and the EEDF does not change signiﬁcantly, the dependence of the electron density can be obtained. Another possibility is to use proper ratios of emission lines where one of the quantities cancels out, a typical example being the so-called actinometry where the emission is related to an argon line and information on the density of the particle considered is obtained while electron density and rate coeﬃcient cancel. This method, however, depends on the same excitation energy for both excited stated involved. In practise, more processes than those considered by the simple corona model will often contribute to the emission signal. It is therefore important to select those emission lines which fulﬁl the requirement of excitation from the ground state. On the other hand, if additional excitation paths are known which signiﬁcantly contribute to the population of the upper state, it is also possible to access additional quantities. For instance, a stepwise excitation via metastable states (e.g. of the working gas argon) may give information on the densities of these states. One of the main applications of OES, however, remains the identiﬁcation and monitoring of species present in the process on a qualitative basis. In reactive sputtering, this is important for the density of sputtered particles, dissociation products of the reactive gas as well as for impurities. 8.4.2 Plasma Emission Monitoring Probably the most important practical use of time-averaged optical emission in reactive sputtering processes is the process stabilisation by the so-called plasma emission monitoring (PEM) [89, 90]. The method is applied to the transition mode of reactive sputtering between reactive and metal mode. It makes use of the fact that for many metals, which are sputtered reactively, the sputter yield is extremely diﬀerent for the metal itself and the compound containing the metal and the reactive gas. Mostly, the sputter yield of the metal is much higher. If the plasma parameters were exactly the same for

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all modes or target conditions, then the metal sputter rate would be proportional to the fraction of the target surface being pure metal. According to (8.3), the emission intensity of any line of that metal should then be proportional to the metallic fraction of the target. Indeed, such an eﬀect is seen for many metals – the deposition rate is a monotonic function of the metal emission intensity [91] when the ﬂow of reactive gas is changed. However, the plasma parameters will not remain constant when the working gas is changed. The changes in the emission intensity are then (see (8.3) and (8.4)) the sum of changes in the sputter rate, the electron density and the electron temperature. Fortunately, for many metals, the diﬀerence of the sputter yield between metal and compound is so big that changes in the sputter rate dominate over the changes in the plasma properties so that the condition of unchanged plasma parameters is approximately fulﬁlled. The emission intensity is thus still a unique function of the sputter rate. This is particularly the case in the transition region of reactive sputtering, where small changes in the gas mixture (or reactive gas ﬂow) and consequently small plasma changes are accompanied by strong changes in the compound surface coverage and therefore in the sputter rate. The PEM technique uses this to stabilise the deposition process by taking the metal emission signal as input parameter for the reactive gas ﬂow. Changes in the emission therefore lead to correction changes in the gas ﬂow rate. There are, however, a few material systems where this simple procedure fails because metal density changes are not dominating the plasma changes (e.g. SnOx deposition [91]) and a more sophisticated control is necessary. 8.4.3 Time-Resolved OES in Pulsed Reactive Sputtering Time-resolved OES has been applied to pulsed sputtering processes to study the temporal development of the discharge within one pulse. It is found that the argon emission evolution during the ‘on’ phase in principle reproduces the waveform of the target current quite well [40, 42, 92]. The studies typically concentrate on emission lines of the sputter gas argon as for this, at least one quantity of (8.3) (the argon ground state density) is constant. Temporal changes in the argon emission intensity therefore reﬂect the electron properties and may be compared to probe results. Diﬀerent authors observe a peak in the intensity just at the beginning of the ‘on’ phase within the ﬁrst microsecond (see Fig. 8.33, cf. also Figs. 8.10 and 8.11). This can – according to (8.3) and (8.4) – be either correlated to a temporal increase in the electron temperature [27, 92] which has been measured with single probes [27–30] or a temporal increase of the plasma density, observed with a double probe [39, 42] or a single probe [45]. In addition, Welzel et al. and Dunger et al. [42] observe a second, even more pronounced emission peak after some microseconds, exactly at the position where they measure a maximum in the density with the double probe (cf. Figs. 8.10 and 8.11). As mentioned above, the pronunciation of this strong peak is due to their power supply which exhibits a strong voltage overshoot. A comparison

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Fig. 8.33. Temporal development of two argon lines and a titanium line for a pulsed discharge at 20 kHz and 80% duty cycle. The argon line at 750.4 nm shows a peak at the beginning of the ‘on’ phase (10 μs) and a rapid decay in the ‘oﬀ’ phase (0 μs), the titanium line does not (from [92])

of diﬀerent argon emission lines reveals that transient phenomena are reproduced diﬀerently depending on the emission line. Some lines, namely that at 750.4 nm and lines in the spectral region of 400 nm, show very sharp and high peaks, whereas the peaks of other lines (e.g. 763.5, 811.5 nm) are broader and weaker [40, 92–94]. This shows that the description with the simple corona model is only an approximation and other processes also contribute to the emission. Welzel et al. [93] have studied a single exponential decay of the manifold of red argon lines in the ‘oﬀ’ phase of a pulsed magnetron discharge and observed diﬀerent decay rate constants. The analysis of those proved that the values of the decay constant are correlated to the upper state of the observed transition (see Fig. 8.34). Comparison to cross sections for the excitation of the upper states [95, 96] proved that shortest decay constants which matched their electron density decay (∼700 ns), belonged to states which were mainly excited directly from the ground state (750.4 nm).

J.W. Bradley and T. Welzel

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Fig. 8.34. Decay constants of argon emission lines corresponding to diﬀerent excited states (the decay constant obtained for the charge carrier density has been determined by a double probe to 700 ns) on the left side compared to the ratio for cascaded to direct excitation and the cross section for excitation from metastable argon on the right side. Excited states which have low contribution of cascaded excitation and excitation from metastables show fastest single exponential decay (from [93])

Other states, which are signiﬁcantly excited from metastable argon or through cascades from higher states, decay more slowly (cf. Fig. 8.34). Similar investigations were carried out by Belkind et al. and Lopez et al. [27, 92, 94]. They analysed the emission in the ‘oﬀ’ phase with an obvious two-step decay and found initial decay constants of the 750.4 nm argon line of less than 1 μs, similar to the decay of the plasma density. The subsequent decay, however, had a higher decay constant of 4 μs. Other argon lines which are more inﬂuenced by the metastable states (763.5, 772.4 nm) decay slowly with a constant of about 4 μs from the beginning (cf. Fig. 8.33). The authors explain the very rapid decay with the loss of fast electrons as direct excitation necessitates 13 eV electron energy. The longer decay rate is, however, not due to the slow bulk electrons as ambipolar diﬀusion would require several 10 μs. It is rather a consequence of the diﬀusion and loss of metastable argon atoms [27, 92, 94] from which an electron energy of only 3 eV is needed to excite the emitting states. The argumentation is in good agreement with the explanation of the decay rates observed with single probes (see above). Lopez et al. and Belkind et al. also studied the temporal decay of metal atom and oxygen atom emission in reactive sputtering of an Al [27,94] or Ti target [27,92]. The oxygen emission was observed to initially decay as fast as the 750.4 nm argon line due to similarly high excitation energy and the loss of fast electrons. The subsequent decay was more complex resulting from a variety of excitation channels. The decay of both metal lines is similarly slow as for the slow argon decay. The authors conclude that this is either due to the diﬀusion of the metal atoms or a possible excitation via metastable argon. Swindells et al. [45] validated the peak they observed in the electron temperature just at the start of the ‘oﬀ’ phase with OES using the argon line at 750.4 nm to monitor the short-lived ‘ﬂash’ of high energetic electrons (see Fig. 8.35). In agreement with their single probe measurements for the electron temperature they observed a signiﬁcant peak in the emission when

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ne, Teff, IntAr750nm and ld [arb. units.]

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Fig. 8.35. Traces of the discharge current (Id ) – solid line, electron density (ne ) – squares, eﬀective electron temperature (Te,eﬀ ) – triangles and optical emission of the 750.4 nm line (IntAr 570 nm) – circles for a 25 kHz pulsed discharge with 90% duty cycle in front of a grounded substrate holder. The argon emission at the transition from ‘on’ to ‘oﬀ’ at 36 μs matches a peak in the eﬀective electron temperature (from [45])

the substrate is grounded due to the electrons accelerated by the substrate sheath during the period of very high potential. Conditions where the substrate ﬂoated or was removed only led to a weak increase in the electron temperature with no increased emission. As mentioned by the authors, in this situation there is still electron acceleration from the surrounding walls. In the case of low duty cycles (10% and less) but also quite long pulse ‘on’ phases accompanied by high-peak currents, time-resolved OES is suited to observe a diﬀerent physical eﬀect close to the target. Vlcek et al. [48] studied the temporal evolution of diﬀerent argon and copper emission lines in front of a copper target. The lines for each atom spun a wide range of excitation energies. At ﬁrst, all argon lines increased with the target current rise, followed by the set of copper lines. After about 50–70 μs the emission of argon atoms and ions, however, started to slowly decrease whereas the copper emission and the discharge current rose slightly further to their saturation value. This drop in the argon emission was practically independent of the excitation energy. According to (8.3) and (8.4) the most likely reason for such a behaviour is a change in the ground state density, i.e. the argon density is decreasing after some time. Vlcek et al. [48] explain this by the gas-rarefaction due to energy transfer from sputtered copper atoms to the argon gas. The same eﬀect has been observed by Cada et al. [97] who sputtered a Ti target in an Ar/CH4 gas mixture: target current and Ti emission rise simultaneously to their saturation value, whereas emission from gas species (Ar and CH) had a peak within less than 100 μs after the start of the ‘on’ phase and then dropped by about 25%

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for the rest of the ‘on’ phase. Cada et al. suggest from their observations with the pulse parameters that the gas-rarefaction during deposition may be controlled by the length of the ‘oﬀ’ phase.

8.5 Optical Imaging An important tool in the armoury of plasma diagnosticians is optical imaging. Like all OES methods, it is non-perturbing and can give us information on the spatial distribution of electronic transitions in chosen neutral or ionic species in the plasma. It can be performed time-resolved, with time-resolution in the 10s of ns when using modern ICCD cameras. In many if not all cases, optical ﬁlters are employed between the detector and the plasma to give transmission at particular wavelengths in the optical spectra. In spatially symmetric plasmas, such as the planar circular magnetron, Abel inversion [98] can be used to give radial proﬁles of plasma emission. Together with axial information, a quasi-3D image of the plasma excitation can be produced. However, although it may be possible to determine the relative levels of excitation through different transitions (i.e. due to the presence of hot electrons) little quantitative work has been done with 2D OES to diagnose the plasma excitation (electron) temperature or density so far. In reactive magnetron sputtering 2D imaging has been carried out for both plane images of the cathode (either circular or rectangular) and across the plasma in conjunction with Abel inversion for cylindrical symmetrical systems. For instance, face-on imaging was carried out in a planar magnetron by Tomasel et al. [99] to look at energetic electrons in the race-track, in particular using a high-speed camera to study transient arcing phenomena associated with reactive sputtering with a poisoned target. It was shown how the perturbation produced by the injected electrons travels in the E × B direction with minimum average speeds of approximately 7.4 × 105 m s−1 . Optical imaging of the plasma above a rectangular titanium cathode during the evolution of the plasma in DC-pulsed operation was conducted by Zhu et al. [100]. Time-resolved images were taken using Argon spectral ﬁlters and a Roper Scientiﬁc ICCD camera with a time resolution of 0.05–0.2 μs. It was found that at the beginning of the ‘on’ phase, the discharge initially starts preferentially in two opposite curved sections (‘cross corners’) of the magnetron race track, where it exhibits the most intense plasma emissions. During the rest of the ‘on’ phase, the emissions from the straight sections of the racetrack of the magnetron are always slightly more intense than the emissions from the curved sections of the racetrack. This pattern extends into the start of the ‘oﬀ’ phase, when the power is turned oﬀ. The study was extended to incorporate temporal behaviour of the various emission lines (Ar, O, Ti) using spectral ﬁlters [101] during the sputter

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Fig. 8.36. Images showing the spatial variation of light intensity, obtained using the 750 nm ﬁlter, at key times in the cycle, t = 0.00 μs (a), 0.40 μs (b), 1.15 μs (c), 3.08 μs (d) 5.45 μs (e) and 6.75 μs (f) (from [102]). A distinct region of plasmas bright moves way from the target at approximately the ion acoustic speed. ‘On’ time is from 0 to 5.45 μs – ‘oﬀ’ time is 5.45 to 10 μs

deposition of TiO2 ﬁlms. The optical emissions were seen to persist for several microseconds into the ‘oﬀ’ phase. In the pulsed DC magnetron imaging along the plasma length has been conducted by Bradley et al. [102] and Kvasnica et al. [103]. In the former the temporal and spatial evolution of selected excited species 750.4, 751.5, 810.4 and 811.5 nm (Ar I) was studied using a titanium target pulsed at frequency of 100 kHz, in an argon atmosphere. The radial information of the emissivity was determined using the Abel inversion technique. The results show strong excitation of the observed species above the racetrack in the ‘on’ phase, and the possible development of an ion acoustic wave, initiated after the ‘oﬀ’ to ‘on’ transition (see Fig. 8.36). The ‘on’ to ‘oﬀ’ transition is accompanied by a burst of light from the plasma bulk consistent with the transient plasma potential reaching about +200 V. The results were consistent with a release of secondary electrons from the grounded substrate and walls due to ion bombardment [45], as well as an increased conﬁnement of energetic plasma electrons. In a detailed study tomography techniques were used to give more information on the plasma [104].

8.6 Laser-Induced Fluorescence Advanced laser diagnostic techniques such as LIF [105] have been used to provide information on the spatial distribution of species as well as their velocities (energy distribution function) in reactive magnetron systems. LIF is a technique where the wavelength of an incident laser beam is tuned to an absorption line of an atom, molecule, radical or molecular ion

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and the subsequent ﬂuorescence radiation is detected by the same means as used for optical emission spectroscopy. Therefore, in contrast to OES, it is possible to directly access optically inactive species, e.g. in their ground or some metastable state in the plasma. The technique is still non-invasive. Spatial information on the ﬂuorescence can be obtained with a video camera or by a perpendicular scanning of the laser beam with the detection optics. The velocities of particles may be measured through Doppler broadening. Doppler shifting can be used to study the energy distribution of sputtered atoms in the forward direction with the laser directed to the target (see e.g. [106]). Absolute densities may be obtained from the measurements by calibrating the ﬂuorescence signal. This calibration is achieved using Raleigh scattering in the working gas with a known scattering cross section [107, 108]. The calibration factor is obtained from the slope of the scattering signal vs. the gas pressure. The gas pressure variation enables a separation of the scattering signal from any reﬂection. Another calibration possibility is the use of an absorption transition of a species of known density (mostly the working gas) which has a known absorption cross section [109]. For many reactive species being of interest in reactive sputtering (e.g. O, N, H) the excitation energy of the lowest energy level is higher than that obtained even with a UV laser. In this case, two-photon LIF is used where the simultaneous absorption of two photons in the visible or UV range is used to bridge the energy gap. One of the earliest uses of LIF reported in the magnetron conﬁguration was by Goeckner [110], who applied sub-Doppler LIF to measure the velocity distributions of ionic species. It was found that the radial proﬁles of the excited-state ion density and the electron density are peaked in the electron trap. Outside the trap, the random ion energies for the azimuthal and radial components were at room temperature. Inside the trap, the random energy for the azimuthal component had a peak to 0.32 eV, while for the radial component it had a peak of 0.13 eV. LIF has also been used to measure the energy and density distribution of Ar ions in the plasma of a cylindrical magnetron discharge [111]. The investigations revealed that the density of the ions has a broad maximum extending into the negative glow and positive column. The spatial distribution of the eﬀective ion temperature estimated from the line proﬁle has a shape similar to that of the ion density distribution, with maximal value also inside the region of the negative glow but closer to the cathode surface. The peak temperature value is in the eV range perpendicular to the electric ﬁeld and somewhat above 10 eV in the direction of the ﬁeld. For the sputter species LIF has also been applied to determine the speed of the atoms, for instance the velocity distribution of Fe atoms [112] in the DC magnetron conﬁguration. In [112] Doppler-shifted LIF imaging spectroscopy was used to determine the spatial distributions of the velocity distribution functions of Fe atoms from a cathode with an Fe target 50 mm in diameter. At low gas pressure, the velocity distribution function in the region adjacent to the target was a broad one with a fast average velocity toward the

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Fig. 8.37. Typical excitation spectrum of LIF observed at a gas pressure of 3 mTorr, together with the separation of the components originating from the incident and reﬂected laser beam. The laser irradiated the plasma from the direction perpendicular to the target surface. Taken from [117]

downstream plasma. At a high gas pressure, Fe atoms had low average velocity and the width of the velocity distribution function was narrow in the entire discharge space. Figure 8.37 shows a typical excitation spectrum observed at r = 0 mm and z = 5 mm. The sputtering source was inserted from the horizontal port, and the Ar gas pressure was 3 mTorr. The plots shown in Fig. 8.37 were obtained by an averaging technique at the detector. It was found that Fe atoms are energetic immediately after the ejection from the target, but during the transport toward the downstream plasma, the energy of Fe atoms is reduced and the velocity distribution function is thermalised by collisions with ambient Ar gas. The technique has also been used to good eﬀect in determining the spatial distributions of sputtered species densities in a conventional planar magnetron sputtering plasma source used for depositing Ti ﬁlms inside trenches formed on RF-biased SiO2 substrates, e.g. Ti and Ti+ [113,114], Indium in deposition of ITO [115], Indium and Ar in [116] and copper atoms in [117]. In [113] the results revealed that the density ratio of Ti+ to Ti in the downstream region increased with the gas pressure up to 0.3, while in the upstream region, it was small (<0.05) and was roughly constant with the gas pressure. In [114,115], 2D-LIF and 2D-OES proﬁles of the sputtered In atoms and the excited species were measured and compared to each other. The density proﬁles were clearly diﬀerent from the In emission proﬁles. From the semi-quantitative evaluation of the In atom ﬂux onto the substrate using experimental LIF and deposition rate data, it was indicated that the sputtered particles are mostly atomic species for O2 pressures less than 10−4 Torr. In [116] it was found that using Abel inversion, the optical emission intensity

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proﬁle of excited In atoms was slightly broadened toward the discharge centre axis and the target compared to that of excited Ar atoms. Welzel et al. used LIF to investigate an additional aluminium ﬂux to the substrate when depositing cubic boron nitride ﬁlms [118]. The BN ﬁlms were prepared by reactive RF magnetron sputtering of an h-BN target in Ar/N2 atmosphere and the additional Al ﬂux – intended to modify the BN lattice spacing – was provided by a DC driven peripheral Al ring electrode. The LIF results showed that the Al gas phase density is drastically decreased to 40% when only 3% nitrogen are added to pure argon due to a nitriding of the Al electrode [118]. In pure N2 , the Al density was only about 8% of that for pure argon. Time-resolved LIF measurements revealed that the nitriding occurred within less than a minute but a cleaning of the electrode took about 5 min in pure argon.

8.7 Summary The international eﬀort to understand the fundamental physical and chemical processes in reactive magnetron sputtering has been signiﬁcant and has aided in the development of new discharge devices, better processes for industry and above all really excellent basic science. This work will undoubtedly continue to grow in the future with the development of new and better diagnostic techniques. Not only will there be exciting new plasma operating regimes to investigate in existing magnetron-type systems such as ultra-high power pulsing, but also there will be entirely new plasmas to study such as atmospheric pressure reactive deposition systems, micro-plasmas, dielectric barrier and atmospheric glow discharges.

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9 Optical Plasma Diagnostics During Reactive Magnetron Sputtering S. Konstantinidis, F. Gaboriau, M. Gaillard, M. Hecq, and A. Ricard

9.1 Introduction Magnetron plasmas are used to sputter metal in pure Ar gas and in Ar−N2 , Ar−O2 gas mixtures for reactive sputtering to synthesize pure metal thin ﬁlms or their corresponding nitride and oxide compounds. Since the 70s, several plasma diagnostics tools have been developed [1–3]. Amongst them, optical diagnostic methods are playing a very important role to characterize magnetron plasmas. Optical diagnostics are “in situ” experimental methods which allow studying the plasma composition as excited and metastable atoms, ions, molecules and radicals (from dissociated reactive molecules such as oxygen or nitrogen). Sputtered metal atoms and their respective ionic populations are analysed as well to estimate the ionization rate of the metallic vapour. The later is a very important parameter for thin ﬁlm growth. These diagnostic tools also oﬀer the advantage of being non-intrusive, easy to use, and generally inexpensive. The optical emission spectroscopy (OES) of magnetron plasmas is ﬁrst described in Sect. 9.2. However, by OES, only the radiative plasma species are detected. These species only represent a small fraction (∼10−8 ) of the total density of the species considered [4]. Therefore, to study the whole plasma population, we will show how to interpret the measured emission intensities by means of kinetic equations involving ground and radiative states. In Sect. 9.3, we show how to measure the absolute atom densities thanks to atomic absorption spectroscopy (AAS) and, in Sect. 9.4, thanks to laser induced ﬂuorescence (LIF). The eﬀect of the ampliﬁcation of a DC magnetron plasma by means of a secondary inductively coupled plasma produced by a RF coil superimposed to the magnetron cathode is also presented. In the case of the well-known transition from metal to poisoned regime in reactive sputtering of titanium nitride, we demonstrate that there is a correlation between neutral titanium density, as determined by AAS, and the Ti+ signal obtained from glow discharge mass spectroscopy (GDMS).

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In Sect. 9.5, the optical diagnostic of high-power impulse magnetron sputtering (HiPIMS) discharges is considered, for both pure argon and for reactive Ar−N2 and Ar−O2 gas mixtures. HiPIMS is a recently developed very attractive technique employed to strongly ionize the sputtered metallic vapour.

9.2 Emission Spectroscopy of Magnetron Plasmas The experimental results reported hereafter have been obtained in diﬀerent deposition chambers. In the ﬁrst reactor, labelled R1 and schematically reproduced in Fig. 9.1, a 10 cm in diameter titanium target is DC power supplied to be sputtered in pure argon [5]. The vacuum chamber is equipped of a one-turn copper coil that can be RF power supplied. This feature is used to generate a secondary, dense plasma, that is superimposed to the DC magnetron plasma to excite and ionize the sputtered metallic vapour. The DC power ranges between 100 and 1,500 W (a power density comprised between ∼1.3 and ∼19 W cm−2 ). The coil in R1 is 12 cm in diameter and is set up 4 cm above the magnetron target. The RF power on the coil can be increased

gas inlet

Substrate holder

Collimators + lens

collimators

Ti lamp Optical fiber

A1 cm

lenses Cu coil

spectrometer

Pulse generator

4 cm Ti target N

S

N

cooling

DC Power supply

magnets

Matching network 13.56 MHz RF generator

Oscilloscope Fig. 9.1. Representation of a DC magnetron cathode equipped with a RF coil for magnetron ampliﬁcation, from [13]. The optical ﬁbre needed for OES experiments is set in front of a quartz window, on the opposite wall. The hollow cathode lamp used as reference for AAS (Perkin Elmer, Lumina) is set behind this window. The oscilloscope is used when the optical source is pulsed

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up to 500 W. Optical diagnostic tools are set 1 cm above the coil, close to the substrate. In the second deposition device, R2, the magnetron cathode and the RF coil are both 15 cm in diameter. The coil is set up 3 cm above the target surface. The metal ﬂux is collected on a substrate located 5 cm away from the coil. The DC magnetron that is either equipped with a Cu or a Ti target is power supplied from 100 to 1,500 W (0.5–8.5 W cm−2 ) and the power on the RF coil can be adjusted between 100 and 1,200 W [6]. The Ar gas pressure ranges from 15 to 30 mTorr (2–4 Pa). The optical spectroscopy is performed through a quartz window as shown in Fig. 9.1. A quartz window is employed so as to let UV photons to be detected. Most intense lines emitted by metal atoms are generally in this pat of the electromagnetic spectrum (see simpliﬁed energy level diagrams represented on Fig. 9.3). Usually, one can set an array of collimators in front of the collecting optical ﬁbre and/or the viewport to prevent the deposition of a coating. Once collected by the optical ﬁbre, the light is transported to the monochromator. The monochromator is typically built around an active device: the diﬀraction grating (in this case, composed of 1,200 grooves mm−1 ). The later allows selecting with accuracy the photons according to their wavelength. As the diﬀraction grating rotates, each wavelength is transmitted to the detector and the spectrum is, step by step, displayed. The detector can be either a photomultiplier tube (PMT) or a charge coupled device (CCD). A typical emission spectrum obtained with the reactor R1 (100 W on the Ti DC cathode, 0 and 500 W on the RF coil, Ar gas pressure of 30 mTorr) is reproduced in Fig. 9.2 for the 350–380 nm spectral range. Lines coming from the radiative relaxation of excited Ti and Ti+ atoms are clearly identiﬁed. The Ti and Ti+ energy levels (ground and metastable states) are reproduced in Fig. 9.3a,b. The Ti resonance lines (whose lower state is the ground one, at 0.0 eV energy) of Fig. 9.2 are corresponding to a transition to the three ground state sublevels (a3 F2,3,4 ). The low-energy level of the Ti+ line on this spectrum (Fig. 9.2) is the Ti+ (a2 F ) level which stands 0.6 eV

Fig. 9.2. Typical emission spectrum as obtained from titanium sputtered in pure argon, at 30 mTorr, 100 WDC . The dotted curve relates the evolution of Ti neutral and ions emission intensities when the RF coil is power supplied with 500 WRF , 100 WDC , 30 mTorr

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λ = 1048 Å λ = 1067 Å

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Fig. 9.3. (a) and (b) are simpliﬁed Grotrian diagrams of Ti (I) and Ti (II) with some of their respective metastable levels. Simpliﬁed Ar I diagram is reproduced in (c). In (c), the transition appearing at 750.4 nm in the optical spectrum corresponds to a transition between the 3p4p and the 3p4s levels. The 3p4s level comprises two metastable states

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above the Ti+ (a4 F ) ground state. From the energy level diagram represented in Fig. 9.3a,b, it appears that the excitations of Ti and of Ti+ radiative states require about 3–4 eV (considering an excitation from the Ti+ ground state for the ion line). This is a relatively small amount of energy compared with Ar radiative states which are lying at about 11–13 eV above the ground state (see Fig. 9.3c). As a consequence, the excitation of Ti and Ti+ atoms will require electrons of lower energy compared to argon excitation. It is useful to characterize a PVD reactor by recording the spectral line intensities versus the power (or the current) of the magnetron cathode in a Log–Log scale. An example [7] of spectral line intensities versus cathode current in Log–Log scale is reproduced in Fig. 9.4, in the case of the R1 106

I(Ar) (5mTorr -750.4 nm)

y = 64.226 * x^(1.12) R= 0.99574 y = 44.443 * x^(1.2738) R= 0.99895

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y = 0.0052918 * x^(2.4313) R= 0.9999

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I (mA)

Fig. 9.4. Variations in Log/Log scale of Ar (I) and Ti (I) line intensities versus the DC magnetron current at Ar pressures of 5 and 10 mTorr [7]

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reactor with a Ti cathode. In Fig. 9.4, one can observe the linear variations of the Ar 750.4 nm and Ti 365.3 nm line intensities. The slopes are 1.2 (±0.1) for the argon line and 2.5 (±0.1) for the titanium one. Such variations can be interpreted by considering the reaction kinetics [7]. The intensity IA∗ of an atom A in an excited state A∗ is given by the following equation: hc IA∗ = c(λ) nA∗ νA∗ , (9.1) λ where c(λ) is the spectral response of spectrometer, λ is the wavelength, nA∗ is the density of radiative state A∗ and νA∗ is the line radiative frequency. The density nA∗ is assumed to be produced by a direct electron excitation as follows: (9.2) e + A → e + A∗ with a reaction rate CA∗ This reaction rate involves the integrate of the collision cross section and the electron energy distribution function (EEDF) which is related to the electron temperature. Then, assuming that the stationary regime is reached between production by electron collisions and destruction by radiative relaxation, one can write the following equation for the density of state: ne nA CA∗ , (9.3) n A∗ = νA∗ with ΣνA∗ the total loss frequency of A∗ by radiative emission. At a constant gas pressure, the electron temperature can be assumed as being constant. It results that CA∗ is a constant for a given radiative state A∗ . Thus from (9.1) and (9.3), one can deduce a new expression for emission intensity, which involves the ground state density of atom A in the plasma: IA∗ = KA nA ne , with KA = c(λ)

(9.4)

hc νA∗ CA∗ . λ ν A∗

Now if A is considered as being an argon atom, then nA = nAr = const., as the discharge pressure and temperatures (see examples hereafter) are kept constant during the measurements. In the present experimental conditions, argon pressure is relatively low and titanium does not present a high sputtering yield so the collision frequency of argon atoms with sputtered titanium atoms can be considered as small. Moreover, the cathode current (power) density is low. Therefore one can reasonably assume that the sputtering wind will not induce a signiﬁcant heating of the argon gas and that the gas temperature is held constant. Hence (9.4) is reduced to: IAr∗ = MAr ne ,

(9.5)

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with MAr = KAr nAr . In Fig. 9.4a, the following linear relation is observed Log IAr∗ = 1.2 Log IK , with Ik standing for the discharge current. Thus, from (9.5) and the relation between Ar emission intensity and target current, a relation between electron density and target current is determined [7]: ne ∼ IK 1.2

(9.6)

The result given by (9.6) allows characterizing the PVD reactor R1 (Fig. 9.1). When the DC power (PK ) supplied to the magnetron cathode is considered, with Pk = IK VK , VK being the cathode voltage, one obtains: ne ∼ PK 1 . Now, let us consider that A is a titanium atom (in (9.4)), consequently: ITi∗ = KTi nTi ne .

(9.7)

At this point, the variation of nTi with IK must be calculated. The Ti atoms are produced by sputtering the Ti target. Target sputtering is induced by Ar+ ions. The sputtering yield is labelled STi . By assuming a dominant loss by Ti , and assuming diﬀusion towards the reactor walls [7, 8], with a frequency νD a steady state between production by sputtering and loss by diﬀusion (the plasma is DC power supplied), the following equation is written: nTi =

STi nAr + , Ti νD

(9.8)

with nAr+ = kne , as argon ions are produced from electron collisions with argon atoms whose density is considered to be constant in our experimental conditions. Consequently, the following relation for the density of titanium neutral ground state is found: nTi =

STi kne . Ti νD

It follows, by replacing nTi in the expression of the Ti line intensity (9.7), that the line intensity is proportional to the square of the electron density ne as depicted by (9.9) hereafter: ITi∗ = MTi ne 2 ,

(9.9)

with MTi = KTi STi k/νD Ti being a constant at a given gas pressure. Since, in (9.6), ne ∼ IK 1.2 , from (9.9), therefore a slope of 2.4 in the LogIT i∗ vs. LogIK diagram has to be found. This value is close to the experimental slope of 2.5 found in Fig. 9.4a [7]. In conclusion, it can be considered that the diﬀusion to the walls is the dominant loss mechanism of titanium atoms in such a low-pressure magnetron plasma.

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500 WDC - 400WRF-17m Torr -9% N2

N2

600

Intensité ( ua )

500 N2

400 300

Ti

200

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100 0 −100 330

340

350

360 370 λ ( nm.)

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390

400

Fig. 9.5. Emission spectrum in Ar−N2 obtained with a nitrided titanium cathode, from [7]

The optical diagnostic of magnetron discharges during reactive sputtering is now examined. The spectrum of a reactive Ar−N2 gas mixture obtained in the reactor R2 (equipped for titanium sputtering) is reproduced in Fig. 9.5 for the 330–395 nm wavelength range [7]. The Ti lines are now accompanied by the N2 bands which are identiﬁed as belonging to the N2 , second positive (2nd pos.) system. The potential curves of the N2 molecule are reproduced in Fig. 9.6. The N2 2nd pos. is emitted between the N2 (C, v ) and N2 (B, v ) vibrational levels. Eleven electronvolt electrons (if we assume electron – nitrogen molecule collisions) are required to produce the excited nitrogen molecule in its N2 (C) state. One should note that approximately the same amount of energy is required to generate Ar (3 P2 ) metastable atoms (see Fig. 9.3c). Therefore, one can understand that an excitation transfer between the Ar metastable atoms and N2 molecule can occur [4, 7]. This reaction is depicted by the reaction (9.10) hereinafter: (9.10) Ar(3 P2 ) + N2 → Ar + N2 (C, v = 0) The reaction (9.10) explains the strong emission of the 2nd pos. bands observed in Fig. 9.5. It has been observed that reaction (9.10) is particularly eﬃcient as the RF plasma is added to the DC magnetron discharge [7]. In Fig. 9.7, the variations of the N2 + (391.4 nm)/N2 (380 nm) intensity ratio are reported ﬁrst, versus the DC power supplied to the magnetron and secondly, versus the RF power applied to the coil (for a given DC power).

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Fig. 9.6. Potential curves of N2 and N2 + with the N and N+ associated states

Fig. 9.7. Variations of I(N2 + )/I(N2 ) versus the RF power in Ar−N2 , with a nitrided cathode. The curve drawn with the stars stands for the I(N2 + )/I(N2 ) versus the DC power, without RF secondary plasma [7]

These two bands are usually selected [4] to determine the electron temperature in pure N2 discharges when the corresponding radiative states are directly excited through electron collisions with the N2 molecule in its ground state. Such a method must be discarded in Ar−N2 gas mixture since reaction

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(9.10) happens. Without the RF power turned on (i.e. without ampliﬁcation of the magnetron discharge), the intensity ratio is close to 1 and slowly increased as the DC power increases. By supplying the RF secondary plasma, the intensity ratio quickly drops to a value lower than 0.1. This result is the direct consequence of reaction (9.10) which promotes the N2 2nd pos. band emission at 380 nm. This observation indirectly indicates that the RF plasma produces large amounts of Ar metastable atoms. This assumption is corroborated by experiments carried out in [9]. In this paper [9], the authors demonstrate that the mass spectra recorded by GDMS are enriched in Ar2 + . The production of the Ar2 + molecular ion is closely related to the presence of Ar metastable atoms as shown by the following reaction: Arm + Ar → Ar2 + + e. (9.11) Magnetrons are also commonly used to deposit ceramic, non-conductive, coatings such as metal oxide layers (titanium [10] and aluminium oxides [11] are a well-known compound). To avoid arcing, DC bipolar pulsed power supplies have been implemented. A typical evolution of voltage with time is presented in Fig. 9.8. To gain insights on these time-dependent plasmas, time-resolved OES has been implemented, for example by using high-speed CCD detectors. Some results [10, 11] have been obtained in these circumstances, from such plasmas run in poisoned regime (Ar−O2 mixing ratio of 1:4). As the discharge is turned oﬀ, decay time of the line emission intensities are observed to be ∼1 or ∼4 μs long. Fast decay time is, in these oxide mode conditions, related to the rapid decrease of fast electron density in the plasma, as the sheath collapses. Slow relaxation involves an excitation transfer from Ar metastable state (see Fig. 9.3c) as discussed in [11, 12]. Discharging the dielectric surfaces +

+

+ Time

Voltage

0

-

-

trev

ton

-

tcycle

Sputter-deposition of dielectric layers, charging up dielectric surfaces Fig. 9.8. Ideal voltage sequence applied to asymmetrical bi-polar pulsed dc sputtering of dielectrics, from [11]

9 Optical Plasma Diagnostics During Reactive Magnetron Sputtering

311

As it has been exposed in the present section, OES helps towards understanding the reactive magnetron plasma chemistry. In spite OES allows to determine relative evolution of excited species and excitation mechanisms, it does not give access to the absolute densities of the plasma species (excepted if actinometry experiments are carefully set up [12]). To acquire absolute number densities of either background gas (metastable) atoms or sputtered atoms and ions, implementing AAS or LIF is required. AAS is the focus of the following section. The Chap. 4 deals with the use of a (dye) laser as optical source for LIF.

9.3 Resonant Absorption Spectroscopy of Magnetron Plasmas A typical experimental set-up for absorption spectroscopy of reactive plasma is reproduced in Fig. 9.1 [5]. To detect Ti atoms and Ti+ ions, a titanium hollow cathode is placed in front of the reactor quartz window. This lamp emits the characteristic spectrum of the titanium atoms. As the energy of the photons coming out of the source obviously matches the energy level separation of the titanium atoms, they can be absorbed by the sputtered titanium atoms populating the plasma. Therefore this particular absorption method is called resonant absorption spectroscopy. In the experimental setup, two lenses allow to send and to detect a parallel beam through the reactor. A beam converging in the centre of the reactor can also be used to increase the lamp intensity. The source beam is collected by an optical ﬁbre set-up in front of the opposite window. An array of collimators protects the two reactor windows against coating deposition. The collected light is ultimately analysed by an optical spectrometer as shown in Fig. 9.1. The hollow cathode lamp can be pulsed [13] by means of an external generator. By pulsing the hollow cathode, a larger amount of energy is supplied during a short period of time. Hence, strong excitation and ionization rates of the titanium (metal) vapour inside the lamp are reached. Consequently, the sensitivity of the technique is improved, especially regarding the detection of titanium (metal) ions. Moreover, because the lamp signal is pulsed and consequently exhibits a time variation, time-resolved AAS (TR-AAS) experiments can be carried out as well. In the set-up reproduced in Fig. 9.1, the line intensity is measured thanks to a PMT. When the lamp is driven by the pulse generator, an oscilloscope helps to record the time-dependent signal coming out of the PMT. The determination of the absolute number density of the absorbing atoms requires the measurement of AL , the absorption coeﬃcient, along the distance L. The reactor diameter in Fig. 9.1 is chosen as the value of L. The plasma

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can be considered as homogenous with dominant diﬀusion towards the reactor walls. AL is expressed as follow: AL = 1 −

It . I0

(9.12)

In this relation, I0 is the source line intensity and It is the light intensity transmitted through the plasma, with It = Ips − Ip . Ips is the light intensity collected simultaneously from both the optical source and the plasma and Ip is the intensity coming from the plasma only. The measurement of I0 and It is performed with the slits of the spectrometer largely opened to record the full line proﬁle. The optical depth of the medium kσ0 L must be ﬁrst determined before accessing the absolute density of absorbing atoms n. The relation between the absorption coeﬃcient and the optical depth is transcribed by (9.13) here below: AL =

∞ (−1)m+1 (kσ0 L)m . m!(1 + mα2 )1/2 m=1

(9.13)

In Fig. 9.9, the evolution of the optical thickness kσ0 L with AL for several values of the α = δσ0 /δσp parameter is reproduced (see details in [13]). In these expressions, σ0 = 1 /λ0 is the wave number (in cm−1 ) at maximum intensity

Fig. 9.9. Optical thickness kσ0 L versus AL for diﬀerent values of the parameter α from 1.4 to 3.0. This array of curves is obtained by calculation through (9.13)

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(λ is the wave length) and δσ0 and δσp are the half-intensity broadenings (in cm−1 ) of the source and plasma lines, respectively. Finally, the optical depth is related to n by the following mathematical relation: 8.25 × 10−13 fL kσ0 L = n. (9.14) δσp The source broadening δσ0 must be worked out by optical measurements at high-spectral resolution (large focal length spectrometers, Fabry–Perot or Fourier interferometers). The plasma broadening δσp can be calculated if the mechanisms of line broadening are known (Doppler, Stark, Zeeman, pressure broadenings). In the case of PVD plasmas driven at low gas pressure and low electron density (lower than 1014 cm−3 ), the Doppler broadening prevails, with: δσp = σ0 7.16 × 10−7 (T /M )1/2 .

(9.15)

T is the temperature of the absorbing atoms (in K) and M their molecular mass (in amu). Results measurements of Ar metastable and resonant atoms densities versus the gas pressure in a plasma generated by a RF supplied magnetron cathode [14] is reported in Fig. 9.10. In this case, the optical source is an Ar Philips lamp whose the line broadening has been measured with a Fabry– Perot interferometer and the plasma line broadening is calculated by using (9.15) for a gas at room temperature (for a low magnetron power of 50 W). At higher power, the measurement of the plasma temperature is required because gas heating can be induced due to the sputtering wind [15, 16]. The density of sputtered metal atoms can be determined through AAS diagnostic as well. But it is essential to determine the temperature (i.e. the velocity) of the sputtered atoms. If the discharge is run at a relatively high pressure, sputtered metal atoms can be considered has being thermalized by their collision with background gas. In the present case, 6 cm away from the magnetron target, a pressure of 20–30 mTorr is enough. In fact the product “pressure × distance” has to be large enough to guarantee that thermalization is reached. As the metal atoms are thermalized, one can measured the metal temperature indirectly, by estimating the gas temperature. We assume Doppler broadening of the titanium spectral lines. As we will see in Sect. 9.4, LIF can help to measure atom velocity (i.e. translational temperature). Gas temperature measurement can also be carried out by injecting N2 into Ar and by recording rotational spectrum of nitrogen and, subsequently, by estimating the rotational temperature of the nitrogen molecule. Rotation and translation are well coupled in N2 so the rotational temperature can be assumed as being equal to the translational temperature, i.e. the gas temperature [17]. The rotational structure of the N2 (B, v − A, v ) transitions (see Fig. 9.6), called the ﬁrst positive bands (1st pos.), can be used for this purpose. The N2 (B, 2 − A, 0) band at 775 nm is reproduced in Fig. 9.11,

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50W

1010

3P

2

3P

1

1P

1

3

P0

109

0

50

100

150

p [mTorr]

Fig. 9.10. Density of Ar metastable and resonant atoms versus gas pressure in PVD magnetron plasma at 1 and 3 cm above a RF cathode, from [14]

Fig. 9.11a corresponds to the computer calculated structure with a resolution of 0.2 nm and, in Fig. 9.11b is related to an experimental spectrum of a RF plasma [17] obtained with a Jobin-Yvon spectrometer HR 460 (focal length of 46 cm, grating with 1,200 gr mm−1 ) with a slit aperture of 0.1 mm. The rotational temperature is obtained by comparing both the experimental and calculated P1 /P2 sub-band intensity ratios, as indicated in Fig. 9.11c. With a P1 /P2 ratio equal to 1, a rotational temperature of 400 K is deduced. The method is sensitive for temperatures lower than 1,000 K. Also one should note that the N2 upper level (B) of the 1st pos. band is not concerned by reaction (9.10) which induces an overheating of the N2 (C, 0) rotational states [4]. Thus the above-mentioned method can be applied in Ar−N2 gas mixtures. In these working conditions, the neutral gas temperature obtained from the rotational N2 temperature is found to increase from 300 to 700 K as the DC power increases. The results presented in Table 9.2 are obtained when the

9 Optical Plasma Diagnostics During Reactive Magnetron Sputtering

P2

P1

P2

P1

Arbitrary Units

(a)

315

Arbitrary Units

(b)

768

770

772 774 Wavelength, nm

776

778

1.5

(c)

1.4

P1/P2, a.u.

1.3

195 Trot[K] = (P1/P2 _ 0.52)

1.2 1.1 1.0 0.9 0.8 0.7 0.6

0

200

400

600

800

1000

1200

1400 1600

Rotational Temperature in K

Fig. 9.11. Calculated (a) and obtained experimentally in E mode of the N2 discharge (b) spectra of the rotational 775.3 nm sub-band of nitrogen, from [17]. (c) Relation between the rotational temperature and P1 /P2 spectral peaks ratio based on synthetic spectrum, from [18]The results obtained with the reactor R1 at 30 mTorr are reported in Table 9.1 for DC powers ranging from 100 to 1,500 W [17].

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Table 9.1. Variations of gas temperature and titanium neutral density versus DC power with no RF WDC (W)

100

200

300

T (K) 300 300 300 nTi (1010 cm−3 ) 7.6 12 20 Argon pressure is 30 mTorr, from [17]

500

750

1,000–1,500

400–300 14

400–500 20

500–700 17

Table 9.2. Variations of gas temperature and titanium neutral density versus RF power with 200 WDC WRF (W) T (K) nTi (1010 cm−3 )

0

100

200

300

500

300 12

300 7.8

400 4.7

400 1.6

450–500 0.93

Argon pressure is 30 mTorr, from [17]

coil RF power is on. With a DC power of 200 W, the gas temperature increases from 300 to 500 K when the RF coil power increases from 0 to 500 W. Thanks to the estimation of the gas temperature, the Ti density has been determined. The corresponding δσp values required for the calculus of the density have been obtained by using the temperatures reported in Tables 9.1 and 9.2. The δσ0 values were calculated from (9.15) by assuming a Ti atom temperature of 650 K in the hollow cathode lamp [17]. A recent publication [19] reports a nickel atom temperature of about 600 K in a nickel hollow cathode lamp supplied with a 15 mA current. For the DC magnetron discharge run at 30 mTorr, the Ti density has a nearly constant value as shown in Table 9.1. Density of the neutral Titanium ground state lies between 1 and 2 × 1011 cm−3 when the DC power increased from 200 to 1,500 W (the uncertainty on the density is generally assumed to be in the order of 30%). When the RF coil power increases, for a constant DC power of 200 W, from Table 9.2 one can observe that the Ti density strongly decreases with the RF power. Such a decrease could be attributed, at ﬁrst approximation, to an increase of Ti ionization induced by the RF secondary plasma. Every Ti neutral atom disappearing would be turned into a Ti ion. Therefore, the ionization rate should be very high (>70%). To conﬁrm this interpretation, the densities of Ti+ ions and Ti metastable atoms have been measured for the DC magnetron cathode ampliﬁed by the RF plasma. The pulsed the optical source is used for this purpose to increase the sensitivity of the technique. The intensity of the Ti and Ti+ lines in the pulsed optical source is, as previously explained, strongly enhanced. In Fig. 9.12, the emission spectrum obtained with the pulsed source is reproduced (Fig. 9.12a). For comparison, the spectrum recorded with the conventional DC source is also presented (Fig. 9.12b). Clearly, thanks to the pulsed source, the Ti+

9 Optical Plasma Diagnostics During Reactive Magnetron Sputtering 0.35

0.045 Ti

0.040

Ti

0.30

Ti

Ti +

0.035

Intensity (A.U.)

Intensity (A.U.)

Ti

0.030 0.025 0.020 0.015 0.010 360

317

Ti

Ti

0.25 0.20 0.15 0.10

Ti +

0.05

362

364

366

368

370

372

0.00 360

362

364

366

368

Wavelength (nm)

Wavelength (nm)

(a)

(b)

370

372

Fig. 9.12. Hollow cathode lamp spectrum (a) in pulsed mode (150 μs, 55 Hz, 600 mA), (b) in DC mode (40 mA). Integration time of 1 s, taken from [13] Table 9.3. Density of Ti atoms from Ti 363.5 nm, f = 0.22, δσ s = 14 × 10−2 cm−1 , δσ p = 4.8 × 10−2 cm−1 at WRF = 0 and 6.1 × 10−2 cm−1 at 500 WRF RF power (W) 0 500

AL

α

0.57 0.39

kσ0 L

nTi2 (cm−3 )

nTi total (cm−3 )

10 1

1.2 × 10 2.3 × 1010

3.5 × 1011 1 × 1011

2.9 2.3

11

The total nTi density is the addition of all the Ti (a3 F2,3,4 ) sub-levels measured densities, from [13] Table 9.4. Density of Ti+ ions from Ti+ 324.2 nm, f = 0.18, δσs = 14 × 10−2 cm−1 , δσp = 5.5 × 10−2 cm−1 at WRF = 0, T = 300 K and δσp = 7.1 × 10−2 cm−1 at 500 WRF , T = 500 K RF power (W)

AL

α

kσ0 L

nTi + 3/2 (cm−3 )

nTi + total (cm−3 )

0 500

0.02 0.08

2.6 2

0.06 0.19

1.1 × 109 4.5 × 109

1.4 × 1010 4.8 × 1010

ionic line at 368.5 nm is strongly enhanced in comparison to Ti lines at 363.5, 364.3 and 365.3 nm. Hence, it is possible to detect the Ti+ ions by optical absorption. But, before calculating densities, it is necessary to evaluate the pulsed source line width δσ0 . As discussed in [13], the δσ0 half-intensity broadening of Ti lines in the pulsed source is determined by comparing it with the DC source. Same values of δσ0 have been estimated for Ti and Ti+ lines. Values of Ti atom density are reported in Table 9.3 for two RF power supplied to the coil: 0 and 500 W [13]. As for the results presented in Table 9.2, the Ti atom density decreases with the RF power. In Table 9.4, the Ti+ ion density in the same conditions as in Table 9.3 are reported. A sensitive increase of Ti+ density with the RF power is eﬀectively observed. The Ti+ /Ti ratio increased from 4% at WRF = 0 W to 48% at WRF = 500 W.

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Table 9.5. Density of Ti metastable atoms from Ti, 498.2 nm, f = 0.29, δσ s = 10 × 10−2 cm−1 , δσ p = 3.5 × 10−2 cm−1 at WRF = 0 and δσ p = 4.5 × 10−2 cm−1 at 500 WRF RF power (W) 0 500

AL 0.35 0.43

α 2.9 2.2

kσ0 L

nTiM11/2 (cm−3 )

nTiM total (cm−3 )

2 2

1.4 × 10 1.8 × 1010

6.8 × 1010 5.9 × 1010

10

The total density is the addition of all the Ti (a5 F1,2,3,4,5 ) sub-levels measured densities, from [13] Table 9.6. Density of Ti+ metastable ions from TiM + , 375.9 nm, f = 0.2, δσ s = 14 × 10−2 cm−1 , δσ p = 4.5 × 10−2 cm−1 at 300 K and 5.9 × 10−2 cm−1 at 500 K RF power (Watt)

AL

α

kσ0 L

nTi + M7/2 (cm−3 )

0 500

0.01 0.03

3 2.4

0.03 0.08

0.4 × 109 1.4 × 109

The total nTiM + density is the addition of sub-levels nTi+ M densities, from [13]

nTi

M

+

total (cm−3 )

0.4 × 109 2.8 × 109 5/2,7/2

measured

The total nTi + density is the addition of sub-levels measured densities, from [13]. But, as previously suspected, the decrease of Ti neutrals with the RF power was only partially at the beneﬁt of the Ti+ ions. A loss of 2.5 × 1011 cm−3 Ti atoms is found while only 3.4 × 1010 Ti+ ions are produced. To ﬁnd out where the missing titanium atoms are, other energetic species such as Ti and Ti+ metastable atoms have been investigated [13]. The results are reported in Tables 9.5 and 9.6. An increase of Tim /Ti ratio from 20% at WRF = 0–59% at WRF = 500 W is deduced from the measurements. For the + Ti+ metastable ions (Ti+ m ), an increase of the Tim /Ti from 0.1% at WRF = 0–3% at WRF = 500 W is obtained. In conclusion, there is a production of Ti metastable atoms by the RF coil at the detriment of Ti+ ions. Gas heating also plays a role in the disappearance of the Ti neutral atoms. As the pressure is kept constant, if the temperature increases, the local density has to decrease correspondingly. Finally, the titanium ionization rate calculated thanks to the densities obtained by absorption spectroscopy is found to be only ∼25%. This low ionization rate is one of the reasons to change the ionization process of the sputtered metal atoms. For this purpose, HiPIMS is a very promising technique. The optical diagnostic of HiPIMS discharges is presented in Sect. 9.5. Other studies involving AAS have been carried out on magnetron glow discharges. In [20] the authors show that it is possible to implement spatially resolved AAS. In their paper, metal densities are measured along the magnetron – substrate axis. Andrews et al. [21] demonstrate, thanks to an absorption technique which does not make use of a hollow cathode lamp,

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319

0.7

Ionization Fraction ξ

0.6

z=15 mm z=21 mm

0.08

z=27 mm

0.06

0.5

0.04 0.4

0.02 0

0.3

0

1

2

3

4

5

0.2 0.1 0 0

5

10

15

20

25

30

Ar Pressure (Pa) Fig. 9.13. Variations of ionization fraction calculated by using number densities of Ti (II) and Ti (I) for diﬀerent axial position, z = 15, 21 and 27 mm. Applied RF power was constant at 200 W, from [22]

that copper metastable states are also produced in large quantities in a RF ampliﬁed magnetron discharge for copper deposition. On another hand, Nakamura et al. [22] show an increase of the ionization rate (ionization fraction) of titanium with the increase of pressure (Fig. 9.13). In reactive sputtering plasmas, in example, when nitrogen is added to argon, the eﬀect of the cathode poisoning by N2 can be monitored thanks to OES. As reproduced in Fig. 9.14, the Ti atom density, as obtained by resonant absorption spectroscopy, dropped with the cathode poisoning. The transition between a metallic and a nitrided Ti cathode surface was obtained for a gas mixture of 4% N2 in Ar in the experimental conditions of Fig. 9.14 [23]. This transition is observed at the same N2 percentage with or without the RF power on the coil. Moreover, the same transition is obtained by detection with a mass spectrometer [23]. This last result implies that, in these working conditions, GDMS can be used to relate the density of neutral sputtered species as well although the technique is only capable of diagnosing ions. In the work presented in [24], the authors show that the titanium density is two orders of magnitude lower in the reactive Ar−O2 regime than in the discharge run in pure argon. They also present spatially resolved measurements, along the discharge radius, in pure argon and Ar/O2 reactive discharges. The density distribution of titanium atoms, in both conditions, is not homogeneous along the chamber radius and the density distribution changes signiﬁcantly as the pressure increases from 0.35 to 3.5 Pa (Fig. 9.15a, b).

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Fig. 9.14. Density of Ti atoms obtained by resonant absorption spectroscopy (closed squares) and compared with mass spectroscopy (open squares). 3.9 Pa, WDC = 500 W (a): WRF = 0 and (b): WRF = 500 W. Taken from [23]

9.4 Laser Spectroscopy of Magnetron Plasmas This section presents the technique of LIF at one photon, usually referred as LIF and its capability as plasma diagnostic. After some words about the history of this technique, the physical principles will be presented. Finally, some typical applications for magnetron discharges will be presented. 9.4.1 Previous Works Laser-induced ﬂuorescence is nowadays a widely used technique for the detection of atomic and molecular species in gaseous environments with excellent space and time resolution [25–28]. Besides, laser-based plasma diagnostic techniques have largely contributed to advances in the understanding of active plasma kinetics. The LIF technique is strongly related to the development

9 Optical Plasma Diagnostics During Reactive Magnetron Sputtering

321

Ti Atom Density x1010 (cm−3)

(a) 1.2 z=9mm

1.0

z=12mm z=21mm z=27mm

0.8

0.6

0.4

0.2

0.0 0

10

20

30

40

50

Radial Distance r (mm)

Ti Atom Density x1011 (cm−3)

(b)

3

z=9mm z=12mm z=21mm

2

z=27mm

1

0 0

10

20

30

40

50

Radial Distance r (mm) Fig. 9.15. Variation of radial proﬁle of Ti atom densities with axial distance z in pure Ar discharge at 0.35 Pa (a) and 3.5 Pa (b). RF power supplied to the magnetron is 200 W, from Nakamura et al. [24]

of lasers diagnostics [29] and has been for many years used for plasma diagnostic [30–32]. It has been applied to a wide range of discharges and species [33–39]. In magnetron discharges, it is mainly used to probe the sputtered particles density like titanium [40], iron [41] but also for argon atoms [42, 43] and helium [44].

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9.4.2 Principle and Achievements LIF technique is really powerful as it may give information on the velocity, the relative or absolute density and the temperature of the probed species. One-photon absorption LIF is largely used to detect ground state, long-lived or non-radiative atoms, molecules and ions (Al, Fe, Cu, Ti, Ti+ ). For some species (H, N, O, C, F), their ﬁrst exciting levels, optically connected to the ground state, are at energies above 6.5 eV. For theses species, the photo-excitation is only possible with VUV photons. This experimental diﬃculty can be overcome by absorption of two photons to excite the species on the radiative level: the two-photons laser induced ﬂuorescence (TALIF) technique. In this section, we will focus on one-photon absorption LIF since the species detected in magnetron sources are Fe, Cu and Ti. Brieﬂy, the technique is based on the interaction between a laser beam and atoms (molecules and ions) under study [26, 28]. The LIF can be described as a two-step process. First, a speciﬁc atomic or molecular species in its ground state 1 (of energy E1 ) is excited by resonant absorption of laser photons (energy hυlaser ) to a higher energy electronic level 3 of energy E3 with hυlaser = E3 − E1 . Then, the excited state relaxes by spontaneous emission of a ﬂuorescence radiation to a lower state 2 of energy E2 with hυLIF = E3 − E2 . The LIF radiation is emitted in the whole space surrounding the interaction volume. A simpliﬁed three-level scheme of LIF in atoms and molecules is given in Fig. 9.16. The LIF spectroscopy can be used in two diﬀerent ways: – The ﬂuorescence spectrum: the laser frequency is ﬁxed and the ﬂuorescence line is scanned thanks to a monochromator as in a typical OES set-up. This technique gives information on the structure of the ﬂuorescence line. In this case, resolution of detection system should be high enough to resolve the line shape. – The excitation spectrum: the laser frequency is scanned around the excitation frequency. The information collected is related to the excitation line.

ion: A

31

emiss

ion: B

neous

emiss

LEVEL 2 - final state

sponta

lated Stimu

B13 ption:

32

absor

:A ce en

sc

e or

LASER V 10

flu

31

LEVEL 3 - excited state

LEVEL 1 - initial state

Fig. 9.16. Energy diagram as involved in laser induced ﬂuorescence technique

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This set-up does no request a monochromator but only a simple narrow band-pass ﬁlter in front of the detector. In this case, high-spectral resolution can be achieved since it depends only on the line width of the laser and of absorption line. Density of Particles on the Initial State Under some experimental conditions, the ﬂuorescence signal is directly proportional to the density of initial state. Brieﬂy, the intensity of the LIF signal is: I32 αA32 × n3 , where A32 is the Einstein transition probability for spontaneous emission from level 3 to level 1 and n3 is the population density of the excited level 2. Let us describe the rate equation for n3 with considering all the creation and loss terms for the excited level 3. Creation Terms for the Excited Level 3 We can write the gain of population on level 3 as a sum of three diﬀerent terms: – Grad corresponds to radiative de-excitation from levels i of higher energy to the level 3, with the corresponding Einstein probability Ai3 (s−1 ) – Ge corresponds to electronic collisions with atoms in the ground state 1, with the rate coeﬃcient ke1 (cm3 s−1 ) – Gabs corresponds to the resonant absorption of laser photons from the ground state 1 to the excited level 3, with the Einstein coeﬃcient B13 (m3 J−1 s−2 ). The mean energy density of the laser beam is noted −1 u13 (J m−3 s or W m−3 ) These creation terms can be written as (in cm−3 s−1 ): Grad = Ai3 × ni (t) i>3

Gabs = n1 (t) × u13 × B13 , Ge = ne × n1 (t) × ke1 . The product u13 × B13 (s−1 ) corresponds to the resonant absorption probability from the ground state 1 to the upper level 3. It is usually possible to neglect the Grad term as the population density of an excited level is exponentially decreasing with increasing energy. For titanium atoms, the upper level used for LIF scheme is not radiatively connected with higher energy levels. For copper atoms, the energy between excited levels and ground state is high, so density of atoms in excited state is very low and as a consequence their contribution Grad can be neglected. Besides, for typical DC magnetron discharge conditions, electronic density is in the range of 109 –1010 cm−3 in plasma bulk, then u13 × B13 ne × ke1 .

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Loss Terms for the Excited Level 3 We can write the loss terms as a sum of ﬁve diﬀerent terms: – Lrad corresponds to radiative de-excitation from level 3 to any levels j of lower energy, with Einstein probability A3j (s−1 ) – Le corresponds to electronic collisions with excited species on level 3, with the rate coeﬃcient ke3 (cm3 s−1 ) – Ldif corresponds to diﬀusion to the walls with the frequency υwall (s−1 ) – LQ corresponds to quenching by other heavy particles (density Ym in cm−3 ) with the rate coeﬃcient kYm3 (cm3 s−1 ) – Lstm corresponds to stimulated emission with the Einstein coeﬃcient −2 B31 (m3 J−1 s ) These terms can be expressed (in cm3 s−1 ) as follow: A3i = n3 (t) × A3 , Lrad = n3 (t) × i<3

Le = ne × n3 (t) × ke3 , Ldiﬀ = n3 (t) × υwall , Ym × kYm 3 = n3 (t) × Qm , LQ = n3 (t) × m

g1 . Lstm = n3 (t) × u13 × B31 = n3 (t) × u13 × B13 × g3 The product u13 × B31 (s−1 ) corresponds to the probability for which the resonant laser radiation leads to a stimulated emission from the upper level 3 to the lower level 1; with g1,3 the degenerance values of the upper and lower levels of the transition and Blk , Bkl and Akl the Einstein coeﬃcients for absorption, stimulated and spontaneous emission, respectively. Usually, radiative de-excitation frequency is of the order of 107 –108 s−1 . According to low electronic density, this loss frequency is much higher than electronic collisions. Diﬀusion frequency in a planar cylindrical magnetron for titanium is estimated to be 250 s−1, so this term can be neglected. Relation Between Initial (1) and Upper (3) Level Densities The time evolution of the density of level 3 is equal to the diﬀerence between creation terms and loss terms. In a stationary state, with considering the previous assumptions, we obtain: n3 =

n1 (u13 B13 ) . (A3 + Qm ) + u13 B31

(9.16)

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Relation Between Fluorescence Signal and Initial Level (1) Density It is known that the spontaneous emission intensity I32 corresponding to the transition from level 3 (density n3 ) to level 2 is the isotropic energy emitted by unit of time in an experimental volume Vexp (cm−3 ) and detected through a body angle Ω (rad). It is expressed as: ! ∞ K32 × Vexp × Ω I32 = × n3 × hυ32 × A32 P32 dυ, (9.17) 4π 0 where K13 gathers all terms related to detection (transmission factors of windows and ﬁlters, quantum eﬃciency of detector) and P13 is the line proﬁle. The line proﬁle is automatically integrated by using a photomultiplicator as a detector with a rough band-pass ﬁlter (few nm) to cut unwanted frequencies. It is therefore possible to obtain a relation between initial state density and ﬂuorescence signal with combining (9.16) and (9.17): I32 αhυ32 × A32 ×

n1 (u13 B13 ) . (A3 + Qm ) + u13 B31

(9.18)

If laser beam energy density is high enough to ignite stimulated emission, then u13 B31 A3 + Qm and upper level 3 is saturated and is in equilibrium with initial level 1. The ﬂuorescence signal is then independent on laser beam energy: u13 B13 g1 = nsat . (9.19) I32 αnsat 1 × 1 × u13 B31 g3 If laser beam energy density is low enough that u13 B31 A3 + Qm (as it is the case for laser beam energy around 100 μJ), the ﬂuorescence signal depends linearly on the level 1 density and on the laser energy: I32 αhυ32 × A32 × n1

(u13 B13 ) . (A3 + Qm )

(9.20)

Fluorescence intensity is then proportional to the density of the probed specie if many processes are neglected: ampliﬁed spontaneous emission, photoionization and REMPI (absorption of a third laser photon). Exclusion of these processes can be justiﬁed when examining the dependence of the LIF signal on the laser intensity. Besides, quenching of the excited level has to be taken into account to correct the LIF signal. Experiment Laser excitation from the ground state to the excited electronic state is accomplished with a tunable UV laser system; generally a dye laser pumped by a YAG laser or an excimer laser coupled to non-linear crystals. The laser beam is

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Fig. 9.17. Representation of the LIF spectroscopy set-up used for measurement of Ti (I) and Ti (II) densities

focused into the centre of the reactor. The LIF light is detected at right angle from the laser beam direction with a PMT or a monochromator. Usually, the resulting electrical signal is integrated, averaged and stored in an acquisition system triggered with the laser. Spatial resolution can be obtained by moving together the laser beam and the optical detection system. 9.4.3 Application to Magnetron Discharges Typical experimental set-up for LIF measurements are drawn in Fig. 9.17. The laser beam is introduced in the reactor parallely or perpendicularly to the target and ﬂuorescence is detected in a diﬀerent direction, here 90◦ . This way is often used to avoid detection at the same wavelength of the laser to prevent distortion of the ﬂuorescence signal. The ﬂuorescence signal is often directly detected by a photomultiplier (PM) after passing through focalization lens(es) and a ﬁlter centred on ﬂuorescence wavelength, without monochromator. Only a few articles have been devoted to LIF measurements in sputtering magnetron plasmas due to the complexity of the diagnostic compared to OES. The published papers essentially deal with the determination of atom and ion density proﬁles, ion temperature and velocity close to the cathode surface and in the downstream plasma region. In 1990, Goeckner et al. reported for the ﬁrst time LIF characterization of argon ions [43]. They show that Ar+ ion density proﬁle versus distance from the target is peaked in the trap region at nearly the same position as the electron density proﬁle. More recently, Gracin et al. [42] have shown that the density of the Ar+ ions has a broad maximum and decreases much faster towards the cathode than in the opposite direction as mentioned by Goeckner et al. [43]. Nafarizal et al. measured the two-dimensional distributions of Ti and Ti+ densities as a function of power

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and gas pressure [40]. Ti atoms are concentrated near the target due to limited diﬀusion of sputtered atoms. On the other hand, Ti+ ion proﬁle exhibits as Ar+ [43] a maximum at a distance of 4–5 cm from the target where plasma density is higher. Ti and Ti+ densities increase with the gas pressure. They have also shown that a higher discharge pressure rather than a higher plasma power is eﬃcient to obtain higher Ti+ density. For these authors, the density of Ti+ ions reaches 1010 cm−3 and Ti density is 3 × 1011 cm−3 at a distance of 4 cm from the target for a 100 mTorr gas pressure and 75 WDC power. By measuring the Doppler broadening of the excitation spectrum of LIF, Shibagaki et al. and Goeckner et al. evaluated the velocity distribution function of Fe toms and Ar+ ions, respectively, at many positions in the discharge space [41, 43]. Close to the cathode surface, the Fe atoms velocity distribution exhibits asymmetric shape with positive velocity indicating that the ions are moving towards the downstream region. Moreover, the distribution is very broad showing that the Fe atoms have very high kinetic energy near the target. At a gas pressure of 3 mTorr, Fe atoms have an average velocity of 3.6 km s−1 in the region adjacent to the cathode. The distribution becomes symmetric when going perpendicularly far from the target indicating that the Fe atoms are thermalized due to collisions with argon gas. Goeckner et al. made the same observations for Ar+ ions; ion temperature is 0.64 eV at the centre of the discharge while ions are thermalized at the edge of the plasma [43].

9.5 Optical Diagnostic of High-Power Impulse Magnetron Sputtering Discharges In the last couple of years, several ionized physical vapour deposition (IPVD) methods have been implemented to increase the ionization rate of the sputtered metallic vapour. As indicated in Sect. 9.2, some of them are based on the superimposition of a secondary plasma produced for example by an inductive coil [13, 45] (that is found to produce large amounts of metastable argon and metal atoms instead of metal ions, see Sect. 9.3), other by assisting the magnetron plasma by a microwave sustained glow discharge [46, 47]. In this ﬁeld of prospection, high-power impulse magnetron sputtering (HiPIMS, also known as HPPMS for high-power pulsed magnetron sputtering) is a very promising technique [48]. It is based on the production, at the magnetron target, of electric impulsions whose duration ranges from a few μs up to tens or hundreds of μs (see Fig. 9.18a,b for typical I−V characteristics). The power supplied to the plasma during the impulsion is typically two or three orders of magnitude higher than in conventional DC magnetron discharges. Typical power densities are in the order of kW cm−2 . The duty cycle is kept low to maintain the average power density to values that are not detrimental to standard magnetron targets. In these conditions, several articles report ionization rates higher than 50% [40–51]. However, because of the intrinsic characteristics of the impulse discharge (time evolution and high-power loads) and the

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−1000

0.5 m

50

0.0

0

−0.2

−2

−0.4

−4

−0.6

−6

−0.8

−8

−1.0 −1.2

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0 0

Discharge current (x10A)

Torr

20 mTorr

100

2 mTorr

(ii) 150

0.2

2

100

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−1.4 0

5

10

15

20

25

Time (μs)

Time (μs)

(a)

Discharge voltage (x1000V)

−800

0.5 mT orr

mT orr 20

2m

−600

Tor r

(i)

−400

Discharge current (A)

Target voltage (V)

0 −200

(b)

Fig. 9.18. Typical current–voltage characteristics of (a) 100 μs long HiPIM discharge at diﬀerent argon pressures, from [48] and (b) for shorter impulsions (10 μs), from [59]

large amount of metal ions generated, the underlying gas phase physics has to be studied. For this purpose optical diagnostic tools such as OES or AAS are used. Obviously several articles are dealing with the estimation of the ionization rate R of the sputtered vapour to conﬁrm the position of HiPIMS as an IPVD technique. Beside the value of R = 70% estimated from deposition rate measurements with biased substrates [49], several authors have estimated the ionization rate by means of optical diagnostics. One can use ion to neutral line intensity ratios, assuming similar excitation energies for both species, to estimate the ionization rate. In this particular case, intensities can by qualitatively related to densities (see previous sections). In [51–53], emission spectra obtained from HiPIMS and DC, DC ampliﬁed by an ICP or DCpulsed discharges are compared (see Fig. 9.19). In the spectra recorded with HiPIM discharges, the metal ions to metal neutral intensity ratio is strongly enhanced. These are the ﬁrst evidences of a strong ionization by the dense pulsed plasma. It is generally assumed that in DC discharges R < 10%; see values determined in [51–60]. By means of theoretical ﬁtting of OES spectra, Bohlmark [51] has determined a value R = 90% for HiPIMS.Ehiasarian even reports [53] the emission from twofold ionized chromium atoms. In the same article is presented increasing intensity ratios for chromium singly charged to neutral (Cr+ /Cr) and doubly charged to neutral line (Cr2+ /Cr) as a function of the target peak current. In [50], it appears that one can inﬂuence the

9 Optical Plasma Diagnostics During Reactive Magnetron Sputtering High Power Pulsed Magnetron Sputtering

OPTICAL EMISSION INTENSITY, A.U.

6000 4000

Ti (0)

0 360

Ti (0)

Ti (1+)

2000 365

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Ti (1+)

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RF Coil Enhanced Magnetron Sputtering

0.05

0.00 360

365

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375

380

Magnetron Sputtering

15 10 5 0 360

365

370

375

380

WAVELENGTH, nm Fig. 9.19. Comparison between optical emission spectra from magnetron discharges for titanium sputtering in argon. Comparison of emission intensities between (top) HiPIMS discharge, (middle) RF coil ampliﬁed magnetron discharge and (bottom) conventional DC plasma, taken from [53]. Neutral lines are labelled by Ti (0) and ion lines by Ti (1+)

plasma composition, more speciﬁcally the ionization rate, by changing the pulse duration. The ionization rate is obtained from both line intensity ratio but also from AAS experiments. These results conﬁrm that HIPIM discharge is a good candidate for IPVD as generally, R > 50%. As the HiPIM discharges intrinsically develops a time-dependent behaviour, it seems necessary to use diagnostic tools capable of time-resolved measurements to probe the evolution of the plasma chemistry as a function of time, during the discharge itself but also through the post-discharge. In [50, 53–56], it is shown that the plasma composition evolves as time goes on. Argon neutral emission appears at ﬁrst as it is the background gas; argon is excited as the discharge breakdown occurs. As Ar+ ions are produced, the signal rises along with the discharge current. Then the signal from the sputter neutral metal develops. The emission from ionized metal atoms is detected afterwards. A decrease of the argon line intensity accompanies the increase of metal ion signal. This decrease is attributed to momentum transfer from sputtered metal atoms to background gas (remember the large target current density) and as a consequence of this sputtering wind [15], argon density decreases in the magnetron vicinity. Therefore, there is a transition from argon plasma to metal/argon plasma. It appears that this transition is a function of the pulse duration [50]. The cooling of the electrons by the massive intro-

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duction of low ionization potential metal atoms in the plasma might also lead to the decrease of argon signal as argon excitation originates from metastable state at 11.5 eV. Other studies were performed using TR-AAS, by means of a pulsed optical source [13, 58, 59]. By this method, time-resolved measurements of the ionic current at the substrate were correlated to the ion ﬂuxes reaching the substrate surface and one could identify that Ar+ ions were the ﬁrst to reach the substrate [60, 61]. Ar+ ions arrive almost simultaneously with the discharge current at the magnetron. To interpret this result it is assumed that argon atoms are ionized, close to the substrate, by the fast electron beam generated by the high discharge voltage. A second wave of ions attains the surface later, during the post-discharge. It is composed of the sputtered metal ions travelling from the target to the substrate. Their drift speed is of the order of 103 m s−1 [54,58,59]. In [59] the way to accelerate the diﬀusion kinetics thanks to an ICP superimposed to the HiPIM discharge is presented (see Fig. 9.20). This suggests that metal ions obey to ambipolar diﬀusion. When supplying hot electrons to the target-substrate gap (i.e. by means of the ICP), one can accelerate ions. In [60] authors conﬁrm that, in HiPIMS experiments done at high pressure (4 Pa), ambipolar diﬀusion is the driving force for titanium ions while Fick’s law rules the diﬀusion of titanium neutrals. As highlighted by results obtained from TR-AAS and presented on Fig. 9.21, Ti and Ti+ density proﬁles are correlated to 1D diﬀusion and ambipolar diﬀusion models, respectively. In the same article, authors show by means of time-resolved

Substrate current density (mA / cm2)

magnetron current 14

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400 WRrf

12

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200 Wrf 10

−3

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100 Wrf −4

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50 Wrf 4

O Wrf 2

−5 −6

magnetron current density (A / cm 2)

0

16

0 −50

−7 0

50

100 150 200 250 300 350 400 450 500 550

Time (μs)

Fig. 9.20. Time-resolved ion saturation current at the substrate at 10 mTorr, with and without the ICP superimposed to the HiPIM discharge, from Konstantinidis [59]

9 Optical Plasma Diagnostics During Reactive Magnetron Sputtering 10

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2.0x10 10 1.6x10 10 1.2x10 9 8.0x10 9 4.0x10 0.0

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(a)

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z = 14 cm

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5x10 10 4x10 10 3x10 10 2x10 10 1x10 0

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7x1010 6x1010 5x1010 4x1010 3x1010 2x1010 1x10 0

Absorption measurements Ambipolar diffusion model

z = 14 cm

(a)

11

1.0x10 10 8.0x10 z = 10 cm 10 6.0x10 10 4.0x10 10 2.0x10 0.0

(b)

11

2.5x10 11 2.0x10 11 1.5x10 11 1.0x10 10 5.0x10 0.0

(c)

z = 6 cm

0

2

4

6

8

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Time in the post-discharge (ms)

Fig. 9.21. Through the post-discharge of a HiPIMS experiment run at 4 Pa for Titanium deposition, the density proﬁles of titanium neutrals and ions can be, respectively, superimposed to a 1D diﬀusion and ambipolar diﬀusion proﬁles [60]

Fig. 9.22. TR-OES of a reactive HiPIMS discharge produced in an Ar/O2 mixture, at 7 mTorr, for the deposition of titanium oxide thin ﬁlms

Langmuir probe diagnostic that electron and metal ions diﬀuse together in the post-discharge. Some experiments have also been carried out in reactive discharges, for the deposition of oxides [61–63], nitrides [64] and carbides [65]. Some results on the optical diagnostic of the HiPIMS reactive discharge have lead to the conclusion that nitrogen molecules are highly vibrationally excited, with estimated vibrational temperature of ∼7,000 K, which is higher than in DC discharges. Other results (see Fig. 9.22) obtained from time-resolved OES show that a high ionization rate (i.e., the intensity ratio of Ti+ on Ti neutral is high) of

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the titanium vapour is still achievable despite the fact that the discharge was run in the so-called “poisoned regime” [66]. On the same ﬁgure one can see that emission from the O2 + molecular ion (band head at 602.4 nm) appears only at the beginning of the pulse and quickly fades while emission intensity from O atoms (emission line at 777 nm) rises as the pulse goes on. This would indicate also a strong dissociation of oxygen molecules. To compare HIPIM and DC magnetron discharges, the relative dissociation rates are calculated, in both cases, from the intensity ratio obtained by dividing the intensity of O (777 nm) lime intensity by the intensity coming from the O2 + band head (602.4 nm). This ratio can be, at ﬁrst approximation, related to the density ratio of O atom on O2 molecule, i.e. to the dissociation rate of O2 in two O atoms [67]. From these experiments and calculation, it appears that the dissociation rate is ten times higher for HiPIMS discharge. Then from these results one can conclude that the large amount of energy supplied to the plasma leads to the production of a strongly ionized metal vapour but also to a highly reactive atmosphere as it is known that, for example, O atoms are highly reactive species in reactive sputter deposition processes [68]. In conclusion, the results obtained from optical characterization of HiPIMS discharges gathered in this section reveal that this technique is a good competitor for IPVD. Therefore, HiPIMS looks as an interesting deposition method for microelectronic device fabrication as one can promote conformal deposition [69], for example in high aspect ratio trenches. HiPIMS deposited thin ﬁlms are also interesting in optical and mechanical applications as they are found to be denser [63, 70], with a higher refractive indices [57, 59] or with enhanced wear resistance capabilities [64] than ﬁlms obtained by conventional sputtering methods.

9.6 Conclusion Optical diagnostics are powerful techniques that give a large insight of reactive magnetron plasma chemistry and physics. Kinetic mechanisms can be determined as well as plasma composition. Thanks to LIF, atom densities and speeds are measured. Absorption spectroscopy allows determining absolute densities which is of tremendous importance to estimate ﬂuxes of incoming species at the substrate position or to calculate the ionization rate of the sputtered metal vapour in ionized magnetron processes. On the other hand, OES is used to control the ﬁlm composition during reactive magnetron sputtering. By monitoring the line intensity of the metal atoms sputtered in the plasma, the gas mixture is continuously adjusted and, as soon as the line intensity changes, the mixture is adapted thanks to a feedback control loop. In such conditions, it is possible to work into the transition zone, between the metal and the poisoned regimes. To some extent, these diagnostic tools can also oﬀer time-resolved capabilities. Time-resolved measurements are important, for example, in DC-pulsed

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and HiPIMS devices used for thin ﬁlm deposition. Therefore, optical spectroscopy diagnostic tools can help researchers as well as R&D engineers to carefully control and understand magnetron plasmas during reactive sputtering.

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55. P. Vasina, M. Mesko, M. Ganciu, J. Bretagne, C. Boisse-Laporte, L. De Poucques, M. Touzeau, Europhys. Lett. 72(3), 390 (2005) 56. J. Vlcek, P. Belsky, A.D. Pajdarova, M. Kormunda, J. Lestina, J. Musil, in Proceedings of the XIV International Conference on Gas Discharges and their Applications, Liverpool, UK, 2002, p. 92 57. S. Konstantinidis, A. Ricard, M. Ganciu-Petcu, J.P. Dauchaut, M. Wautelet, M. Hecq, Proceedings of the 46th Annual Technical Conference of the Society of Vacuum Coaters, San Francisco, USA, 2003, p. 452 58. L. de Poucques, J.C. Imbert, C. Boisse-Laporte, P. Vasina, J. Bretagne, L. TeuleGay, M. Touzeau, Plasma Sources Sci. Technol. 14(2), 321 (2005) 59. S. Konstantinidis, M. Ganciu, J.P. Dauchot, M. Hecq, App. Phys. Lett. 88-1, 21501 (2006) 60. L. de Poucques, J.C. Imbert, C. Boisse-Laporte, J. Bretagne, M. Ganciu, L. Teule-Gay, M. Touzeau, Plasma. Source Sci. Technol. 15, 661 (2006) 61. J.A. Davies, W.D. Sproul, D.J. Christie, M. Geisler, in Proceedings of the 47th Annual Technical Conference of the Society of Vacuum Coaters, Dallas, USA, 2004, p. 215 62. D.A. Glocker, M.M. Romach, D.J. Christie, W.D. Sproul, in Proceedings of the 47th Annual Technical Conference of the Society of Vacuum Coaters, Dallas, USA, 2004, p. 183 63. S. Konstantinidis, J.P. Dauchot, M. Hecq, Thin Solid Films 515, 2006, 1182 64. A.P. Ehiasarian, W.-D. Munz, L. Hultman, U. Helmersson, I. Petrov, Surf. Coat. Technol. 163–164, 267 (2003) 65. J. Alami, P. Ecklund, J. Emmerlich, O. Wilhelmesson, U. Jansson, H. Hogberg, L. Hultman, U. Helmersson, Thin Solid Films 515, 1731 (2006) 66. D. Depla, S. Heirwegh, S. Mahieu, J. Haemers, R. De Gryse, J. Appl. Phys. 101(1), 13301 (2007) 67. V. Vancoppenolle, P.Y. Jouan, A. Ricard, M. Wautelet, J.P. Dauchot, M. Hecq, Appl. Surf. Sci. 205(1–4), 249 (2003) 68. R. Snyders, R. Gouttebaron, J.P. Dauchot, M. Hecq, Surf. Coat. Technol. 200(1–4), 448 (2205) 69. J. Alami, P.O.A. Persson, D. Music, J.T. Gudmundsson, J. Bohlmark, U. Helmersson, J. Vac. Sci. Technol. A 23(2), 278 (2005) 70. B.M. Dekoven, P.R. Ward, R.E. Weiss, D.J. Christie, R.A. Scholl, W.D. Sproul, F. Tomasel, A. Anders, in Proceedings of the 46th Annual Technical Conference of the Society of Vacuum Coaters, San Francisco, USA, 2003, p. 158

10 Reactive Magnetron Sputtering of Indium Tin Oxide Thin Films: The Cross-Corner and Cross-Magnetron Eﬀect H. Kupfer and F. Richter

10.1 Introduction With ITO, which is frequently used as a transparent electrode [1, 2], two contradicting demands can be in principle fulﬁlled at the same time: high optical transparency and low electrical resisitivity. To realise this homogeneously over the whole substrate in the case of dynamic deposition in an inline sputtering system necessitates a very homogeneous process in the case of static deposition, i.e. using ﬁxed substrates. During these static depositions we found a lateral distribution of ﬁlm properties which did correspond to the so-called cross-corner eﬀect (CCE) or cross-magnetron eﬀect (CME). The CCE/CME is being discussed in the literature since the year 2000 as an inhomogeneous target erosion in rectangular magnetron sputtering. It was found that in certain cases, in particular for magnetrons with strong magnetic ﬁelds, sputter erosion was higher in the curves of the rectangular magnetron as along the side tracks. This was reason for concern with respect to target utilisation. However, as we have found, the CCE/CME is not only reﬂected in a distinct inhomogeneity of target erosion but appears also in form of a lateral distribution of ﬁlm properties. In the case of our ITO ﬁlms (cf. Sect. 10.4) these inhomogeneities were so severe that they could not be tolerated, despite the fact that the target erosion was practically homogeneous. This ﬁnding illustrates that even if rectangular magnetrons are nowadays usually improved with respect to homogeneous target erosion, CCE/CME can still be a problem which needs attention. In the following, we ﬁrst present results from the literature about CCE/ CME in the light of target erosion inhomogeneity was well as simulation work revealing how the conﬁguration of magnets inﬂuences the magnetic ﬁeld distribution which ﬁnally causes an inhomogeneous plasma distribution and target erosion (Sect. 10.2). In Sect. 10.3, results of in situ measurements in magnetron sputtering are given which show how the CCE/CME appears as a lateral distribution of both charge carrier density and optical emission from

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the plasma. In Sect. 10.4, we present our results about indium tin oxide (ITO) deposition which illustrate how the CCE/CME can impact the homogeneity of ﬁlm properties to a large extent (Sect. 10.4). Finally, we suggest a mechanism for the formation of inhomogeneous ﬁlm property distributions in ITO ﬁlms based on the crucial role of atomic oxygen.

10.2 The CCE and CME as an Inhomogeneous Target Erosion The CCE/CME was observed for the ﬁrst time as novel, strong magnetic materials (based on rare earth elements) were introduced in the construction of magnetron sputtering sources. In 2000, Shidoji et al. [3] reported that an anomalous target erosion had been found for rectangular magnetrons having strong magnetic ﬁelds. The erosion was anomalously increased at the boundary from the curved section and the straight part of the rectangular magnetron. However, this increase appears only at one side of the curved section. This can be seen from Fig. 10.1 which was taken from a later paper [4]. Another piece of empirical results is provided by Fig. 10.2 (courtesy of Dr. P. Polcik, Plansee) which shows cross sections of a rectangular TiAl target (33/67 at. %; 12 × 170 × 830 mm3 ) taken every 70 mm.

Fig. 10.1. Photograph of an eroded rectangular target sputtered with a conventional magnetron cathode, showing a faster etching in the upper left corner area (ﬁgure taken from [4] with permission)

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Fig. 10.2. Cross sections of a used TiAl 33/67 at.% target which was applied for deposition of wear resistant TiAlN coatings. The upper cross section is positioned in the curved part of the racetrack. The distance between individual sections is 70 mm. Courtesy of P. Polcik, Plansee GmbH

In their investigation of the CCE [3], Shidoji and co-authors used a hybrid model presented by them in [5], combining a Monte Carlo simulation [6] and a relaxation continuum model. This enabled them to achieve a self-consisting simulation of the DC magnetron discharge. In these calculations, the magnetic ﬁeld distribution in front of the target is calculated from the arrangement of the permanent magnets. They consider a rectangular-shaped centre magnet surrounded by a rectangular arrangement of two longer and two shorter bars forming the outer magnet. This arrangement always yields – just for geometrical reasons – a distinctly smaller magnetic ﬁeld in the curved section in comparison to that at the straight part. In the following these magnetic ﬁeld strength values will be denominated as Bmax (straight part) and Bmin (curved section), respectively. In [3], for the realistic example of a Sm−Co magnet with yoke the magnetic ﬁeld at the target surface was calculated for those places where the magnetic ﬁeld is parallel to the target surface, i.e. Btot = B|| and B⊥ = 0, respectively, which are known to be most eroded by energetic ion impact. The authors received a value of Bmax = 970 G along the straight section while in the middle of the curved part only Bmin = 730 G was obtained. Moreover, the simulation shows that the asymmetry of the CCE is due to the E × B drift: The increased erosion rate appears where the electrons exit the curve. The essential mechanism is illustrated in Fig. 10.3. Here, the electrons are drifting from a region A which has a high magnetic ﬁeld, Bmax , of 1,000 G through a region B with a lower magnetic ﬁeld, Bmin , of 620 G (thus modelling the curved region) further into another A type region. Considering that the mean kinetic energy of the electrons and therefore their ability to ionise gas particles is practically constant along the racetrack, the inhomogeneity of target erosion is only determined by the inhomogeneous

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plasma density distribution. This, on its part, can be understood as being due to a modiﬁcation of the electron drift velocity by the varying magnetic ﬁeld. In general, the E × B drift velocity is proportional to the electric ﬁeld and inversely proportional to the magnetic ﬁeld. Hence, if the drifting electrons enter region B, their drift velocity increases suddenly according to the reduction in the magnetic ﬁeld strength, thus causing a spatial minimum of the electron density. Within region B, the trapping of electrons is reduced owing to the smaller magnetic ﬁeld strength. Hence, the electrons are more easily accelerated by the electric ﬁeld thus causing an increase of the average height of the E × B ﬂux above the cathode. At a larger distance from the cathode, the drifting electrons experience a smaller electric ﬁeld which yields a gradual reduction of the mean drift velocity as can be seen in the ﬁgure. Eventually, when the drift current enters the high magnetic ﬁeld region, the drift velocity undergoes an additional, sharp decrease connected with the formation of a spatial maximum in the electron density. The existence of this maximum is the very nature of the CCE. It comes out that this eﬀect exists only for relatively large magnetic ﬁelds as those used in Fig. 10.3. Figure 10.4 shows the inﬂuences of (1) the maximum magnetic ﬁeld strength Bmax (existing at the straight parts) and (2) the ratio Bmin /Bmax on the relative increase of the erosion depth. The latter is the ratio of the maximum erosion depth (i.e. the erosion depth in the “CCE corner”) to the erosion depth in the middle of the straight region. A relative increase of the maximum erosion rate up to 50% can be expected, however, for a maximum magnetic ﬁeld strength of ≤100 G the CCE does practically not exist. It should be mentioned that Shidoji et al. [3] used the realistic rectangular magnet assembly to determine the magnetic ﬁeld strength along the racetrack, however, the Monte Carlo simulation delivering the drift velocity

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(cf. Fig. 10.3) as well as electron energy and density (not shown here) was performed assuming a straight magnetron system without any curved section: Strong (type A region) and weaker magnets (B regions) were simply periodically arranged in longitudinal direction. This restriction was overcome by Fan and co-workers [4]. In their simulations they used a somewhat diﬀerent magnet arrangement consisting of two straight bars for the outer magnets which were completed by two arches at the curved part rather than two shorter bars oriented perpendicular as it was done in [6]. The centre magnet was again a bar which, however, had rounded ends in form of two half cylinders. Moreover, they considered the real curved structure of the magnets described above not only for the calculation of the magnetic ﬁeld distribution but also in the Monte Carlo simulations. From the Monte Carlo simulations the threedimensional distribution of ionisation position was received which could be utilised to predict the target erosion distribution. Essentially, Fan et al. [4] with their more realistic calculation conﬁrmed the ﬁndings of Shidoji et al. Their magnet system was equally strong corresponding to about 1,000 G at the straight part and showed a similar distinct reduction in the curved region. Based on this and taking into account their somewhat diﬀerent process parameters (e.g. the argon pressure was 2 mTorr in comparison to 5 mTorr in [3]) they predicted an increase of the erosion rate at the maximum by about 65%. An advantage of their approach was the possibility to “play around” with the size and shape of the magnets to see how the CCE can be reduced. Using half cylinders with larger radius (30 mm instead of 10 mm) but slightly reduced height (30 mm instead of 35 mm) as the endpieces of the centre magnet, they received a ﬁeld distribution which did not vary much along the

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racetrack. Monte Carlo simulation based on this ﬁeld distribution delivered a quite homogeneous target erosion as can be seen from Fig. 10.5. The authors point out that “to eliminate the CCE a general principle is that the magnetic ﬁeld should be designed to allow electrons drifting in a consistent velocity along the racetrack above the target”. Lopp et al. [7] were the ﬁrst to the author’s knowledge who used the term cross-corner eﬀect. Analogous to Fan et al. they also conﬁrmed the ﬁndings in [3] by doing MC simulation of the plasma density distribution based on the true three-dimensional form of the magnetron rather than using Shidojis “equivalent straight magnetron”. They assumed a magnetron having a ﬁeld strength of 100 G in the curve and 200 G at the straight part and found a strongly increased target erosion at the outlet of the curve. Their numerical results proved to be also in very good quantitative agreement with the experiment as it is shown in Fig. 10.6. They get an increase of the target erosion rate of about 40%. Considering their Bmax = 200 G as well as the given Bmin /Bmax = 0.5 this ﬁts nicely into the results of Shidoji et al. given in Fig. 10.4. Another interesting result from this work is presented in Fig. 10.7 [8]. This ﬁgure shows the points above the target where – following the simulation results – ionisation takes place. One can clearly see that at the regions of increased target erosion (“CCE corners”) the ionisation points are frequently located in larger heights. However, most of the plasma is still close to the target surface, so we see an extension of the plasma towards the substrate rather than an “upwards turn” of the E × B ﬂux. In another paper [9] these authors showed that matching of curved and straight part of the magnetron in ﬁeld strength is a necessary condition for homogeneous target erosion rather than a suﬃcient one. Their calculations substantiate that the distribution of plasma density and target erosion may still depend on the form of the magnetic ﬁeld above the target even if the ﬁeld strength in the relevant region (where B⊥ = 0 at the target surface) is one and the same. In Fig. 10.8 the distribution of inclination of the magnetic ﬁeld lines is presented, showing that the volume with magnetic ﬁeld parallel to the

10 Reactive Magnetron Sputtering of Indium Tin Oxide Thin Films Erosion depth [a.u.] 0.0 _ 2.5 2.5 _ 7.5 5.0 _ 7.5 7.5 _ 10.0 10.0 _ 12.5 12.5 _ 15.0

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target surface, i.e. perpendicular to the electric ﬁeld is smaller in the curve than at the straight part. This, however, is the volume where the plasma is concentrated. By changing the arrangement of magnets and using properly designed iron shunts the authors were able to change the spatial magnetic ﬁeld distribution in the curve (cf. “modiﬁed curve” in Fig. 10.8) which enabled them to homogenize the plasma distribution above the magnetron to a large

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Fig. 10.8. Angle between the magnetic ﬁeld direction and a horizontal plane at the straight part and curved section, respectively, and the increase of the horizontal magnetic ﬁeld region in the curved section using a varied magnet arrangement (ﬁgure taken from [9] with permission, by courtesy of The Society of Vacuum Coaters)

extent yielding an increase of the target utilisation from 38 to 44% for a large, 3,000 mm long magnetron [9]. Yang et al. [10] conﬁrmed the results reported in [9] as they found both experimentally and from MC simulation that preventing the CCE cannot be accomplished by just keeping B|| = const. at all places with B⊥ = 0 at the target surface. In addition, the magnetic ﬁeld must be tailored such that the radial position of all these B⊥ = 0 places is the same both along the straight part and within the curves. In our opinion this is just another formulation as that used by Lopp et al. [9] for the general condition that the cross section of the magnetic ﬁeld distribution taken perpendicular to the E × B drift should be as constant as possible along the racetrack. Buyle et al. [11] did similar Monte Carlo simulations to retrace the high energy electrons in magnetron sputtering. They also found an increase in ionisation just after the electrons have performed the turn at the end of the magnetron and related this to the CCE. Moreover, they determined the average height of the drifting electrons above the target surface and found that this height has a maximum value just after the turn, thus causing a reduced drift velocity and increased ionisation per unit length along the racetrack in principle agreement to the results discussed above. Similarly to Shidoji [3] and Fan [4] they deﬁned a quantity AH describing the relative amount of extra

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ionisation owing to the CCE and investigated the dependence of this quantity on several parameters. In Fig. 10.9 their results are shown for the maximum horizontal magnetic ﬁeld strength (existing at the straight region), for the gas pressure as well as for the length of the target. The ﬁrst dependence can be compared with the results of Shidoji (Fig. 10.4) yielding a qualitative agreement as the CCE increases with ﬁeld strength. However, Buyle et al. get a sharp bend at around 750 G followed by a decrease rather than a gradual reduction of the slope. Such contradictions illustrate that further work is necessary as the models used are simpliﬁed in several respects. Another important result of Buyle et al. is that the inﬂuence of the magnetic ﬁeld depends on the gas pressure. This is important with respect to the eﬀorts to optimise the magnet conﬁguration of the magnetron to reduce the CCE (the so-called “magnetic ﬁeld tuning”).

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Finally, the so-called CME [12] shall be mentioned. This eﬀect appears in the case of a so-called twin or dual magnetron [13, 14] where two rectangular magnetrons are arranged parallel to each other and operated with middle frequency power of typically 10–250 kHz in such a way that both magnetrons alternately act as anode and cathode. In this case, the normal CCE appearing in one single cathode – or in two cathodes if they are powered “in parallel” – is superimposed by the interaction between the two targets (cf. Fig. 10.10). The E × B drift at both targets gets strongly modiﬁed because of the now unsymmetrical, strongly inclined electric ﬁeld. This yields an increased plasma density between the targets and causes a general increase of plasma density along their “inner straights”. Due to this, the maxima of target erosion which are situated at the “inner straights” (maxima B and C) are enhanced, while the maxima at the “outer straight” of each single cathode (i.e. maxima A and D) get much reduced. Finally, the two-target arrangement has in total two spatial maxima of plasma density.

10.3 Evidence of the CCE and CME From In Situ Measurements 10.3.1 Introduction Despite the fact that the very nature of the CCE is a plasma densiﬁcation at the exit of the curved section of the erosion track of a rectangular target (cf. Sect. 10.2), there are only few investigations of the CCE by plasma property measurements. In the following we present results from the literature as well as – in somewhat more detail – of our own investigations. The time dependent optical emission of the magnetron plasma was investigated by Zhu et al. [15, 16] using an asymmetric bipolar-pulsed magnetron discharge. The authors mapped the emission distribution along the racetrack

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close to the target, using either the Ar emission at 750 nm or integrating the optical emission in the wavelength range from about 250 up to 850 nm. They found a spatial redistribution of the plasma emission intensity during the ontime of the sputter pulse. During the ignition of the plasma discharge, i.e. at the beginning of the on-time they obtained a stronger optical emission in the curved sections of the erosion track than in the straight part. Later on, in the steady-state phase of the sputter pulse, the relationships were reversed: The emission of the straight section is slightly more intense than that of the curved sections. In the ﬁrst instance, the authors explain their ﬁndings with the fact that the acceleration of electrons by the increasing electric ﬁeld at the beginning of the voltage pulse depends on the magnetic ﬁeld. At the curved section of the racetrack, where the magnetic ﬁeld is weak, the emerging electric ﬁeld enables the electrons to move higher and to gain more kinetic energy than in the straight sections of the erosion track. Hence, the excitation of Ar atoms by energetic electrons starts in the curved section of the racetrack. Later on, during the steady-state period of the negative sputter pulse a high discharge voltage is reached and the electrons get enough kinetic energy to excite Ar atoms also in the straight sections of the erosion track. There, the magnetic ﬁeld is stronger than in the curved sections resulting in a more intense optical emission. Both optical emission measurement and accompanying simulation work showed an increase of the emission intensity at the exits of the curved sections of the erosion track, thus clearly indicating a CCE in this magnetron discharge. The increased emission correlating to an increased plasma density can be measured during both the ignition period of the pulse and the steady-state period. Their spatial positions correlate with those where a transition from a weaker to a stronger magnetic ﬁeld takes place. The latter yields a reduction of the E × B drift velocity of the electrons which causes an intensiﬁed excitation and ionisation of the process gas as discussed in Chap. 2. The increased optical emission at the exit of the curved section as well as the diﬀerent distribution of the plasma emission in height in comparison to the entrance into the curved section could be shown very impressively by Lopez et al. [16]. Figure 10.11 shows this emission intensity distribution. In our group, the CCE (in case of the single magnetron) and CME (for the dual magnetron) were investigated by time integrating OES and Langmuir double probe measurements close to the substrate [17–19] to correlate the process parameters to the properties of the growing ITO ﬁlms. The magnetron source was formed by two separate single targets, each 400 mm in length and 130 mm in width. They were assembled vertically with a distance of the target centre lines of 340 mm. The two single magnetrons can be powered as a dual magnetron as well as two single magnetrons. In the dual magnetron case they were alternately used as anode and cathode without a separate anode electrode. In the single magnetron mode both target were supplied in parallel with a unipolar power and a separate hidden anode

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Fig. 10.12. Target assembly together with measurement tracks for the plasma property analysis (a) and positions of substrates in ﬁlm deposition experiments (b)

behind a plasma shielding was used for each of the targets [20]. A sine wave generator as well as a DC-pulse generator was applied to involve diﬀerent discharge types. The substrates were situated in a distance of 110 mm from the target. The OES and Langmuir probe measurements were performed 90 mm from the target position, i.e. 20 mm above the substrate position. This measuring position was chosen to obtain information on the plasma inﬂuencing the ﬁlm growth. All measurements were done with the process operating in the transition mode of the targets close to the border to the metallic mode. The total pressure was held constant at 0.4 Pa. This enables a very sensitive correlation of the plasma measurement results to the ﬁlm properties, which is described in more detail in Chap. 4. The optical emission of the plasma was measured using a tube collimator, monitoring along the straight section of the racetrack of the target as indicated in Fig. 10.12 (measurement line 1). A Jobin-Yvon spectrometer (type HR 460S) with a resolution of 0.1 nm was used. The Langmuir double probe measurements were performed also along the vertical line 1 as well as along three horizontal measurement lines (nos. 2–4, see Fig. 10.12). More experimental details were described elsewhere [17, 18, 21].

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The thermal load of the substrate was determined laterally resolved using a heat probe consisting of three NiCr–Ni thermocouples, each bonded on a well deﬁned Cu plate with a diameter of 18 mm. This probe was suited to measure the three positions at one horizontal track simultaneously. It was placed successively at tracks 2, 3 and 4, thus measuring the nine substrate positions, which were used for ﬁlm deposition experiments (see Fig. 10.11). The probe was held on ﬂoating potential, i.e. it was hit by equal ﬂuxes of ions and electrons. To calculate the heat ﬂow towards the substrate, the gradient of the temperature–time curve of the heating up and cooling down cycle was evaluated. This was done at a reference temperature of 330 K to keep the measurement errors low. 10.3.2 The CCE and the Plasma Properties of Unipolar-Pulsed Single Magnetron Discharges First, we present the distribution of the charge carrier density and electron temperature Te of a unipolar DC-pulsed single magnetron discharge determined by Langmuir double probe measurements along track 2. This track crosses both the regions where the drifting electrons enter and exit the curved section of the racetrack. Since the charge carrier density was calculated from the ion saturation current of the Langmuir double probe, in the following the charge carrier density is denominated by ni . It is assumed that the electron density is equal to the ion density (ni = ne ). In all experiments described here the E × B drift current is ﬂowing clockwise. Both magnetron sources were working parallel at an average discharge power of 1.6 kW per target. The charge carrier density (Fig. 10.13) shows a strong asymmetric structure in front of each magnetron source [18]. The ni values increases from 2 × 1010 cm−3 on the left target side to 4.5 × 1010 cm−3 on the right target side. Outside of the targets ni fastly drops down to values of about 1 × 109 cm−3 . The electron temperature in front of target 2 is about 5 eV. In front of target 1 a somewhat higher Te of about 6 eV was measured. Figure 10.13 shows clearly an increased charge carrier density in front of the substrates at those positions, where in agreement with the results presented in Sect. 10.2 an increased plasma density due to the CCE is to be expected. Following the model calculations of Lopp et al. [9] and Buyle et al. [11] at those positions not only the plasma density is increased but also the height of the electrons above the racetrack is larger than elsewhere. This might be the reason for the fact that we see a distinct increase of the plasma density 20 mm above the substrate but do not ﬁnd an inhomogeneity in the growth rate (cf. Sect. 10.4.1.).

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Fig. 10.13. Charge carrier density ni and electron temperature Te measured along track 2; unipolar DC-pulsed single magnetron discharge, P = 1.6 kW per target, ptot = 0.4 Pa, FAr = 40 sccm, FO2 = 63 sccm. Figure taken from [18] with permission, Copyright Wiley-VCH Verlag GmbH & Co. KGaA

10.3.3 The CME and the Plasma Properties of Bipolar-Pulsed Dual Magnetron Discharges The plasma property investigations by Langmuir double probe measurements during dual magnetron powering were performed along the tracks 2, 3 and 4 (horizontal) and along track 1 (vertical measurement). We have applied sine wave-powered as well as DC-pulsed bipolar discharges. In case of the sine wave powering, the discharge power per target was adjusted to P = 2.0 kW per target. This value has provided a very similar deposition rate as in the bipolar DC-pulsed case where P = 1.6 kW per target was applied. Hence, these parameters allowed a reasonable comparison of the diﬀerent discharge powering modes. In Fig. 10.14 the charge carrier density and electron temperature data are shown which were measured along tracks 2 and 4 in case of the sine wave-powered dual magnetron. Firstly it can be seen that the charge carrier density above the substrate is generally by about one order of magnitude higher than for the unipolar-pulsed single magnetron discharge. This strong increase of ni can be ascribed to the distinctly diﬀerent anode conditions in those two cases: In single magnetron sputtering, a hidden anode is situated behind a plasma shield on either side very close to the magnetron target. In case of the dual magnetron sputtering, the target of the second source is acting as the anode. This anode is situated relatively far from the cathode (cf. Fig. 10.12a) and it is – which is even more important – additionally separated by the plasma shields surrounding both

10 Reactive Magnetron Sputtering of Indium Tin Oxide Thin Films (a)

351

(b)

Fig. 10.14. Charge carrier density ni (a) and electron temperature Te (b) measured along tracks 2 and 4; sine wave-powered dual magnetron discharge, P = 2.0 kW per target, ptot = 0.4 Pa, FAr = 40 sccm, FO2 = 61 sccm

targets. These plasma shields constrain the electrons on their path to the distant anode into the region close to the substrates. Moreover, since the charge carriers are coupled to the magnetic ﬁeld lines they are led preferentially to the usually poisoned target centre and not to the clean sputter groove. This eﬀect of a so-called magnetically shielded anode [22] inhibits an eﬀective operation of the anode. This increases additionally the plasma density in the substrate region. Second, the distribution of the charge carrier density exhibits a characteristic asymmetry corresponding to the CME. Along track 2, the maximum value in front of target 1 is 6.0×1010 cm−3 in comparison to 2.2×1010 cm−3 in front of target 2. Qualitatively, along track 4 the distribution is mirrored with respect to trace 2. However, the charge carrier density seems to be generally increased in comparison to trace 2. For instance, the total maximum – now in front of target 2 (cf. Fig. 10.10) – reaches 7.7 × 1010 cm−3 . We attribute this to the fact that a part of the grounded substrate transport system was situated not far from track 4 and may have slightly inﬂuenced the plasma. Electron temperature values of typically 3.5 eV could be measured (cf. Fig. 10.14b). A slight minimum was always visible close to the middle of the targets where the plasma density was maximum. Langmuir probe measurements along the vertical track 1 conﬁrmed qualitatively the ﬁndings of the measurements along the horizontal tracks. Again, we show the results for the case of sine wave powering. The charge carrier density is continuously decreasing at increasing z values (Fig. 10.15). From the maximum at z = −100 mm the charge carrier density decreases steadily in both directions. For comparison, the optical emission intensity of diﬀerent emission lines (420.1 nm argon and 451.1 nm indium line) is also shown in Fig. 10.15. The distribution of the emission intensity agrees with that of the charge carrier density.

H. Kupfer and F. Richter 3.5

charge carrier density

3.0 ni [1010 cm−3]

250000

Ar I, 420.07 nm In I, 451.13 nm

200000

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100000

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Intensity [cts./s]

352

50000

0.5 0.0 0

50

100 150 200 250 300 Vertical Position [mm]

350

0 400

Fig. 10.15. Optical emission intensity of diﬀerent spectral lines together with the charge carrier density in a sine wave-powered dual magnetron discharge; measurement track 1 (vertical position dependence), P = 2.0 kW per target, ptot = 0.4 Pa, FAr = 40 sccm, FO2 = 61 sccm. The target is extended from 0 to 400 mm

Fig. 10.16. ni and Te along measurement track 2 of theDC bipolar pulsed in comparison to the sine wave-powered dual magnetron discharge; P = 2.0 kW per target for sine wave, P = 1.6 kW per target for the DC-pulsed bipolar discharge; ptot = 0.4 Pa, FAr = 40 sccm, FO2 = 61 sccm

The results obtained from bipolar DC-pulsed discharges (P = 1.6 kW per target) are similar with those of sine wave driven discharges (P = 2.0 kW per target) as it is shown in Fig. 10.16: The charge carrier densities presented for both types of powering along track 2 exhibit the same asymmetric distribution. Within the error of measurement the plasma density values for both discharge types are even quantitatively equal at the discharge powers used [19]. The remaining small diﬀerence of the position of the ni maximum in front of target 1 can be explained with slightly changed experimental conditions due to a modiﬁcation of the transport system for the Langmuir probe.

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353

The electron temperature distribution shown in Fig. 10.16b is also practically the same for bipolar DC-pulsed and sine wave-powered discharges. In conclusion, when powered as a dual magnetron our cathodes show close to the substrates an inhomogeneous charge carrier and electron temperature distribution which corresponds to the phenomenon of the CME. The ni and Te distributions obtained with sine wave and pulsed DC bipolar-pulsed powering were the same within the error of measurement when the above-mentioned discharge powers were used. 10.3.4 The CME and the Thermal Load of the Substrates We have measured the thermal load of the substrates using the heat probe described in Sect. 10.3.1. For these measurements, the two magnetrons were bipolar powered as a dual magnetron using the sine wave generator. The process parameters equal those of the experiments to investigate the plasma properties (P = 2.0 kW per target, target-substrate distance = 106 mm). Figure 10.17 shows the lateral distribution of the heat load of the substrate, clearly indicating practically the same distribution as the charge carrier density (cf. Figs. 10.14a and 10.15a). Taking into account that the charge carrier current density and the radiation of the plasma towards the substrate is proportional to the plasma density in front of the substrate [23], these ﬁndings let one conclude that energy supply

Fig. 10.17. Distribution of the heat ﬂux to the substrates in dependence on the position in front of the targets. Sine wave-powered discharge, P = 2.0 kW per target, ptot = 0.4 Pa, FAr = 40 sccm, FO2 = 65 sccm. Figure taken from [19] with permission, Copyright Wiley-VCH Verlag GmbH & Co. KGaA

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from plasma is the dominating mechanism and other contributions (cf. [24]) do play a minor role. In reference to the results we can conclude that the inhomogeneous plasma density in front of the substrates is reﬂected in the distribution of the heat ﬂux towards the substrate [19], conﬁrming the inﬂuence of the CME on the plasma properties in the substrate region.

10.4 CCE, CME and Film Property Distribution: ITO as an Example 10.4.1 Introduction It is obvious that an inhomogeneity of a deposition process as represented by the CCE/CME will also be reﬂected in the ﬁlm properties. For instance, Menner et al. [25] have investigated the deposition of ZnO:Al ﬁlms by reactive dual magnetron sputtering and found a distinct inhomogeneity of the ﬁlm transparency. In particular, strongly absorbing (“blackened”) regions were observed with a lateral distribution resembling the CME. They explained this increased optical absorption by the existence of Zn precipitates in the ﬁlms due to a locally increased Zn sputter rate caused by the CCE. The original lateral constant O2 partial pressure was considered to be not suﬃcient to fully react the increased Zn supply at those places. Using an additional oxygen supply close to the strongly absorbing regions the process could be homogenised. In contrast to Menner et al. our magnetron did not show an noticeable inhomogeneous target erosion and metal supply, respectively. Using a surface proﬁlometer, we have carefully investigated the ﬁlm thickness distribution above the targets in diﬀerent powering modes and did not ﬁnd any asymmetry corresponding to the CCE/CME. As an example we show in Fig. 10.18 the ﬁlm thickness distribution along track 2 which reveals the typical maximum at the axis of symmetry of the magnetron, however shows one and the same value at measurement positions 1 and 3 (cf. Fig. 10.12b) in contrast to the strong variation of the charge carrier density measured along the same line (cf. Fig. 10.14a, vertical position = +100 mm). We have also investigated the lateral distribution of the oxygen partial pressure by sampling the gas by a drain tube and analysing it using a mass spectrometer. Measurements along the tracks 1 and 3 (cf. ﬁg. 12a) could conﬁrm that within the error of measurement the oxygen partial pressure was one and the same all over the space between targets and substrates. Nevertheless, we found a noticeable CCE/CME in form of a corresponding inhomogeneity of the plasma parameters (cf. Sect. 10.3) which might have an inﬂuence on the ﬁlm properties. ITO was used as an example to investigate this question since ITO is a material which may combine two contradicting properties, high electrical conductivity and low optical absorption. To fulﬁl these contradicting demands at the same time necessitates a high level of process

10 Reactive Magnetron Sputtering of Indium Tin Oxide Thin Films

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500 450 400 350 300

target

250 200 150 100 −12 −10 −8

target center line −6

−4 −2 0 2 4 Horizontal position [cm]

6

8

10

12

Fig. 10.18. Film thickness distribution in front of target 2 measured along track 2. Sine wave-powered discharge, P = 2.0 kW per target, ptot = 0.4 Pa, FAr = 40 sccm, FO2 = 65 sccm

control. Any deviation from the optimum conditions can easily be detected, in particular if no substrate movement is used. Therefore, to investigate the inﬂuence of the CCE and the CME on the properties of the deposited ITO ﬁlms we performed static deposition experiments. By doing so, the lateral ﬁlm property distribution represents a “ﬁngerprint” of the local process properties in front of the substrates which enables the characterisation of the correlation between process and ﬁlm. Three glass substrates were assembled along each of the horizontal tracks 2, 3 and 4, respectively (cf. Fig. 10.12a) and the ﬁlms were investigated with respect to their structure, optical absorption and electrical resistivity. The experiments were done using the target powering modes already applied for the in situ measurements (cf. Sect. 10.3). The intensity of the 451 nm indium spectral line was used to control the oxygen partial pressure by means of a fast piezoelectric valve which enabled the operation in the transition mode (see Fig. 10.19) [17]. For the static depositions we used oxygen ﬂow values close to the maximum because of the high growth rates available. In addition, such operation near the border to the metallic mode is sensitive to lateral inhomogeneities of the process conditions which may be indicated by reduced ﬁlm transparency. In Fig. 10.20, the combination of optical absorption and electrical resistivity of ITO thin ﬁlms is shown. The data are from own experiments as well as from the literature. It can be seen that the optical transparency changes monotonously with the oxygen ﬂow while the electrical resistivity goes through a minimum. The own data were received using substrate movement during deposition. Hence, the values given represent the process as a whole and do not consider lateral inhomogeneities. The ﬁgure is only aimed to give the general impression of the dependence of transparency and electrical resistivity on the oxygen supply.

12.0

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PO2 [10−2 Pa]

356

0 30

40

50 60 70 Flow Rate O2 [sccm]

80

Fig. 10.19. Oxygen partial pressure and dynamic deposition rate in the transition region in dependence on the oxygen ﬂow, FO2 . Sine wave-powered discharge, P = 2.0 kW per target, ptot = 0.4 Pa, FAr = 40 sccm. Figure reprinted from [19] with permission from Elsevier

Resistivity [10−3 Ω cm]

Resistivity Extinction Coefficient

0.021

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100

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Fig. 10.20. Optical extinction coeﬃcient k and electrical resistivity of 500 nm thick ITO ﬁlms grown in the transition mode in dependence on the oxygen gas ﬂow rate (sine wave-pulsed dual magnetron, P = 2 kW per target, ptot = 0.4 Pa, FAr = 40 sccm). The own values were schematically complemented with literature data (dashed lines)

10.4.2 Unipolar DC-Pulsed Single Magnetron: CCE and ITO Film Properties We have deposited ITO ﬁlms in the transition mode at an oxygen ﬂow FO2 = 63 sccm with the two cathodes powered in the unipolar DC-pulsed mode. The operation point was chosen such that the inhomogeneity of the process was

10 Reactive Magnetron Sputtering of Indium Tin Oxide Thin Films Target 1

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5.1

Fig. 10.21. Photographs of the ITO coated glass substrates for a qualitative demonstration of the optical absorption and the electrical resistivity (given in 10−3 Ω cm) in dependence on the substrate position according to Fig. 10.12b (unipolar DC-pulsed single magnetrons, P = 1.6 kW per target, ptot = 0.4 Pa, FAr = 40 sccm, FO2 = 63 sccm)

easily visible in the lateral distribution of optical transparency and electrical resistivity. The results are given in Fig. 10.21. The lowest optical absorption is found at substrate positions in front of the exit of the curved section, where high charge carrier density values ni were measured. On the other hand, at the diagonally opposite corners, where ni is low, the optical absorption is increased. Obviously, the inhomogeneous plasma density distribution due to the CCE (cf. Fig. 10.13) causes a corresponding inhomogeneity of the optical absorption which is usually the bigger the smaller the plasma density is. However, the optical absorption did not always change monotonously with plasma density. Figure 10.21 reveals that the absorption of the samples placed at the vertical axis of symmetry of a target is always higher than that of their neighbouring samples positioned left or right above the racetrack, i.e. having the same z value. In contrast, the ni value of the samples in the middle is not minimal but always between that of the neighbouring samples (cf. Fig. 10.13 for track 2 as an example). From that we conclude that the relevant parameter which determines the transparency of the ﬁlms is ni /R (R, growth rate) rather than the plasma density ni alone. This assumption is reasonable since any eﬀect of the plasma (for instance the impact of a certain number of energetic ions per area and time interval) has to be related to the ﬁlm volume grown per unit time which – on its part – is proportional to the growth rate R. More arguments for using ni /R are given in Sect. 10.5. As it was shown in Fig. 10.18 the growth rate R has a maximum value at the vertical axis of symmetry. Due to that, the courses of ni /R in horizontal direction become minimal above the axis of symmetry which corresponds to

358

H. Kupfer and F. Richter Target 1

Target 2

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Fig. 10.22. Qualitative demonstration of optical absorption and electrical resistivity (given in 10−3 Ω cm) for ITO ﬁlms deposited in the transition mode on glass substrates by reactive dual magnetron sputtering using either bipolar DC (Fig. 10.22a) or sine wave powering (Fig. 10.22b). Bipolar DC powering: P = 1.6 kW per target, ptot = 0.4 Pa, FAr = 40 sccm, FO2 = 61 sccm, sine wave powering: P = 2.0 kW per target, ptot = 0.4 Pa, FAr = 40 sccm, FO2 = 61 sccm. Figure 10.22b taken from [21] with permission, Copyright Wiley-VCH Verlag GmbH & Co. KGaA

the minimum of transparency. In conclusion, the absorption of the ﬁlms always showed a monotonous relationship with the ratio ni /R but not always with the plasma density. 10.4.3 Bipolar-Pulsed Dual Magnetron: CME and ITO Film Properties Figure 10.22 shows the lateral distribution of optical absorption and electrical resistivity of ITO ﬁlms deposited by dual magnetron sputtering in the transition mode using either bipolar DC [17] or sine wave pulsed powering. Again we ﬁnd a distinct inhomogeneity of optical absorption which is similar in both cases. This inhomogeneity corresponds to the plasma density distribution which was also similar for both powering modes (cf. Fig. 10.16a for track 2 as an example) and indicates the existence of the CME. Again the results suggest us to use ni /R rather than ni to describe the formation of transparency and other ﬁlm properties. As an example we consider the ﬁlms grown at positions 2 and 3 of target 2 which have nearly the same (quite low) transparency but diﬀerent plasma densities: For example in case of bipolar DC pulsed powering (Fig. 10.22a) at position 3 the plasma density was measured to be ni = 1.3 × 1010 cm−3 while at position 2 it was one and a half as much (2.1 × 1010 cm−3 ). Considering the higher growth rate at position 2,

10 Reactive Magnetron Sputtering of Indium Tin Oxide Thin Films 0.40

FWHM [deg.]

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359

0.35 0.30 0.25 0.20

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]

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riz Ho

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riz Ho

1

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Fig. 10.23. FWHM values (averaged over the seven strongest peaks) of ITO ﬁlms deposited in the transition mode by DC bipolar-pulsed dual magnetron sputtering (a) in comparison to ITO deposited by a sine wave-powered dual magnetron discharge (b); Bipolar DC-pulsed discharge: (P = 1.6 kW per target, ptot = 0.4 Pa, FAr = 40 sccm, FO2 = 61 sccm), sine wave-powered discharge: (P = 2.0 kW per target, ptot = 0.4 Pa, FAr = 40 sccm, FO2 = 61 sccm)

ni /R is still somewhat bigger in the middle of the target (i.e. at position 2) but not as much as ni is. The remaining diﬀerence can be explained by the fact that the electron temperature is reduced at position 2 (cf. Fig. 10.15b). The role of Te will be discussed in Sect. 10.5. In addition to the optical and electrical ﬁlm properties the structure of the ﬁlms was investigated by X-ray diﬀraction (XRD). In Fig. 10.23, the full width at half maximum (FWHM) for the nine ﬁlms grown opposite to target 2 using bipolar DC pulsing and sine wave powering [19], respectively, are shown. The distribution of the FWHM values is very similar in both cases, indicating that the distribution of plasma parameters (which was also nearly the same in both cases – cf. Fig. 10.16) is determining the ﬁlm structure rather than the particular kind of powering. As a clear tendency, the ﬁlms grown in front to high plasma density have an increased XRD line width which indicates a decrease of the grain size and increase of microstrain. The growth of larger grains is hindered by the ion bombardment. The lattice constant perpendicular to the surface is approximately the same for bipolar DC pulsed and sine wave pulsing, and it is increased for those positions where the FWHM is large (Fig. 10.24). This indicates the existence of compressive macroscopic stress in the ﬁlms. The direct measurement of the mechanical ﬁlm stress (sin2 Ψ -method) for selected samples grown under sine wave pulsing has revealed compressive stress with a value of −310 MPa for dark ITO ﬁlms (pos. 7 at target 1) and −1,040 MPa for bright ITO ﬁlms (pos. 3 at target 1). To calculate these stress values, a Young’s modulus of 116 GPa was assumed for the ﬁlms [26]. Both the reduced grain size and the increased microstrain contribute to the enlarged FWHM values at positions where transparent ﬁlms are growing.

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Lattice Parameter [Å]

10.24 10.22 10.20 10.18 10.16

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Fig. 10.24. Lattice spacing of ITO ﬁlms deposited in the transition mode by bipolar DC-pulsed dual magnetron sputtering (a) in comparison to ITO deposited by a sine wave-powered magnetron discharge (b) Bipolar DC-pulsed discharge: P = 1.6 kW, ptot = 0.4 Pa, FAr = 40 sccm, FO2 = 61 sccm, sine wave-powered discharge: P = 2.0 kW per target, ptot = 0.4 Pa, FAr = 40 sccm, FO2 = 61 sccm

Contrariwise, at the diagonal opposite corners of the dual magnetron where the ﬁlms are absorbing (pos. 7 of target 1, pos. 3 of target 2), the FWHM is low, corresponding to large grains.

10.5 CCE, CME and the Role of the Atomic Oxygen in the Process Gas In the previous chapter we have shown that for diﬀerent powering modes the optical, electrical and structural ITO ﬁlm properties did depend on the ratio of the charge carrier density to deposition rate (ni /R). The value of this ratio at a particular substrate position obviously determined structure and properties of the ﬁlm grown at this position. Existing inhomogeneities of ni /R (for instance due to the CCE or CME) did cause corresponding distributions of the ﬁlm parameters. In the following we will suggest a physical mechanism which determines the ITO ﬁlm formation and which in the special cases discussed above is represented by the quantity ni /R. Proceeding from the assumption that any incorporation of oxygen in the ITO structure – either chemically bound in the lattice or in form of interstitial atoms – necessitates the preceding dissociation of the oxygen molecule, we postulate the distinctive role of dissociated oxygen, denoted in the following as O∗ . We do not make any special assumption about the physical nature of the O∗ particles which may represent any atomic oxygen species (radicals, ions, atoms) being either in the ground state or in an excited state. In [27] already Mientus et al. pointed out to the important role of the atomic oxygen for the ITO ﬁlm formation.

10 Reactive Magnetron Sputtering of Indium Tin Oxide Thin Films

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We consider the relative ﬂux of dissociated oxygen, i.e. the ﬂux jO∗ of O∗ particles divided by the total ﬂux jtot of ﬁlm forming particles towards the substrate as the quantity which determines the character of the deposition process. Depending on the value of jO∗ /jtot , the process may be more or less reactive or metallic, and this local character of the process will vary across the substrate surface when jO∗ /jtot is not constant. We consider the dissociation of molecular oxygen to be due to the impact of electrons of the plasma. Therefore, the number density of dissociated oxygen (O∗ ) particles in front of the substrate shall be proportional to the oxygen partial pressure pO2 , the electron density ne , and a rate coeﬃcient k(Te ) which is depending on the electron temperature Te . The reader should keep in mind that the electron density equals the ion density. The ﬂux jO∗ of dissociated oxygen towards the substrate (number of O∗ particles per area and time) can be considered proportional to the number density of O∗ mentioned above, so we get (10.1) jO∗ ∝ ne pO2 k(Te ). On the other hand, the total ﬂux of ﬁlm forming particles, jtot , is proportional to the growth rate R: (10.2) jtot ∝ R. Finally we get from (10.1) and (10.2): jO∗ /jtot ∝ ne pO2 k(Te )/R.

(10.3)

This is the general expression describing the ratio of atomic oxygen and total ﬂuxes towards the substrate, thus ruling the local reactive/metallic character of the process. In the cases which we have investigated above, a somewhat simpler expression holds. As we have measured (cf. Sect. 10.4.1), the oxygen partial pressure pO2 was constant across the substrate. The same was true (with one exception discussed below) for the electron temperature, Te . Hence, for consideration of the lateral homogeneity of the process, pO2 and Te can be neglected here, and we get for the experiments described above jO∗ /jtot ∝ ne /R

(10.4)

as special case of (10.3). In Fig. 10.25 we have arranged the samples shown in Fig. 10.22a (target 1 and 2, samples 1–3 and target 2, samples 6 and 9) with their resistivity and absorption in dependence on the ni /R values which were measured for the positions of the particular sample. (Since, strictly speaking, the Langmuir probe measurements deliver ni rather than ne , notwithstanding that these parameters are equal in a quasi-neutral plasma, we use ni in the ﬁgure because it is the measured quantity.) The absorption was simply characterised introducing a quantity called absorption grade which was determined by comparison of the samples with a set of calibration samples having absorption grades of 1–5. The calibration samples were chosen such that the absorption

H. Kupfer and F. Richter

Resistivity [10−3 Ω cm]

8.0

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Extinction Coeff. k [a.u.]

362

0.0 0.5

j (O*) Fig. 10.25. The optical extinction coeﬃcient k and the electrical resitivity depending on the ratio ni /R (bipolar DC-pulsed dual magnetron deposition, P = 1.6 kW per target, ptot = 0.4 Pa, FAr = 40 sccm, FO2 = 61 sccm)

grade was proportional to the extinction coeﬃcient. We can see that both local absorption and local resistivity of the ﬁlm show qualitatively the same general behaviour with decreasing ni /R as the average values of these quantities do with increasing total oxygen ﬂow (cf. Fig. 10.20). We postulate that in both cases the relative ﬂux of dissociated oxygen, jO∗ /jtot , is the quantity which does determine composition and properties of the ﬁlm. First, we consider the process as a whole, using average values both for process parameters and ﬁlm properties thereby neglecting lateral inhomogeneities. For the process a total jO∗ /jtot exists which depends – analogue to (10.3) – on the average values of ni , k(Te ), R and pO2 . When a process is operated at a certain discharge power, the ﬁrst three parameters are practically constant and the oxygen partial pressure is the only variable left. When we now increase the oxygen ﬂow rate FO2 , the oxygen partial pressure decreases linearly as shown in Fig. 10.19. Hence, the increasing oxygen ﬂow rate in Fig. 10.20 corresponds to a linearly decreasing oxygen partial pressure and – considering (10.3) – a linearly decreasing total jO∗ /jtot . The same is true for Fig. 10.25, which shows decreasing ni /R and, hence, decreasing jO∗ /jtot from left to right. In conclusion, Fig. 10.20 can be understood as a presentation of the total jO∗ /jtot for the process as a whole, determining the average values of absorption and electrical resisitivity in dependence on FO2 . Similarly, Fig. 10.25 considers the local distribution of jO∗ /jtot as well as the local values of absorption and resisitivity. In any case, the ﬂux ratio jO∗ /jtot represents the total and local character (reactive vs. metallic) of the process, respectively. Now, let us return to the samples shown in Fig. 10.22a, b which, in a few cases, exhibited a non-monotonous dependence of the absorption on ni /R (cf. the discussion in Sect. 10.4.3). In those cases the electron temperature of neighbouring samples was distinctly diﬀerent and therefore (10.3) has to be

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used rather than (10.4). By doing so, the clearly reduced electron temperature for sine wave and DC-pulsed biploar dual magnetron sputtering above the middle of the target (cf. Fig. 10.14b) delivers a further reduction of jO∗ /jtot at these position thus yielding a monotonous dependence on the absorption. The inﬂuence of the electron temperature becomes even more clear when the dual and single magnetron sputtering processes are compared. As it was done throughout this paper, for the two DC-pulsed discharges (unipolar single and bipolar dual magnetron) one and the same total power of 1.6 kW per cathode was used, corresponding to a power density of 3.08 W cm−2 , while for the sine wave-pulsed dual magnetron a total power of 2.0 kW per cathode was applied yielding 3.85 W cm−2 . In accordance with these similar power densities the maximum growth rates achieved in the transition mode close to the border to the metallic mode (cf. Fig. 10.19) were also close to each other: We found 3.75 and 3.67 nm s−1 for the unipolar DC-pulsed single and bipolar DC-pulsed dual magnetron, respectively. The sine wave driven dual magnetron with its higher power density had a somewhat larger deposition rate of 4.11 nm s−1 . In contrast to that, the plasma parameters were quite diﬀerent. Taking the horizontal tracks as an example (see Figs. 10.13 and 10.14) we see that for a practically equal discharge power of 1.6 or 2.0 kW per target the average plasma density in the case of unipolar DC-pulsed single magnetron is about one order of magnitude smaller than for the two powering versions of dual magnetron sputtering. On the other hand, the single magnetron sputtering has an electron temperature of 4–7 eV (Fig. 10.13), which is clearly higher than the 3–4 eV found for dual magnetron sputtering (cf. Fig. 10.14b). Taking into consideration these diﬀerent plasma parameters we will now discuss the pO2 = f (FO2 ) curves measured for the three powering modes which are shown in Fig. 10.26. It can be seen that the three curves distinctly diﬀer from each other. With respect to the vertical position the two dual magnetron curves are very similar to each other while the curve for the unipolar DC pulsing of two single magnetrons has distinctly higher pO2 values at the same FO2 . We explain this behaviour [18] considering both the formation and consumption rates of dissociated oxygen. The consumption rate is practically equal in all three cases since the ﬁlms were always stoichiometric oxide and the growth rate (being within 3.9 ± 0.2 nm s−1 for all three cases) can be considered constant taking into account the larger errors existing for plasma density and electron temperature. In the steady state, the consumption rate is equal to the formation rate, therefore ni pO2 k(Te ) (cf. (10.1)) should also be one and the same for all three powering modes. Now we compare the quantities on the right-hand side of (10.1) for these cases: With the single magnetron in comparison to the dual magnetron, ni is smaller by a factor of ten and pO2 is increased by a factor of 1.5. This lets one conclude that the same O∗ formation is achieved if k(Te ) for the single magnetron is by a factor of 6–7 higher than for the dual magnetron.

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12.0 Bipolar d.c. Unipolar d.c. Sine-wave

pO2 [10−2 Pa]

10.0 8.0 6.0 4.0 2.0 0.0 30

40

50 60 Flow Rate O2 [sccm]

70

Fig. 10.26. Dependence of the oxygen partial pressure pO2 on the oxygen ﬂow rate FO2 for the two DC-pulsed modes (both P = 1.6 kW per target, R = 3.67 and 3.75 nm s−1 , respectively) and the sine wave-powered process (2.0 kW per target; R = 4.11 nm s−1 )

This agrees well with the fact that the electron temperature was found to be nearly twice as big as for the single magnetron. Now, we consider the position of the curves with respect to the FO2 scale in Fig. 10.26. It can be seen that the location of the FO2 maximum (marking the border between transition and metallic mode) for the two DC-pulsed modes is similar while the curve for the sine wave-powered mode is shifted towards larger FO2 values. This maximum position marks the maximum oxygen consumption of the process and is clearly related to the maximum growth rate which can be achieved. This growth rate for the sine wave-driven dual magnetron process was 4.11 nm s−1 and hence by 11–12% bigger than the rate values for the two DC-pulsed processes. This agrees well with the maximum ﬂow rate of 74 sccm (sine wave) in comparison to the two other processes having about 64 and 67 sccm, respectively. In conclusion, we have investigated both single and dual magnetron sputtering of ITO thin ﬁlms in an argon–oxygen atmosphere using an InSn target. It could be shown that the formation and incorporation of dissociated oxygen (O∗ ) particles determines both the total and local character (reactive vs. metallic) of the process. Lateral inhomogeneities of the relative incorporated ﬂux of O∗ , jO∗ /jtot , can emerge due to a lateral distribution of one or more of the quantities plasma density, electron temperature and growth rate, and may cause a corresponding lateral inhomogeneity of ﬁlm structure, optical absorption and electrical resistivity. This inhomogeneity can be described as a consequence of a particular variation of the local character of the process. As

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an example we have shown that a lateral distribution of plasma density and electron temperature in form of the cross-corner and cross-magnetron eﬀect deteriorates the homogeneity of ITO ﬁlms to a large extent. This interpretation of the local character of the process agrees well with the consideration of its total character (reactive vs. metallic) which can also be most consistently interpreted as being dependent on the relative incorporation ﬂux of O∗ . Acknowledgments. The authors appreciate ﬁnancial support of the State Ministry of Economic Aﬀairs and Labour of Saxony as well of the European Union.

References 1. B. Szyszka, Vakuum in Forschung und Praxis, 1, 38–45 (2001) 2. M. Katayama, Thin Sol. Films 341, 140–147 (1999) 3. E. Shidoji, M. Nemoto, T. Nomura: J. Vac. Sci. Technol. A 18(6), 2858– 2863 (2000) 4. Q.H. Fan, L.Q. Zhou, J.J. Gracio: J. Phys. D: Appl. Phys. 36, 244–251 (2003) 5. E. Shidoji, H. Ohtake, N. Nakano, T. Makabe, Jpn. J. Appl. Phys. 38, 2131– 2136 (1999) 6. E. Shidoji, M. Nemoto, T. Nomura, Y. Yoshikaw, Jpn. J. Appl. Phys. 33, 4281– 4284 (1994) 7. A. Lopp, J. Trube, M. Geisler, M. Ruske, H. Claus, in The Society for Information Display’s International Conference (SID 02), May 19–24, 2002, Boston, MA, USA, Digest of Technical Papers, p. 29 8. Figure 10.7 belongs to the work published in [9] but was not contained in the article due to space limitations. It was, however, shown in the oral presentation 9. A. Lopp, C. Braatz, M. Geisler, H. Claus, J. Trube, in The Society of Vacuum Coaters 45th Annual Conference, April 13–18, 2002, Lake Buena Vista, CA, USA; Conference Proceedings ISSN: 0737–5921 10. Y. Yang, X. Liu, L. Cha, S. Xu, C. Fan, in The Society of Vacuum Coaters 49th Annual Conference, April 22–27, 2006, Washington, DC, USA, Conference Proceedings SSN 0737-5921, pp. 173–177 11. G. Buyle, D. Depla, K. Euﬁnger, R. de Gryse; W. de Bosscher, in SVC 2005 Meeting, 48th Technical Conference Proceedings, 2005, pp. 254–259 12. To the best of our knowledge, the designation cross magnetron eﬀect was ﬁrst used in: A. Lopp, M. Geisler, J. Trube, Business and Technical News from Applied Films “Precision”, August 2002, p. 24f 13. G. Br¨ auer, M. Ruske, J. Szczyrbowski, G. Teschner, A. Zmelty, Vacuum 51, 655 (1998) 14. S. Schiller, K. Goedicke, J. Reschke, V. Kirchhoﬀ, S. Schneider, F. Milde, Surf. Coat. Technol. 61, 331 (1993) 15. W. Zhu, G. Buyle, J. Lopez, S. Shanmugmurthy, A. Belkind, K. Becker, R. de Gryse, New J. Phys. 8, 146 (2006) 16. J. Lopez, W. Zhu, A. Freilich, A. Belkind, K. Becker, IEEE Trans. Plasma Sci. 33, 348 (2005) 17. H. Kupfer, R. Kleinhempel, B. Graﬀel, Th. Welzel, Th. Dunger, F. Richter, W.-M. Gnehr, T. Kopte, Surf. Coat. Technol. 201, 3964–3969 (2006)

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18. T. Dunger, H. Kupfer, B. Graﬀel, R. Kleinhempel, J. Lukaˇs, T. Welzel, F. Richter, Plasma Processes Polym. 4, 5282–5286 (2007) 19. R. Kleinhempel, B. Graﬀel, J. Lukas, H. Kupfer, T. Dunger, T. Welzel, F. Richter, Plasma Processes Polym. 4, 5325–5329 (2007) 20. P. Frach, K. Goedicke, C. Gottfried, H. Bartzsch, Surf. Coat. Technol. 142–144, 628–634 (2001) 21. R. Pintaske, Th. Welzel, N. Kahl, M. Schaller, J. Hahn, F. Richter, Surf. Coat. Technol. 90, 275 (1997) 22. H. Bartzsch, P. Frach, K. Goedicke, Surf. Coat. Technol. 132, 244–250 (2000) 23. B. Chapman, Glow Discharge Processes (Wiley, New York, 1980), p. 69 24. H. Kersten, H. Deutsch, H. Steﬀen, G.M.W. Kroesen, R. Hippler, Vacuum 63, 385–431 (2001) 25. R. Menner, M. Oertel, M. Powalla, M. Dimer, S. Rehn, S. Str¨ umpfel, B. Dimmler, in Proceedings of the 19th European Photovoltaic Solar Energy Conference, 7–11 June, Paris, France 26. D.G. Neerinck, T.J. Vink, Thin Sol. Films 278, 12–17 (1996) 27. R. Mientus, K. Ellmer, Surf. Coat. Technol. 142–144, 748–754 (2001)

11 Reactively Sputter-Deposited Solid Electrolytes and Their Applications P. Briois, F. Lapostolle, and A. Billard

11.1 Introduction PVD processes represent an attractive set of deposition techniques for metal coatings or ceramic ﬁlms, and are used in such widely diﬀering domains as mechanical engineering, optics, electronics, the chemical industry, aeronautics, etc. Recent developments are also devoted to energy and environment applications based on the synthesis of solid electrolyte or mixed conductor coatings. This paper is then dedicated to a non-exhaustive review of applications of ionic conductor coatings obtained by PVD processes, more precisely, by reactive magnetron sputtering. The main trends of magnetron sputtering processes are widely described in the literature [1–5] and are discussed in detail in previous chapters of this book. The main trends to be taken into account to perfectly control a sputtering process can be summarized as follows: – The sputtering yield, deﬁned as the number of sputtered atoms per impinging ion, increases with the ion energy and mass and with the decreasing cohesion energy of the material to be sputtered [6,7]: the sputtering yield of a ceramic material is often about one order of magnitude lower than that of the corresponding metal. – The spatial distribution of the sputtered atoms is more acute for low-Z materials and with increasing energy of the impinging ions [8,9]. This has strong consequences on the resulting composition of coatings sputtered from multi-element targets [7, 10–12]. – The energy of the impinging atoms on the building coating conditions its morphology and internal stress [13–16]: dense coatings are often associated with compressive internal stress, whereas columnar porous coatings are usually submitted to tensile internal stress. The energy of the impinging sputtered atoms increases with decreasing the deposition pressure and the target-to-substrate distance, but is also favoured by normal incidence of the metal stream and by a negative bias voltage of the substrate. Moreover,

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it is quite a monotonic function of the MT /MG ratio (MT , target mass; MG , gas mass) [17–19]. – Metastable structures and ﬁne microstructures of sputter deposited coatings are merely linked to the high cooling rate associated with the condensation of the impinging metallic vapour [7]. According to the confusion principle, the coating amorphization is more likely to occur when a large number of diﬀerent elements are combined and when their atomic radii diﬀer [7, 20]. – Ceramic coatings can be synthesized either by sputtering a ceramic target, usually using a radiofrequency polarization of the insulating target, or more advantageously by sputtering a metal or metallic alloy target in the presence of a reactive argon-reactive gas mixture [21–26]. This later method is preferred to allow high rate deposition of ceramic coatings but presents two major drawbacks, i.e. microarcs at the periphery of the target which degrade the physical quality of the coatings [27] and an unstable behaviour of the sputtering mode [28]. Intensive studies performed to avoid these drawbacks have led to the use of pulsed DC discharges [29,30] and numerous techniques to either stabilize the sputtering mode [31–33] or to control its undesired eﬀects, i.e. low deposition rate of the stoichiometric ceramic compound [34–36]. To complete this rapid overview of the main trends of reactive sputtering, let us mention that methods based on optical emission spectroscopy (OES) developed for plasma emission monitoring (PEM) [35] can also be advantageously used to in situ investigate the chemical properties of sputter deposited coatings [12, 37], as well as those of growing transparent coatings by optical transmittance interferometry (OTI) [38, 39]. The strong improvement during the three past decades in the understanding of the mechanisms of reactive sputtering mentioned above and developed in details in previous chapters of this book have allowed the development of numerous applications in the ﬁelds of energy and environment applications. This is particularly true for inorganic solid electrolytes which exclusively concern oxide coatings, i.e. the most diﬃcult materials to be high rate deposited using magnetron sputtering. In this paper, we ﬁrst review the basic crystallographic properties of the most common electrolytes and mixed conductor materials available for energy and environment applications. Section 11.2 is ascribed to the description of diﬀerent applications where ionic or mixed conductor coatings should be advantageously grown by PVD processes. For each application, we ﬁrst describe the principle and requirements for the electrolyte. Then we review the literature where such coatings have already been synthesized by sputter deposition.

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11.2 Crystallographic Basis of the Solid Electrolyte The main property of solid electrolytes is their rather good ionic transport property associated with a poor electronic conduction, i.e. very good electrical insulation, this former characteristic being useful for many applications in electrochemistry. Thus, material choice depends on several factors as a function of the targeted application, the most important one remaining the character of the ion to be carried: H+ , Na+ , Li+ or O2− . However, ionic transport properties can also be associated with rather good electronic conductivity. Materials which exhibit such properties are called mixed conductors and also present a strong interest in electrochemistry applications. In most cases, the transport properties of the electrolytes are in close relation with their structure. In the following, we describe the main classes of solid electrolytes as a function of the nature of the ion to be carried. 11.2.1 O2− Carriers This kind of material can be divided into six main structural families: – Fluorite structure: This structure derives from CaF2 (Fig. 11.1) and remains the reference electrolyte structure in nowadays solid oxide fuel cell (SOFC) devices. It is constituted by a face-centred cubic (fcc) lattice structure of cations that are eightfold coordinated in a cubic environment of anions located in all tetrahedral positions. Cation substitution by another aliovalent one, i.e. with a diﬀerent oxidation state, allows ﬂuorite structure stabilization and, as a consequence, oxygen vacancies generation to keep the material electro-neutrality. The creation of such a vacancies network oﬀers high mobility to O2− ions.

Fig. 11.1. The ﬂuorite (AO2 ) oxide structure. The dark spheres represent the A cation sites and the clear spheres the oxygen sites [40]

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Fig. 11.2. Projection of the structure of Li0.30 Ca0.35 TaO3 along the three primitive cubic directions showing the three tilts system a+ b− b− of the TaO6 octahedra [41]

Fig. 11.3. Pyrocholore structure of Sm2 Zr2 O7 [42]. The big spheres are Sm and the octahedra are ZrO6

– Perovskite structure: With an ABO3 stoichiometry, this structure shows BO6 octahedral stacking where cations A are located in spaces also called perovskite cages (12-fold coordinated – Fig. 11.2). This phase oﬀers the possibility to realize a double cationic substitution (A, B), leading to vacancies formation in the anionic sub-network, as observed in the case of ﬂuorite structure. – Pyrochlore structure: This A2 B2 X7 structure consists in a 3D network of octahedrons (B2 X6 ), delimiting tunnels where cages are located every six tunnel crossing (Fig. 11.3). Cations A are located in the cages with an anion X. This structure could be considered to be distorted ﬂuorite-like ordered on cationic sites, more or less anions deﬁcient. – Brownmillerite structure: The lattice of brownmillerite-type Ca2 Fe2 O5 consists on alternating perovskite layers of corner-sharing Fe2 O6 octahedra

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Ca O2

Fe1

O3

O1

Fe2

b a c

Fig. 11.4. Crystal structure of Ca2 Fe2 O5 brownmillerite, drawn based on the Rietveld reﬁnement results [43]

and layers of FeO4 tetrahedra (Fig. 11.4). This structure is often considered as an oxygen deﬁcient perovskite where the oxygen vacancies ordered along (010) planes contribute to ionic conductivity. At high temperatures, vacancies are disordered, leading to a higher conduction of O2− ions. – Aurivilius phase structure: Ionic conductors of this family mainly concern bismuth-metal-vanadium oxide (BIMEVOX) which derive from Bi4 V2 O11 oxygen deﬁcient compound (Fig. 11.5). This structure consists in a stack of [Bi2 O2 ]2+ and perovskite layers disordered and oxygen deﬁcient [VO3,5 0,5 ]2− . It crystallizes in three distinct allotropic forms as a function of the temperature. From ambient to 430 ◦C, the structure is monoclinic (α) with an A2 space group. In the 430–570 ◦C temperatures range, it is orthorhombic (β) with an Amam space group. Finally, for the highest temperatures in the solid state, the structure is tetragonal (γ), exhibiting an I4/mmm space group. – Apatite structure: Compounds crystallizing in apatite structure have an A10−y (BO4 )6 Ox stoichiometry, with y = 0 or 0.67 and 3 ≥ x ≥ 1, where A is a rare earth or an alkaline earth and B = Si, Ge, Al, P. These materials exhibit anisotropic ionic conductivity properties, which is one order of magnitude higher along c-axis than in the a–b plane. This can be explained considering the hexagonal space group (P 63 /m) of these compounds. The general structure is presented in Fig. 11.6. It consists in isolated BO4 tetrahedra with the A cations located in two cavity sites, one

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Fig. 11.5. BIMEVOX structural model (a) V surrounding in Bi4 V2 O11 and (b) V, Co surrounding in BICOVOX.10 [44]

7-coordinate and the other 9-coordinate. The extra oxide anions occupy channels running through the structure, presumed to be responsible for the high ionic conduction. The presence of element A cationic vacancies can also increases the oxide ions mobility along the c-axis. – LAMOX structure: Lanthanum–molybdenum oxide (LAMOX) family derives from La2 Mo2 O9 compound (Fig. 11.7), known for a long time, but the

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Fig. 11.6. Apatite structure of lanthanum silicate [45]. Tetrahedra correspond to BO4 , dark spheres to A cation sites and white spheres to oxide ions channels

La2Mo2O9 O2

La

G.S: P213 a=7,2014(5) Å à 670°C

O1 O3 Mo

c

b a

Fig. 11.7. High-temperature structure of lanthanum molybdate [46]

ionic conduction of which has only recently been highlighted. Explanation of the ionic conduction mechanism gave birth to the “lone pair substitution” concept. At room temperature, La2 Mo2 O9 presents a slightly distorted monoclinic structure (α-La2 Mo2 O9 ). Above about 580◦C, β-La2 Mo2 O9 is cubic with a P 21 3 space group. The phase transformation of LAMOX around 580◦C consists in an order/disorder transition. It is accompanied by an increase in the lattice volume and an increase in the ionic conductivity of at least 2 orders of magnitude which reaches about 6.10−2 S cm−1 at 800◦C.

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Fig. 11.8. Structure of A2 MO4+δ compounds showing the interstitial oxygen atoms and its tetrahedral coordination [47]

11.2.2 H + Carriers Five main structure families exhibit interesting proton conduction properties: K2 NiF4 , KH2 PO4 , A2 O5 -nH2 O, Perovskite (ABO3 ) and Pyrochlore. The two last structures having already been described in the paragraph dedicated to oxide ion conductors, we present here only the formers structures: – K2 N iF4 structure: This structure can be described as octahedrons planes stacks of perovskite ABO3 , shifted by (1/2 1/2 1/2) each other so that the planes appear to be linked by NaCl-like AO leafs (Fig. 11.8). This structure can be oversaturated with O (F element) to give K2 NiF4+δ . In this case, the mechanism of conduction may be provided inside the ions network, also called F interstitials. – KH2 P O4 (KDP) structure: This structure consists in a 3D H-bonded network that can be viewed as a stack of 2D H-bounded planes consisting of two sets of mutually perpendicular 1D H-bounded chains (Fig. 11.9). The chains propagate along the a and b crystallographic directions and the H-bonds in the respective a and b directions are labelled as a- and b-bonds. The H-bonds connect together PO4 tetrahedra in a way that each tetrahedron makes four bridges (two following direction a and two following direction b) to the surrounding tetrahedra. The process of ionic conductivity is believed to involve jumps of protons from a-bonds to the nearer b-bond.

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Fig. 11.9. The schematic crystal structure of tetragonal KDP [48]

11.2.3 N a+ Carriers Nowadays, the best known ceramic Na+ conductors are β-alumina and NASICON: – β-alumina: Al3+ and O2− ions are structured like a MgAl2 O4 spinel. They are commonly called “spinel block”. Al3+ and Mg2+ ions are located in octahedral and tetrahedral positions, respectively. Spinel-block planes are split up by other plans including Na+ and O2− . This inter-planar space leads to good conductivity. Nevertheless, this conductivity is only restricted to this plane and the motion is quite diﬃcult along c-axis, leading to important conductivity anisotropies. Conduction planes of βalumina are mirror plans with an fcc organization of oxide ions. Despite the spinel is cubic, addition of planes containing Na+ ions gives rise to hexagonal β-alumina (Fig. 11.10). – NASICON: Sodium super ionic conductor (NASICON) corresponds to compounds based on sodium, zirconium, silicon and phosphorus oxides with an equilibrium stoichiometry Na1+x Zr2 Six P3−x O12 (0 < x < 3). Contrary to most of the ionic conductors, transport properties of NASICON do not proceed from vacancies mechanism, but from a particular structural organization. Indeed, basic structural units 2ZrO6 3(P, Si)O4 combine together to build a 3D rhombohedral network (R-3c), run down by a 3D network of interconnected channels receiving Na+ ions in interstitial positions (Fig. 11.11).

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C A B⬘ C A C

B

A

C

B⬘

A⬘

A

B

C

C

B

A

A

B

C⬘

C⬘

A

A

B

B

Al+++

O− −

Na+

Fig. 11.10. Crystal structures of β- and β -aluminas. The Na atoms in β- and β -aluminas are shown in BR and (1) sites, respectively [49]

Na+2

Na+1 Na+2 Na+1 [001]

[110]

Fig. 11.11. Structure of Na3 Zr2 Si2 PO12 [50]. Large channels between ZrO6 octahedra and (Si, P)O4 tetrahedra allow the fast ion conduction of Na+

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11.2.4 Li+ Carriers Li+ conductor elecrolytes crystallize in diﬀerent structures mentioned above: ABO3 perovskites (with A = La, Ti and B = Li), LISICON which derive from the NASICON structure with (PO4 )3− groups and metallic elements such as Si, Al, Ge, V. Pyrochlore phases are also employed, as well as lithium phosphorus oxynitrides (LIPON), phosphates (LiPO4 ), borides (LiBO2 ) or zirconates (LiZrO3 ). Note that most of these materials which are amorphous when they are sputter deposited, are called lithium glasses and can reach ionic transport properties comparable to those of NASICON–NASIGLASS, i.e. around 10−3 S cm−1 at room temperature. 11.2.5 Mixed Conductors Mixed conductors are compounds presenting both ionic and electronic conductivity components. Thus, electrons and ions may react with every material grains and not only at the interface. Nowadays, main used compounds crystallize in perovskite structure, and many works are carried out on K2 NiF4 structures. Crystallographic data of these structures were given before.

11.3 Application of Solid Electrolytes 11.3.1 Solid Oxide Fuel Cells SOFCs produce electrical energy from an eﬃcient environment-friendly electrochemical process (Fig. 11.12) [51, 52]. A SOFC cell is composed of an electrolyte (YSZ) ﬂanked by two porous electrodes. The cathode, usually constituted by La1−x Srx MnO3 (LSM) [51] is the place where air electrocatalytically produces oxide ions (1/2 O2 + 2e− → O2− ) which cross the electrolyte and react with the fuel at the anode, often consisting in a Ni-YSZ cermet [51], to produce water vapour (or carbon dioxide) and electrons (H2 (CO) + O2− → H2 O (CO2 ) + 2e− ) following the overall reaction: H2 (CO) + 1/2 O2 → H2 O (CO2 ). The electrolyte must be dense and perfectly gastight to avoid the diﬀusion of gaseous species form any side to the other which otherwise should lead to a strong and uncontrolled exothermal and exploding reaction. The ﬁrst democratization lock of SOFCs proceeds from their relatively high working temperature (1000 ◦C). Such temperatures lead to an increased reactivity between the diﬀerent components of the fuel cell and thermal stresses, requiring the use of very expensive and brittle ceramic materials [53]. It is possible to overcome these eﬀects by decreasing the working temperature around 800◦ C [52]. Nevertheless, intermediate temperature SOFCs (IT-SOFCs) exhibit lower performances than SOFCs but several ways can be foreseen to limit these harmful eﬀects. At the electrolyte level, this can

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1 O +2e' → O2− 2 2

-

2e

Cathode : porous structure Cathode : porousstructure

2O2−

Electrolyte Electrolyte

La1-xSrxMnO3 - δ

2O2−

H2 +

1 O → H2O 2 2

YSZ YSZ cermet Ni-YSZ

Anode::porousstructure porous structure Anode

H2+O 2 - → H2O+2e' 2e

-

Fuel H2, CH4

H2O

Fig. 11.12. Elemental cell of a SOF

be achieved by the decrease of about one order of magnitude of the thickness [54, 55] and/or the synthesis of new materials exhibiting higher ionic conductivity than YSZ, the reference electrolyte [52–54]. At the electrodes level, this goes through the use of mixed conductors exhibiting better electrocatalytic performances than the conventionally used lanthanum perovkite. In this context, PVD techniques are of particular interest to ensure the synthesis of thin and supported electrolytes [56]. In the following, we ﬁrst describe the main classes of solid electrolytes involved for IT-SOFC and then, we review their main characteristics when deposited by magnetron sputtering. Conventional Fluorite Structure O2− Conductor Electrolytes Zirconia-Based Electrolytes Zirconium dioxide crystallizes in the monoclinic form with low conduction properties of oxide ions O2− . Nevertheless, addition of dopants allows the creation of an anionic vacancies network and the tetragonal or cubic phase stabilization of zirconia [57,58]. The ﬁnal structure is a function of the doping element concentration, then avoiding martensitic transformation during the monoclinic to tetragonal transition, which can be the origin of cracks birth when using at high temperatures. The control of dopant concentration leads to the control of vacancies rate and that of the material structure [59]. The nature of the dopant R is imposed by its atom size (steric eﬀect), but also by its cost. R3+ atom size must be as close as possible to that of Zr4+ (0.084 nm) to avoid a jammed conduction due to the use of too large ions [59]. In the ﬁeld

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0.2

0.1

Migration enthalpy ? Hm, kJ/mol

s 1273K,S/cm

0.3

110

Eu3+

Sc3+

80

? Ha

100

Gd3+

90

s

Er3+

80 70

Yb3+

60

Dy3+ Y3+

40

Zr 4+ ? Hm

20

Association enthalpy ? Ha, kJ/mol

0.4

379

60 0.85

0.90 0.95 1.00 1.05 Dopant cation radius, Å

Fig. 11.13. Evolution of the ionic conductivity as a function of the additional element nature [60]

of SOFCs, the most used dopant remains yttrium, while a scandium addition leads to higher ionic conductivities (Fig. 11.13). Scandium substitution is unusual for its price and its availability, but also due to the rhombohedral to cubic phase transition at 650◦ C [61, 62]. The cubic structure stabilization is however possible by a double substitution with aluminum [61] or gadolinium oxide [62]. It is then necessary to enrich zirconia around 11 mole% Sc2 O3 to avoid the ionic conductivity deterioration with time [63, 64]. Yttrium stabilized zirconia is widely used because of its good chemical stability in reducing and oxidizing environments [65]. It also exhibits pure ionic conduction in the SOFCs working ﬁeld. That is why cubic phase is currently used in SOFCs. Optimal electrical properties are reached with, at least, an addition of 8 mole% Y2 O3 (Fig. 11.14) [64, 66]. Two ways are available to deposit thin YSZ ceramic ﬁlms by magnetron sputtering. On one hand, it is possible to sputter a ceramic target at the right composition in radio frequency (RF) mode [60, 67–70]. On the other hand, it can be achieved via the sputtering of one or several DC-biased metallic targets in the presence of a reactive argon–oxygen gas mixture [71–80]. To avoid instabilities often occurring with reactive sputtering, many works focused on the RF sputtering method. With this method, the deposition rate is quite low and strongly depends on the RF power applied to the target, the substrates bias or the oxygen partial pressure. Nevertheless, these deposition rates remain lower than 1 μm h−1 , and many studies have already shown that

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400°C

Log (s,O-1cm-1)

-3.90 -4.30

-4.70

1000°C

-0.90 -1.20 -1.50

0

4

8

12

16

mol % Y2O3 Fig. 11.14. Evolution of the ionic conductivity as a function of Y2 O3 content (open circle) single crystal, (ﬁlled circle) polycrystal [59]

YSZ

YSZ NiO

(a) 200W

10 μm

(b) 300W

NiO

10μm

Fig. 11.15. Cross section SEM micrographs of YSZ ﬁlms grown on NiO substrate at (a) 200 W and (b) 300 W [67]

it drastically decreases with increasing oxygen partial pressure. Moreover, as YSZ targets sputtered without oxygen reﬁlling in the plasma lead to a partially oxidized ﬁlm, then requiring an oxidation heat treatment after the deposition run, a slight addition of O2 in the sputtering atmosphere is required. RF sputtered YSZ coatings are commonly columnar (Fig. 11.15), with a more marked eﬀect as the ﬁlm thickness increases. Coating densiﬁcation is then required via a heat treatment at quite high temperatures (≈1600◦C). However, it is important to minimize this temperature to avoid reaction between fuel cell components, which could be harmful for the future stack integrity and use. For example, between the commonly used cathode (lanthanum manganite,

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LSM) and the YSZ ﬁlm, an insulating La2 Zr2 O7 pyrochlore phase appears at 1,200◦ C [53, 75]. This phase disrupts optimal working conditions. Moreover, such heating requires the use of thermo mechanically compatible materials, particularly considering the thermal expansion coeﬃcient (TEC), to minimize interface stresses that could decrease the layers cohesion. YSZ reactively sputter deposited on porous and dense substrates is also widely cited in the literature [71–80]. Zirconium and yttrium showing related atomic weights, it is possible to sputter either a Zr–Y composite [71, 73] or sintered target or two distinct targets of Zr and Y [72], respectively. Barnett et al. have deposited YSZ on various substrates that have been heat treated at 300◦C after deposition. Deposition rates of 3 μm h−1 can then be obtained, without any visible cracks after annealing [56]. YSZ sputter deposited thin ﬁlms electrical properties are close to those reached with other deposition techniques and are close to those of the bulk material [81]. Nevertheless, they are strongly correlated to the ﬁlm morphology, i.e. to the sputtering conditions, and a granular or grain boundary conduction is achieved for dense or columnar ﬁlms, respectively (Fig. 11.16). Moreover, the working pressure does not have signiﬁcant inﬂuence on the composition, as both constitutive elements of the ﬁlm are similar, but plays a major role on the structure and morphology of the coatings. A previous study has shown that structure strongly depends on the amount of dopant, but also on the stress level. Jankowski and Hayes [73] underlined the inﬂuence of metal to oxygen ratio and of the deposition rate as a function of reactive gas ﬂow via Auger spectroscopy. Wazenberg et al. [74] and Hobein et al. [77] pointed out the importance of the heat treatment after the deposition of YSZ coatings with various thicknesses on cermets, against helium tightness. This characterization is of primarily importance considering the future use of electrolyte in SOFCs. For example, Srivasta et al. [78] observed power densities of about 400 W cm−2 at 800◦C at a voltage of 0.7 V for a “button” cell battery, but lower densities for larger cells.

PP=0.59Pa = 0.59Pa

PP== 4Pa

Fig. 11.16. Eﬀect of argon pressure on the morphology of YSZ coatings observed by SEM [76]

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Zr−Y metallic alloys have also been sputter deposited on porous substrates by Y−I. Park et al. [79], with various yttrium contents. After deposition, annealing treatments have been performed in the 400–1000◦C temperature range, allowing metal oxidation and volume expansion leading to pores elimination, i.e. denser ﬁlms. Thus, the ﬁnal coatings are perfectly gastight, which is favourable to electrolyte use in SOFCs, and present measurable ionic conductivity of 3.42 × 10−9 S cm−1 at room temperature. In its PhD studies in progress, Coddet used PEM to synthesize YSZ coatings on large area substrates, i.e. in the presence of unstable sputtering conditions, from Zr and Y metallic targets sputtered simultaneously on a rotating substrate holder in the presence of a reactive argon oxygen gas mixture. PEM consists in measuring the optical line intensity of a sputtered metal species, e.g. Zr, and to maintain it by monitoring the oxygen ﬂow rate to allow the deposition into the hysteresis domain [28]. Figure 11.17 indicates that both Y2 O3 molar content into the coatings and the deposition rate increase with increasing the intensity of Zr optical emission line (I ∗ /I ∗ Zr ) monitored. On the other hand, increasing I ∗ /I ∗ Zr yields less and less oxidized coatings which also become less and less transparent. Annealing treatments performed under air at 500◦C for 2 h led to the complete oxidation of all the coatings. As shown by Fig. 11.18, the annealing of already oxidized coatings has no peculiar inﬂuence on their morphology whereas the complete thermal oxidation of an oxygen deﬁcient as deposited ﬁlm clearly favours its compactness. 50 45

at.% Y/ RD (nm.min−1)

40 35 30 RD

25 20

at.% Y

15 10 Transparent (fully oxidized) coatings

5

Absorbing (partially oxidized) coatings

0 40

45

50

55 100.I*/I*Zr (%)

60

65

70

Fig. 11.17. Evolution of the Y content into YSZ coatings and of the deposition ∗ monitored by PEM rate as (RD ) a function of the emission line intensity I ∗ /IZr

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Fig. 11.18. Brittle-fracture cross sections of as deposited (a, c) and annealed at 500 ◦ C (b, d) YSZ coatings fully oxidized (a) or not (c) in their as deposited state. The substrate is porous alumina (Keralpor 99 commercialized by Kerafol Gmbh) 3.0 RYSZ

2.5

−Zim / kΩ

2.0

CPEelectrode

CPEYSZ

1.5 1.0 measurement fit

0.5 0.0 0.0

0.5

1.0

1.5 2.0 Zreal / kΩ

2.5

3.0

3.5

Fig. 11.19. Typical impedance spectrum measured at 337 ◦ C of a sputtered YSZ ﬁlm and the equivalent circuit used for ﬁtting the data [80]

These recent results conﬁrm the method proposed by Park et al. [79] owing to the interest for SOFC to synthesize metallic or partially oxidized electrolyte coatings and to further oxidize them thermally to obtain dense coatings on porous substrates. Complex impedance spectroscopy characterizations show one contribution in a Nyquist diagram [72,80] (Fig. 11.19), contrary to bulk material showing a

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grain contribution in the high frequencies range and a grain boundary contribution for intermediate frequencies [82]. This is a characteristic of thin ﬁlms and/or nanomaterials [83]. Previous works showed that YSZ thin-ﬁlm morphology is strongly dependent on the working pressure [76]. According with Thornton [13], increasing the argon pressure favours the growth of columnar and porous coatings. We have also shown that the ionic conduction, which is governed by grains phenomena in dense coatings [72], becomes grain boundary-dependent with increasing the porosity of the ﬁlm [76]. Ceria-Based Electrolytes Contrary to zirconia, doping is not required to stabilize the ﬂuorite structure of CeO2 . This material is a mixed conductor. Undoped ceria exhibits a low ionic conductivity. Thus, a dopant addition is required to increase the O2− conduction and to decrease the electronic conduction. As with zirconia, Ce4+ ion substitution by a dopant R3+ cation leads to vacancies creation to conserve the crystal electroneutrality. Steele has shown that addition of a dopant in the range 8–12 mole% allows the creation of 2–3% vacancies. [84]. Doping also decreases ceria reducibility against low oxygen partial pressures [85]. Ce4+ ion is quite large (r = 0.097 nm) and oﬀers a broad range of dopant choice. However, two criteria have to be observed regarding to the dopant nature. Firstly, steric eﬀect has to be considered and the diﬀerence between the atomic radius of Ce4+ ion and the dopant must be minimized to avoid the creation of too much stresses during the substitution process. Secondly, an attention must be paid to the dopant availability and cost. Opinions diﬀer about the dopant oﬀering the best properties in terms of conductivity and stability in reducing environments. As it is shown in Fig. 11.20, samarium enrichment leads to the best conductivities. However,

Sm

Log (sT / S.cm−1.K)

2

Gd Dy Y

1.8

Yb

Ho

Nd La

1.6 0.1 0.11 Ionic radius /nm

0.12

Fig. 11.20. Evolution of ceria ionic conductivity as a function of the additional element radius [90]

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due to its price and availability, gadolinium is the best potential candidate for YSZ replacement as IT-SOFCs electrolytes. Whatever the chosen dopant, ceria based compounds show higher ionic conductivity than those reached with zirconia based compounds, in the temperature range of IT-SOFC [86,87]. Optimum rate of gadolinium oxide (Gd2 O3 ) or samarium oxide (Sm2 O3 ) is located around 10 mole% to achieve convenient electrical properties [84]. From Steele [84] or Badwal [85], gadolinia doped ceria (GDC) is less reducible than samaria doped ceria (SDC), which is in opposition with the observations of Yahiro et al. [88] and Eguchi et al. [89]. Many authors are focusing on gadolinium doping, which seems to be the best compromise between reducibility resistance and conduction properties [84, 86]. Around 700◦C, GDC ionic conductivity is much higher than that of YSZ, as well for bulk materials [84] as for sputter deposited coatings [71]. A doping rate of 10 mole% oﬀers a wider ionic conduction range than a doping of 20 mole% [84]. It is also compatible with electrodes materials [65,91]. However, this kind of material exhibits two major negative points. The ﬁrst one remains its mechanical stability. The second, located at the anodic level of the cell, which corresponds to a reducing environment, leads to ceria destabilization with Ce4+ ion reducing into Ce3+ [84, 85]. This reduction is also accompanied with an expansion of 6 or 8% in the volume if the resulting compound is Ce4 O7 or Ce2 O3 [85], respectively. This structural modiﬁcation gives rise to cracks, which is very harmful for the future working of the cell. Moreover, Ce3+ ion occurrence leads to an increase in the electrical conductivity to the detriment of ionic one [55, 75, 84]. GDC ﬁlms were deposited by RF sputtering in a reactive argon–oxygen (ratio 9:1) mixture [92] on a rotating substrate holder at diﬀerent temperatures. The deposition rate was around 2.5 nm min−1 , and the structure of the coating always remained ﬂuorite. Moreover, the coating content conserved that of the target, which is attributed to the close atomic numbers of Ce and Gd [76]. Impedance spectroscopy measurements performed on the target show two contributions in the Nyquist diagram, as expected for bulk materials, whereas it exhibits only one contribution for the ﬁlm [82]. This behaviour is conformable to other observations done on YSZ coatings [72, 80, 90] and on GDC coatings reactively sputter-deposited by others [93]. Uhlenbruck et al. [94] have also deposited GDC on dense YSZ membranes from a metallic Ce-Gd (80–20 at.%) target in reactive DC mode. They obtained a deposition rate of 12 nm min−1 , higher about ﬁve times that obtained by Chiodelli et al. [92] in RF mode. The ﬁlm crystallinity increases with the deposition temperature which has no importance on the ﬁlm composition. However, the substrate temperature conditions the ﬁlm morphology: the coatings deposited at room temperature presents a cauliﬂower like columnar structure whereas that deposited around 800 ◦ C is constituted of very thinner columns (Fig. 11.21). Gourba et al. [93] have also deposited GDC coatings by DC sputtering in the presence of reactive argon–oxygen gas mixtures of a Ce−Gd (90–10 at.%)

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Fig. 11.21. SEM brittle fracture cross sections of GDC (CGO) coatings deposited on dense YSZ membranes at room temperature (top) and at 800◦ C (bottom) [94]

metallic target. To improve the deposition rate of fully oxidized coatings, oxygen ﬂow rate is in situ controlled by optical transmission interferometry (OTI) [38,39]. The brittle fracture cross section of ﬁlms deposited at 0.5 Pa on polished AISI 430 or on porous Ni-YSZ cermets shows a quite dense morphology of GDC coatings (Fig. 11.22). This study also indicates that the nature of the substrate has no inﬂuence on the ﬁlm crystallinity and that coatings between 0.5 and 5.5 μm thick always present the expected ﬂuorite structure of GDC [93]. As expected, the resistance of the coatings increases with their thickness. As already mentioned, despite quite good ionic transport properties, GDC presents the main drawback of an insuﬃcient stability in the presence of reducing atmospheres. An alternative solution has been proposed to overcome this drawback; it consists in protecting the anodic side of GDC by a thin YSZ barrier [42, 89, 95] (Fig. 11.23). For Brahim et al. [95], only one contribution is visible on the Nyquist diagrams whatever the YSZ to GDC thickness ratio and the total thickness of the bilayer. As expected, the ionic conductivity of the bilayer is improved by decreasing the YSZ to GDC thickness ratio. The same concept of sputter deposited bilayer coatings has also be developed by Yoo [96] in the case of samarium-doped ceria protected by scandium doped zirconia, i.e. the best ionic conductors deriving from ceria and zirco-

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Fig. 11.22. Brittle-fracture cross section SEM micrographs of GDC coatings deposited on a dense stainless steel substrate [71]

Fig. 11.23. Brittle fracture cross section of a dense GDC-YSZ bilayer deposited on a porous substrate [95]

nia, respectively. The cell developed from this conﬁguration allowed power densities up to 360 mW cm−2 at 600◦ C with a perfect stability all over the test duration, i.e. up to 130 h, in a humid fuel atmosphere 20% H2 in Ar (3% H2 O). New Electrolyte Materials These new materials exhibit much higher ionic conductivities than those of the conventional ﬂuorite structure materials because the anionic conduction is not governed by vacancies mechanisms, but by conduction paths proper to the structure. LAMOX Laﬀez et al. [97] have ﬁrst deposited lanthanum molybdate coatings on a porous alumina substrate by RF sputtering of a La2 Mo2 O6 ceramic target.

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By increasing the oxygen ﬂow rate, they obtained pure La2 Mo2 O9 . The ﬁlms, initially amorphous, crystallize after annealing in air over 650◦ C. They also observed a densiﬁcation of the ﬁlm by increasing the La/Mo atomic ratio. The eﬀect of a partial substitution of La by Y has also been studied in such materials deposited on both dense and porous (Ni-YSZ cermet) substrates. The substitution of La by Y allows the stabilization at room temperature of the high temperature phase, known as the more conductive one [98]. LAMOX coatings were synthesized by Briois et al. [99] in DC mode by co-sputtering La–Y and Mo metallic targets in the presence of a reactive argon oxygen gas mixture. In that case, the substrate holder is rotating to allow a mixing of the metallic vapour incoming from each target, which also yields a much higher lateral homogeneity, as well for the composition as for the thickness distribution of the coating [100]. The composition of the ﬁlms is ascribed to the discharge current dissipated on each target as a function of the oxygen ﬂow rate and to the target to substrate holder distance. As with Laﬀez et al. [97], the as deposited coatings are amorphous and present a glassy aspect cross section. They crystallize around 400◦ C, and their microstructure coarsens after treatments at higher temperature. However, increasing the annealing temperature produces micropores in the thickness of the coating. This phenomenon is expected to be correlated with the increase of the ﬁlm resistance observed after several cycles of heating: at the amorphous state, the activation energy is much higher than that of bulk La1.8 Y0.2 Mo2 O9 . After the ﬁrst crystallization treatments, it becomes comparable to the literature data and exhibits a signiﬁcant and progressive degradation during the following heat treatments [81]. Nevertheless, this class of materials presents a major drawback for SOFC applications resulting from its reduction at high temperature in the presence of a reducing atmosphere. Indeed, electrochemical measurements performed as a function of the oxygen partial pressure exhibit an increase of the electronic conductivity and a decrease of the ionic conductivity with decreasing oxygen partial pressure [101]. The solution proposed by George et al. [102] consists in a double substitution of La by Y to stabilize the high-temperature structure and of Mo by W to improve the resistance to the reduction of LAMOX in reducing environments. Apatite Lanthanum silicates are presently the best candidates from the electrochemists community and fuel cell device-testers point of view [102] to replace YSZ in a SOFC application. Apatite synthesis from La and Si metallic targets in a reactive gas mixture has already been achieved, but with quite low deposition rates [103]. The coatings are amorphous in their as deposited state and crystallize in the apatite structure around 900◦C. According to the work of Park et al. [79] about Zr−Y metallic ﬁlm post oxidized, La−Si coatings with various compositions have also been deposited with deposition rates at least

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Fig. 11.24. Brittle-fracture cross section SEM micrographs of La−Si−(O) coatings deposited on a porous Ni−YSZ substrate: (a) before annealing in their metallic state and (b) after annealing in their apatite structure

one order of magnitude higher than as deposited oxides [104]. X-ray diﬀraction measurement showed that the formation of the LaSi2 phase ﬁrst occurred at intermediate temperatures for the ﬁlms deposited with higher Si contents while the ﬁlms deposited with lower Si contents remained amorphous up to the start of the oxidation process. The lanthanum silicate apatite-like phase (La9.33 Si6 O26 ) was obtained only after annealing at 900◦C [105]. Thermogravimetric measurements also showed that the thermal oxidation of as-deposited amorphous La−Si metallic coatings produced a drastic increase of the mass during their crystallization [106]. This behaviour is expected to proceed from an easier movement of oxygen in a crystalline apatite structure. HPPMS technology was also used to deposit La−Si coatings. The corresponding power supply leads to a strong ionization of the sputtered species [107, 108] that can improve the coating compactness by an energetic ion bombardment. First results are promising, especially after the synthesis of a dense layer on a cermet exhibiting lower activation energies than those observed on bulk materials. SEM observations of the brittle-fracture cross section presented in Fig. 11.24 show a dense morphology despite the porosity of the cermet substrate. Proton Conductors Stotz and Wagner ﬁrst quantiﬁed the solubility of water in some oxides and its impact on their transport properties [109]. The ﬁrst oxide to be identiﬁed, which was predominantly proton conducting, was a doped (yttrium, lanthanum or samarium) thorium oxide, but this was only at low partial pressure of oxygen (high pH2 ) and temperatures above 1200◦C [110]. In 1980, the systematic investigation by Takahashi and Iwahara, on the conductivity of compounds with the perovskite structure in hydrogen or water containing atmospheres, revealed several materials with either pure oxide, mixed oxide-proton or pure proton ionic conductivity [111]. The highest proton

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conductivities were observed in cerates which were ﬁrst reported by Iwahara et al. [112]. More recently, the proton conductivity of other families of oxides has been studied. These include zirconates MZrO3 (M = Ca, Sr, Ba) [113, 114] and rare-earth oxides such as La2 O3 and Y2 O3 [115–117]. KTaO3 [118] and LiNbO3 [119] were found to have rather low proton conductivities. Figure 11.25 compares the conductivities of a selection of the proton conductor materials. Despite their recent interest for low temperature fuel cells applications, only few studies deal with proton conductor sputter deposited coatings. These study only deal with perovskite structure barium cerate or strontium zirconate, which constitute the best proton conductor materials. He et al. [121] deposited Y doped barium cerate coatings by RF sputtering of a BaCe0.9 Y0.1 O3 sintered target on MgO single crystal substrates at temperatures up to 750◦ C. The coatings present a strong (002) texture with the presence of a low amount of CeO2 , which is lower when the deposition temperature is about 550◦ C. Ph.D. studies of Arab Pour Yazdi in progress also concern the deposition at room temperature of Y doped barium cerate coatings by pulsed DC reactive Temperature (°C) 400

200

100

2

0 NaOH 1M

logS T (Scm-1T)

0 -2 -4

Y:SrZrO3 single cristal Y2O3 undoped Nd:BaCeO3

Ni:KTaO3

-6 Y: SrCeO3 -8 Fe:LiNbO3

-10 1

2 1000 / T(K)

3

4

Fig. 11.25. Proton conductivity of some oxides compared to the conductivity of 1 M NaOH aqueous solution [120]

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Fig. 11.26. Composition evolution along a radius of the rotating substrate holder of co-sputtered barium cerate coatings reactively deposited at high pressure as a function of the discharge current dissipated on the Ce0.9 Y0.1 target (P = 2.5 Pa)

co-sputtering of Ba and Ce0.9 Y0.1 metallic targets. As with other studies [99, 100], the substrates are positioned on a rotating substrate holder. Due to the high atomic number of Ba, a strong resputtering is observed at low deposition pressure (0.5 Pa) next to the target position, associated with a strong evolution of the coating composition as a function of its position from the centre of the substrate holder. Increasing the pressure around 2.5 Pa allows the deposition of coatings with reduced composition heterogeneity. Then, the coating content is mainly a function of the relative discharge current dissipated on each target (Fig. 11.26). Contrary to He [121] which obtained crystallized and stable coatings by in situ heating, the as deposited coatings at room temperature are amorphous. Moreover, due to the strong reactivity of Ba, the areas which contain more Ba than Ce + Y react to produce barium carbonate BaCO3 accompanied with a strong degradation of the ﬁlms integrity (Fig. 11.27). Compared to barium cerate, strontium zirconate is less conductive but is also strongly less sensitive to carbonation. Y-doped SrZrO3 thin ﬁlms were then also deposited on various substrates by co-sputtering on a rotating substrate holder of metallic Sr and Zr0.84 Y0.16 targets in the presence of reactive argon–oxygen gas mixtures [122]. As with barium cerate, as-deposited coatings are amorphous whatever their composition and crystallize around 400◦C in the convenient perovskite structure when the current applied to the Zr−Y target ranges between 0.55 and 0.6 A, whereas that of the Sr is ﬁxed at 1 A. It is shown that TECs of the ﬁlm and of the substrate has to be adapted to avoid cracks during annealing treatments to guarantee the gastight of the ﬁlm.

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a

b

Fig. 11.27. Top view (a) and cross section (b) SEM observation of a carbonated amorphous barium cerate sputter deposited coating

Cathode Current Collector

15 mm

Protective Coating

Anode Electrolyte Cathode

Substrate

Anode current Collector

Fig. 11.28. Scheme of a lithium all solid state sputter deposited microbattery [123]

11.3.2 Microbatteries Among the diﬀerent energy micro-sources, we focus here our attention on the micro-accumulators based on the transport of Li+ . In such a device, each component is between some tens of nanometres and some micrometers thick and the whole thickness of the stack is about 10 μm (Fig. 11.28) [123,124]. Due to the strong reactivity of lithium, a barrier layer, called encapsulation layer, is also required to protect the micro-accumulator against the atmosphere. To be compatible with the microelectronics industry, all the constitutive layers of a micro-accumulator must be synthesized directly on the electronics components (“above IC” process) and must support constraints related to the assembly processes, particularly the “solder reﬂow” technique commonly used to connect the cheap to the ﬁnal component and which induces a heating for some minutes over about 250◦ C.

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In a microbattery, the electrolyte ensures the transport of ions and must prohibit the electronic conduction to avoid short circuits. Hence, its main characteristic is a high-ionic conduction at room temperature. The electrolyte must also be stable in a wide range of potential, which mainly implies the use of lithium glasses. In the case of all solid systems, the most employed electrolyte is LIPON (e.g. Li3±x PO4−y Ny ). This compound has a relatively low ionic conductivity of about 2 × 10−6 S cm−1 [125], but presents an excellent electrochemical + stability up to potentials around 5.5 V vs. Li/Li and also an excellent ther◦ mal stability over 300 C. LIPON coatings are systematically deposited by RF sputtering of a Li3 PO4 in pure nitrogen [126–129]. Within the experimental accuracy of Li chemical measurements, no signiﬁcant evolution of Li content is observed with the experimental conditions [126, 130]. However, a signiﬁcant increase of the deposition rate can be related to the increase of the Li3 PO4 target density [131], whereas the N/P composition ratio decreases with increasing the RF power and the target to substrate distance and with decreasing the nitrogen partial pressure [132]. This parameter which governs the ionic conductivity of LIPON and which mechanisms are still not perfectly understood [133] must be accurately controlled; increasing the N/P ratio increases Li+ transport properties in LIPON. Other electrolytes with higher ionic conductivity than LIPON have also been developed. The best conductivities of about 10−3 S cm−1 are obtained with vitreous sulphide or nitride electrolytes such as B2 S3−Li2 S−LiI, P2 S5− Li2 S−LiI and Li3 N [134, 135], but they decompose at low potential. Moreover, their strong hygroscopic behaviour makes their industrial application very diﬃcult to envisage. LISICON fast ionic conductors such as Li3 Zn0.5 GeO4 and Li0.3 La0.57 TiO3 present a domain of electrochemical stability in the range 0–4.8 V vs. Li and an excellent ionic conductivity of about 10−3 S cm−1 , but both properties are not obtained simultaneously [136]. Moreover, no work in the literature mentions the deposition of LISICON by sputtering techniques. Among the attempts to improve both the electrochemical stability and the ionic conductivity of lithium conductor electrolytes, let us mention the works of Bates et al. [125] which sputtered a target composed of Li3 PO4 and Li4 SiO4 to deposit Li3.6 (Si0.19 P0.2 )O4 whose ionic conductivity was only 2 × 10−7 S cm−1 . On the basis of this work, Lee et al. [137] also sputtered a target composed of 80% Li3 PO4 and 20% Li2 SiO3 . The LISIPON ﬁlm obtained, Li1.9 PSi0.28 O1.1 N, presents an excellent electrochemical stability up to 4.5 V vs. Li and an ionic conductivity slightly higher than that of LIPON of about 8.8 × 10−6 S cm−1 at room temperature. If the electrolytes performances are predominant in a microbattery, the properties of the electrodes also condition its capacity and lifetime. The best results were obtained with positive electrodes deriving from LiMn2 O4 [124, 138–140], LiCoO2 [141] or V2 O5 [124], obtained by RF sputtering. Nonetheless, the coatings, initially amorphous and which present a poor capacity of less than 10 μA h cm−2 μm−1 , must be submitted to a crystallization

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treatment between 600 and 900◦ C to present their best capacities up to 120 μA h cm−2 μm−1 [124]. Conventionally, the positive electrode should be Li metal. However, due to its strong reactivity, new materials are still investigated which present a strong ability to intercalate Li. Among the numerous researches about positive electrode, let us mention the more promising synthesized by magnetron sputtering such as LiMVO4 (M = Ni, Co, Cd, Zn) [142, 143] and tin–silicon oxynitrides, lithiated (LiSiTON) or not (SiTON), which present an excellent cyclability [144]. Finally, let us mention recent developments performed with Si [145] and Ge [146, 147] positive electrode coatings which are expected to allow the best capacities due to their strong intercalation ability up to 4.4 Li atom per Si or Ge atom. Nonetheless, the main problem to be overcame results from the strong volume expansion of more than 200% proceeding from full Li intercalation. Solid State Electrochemical Gas Sensors In recent years, highly sensitive and selective detection of various gases present in the environment has become of primarily interest, particularly for emission control or atmospheric environmental monitoring. Up to now, the control and monitoring of these pollutants is limited by the high cost of the techniques required for the regulation. Among the various civil, industrial or military applications, and due to its considerably lower cost and miniaturization capabilities, the development of reliable solid state gas sensors is nowadays widely studied [148, 149]. The sensor’s requirements are diﬀerent for a given ﬁeld of application and a large number of solid state gas sensors are available in the literature. However, the simplest ones remain sensors using semiconductors or solid electrolytes oxides as active elements, based on changes in electrical parameters. Solid electrolyte (or electrochemical) sensors can be produced with different ionic conductor oxides as a function on the targeted gas. It is one of the most promising gas sensors for commercial application because of its high selectivity, ease of use, fast response and simplest elaboration. They are generally categorized into diﬀerent families, depending on the mode of operation. Indeed, it is possible to distinguish the classical potentiometric and amperometric sensors, but also coulometric, pump-gauge, semi-conducting and impedancemetric sensors [150, 151]. This part does not aim to describe in details the science of sensors and major coatings sputter deposited are performed in these two ﬁelds. That is why only basic features about potentiometric and amperometric will be developed here. Potentiometric sensors lead to an electromotive force (e.m.f.) measurement, while amperometric allow the record of an electric current [151]. For example, oxygen content can be measured with a potentiometric sensor based on a simple oxide ion conductor. However, the detection and measurement of the most important environmental gaseous pollutants, such as CO, CO2 , NOx , SOx , H2 , Cl2 , NH3 , CH4 ,

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and H2 S, is more diﬃcult to realize and require more complicated approaches with auxiliary or electrocatalytic electrodes. Potentiometric Sensors Potentiometric gas sensors are based on thermodynamic activity gradients of electrochemically active species between a working electrode and a reference. The simplest type of potentiometric sensors uses a solid electrolyte that conducts an ion of the species to be detected (equilibrium electrode reaction). Thus, oxygen content can be measured with a potentiometric sensor based on oxygen ion conductor such as YSZ or scandia-stabilized zirconia (SSZ) [152], apatite-like structure [153] or perovskites [151]. It is also possible to use β-alumina as NO sensors, where Na+ can be ion exchanged with NO+ such that it conducts NO+ [154]. In some cases, common electrolytes can be used with the adjunction of an auxiliary electrode to establish equilibrium between the species to be detected and the mobile species in the electrolyte. For example, YSZ or NASICON can be employed in NO sensors with the application of a nitrate-containing auxiliary electrode [155, 156]. Sometimes, the poor stability of auxiliary electrodes often limits the use of such sensors conﬁguration in high temperatures applications, like combustion process monitoring. It is then possible to ﬁnd an alternative solution without auxiliary electrodes, but based on kinetically limited non-equilibrium potentials measured by solid electrolytes. These sensors are referred as mixed potential sensors and can be synthesized by the adjunction of a simple or mixed oxides electrode. Simple oxides used as electrodes in mixed potential sensors are commonly semiconductors like WO3 , SnO2 , NiO, ZnO, V2 O5 or indium–tin oxide (ITO), with other metals or oxide additions. Semiconductors as simple oxide electrode have been extensively studied in the literature and will not be considered here, our attention being focalized on ionic conductor oxides. Mixed oxide electrodes elaboration, with more complicated crystal structures, leads to further improvements to sensors performances. Mixed oxides are formed with spinel or perovskite-like structures. For example, adjunction of Li2 CO3 −BaCO3 or Pr6 O11 doped SnO2 as auxiliary electrode is possible for NASICON in the ﬁeld of CO2 and H2 S sensors, respectively [157, 158]. Amperometric Sensors Electrochemical sensors can also operate in the amperometric mode. Amperometric sensors are based on electrochemical cells consisting of working, counter and reference electrodes which are in connection through an electrolyte phase [159]. First developments of amperometric gas sensors used to involve an electrolyte solution incorporating a working electrode and a second one as counter and reference. For robustness and miniaturization purposes, the liquid phase of the conventional electrochemical cell was removed and has

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been replaced by solid electrolyte materials, i.e. solid phase ionic conductors. YSZ [160–162], widely used in potentiometric gas sensors, ReTmO3 (Re = rare earth, Tm = transition metal) [163–165] or other cation conducting inorganic materials [166–169] (i.e. sodium and lithium conductors, NASICON and LISICON) may be used in amperometric mode for oxygen, NOx , CO2 or H2 O sensing detection. Amperometric sensor selectivity is still delicate as any species containing the mobile ion can contribute to the current and thus interfere with the sensor response. Further improvements of the selectivity may be achieved at the material level. It is for example possible to use spinel oxides like CdCr2 O4 [170], MgAl2 O4 [171] associated with the YSZ electrolyte. Selectivity can also be provided via electrolyte doping by transition metals [163, 165]. Other authors report the use of a gold-counter electrode covered by NaNO2 and WO3 deposited on the sensing electrode to achieve NOx selectivity [168]. Physical Vapour Deposition for Gas Sensors: Magnetron Sputtering Considerations Many solid electrolyte microsensors are based on the same principles as those from macroscopic or thick-ﬁlm sensors. Macroscopic and thick ﬁlm ionic devices have been extensively investigated in the literature but there is still a lack of knowledge about ionic conduction in thin solid electrolyte ﬁlms and properties of microelectrodes on thin-ﬁlm ionic conductors [172]. In the ﬁeld of solid electrolyte thin ﬁlms, several methods of deposition are available, like electron beam evaporation, pulsed laser deposition or magnetron sputtering. In this later case, a few works can be found in the literature and most of them report attempts using RF sputtering from composite target at a given composition, while metallic or reactive DC sputtering remains at its beginning. The objectives of this chapter are to propose an overview and to discuss the recent developments of sputter-deposited ionic conductors thin ﬁlms dedicated to gas sensors. YSZ Among all the materials synthesized by magnetron sputtering in the ﬁeld of sensors, yttria-stabilized zirconia is probably the most studied phase as it has been extensively investigated as a material for refractory uses, tribological coatings, thin ﬁlms with high dielectric constant in integrated circuits, or for applications to fuel cells (see section “Conventional Fluorite Structure O2− Conductor Electrolytes”). . .. When compared to thick ﬁlms, thin YSZ ﬁlms are well suited for oxygen-permeable electrolyte for gas sensors because it is expected to have higher conductance and thus to promote higher eﬃciency. Figure 11.29 gives a schematic example of the process for reactively DC sputtered YSZ-based sensor fabrication from [173] and a planar SOx sensor incorporating a bi-electrolyte has been developed in [174].

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Sputtering deposition parameters have a major inﬂuence on the resulting phase composition and microstructure of the YSZ ﬁlms that strongly govern ionic conductivity of the electrolyte and thus the eﬃciency of the sensors. As already seen in this chapter, there is basically two major magnetron sputtering techniques to deposit YSZ thin ﬁlm, RF [174–176] or DC [173, 177–181], depending on the nature of the target(s) to be sputtered, i.e. ceramic or metallic, respectively. At the composition level, it is important to control the Y2 O3 molar fraction, depending on the structure to be stabilized and the working temperature of the devices. Much attention has been paid to the development of 8YSZ (8 mole% Y2 O3 ) which has a stable cubic ﬂuorite structure and high ionic conductivity at elevated temperature. Tetragonal zirconia doped with 3 mole% Y2 O3 has also been studied by reactive sputtering [179] and may show comparable conductivity to 8YSZ below 600◦C. The control of the sputtering process is of primarily importance and good results are generally

(a) Silicon water

(b) oxidized

Thermally grown SiO2

(C) Patterned and oxidized Etched

Porous Pt (d) Deposited Ni-NiO reference and Porous Pt

Ni-NiO YSZ electrolyte

(e) Deposited YSZ electrolyte Gold connector (f) Deposited Gold connector Pt working electrode (g) Deposited Pt working electrode

Sputter deposited SiO2 (h) Deposited SiO2 insulator

Fig. 11.29. Schematic process for a reactively DC-sputtered YSZ-based potentiometric sensor [173]

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achieved via DC sputtering of one or several metallic targets in Ar−O2 mixtures, coupled with an in situ optical monitoring of the system [177,178]. Thus, target contamination is controlled, leading to higher deposition rates for fully oxidized coatings. Moreover, it is possible to control the content of yttria in zirconia, i.e. YSZ structure, during co-sputtering of two metallic targets, via the control of the applied intensity on each cathode [177]. NASICON Up to now, only few attempts have been made for NASICON sputter deposition [182–184]. Main results seems to reveal heterogeneous chemical composition in the ﬁlm and that classical RF sputtering of composite oxide target is unsuitable for the synthesis of homogeneous Na1+x Zr2 Six P3−x O12 thin ﬁlms [183]. Deviation from the targeted composition is systematically observed and is expected to originate from the high mobility of Na+ species. However, the same authors developed a new sputtering method to achieve the deposition of dense and chemically homogeneous NASICON thin ﬁlms with good physical properties. This method is based, on the one hand, on the co-sputtering of two targets parallel to a rotating substrate holder. On the other hand, it is based on the high-frequency DC supply of a ceramic target (Na3 PO4 ). Perovskites Perovskites structures have also been studied via RF magnetron sputtering as sensing electrodes. A comparison between deposition methods (RF sputtering and dipping) is available and shows that sensing properties of perovskites-like La0.8 Sr0.2 Co1−x Nix O3−δ mixed oxides strongly depends on the ﬁlms morphology [185]. A the lower temperatures (180◦ C), a better sensitivity to CO is observed for the coatings synthesized by the dipping method, due to the largest overall porosity, i.e. largest surface reaction. One can note that the RF sputter deposited coatings in this study were grown at a total pressure of 0.133 Pa, which is very low and thus leads to dense ﬁlms. Indeed, works in progress in the ﬁeld of catalysis (TiO2 , La0.7 Sr0.3 MnO3 ) clearly establish correlations between the deposition pressure, the morphology and the activity of the ﬁlm, in close relation with the number of available adsorption sites [100, 186]. On the other hand, a comparison between three PVD methods (RF magnetron sputtering, pulse laser deposition and electron beam evaporation) for mixed oxides perovskites La1−x Srx CrO3 in the ﬁeld of gas sensors is also available in the literature [187, 188]. Among the three techniques explored, authors show that RF magnetron sputtering process is the most viable for thin ﬁlm mixed potential sensor applications as it produces high quality thin ﬁlms with density, microstructure and phase purity quite similar to bulk La0.8 Sr0.2 CrO3 . In this case, the ﬁlm growth temperature is as low as ambient (<100◦ C) but with a very low deposition rate (about 150 nm h−1 ) that may be overcome by sputtering from metallic targets.

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Another promising attempt has been done with RF sputter deposition of BaTiO3 –CuO on alumina for CO2 gas sensors [189]. Thin sensing layers for CO2 detection were then developed and authors report a linear sensor response in the range 0–500 ppm, which is suitable for indoor air quality or greenhouses application, requiring an operating range around 300 ppm. Neodymium cobaltite (NdCoO3 ) thin ﬁlms have also been RF magnetron sputter deposited on polycrystalline alumina and single crystalline SrTiO3 [190] from a target with the desired composition. During the deposition process, substrates have to be heated at 700◦ C and the coatings are annealed at 900◦C in pure oxygen after deposition, probably to oﬀset the loss in oxygen content due to the sputtering mode and achieve the perovskite structure. Nevertheless, the sensing properties towards CO have shown good response in the 250–400◦C temperature range, for CO concentrations until 1,000 ppm. 11.3.3 Smart Windows

ec tr an och sp ro ar mi en c f t c ilm Gl on as du s ct o

El

Tr

(G

la ss ) Tr an s lo pa n (o st ren r e or t c le ag on ct e ro fil duc ch m to r ro m lo ic n co fil (e n m le d ) ct uc ro to ly r te )

ELECTROCHROMIC DEVICE

r

As deﬁned by Granqvist [191, 192], electrochromic materials can change their optical properties upon charge insertion/extraction. When thin ﬁlms of such materials are integrated in devices, it becomes possible to modulate the transmittance (T ), reﬂectance (R), absorbance (A) and emittance (E) between widely separated extrema. The basic design of an electrochromic “smart window” device is given in Fig. 11.30, and shows a comparable assembly to thin-ﬁlm electrical battery [193]. The key properties of electrochromic materials are the switching times, contrast ratios, coloration eﬃciency, electrochromic memory and time stability. Many inorganic electrochromic thin ﬁlms are oxides or oxide-based like

lons

+

-

Fig. 11.30. Basic design of an electrochromic device [193]

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H

ELECTROCHROMIC OXIDES:

Li Be

Cathodic coloration

He B

C

N

O

F

Ne

Al Si

P

S

Cl Ar

Na Mg

Anodic coloration

K Ca Sc Ti

V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr

Rb Sr Y Zr Nb Mo Tc Cu Rh Pd Ag Cd In Sn Sb Te Cs Ba La Hf Ta W Re Os Ir

I

Xe

Pt Au Hg Tl Pb Bi Po At Rn

Fr Ra Ac Fig. 11.31. Part of the periodic table of elements showing transition metals whose oxides exhibit electrochromic properties [195]

WO3 , NiO, Ta2 O5 , V2 O5 , IrO2 and other mixed oxides [194]. Figure 11.31 gives an example of metal oxides well known for their electrochromic properties. As it can be seen in Fig. 11.30, the central part of the construction is a pure ionic conductor (electrolyte) and can be organic (polymer) as well as inorganic (solid oxide). To achieve the best ion mobility, proton (H+ ) or lithium (Li+ ) ion conductors are preferred. Nonetheless, recent works have shown the eﬃciency of Na+ owing to the colouration of WO3 [184]. The electrolyte must exhibit good ion conductivity and good adhesion. More information about the materials used and the devices conﬁguration can also be found in [196]. Magnetron sputtering is well suited for the deposition of electrochromic metal oxides. One of its major advantages remains the possibility to deposit at relatively low temperatures such as it is possible to coat polyester foils. Another advantage is the possibility to deposit from several metallic/oxide targets in pure and/or pulsed DC mode and to easily control the ﬁlm composition, structure and morphology. Thin ﬁlms homogeneity is also of primary importance, especially in large scale applications, and the substrates can be moved below the targets, with the use of a rotating substrate holder for example. WO3 is one of the most promising inorganic electrochromic materials due to its excellent properties, especially for the amorphous tungsten oxide ﬁlms which have the advantages of high-response speed, long-term stability and good ionic and electronic properties. Many studies have been focused on WO3 sputtering, either by RF or DC, or from metallic or oxide targets [197–211]. Other materials have also been sputtered and studied, like Ta2 O5 [212–214], V2 O5 [215, 216], Nb2 O5 [217, 218], MoO3 [219, 220], Bi2 O3 [221] or mixed oxides [222,223], where the ﬁnal properties strongly depend on the sputtering conditions. In particular, a high-deposition pressure and an amorphous structure are favourable parameters. Most of the studied electrochromic materials are often mixed conductors. Depending on the number of layers to achieve the elaboration of an electrochromic display, it is possible to sputter each constitutive ﬁlm continuously

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in one system. An example of electrochromic display synthesis by a hybrid DC/RF sputtering is available in the literature with WO3 as electrochromic ﬁlm, NiO as counter electrode, LiNbO3 as Li+ ion conducting ﬁlm and ITO as electronic conducting layers [224]. In certain conﬁgurations, when using Li ion conductors, WO3 seems to have tendency to trap Li+ due to irreversible chemical reactions between the electrochromic matrix and the inserted Li ions, which may lead to degradation, delamination and cracking of the ﬁlms, thus reducing the electrochromic device performances [225]. An alternative has been developed via continuous RF sputtering of an electrochromic device based on WO3 , V2 O5 and LIPON as protective layer [226]. Ta2 O5 is also suitable for ionic conductor in electrochromic devices as shown in Fig. 11.32. Ta2 O5 mixed conductors have been reactively RF sputterdeposited on WO3 /ITO with the aim to develop electrochromic devices [212]. In this case, a correlation between the measured ion current and the refractive index suggested a link between ﬁlm porosity and ionic conduction. A shapedependent conductance exists in samples with few voids inclusions, whereas it seems to be less selective for increased porosity. Anyway, results show that Ta2 O5 ﬁlms are suitable for their use in ionic conducting applications. A special attention must however been paid on the hydration degree which has a strong inﬂuence on the proton conductivity of Ta2 O5 that can vary over several orders of magnitude [228]. Other studies also report co-sputtering of Ta2 O5 and NiO dedicated to electrode enhancement in the ﬁeld of all solid state electrochromic devices [229]. In this study, NiO nano-dots were embedded in a Ta2 O5 matrix leading to nanocomposites electrodes with superior durability when compared to single NiO electrodes. Owing to its capacity to host large amounts of lithium, sputtered V2 O5 ﬁlms also received an attention from researchers and particularly as counter electrode [226, 230, 231]. Oxygen partial pressure during the deposition is of

transparent conductor (e.g. ITO)

e− counter electrode (e.g. NiO)

H+

V

ion conductor (e.g. Ta2O5) electrochromic layer (e.g. WO3)

e−

transparent conductor (e.g. ITO)

substrate (glass or plastic)

Fig. 11.32. Scheme of a typical solid state monolithic electrochromic device [227]

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primarily importance since the electrochromic properties of such ﬁlms strongly depend on the oxidation state of the transition metal in the oxide. Thus, various vanadium valence states could result in the synthesis of V2 O3 , VO2 , V2 O5 , or mixed oxides as a function of the total oxygen ﬂow rate during sputtering [232]. To preserve the ion-storage properties and to compensate the unwanted multicolour electrochromism, vanadium pentoxide can be mixed with other transparent oxides such TiO2 or ZrO2 . In this ﬁeld, Masetti et al. studied CeO2 insertion into V2 O5 by RF sputtering of a mixed CeO2 –V2 O5 target in an Ar−O2 atmosphere [231]. They observed changes in the ﬁlms coloration, from yellowish to transparent, upon Li+ insertion. However, after cycling, optical constants of their layers did not restore to their original values and authors attribute this phenomenon to Li+ which remains trapped in the ﬁlm. Moreover, this is accompanied with an expansion of the ﬁlm thickness, able to induce stresses at ﬁlm–substrate interface and, as a matter of fact, may lead to a reduction of the device lifetime. An interesting ionic conductor compound remains LiNbO3 which has already been developed as the ion conducting (solid electrolyte) in an electrochromic ﬁve-layer window device [233]. LiNbO3 thin ﬁlms exhibit lower conductivity than bulk material, due to a lithium deﬁciency. Several approaches are available to overcome this problem, such as co-sputtering of LiNbO3 and Li oxide [234] or Li insertion after deposition [235]. To improve Li+ mobility, another approach has been chosen by Nguyen et al. [236] by changing ﬁlm microstructure via nitrogen incorporation during the sputtering process. Such lithium–niobium oxynitride seemed to exhibit better Li ion mobility by four orders of magnitude compared to Li-deﬁcient ﬁlms. From these authors, this improvement is believed to be associated with the presence of nitrogen in the ﬁlm structure, which creates more cross links in the network of Nb2 O5 , thus leading to a higher Li mobility. From our knowledge, there is no study dealing with reactive DC sputtering of such compounds from metallic targets, which is still a leak in this ﬁeld. Thus, there is still a lot of works to develop this kind of coatings by DC magnetron sputtering, allowing a better control of the ﬁnal properties of the ﬁlms at highest deposition rates, which is, from an industrial point of view, of primarily importance.

11.4 Conclusion Numerous functional applications exploit the particular properties of ionic or mixed conductors. The miniaturization of a lot of devices makes an increase part of solid electrolyte coatings to be required. Unfortunately, among the numerous methods susceptible to produce thin electrolyte coatings, very few deal with sputtering processes. This is particularly due to the fact that most of the electrolyte are synthesized by RF sputtering of ceramic targets which limits drastically the deposition rate. Moreover, several physical properties are often required besides the own electrochemical characteristics of the elec-

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trolyte, such as density–porosity, gastight, adhesion, etc. Their control is based on a good knowledge of the main parameters governing sputtering processes. This is particularly true in the case of reactive pulsed-DC sputtering which constitutes an interesting alternative to RF sputtering owing to the higher deposition rate of such materials. In this chapter, we have ﬁrst presented the crystallographic basis of the most common electrolytes. Then, some applications using electrolyte coatings have been presented and have been illustrated with examples where sputtering was used. For SOFCs, the tendency is to replace YSZ by a better ionic conductor to allow a decrease of the operating temperature which is the condition of the democratization of this environmental friendly energy generation concept. Among the numerous compounds available, the most promising are apatite structure lanthanum silicates and perovskite structure protonic conductors which combine a high-ionic conduction and a rather high inertness against reducing environments. In the ﬁeld of microbatteries, the best electrolytes are Li+ conductors. Up to now, LIPON presents the best compromise between ionic conduction and electrochemical stability at high potential. New materials such as LISICON have been developed but they were never able to improve both the ionic conduction and the electrochemical stability. The most promising studies concern LISIPON whose conductivity is about four times that of LIPON with a slightly lower electrochemical stability up to 4.8 V vs. Li, against 5.5 V vs. Li for LIPON. Nonetheless, the main improvement of microbatteries performances is expected to proceed from the development of new electrodes which constitutes the major literature in that ﬁeld. The development of micro-gas sensors using magnetron sputtering is at its beginning. Indeed, very few works deal with thin ﬁlms microsensors and most of them concern conventional YSZ electrolytes or perovskite structure mixed conductors. In smart windows, sputtering is used for a long time as well for the deposition of electrochromic and counter electrodes as for that of the electrolyte. If most of the studies about all solid smart windows are based on the migration of H+ or Li+ , some data in the literature indicate that recent developments of Na+ conductor electrolytes make also NASICON as possible candidates for this application. It was then shown here that very interesting application of ionic conductor coatings have been investigated using magnetron sputtering. However, this alternative method is only few studied compared for example to sol–gel methods for most of the applications. Nonetheless, these few studies clearly show the strong potential of magnetron sputtering for applications using electrolyte coatings and foreshadow further investigations and developments, especially in the ﬁelds of energy generation and environment.

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12 Reactive Sputtered Wide-Bandgap p-Type Semiconducting Spinel AB2O4 and Delafossite ABO2 Thin Films for “Transparent Electronics” A.N. Banerjee and K.K. Chattopadhyay

12.1 Introduction Reactive sputtering is one of the most widely used techniques for preparing compound thin ﬁlms (such as oxides, nitrides, carbides, etc.) by sputtering metal targets in an active gas atmosphere (Ar + O2 /N2 /CH4 , etc.) [1–4]. In this chapter, we have discussed, in details, the formation of spinel and delafossite materials of the form AB2 O4 and ABO2 (A and B may be monovalent, divalent, trivalent, or tetravalent cations, depending on the crystal structure, described later) by reactive sputtering technique. Specially, wide bandgap, ptype semiconducting, and transparent oxide materials with delafossite and spinel structure, having interesting applications in “Transparent Electronics,” have been discussed in details. In Sects. 12.2–12.5, a detailed review on the structural, optical, and electrical properties of these p-type transparent conducting oxides (p-TCOs), deposited by reactive sputtering technique, has been presented and the origin of p-type conductivity of these materials has been discussed with considerable attention. Most of the results presented in these sections are reported by various authors working on this ﬁeld. In Sect. 12.6, synthesis and electro-optical characterization of one of the very important delafossite, p-type semiconducting, and wide-bandgap material, such as CuAlO2 , produced by our group via reactive sputtering technique, have been discussed in details. Detailed discussions on spinel- and delafossitestructured material can be found in various literatures [5–14]. Also, detailed reviews on the p-TCO materials have been published by us and others [15–17], which cover the syntheses and properties of a range of p-TCO materials reported so far.

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12.2 Spinel and Delafossite Material 12.2.1 Spinel Materials Spinel structure is an important ternary metal oxide crystal structure shown in Fig. 12.1. The spinel structure (sometimes called garnet structure) is named after the mineral spinel (MgAl2 O4 ). The oxide may be written in the form of IV II II+ AII BIII and 2 O4 (called 2–3 spinel) or A B2 O4 (called 4–2 spinel), where A IV+ III+ are the divalent and tetravalent cations of type-1 and B and BII+ are A the trivalent and divalent cations of type-II, respectively. In “normal” spinel structure, 12.5% of the tetrahedral sites and 50% of the octahedral sites of this structure are occupied by A and B cations, respectively, and there are 32 O2− ions in a unit cell. On the other hand, in the “inverse” spinel structure, the site occupancies of two types of cations are swapped. Also, there are some intermediate phases with the formula (A1−x Bx )[Ax B2−x ]O4 also exist. Here, cations in the square brackets occupy the octahedral sites and cations in the parentheses occupy the tetrahedral sites. The spinel crystal structure has a closed-packed fcc array of anions, with space group Fd¯ 3m or O7h . When an fcc cubic cell of edge a and occupied by A atoms is subdivided into eight octants with edge a/2, four of the octants are occupied by AO4 clusters and the other four of the octants are occupied by B4 O4 clusters. The A atom is centered on the AO4 tetrahedron cluster with four nearest-neighbor O atoms, while the B atom is at the corner of the octahedron cluster with six nearest-neighbor O atoms. The O atoms are positioned in the same way in all octants with one A atom and three B atoms as their nearest neighbors. In an inverse spinel structure, the tetrahedral sites are occupied by B atoms while the octahedral sites are occupied by equal numbers of A and B atoms.

O

T

T

O

T

O

O O A B T O Fig. 12.1. Spinel crystal structure

T

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The spinel structure is very ﬂexible with respect to the cations it can incorporate. There are over 100 known compounds with this type of crystal structure. In particular, the two cations (say, A and B) can mix, so that the composition with respect to one unit cell can become (A8 )(B16 )O32 , or A8 (A8 B8 )O32 = A(AB)O4 in regular chemical spelling, or (A8/3 B16/3 ) (A16/3 B32/3 ) O32 , and so on, with the atoms in the brackets occupying the respective site at random. Examples of ternary metal oxides with 2–3 spinel structure are MgAl2 O4 , MgGa2 O4 , ZnAl2 O4 , ZnGa2 O4 , ZnIn2 O4 , ZnIr2 O4 , ZnCo2 O4 , ZnRh2 O4 , CdAl2 O4 , CdGa2 O4 , CuAl2 O4 , CuMn2 O4 , NiCo2 O4 , NiFe2 O4 , NiCr2 O4 , LiTi2 O4 , LiMn2 O4 , LiAl2 O4 , CdRh2 O4 , FeCr2 O4 , FeV2 O4 , MgCr2 O4 , ZnFe2 O4 , ZnMn2 O4 , FeAl2 O4 , HgCr2 O4 , etc. Similarly, examples of ternary metal oxides with 4–2 spinel structure are MoAg2 O4 , MnFe2 O4 , GeCo2 O4 , GeMg2 O4 , GeZn2 O4 , GeCd2 O4 , NbZn2 O4 , TiFe2 O4 , SiMg2 O4 , SiZn2 O4 , SiCd2 O4 , etc. It is noteworthy that some of the binary metal oxides such as Fe3 O4 also exhibit spinel crystal structure. But in this case, the AII+ and BIII+ cations are same element (Fe) but exhibit both +2 +2 and +3 valence states (as Fe+2 OFe+3 Fe+3 2 O3 = Fe 2 O4 ), respectively. Also, it is worthwhile in mentioning that there are some reports on quaternary oxides having spinel structure, such as LiFeTiO4 [18], Ca4 Fe1.5 Al17.67 O32 [19], Mn(2−x) CO2x Ni(1−x) O4 [20] FeCoCrO4 (Fe+3 Co+2 Cr+3 O4 or Fe+3 Co+3 Cr+2 O4 or Fe+2 Co+3 Cr+3 O4 ) [21], etc. Besides oxides, there are some ternary nonoxides exist which are having spinel structure, such as AgAl2 S4 , CaIn2 S4 , CuTi2 S4 , CuIr2 S4 , ZnCr2 S4 , FeIn2 S4 , CuCr2 Te4 , CuCr2 Se4 , CdCr2 Se4 , Li2 NiF4 [22, 23], etc. MgAlON [24] is an oxynitride material having spinel structure. Example of binary nonoxide spinel material includes γ-Ge3 N4 , Co3 O4 (sometimes written as CoCo2 O4 ), etc. [25, 26]. Lastly, examples of inverse spinel include SnMg2 O4 , CdIn2 O4 , MgIn2 O4 , CuFe2 O4 , CuCr2 O4 , SnCd2 O4 , SnZn2 O4 , LiCuVO4 , LiNiVO4 , MnIn2 S4 , etc. [27–30]. As far as applications of spinel materials are concerned, many of the spinels have interesting electronic and magnetic properties [31] and, therefore, suitable for various technological applications, which include superconductors [32, 33], magnetic core materials [34, 35], high-frequency devices [36], cathode material for commercial lithium secondary batteries [18, 36], magnetic semiconductors for spintronics applications [37], gas sensors [26], etc. Since many of the spinels are common minerals, therefore, in addition to the materials science studies, some of the spinel materials also have great importance geophysical studies [38–41]. Also the study of large bandgap spinels (e.g., MgAl2 O4 , SnCd2 O4 , SnZn2 O4 , CdIn2 O4 , etc.), with high electroconductivity, opens many interesting applications in optoelectronic device technology. These wide-bandgap materials are transparent in the visible and infrared regions and therefore have important applications in transparent electrodes, ﬂat panel displays, infrared windows, missile domes, thin ﬁlm solar cells, low-energy architectural window coatings, and many such applications [27, 42–50]. Also, CdTe solar cells using Cd2 SnO4 /Zn2 SnO4 as transparent conductor layers have achieved the highest cell eﬃciency

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known for this system [51]. And lastly, within the class of transparent spinel oxides, p-type semiconducting, wide bandgap, and transparent spinel oxides (e.g., NiCo2 O4 , ZnIr2 O4 , ZnRh2 O4 , etc. [52–55]) have recently generated great interest in the ﬁeld of optoelectronic device technology for the possible applications in “Transparent Electronics” [56]. Therefore, these reports have rekindled the interest to study the fundamental physics in spinel oxide systems. 12.2.2 Delafossite Materials Delafossite structure is another important crystal structure for ternary metal oxides. The oxides are generally of the form of AI BIII O2 , where AI+ represents the monovalent cation and BIII+ represents the trivalent cation. The structure, as shown in Fig. 12.2, consists of an alternative stacking of AI and layers of nominal BIII O2 composition consisting BIII O6 octahedra sharing edges. Each AI atom is linearly coordinated with two oxygen atoms to form an O−AI −O dumbbell unit placed parallel to the c-axis. O atoms of O−AI −O dumbbell link all AI layers with the BIII O2 layers [12–14]. On the other hand, each oxide I ion in the BIII O2 layer forms a “pseudotetrahedral coordination (BIII 3 A O)” III+ I+ with the neighboring B and A ions. Ternary metal oxides having this type of crystal structure include PdCoO2 , PtCoO2 , PtCrO2 , PtRhO2 , CuAlO2 , CuFeO2 , CuGaO2 , CuScO2 , CuYO2 , CuCrO2 , CuInO2 , CuRhO2 , CuLaO2 , CuPrO2 , CuNdO2 , CuSmO2 , CuEuO2 , AgInO2 , AgScO2 , AgCrO2 , AgGaO2 , AgCoO2 , AgFeO2 , AgRhO2 , AgAlO2 , etc. Quaternary oxides with delafossite structure include AgNi1−x Sbx O2 , AgZn1−x SbxO2 , CuGa1−x Fex O2 , CuIn1−x Cax O2 , AgIn1−x Mgx O2 , CuCo1−x Tix O2 , CuNi1−x Tix O2 , CuCu1−x Tix O2 , CuNi1−x Snx O2 , CuFe1−x Vx O2 , AgNi1−x Tix O2 , etc. [12–17].

Fig. 12.2. Delafossite crystal structure

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Table 12.1. Various properties of spinel and delafossite crystal structures Structure

Stoichiometry Space Coordination no. group (CN)/geometry Spinel AB2 O4 Fd¯ 3m A: CN = 4/tetrahedral coordination B: CN = 6/octahedral coordination O: CN = 4/distorted tetrahedral coordination Delafossite ABO2 R¯ 3m A: CN = 4/square planer coordination B: CN = 6/octahedral coordination O: CN = 1A + 3B/tetrahedral coordination

Representative oxides NiCo2 O4 , MgAl2 O4 , MgGa2 O4 , ZnAl2 O4 , ZnGa2 O4 , ZnIn2 O4 , ZnIr2 O4 , ZnCo2 O4 , ZnRh2 O4 , CdAl2 O4 , CdGa2 O4 , etc. CuAlO2 , CuFeO2 , CuGaO2 , CuScO2 , CuYO2 , CuCrO2 , CuInO2 , AgInO2 , AgScO2 , AgCrO2 , AgGaO2 , PdCoO2 , etc.

As far as applications of delafossite materials are concerned, these materials have potential applications in thermoelectric devices [57–62], ﬁeld-emission displays (FEDs) [63], ozone sensors [64], photocatalytic hydrogen generators [65], magnetic semiconductors for spintronics [66], etc. But, as most of the delafossite materials are wide-bandgap transparent materials, therefore they have lots of applications in optoelectronics technology. Especially, as most of these materials are p-type semiconducting transparent oxides, they have potential applications in “Invisible” or “Transparent Electronics” [15–17, 56]. Detailed review of various p-TCOs with spinel and delafossite structure is discussed in subsequent sections (Table 12.1).

12.3 p-Type Transparent Conducting Oxides Based on Spinel and Delafossite Structure 12.3.1 Introduction to Transparent Conducting Oxides Transparent conducting oxides (TCOs) are very important materials that create great interest within materials scientists for its overwhelming applications in the ﬁeld of optoelectronic device technology. The characteristics of such ﬁlms are high room temperature electrical conductivity (∼103 S cm−1 or more) and high optical transparency (more than 80%) in the visible region. TCOs are well known and widely used for a long time in optoelectronics industries as well as in research ﬁelds. After the ﬁrst report of transparent

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conducting cadmium oxide (CdO) thin ﬁlm by Badekar [67] in 1907, extensive works have been done in the ﬁeld of TCO technology to prepare new types of TCOs with wide ranging applications [68–78]. Technologically, these TCOs are being used extensively in various ﬁelds, which include solar cells, ﬂat panel displays (FPDs), low-emissivity (“low-e”) windows, electromagnetic shielding of cathode-ray tubes in video display terminals, electrochromic (EC) materials in rear-view mirrors of automobiles, EC-windows for privacy (so-called smart windows), oven windows, touch-sensitive control panels, defrosting windows in refrigerators and airplanes, invisible security circuits, gas sensors, biosensors, organic light-emitting diodes (OLED), polymer light-emitting diodes (PLED), antistatic coatings, cold heat mirrors, etc. [67–70, 74, 75, 79–90]. Also some new applications of TCOs have been proposed recently such as holographic recording medium, high-refractive index waveguide overlays for sensors and telecommunication applications, write-once read-many-times memory chips (WORM), electronic ink, etc. [91–94]. And lastly, the low-temperature deposition of TCOs onto poly(ethylene terephthalate) (PET), polyamides, and other polymer substrates in roll-coating processes for touch-screen and infrared reﬂector applications is the recent challenges for the TCO industries [95–97]. Possibility of the aforementioned novel applications of TCOs is based on the fact that the electronic bandgap of a TCO is higher than 3.1 eV (corresponding to the energy of a 400 nm blue photon). So visible photons (having energy between 2.1 and 3.1 eV) cannot excite electrons from valence band (VB) to the conduction band (CB) and hence are transmitted through it, whereas they have enough energy to excite electrons from donor level to CB (for n-type TCO) or holes from acceptor level to VB (for p-type TCO). And these acceptor or donor levels are created in the TCOs by introducing nonstoichiometry and/or appropriate dopants in a controlled manner. A schematic representation of the bandgap designing for transparent conductors is shown in Fig. 12.3. 12.3.2 Transparent Electronics Although the TCOs have vast range of applications as mentioned above, very little work has been done on the active device fabrication using TCOs [98,99]. This is because most of the aforementioned TCOs are n-type semiconductors. But the corresponding p-TCOs, which are essential for junctional devices, were surprisingly missing in thin ﬁlm form for a long time, until in 1997, Kawazoe et al. [100] reported the p-type conductivity in a highly transparent thin ﬁlm of copper aluminum oxide (CuAlO2+x ). This has opened up a new ﬁeld in optoelectronic device technology, the so-called “Transparent Electronics” or “Invisible Electronics,” where a combination of the two types of TCOs in the form of a p–n junction could lead to a “functional” window, which transmits visible portion of solar radiation yet generates electricity by the absorption of UV part [56]. It must be mentioned here that the ﬁrst report of semitransparent p-type conducting thin ﬁlm of nickel oxide was published in 1993 by Sato

12 Reactive Sputtered Wide-Bandgap p-Type Semiconducting

4

Visible photons

3

Slight absorption due to electron activation (n-type material)

0

100

Conduction Band

%T

0

Donor level (n)

2

1

419

eV

eV

Acceptor level (p) Valence Band

100

%T

0

Slight absorption due to hole activation (p-type material)

Fig. 12.3. Bandgap designing for transparent conductors. Visible photons (2.1– 3.1 eV) do not have enough energy to excite electrons from valence band to conduction band, but have enough energy to excite holes (for p-type) from acceptor level to VB or electrons (for n-type) from donor level to CB (after [38]). Right-hand side shows the transmittance of the TCO with respect to incident radiation. The arrow “ ” indicates the transmittance graph for a p-type TCO, where a slight absorption can be observed (indicated by shaded part) at low-energy region, due to the activation of holes from acceptor level to VB. Similarly, the arrow “ ” indicates the same for n-type TCO, where slight absorption at low-energy region takes place due to electron activation from donor level to CB

et al. [101]. They observed only 40% transmittance of the NiO ﬁlms in the visible region and when they tried to fabricate an all-TCO p–i–n diode of the form p-NiO/i-NiO/i-ZnO/n-ZnO, the visible transmittance further reduced to almost 20%. Although this low transmittance was not favorable for superior device applications, but still this report was an important milestone in the ﬁeld of “Transparent Electronics” and in the development of TCO technology. Now for diverse device applications, it is utmost important to prepare various new types of p-TCOs with superior optical and electrical characteristics, at least comparable to the existing, widely used n-TCOs, which are having transparency above 80% in the visible region and conductivity about 1,000 S cm−1 or more. Intense works have been done for the last few years in this direction to fabricate new p-TCOs by various deposition techniques. Also, quite a number of works have been carried out for proper understanding of the structural, optical, and electrical characteristics of p-TCOs. As this is an emerging ﬁeld in TCO technology, preparation of new materials as well as existing materials with new deposition techniques is the need of the hour.

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Other p-TCO Delafossite structure (ABO2) [A: Cu+, Ag+] [B: Al+3, Ga+3, In+3, Cr+3, Fe+3, Spinel oxide Co+3, Y+3, La+3, Sc+3 etc.] Mixed (AB2O4) oxide Cu2SrO2 [A: Ni2+, Zn2+] (Ag2O[B: Ir3+, Rh3+, Co3+] In2O3)

Ni-based spinel p-TCO (NiB2O4) Cu-based delafossite p-TCO (CuBO2)

Ag-based delafossite p-TCO (AgBO2)

Zn-based spinel p-TCO (ZnB2O4)

Binary oxide (NiO, p-ZnO)

Layered Oxychalcogenide [(AO)BCh] [A: La+3, Pr+3, Nd+3, Sm+3, Gd+3, Y+3 etc.] [B: Cu+, Ag+], [Ch: S−2, Se−2]

Fig. 12.4. Chart of various p-TCO materials reported so far. Here, the doped versions of Cu-based delafossite p-TCOs have been mentioned only

A chart of various p-TCO materials developed so far for potential applications in “Transparent Electronics” is furnished in Fig. 12.4. 12.3.3 p-TCO with Spinel Structure Amongst various p-TCOs based on spinel structure, cobalt nickel oxide (NiCo2 O4 ) is the ﬁrst material reported to have p-type conductivity with reasonable visible transparency (∼40–60%) [52], in thin ﬁlm form. A variation in the conductivity is observed in this material with a change in the Ni:Co ratio and at Ni:Co = 1:2, the highest conductivity in these ﬁlms was observed around 16.0 S cm−1 . It has also been proposed by various authors that Ni+3 ions located on octahedral sites within the spinel lattice enhance the conductivity of the ﬁlm [102]. Figure 12.5 shows the variation of resistivity of Ni−Co−O thin ﬁlms with composition x (=Co/{Co + Ni}). Minimum resistivity obtained at x = 0.67. These ﬁlms also showed good transparency in the infrared region, extending its application into infrared optics [52, 103]. Another group of p-type semiconducting transparent spinel oxides, based on Zn-(d6 ) transition metals, is ZnB2 O4 (B = Co, Rh, Ir) [54, 55], which shows optical bandgaps around 3 eV and electrical conductivity as high as 2.0 S cm−1 . Figure 12.6 shows the electrical conductivity of ZnRh2 O4 thin ﬁlm and Fig. 12.7 shows the optical transparency of ZnB2 O4 (B = Co, Rh, Ir) thin

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Fig. 12.5. Variation of resistivity of Ni−Co−O thin ﬁlms with composition x (= Co/ {Co + Ni}). Minimum resistivity obtained at x = 0.67 (after [53])

Fig. 12.6. Temperature variation of electrical conductivity of ZnRh2 O4 thin ﬁlm (after [55]). Ea is the activation energy, which is the minimum energy required to transfer an electron from donor level to CB (for n-type material) or holes from acceptor level to VB

ﬁlms deposited on quartz substrates. Also Table 12.2 shows the optoelectrical properties of various spinel p-TCOs. As far as deposition of spinel p-TCOs is concerned, Windisch and coauthors [52, 53, 103] used both physical and chemical techniques to prepare Ni-based spinel ﬁlms (e.g., NiCo2 O4 ). For chemical method, they have used spin-coating technique [53] with a precursor solution containing the respective metal nitrates and an organic complexant. Subsequent thermal annealing induced oxide formation during which the organic component was fully oxidized to gaseous products. On the other hand, physical deposition of NiCo2 O4 involved radio frequency (RF) magnetron sputtering technique [52]. The target used was Ni−Co alloys with a RF power of 200 W. It has been

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Fig. 12.7. Spectral variation of optical transmittance of (1) ZnCo2 O4 , (2) ZnRh2 O4 , and (3) ZnIr2 O4 thin ﬁlms (redrawn from [54] with permission)

observed that the quality of the RF sputtered ﬁlm is better than that of solution-deposited ﬁlm [53] and with increasing Ni concentration, the ﬁlm showed enhanced electrical conductivity up to a value of x = 0.67. The ﬁlm composition can be expressed as Ni1+x Co2−x O4 , and with x = 0.5, the ﬁlm showed best electro-optical properties. Various deposition parameters of RF sputtered NiCo2 O4 ﬁlm are furnished in Table 12.3. The same group also used a “combinatorial” sputtering technique to deposit an array of ﬁlms with varying ﬁlm compositions with a single run under identical deposition conditions [103]. This special technique was used to study the eﬀect of selected gas compositions on the deposited ﬁlms. And, they have observed that the optimum conductivity from combinatorially deposited ﬁlms containing equal parts of nickel and cobalt (i.e., Ni1.5 Co1.5 O4 ) is achieved when sputtered in a gas mixture of 50% argon and 50% oxygen from oxide targets, with the best ﬁlm conductivity of 375 S cm−1 achieved using growth conditions that promote complete oxidation. For the deposition of Zn-based spinel p-TCO ﬁlms (e.g., ZnRh2 O4 , ZnCo2 O4 , ZnIr2 O4 , etc.), Dekkers et al. [54] used pulsed laser deposition (PLD) technique from respective sintered targets. Various electro-optical properties of these ﬁlms are furnished in Table 12.2. On the other hand, Mizoguchi and coauthors [55, 104] used RF sputtering technique to deposit crystalline as well as amorphous ZnRh2 O4 thin ﬁlms on silica glass substrates. They have used identical sputtering conditions for both crystalline and amorphous ﬁlms but postannealing treatment was done on a-ZnRh2 O4 ﬁlms to get the crystalline phase of the ﬁlm. Various deposition conditions of these ﬁlms are furnished in Table 12.3. As far as reactive sputtering of spinel p-TCOs is concerned, Kim and coauthors [37] used reactive magnetron cosputtering technique to deposit ZnCo2 O4 thin ﬁlm from metallic targets. Detailed discussions of the reactively sputtered spinel p-TCOs are furnished in later sections. 12.3.4 p-TCO with Delafossite Structure Delafossite-structured oxides (ABO2 ; A: monovalent cation, B: trivalent cation) can be divided into two groups: one having A-d10 (e.g., A = Cu, Ag)

Spin coating RF magnetron sputtering RF sputtering RF sputtering Pulsed laser deposition PLD PLD

NiCo2 O4 NiCo2 O4

ZnCo2 O4 ZnIr2 O4

ZnRh2 O4 a-ZnRh2 O4 ZnRh2 O4

Deposition technique

Material

100–300 100–300

100 100–300 100–300

100 100

Average ﬁlm thickness (nm)

26 60

2.26 2.97

2.1 2.1 2.74

– –

∼65 ∼20 – – 55

Direct bandgap (Eg-direct ) (eV)

Transmittance (T ) (%)

0.39 3.39

0.7 1.9 2.75

16.67 3.3 × 102

Room temp. conductivity (σRT ) (S cm−1 )

Table 12.2. Optoelectrical properties of various spinel p-TCOs

41.7 46.9

37 29 22.1

– –

Activation energy (Ea ) (meV)

+131.4 +53.9

+140 +78 +63.4

– –

Room temp. Seebeck coeﬀ. (SRT ) (μV K−1 )

[54] [54]

[55] [104] [54]

[53] [52]

Ref.

12 Reactive Sputtered Wide-Bandgap p-Type Semiconducting 423

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Table 12.3. Various deposition parameters of RF sputter-deposited spinel p-TCO ﬁlms Material RF power (W) Base pressure (Pa) Sputtering gas(es) Sputtering pressure (Pa) Target Substrate Substrate temp. (◦ C) Postannealing time (min) Postannealing temp. (◦ C) Reference a

NiCo2 O4

ZnRh2 O4

a-ZnRh2 O4

200 1.33 × 10−4 O2 a

180 – Ar + O2 (9:1 vol.%) 13.0 ZnRh2 O4 pellet Silica glass

180 – Ar + O2 (9:1 vol.%) 13.33 ZnRh2 O4 pellet Silica glass

Ambient

Room temperature – – [105]

1.33 Co−Ni alloys Quartz, sapphire, Si Ambient – – [52]

60 1,240 [55]

Sputtering was done in 100% oxygen atmosphere

conﬁguration and the other with A-d9 (e.g., A = Pt, Pd) conﬁguration. Generally, d10 cations show semiconducting behavior, whereas d9 cations show metallic conductivity [12–14]. As we are dealing with p-TCOs, therefore we will discuss only the d10 -based delafossite materials here. The d10 -based delafossite materials are two types: Cu- and Ag-based delafossite materials (CuBO2 and AgBO2 ; B: trivalent cation). Amongst various Cu-based delafossite materials, CuAlO2 is the ﬁrst and most important material in this group. Although this material is known to exist for nearly 50 years [106] and back in 1984, its p-type conductivity was ﬁrst reported by Benko and Koﬀyberg [107], but Kawazoe et al. [100] ﬁrst prepared it in transparent thin ﬁlm form for possible application in p-TCO technology. The structural properties of this material were extensively studied by Ishiguro et al. [100–108,108,109,109,110]. The structure is shown in Fig. 12.2. It belongs to R¯3m (D3d ) space group with rhombohedral crystal structure [108]. Other p-TCO thin ﬁlms belonging to this group are copper gallium oxide (CuGaO2 ) and copper indium oxide (CuInO2 ) [111–113]. The lattice parameters of these materials were reported in various papers [12–14, 107, 114, 115]. Also, the band structures of these materials were calculated by Yanagi et al. [116], Robertson et al. [117], and Ingram et al. [118] in detail. Doped versions of some similar types of p-TCO thin ﬁlms have also been reported which include iron-doped copper gallium oxide (CuGaO2 :Fe), calcium-doped copper indium oxide (CuInO2 :Ca), magnesium-doped copper scandium oxide (CuScO2 :Mg), magnesium-doped copper chromium oxide (CuCrO2 :Mg), calcium-doped copper yttrium oxide (CuYO2 :Ca), etc. [112, 113, 119–122]. Crystallographic data as well as band structure calculations of these materials had also been reported in various papers [114,123,124]. Preparation of some other highly resistive (∼106 Ω cm) new delafossite materials

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such as CuFe1−x Vx O2 (x = 0.5), CuNi1−x Sbx O2 , CuZn1−x Sbx O2 , CuCo1−x Sbx O2 , CuMg1−x Sbx O2 , CuMn1−x Sbx O2 (x = 0.33) in powder form had been reported by Nagrajan et al. [17, 125] (but no thin ﬁlm preparation of these materials has been reported so far). Preparation of 10% Sn-doped CuNi1−x Sbx O2 thin ﬁlm has been reported by the same group [119,125], having reasonable visible transparency (60%) and conductivity (5 × 10−2 S cm−1 ). Electro-optical properties of various delafossite p-TCOs are furnished in Table 12.4. It has been observed that most of the p-type semiconducting delafossite materials are Cu-based. Corresponding Ag-based delafossite materials are diﬃcult to synthesize by simple solid-state reaction [119, 126]. The ﬁrst report of Ag-based delafossite thin ﬁlm was AgInO2 , which is n-type in nature [127]. Later, Nagrajan et al. [128] reported that Mg-doped AgInO2 powder (AgIn1−x Mgx O2 , x = 0.1), when treated with ﬂuorine or highpressure oxygen, p-type nature was observed with conductivity as low as 10−6 S cm−1 . A series of similar types of delafossite materials have been synthesized by the same group [128], but only in powder form, which include AgScO2 , AgCrO2 , AgGaO2 , etc. All of these pellets showed very low conductivity (∼10−6 S cm−1 ) and no thin ﬁlm preparations of these materials have been reported so far. On the other hand, the ﬁrst report of Ag-based delafossite thin ﬁlm with p-type conductivity was reported by Tate et al. [119], which is silver cobalt oxide (Agx CoO2 , x < 1). The ﬁlm showed reasonable conductivity (2 × 10−1 S cm−1 ) and almost 50% transparency in the visible region with a direct bandgap value of 4.15 eV (shown in Figs. 12.8 and 12.9). The better conductivity of this ﬁlm over other Ag-based delafossite materials may be attributed to the greater degree of mixing between Co 3d10 orbitals and O 2p6 orbitals, resulting in larger delocalization of holes [129,130]. Doped versions of some other Ag-based delafossites have also been reported such as AgNi1−x Sbx O2 , AgZn1−x Sbx O2 (x = 0.33), etc. [119] but only in powder form. Also, no comments on the nature of conductivity of these powders were given in the literature. Regarding relative comparison between Cu-based delafossites and Ag-based delafossites, it has been suggested [131] that the former group can be better candidate for transparent conductor because of their greater hole mobility, which is due to the Cu 3d character of the valence band edge of Cu-based delafossites. Whereas for Ag-based delafossites, the valence band edge possesses O 2p character and d-manifold holes are more mobile than that of p-manifold [128]. 12.3.5 Other Deposition Techniques: PLD, RF Sputter Deposition, Magnetron Sputtering with RTA, and Ion Exchange Method Growth technique plays the most signiﬁcant role on the properties of the ﬁlms. Diﬀerent deposition routes yield ﬁlms with diverse structural,

Undoped Undoped Fe Ca Undoped Mg Undoped Ca Undoped Mg

Ni Sb Sn Undoped

CuAlO2 CuGaO2 CuGa1−x Fex O2 CuIn1−x Cax O2 CuCrO2 CuCr1−x Mgx O2 CuYO2 CuY1−x Cax O2 CuScO2 a CuSc1−x Mgx O2 b

CuNi1−x Sbx Sny O2

0.66 0.33 0.033 –

– – 0.5 0.07 – 0.5 – 0.01–0.02 – 0.05

Percentage of doping

150

∼200

230 500 150 170 250 270 200 240 110 220–250

Average ﬁlm thickness (nm)

50

70 80 60 70 40 50 60 50 40 80 60 25 15 60

T (%)

4.15

3.5 3.6 3.4 ∼3.9 ∼3.1 3.1 ∼3.5 3.5 ∼3.3 3.3–3.6 3.3–3.6 3.3–3.6 3.3–3.6 3.4

Eg -direct (eV)

0.2

0.34 0.063 1.0 0.028 1.0 220.0 0.025 1.05 30.0 ∼0.07 ∼0.1 ∼0.8 ∼20.0 0.05

σRT (S cm−1 )

+220

+214 +560 +500 +480 – +150 – +275 – – – – – +250

SRT (μV K−1 )

[119]

[119]

[116] [111] [119] [112] [121] [17, 121] [17, 122] [17, 122] [17, 120] [119, 132]

Ref.

b

Maximum of 25% oxygen was intercalated The variation of transparency of the ﬁlms at the expense of conductivity was due to a variation of oxygen pressure from 3 (for most transparent ﬁlm) to 15,000 Torr (for least transparent ﬁlm). Also according to [132], the doping concentration of Mg was 1% c The Ag:Co ratio was 1.1:1

a

AgCoO2 c

Dopant

Material

Table 12.4. Delafossite p-TCO thin ﬁlms with diﬀerent doping concentrations and their respective optoelectrical parameters

426 A.N. Banerjee and K.K. Chattopadhyay

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427

Fig. 12.8. Optical transmission of AgCoO2 thin ﬁlm (redrawn from [119] with permission)

Fig. 12.9. Determination of direct bandgap of AgCoO2 thin ﬁlm (redrawn from [119] with permission)

optical, and electrical properties. Even for the same deposition technique, slight variation in the deposition parameters produces ﬁlms with diﬀerent properties. So it is very important to have a comparative study on the properties of various ﬁlms produced by diﬀerent deposition routes. Detailed description of diﬀerent deposition techniques along with their schematic diagrams and related parameters is reported in various literatures [71, 74, 133– 136]. Here we discuss brieﬂy various deposition procedures used to deposit delafossite p-TCO thin ﬁlms. PLD is a one of the important but relatively new and very eﬃcient technique to deposit epitaxial ﬁlms. Although a bit costly, but highly phase pure ﬁlms with high-accuracy thickness can be prepared by this method. Delafossite p-TCO ﬁlms prepared by this method include CuAlO2 [100, 116, 137–139], CuGaO2 [111, 137], CuInO2 :Ca [112], CuScO2 [140–142], etc. The deposition environment for most of the aforementioned reports was oxygen whereas the ﬁlms were grown with an elevated substrate temperature. Postdeposition annealing was also done in most cases to induce excess oxygen for enhancing p-type conductivity as described later. Sputtering is another popular thin ﬁlm growth technique used extensively around the globe. As it is relatively cost-eﬀective with respect to PLD and

428

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large-area deposition is possible by this process, large-scale production of ﬁlms for diverse applications can be done by this technique. Both reactive and nonreactive forms of direct current (DC), RF, magnetron, as well as ion beam sputtering techniques have been used for deposition of various delafossite p-TCOs. RF sputtering of CuAlO2 [138, 139], CuGa0.5 Fe0.5 O2 [119], CuCr0.95 Mg0.05 O2 [121], CuScO2+y , CuSc0.95 Mg0.05 O2 [119, 120], CuNi0.67 Sb0.3 Sn0.033 O2 [119,125], AgCoO2 [119], etc., has been reported. Pulsed magnetron sputtering of p-CuAlO2 ﬁlms was prepared by Alkoy and Kelly [126]. On the other hand, DC sputtering of CuAlO2 thin ﬁlm has been reported by us [15, 16, 57, 63, 143, 144], which is more cost-eﬀective procedure. Also, in DC sputtering of oxide targets, the control of stoichiometry is almost automatic, whereas for RF sputtering, the target stoichiometry is to be adjusted suitably to compensate material loss from the substrate [74]. In all of the aforementioned reports, the targets used were the corresponding sintered pellets, arranged properly in the deposition chamber. Tables 12.5 and 12.6 represent various deposition parameters of delafossite p-TCO ﬁlms synthesized by RF and DC sputtering. Also Figs. 12.10–12.15 show various characteristics of sputter-deposited delafossite p-TCO thin ﬁlms. Reactive sputtering of delafossite p-TCOs has been used extensively by various researchers, which is discussed in details in later sections. Table 12.5. Diﬀerent deposition parameters of delafossite p-TCO ﬁlms synthesized by RF magnetron sputtering Material RF power (W) Electrode distance (mm) Base pressure (Pa) Sputtering pressure (Pa) Target Substrate Substrate temp. (◦ C) Postannealing time (min) Postannealing temp. (◦ C) Reference

CuAlO2

CuGaO2 :Fe

CuCrO2 :Mg

CuNi2/3 Sb1/3 O2 :Sn

65 40

80 30

90 38

80 –

–

–

9.3 × 10−4

–

13.33 (Ar:O2 = 4:1)

1.33 (Ar press)

13.33 (Ar:O2 = 4:1/9:1)

CuGa0.5 Fe0.5 O2 pellet Fused silica

CuCr1−x MgO2 pellet Fused quartz

4.53 (O2 press) CuAlO2 pellet α-Al2 O3 (001) Ambient

CuNi0.67 Sb0.3 Sn0.03 O2 pellet SiO2 , YSZ (100), Al2 O3 (001) 500

100

450–750

90

90

2.5 (RTA in Ar)

180

1,050a

800 (N2 atmos.)

600–900

900 (in air)b

[138]

[119]

[121]

[119, 125]

a

Ex situ in a Lindberg box furnace containing small amount of CuAlO2 powder

b

Also for some cases, RTA in air at 900◦ C was performed

12 Reactive Sputtered Wide-Bandgap p-Type Semiconducting

429

Table 12.6. Deposition parameters of DC sputtering for CuAlO2 thin ﬁlm Material

CuAlO2 thin ﬁlm

Electrode distance (mm) Target Substrate Sputtering voltage (V) Current density (mA cm−2 ) Base pressure (Pa) Sputtering pressure (Pa) Sputtering atmosphere Substrate temperature (◦ C) Deposition time (min) Postannealing time (min) Postannealing temperature (◦ C) Postannealing atmosphere (pressure) Reference

18 Sintered CuAlO2 pellet Si (400) and glass 1,100 10 10−4 20 Ar + 40 vol.% O2 180 240 60 200 O2 (20 Pa) [143]

Fig. 12.10. XRD pattern of CuCr0.95 Mg0.05 O2 thin ﬁlm deposited by RF sputtering technique (redrawn from [121] with permission). Asterisk marks are from indium contacts

A combined process of magnetron sputtering and rapid thermal annealing (RTA) was used by Shy et al. [145] to prepare single crystalline delafossite p-type conducting CuAlO2 thin ﬁlms on sapphire substrate. Firstly, Cu2 O and Al2 O3 precursor ﬁlms on sapphire were deposited by reactive magnetron sputtering in an Ar + O2 atmosphere. Cu and Al metal targets were used and reacted to form Cu2 O and Al2 O3 , respectively. The precursor ﬁlms were deposited without substrate heating. Subsequent CuAlO2 formation process was performed in air ambient by RTA. The specimens were heated up to 1,100 OC with a heating rate of 50 OC s−1 and kept at the designated temperature for 40 min. A typical sandwich structure of Al2 O3 /Cu2 O/sapphire and the reaction mechanism before and after annealing is shown in Fig. 12.16.

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Fig. 12.11. XRD pattern of (a) AgCoO2 thin ﬁlm deposited by RF sputtering and (b) target (redrawn from [119] with permission)

Fig. 12.12. XRD pattern of DC sputtered-deposited CuAlO2 thin ﬁlm (after [143])

Fig. 12.13. Optical transmittance and reﬂectance spectra of CuAlO2 thin ﬁlm deposited by DC sputtering. Inset shows the spectral variation of absorption coeﬃcients (α) (after [143])

12 Reactive Sputtered Wide-Bandgap p-Type Semiconducting

431

2

ln σ

1 0 -1

ta = 90 min ta = 60 min ta = 30 min

-2 2.0

2.2

2.4 2.6 2.8 3.0 1000 / T (K-1)

3.2

3.4

Fig. 12.14. Temperature variation of conductivity of CuAlO2 thin ﬁlm deposited by DC sputtering at diﬀerent postdeposition oxygen annealing time (after [57])

Fig. 12.15. XRD patterns of CuAlO2 thin ﬁlms deposited by RF magnetron sputtering: (a) as-deposited ﬁlm and (b) postannealed at 1050◦ C (after [138], reproduced by permission of ECS – The Electrochemical Society). The intensity axis is in logarithmic scale

Al2O3 (200 nm)

Cu2O + Al2O3 → 2CuAlO2

Cu2O (500 nm)

CuAlO2 (360 nm) ~ 1000 OC

Sapphire

Air annealing

Sapphire

Fig. 12.16. Sandwich structure of Al2 O3 /Cu2 O/sapphire before and after annealing. Also the typical reaction process is furnished

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Ion exchange method is another interesting procedure by which several delafossite materials have been synthesized such as CuAlO2 from LiAlO2 [146], CuInO2 from CuCl, Agx CoO2 (x < 1) from NaCoO2 and AgNO3 [119], AgNi0.67 Sb0.33 O2 from LiNi0.67 Sb0.33 O2 and AgNO3 , AgZn0.67 Sb0.33 O2 from LiZn0.67 Sb0.33 O2 and AgNO3 [125], etc. Although no ﬁlm preparation was reported by this method, this process may become an important target preparation procedure for PLD or sputtering. Also, based on ab initio electronic structure calculations, new methods have been proposed by Yoshida and coauthors [147, 148] to fabricate highconducting p-CuAlO2 . They proposed that, in thermal nonequilibrium PLD or molecular beam epitaxy (MBE) crystal growth techniques, induction of high concentration of Cu vacancies in the material, to form impurity band, by reducing the Cu vapor pressure during deposition might enhance the p-type conductivity in the material. On the other hand, doping of Mg or Be at Al sites to form acceptor levels by decreasing the Al vapor pressure and increasing the Cu vapor pressure during low-temperature PLD, MBE, or MOCVD process might also increase the p-type conductivity of the material (Tables 12.7 and 12.8). 12.3.6 Reactive Sputtered p-TCO It is well known that reactive sputtering has the advantage over conventional (RF or DC) sputtering from oxide targets, due to the fact that plasma density would be better in former case due to the high conductivity of elemental targets or metal powders, leading to better uniformity of the ﬁlms. Also, the intermediate step of sintering procedure to form the target pellet can be avoided by this method. Both RF magnetron reactive cosputtering and DC reactive sputtering have been adopted by various groups. As DC sputtering can be applied conveniently for low resistive targets, whereas RF sputtering is convenient only for high resistive (or insulating) targets, therefore, keeping an eye on the cost-eﬀectiveness of the deposition techniques, various groups concentrated their attention more onto the DC reactive sputtering technique to deposit p-TCO ﬁlms from metal targets. As far as reactive sputtering of spinel p-TCO ﬁlms is concerned, Kim and coauthors [37] deposited ZnCo2 O4 thin ﬁlms on SiO2 (200 nm)/Si substrate by reactive magnetron sputtering technique. This group had used a combinatorial approach of DC and RF magnetron cosputtering of elemental Co and Zn targets in an oxygen-diluted Ar atmosphere and at an elevated substrate temperature (600◦ C). For Co targets, they have used DC source with a sputtering power of 200 W, whereas, RF source had been used for Zn target with an RF forward power of 100 W and a ﬁxed total sputtering power ratio (PCo /PZn ) of 2.0. They have observed that the sputtering power ratio between Co and Zn targets is a critical growth parameter for the formation of the spinel phase. Details of various reactive sputtering parameters for reactive deposition of spinel ZnCo2 O4 have been furnished in Table 12.9.

85

80

40–240

500–700

500

250

Pulsed magnetron sputtering DC sputtering

DC sputtering

MOCVD

40

85

85

180

RF magnetron sputtering

70 80

Average visible transmittance (%)

500 230

Thickness (nm)

PLD PLD

Growth technique

2.0

0.39

0.08

0.1–0.2

–

0.095 0.34

Room temp. conductivity (S cm−1 )

120

196

260

–

–

+128

+213

–

3.7 × 1017

1.2 × 1018

2.6 × 1019

–

+183 +214

Room temp. Seebeck coeﬀ. (μV K−1 )

–

–

1.3 × 1017 2.7 × 1019

∼200 220

–

Carrier concentration (cm−3 )

Ea (meV)

[149]

[57]

[143]

[126]

[138]

[100] [116]

Ref.

– Films were postannealed in O2 atmosphere (1.3 Pa) Preliminary Hall and TEP measurements conﬁrmed p-type conductivity The indirect bandgap was estimated to be 1.6 eV Films were postannealed in O2 atmosphere (20 Pa) for 60 min Films were postannealed in O2 atmosphere (20 Pa) for 90 min The ﬁlms were a mixture of CuAlO2 , Cu2 O, and CuAl2 O4 (continued)

Remarks

Table 12.7. Optical and electrical properties of delafossite p-CuAlO2 thin ﬁlms synthesized by various growth techniques

12 Reactive Sputtered Wide-Bandgap p-Type Semiconducting 433

1,000

1,100

30–70

420

Spincoating technique Spray pyrolyses

Sol-gel synthesis

60

1,000

Dip coating

–

–

90

3,500

Dip coating

60

50–85

40

360

–

120

RTA

E-beam evaporation

PEMOCVD

0.004

–

–

–

140

–

5 × 10−3

2.4

–

–

–

32

–

0.57

1.0

17.08

–

–

–

–

5.4 × 1018

–

–

–

–

–

–

–

1018 –1020

–

–

1.17 × 1020

Table 12.7. (continued)

[157]

[156]

[155]

[154]

[153]

[145]

[152]

[150, 151]

For those samples annealed in air for 5 min (at 350◦ C) Hole concentration decreases with increasing water vapor pressure RTA was performed over 1, 000◦ C Films were annealed in air (at 500◦ C) for 180 min Results given for ﬁlms deposited via nitrate route Film is nanocrystalline in nature with grain size around 14–16 nm Transmittance increases as Cu:Al ratio approaches to 1.0 High resistivity is due to porous structure of the ﬁlm

434 A.N. Banerjee and K.K. Chattopadhyay

a

60 40–60

150–200 150

0.20

0.05

220

0.08 1.0

70 30 30–40

20.0

30.0

1.0

15

40

50–70

Average Room visible temp. contransmittance ductivity (%) (S cm−1 )

200–300

200–300

250

110

150

Thickness (nm)

70

–

–

–

20a 170

– –

–

–

–

+220

+250

+150

– –

–

–

+500

Room temp. Carrier concentra- Seebeck coeﬀ. (μVK−1 ) tion (cm−3 )

– –

95

110

100

Ea (meV)

For low value of Ea , the word “activation” should be used with caution

CuNi0.67 Sb0.3 O2 :Sn AgCoO2

CuCrO2 :Mg

CuCrO2

RF sputtering RF sputtering RF sputtering RF sputtering

RF sputtering RF sputtering

CuScO2

CuScO2 :Mg

RF sputtering

Method

CuGaO2 :Fe

Material

–

Films were postannealed in N2 atmosphere at 800◦ C for 90 min and 50% Ga replaced by Fe Actual formula was given as CuScO2+y 5% Mg doping for Sc. Also the variation in σRT and T was due to change in postdeposition O2 annealing pressure

Remarks

[119, 121] 5% Cr replaced by Mg [119, 125] 10% Sb replaced by Sn [119] Ag:Co = 1.1:1.0

[119] [119, 121]

[119]

[120]

[119]

Ref.

Table 12.8. Optical and electrical properties of diﬀerent Cu- and Ag-based delafossite p-TCO thin ﬁlms (other than CuAlO2 ) synthesized by RF sputtering technique

12 Reactive Sputtered Wide-Bandgap p-Type Semiconducting 435

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Table 12.9. RF magnetron reactive cosputtering of spinel and delafossite p-TCO ﬁlms Material RF power (W) Targets Substrate Substrate temp. (◦ C) Base pressure (Pa) Deposition pressure (Pa) Sputtering atmosphere Postannealing Reference

ZnCo2 O4

Cu−Al−O ﬁlms (a mixture of CuAlO2 and CuO)

Zn power: 100 Co power: 200a Metallic Zn and Co SiO2 (200 nm)/Si 600 2.0 × 10−4 1.33 Ar + O2 c – [37]

Al power: 60–110b Cu power: 30 Metallic Cu and Al Glass 100 – – Ar + 5% O2 None [158]

a

For Co target, DC source had been used For Al power, 110 W single phase amorphous CuAlO2 was formed c O2 partial pressure is varied from 10 to 90% b

This group had also varied the ratio of oxygen partial pressure to a constant total working pressure (10 mTorr) during deposition from 10 (with O2 partial pressure 1 mTorr) to 90% (with O2 partial pressure 9 mTorr) and observed that the ﬁlms deposited with a oxygen partial pressure ratio less than 70% showed n-type conductivity, whereas, those deposited above 80% oxygen partial pressure ratio are p-type conducting [37]. Figure 12.17 shows various electrical parameters of ZnCo2 O4 thin ﬁlm under diﬀerent oxygen partial pressure ratio. Also, Table 12.11 describes various optoelectrical parameters of spinel p-ZnCo2 O4 thin ﬁlms prepared by reactive magnetron cosputtering technique. Reactive sputtering of delafossite p-TCO thin ﬁlms involves both RF and DC reactive sputtering techniques. For RF sputtering, Ong and Gong [158] used RF magnetron reactive cosputtering of Cu and Al metal targets to synthesize transparent p-type Cu−Al−O ﬁlms (a mixture of delafossite CuAlO2 and CuO). This group used 30 W ﬁxed RF power for Cu target, but a variable power (60–110 W) for Al target, as the sputtering yield of Al is less than that of Cu in Ar + O2 environment. Various sputtering conditions for the ﬁlm growth are furnished Table 12.9. With varying Al power, they obtained Cu−Al−O ﬁlms with a varied Cu/Al ratio from 10 to 0.9%, and at an Al power of 110 W, they obtained single phase amorphous p-CuAlO2 thin ﬁlm. Also from the absorption data, they have observed a blueshift of the bandgap of this multiphase ﬁlm (mixture of CuAlO2 and CuO) with an increase in the Al content within the ﬁlm. Whether this bandgap widening is due to BursteinMoss shift [159] or may be attributed to the quantum conﬁnement eﬀect put forward by Brus [160] is still not clear and intense research is needed in this direction to explore the exact mechanism. Figures 12.18 and 12.19 show the

12 Reactive Sputtered Wide-Bandgap p-Type Semiconducting

437

Fig. 12.17. Conductivity (σ), electron concentration (n), hole concentration (p), and mobility (μ) of ZnCo2 O4 thin ﬁlm at various oxygen partial pressure ratio (after [37])

Fig. 12.18. Bulk resistance of RF magnetron reactive sputter-deposited Cu−Al−O thin ﬁlms with diﬀerent Cu/Al atomic ratio and at diﬀerent Al power (from 60 to 90 W) (after [158])

variation in the bulk resistance and optical bandgap values of Cu−Al−O thin ﬁlms with diﬀerent Cu/Al atomic ratio, respectively. As far as DC reactive sputtering is concerned, Tsuboi et al. [161, 162] used facing targets of Cu and Al metals and a rotating substrate to synthesize CuAlO2 ﬁlms by DC reactive sputtering. A schematic diagram of the apparatus is shown in Fig. 12.20. As shown in the ﬁgure, the discharge plasma could be conﬁned between the facing targets by magnetic ﬁeld and the substrate was placed outside the plasma region to avoid bombardments of high-energy particles. The sputtered Cu and Al atoms were alternately

438

A.N. Banerjee and K.K. Chattopadhyay

Fig. 12.19. Blueshift of fundamental absorption edge of RF magnetron reactive sputter-deposited Cu−Al−O ﬁlms with diﬀerent Cu/Al atomic ratio (after [158])

Fig. 12.20. DC reactive sputtering system with two pairs of opposite facing targets and a rotating substrate (after [161])

deposited on the quartz substrate at 300◦ C for about 4 h by controlling a pulse motor connected with the substrate holder. The sequential period of Cu deposition (tCu ) was ﬁxed to 1 s, whereas the same for Al (tAl ) was varied from 3 to 15 s to vary the Cu/Al ratio in the ﬁlm. The total ﬁlm thickness was in the range of 400–800 nm. The ﬁlms were postannealed at temperatures of 500–1050◦ C for 4 h in the nitrogen ﬂow under atmospheric pressure. Various sputtering parameters for this ﬁlm growth are furnished in Table 12.10. Figure 12.21 shows the composition of the ﬁlm with diﬀerent postannealing time. The [Cu]/[Al] ratio in the as-deposited ﬁlms decreased with increasing tAl . Figure 12.22 shows the optical transmis-

12 Reactive Sputtered Wide-Bandgap p-Type Semiconducting

439

Table 12.10. Various sputtering parameters of reactive DC sputtered delafossite p-TCO thin ﬁlms Material Target

Electrode distance (mm) Sputtering voltage (V)

Current density (mA cm−2 )

Base pressure (Pa) Sputtering pressure (Pa) Sputtering atmosphere Substrate Substrate temperature (◦ C) Deposition time (min) Postannealing time (min) Postannealing temp. (◦ C) Postannealing atmosphere Reference a

CuAlO2 thin ﬁlm

CuAlO2 thin ﬁlm

CuAlO2 thin ﬁlma

Elemental Cu and Al metal (facing) targets –

Mixture of Cu + Al metal powder pellets 18

Cu/Al alloy (with 1:3 ratio) 65

Cu-facing targets = 750 Al-facing targets = 350 Cu-facing targets ∼1.17 Al-facing targets ∼7.0 –

1,000

292–394

12

200–300 mA (current)

10−4

5 × 10−4

0.53

20.0

4.0

Ar + O2 (4:1)

Ar + O2 (3:2)

Ar + O2

Quartz (rotating) 300

Si (400) and glass 200

Glass 250

240

240

–

240

60

–

> 700

220

–

O2 (20 Pa)

–

[163, 164]

[165]

N2 (ambient pressure) [161]

This process involved DC reactive magnetron sputtering

sion spectra of DC reactive sputter-deposited p-CuAlO2 thin ﬁlm at diﬀerent Cu/Al ratios. Similarly, DC reactive magnetron sputtering of p-CuAlO2 ﬁlm was done by Reddy and coauthors [165], where a target of Cu/Al alloy (with 1:3 ratio) was used to deposit CuAlO2 ﬁlm on glass substrate. This group has systematically studied the change in electrical, optical, and structural properties of p-CuAlO2 thin ﬁlms with a variation in the oxygen partial pressure during deposition. Figures 12.23 and 12.24 show the variation in diﬀerent electrical and optical properties of these ﬁlms with respect to oxygen partial pressure. It must be mentioned here that, in most of the sputtering procedures indicated

440

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Fig. 12.21. Composition of as-deposited and postannealed p-CuAlO2 thin ﬁlms (after [161])

Fig. 12.22. Optical transmission spectra of p-CuAlO2 thin ﬁlms postannealed at 1050◦ C. Cu/Al ratio in the ﬁlms varied from (a) 1.8, (b) 1.7, (c) 1.1, and (d) 0.7 (after [161])

above, the sputtering atmosphere was taken as Ar and O2 and the depositions were done in an elevated substrate temperature. Postannealing of the ﬁlms was also performed in many cases to get better p-type conductivity. In some cases, RTA of the ﬁlms was also done to get higher crystallinity and transparency [120, 121]. Various deposition parameters of DC reactive sputter-deposited delafossite p-TCO thin ﬁlms are furnished in Table 12.10. Also various electro-optical parameters of diﬀerent DC reactive sputtered thin ﬁlms are furnished in Table 12.11.

12 Reactive Sputtered Wide-Bandgap p-Type Semiconducting

441

Fig. 12.23. Variations in electrical resistivity (ρ), Hall mobility (μ), and carrier concentration (n) of DC reactive sputtered p-CuAlO2 thin ﬁlms (after [165])

12.4 Transparent Junctions Based on Spinel and Delafossite Oxides Junctional devices fabricated by both n- and p-types of TCO thin ﬁlms are the key structure for “Invisible Electronics” [56]. The simplest of them is the p–n junction diodes with rectifying properties. The importance of these types of devices lies in the fact that “functional windows” can be fabricated by these devices, which would transmit the visible solar radiation but absorb the UV part of it [100]. Thus simultaneously, these devices can act as “UV shields” as well as “electricity generators” by the UV absorption. Fabrication of a number of all-TCO diodes based on spinel and delafossite p-TCO ﬁlms has been reported, which includes both p–n and p–i–n homojunctions and heterojunctions as well as transparent ﬁeld-eﬀect transistors (TFETs). A schematic diagram of all-TCO diode is shown in Fig. 12.25. As far as all-TCO junction based on spinel structure is concerned, Ohta et al. [166] ﬁrst reported p–n heterojunction of the form p-ZnRh2 O4 / n-ZnO on indium tin oxide (ITO)-coated YSZ (111) substrate. The n- and p-layers were deposited by PLD technique. A schematic diagram of the structure is shown in Fig. 12.26 and corresponding I–V curve is given in the inset. The curve shows rectifying properties with threshold voltage around 2.0 V.

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A.N. Banerjee and K.K. Chattopadhyay

Fig. 12.24. Optical transmittance spectra of DC reactive magnetron sputtered p-CuAlO2 ﬁlm at diﬀerent oxygen partial pressures (after [165])

Most of the groups have chosen ZnO as the n-layer mainly because of less lattice mismatch between p-layers, which is necessary to fabricate proper rectifying junctions. For n-ZnO/p-ZnRh2 O4 rectifying junction, Ohta et al. [166] have selected ZnO epitaxial layer as the n-type material mainly because of the sixfold symmetrical oxygen conﬁguration in (0001) plane of ZnO, which is similar to that in the (111) plane of ZnRh2 O4 with the sixfold symmetry. The mismatch is very low and more importantly, no chemical reaction was expected to take place between the two layers even at high temperature because no other crystalline phases have been reported in the equilibrium Zn−Rh−O system [166]. The same group has also demonstrated amorphous oxide p–n junction diodes based on other crystalline material spinel ZnRh2 O4 [104,167]. The diode was formed on glass and plastic substrates with ITO and Au as ohmic contacts. The structure of the diode is shown in Fig. 12.27 and the corresponding I–V characteristic is shown in the inset. Some of the diode characteristics are furnished in Table 12.12. Amorphous semiconductors are highly favorable for large-scale production of many devices like solar cells, ﬂat panel displays, etc. The advantage of using amorphous materials in these devices lies in the fact that low-temperature deposition of amorphous thin ﬁlms on large substrates is possible and also the problem of lattice mismatching in p–n junctions can be minimized by using amorphous materials [167]. Therefore, tremendous opportunities lie ahead in the ﬁeld of amorphous oxide-based p–n junctional devices. As far as delafossite p-TCO-based transparent junctions are concerned, Hoﬀman et al. [168] fabricated p–i–n heterojunction of the form p-CuYO2 : Ca/i-ZnO/n-ITO. The I–V characteristics are shown in Fig. 12.28. They have observed visible transparency of the structure around 35–65%. Similarly, Jayaraj et al. [122, 169] fabricated p–n heterojunction using p-CuY1−x Cax O2

Reactive DC sputtering Reactive DC magnetron sputtering

CuAlO2 120–130

500

400–800

CuAlO2

CuAlO2

250

RF magnetron reactive cosputtering Reactive DC sputtering

CuAlO2

Thickness (nm)

400

Growth technique

ZnCo2 O4 RF magnetron reactive cosputtering

Material

70–75

85

50–60

20–80

–

Average visible transmittance (%)

0.32

0.22

0.01–0.1

–

1.5–2.0

Room temp. conductivity (S cm−1 )

–

250

–

–

–

Ea (meV)

–

+115 –

–

4.4 × 1017 4.5 × 1017

–

–

2.41 × 1020

–

Room temp. Seebeck coeﬀ. (μV K−1 )

Carrier concentration (cm−3 )

Remarks

[161] With facing metal targets and rotating substrate. Films were annealed at 1,050◦ C in N2 atmosphere [154, Target was Cu + Al 163] metal powder pellets [165] The best electrical properties were obtained at 6 × 10−4 mbar

Oxygen partial pressure ratio more than 80% gives spinel p-ZnCo2 O4 ﬁlms [158] Small amount of CuO was present in the ﬁlm

[37]

Ref.

Table 12.11. Optical and electrical properties of diﬀerent spinel and delafossite p-TCO thin ﬁlms synthesized by reactive sputtering techniques 12 Reactive Sputtered Wide-Bandgap p-Type Semiconducting 443

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A.N. Banerjee and K.K. Chattopadhyay

Electrical leads Metallic contacts

d1

p-TCO n-TCO

d2

Glass / plastic Fig. 12.25. All-TCO p–n junction diode on glass or plastic substrate

Fig. 12.26. Current–voltage characteristics of ITO/n-ZnO/p-ZnRh2 O4 /Au diode (after [166]). Inset is the schematic structure of the diode

(x = 0.01–0.02)/n-Zn1−x Alx O (x = 0.02) structure. They observed rectifying I–V characteristics with a turn-on voltage between 0.4 and 0.8 V (shown in Fig. 12.29). Also, Tonooka et al. [170] reported the fabrication of n-ZnO/p-CuAlO2 diode structure with rectifying characteristics and observed a photovoltaic eﬀect (as large as 80 mV) under illumination of blue radiation. Although the performance of the diode was restricted by the low crystallinity of the CuAlO2 layer, the forward-to-reverse current ratio showed a moderate value of 90 between −1.5 and +1.5 V. Also the transparency of the structure was 40–70% in the visible region. The diode structure and transparency of the diode are shown in Fig. 12.30. We have recently reported the fabrication of

12 Reactive Sputtered Wide-Bandgap p-Type Semiconducting

445

Fig. 12.27. Current–voltage characteristics of amorphous oxide-based diode of the form glass/ITO/n-InGaZnO4 /p-ZnRh2 O4 /Au (after [104]). Inset: corresponding device structure

p-CuAlO2+x /n-Zn1−x Alx O heterojunction diode by a combination of costeﬀective physical (sputtering) and wet-chemical (sol-gel) processes [146]. The diode shows 60% visible transparency with turn-on voltage around 0.8 V. The approximate equilibrium energy band diagram depicted that this low turn-on voltage is due to the presence of some midgap energy levels, which might have been induced as a result of excess oxygen intercalation during sputtering of the p-layer. Also, some unintentional impurity incorporation during sol-gel process may not be ruled out as another reason for the formation of these midgap energy levels [146]. The I–V characteristics and optical transparency of the diode are shown in Fig. 12.31. Also, some of the electro-optical properties of all the aforementioned junctions are furnished in Table 12.12. Besides heterojunctions, fabrication of p–n homojunctions was also reported by few authors. Importance of the homojunctions lies in the fact that lattice matching is supposed to be automatic during the formation of diodes. First all-delafossite p–n homojunction diode was fabricated by Yanagi et al. [113]. The diode structure was of the form of YSZ (111)/ITO/p-CuInO2 :Ca/n-CuInO2 :Sn/ITO (shown in Fig. 12.32). Calciumand tin-doped copper indium oxide ﬁlms were used as the p- and n-layers, whereas ITO was used as metallic electrodes. They observed rectifying properties of the junction with turn-on voltage ∼1.8 V, which is shown in Fig. 12.32. Various electro-optical parameters of deferent all-transparent homojunction diode are furnished in Table 12.12.

n-ZnO/ p- ZnRh2 O4

Au ITO ∼2.1 103 at ±5.0 V [104, 167] The n- and p-layers were deposited at room temperature

[166] The diode exhibits photovoltage with UV-light illumination

RF sputtering

[168] The ZnO layer becomes semi-insulating after RTA at 600◦ C with n ∼ 1017 cm−3

In In ∼4.0 60 at ±4.0 V

RF magnetron sputtering RF sputtering

Reactive coevaporation

RF sputtering

–

– 9.6 × 1020 Glass

5 × 1019 ∼1020 Glass

– 4.2 × 1016 Glass/plastic

ITO n+ -ZnO 0.4–1.0 90 at ±1.5 V

PLD

PLD

– Glass

400 – 400 –

n-ZnO/ p-CuAlO2

ITO ITO 1.8 10 at ±4.0 V

PLD

–

PLD

– – YSZ (111)

400 – 400 –

n-CuInO2 :Sn/ p-CuInO2 :Ca

Sol-gel dip coating Ag Ag 0.8 30 at ±4.0 V

–

Sputtering

– 3.0 × 1017 Glass

500 – 600 2.6 × 1017

n-Zn1−x Alx O/ p-CuAlO2+x

[122, 168, 169] [170] [113] [146] No ZnO layer grown The diode The diode postannealing at 250◦ C showed showed 60–80% showed 40% transparency in was done for the transparency in good rectifying the visible region p-layer during the visible region property diode formation

RF magnetron sputtering In ITO 0.4–0.8 190 at ±3 V

Reactive coevaporation in O2 atmosphere –

300 – 250 ∼1019

n-Zn1−x Alx O/ p-CuY1−x Cax O2

300 250 200 1 × 1019

n+ -ITO/ i-ZnO/p+ CuYO2 :Ca

300 – 300 –

a-InGaZnO4 (n)/aZnRh2 O4 (p)

Au ITO ∼2.0 –

PLD

n-Layer

p-Side n-Side Turn-on voltage (V) Forward-to-reverse current ratio Reference Remarks

Electrodes

–

i-Layer

Thickness (nm) p-Layer – i-Layer – n-Layer – Carrier concen- p-Layer – tration (cm−3 ) i-Layer – n-Layer – Substrate ITO-coated YSZ (111) Deposition p-Layer PLD technique

Diode structure

Table 12.12. Parameters of deferent all-transparent diodes

446 A.N. Banerjee and K.K. Chattopadhyay

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Fig. 12.28. I–V characteristics of n+ -ITO/i-ZnO/p+ -CuYO2 :Ca heterojunction diode for undoped and Al-doped intrinsic ZnO layer (after [168])

Fig. 12.29. I–V curve of p-CuYO2 :Ca/n-ZnO:Al transparent diode (after [122]). Inset shows the corresponding diode structure

Another important area in the ﬁeld of “Transparent Electronics” is the fabrication of TFETs [89]. Prins et al. [171,172] reported the fabrication of ferroelectric TFETs, based on transparent SnO2 :Sb thin ﬁlms. They have observed the ﬁeld-eﬀect mobility around 10 cm2 V−1 s−1 , with an on/oﬀ current ratio ∼104 . Later various groups [173–175] reported the fabrication of ZnO-based TFETs with reasonable device properties. Recently, Nomura, Ohta, and coauthors [176, 177] reported the successful fabrication of high mobility top-gate TFETs based on single crystalline transparent InGaO3 (ZnO)5 thin ﬁlm. The −1 device shows the mobility as high as 80 cm2 V s−1 with on/oﬀ current ratio 6 ∼10 and more than 80% transparency in the visible and near-infrared region. A schematic diagram of TFET structure is shown in Fig. 12.33. The deposition techniques for the fabrication of these TFETs include PLD [171,172,174], ion beam sputtering [173], RF magnetron sputtering [175], reactive solidphase epitaxy [176], etc. But, till date (as far as literature survey depicts),

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Fig. 12.30. Optical transparency of n-ZnO/p-Cu−Al−O diode. Inset shows the corresponding diode structure (after [170])

I (μA)

0.9 0.6 0.3

100 Transmittance (%)

1.2

80

n-Zn1-xAlxO/p-CuAlO2+x/glass

60

Cu wire Ag

40

p-CuAlO2

20 0

n-ZnO: Al Glass

400

500 600 700 Wavelength (nm)

800

0.0 −4

−2

0

2

4

V (volt) Fig. 12.31. Rectifying I–V curve of p-CuAlO2+x /n-Zn1−x Alx O diode. Inset: optical transmission of the diode structure (after [146])

there are no reports of TFETs based on any spinel or delafossite p-TCOs. In spite of that, these reports provide a signiﬁcant step toward the realization of “Invisible Electronics.”

12.5 Origin of p-Type Conductivity in Wide-Bandgap Spinel and Delafossite Oxide Materials It has been found that most of the existing TCOs are n-type, whereas it is very diﬃcult to prepare binary metal oxides with p-type conductivity. A possible reason for this has been described by Kawazoe et al. [100,137], where

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Fig. 12.32. I–V characteristics of all-delafossite diode consist of p-CuInO2 : Ca/n-CuInO2 :Sn layers as shown in Fig. IX-6(a) (after [113])

Gate insulator

VGS

Source

VDS

Top Gate

Drain

Active channel Substrate Fig. 12.33 Schematic diagram of top-gated TFET structure (after [176])

they argued that this is probably because of the electronic structure of these metal oxides. Strong localization of holes (it can be successfully introduced by intentional substitutional doping or by producing nonstoichiometry within the material) at oxygen 2p levels or an upper edge of the valence band due to high electronegative nature of oxygen, i.e., this localization is due to the ionicity of metallic oxides. O 2p levels are far lower lying than the valence orbit of metallic atoms [178], leading to the formation of deep acceptor level by the holes. In other words, the holes, therefore, have high probability to be localized around the oxygen atoms. Hence these holes require high enough energy to overcome large barrier height to migrate within the crystal lattice, resulting in poor conductivity and hole mobility. A possible solution proposed by Kawazoe et al. [137] is to introduce a “degree of covalency” in the metal-oxygen bondings to induce the formation of an extended valence band structure, i.e., the valence band edge should be modiﬁed by mixing orbitals of appropriate counter cations that have energyﬁlled levels comparable to O 2p level. This would reduce the strong coulombic

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Bottom of CB

Eg

Top of VB

d10 s0

O 2p6

(Cu+, Ag+) Fig. 12.34. CMVB method. Energy levels are not to the scale (after [137])

force by oxygen ions and thereby delocalizing the holes. This is the essential approach to obtain p-TCO, which is called “chemical modulation of the valence band (CMVB)” [137]. But the next requirement is the choice of appropriate cationic species that will serve for CMVB technique. Investigations showed that the required cationic species are 3d10 -closed shell of Cu+ ions and 4d10 -closed shell of Ag+ ions [137, 178]. Although some transition metal cations with open dshell may fulﬁll the energy requirement [179] for CMVB technique, but they usually show strong coloration due to d–d transition, which is expected but not wanted for transparent materials. Hence, focus had been concentrated on the cations mentioned above, with closed (d10 s0 ) electronic conﬁguration. Figure 12.34 shows a schematic illustration of CMVB technique. Both of the atomic orbitals are occupied by electron pairs, and the resulting antibonding level becomes the highest occupied level, i.e., the valence band edge. Next is the structural requirement for designing p-TCO materials. Tetrahedral coordination of oxygen ions is advantageous for p-type conductivity, as it acts in reducing the localization behavior of 2p electrons on oxide ions [137]. The valence state of the oxide ions can be expressed as sp3 in this conformation. Eight electrons (including 2s2 ) on an oxide ion are distributed in the four σ bonds with the coordination cations. This electronic conﬁguration reduces the nonbonding nature of the oxide ions and increases the delocalization of holes at the valence band edge (that is why Cu2 O is a p-type conducting oxide [180–183]). But Cu2 O, although p-type in nature, has rather small bandgap (2.17 eV) [181]. This is probably because of the three-dimensional interactions between 3d10 electrons of neighboring

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451

Cu+ ions. It is expected that the low-dimensional crystal structure would suppress this interaction [116]. As we are interested in TCOs, bandgap of the material (Eg ) should be greater than 3.1 eV. Hence enlargement of bandgap would be another structural requirement for designing p-TCO, so that there is no absorption of visible photons. Materials with delafossite crystal structure ABO2 (A: monovalent ions, Cu+ , Ag+ ; B: trivalent ions, Al+3 , Ga+3 , In+3 , Cr+3 , Fe+3 , Co+3 , Sc+3 , Y+3 , etc.) [12–14] were chosen as the candidates for p-TCOs for several reasons. Firstly, if we investigate the delafossite structure as shown in Fig. 12.2 (and discussed in details in Sect. 12.2), we see that the “pseudotetrahedral coordination (B3 AO)” with the neighboring B and A ions reduces the nonbonding nature of the oxide ions and, therefore, delocalizes the holes at the valence band edge. Secondly, this layered structure (O−A−O dumbbell layer and BO2 layer) eﬀectively reduces the dimension of crosslinking of A ions and, thus enlarging the bandgap [100]. And ﬁnally, another important factor in this structure is the low coordination number of the A ions, due to the large separation from oxygen ligands, which is the result of the strong coulombic repulsion between 2p electrons in oxygen ligands and A-d10 electrons. This leads to the A-d10 energy levels almost comparable to the O 2p level, resulting in a high degree of mixing of these levels, which is essential for CMVB technique [119]. The cause of p-type conductivity shown by p-TCO materials is due to excess oxygen (or metal deﬁcit) within the crystallite sites of the material, i.e., the defect chemistry plays an important role. This deviation from the stoichiometric composition of the components can be induced by regulating the preparation condition of the materials. The defect reaction for a delafossite material of the form AI BIII O2 may be represented by the following equation [60, 184] − ≡ + O2 ↓= 2OxO + VA (12.1) I + VBIII + 4h where “OO ” denotes the lattice oxygen, “V” denotes the vacancies of monovalent cation AI and trivalent cation BIII , respectively, and “h” denotes the hole. Superscripts x, −, and + denote eﬀective neutral, negative, and positive charge states, respectively. The symbol ↓ denotes the dissolution of oxygen within the material during oxidation. Also, intercalation of excess O−2 ions in the interstitial sites may trap electrons, leaving behind empty states in the valence band, which act as holes. The formula for oxygen-excess delafossite ﬁlms may be written as AI BIII O2+x (AI = Cu+ , Ag+ and BIII = Al+3 , Ga+3 , In+3 , Y+3 , Sc+3 cations, etc.). The value of x, i.e., the percentage of excess oxygen, may be as low as 0.001% in CuAlO2+x thin ﬁlm [56] to more than 25% in CuYO2+x polycrystalline powder and CuScO2+x thin ﬁlms [128,185–187]. Figure 12.35 shows schematic representation of nonstoichiometric ABO2 crystal with “excess” oxygen in lattice sites and interstitial sites. Figures 12.14, 12.36, and 12.37 show some experimental evidences in support of the theory of enhanced p-type conductivity due to excess oxygen.

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“Excess” oxygen atom at B-site as O-2

“Excess” oxygen in the interstitial site as O-2

c “Excess” oxygen atom at A-site as O-2

a Oxygen atom

A atom

B atom

“Free” hole

Fig. 12.35. Nonstoichiometric ABO2 structure with “excess” oxygen in lattice sites and interstitial sites

Fig. 12.36. Evidence for the increase in conductivity of CuScO2+x :Mg thin ﬁlms for diﬀerent postannealing O2 pressure. Increase in conductivity leads to decrease in the transparency of the ﬁlms (after [119])

Conductivity (S cm-1)

20

24

16

20

12

16

8

12

4

conductivity carrier conc.

0

8 4

453

Carrier conc. (x 1019 cm-3)

12 Reactive Sputtered Wide-Bandgap p-Type Semiconducting

0 4 8 12 16 Post - deposition air - annealing time (min) Fig. 12.37. Increase in conductivity of Cu−Al−O thin ﬁlms with increase in annealing time. Evidence in support of enhanced p-type conduction is due to excess oxygen (after [150, 151])

Oxygen intercalation in delafossite p-TCOs only showed a maximum reported conductivity around 3 × 101 S cm−1 [120]. But this is still quite less than that of commercially available n-TCOs like ITO, which is having room temperature conductivity more than 1 × 103 S cm−1 . So next attention was focused on the substitutional doping of these materials by appropriate dopants to increase the conductivity. Doping of CuAlO2 was ﬁrst attempted, as it was the ﬁrst reported material amongst p-TCOs. Several groups theoretically calculated the eﬀects on the electronic behavior of the material due to the presence of various cations in Cu and/or Al sites. Lali´c et al. [188–190] showed that Cd and Zn substitutions on Cu site would produce n-type conductivity in the material, whereas Ni doping in Cu sites would enhance the p-type conductivity of the material. But Cd doping on Al sites would have no eﬀect on the electrical properties of the material. Preparation of a solid solution of galliumdoped copper aluminum oxide in the form of CuAl1−x Gax O2 (0 ≤ x ≤ 0.5) was reported by Shahriari et al. [191]. But no ﬁlm preparation of this material was reported by them. Also, no other experimental data on the doping of CuAlO2 thin ﬁlm has yet been reported. Heavy doping (∼50%) of CuGaO2 by Fe+3 in Ga sites has been reported by Tate et al. [119]. Their strategy was to combine high transparency of CuGaO2 thin ﬁlm (∼80% in visible region [111]) with better conductivity (over other Cu- and Ag-based delafossites [12–14]) of CuFeO2 pellets (2.0 S cm−1 [12–14, 192]). Both the polycrystalline powder and thin ﬁlm of CuGa1−x Fex O2 (0 ≤ x ≤ 1) have shown p-type conductivity. It was observed that high Fe doping had increased the conductivity of the ﬁlm from 2 × 10−2 S cm−1 (for undoped CuGaO2 thin ﬁlm) to almost 1.0 S cm−1 for CuGa1−x Fex O2 (x = 0.5) thin ﬁlm, whereas transparency of the ﬁlms became ∼60% in the visible region [119]. The temperature variation of conductivity of undoped and Fe-doped CuGaO2

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Fig. 12.38. Temperature dependence of conductivity of undoped and Fe-doped delafossite CuGaO2 thin ﬁlms, indicating increase in conductivity with doping (after [119])

thin ﬁlms is shown in Fig. 12.38. Doping of CuInO2 , CuYO2 , CuScO2 , and CuCrO2 by divalent cations, e.g., Ca+2 , Mg+2 , etc., were reported by various groups [112, 113, 119–122]. When a trivalent cation was replaced by a divalent one, one empty state in the valence band was created, which acts as a hole, thus increasing hole conductivity. The method may be described by the following equation +3

(MIII +3

+ 3e− ) ↑= (MII

+2

+2

+ 2e− ) ↓ + V− + h+

(12.2)

where MIII and MII are the trivalent and divalent cations, respectively, V− is the vacant state which has been occupied by an electron e− , and h+ is a “free” hole. The symbols ↑ and ↓ denote the replacement of trivalent cation by divalent one in the lattice sites. Such doped delafossite ﬁlms like CuCr1−x Mgx O2 (x = 0.05), CuY1−x Cax O2 (x = 0.01–0.02), CuSc1−x Mgx O2 (x = 0.05) showed better hole conductivity over the corresponding undoped ﬁlms. The temperature variations of the aforementioned doped ﬁlms are shown in Fig. 12.39. Some Ag-based delafossite materials like AgBIII O2 (BIII = Sc+3 , Cr+3 , +3 Ga , etc.) with 5% Mg doping at BIII sites were reported by Nagrajan et al. [128]. The conductivities of these sintered powders were very low (∼10−5 –10−4 S cm−1 ) and also no ﬁlm preparation of these materials was reported anywhere so far. There are also reports in the literature about the double substitution of trivalent BIII sites by divalent and pentavalent cations, e.g., CuFe1−x Vx O2 (x = 0.5), CuNi1−x Sbx O2 , CuZn1−x Sbx O2 , CuCo1−x Sbx O2 , CuMg1−x Sbx O2 , CuMn1−x Sbx O2 , AgNi1−x Sbx O2 , AgZn1−x Sbx O2 (x = 0.33), etc., but all in the form of sintered powder [125, 128]. Also, triple substitution of trivalent cation had been reported by Tate and coauthors [119, 125] in the form of CuNi1−x Sbx Sny O2 (x = 0.3, y = 0.033). Thin ﬁlm of this material showed

12 Reactive Sputtered Wide-Bandgap p-Type Semiconducting

455

Fig. 12.39. Temperature dependence of conductivity of some doped delafossite thin ﬁlms (after [121])

an average of 60% transmittance with a room temperature conductivity of 5 × 10−2 S cm−1 . The exact electronic structure and conduction mechanism of these types of materials are yet to be explored completely. Tremendous opportunities are there to carry intense research work in this ﬁeld. Regarding the transparency and p-type conductivity in spinel oxide materials, the process is diﬀerent than that of delafossite materials. For Ni-based spinel p-TCO ﬁlms such as NiCo2 O4 , it was found that disorder-induced small polaron hopping of holes contributes to p-type conductivity, resulting in high values of σRT , approaching 103 S cm−1 at the expense of some transparency in the visible region [52, 103]. These compositions were developed as infrared TCO materials. For Zn-d6 transition metal oxide-based spinel materials, the low-spin ground state of transition metal oxides with d6 conﬁguration (such as Co, Rh, Ir), under octahedral crystal environment, behaves like Cu-d10 closed shell conﬁguration, and therefore leads to p-type conductivity and optical transparency [54, 55], similar to delafossite materials. The ligand ﬁeld splitting of M-d6 (M = Co+3 , Rh+3 , Ir+3 ) due to octahedral surroundings of sixfold oxygen ions leads to the enhancement of the bandgap of these materials [5, 54, 55]. Tremendous opportunities lie ahead to explore new kinds of spinel p-TCO materials using various models and theories.

12.6 Reactive DC Sputter Deposition of Delafossite p-CuAlO2+x Thin Film 12.6.1 Introduction As discussed in the previous sections, p-TCO thin ﬁlms are very important materials in the ﬁeld of optoelectronic device technology for the realization of “Transparent Electronics” [56]. Besides delafossite- and spinel-based p-TCO

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thin ﬁlms, mentioned in the earlier sections, some other types of p-TCO ﬁlms also exist, such as undoped and K-doped SrCu2 O2 [193, 194], oxysulﬁdes like (LaO)CuS/Se [195, 196], mixed oxide like In2 O3 −Ag2 O [197], and binary oxides such as NiO [198], p-type ZnO [199–203], etc. These p-TCO ﬁlms have been reported to show very good electrical and optical properties with maximum visible transmittance around 90% for p-ZnO ﬁlms [203] and maximum room temperature conductivity (σRT ) as high as 140.0 S cm−1 for (La1−x Mgx O)CuSe ﬁlms [204]. Copper aluminum oxide (CuAlO2 ) is the ﬁrst and the most important p-TCO material reported in thin ﬁlm form [100], which has reasonable optical and electrical properties for diverse device applications. The reported visible transparency of this material is around 80% with a direct bandgap value of 3.5 eV, whereas the room temperature conductivity (σRT ) is 0.34 S cm−1 with a carrier concentration ∼3.0 × 1019 cm−3 [138]. Although the reported transparency is quite high, but the hole concentration is one to two orders of magnitude lower than the corresponding well known and widely used n-TCO thin ﬁlms, e.g., ITO, ZnO, SnO2 , etc. Therefore, as far as technological aspects are concerned, improvement in the electrical characteristics of this material is very important along with the reproducibility with the required optoelectrical properties. We have previously reported an increase in the excess oxygen content as well as an increase in the p-type conductivity of DC sputtered CuAlO2+x thin ﬁlms with an increase in the postdeposition oxygen annealing time [80, 165]. Also we have reported very good thermoelectric and ﬁeldemission properties of p-CuAlO2 thin ﬁlms synthesized by DC sputtering technique [57, 63]. As far as thermoelectric properties of p-CuAlO2 thin ﬁlms are concerned, various groups reported enhanced thermoelectric properties of these ﬁlms [82, 83], indicating its potential applications in thermoelectric converters. Also, regarding the ﬁeld-emission studies of widegap p-CuAlO2 ﬁlms are concerned, our group has ﬁrst reported the low-threshold ﬁeld-emission properties of DC and reactive sputtered p-CuAlO2 thin ﬁlms [63, 164], which indicate that this material can become an interesting alternative to the conventional ﬁeld emitters like carbon nanotubes (CNT), silicon carbide nanorods (SiC), diamond or diamond-like carbon ﬁlms (DLC), amorphous carbon (a:C), etc. [205, 206]. In this section, we have reported the synthesis of p-CuAlO2 thin ﬁlms by reactive DC sputtering technique by our group. Also the structural, optical, electrical, and thermoelectric properties of these ﬁlms are investigated with considerable attention and discussed in details. This may help in understanding the reactive sputtering process to deposit p-CuAlO2 and similar types of p-TCO thin ﬁlms and their potential application in “Transparent Electronics.”

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12.6.2 Synthesis Target Preparation First of all, the target for reactive sputtering was done by mixing ultra pure metallic powder of Cu (99.999%) and Al (99.999%) with 1:1 atomic ratio thoroughly for 1.5 h. The mixture was then pressed within a grooved aluminum holder with appropriate hydrostatic pressure to form the required target. Negative terminal of the DC power supply was connected to the target and the substrates (Si and glass) were placed on the grounded electrode. Film Deposition Prior to the deposition, the chamber was evacuated by standard rotary and diﬀusion pumping arrangements to a base pressure of 10−6 mbar. Subsequently, the chamber was ﬂushed with Ar several times and then the target was presputtered at 0.05 mbar in Ar atmosphere for 10 min to remove the contaminations, if any, present on the target surface. The target-to-substrate distance was kept at 1.8 cm whereas the sputtering voltage was 1.0 kV, with a current density around 12 mA cm−2 . During deposition, a mixture of Ar and O2 was used as the sputtering gases (with 3:2 vol. ratio, respectively, controlled by mass-ﬂow meters) and the sputtering pressure was kept at 0.2 mbar. The substrate was kept at an elevated temperature of 475 K. The details of the deposition procedure were reported elsewhere [163]. After every 2 h of deposition, the ﬁlms were postannealed in the same vacuum chamber at 493 K for 1 h (at pressure 0.2 mbar) maintaining the oxygen ﬂow. For this, the Ar ﬂow was turned oﬀ and a corresponding proportional increase in the O2 ﬂow was manifested to keep the chamber pressure to a constant value of 0.2 mbar. The average ﬁlm-deposition rate on Si substrate was 0.45 ˚ A s−1 where that for −1 ˚ glass substrate was 0.34 A s . Therefore for a deposition time of 4 h, the ﬁlm thickness on Si substrate was around 650 nm and that on glass substrate was 500 nm, respectively. Characterization The deposited thin ﬁlms were characterized by X-ray diﬀraction (XRD, Philips PW 1730/PW 1710, by CuKα line) to study the structural properties. UV–Vis–NIR spectrophotometer (Shimadzu-UV-3101-PC) was used to determine the optical properties. It is a double beam spectrophotometer with integrating sphere attachment for reﬂectance measurement within the wavelength range of 190–2,600 nm. The attachment is mainly used for measurement of both transmittance and diﬀuse/specular reﬂectance of the ﬁlms. The integrating sphere equipped with photomultiplier (UV–Vis region) and PbS cell (NIR region) detectors. Both the optical transmission and reﬂection spectra of the ﬁlms deposited on glass substrates were recorded taking similar glass

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as reference, and hence the spectrum gives transmittance and reﬂectance of the ﬁlms only. Thermoelectric power and Hall eﬀect studies were used to determine the type of conduction taking place within the deposited ﬁlms. For thermoelectric power measurement (temperature variation of Seebeck coeﬃcient), a temperature gradient across the sample was created by keeping one end of the ﬁlm in a hot-head and the other in a cold-head. The hot-head temperature was varied from room temperature to 460 K, whereas the cold-head was kept at room temperature. And these temperatures of the hot and cold ends of the ﬁlm were measured by proper thermocouple arrangements. The thermo-emfs generated between the hot and cold ends of the sample, at diﬀerent hot-end temperatures, were used to determine the Seebeck coeﬃcients (S) of the material. The entire system was kept under vacuum condition. For Hall study, we have used van der Pauw method, with rectangular van der Pauw conﬁguration. The electrical connections were made at the four corners of the sample. For the measurement of Hall voltage and related parameters, an electromagnet (Polytronic Corporation) with 4 in. pole pieces was used along with a stabilized power supply (current range 0–6 A, voltage range 0–100 V) to monitor the ﬁeld strength. The distance between the pole pieces could be varied and for a separation of 3.0 cm of pole pieces, the ﬁeld strength could be adjusted to a maximum of 10 kG. The ﬁeld within the measuring system was determined by using Diﬀerential Gaussmeter. The sheet resistance and temperature dependence of electrical conductivity of the ﬁlms were studied by linear four-probe method using Kiethley electrometer (Model – 6514) from 300 to 550 K. All the contacts were made with silver paint, which showed linear I–V characteristic over a wide range of applied voltage. 12.6.3 Results and Discussion Structural Properties Figure 12.40 shows the XRD spectrum of the ﬁlm deposited on Si substrate with background correction. It shows a strong (006) orientation. Previous

Fig. 12.40. XRD pattern of the reactive DC sputtered CuAlO2 thin ﬁlm

12 Reactive Sputtered Wide-Bandgap p-Type Semiconducting

459

Table 12.13. Crystal data for CuAlO2 [108, 114, 117, 207] System – rhombohedral Space group – R¯ 3m (D3d ) a = 2.858 ˚ A = b, c = 16.958 ˚ A α = 28.1◦ = β Cu−O = 1.86 ˚ A, Al−O = 1.91 ˚ A, Cu−Cu = 2.86 ˚ A Table 12.14. Comparison between the JCPDS d values [207] and observed d values of reactive sputtered CuAlO2 thin ﬁlms hkl 0 0 1 0 1 1 0

0 0 0 1 0 0 1

3 6 1 2 4 7 8

dJCPDS (˚ A)

dreactive (˚ A)

5.61 2.82 2.44 2.376 2.133 1.732 1.612

5.67 2.79 2.48 2.374 2.111 – 1.618

workers [124,138] also obtained similar orientation for CuAlO2 ﬁlms deposited by PLD method on sapphire substrate. We have also observed strong (006) orientation in our previously reported DC sputtered CuAlO2 thin ﬁlms deposited on Si substrates [143]. Along with the above peak, other peaks were also observed in the XRD spectrum which could be assigned for (003), (101), (012), (104), and (018) reﬂections of crystalline CuAlO2 . Also no peaks corresponding to starting materials, e.g., Cu and Al metal powders as well as their oxides, were found in the pattern. This conclusively indicated that the reactants were properly mixed to give the proper phase of the copper aluminum oxide and no residual metal oxides remained in the ﬁlm. As far as other previously reported reactive sputtered-deposited copper aluminum oxide thin ﬁlms are concerned, most of the reports indicate phase impure ﬁlms, which contain a mixture of CuAlO2 , Cu2 O, CuAl2 O4 , and CuO [158, 161, 162, 165]. Table 12.13 gives various crystal data of CuAlO2 and Table 12.14 compares experimentally obtained d values of reactive sputtered CuAlO2 thin ﬁlm with JCPDS value [207]. The information on particle size of very small crystallites from the measured full-widths-at-half-maximum (FWHM) of the diﬀraction peaks can be estimated from the well-known Scherrer formula [208] L=

xλ , β1 cos θ

(12.3)

where L is the particle size, β1 is the particle broadening of diﬀraction peaks measured at FWHM of the peak at a certain 2θ value, x is a correction factor

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A.N. Banerjee and K.K. Chattopadhyay

(=0.9), and λ is the wavelength of the X-ray used. It is to be mentioned here that, when the size of the individual crystallites in a polycrystalline sample is less than 100 nm, the term “particle size” is usually used [208]. In polycrystalline thin ﬁlms, due to the interaction between grains of the ﬁlms as well as that with the substrate, a single grain in the polycrystalline thin ﬁlm is not free to deform in the same way as an isolated crystal would, if subjected to the same deforming force. As a result of this restraint by its neighbors, a deformed grain in a polycrystalline aggregate is usually in a state of tension or compression. Thus an “internal stress” or “residual stress” is generated within the ﬁlms. This residual stress produces uniform or nonuniform strain within the ﬁlm. If the grains are subjected to a uniform tensile strain at right angles to the X-ray reﬂecting planes, corresponding diﬀraction peaks shift to the lower angles but do not change otherwise. Similarly for uniform compressive strain, the diﬀraction peaks shift to the higher angles with no change otherwise. On the other hand, if the strain is nonuniform then the diﬀraction peak will be broadened, which is called “strain broadening” [208]. The relation between this broadening and the strain can be obtained by diﬀerentiating the Bragg’s law as follows [208] 2Δd sin θ + 2d cos θΔθ = 0, Δd tan θ, d ⇒ Δ(2θ) = −2ε tan θ, [Δd/d = ε], ⇒ Δθ = −

(12.4)

⇒ Δβ = −2ε tan θ, [β = 2θ], where Δβ is the extra broadening of the diﬀraction peaks over and above the instrumental breadth (therefore also called “instrumental broadening”), ε is the strain generated within the ﬁlms, and θ is the Bragg angle. Now the above equation contains both tensile and compressive strain and must be divided by two to obtain maximum tensile strain alone or maximum compressive strain alone, if these two are assumed equal. Hence, the equation for strain broadening for only one type of strain will be Δβ = −ε tan θ.

(12.5)

Now if both the eﬀect of “particle-size broadening” and “strain broadening” is taken into consideration, then the total broadening (β) can be expressed as a linear combination of (12.3) and (12.5) as follows [208] λ + ε tan θ L cos θ β cos θ 1 ε sin θ ⇒ = + , λ L λ β = β1 + |Δβ| =

(12.6)

where β is the FWHM of the observed peaks, L is the eﬀective particle size, and ε is the eﬀective strain. A plot of β cos θ/λ vs. sin θ/λ will be a straight

12 Reactive Sputtered Wide-Bandgap p-Type Semiconducting

461

0.20 0.15

β Cosθ / λ

0.10 0.05 0.00 -0.05 -0.10 -0.15 0.05

0.10

0.15

0.20 Sinθ / λ

0.25

0.30

Fig. 12.41. Determination of strain and particle size of CuAlO2 ﬁlm deposited by reactive sputtering

line, slope of which will give the estimation of the eﬀective strain, whereas the intercept on β cos θ/λ-axis will carry the information of the eﬀective particle size. Figure 12.41 represents the plot of β cos θ/λ vs. sin θ/λ, obtained from the XRD pattern of the CuAlO2 thin ﬁlm deposited by reactive sputtering on Si substrate (shown in Fig. 12.40). Slope of the graph depicts the strain value as 2.70 × 10−2 and the intercept on y-axis gives the particle size as ∼32 nm. Compositional Analyses Composition analyses were done by A Leica S-440 Oxford ISIS Energy Dispersive X-Ray (EDX) instrument. The instrument has the capability to detect elements from Boron (5) to Uranium (92) with less than 5% accuracy. In reactive DC sputtering method, ﬁlms were postannealed for 60 min in oxygen atmosphere and the composition of the ﬁlm was in the ratio of Cu:Al:O = 1:1:2.08. Therefore, the chemical formula of the ﬁlms may be written as CuAlO2.08 . This means that the percentage of excess oxygen in the reactive sputtered ﬁlms is around 4 at.%. It has been observed that the percentage of excess oxygen within the reactive sputtered ﬁlms is close to that of DC sputtered ﬁlms with ta = 90 min [144].

A.N. Banerjee and K.K. Chattopadhyay 100

100

80

80

60

Transmitance

60

Reflectance 40

40

20

20

0 300

600

900

1200

Reflectance (%)

Transmittance (%)

462

0 1500

Wavelength (nm) Fig. 12.42. UV–Vis–NIR spectra of reactive DC sputtered CuAlO2 thin ﬁlm

UV–Vis–NIR Measurements Optical properties of CuAlO2 thin ﬁlms are extremely important because of its possible applications in the ﬁeld of optoelectronics technology. High transparency coupled with high conductivity is the main feature for TCOs as mentioned earlier. Therefore, detailed optical characterization and determination of related parameters are the most signiﬁcant part of the analyses of TCOs. Following this point of view, we have studied the optical properties of reactive sputtered CuAlO2 thin ﬁlms in details. The ﬁlms were deposited on glass substrates and the ﬁlm thicknesses were measured around 500 nm from cross-sectional SEM (not shown here). Figure 12.42 shows the UV–Vis–NIR spectra of reactive DC sputtered CuAlO2 thin ﬁlm in the wavelength range of 300–1,500 nm. These ﬁlms were postannealed for 60 min. The average visible transmittance of the ﬁlm is found to be ∼85–90%. Now, we have critically analyzed the variations of transmittance (T ) and reﬂectance (R) in terms of absorption coeﬃcients (α) to derive information on the optical transitions occurring in these ﬁlms. The transmittance (T ), reﬂectance (R), and absorption coeﬃcient (α) of a specimen are related by the equation [209] (1 − R)2 e−αd , (12.7) T = 1 − R2 e−2αd where d is the ﬁlm thickness and here the multiple internal reﬂections within the ﬁlm are considered. Now at the region of fundamental absorption, α will be quite high, so also αd. So we can neglect the second term of the denominator of (12.7) and rewrite it as [209, 210] T ≈ (1 − R)2 e−αd .

(12.8)

12 Reactive Sputtered Wide-Bandgap p-Type Semiconducting

463

Film Io

IoR Io(1-R)e−αd d Fig. 12.43. Incident (Io ), reﬂected (Io R), and transmitted [Io (1 − R)e−αd ] rays in a thin ﬁlm of thickness d. Multiple internal reﬂections are neglected

Knowing T, R, and d, absorption coeﬃcients can be determined. If R is not known, then from transmittance data of two samples of known thicknesses d1 and d2 , α can be obtained from the relation [209] T1 ≈ eα(d2 −d1 ) . T2

(12.9)

Beyond the absorption edge if one can observe the interference eﬀect in the transmittance and reﬂectance spectra due to the multiple internal reﬂections within the ﬁlm, then it will be possible to ﬁnd the refractive index (n) of the material by measuring the wavelengths (λ1 and λ2 ) at two adjacent maxima. The expression will be [209] n=

λ1 λ2 . |λ1 − λ2 |

(12.10)

Now, according to the schematic diagram shown in Fig. 12.43, in the spectral region of fundamental absorption, as a ﬁrst approximation, T, R, and α will be related by the following equation [211] (here, we have neglected the internal multiple reﬂections for TCOs, unlike (12.7) and (12.8)) T ≈ (1 − R)e−αd and R=

(n − 1)2 + k 2 , (n + 1)2 + k 2

(12.11)

(12.12)

where n is the refractive index and k is the extinction coeﬃcient, which is related to the wavelength (λ) and absorption coeﬃcient (α) by the following equation: λα k= . (12.13) 4π Now, for transparent medium (as in our p-CuAlO2 ﬁlms), k 2 (n − 1)2 and (12.12) will be reduced to

464

A.N. Banerjee and K.K. Chattopadhyay

α (cm-1)

105

104

103

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

hν (eV) Fig. 12.44. Energy dependence of absorption coeﬃcients

Refractive index (n)

n k 1.35

0.16

0.12 1.30

0.08 1.25

0.04

Extinction coefficient (k)

0.20

1.40

1.20 400

600

800

1000

1200

0.00 1400

Wavelength (nm) Fig. 12.45. Spectral variation of extinction coeﬃcients and refractive indices of reactive sputtered CuAlO2 ﬁlm

√ 1+ R √ n= 1− R

(12.14)

and the absorption coeﬃcients (α) can be calculated by rewriting (12.11) as

1 1−R . (12.15) α = ln d T The spectral variations of α, n, and k are shown in Figs. 12.44 and 12.45. It has been observed that the refractive index varies between 1.2 and 1.3 in the wavelength range of 300–1,300 nm. Although there are no reported data on the refractive indices of CuAlO2 thin ﬁlm, but these data are reasonable when compared with other TCOs such as ITO (1.75–2.0 in the wavelength

12 Reactive Sputtered Wide-Bandgap p-Type Semiconducting

465

range of 400–1,200 nm [212]) and CdO (1.31–2.84 in the wavelength range of 500–2,500 nm [213]). In the range of the onset of absorption edge, the absorption coeﬃcients (α) can be described by the relation for parabolic bands, i.e., [209, 210] (αhν)1/n = A(hν − Eg ),

(12.16)

where Eg is the bandgap of the material, the exponent n depends on the type of transition. For direct allowed transition, n = 1/2; for indirect allowed transition, n = 2; and for direct forbidden transition, n = 3/2. The factor A also depends on the type of transition. For direct allowed transition, 3/2 m∗ m∗ e2 2 m∗h+me∗ e h ; A≈ nch2 m∗e for direct forbidden transition,

A=

2 4e

∗ m∗ h me ∗ m∗ h +me

5/2

3 nch2 m∗e m∗h hν

;

and for indirect allowed transition, A∝

(m∗h m∗e )3/2 , π 4 h6

where n is the refractive index of the material, m∗h and m∗e are the eﬀective masses of holes and electrons, respectively) [214]. To determine the possible transitions, (αhν)1/n vs. hν were plotted for diﬀerent values of n. The (αhν)2 vs. hν and (αhν)1/2 vs. hν plots for reactive sputtered-deposited CuAlO2 thin ﬁlm are shown in Fig. 12.46. Extrapolating the linear portion of the graphs to the hν-axis, we have obtained the direct and indirect bandgaps as ∼3.90 and 1.89 eV, respectively. These values are comparable to those reported previously by Kawazoe et al. (3.5 eV) [100] and Yanagi et al. (3.5 and 1.8 eV) [116] for their pulsed laser-deposited CuAlO2 thin ﬁlms and also fall in the range theoretically calculated by Robertson et al. (3.91 and 2.1 eV) [117]. Also Stauber et al. [138] obtained the direct bandgap of their RF sputter-deposited CuAlO2 thin ﬁlm around 3.5 eV, whereas Wang and Gong [150, 151] reported the direct bandgap of their plasma-enhanced chemical vapor-deposited (PECVD) copper aluminum oxide ﬁlms around 3.6– 3.75 eV. As far as the bandgap values of reactive sputtered copper aluminum oxide ﬁlms synthesized by other groups are concerned, Ong and Gong [158] reported these values around 2.9–3.3 eV, Yang et al. [139] around 3.81 eV, Reddy and coauthors [165] around 3.54 eV, and Tsuboi et al. [161,162] around 3.5 eV. These values are slightly less than that of our value, which is mainly because of their phase impure ﬁlms, which contain some amount of CuO, Cu2 O, and/or CuAl2 O4 phases within the copper aluminum oxide samples.

466

A.N. Banerjee and K.K. Chattopadhyay 7x1010

5x1010

150

4x1010 3x1010

Eg-direct

= 3.90 eV

Eg-indirect

= 1.89 eV

100

2x1010

50

(αhν)2 X 108 (eV2cm-2)

( αhν)1/2 (eV1/2cm-1/2)

200

Indirect bandgap Direct bandgap

6x1010

1x1010 0

0 0

1

2

3

4

hν (eV) Fig. 12.46. Determination of bandgaps of reactive sputtered CuAlO2 ﬁlm

Current (μ A)

160

120

80

40

0 0

20

40

60

80

100

120

140

Voltage (V) Fig. 12.47. Veriﬁcation of ohmic nature of the contacts

Electrical Properties Electrical properties of CuAlO2 thin ﬁlms have been studied by standard fourprobe methods. All electrical contacts were made by silver paint, which showed linear I–V characteristics over a wide range of voltages and temperatures. Figure 12.47 shows I–V characteristics of one contact at room temperature indicating ohmic nature of it over the voltage range up to 150 V. The thermally activated conduction of a semiconductor can be given by the relation [135]

12 Reactive Sputtered Wide-Bandgap p-Type Semiconducting

467

2.0 1.5 1.0

ln σ

0.5 0.0 -0.5 -1.0 -1.5 -2.0 2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

(1/ T) x 103 (K-1) Fig. 12.48. Temperature variation of conductivity of reactive sputtered CuAlO2 thin ﬁlm

Ea , σ = σo exp − kT

(12.17)

where σ0 is a temperature-independent factor and Ea is the activation energy of the material. For p-type semiconductor (as in our p-CuAlO2 sample), this is the energy diﬀerence between the acceptor level and the top of the valence band. Therefore, a plot of ln σ vs. 1/T should be a straight line whose slope would carry the information of the activation energy of the material. Temperature variation of the conductivity of reactive sputtered CuAlO2 thin ﬁlm has been studied in the temperature range of 300–550 K according to (12.17) and shown in Fig. 12.48. The ﬁlm thickness was ∼500 nm obtained from crosssectional SEM (not shown here). The temperature variation of conductivity of the CuAlO2 thin ﬁlms was studied below the room temperature by previous authors [100,116], but no study on high-temperature conduction was reported. The straight line nature of the Arrhenius plot indicates the thermally activated conduction as often found in semiconductors. Room temperature conductivity (σRT ) of the ﬁlm was obtained as 0.22 S cm−1 , which is comparable to that obtained by DC sputtered ﬁlms postannealed for 60 min [143]. From the slope of the graph, we get the value of activation energy (Ea ) which corresponds to the minimum energy required to transfer carriers from acceptor level to the valence band and the value of Ea comes out as 250 meV, which is comparable to that of DC sputtered ﬁlms postannealed for 60 min [57]. For other reactive sputtered CuAlO2 ﬁlms, Rao et al. [165] obtained σRT around 0.36 S cm−1 . On the other hand, Tsuboi et al. [161, 162] reported the resistivity of their reactive cosputtered Cu−Al−O thin ﬁlm around 10–102 Ω cm.

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A.N. Banerjee and K.K. Chattopadhyay

Hall measurements of our reactive sputtered ﬁlms were done at room temperature. Hall coeﬃcient of the ﬁlm was determined to be RH = 14.1 cm−3 C−1 , corresponding to carrier density 4.4 × 1017 cm−3 . Positive value of Hall coeﬃcient conﬁrmed the p-type conductivity of the ﬁlm. The carrier concentration of this ﬁlm is comparable to that of DC sputtered ﬁlm postannealed for 60 min [57]. As far as conductivities of previously reported reactive sputtered copper aluminum oxide ﬁlms are concerned, Rao and coauthors [165] obtained the Hall mobility and hole concentration as −1 13.1 cm2 V S−1 and 1.5 × 1017 cm−3 , respectively. Thermoelectric Properties Thermoelectric properties of reactive sputtered CuAlO2 thin ﬁlms have been studied for ﬁlms deposited on glass substrates. The measurements were done from room temperature (300 K) to 550 K. Figure 12.49 shows the temperature dependence of Seebeck coeﬃcients (S) of the ﬁlm. All the Seebeck coeﬃcients are positive in nature, which again conﬁrmed p-type nature of the ﬁlms. Room temperature Seebeck coeﬃcient (SRT ) of the ﬁlm was obtained as +115 μV K−1 . As shown in the Fig. 12.49, the Seebeck coeﬃcients initially decrease from room temperature to around 370 K and then increase to almost +520 μV K−1 , for further increase in temperature. Previously, Kawazoe et al. [100] and Yanagi et al. [116] obtained the room temperature Seebeck coeﬃcients for their pulsed laser-deposited CuAlO2 thin ﬁlm as +183 and +214 μV K−1 , respectively, which is comparable to our values. On the other hand, Koumoto et al. [60] determined the Seebeck coeﬃcient of CuAlO2 single crystal as well as polycrystal at 600 K around +180 and +150 μV K−1 , respectively. Also Benko and Koﬀyberg [107] reported a relatively high value of SRT (670 μV K−1 ) of CuAlO2 powdered pellets. As far as

Seebeck coeff. (μV K −1)

600

500

400

300

200

100 2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

1000/T (K−1)

Fig. 12.49. Seebeck coeﬃcient vs. 1,000/T of reactive sputtered CuAlO2 thin ﬁlms

12 Reactive Sputtered Wide-Bandgap p-Type Semiconducting

469

reactive sputtered p-CuAlO2 thin ﬁlms are concerned, nobody has mentioned about the Seebeck coeﬃcient of those ﬁlms, but various groups have reported enhanced thermoelectric properties of CuAlO2 as well as similar delafossite materials [80–83] synthesized by various other techniques, which indicate that this type of material may become very good alternative to the commercially available thermoelectric converters. It has been observed that, in our reactive sputter-deposited CuAlO2 thin ﬁlm, SRT increases with the increase in conductivity of the ﬁlms. This observation is consistent with the Hicks model [215, 216], where the natural superlattice structure was proposed to show high thermoelectric ﬁgure of merit (ZT) due to increase in both S and σ according to the following equation ZT =

S 2 σT , κ

(12.18)

where σ is the electrical conductivity, κ is the thermal conductivity, and S is the Seebeck coeﬃcient. To achieve high ZT, increase in S and/or σ and decrease in κ are required. But for simple materials, increase in S leads to a decrease in σ. Similarly, an increase in σ is followed by an increase in κ according to Wiedemann– Franz law. So ZT eﬀectively remains more or less constant. To increase Z, various models have been proposed in the last decade. Amongst them, the most exciting proposal by Hicks et al. [215,216] was superlattice quantum-well materials, having an eﬀective two-dimensional density of states for carriers. This density of state is given by m/π2 a, where m is the carrier mass and a is the quantum-well width. These authors assumed inﬁnite potential barrier with zero barrier width and showed a considerable increase in Z. Later, LinChung and Reinecke [217] and Broido and Reinecke [218] included the eﬀects of thermal transport in the ﬁnite barrier layers and carrier tunneling between layers in the above model to get a modiﬁed Z. Encouraged by these ﬁndings, various new materials, having layered structure, have been investigated in the last few years, which include NaCo2 O4 [219], (ZnO)5 In2 O3 [220], PdCoO2 [58], CuAlO2 [59, 60], etc. Structure of CuAlO2 delafossite has been shown in Fig. 12.2 and described in details in previous sections. This structure suggests that CuAlO2 has a layered structure where carriers can easily move two dimensionally along ab-plane than to move across the Al−O insulating layers (described in Fig. 12.50). In the XRD pattern of our CuAlO2 thin ﬁlm (shown in Fig. 12.40), we have obtained a strong (006) peak, which is typical of a texture where the caxis is perpendicular to the substrate (hence parallel to the normal, n to the substrate, i.e., c n). Now, according to our experimental setup (as described earlier), carriers in the ﬁlms are expected to move along the abplane. Hence, the above argument of two-dimensional conﬁnement of carriers along the ab-plane is valid for our ﬁlms. Although the reason behind the enhanced thermoelectric properties shown by the materials possessing layered structure is still not fully understood, but Koumoto et al. [60] suggested that

470

A.N. Banerjee and K.K. Chattopadhyay

Fig. 12.50. Layered structure of CuAlO2 showing the carriers conﬁned in the abplane

this may be correlated with the low dimensionality of the crystal structure and behavior of electrons and phonons in an anisotropic structural environment. Recently, Wang et al. [221] suggested that spin entropy might be responsible for enhanced thermopower in Nax Co2 O4 having layered structure [219]. Whether this can be correlated with the good thermoelectric properties of CuAlO2 is a question and intense research is needed in this direction. The variation of thermoelectric power (S) with temperature is given by [222] ΔEf k A+ (12.19) S= e kT with

5 −s 2

(12.20)

τ = τo e−s ,

(12.21)

A= and

where k is the Boltzmann constant, e is the electronic charge, ΔEf is the energy diﬀerence between Fermi level and the upper edge of the valence band, τ is the relaxation time for electron scattering, s is a constant, which is different for diﬀerent scattering mechanism, and τo is a constant, which is a function of temperature but independent of the electronic charge, e.

12 Reactive Sputtered Wide-Bandgap p-Type Semiconducting

471

From (12.19), we can obtain the Fermi level (Ef ), from the slope of the S vs. 1/T graph. From Fig. 12.49, we have determined the Fermi energy from the linear portion of the graphs near room temperature, and the value obtained as 100 meV. Previously, Benko and Koﬀyberg [107] have determined the Fermi energy of CuAlO2 powder (σ = 1.69 × 10−3 S cm−1 ) from the thermopower measurement, as 190 meV, which is slightly higher to our sample. This is mainly because we have measured the thermopower of the material as thin ﬁlm form, whereas they had done their measurements on polycrystal pellets. As previously mentioned, from the slope of the ln σ vs. 1,000/T plots (Fig. 12.48), we have obtained the activation energy (Ea = 250 meV) value of our sample, which gives the estimation of acceptor levels. Comparing this value with the Fermi energy of the material, we can say that, according to the band picture, Fermi level lies between the upper edge of the valence band and the acceptor level, which is typical of a nondegenerate p-type semiconducting material with acceptors not fully ionized. Hence a continuous increase in conductivity with temperature was observed for our sample. The values of various optical, electrical, and thermoelectric parameters of the reactive sputtered CuAlO2 thin ﬁlms are furnished in Table 12.15. Figure 12.51 represents the temperature dependence of thermoelectric power factor (σS 2 ) of CuAlO2 thin ﬁlm for the temperature range of 300–460 K. The values range from 3.09 × 10−7 W m−1 K−2 at temperature around 300 K to 5.5 × 10−5 W m−1 K−2 around 460 K. Previously, Koumoto et al. [60] obtained these values roughly as 1.12×10−5 W m−1 K−2 at 550 K for CuAlO2 single crystal and 7.1 × 10−6 W m−1 K−2 at 700 K for CuAlO2 polycrystal. Also Park et al. [59] obtained the power factor for CuAlO2 ceramic as 2 × 10−5 W m−1 K−2 at 550 K. These values are comparable to the values reported by us. Also, recently Kurotori and Sugihara [223] reported signiﬁcant increase in the thermoelectric properties of CuAlO2 , when doped with Zn and Ca. All these reports suggest that this class of material may become very good candidate of thermoelectric converter, and may bring renaissance in the thermopower industry. In summary, highly transparent, p-type semiconducting CuAlO2 thin ﬁlms have been synthesized by reactive sputtering technique. The ﬁlm with thickness ∼500 nm shows almost 80–85% visible transmittance with 0.22 S cm−1 room temperature conductivity. Hall measurements conﬁrmed p-type conductivity with a hole concentration ∼4.4 × 1017 cm−3 . These results indicate that reactive sputtering can become a very good, cost-eﬀective, large-scale synthesis procedure to fabricate p-TCO ﬁlms with enhanced electro-optical properties for potential applications in “Invisible Electronics” as well as in other diverse device technologies. The ﬁlm also showed very good thermoelectric properties indicating its possible use in thermoelectric industries.

500

Thickness (nm)

80–85

Average visible transparency (%) 3.90

Eg -direct (eV)

1.89

Eg -indirect (eV)

0.22

σRT (S cm−1 )

250

Ea (meV)

RH (cm−3 C−1 )

14.1

n (cm−3 )

4.4 × 1017

+115

SRT (μV K−1 )

Table 12.15. Diﬀerent thermoelectric properties of reactive sputtered p-CuAlO2 thin ﬁlm

100

Ef (meV)

472 A.N. Banerjee and K.K. Chattopadhyay

12 Reactive Sputtered Wide-Bandgap p-Type Semiconducting

473

−4.5 −5.0

10

10

log (σ S2) [log (Wm−1K−2)]

−4.0

−5.5 −6.0 −6.5 320

360

400

440

480

T (K)

Fig. 12.51. Thermoelectric power factor vs. temperature of reactive sputtered CuAlO2 thin ﬁlms

12.7 Conclusions and Future Directions 12.7.1 Conclusions Reactive sputtering technique has become one of the interesting and widely used deposition techniques to fabricate binary, ternary, and quaternary metal oxide thin ﬁlms which are having many useful applications in optoelectronics as well as in various other technological ﬁelds. Being a cost-eﬀective procedure, this thin ﬁlm-deposition process has the capability of large-scale production in diverse industrial applications. In this chapter, we have brieﬂy discussed various aspects of reactive sputtering technique and its applications in the ﬁeld of p-TCO thin ﬁlms, especially spinel, AB2 O4 , and delafossite, and ABO2 thin ﬁlms, which are having tremendous applications in “Transparent” or “Invisible Electronics.” Spinel- and delafossite-structured, transparent, p-type semiconducting oxide (p-TCO) materials are recently gained renewed interest in the ﬁeld of optoelectronics technology for the possible fabrication of all-transparent junctional devices which can be used as a “functional” window that would transmit the visible portion of the solar spectrum but absorb the ultraviolet part of it to generate electricity. Here we have reviewed in details the recent developments in the spinel- and delafossite-structured p-TCO materials. Various deposition techniques used to synthesize these types of materials are discussed and especially diﬀerent reactive sputtering techniques used to synthesize spinel and delafossite p-TCO ﬁlms are compared in details. It has been observed that the reactive sputtering of elemental targets in oxygen-diluted argon atmosphere produced dense sputtering plasma, leading to uniform and good quality ﬁlms.

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Also, the origin of the p-type conductivity in these spinel and delafossite oxide ﬁlms is discussed in details. Nature of the cationic species, crystal structure of the material, and nonstoichiometry are found to be playing important roles in the hole conductivity of these materials. Metal deﬁcit or excess oxygen within the material is found to increase the p-type conductivity of these materials. Postdeposition oxygen annealing of the ﬁlms as well as excess oxygen atmosphere during ﬁlm deposition are found to be responsible for the presence of those nonstoichiometric excess oxygen within the ﬁlms. Finally, a detailed discussion on the synthesis and characterization of polycrystalline, p-type semiconducting, transparent, delafossite, and widebandgap CuAlO2 thin ﬁlms by reactive DC sputtering technique has been presented. CuAlO2 , being the ﬁrst reported p-TCO in thin ﬁlm form, found to be one of the very important materials in the ﬁeld of “Transparent Electronics.” The ﬁlms were deposited by reactive sputtering of a target pellet composed of Cu + Al (1:1 atomic ratio) metal powders in Ar + O2 (3:2 vol. ratio) atmosphere under elevated substrate temperature. XRD spectrum conﬁrms the polycrystalline nature of the ﬁlms with small grain size (∼32 nm). The deposited ﬁlms were highly transparent in the visible region with direct and indirect bandgap values of 3.90 and 1.89 eV, respectively. p-Type conductivity was conﬁrmed from both thermoelectric power and Hall eﬀect measurements. Reactive sputtered-deposited transparent p-type semiconducting CuAlO2 thin ﬁlm showed fairly high conductivity with maximum room temperature conductivity in the range of 0.22 S cm−1 and a carrier concentration ∼4.4 × 1017 cm−3 . Also the activation energy of the ﬁlm is found to be 250 meV. Compositional analyses reveal the presence of excess oxygen within the ﬁlm with a chemical formula CuAlO2.08 . FT-IR spectra of the ﬁlms indicated the existence of various bondings among Cu, Al, and oxygen. Thermopower measurements indicate that CuAlO2 may become a candidate material for thermoelectric conversion. CuAlO2 has a natural superlattice structure, with an eﬀective two-dimensional density of states (along ab-plane). This type of layered-structure material could become a good thermoelectric material. Room temperature Seebeck coeﬃcients (SRT ) are found to be +115 μ V K−1 with Ef = 100 meV. An increase in SRT with σRT is observed, which is expected for superlattice materials. The cost-eﬀective fabrication of this technologically important material is extremely important for the large-scale production of device quality ﬁlms. Low-cost physical routes like reactive sputtering technique will enable fabrication of high-quality ﬁlms for diverse device applications. 12.7.2 Future Directions First and foremost future course of the research will be to increase the conductivity of these p-TCO materials. The maximum conductivity of our p-TCO ﬁlms with spinel and delafossite structure is almost two orders of magnitude less than that of commercially available n-TCO ﬁlms. So this may put hin-

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drance in the formation of eﬀective active devices for large-scale production. It is found that nonstoichiometric oxygen intercalation within the material has its limitation to increase the conductivity of the ﬁlm. Excess oxygen intercalation, beyond an optimum value, is found to deteriorate the ﬁlm quality. So intentional doping of the material is the obvious step to increase the conductivity of the ﬁlm. Identiﬁcation of proper dopant and doping procedure should be the focus of the future work to deposit superior device quality ﬁlms for the development of “Transparent Electronics.” Another interesting area of research is the cost-eﬀective fabrication of transparent junctions, without compromising its electro-optical properties. This is important for the large-scale production of various junctional devices with diverse applications. Several groups have used various cost-eﬀective physical and chemical routes for fabrication of transparent junctions, but future work should be aimed to improve the optoelectrical properties of these transparent junctions. Another area of research, which is not yet explored completely, but has tremendous potential, is the thermoelectric properties of delafossite materials. Being a layered-structured material, delafossite ﬁlms can become very good candidate for thermoelectric converters. If proper studies can be done on the thermoelectric properties of these types of superlattice materials, new horizon may open up in the ﬁeld of thermoelectric converters. Also keeping an eye in the tremendous progress in nanotechnology, fabrication and characterization of nanostructured p-TCO thin ﬁlms may become an important ﬁeld of work, because of new and interesting properties exhibited by these nanomaterials. Proper fabrication procedure to get reproducible nanomaterials is the most important future work. Also, in-depth studies of the photoluminescence properties of p-TCO nanoparticles will be another area of research, which is needed to be explored properly. Fabrication of nanostructured p-TCOs, coupled with the already existing and well-known materials of nanostructured n-TCOs, will give an added impetus in the ﬁeld of “Invisible Electronics” for the fabrication of nanoactive devices, which can have high-eﬃcient applications in the optoelectronic device technology. Field-emission property of CuAlO2 (as well as similar wide-bandgap TCO materials) thin ﬁlms is a completely new area of research, which has tremendous opportunities. This material showed very low turn-on ﬁeld comparable to most of the carbonaceous low-threshold ﬁeld emitters like CNT, DLC, diamond, a:C, SiC nanorods, etc. So these types of wide-bandgap TCO materials may become promising alternative to the existing materials in the ﬁeld of FED technology. But, proper emission mechanism in these materials is not very clear till date and very good scopes are there to properly investigate the emission mechanism so that the material properties can be tuned accordingly to get better ﬁeld-emission properties of these ﬁlms. Also, recent study showed that p-CuAlO2 can become a good candidate for ozone sensors. Zheng et al. [64] reported that CuAlO2 has a selective and reversible response to ozone gas at room temperature. All existing commercial

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semiconductor ozone sensors are of n-type [224–226]. This study demonstrated the feasibility of developing an inexpensive p-type transparent ozone sensor. Hence, transparent p–n junction ozone sensors may be fabricated using the p-CuAlO2 and existing n-TCO such as In2 O3 . Photocatalytic hydrogen evolution over delafossite CuAlO2 is another interesting report published recently by Koriche et al. [65]. This group proposed a new photochemical system for water reduction based on p-CuAlO2 and S2− as hole scavenger. They have used coprecipitation method, a new synthetic route, to synthesis CuAlO2 , which increased the surface to volume ratio and delivered a highest H2 production. This report is very interesting and shows newer applications of delafossite p-CuAlO2 material. Also, recently Kizaki et al. [66] proposed a material designing procedure to get CuAlO2 -based dilute magnetic semiconductors. Ab initio calculations showed that Fe- and Mn-doped CuAlO2 -based dilute magnetic semiconductors possess high-Curie-temperature ferromagnetic characteristics. Being a natural p-type transparent semiconductor without intentional doping, CuAlO2 can easily be used for the host of dilute magnetic semiconductors. Also, most importantly, the delafossite structure of CuAlO2 has the advantage of possessing two cation sites, Cu+1 and Al+3 sites, for possible magnetic ion substitution. O−Cu−O dumbbell sites in delafossite CuAlO2 can be partially replaced with magnetic ions. Due to this coordination, one can realize new ferromagnetic dilute magnetic semiconductors from the standpoint of the hybridization of orbitals between 3d orbitals with the impurities and 2p orbitals with the oxygen in CuAlO2 . Regarding spinel p-TCO ﬁlms, NiCo2 O4 shows very good electrocatalytic behavior in many electrochemical processes such as hydrogen evolution, oxygen evolution, organic electrosynthesis, etc. [227, 228]. On the other hand, Reddy et al. [229] reported that nickel ferrite (NiFe2 O4 ), a p-type semiconducting oxide with an inverse spinel structure, could be used as a gas sensor to selectively detect chlorine in air. Also recently, Saadi et al. [230] reported the photoassisted hydrogen evolution of p-type spinel CuM2 O4 (M = Al/Cr/Fe/Mn/Co), indicating newer applications of these types of materials. Therefore, it will not be an exaggeration to say that next decade will see the renaissance of spinel and delafossite, wide bandgap, p-TCO materials and various new, interesting and novel technological applications with these materials are on the verge of exploration. Acknowledgments. The authors wish to thank Department of Science and Technology, Government of India, for ﬁnancial support during the execution of the work reported in this chapter.

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13 Oxide-Based Electrochromic Materials and Devices Prepared by Magnetron Sputtering C.G. Granqvist

13.1 Introduction Radiation in our natural surroundings is characterized by three general features: spectral selectivity, angular dependence, and temporal variability. Regarding spectral selectivity, the solar radiation incident on the atmospheric envelope is conﬁned to the 0.2 < λ < 3 μm wavelength interval, whereas thermal radiation at normal temperatures lies at 2 < λ < 50 μm and visible light as well as light for photosynthesis is at 0.4 < λ < 0.7 μm. The atmosphere is transparent in the main part of the 0.3 < λ < 3 μm and at 8 < λ < 13 μm ranges if the humidity/cloudiness is low. These facts lead to many options for the development of solar energy materials with optimized values of absorptance A, transmittance T , reﬂectance R, and emittance E [1,2]. For example, eﬃcient solar heating requires, ideally, A = 1 for 0.3 < λ < 3 μm and E = 0 for 3 < λ < 50 μm, and eﬃcient cooling via radiation to the clear sky demands R = 1 for 0.3 < λ < 8 μm and 13 < λ < 50 μm while E = 1 should prevail for 8 < λ < 13 μm. Considering windows in buildings, T = 1 for 0.3 < λ < 3 μm and E = 0 for 3 < λ < 50 μm give maximum solar heating jointly with thermal insulation for double glazing, while T = 1 for 0.4 < λ < 0.7 μm and R = 1 for 0.7 < λ < 50 μm give full daylighting at minimum solar heating. Optimized angular properties can boost the performance of spectrally selective surfaces. These and other aspects of solar energy materials have been reviewed in some detail recently [2]. Materials science also gives possibilities to design for temporal variability. This can be done by use of “chromogenics” [3], encompassing photochromic materials (typically darkening under irradiation in the 0.3 < λ < 0.4 μm range), thermochromic ﬁlms (typically increasing R at 0.7 < λ < 3 μm as the temperature exceeds a certain “critical” value that may be at room temperature), “gasochromic” ﬁlms (darkening/bleaching under exposure to reducing/ oxidizing gases), and electrochromic (EC) multilayer structures [4] (changing their absorption at 0.3 < λ < 3 μm under charge insertion/extraction). The purpose of this chapter is to brieﬂy outline electrochromics – mainly from

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the viewpoint of sputtering technology – and discuss its possibilities to revolutionize building technology by allowing rigid or ﬂexible building skins that are able to regulate their throughput of visible light and solar heating to combine energy eﬃciency and indoor comfort. In particular, this technology is capable of alleviating air conditioning loads that are currently much in focus owing to their rapid growth. One example of many is a recent study from Kuwait reporting that more than 75% of the electricity is now consumed by air conditioning at peak load and that the peak load has increased by a factor ∼2.5 from 1991 to 2001 [5]. The present chapter is based on an earlier conference report [6].

13.2 Energy Eﬃciency of Chromogenic Building Skins Modern man normally spends some 90% of his time inside buildings and vehicles, and the quality of the indoor environment hence is of the greatest importance. More and more energy is used to maintain this environment at a level that is both comfortable and healthy. Looking at the EU(15), some 40% of the energy supply are currently used for heating, cooling, ventilation, and lighting of buildings, as well as for appliances. In ﬁnancial terms, this corresponds to ∼4% of the Gross National Product [7, 8]. The energy eﬃciency one can accomplish by use of chromogenic building skins has been diﬃcult to come to grips with, partly since the most fundamental function of a window or glass fa¸cade – that of providing unmitigated visual contact between indoors and outdoors – has not always been adequately appreciated. From a strict energy perspective, it may be beneﬁcial to eliminate the windows, but this is highly detrimental to the well-being and working eﬃciency of the persons using the building, who normally would rather prefer a panoramic view of their ambience. Energy eﬃciency of the windows hence must be reached with an understanding of their need to give transparency. The energy eﬃciency of chromogenic building skins (often referred to as “smart windows” [9]) has been investigated in recent simulations [10–13]. Speciﬁcally, calculations for a standard oﬃce module with well-deﬁned size, window area, lighting demand, occupancy, equipment, etc., showed that the energy savings potential was considerable for the cooling load [10]. The studied oﬃce block was oriented with one fa¸cade facing South and one facing North and the simulations were performed with climate data applicable to Rome (Italy), Brussels (Belgium), and Stockholm (Sweden). When using “smart windows” instead of conventional static solar control windows, the energy for space cooling, on an annual basis, could be reduced by as much as 40–50%. The amount of saved energy is obviously climate dependent. An interesting result of the simulations was that the cooling power could be reduced so that air conditioning might be avoided when “smart windows” are used, thus indicating that the marginal cost for “smart windows” can be more than balanced by the elimination of an air conditioning system. Large energy savings were inherent also in another recent study [11, 12], which also pointed at a number

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of important subjective assets of the technology [13]. Similar analyses can be made with regard to vehicles [14]. An alternative “back-of-an-envelope analysis” of the energy eﬃciency [15] is best expressed by way of an analogue between smart windows and today’s best solar cells, having the same size and orientation: the solar cells can generate a certain amount of energy, which is similar to the energy savings the “smart windows” can provide.

13.3 Electrochromic Device Design and Materials An EC device resembles a thin ﬁlm electrical battery, as evident from Fig. 13.1. The device has ﬁve superimposed layers on a transparent substrate, typically of glass or ﬂexible polyester foil, or positioned between two such substrates in a laminate conﬁguration [4]. The outermost layers are transparent electrical conductors, typically of In2 O3 :Sn (i.e., indium tin oxide, ITO) [16]. One of these layers is coated with an EC ﬁlm, whereas the other is coated with an ion storage ﬁlm, with or without EC properties. Both of these ﬁlms must comprise nanomaterials characterized by well-speciﬁed nanoporosities (analogously with the case of battery electrodes). A transparent ion conductor (electrolyte) is at the middle of device and joins the EC and ion storage ﬁlms. A voltage pulse between the transparent electrodes leads to charge being shuttled between the EC and ion storage ﬁlms, and the overall transparency

Fig. 13.1. Prototype electrochromic device, showing transport of positive ions under the action of an electric ﬁeld (from [4])

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is thereby changed. A voltage pulse with opposite polarity – or, with suitable material combinations, short circuiting – makes the device regain its original properties. The optical modulation requires a DC voltage of as little as 1– 2 V. The charge insertion into the EC ﬁlm(s) is balanced by electron inﬂow from the transparent electrode(s); these electrons can produce intervalency transitions, which is the basic reason for the optical absorption. Regarding materials in EC devices, the ITO can be replaced by ZnO:Al, SnO2 :F, or similar oxides (or, possibly, carbon nanotubes) [17–19]. The global availability of indium does not seem to be fully clear today (2007), and on one hand, it has been stated that it is ample and about as large as that of silver [20], but it has also been claimed that the availability is much too low to allow widespread deployment of indium-containing thin ﬁlm solar cells [21]. The EC ﬁlm is WO3 -based in almost all devices for window applications, whereas there are many possibilities for the counter electrode [4,22,23]. Among the latter, ﬁlms based on IrO2 and NiO have enjoyed much interest recently. IrO2 -based alternatives are inherently expensive, but good EC properties are maintained after dilution with cheaper Ta2 O5 [24]. NiO-based ﬁlms combine moderate cost with excellent optical properties, especially when the NiO is mixed with another oxide characterized by a wide bandgap such as MgO or Al2 O3 [25, 26]. EC devices can use many diﬀerent electrolytes, either being hydrous oxides exhibiting proton conduction or polymers with ion conduction due to added salts. EC devices have been discussed a long time, ever since the display-type devices presented shortly after the discovery of electrochromism in WO3 ﬁlms [27]. Generally speaking, the progress of technologies based on electrochromism has been slow, which may be associated with the necessity of simultaneously mastering a range of nonconventional technologies [6], as follows: 1. The ITO must combine excellent electrical conductivity with very low optical absorption, which is challenging especially for ﬁlms on temperaturesensitive substrates such as polymers [6]. 2. The EC and counter electrode ﬁlms must exhibit well-speciﬁed nanoporosities over large areas, which require nonstandard coating technologies. 3. Viewing the EC device as a “thin ﬁlm battery” makes is evident that charge insertion/extraction and charge balancing must be accomplished by properly controllable and industrially viable techniques, such as gas treatments [28]. 4. The electrolyte must combine good ion conductivity with adhesiveness and high transparency for ultraviolet irradiation. 5. Long-term cycling durability demands adequate strategies for voltage and current control during coloration/bleaching – just as it does for charging/discharging of batteries. All of these challenges can be successfully met, however, and EC technology ﬁnally may emerge as suitable for large-area, large-scale applications [26, 29].

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Fig. 13.2. “Thornton diagram” illustrating the nanostructures of thin ﬁlms prepared by sputtering at diﬀerent argon pressures and substrate temperatures. The melting point of the material is denoted Tm (from [30])

Film porosity on the nanoscale is necessary, as stressed above. Virtually any thin ﬁlm technology may be capable of achieving the desired properties, though with more or less diﬃculty. Regarding sputtering, the deposition parameters should be conﬁned to those giving “zone 1” ﬁlms in the wellknown “Thornton diagram” [30] in Fig. 13.2 showing, schematically, what a sputter deposited ﬁlm looks like under the electron microscope. Thin ﬁlms most often are prepared under conditions such as the ones of the “transition” zone denoted T . Those ﬁlms are compact and it is possible to minimize grain-boundary scattering of the conduction electrons in a metallic ﬁlm. The transparent conducting ITO ﬁlms in EC devices should be of this character [31]. Nanocrystallinity and nanoporosity are found at higher pressure in the sputter plasma, such as in zone 1. In this case, it is possible to have ion conduction in the intercolumnar spaces, as required in EC ﬁlms and in solidstate ionic ﬁlms in general. The speciﬁc nanotopography then accomplished has been referred to as “parallel penniform” at least in the case of TiO2 ﬁlms [32]; a cross-sectional transmission electron image of a 4.2-μm thick ﬁlm of this type is illustrated in Fig. 13.3. For the devices reported on below, DC magnetron sputtering was performed using targets of 99.95% pure tungsten and nickel [33]. An addition of vanadium to the nickel was used in many experiments; this made the target nonmagnetic and hence convenient for magnetron sputtering. Deposition took place in Ar/O2 /H2 with optimized mixing ratio. The target–substrate distance typically was 20 and 25 cm, and the total gas pressure was in the 30–40 mTorr range (cf. Fig. 13.2). From a manufacturing point of view, it is preferable to be able to deposit the ﬁlms under conditions that make them

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Fig. 13.3. Cross-sectional transmission electron micrographs of a nanocrystalline and nanoporous TiO2 ﬁlm (from [32])

ready for device assembly, or to have convenient processes for making the as-deposited ﬁlms ready for this. In the case of tungsten oxide, deposition in Ar/O2 /H2 = 4/2/13 is suitable and leads to blue colored ﬁlms. A key issue with regard to optimizing the gas mixture is to incorporate hydrogen into the ﬁlm without creating oxygen deﬁciency.

13.4 Properties and Applications of Electrochromic Foil Figure 13.4 shows recent characteristic data for a 5 × 5 cm2 ﬂexible EC foil incorporating WO3 , NiO modiﬁed by addition of a wide bandgap oxide such as MgO or Al2 O3 , PMMA-based electrolyte, and ITO ﬁlms [26, 33–35]. The mid-luminous transmittance (T550 , where the subscript denotes wavelength in nanometers) rapidly attains ∼68% upon bleaching and drops to ∼36% during a coloration period of 50 s. Still lower values can be reached with extended coloration times. The modulation is smaller, but still signiﬁcant, for blue light (T400 ) whereas it is larger for red light (T775 ). The substantial transmittance at the ultraviolet end of the spectrum is associated with the oxide added to the NiO. Durability was manifest for several tens of thousands of coloration/bleaching cycles. The open circuit memory is excellent, and the optical properties are maintained virtually unchanged for many hours. The EC foil can be used in a variety of applications related to buildings, vehicles, and others. It can be suspended between glass panes, used as a conventional add-on window ﬁlm, or employed as a lamination material

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80

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400nm 550nm 775nm

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300

Time (sec) Fig. 13.4. Time-dependent transmittance during coloration/bleaching of an electrochromic device, recorded at three wavelengths (from [35])

between rigid glass and polymer panes. The latter application can provide impact resistance, spall shielding, acoustic damping, etc., as added beneﬁts. Figure 13.5 shows a prototype of a “smart window” with four 30 × 30 cm2 EC foils mounted between glass panes. The upper two panels are fully colored while the lower two are fully bleached. Each of the panels can shift gradually and reversibly between the dark and transparent states in about a minute, i.e., during the time it takes for the eye to adapt to diﬀerent lighting conditions. It is important to note that the window maintains its primary function – that of providing unmitigated visual indoors/outdoors contact – irrespective of the state of coloration. The windows cannot give privacy, though. Potential applications in energy eﬃcient buildings and automobiles have provided the main impetus for research and development on electrochromics for several years. However, there are numerous other applications as well, especially with regard to foil-type devices. These can be applied, for example, in ski goggles and visors for motorcycle helmets. These visors can be colored to a chosen degree in the day and bleached in the night. It is especially important that the driving and riding safety can be improved by having the visor bleach before entering tunnels or other dark spaces. Another aspect with a bearing on safety is that facial warming can be signiﬁcantly limited by absorption in the visor [36]. Figure 13.6 illustrates a visor in a motorcycle helmet.

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Fig. 13.5. “Smart window” prototype with four 30 × 30 cm2 panels

Fig. 13.6. Electrochromic visor for a motorcycle helmet in colored and bleached states

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13.5 Conclusion and Outlook Electrochromism was discovered and made publicly known many years ago [37]. However, the progress of EC device technology has been slow. A number of reasons for this were given above. Buildings with “smart windows” based on electrochromism have been tried by the glass and coatings industry for decades, and more or less encouraging results have been reported. For one reason or another, these “smart windows” have not made it to the market. Today, however, the scene seems to be changing and EC roof windows for buildings [38] as well as EC car roofs [39] are available on a limited commercial scale. These EC devices use glass as a base, implying that large substrates and expensive coating units must be used. But cheap production of EC devices is necessary if the technology will be used elsewhere than in niche markets. An alternative route, using web coating by technologies allowing roll-to-roll manufacturing, is now employed for EC prototypes [29]. This EC foil was discussed above. What about the future of electrochromics? Windows with tunable optical properties have long been something of a Holy Grail in “high-tech” architecture [40]. Electrically regulated EC “smart windows” are particularly interesting in view of their potential to provide user-related operation. Such windows make it possible to combine increased indoor comfort for the occupant of the building (less glare and thermal stress) with large energy eﬃciency (especially lowered air conditioning load in cooled spaces), as emphasized above. Therefore, there is a strong incentive for their introduction. Durability, optical switching speed, and size constraints constitute an interrelated problem complex which is not fully solved today. However, consensus is growing that a satisfactory solution can indeed be achieved. Cost is another major concern, but recent progress in manufacturing technology – such as roll-toroll coating of polymer foil – appears to open new avenues toward inexpensive products. It should be realized that electrochromism is an enabling technology of relevance for a vast number of applications, so there may be multiple roads toward devices eventually used in buildings. Contemplating the combined blessings of comfort and energy savings, the recent advances in technology, and the undeniable business opportunities, it may not be far fetched to envisage a gradual introduction of EC “smart windows” on a large scale within a few decades, perhaps leading to such windows being the norm rather than exception in the same way that fenestration with “static” surface-coated glass is today the norm for a number of markets. The EC technology may be combined with facilities to direct daylight deeply into buildings by use of light-guiding devices. By equalizing the light level in a room, the eye – which tends to adjust to the brightest illumination – does not perceive deeper regions as disturbingly dark, and hence there is less need for artiﬁcial lighting. Similar notions, though employing a Venetian blind system, have been discussed recently [41, 42]. Generally speaking, the EC technology leads to new vista in daylighting, which is generally regarded

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as superior to artiﬁcial lighting by giving better task performance, improved visual comfort, and positive mood eﬀects, especially if glare problems are eliminated [43]. Particularly, beneﬁcial eﬀects have been observed concerning student performance in daylit schools [44] and increased sales in daylit stores [45]. On the speculative side, membrane architecture [46, 47] may be merged with EC foil technology to allow lightweight buildings with little embodied energy. These notions are perfectly in tune with “intelligent buildings” [48] and “smart skins” [49]. One can envisage huge membranes allowing the ﬂow of visible light and solar energy to be controlled and optimized. The possibilities oﬀered by such membranes (although then based on glass technology) were in fact pointed out more than 50 years ago by the great visionary Buckminster Fuller [50]. Perhaps this grand vision will come true one day – thanks to electrochromics.

References 1. C.G. Granqvist, Appl. Opt. 20, 2606 (1981) 2. C.G. Granqvist, Adv. Mater. 15, 1789 (2003) 3. C.M. Lampert, C.G. Granqvist (eds.), Large-Area Chromogenics: Materials and Devices for Transmittance Control (SPIE – The International Society for Optical Engineering, Bellingham, 1990) 4. C.G. Granqvist, Handbook of Inorganic Electrochromic Materials (Elsevier, Amsterdam, 1995) 5. M.A. Darwish, Kuwait J. Sci. Eng. 32, 209 (2005) 6. C.G. Granqvist, Sol. Energy Mater. Sol. Cells 92, 203 (2008) 7. M. Santamouris, in Solar Energy: The State of the Art, ed. by J. Gordon (James & James Science Publishers, London, 2001), pp. 1–28 8. C.F. Reinhart, The Future for Renewable Energy 2 (James & James Science Publishers, London, 2002), pp. 79–114 9. J.S.E.M. Svensson, C.G. Granqvist, Sol. Energy Mater. 12, 391 (1985) 10. A. Roos, M.-L. Persson, W. Platzer, M. K¨ ohl, Proceedings of the Glass Processing Days (Tampere, Finland, 2005), pp. 566–569 11. E.S. Lee, D.L. DiBartolomeo, S.E. Selkowitz, Energy Buildings 38, 30 (2006) 12. E.S. Lee, S.E. Selkowitz, R.D. Clear, D.L. DiBartolomeo, J.H. Klems, L.L. Fernandes, G.J. Ward, V. Inkarojrit, M. Yazdanian, Advancement of Electrochromic Windows (California Energy Commission, PIER, 2006), CEC-5002006-052, 87 pages 13. R.D. Clear, V. Inkarojrit, E.S. Lee, Energy Buildings 38, 758 (2006) 14. N.I. Jaksic, C. Salahifar, Sol. Energy Mater. Sol. Cells 79, 409 (2003) 15. A. Azens, C.G. Granqvist, J. Solid State Electrochem. 7, 64 (2003) 16. C.G. Granqvist, A. Hult˚ aker, Thin Solid Films 411, 1 (2002) 17. C.G. Granqvist, in Materials Science for Solar Energy Conversion Systems, ed. by C.G. Granqvist (Pergamon, Oxford, 1991), pp. 106–167 18. K.G.T. Hollands, J.L. Wright, C.G. Granqvist, in Solar Energy: The State of the Art, ed. by J. Gordon (James & James Science Publishers, London, 2001), pp. 29–107

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19. C.G. Granqvist, Sol. Energy Mater. Sol. Cells 91, 1529 (2007) 20. U. Schwartz-Schampera, P.M. Herzig, Indium: Geology, Mineralogy, and Economics (Springer, Berlin Heidelberg New York, 2002) 21. A. Feltrin, A. Freundlich, Conference Record of the 2006 IEEE 4th World Conference on Photovoltaic Energy Conversion, vol. 2, pp. 2469–2472 22. C.G. Granqvist, Sol. Energy Mater. Sol. Cells 60, 201 (2000) 23. C.G. Granqvist, E. Avenda˜ no, A. Azens, Thin Solid Films 442, 201 (2003) 24. J. Backholm, A. Azens, G.A. Niklasson, Sol. Energy Mater. Sol. Cells 90, 414 (2006) 25. E. Avenda˜ no, A. Azens, G.A. Niklasson, C.G. Granqvist, Sol. Energy Mater. Sol. Cells 84, 337 (2004) 26. G.A. Niklasson, C.G. Granqvist, J. Mater. Chem. 17, 127 (2007) 27. S.K. Deb, Sol. Energy Mater. Sol. Cells 39, 191 (1995) 28. A. Azens, L. Kullman, C.G. Granqvist, Sol. Energy Mater. Sol. Cells 76, 147 (2003) 29. C.G. Granqvist, Nat. Mater. 5, 89 (2006) 30. J.A. Thornton, Annu. Rev. Mater. Sci. 7, 239 (1977) 31. I. Hamberg, C.G. Granqvist, J. Appl. Phys. 60, R123 (1986) 32. J. Rodr´ıguez, M. G´ omez, J. Lu, E. Olsson, C.G. Granqvist, Adv. Mater. 12, 341 (2000) 33. A. Azens, G. Gustavsson, R. Karmhag, C.G. Granqvist, Solid State Ionics 165, 1 (2003) 34. A. Azens, A. Avenda˜ no, J. Backholm, L. Berggren, G. Gustavsson, R. Karmhag, G.A., Niklasson, A. Roos, C.G. Granqvist, Mater. Sci. Eng. B 119, 214 (2005) 35. A. Azens, private communication 36. M. Buyan, P.A. Br¨ uhwiler, A. Azens, G. Gustavsson, R. Karmhag, C.G. Granqvist, Int. J. Ind. Ergonom. 36, 11 (2005) 37. S.K. Deb, Philos. Mag. 2, 801 (1973) 38. N.L. Sbar, H.E. Sanders, Proceedings of the 48th Annual Technical Conference (Society of Vacuum Coaters, Albuquerque, 2005), pp. 679–680 39. D. Pender, J.-C. Giron, Abstract Volume, Fall Meeting, Mater. Res. Soc., 110 (2005) 40. M. Wigginton, Glass in Architecture (Phaidon, London, 1996) 41. L.O. Beltr´ an, E.S. Lee, S.E. Selkowitz, J. Illum. Eng. Soc. 26(2), 91 (1997) 42. B.G. Martins-Mogo, L.O. Beltr´ an, in Conference Proceedings: EuroSun 2006, Glasgow, UK, ed. by S. Burek, M.G. Hutchins, H. Lockhart-Ball, S. Abrahamson (The Solar Energy Society, Abingdon, 2006), 6 pages 43. V. Gligor, The Luminous Environment and Oﬃce Productivity, Technical Licentiate Thesis, Department of Electrical and Communication Engineering, Helsinki University of Technology, 2004 44. L. Heshong, R.L. Wright, S. Okura, J. Illum. Eng. Soc. 31, 101 (2002) 45. L. Heshong, R.L. Wright, S. Okura, J. Illum. Eng. Soc. 31, 21 (2002) 46. K. Ishii (ed.), Membrane Designs and Structures in the World (Shinkenchikusha, Tokyo, 1999) 47. K.-M. Koch (ed.), Membrane Structures (Prestel, Munich, 2004) 48. H.W. Kua, S.E. Lee, Building Environ. 37, 231 (2002) 49. D. De Rossi, F. Carpi, E.P. Scilingo, Adv. Colloid Interface Sci. 116, 165 (2005) 50. M.J. Gorman, Buckminster Fuller: Designing for Mobility (Skira, Milan, 2005)

14 Atomic Assembly of Magnetoresistive Multilayers H. Wadley, X. Zhou, and W.H. Butler

14.1 Introduction The continuing ability to create ever higher performance microelectronic and photonic devises has underpinned many of the most important technological developments of the last 50 years. Many of today’s nanoscopically structured devices are made by controlling the condensation of an atomic or molecular vapor at the surface of a substrate. The shapes of the resulting objects and that of the numerous materials within them are controlled using patterning methods and selective etching methods which have been facilitated by rapid advances in lithographic technologies. As technologists seek to incorporate new materials with novel functionalities into their microsystems and devices, the structures they seek to grow have increased in both chemical and structural complexity. The nature of the interfaces between the dissimilar materials used in these devices has also become a critical issue. The research community has responded to these challenges by developing new vapor deposition tools that can precisely control the vapor plumes incident upon a patterned substrate. These tools also attempt to manipulate and control the subsequent chemical reactions and physical assembly processes that occur on and within the vapor deposited ﬁlm. The complexity of this has motivated interest in techniques that permit the visualization of the assembly processes, either experimentally or by modeling and simulation. This chapter is a case study in the application of atomistic modeling and simulation tools to the reactive, ion-assisted vapor deposition of multilayered structures. It is motivated by eﬀorts over the past decade to create a new generation of microelectronic devises that exploit giant magnetoresistive materials. We describe the origins of this eﬀect and the role of the atomic scale defects that can signiﬁcantly reduce the performance of devices. We then introduce an atomistic modeling framework. It is based upon a coupling of precise representations of interatomic force laws for the material systems of interest with high performance molecular dynamics simulation techniques. These tools are used to systematically investigate the deposition of metallic

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multilayers and the growth of dielectric tunneling barriers linking the results with experimentally obtained high resolution images and other atomic scale characterizations of the materials. This has resulted in new insights into the ways in which defects are formed during the atomic assembly process which have led to the development of new deposition tools that seek to eliminate them. This aspect is also addressed in the chapter. 14.1.1 Giant Magnetoresistance New microelectronic devices that make use of electron spin as well as charge have become important in recent years [1–6]. Many are based upon giant magnetoresistance (GMR) [7, 8] and related magnetic tunnel junction (MTJ) [9– 12] multilayers. GMR multilayers are composed of 20–50 ˚ A thick magnetic metal layers based on NiCoFe alloys that sandwich a 20–30 ˚ A thick conductive metal spacer layer such as copper. MTJ multilayers are composed of a pair of 20–50 ˚ A thick NiCoFe alloy layers sandwiching a 10–20 ˚ A thick metal oxide or nitride layer. Both systems can exhibit a large change in their electrical resistance when an external magnetic ﬁeld is varied. These multilayers have been successfully utilized as read head sensors [13–15] by the magnetic recording industry and they may soon form the basis for a new class of nonvolatile magnetic random access memories (MRAM) [15, 16]. Because GMR read heads are highly sensitive, and small in area, the storage capacity of hard disk drives using GMR read heads has been signiﬁcantly increased compared to that achieved using earlier read head material concepts based upon anisotropic magnetoresistance [15]. The MTJ multilayers have dielectric tunnel barriers and are used for nonvolatile MRAM [10,17] as well as for magnetic ﬁeld sensing [18, 19]. Related systems are also being evaluated for spin injection [20] in various spintronic devices [21]. These applications require that the multilayers have a high-GMR ratio (deﬁned as the maximum resistance change divided by the resistance at magnetic saturation), a low saturation magnetic ﬁeld, a high sensitivity (large change in resistance for a small change in applied ﬁeld), a near zero coercivity, a weak temperature dependence, and a high thermal stability. The GMR eﬀect was ﬁrst found in multilayers in 1988 [7, 8]. Experiments [7, 8, 22] and theoretical analyses [23–26] indicated that the eﬀect is strongest when the magnetically inhomogeneous regions are suﬃciently small that the electron mean free path encompasses them. A signiﬁcant reduction in the electrical resistance then occurs if antialigned ferromagnetic moments in diﬀerent regions of the material are aligned by an applied magnetic ﬁeld. Several approaches have been devised to achieve the initial antialignment of the ferromagnetic moments. One utilizes the oscillatory exchange interaction that propagates through the spacer layer [27]. Certain discrete thicknesses (such as 10, 20, 35 ˚ A, etc.) of the spacer layer give a peak in the antialignment force. However, in this state, the magnetic coupling between the layers is usually so strong that a large magnetic ﬁeld is then required to align the moments

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Fig. 14.1. Example of a spin valve in which a FeMn antiferromagnetic layer is used to pin the magnetic moment of a thin Co layer. The moment of the NiFe “sense” layer is able to rotate in response to applied magnetic ﬁelds. The resulting changes to the devises electrical resistivity can be used to detect and measure the applied ﬁeld

to obtain the desired GMR eﬀect. Spin valve structures have been developed to overcome this problem. A schematic example is shown in Fig. 14.1. The thickness of the nonmagnetic Cu spacer layer is chosen to be 25 ˚ A, which is larger than the thickness for the second exchange coupling peak. This eﬀectively avoids the strong exchange coupling between the two magnetic layers. The magnetic moment alignment control is then achieved by using a relatively thick (110 ˚ A) antiferromagnetic FeMn layer to pin the moment of the bottom (22 ˚ A thick) Co layer while allowing the moment of the other ferromagnetic layer to freely respond to an applied ﬁeld. Resistivity changes in GMR multilayers can be measured when an electric current is ﬂowed either perpendicular or parallel to the layers. The former are known as current perpendicular to the plane (CPP) while the latter are referred to current in the plane (CIP). While CIP-GMR read head sensors have been widely utilized, enhancements to their properties are continuously being sought because of their promise for improving the performance of hard disk drives.

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In CIP conﬁgurations, a potential diﬀerence is established along an inplane direction. If the thicknesses of the layers are much smaller than the electron mean free paths, the electrons on the average, traverse many layers without being spin ﬂip scattered as they drift along the in-plane direction. For binary multilayers, the resistance contributed by each spin channel is then proportional to the eﬀective electron scattering rate for that channel. Let us denote the two average scattering rates by 1/t⇑ and 1/t⇓ for spins that are locally majority (up) and minority (down), respectively. In the parallel (P ) moments conﬁguration, the resistance for the majority spin channel (R⇑ ) and for the minority spin channel (R⇓ ) is then proportional to 1/t⇑ and 1/t⇓ , respectively. The current contributed by each spin channel adds in parallel so the total resistance of the bilayer system with parallel moments is R(P ) =

R⇑ R⇓ . R⇑ + R⇓

(14.1)

In the antiparallel (AP) conﬁguration, the average scattering rate for each spin channel will be (1/2)(1/t⇑ + 1/t⇓ ), since each spin channel is a majority spin in half the ferromagnetic layers, and a minority spin in the other half. Again, due to the absence of spin-ﬂip scattering, the two spin channels conduct in parallel. In terms of R⇑ and R⇓ for the parallel alignment, the total resistance of the AP conﬁguration becomes R(AP) =

R⇑ + R⇓ . 4

(14.2)

The GMR ratio, in the limit of thin layers, is then given by GMR(CIP)thin =

(R⇑ − R⇓ )2 . 4R⇑ R⇓

(14.3)

The “thick” limit occurs when the layer thicknesses are much larger than the electron mean free paths. The conductivity can then be treated as local, and there is no diﬀerence between the CIP conductance for parallel and antiparallel moment alignment and thus GMR is zero. MTJs devices exploit the phenomenon of tunneling magnetoresistance (TMR) which was ﬁrst discovered by Julliere [9] in 1975 using Fe/Ge/Co sandwich structures tested at very low temperatures. The magnetoresistance observed for this material system was very small and it attracted little technological interest. However, about 10 years ago it was found that MTJ consisting of a pair of ferromagnetic metals separated by a thin (∼1.5 nm) alumina dielectric tunnel barrier [10, 11] exhibited a much larger TMR ratio of ∼40–50% at ambient temperature [12]. These MTJ multilayers are beginning to be used for nonvolatile magnetic random access memory [10, 17] and for magnetic ﬁeld sensing [18,19]. Such TMR memories are interesting because they promise a number of special properties, such as nonvolatility, radiation hardness, low power consumption, densities comparable to dynamic random

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access memory and access speeds comparable to static random access memory [13,15,28]. The nonvolatility eliminates the need to read information from hard disks each time the machine is started, it is hence possible to design computers with instantaneous reboot capability. It also permits the possibility of restoring a calculation after power interruption. Related tunneling barriers can also be used for spin injection [20] in spintronic devices [21]. Both a high tunneling conductance and TMR eﬀect are desirable for all these applications [10, 15, 18, 19]. The TMR eﬀect arises because electrons can tunnel through the oxide barrier layer when the magnetic moments of the two ferromagnetic layers are aligned. The TMR eﬀect can be easily explained using Julliere’s theory [9], which assumes that the tunneling rate is proportional to the product of the Fermi energy density of states of the two magnetic electrodes. Let us denote the majority Fermi energy densities of states of the bottom and top magnetic layers by Nb and Nt respectively, and the minority Fermi energy densities of states of the bottom and top magnetic layers by nb and nt , respectively. When the magnetic moments of the two magnetic layers are parallel, the states Nb and Nt have the same spin direction and so do the nb and nt states. As a result, the tunneling current (which depends upon the layer polarization) has the form I(P ) ∝ Nb Nt + nb nt . (14.4) When the magnetic moments are antialigned, the states nb and Nt have the same spin direction and the states Nb and nt have the other spin direction. As a result, the tunneling current can be expressed as I(AP) ∝ nb Nt + Nb nt .

(14.5)

Deﬁning the polarization of the bottom and top magnetic layers as Pb =

N b − nb N b + nb

(14.6)

Pt =

N t − nt . N t + nt

(14.7)

and

Then the TMR change is given by TMR =

2Pb Pt I(P ) − I(AP) = . I(AP) 1 − Pb Pt

(14.8)

It can be seen that when the materials are associated with a high-polarization value, a very high-TMR ratio can be obtained. 14.1.2 Atomic Scale Structure Eﬀects The performance of spin valve devices is optimized when they have a high resistance in the AP state, R(AP), a low resistance in the P state, R(P ),

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and can be easy to switch from one state to the other by a small magnetic ﬁeld. The requirement that the moment of one layer rotates easily upon the application of relatively small ﬁelds implies that this layer must have low magnetocrystalline anisotropy and a low magnetostriction. The magnetocrystalline anisotropy causes the moments to prefer to point in certain directions determined by the local crystalline axes. Magnetostriction is a very small change in the dimensions of the sample with direction of the magnetic ﬁeld. It can inhibit rotation of the moments by setting up an elastic interaction in the crystal. Fortunately, certain permalloys (because of their high permeability) comprised of Ni with smaller amounts of Fe and Co have both low magnetocrystalline anisotropy and magnetostriction. Permalloys also have relatively good electrical transport properties that make them well suited for applications in spin valve devices. Practical requirements for the magnetic and electrical properties of spin valve devices generally dictate that at least one of the magnetic layers should be a permalloy [29]. The need for low switching ﬁelds translates into a requirement that interfaces in a spin valve should be very smooth at the nanometer scale. Roughness on this level, especially when it is conformal so that the hills in the layers occur at the same lateral positions in the two ferromagnetic layers, leads to a dipolar magnetic coupling called “orange peel” coupling. This coupling greatly increases the diﬃculty of rotating the moment of one magnetic layer relative to that of the other. Most space layers are made from copper which is a nonmagnetic metal that can be grown easily as a low resistivity ﬁlm. It also can provide a good match to permalloys in the majority spin channel. To increase the antiparallel resistance, Co is usually added at the interface to worsen the matching in the minority channel. The Co can also help prevent intermixing between Cu and permalloy and increases the exchange coupling near the interface between the magnetic and spacer layers. As a result, Co/Cu [30] and the Co/NiFe/Co/Cu [31] multilayers have been found to give high GMR ratios. Generally, interdiﬀusion (i.e. mixing or alloying) at the interfaces between the magnetic and nonmagnetic layers needs be avoided [25, 32]. There are several reasons. When Ni diﬀuses into Cu, it can lose its moment and become a center for spin-independent scattering that reduces the GMR ratio. If Fe or Co diffuse into Cu, an even worse eﬀect arises because they maintain their moment and cause spin-ﬂip scattering. These insights indicate that the interfaces should be smooth at both the intermediate length scales (to avoid orange peel coupling) and the atomic length scale (to avoid spin-ﬂip scattering by magnetic atoms that are not strongly coupled to the moments in the magnetic layer). For CIP Cu/Co multilayers, one can also obtain an increase in the GMR that arises from certain properties of the electronic structure of Co and Cu if the interfaces are atomically smooth. The majority Fermi surface of Co is slightly smaller than the Fermi surface of Cu. This allows majority electrons in Cu traveling in certain directions (nearly parallel to the layers) to be totally reﬂected at

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the Cu−Co interface. This will happen on both sides of the Cu layer if the moments in the ferromagnetic layers are aligned parallel but on only one side if they are antiparallel. Because these electrons stay in the Cu layer where the resistivity is low, the parallel resistance is signiﬁcantly decreased and the GMR is increased. This “wave guide” eﬀect is most eﬀective for atomically smooth interfaces. To summarize, various experimental and theoretical studies have shown that the magnetotransport properties are highly sensitive to the nanoscale layer thickness, interfacial roughness [33] and interlayer chemical mixing of the multilayers [25, 32]. While the intrinsic properties of the material system are important, other nanoscale structural features are also critical. These include layer composition [34,35], interfacial impurities [36], layer texture [37], any buﬀer layer material [38], the presence of surfactants during growth [39], the grain size/morphology of each layer, various lattice defects (vacancies, voids, dislocations, and twins), and perhaps residual stress. While numerous materials have been investigated for use as a barrier layer, including AlN [40], and MgO [41], amorphous AlOx is the most widely used barrier layer today [11]. The AlOx layers are usually created by oxidizing a predeposited aluminum layer. Measurements of the TMR of ferromagnetic metal/AlOx MTJ multilayers as a function of the aluminum layer thickness prior to oxidation [42, 43] have revealed a rapid rise in TMR as the barrier thickness is reduced [42]. However, these measurements also reveal a surprising abrupt disappearance of the TMR when the aluminum thickness is reduced below ∼8 ˚ A. It is thought that this arises because of the formation of discontinuous AlOx layers [43, 44]. The subsequent deposition of the top ferromagnetic layer on an aluminum oxide layer containing holes then creates regions of metal-to-metal contact and a high conductance path for electron transport that bypasses the tunneling barrier. First principles calculations indicate that the conductance and TMR [45– 48] are both sensitive to the barrier layer thickness. They also indicate that the magnitude of the TMR eﬀect depends sensitively upon the barriers height relative to that of the conduction band of the ferromagnetic layer. It also depends on the ﬂatness of the barrier-ferromagnetic metal interface and the perfection of bonding at the interface between the barrier and the ferromagnetic metal. For an ideal structure, the tunnel junction oxide layers should be as thin as possible since the resistance through the insulator barrier layer increases exponentially with the layer thickness. Again, uniform thickness layers with very smooth interfaces are essential for the magnetic coupling between ferromagnetic layers. Chemical mixing between the diﬀerent layers must also be reduced. In addition to mixing in ferromagnetic layers (which may cause a loss of their magnetic properties), mixing in the oxide layer can change its oxidation state. Both can change the eﬀective thickness of the ferromagnetic and tunnel barrier layers. The oxide layers are usually synthesized by oxidation of a predeposited metal layer. As indicated above, if the oxide layer becomes too thin, pinholes form, which cause magnetic short circuits between the adjacent

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ferromagnetic layers. Over-oxidation may also occur in the ferromagnetic layer underlying these pinhole regions. On the other hand, if the metal layer to be oxidized is too thick, a part of the layer may not be suﬃciently oxidized. Even if the layer is fully oxidized, too thick an oxide layer can signiﬁcantly increase the resistance and reduce the TMR ratio. Finally, if the metal surface prior to oxidation is too rough, over oxidation may occur at some spots. The TMR properties then vary from place to place to such an extent that the economical manufacture of the devices on large area substrates becomes impossible. 14.1.3 Deposition and Growth Processes A wide variety of vapor deposition methods have been explored for depositing GMR structures including molecular beam epitaxy (MBE), RF diode sputtering, magnetron sputtering (simpliﬁed as magnetron) and ion beam deposition (IBD). Although the ﬁrst GMR multilayers were discovered using MBE deposition method [7], the method does not yield good GMR properties. Since MBE provides sophisticated control of purity and near thermal equilibrium growth conditions, this observation is somewhat surprising. The sputtering methods including the IBD approaches produce much better GMR properties. The diﬀerence in the GMR properties obtained using these diﬀerent deposition methods must arise from the diﬀerence in the fundamental processing conditions provided by diﬀerent methods. MBE uses evaporation techniques to create depositing vapor plumes that can condense on a substrate surface. The energy of the depositing atoms is near the thermal energy at the melting temperature, typically around 0.1 eV. In sputtering methods, the depositing atoms are created by high energy ion impacts with the target surface. These sputtered atoms have energies between 5 and 30 eV, and are distributed near a cosine distribution with a peak at normal ejection [49]. They are then transported to the substrate and are deposited on the substrate surface. Due to the collisions with the background inert gas atoms during the transport, the energy of the adatoms at the substrate is generally lower than the energy of the sputtered atoms leaving the target. The background pressure therefore provides an important means for controlling adatom energy [50]. In practice, the adatom energy is controlled by selecting a sputtering power, chamber pressure, sputtering gas type and target-substrate distance [51]. Sputtering methods permit inert gas ions to also irradiate the growth surface and assist the surface reconstruction. The thermally activated diﬀusion active during high temperature, low rate deposition can cause interlayer mixing and needs to be avoided during the growth of GMR multilayers. Kano et al. have carried out DC magnetron sputtering depositions of [Co(10 ˚ A)/Cu(10 ˚ A)]100 multilayers at diﬀerent temperatures [52]. They found that the highest GMR ratio was always obtained at the lowest temperature they explored (room temperature). Similarly, experiments have shown that decreasing the deposition rate does not enhance the performance of vapor deposited GMR ﬁlms [53]. Analogous considerations

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apply to the deposition of the metal layers used in the MTJ multilayers. These can usually be grown by sputtering methods [10, 12, 54] while evaporation methods can be used to deposit the aluminum layers used for AlOx barriers [11] since ﬂat, uniform aluminum layers are relatively easily grown by this method.

14.2 Atomistic Simulations The ﬁlm structure formed during reactive sputtering can be studied by several “atomistic” approaches. Ab initio or density-function calculations can be used to determine the energetics, crystal structures, lattice constants, elastic constants, and diﬀusion energy barriers. However, these quantum-mechanical calculations are currently too computationally intensive to permit an exploration of the structures and morphologies that arise in the larger scale systems containing more than 200 atoms. When accurate interatomic potentials are available, it is possible to simulate the structure of thousands or even millions of atoms using molecular dynamics (MD) and therefore to attack problems motivated by the GMR or TMR multilayers. Such potentials also provide a convenient means to identify fundamental phenomena such as diﬀusion mechanisms and to calculate the energy barriers for mass transport either in bulk or at the surface of a material [55]. This information can in turn be used in vary large scale Monte Carlo simulations of structure evolution [56]. 14.2.1 Interatomic Potentials The results of molecular dynamics simulations can only be trusted when interatomic potential functions utilized accurately capture the interatomic forces in the system of interest. In close packed metal systems the forces are roughly spherically symmetric simplifying the functional forms considerably. Complexities are introduced when alloys must be modeled or when a simulation of an interface between two elements is addressed or when the eﬀects of inert gas impacts are studied. Nonmetallic contributions to the binding of many systems of interests (especially the metal oxides used for dielectric barriers) have also forced the use of more complex representations of the forces between atoms and ions. The issues that have led to the potentials used here are discussed below. Metallic Systems The embedded atom method (EAM) potential originally proposed by Daw and Baskes [57] is a high-ﬁdelity interatomic potential widely used for modeling metals (especially the fcc metals). The EAM potential represents well the radically symmetric metallic cohesion that arises from embedding ions in a

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gas of free electrons. Such an embedding energy physically incorporates the many-body eﬀects of the atomic interactions. As a result, EAM potentials have been widely utilized to simulate atomic assembly mechanisms and to investigate the atomic structures of the vapor deposited structures that exhibit GMR eﬀects [58–60]. The original EAM potentials were developed for ensembles of single element atoms and therefore cannot simply be used to model alloys [61]. In addition, the potential cutoﬀ distances where the potential falls to zero is also diﬀerent for individual elemental potentials. A procedure has been developed to create a generalized EAM potential that enables calculations of alloys with any combination of 16 metals (Cu, Ag, Au, Ni, Pd, Pt, Al, Pb, Fe, Mo, Ta, W, Mg, Co, Ti, and Zr) [58, 62, 63]. These potentials are well ﬁtted to basic material properties such as lattice constants, elastic constants, bulk moduli, vacancy formation energies, sublimation energies, and heats of solution. The use of molecular dynamics for the simulation of GMR multilayer assembly from alloy vapors reported here has now become possible due to the development of this potential database. We begin by describing this EAM potential. In EAM potentials, the total energy, E, of a metal atom system can be expressed in the form: E=

1 2

N

φij (rij ) +

i=1,j=1,i =j

N

Fi (ρi ),

(14.9)

i=1

where φij represents the pair interaction energy between two atoms i and j separated by a distance rij . Fi stands for the embedding energy and can be thought of as the energy to embed an atom i into a local site where the electron density is ρi . This electron density can be calculated using ρi =

N

fj (rij ),

(14.10)

j=1,j =i

with fj (rij ) the electron density at the site of atom i arising from atom j at a distance rij away. Alloy EAM potentials can be constructed from elemental EAM potentials by appropriately normalizing the potentials [61] and introducing a uniﬁed cutoﬀ function. The generalized pair potentials take the form: , , A exp −α rre − 1 B exp −β rre − 1 φ(r) = − (14.11) 20 20 , 1 + rre − κ 1 + rre − λ where re is the equilibrium spacing between the pair of atoms, A, B, α, β are four adjustable parameters, and κ, λ are two additional parameters that deﬁne the cutoﬀ.

14 Atomic Assembly of Magnetoresistive Multilayers

507

The electron density function is taken with the same form as the attractive term in the pair potential with the same values of β, and λ: , fe exp −β rre − 1 (14.12) f (r) = 20 . 1 + rre − λ Using the alloy model [61], the pair potential between diﬀerent species a and b can be constructed as a weighted sum of the elemental potentials: 1 f b (r) aa f a (r) bb φ φ (r) + (r) . (14.13) φab (r) = 2 f a (r) f b (r) For the embedding energy functions to work well over a wide range of electron densities, three equations are used to separately ﬁt the electron density in diﬀerent ranges. For a smooth variation of the embedding energy, these equations are required to match values and slopes at their junctions. The equations used take the form:

i ρ − 1 , ρ < ρn , ρn = μρe , ρn i=0 i 3 ρ F (ρ) = Fi − 1 , ρn ≤ ρ < ρo , ρo = νρe , ρe i=0

η η ρ ρ , ρo ≤ ρ. F (ρ) = Fe 1 − ln ρs ρs

F (ρ) =

3

Fni

(14.14)

(14.15) (14.16)

The parameters needed to deﬁne all the 16 metals using this alloy EAM potential format are listed in Table 14.1. Inert Gas Interactions To simulate the eﬀects of inert gas atom or ion impacts with the atoms in a surface during sputtering or ﬁlm growth, both the inert gas – inert gas and inert gas – metal atom interactions must be known. These interactions can be well approximated by a pairwise universal potential [64]. In the universal potential, the pair energy (in eV), Eij , between two atoms i and j, is expressed as Eij = 14.4

4 & ' Zi Zj bk exp ck rij (Zi0.23 + Zj0.23 ) , rij

(14.17)

k=1

˚, and where Zi and Zj are the atomic numbers of species i and j, rij is in A the constants b1 = 0.181, b2 = 0.5099, b3 = 0.2802, b4 = 0.02817, c1 = −6.8323, c2 = −2.0113, c3 = −0.8600, c4 = −0.4303. The coeﬃcients of the

Element r e (˚ A) fe ρe ρs α β A (eV) B (eV) κ λ Fn0 (eV) Fn1 (eV) Fn2 (eV) Fn3 (eV) F0 (eV) F1 (eV) F2 (eV) F3 (eV) η Fe (eV) μ ν

Ag 2.891814 1.106232 14.604100 14.604144 9.132010 4.870405 0.277758 0.419611 0.339710 0.750758 −1.729364 −0.255882 0.912050 −0.561432 −1.75 0 0.744561 −1.150650 0.783924 −1.748423 0.85 1.15

Cu

2.556162 1.554485 21.175871 21.175395 8.127620 4.334731 0.396620 0.548085 0.308782 0.756515 −2.170269 −0.263788 1.088878 −0.817603 −2.19 0 0.561830 −2.100595 0.310490 −2.186568 0.85 1.15

2.885034 1.529021 19.991632 19.991509 9.516052 5.075228 0.229762 0.356666 0.356570 0.748798 −2.937772 −0.500288 1.601954 −0.835530 −2.98 0 1.706587 −1.134778 1.021095 −2.978815 0.85 1.15

Au 2.488746 2.007018 27.562015 27.930410 8.383453 4.471175 0.429046 0.633531 0.443599 0.820658 −2.693513 −0.076445 0.241442 −2.375626 −2.70 0 0.265390 −0.152856 0.469000 −2.699486 0.85 1.15

Ni 2.750897 1.595417 21.335246 21.940073 8.697397 4.638612 0.406763 0.598880 0.397263 0.754799 −2.321006 −0.473983 1.615343 −0.231681 −2.36 0 1.481742 −1.675615 1.130000 −2.352753 0.85 1.15

Pd

Table 14.1. EAM parameters for metals

2.771916 2.336509 33.367564 35.205357 7.105782 3.789750 0.556398 0.696037 0.385255 0.770510 −1.455568 −2.149952 0.528491 1.222875 −4.17 0 3.010561 −2.420128 1.450000 −4.145597 0.25 1.15

Pt 2.863924 1.403115 20.418205 23.195740 6.613165 3.527021 0.314873 0.365551 0.379846 0.759692 −2.807602 −0.301435 1.258562 −1.247604 −2.83 0 0.622245 −2.488244 0.785902 −2.824528 0.85 1.15

Al

3.499723 0.647872 8.450154 8.450063 9.121799 5.212457 0.161219 0.236884 0.250805 0.764955 −1.422370 −0.210107 0.682886 −0.529378 −1.44 0 0.702726 −0.538766 0.935380 −1.439436 0.85 1.15

Pb

508 H. Wadley et al.

˚) r e (A fe ρe ρs α β A (eV) B (eV) κ λ Fn0 (eV) Fn1 (eV) Fn2 (eV) Fn3 (eV) F0 (eV) F1 (eV) F2 (eV) F3 (eV) η Fe (eV) μ ν

2.481987 1.885957 20.041463 20.041463 9.818270 5.236411 0.392811 0.646243 0.170306 0.340613 −2.534992 −0.059605 0.193065 −2.282322 −2.54 0 0.200269 −0.148770 0.391750 −2.539945 0.85 1.15

2.728100 2.723710 29.354065 29.354065 8.393531 4.476550 0.708787 1.120373 0.137640 0.275280 −3.692913 −0.178812 0.380450 −3.133650 −3.71 0 0.875874 0.776222 0.790879 −3.712093 0.85 1.15

2.860082 3.086341 33.787168 33.787168 8.489528 4.527748 0.611679 1.032101 0.176977 0.353954 −5.103845 −0.405524 1.112997 −3.585325 −5.14 0 1.640098 0.221375 0.848843 −5.141526 0.85 1.15

2.740840 3.487340 37.234847 37.234847 8.900114 4.746728 0.882435 1.394592 0.139209 0.278417 −4.946281 −0.148818 0.365057 −4.432406 −4.96 0 0.661935 0.348147 0.582714 −4.961306 0.85 1.15

3.196291 0.544323 7.132600 7.132600 10.228708 5.455311 0.137518 0.225930 0.5 1.0 −0.896473 −0.044291 0.162232 −0.689950 −0.90 0 0.122838 −0.226010 0.431425 −0.899702 0.85 1.15

2.505979 1.975299 27.206789 27.206789 8.679625 4.629134 0.421378 0.640107 0.5 1.0 −2.541799 −0.219415 0.733381 −1.589003 −2.56 0 0.705845 −0.687140 0.694608 −2.559307 0.85 1.15

2.933872 1.863200 25.565138 25.565138 8.775431 4.680230 0.373601 0.570968 0.5 1.0 −3.203773 −0.198262 0.683779 −2.321732 −3.22 0 0.608587 −0.750710 0.558572 −3.219176 0.85 1.15

3.199978 2.230909 30.879991 30.879991 8.559190 4.564902 0.424667 0.640054 0.5 1.0 −4.485793 −0.293129 0.990148 −3.202516 −4.51 0 0.928602 −0.981870 0.597133 −4.509025 0.85 1.15

14 Atomic Assembly of Magnetoresistive Multilayers 509

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universal potential have been ﬁtted to extensive experimental data for low energy ion bombardment of solid surfaces. As a result, the potential represents well the interactions between atoms of a metal surface and inert gas atoms or ions in the vapor phase. Metallic to Ionic Transitions When a metal is oxidized or nitrided, metal atoms lose electrons to become cations and oxygen or nitrogen atoms gain them to become anions. The resulting ionic interactions between the cations and anions of compounds have often been described as a Coulomb interaction assuming ﬁxed charges on the cations and anions [65–70]. The approach leads to potentials that can be easily implemented in eﬃcient MD algorithms and they have been widely used to study bulk oxides [70, 71]. However, this solution cannot be used for the study of metal/metal oxide heterostructures for at least three reasons. First, the ﬁxed charge model can only be used to study cases where the entire system remains in one oxidation state. During metal oxidation or the growth of a metal/metal oxide structure, numerous oxide states with diﬀerent charges on the ions can simultaneously exist within the system. A ﬁxed charge model in this situation cannot ensure even charge neutrality during the simulation of oxidation when the oxygen concentration within the system continuously increases. Second, metal oxidation simulation using a ﬁxed charge model requires injection of charged oxygen ions into the surface. They are brought from the far ﬁeld, where in reality the oxygen atoms would be neutral. The ﬁxed charge model therefore introduces signiﬁcant extra Coulomb energy leading to overestimates of the latent heat of oxygen condensation by more than 10 eV per atom [72]. This can signiﬁcantly aﬀect the predicted atomic assembly sequence. For example, it has been shown that an adatom energy change of only 5 eV can completely change the atomic structures of vapor deposited metal ﬁlms [58, 60]. Finally, a ﬁxed charge potential cannot be used to investigate the interface between a metal and its oxide where the potential must smoothly switch between one dominated by ionic interactions (in the oxide region) to one dominated by metallic interactions (in the metal region). An integrated EAM and charge transfer ionic potential (CTIP) that allow the potential to be transferable from pure metal or pure oxygen local conﬁgurations (where the ionic interactions can be neglected) to a fully developed ionic solid is needed. Several groups have attempted this and then utilized the method to simulate the oxidation of aluminum [73, 74]. In EAM + CTIP models, the total potential energy of the system, E, is expressed as a sum of nonionic energy, EEAM , and charge transfer ionic energy, ECTIP : (14.18) E = EEAM + ECTIP . The ionic energy, ECTIP , depends on the charges on atoms. The charges on atoms dynamically vary depending on local environments. Equation (14.18)

14 Atomic Assembly of Magnetoresistive Multilayers

511

can be normalized such that ECTIP becomes zero when the charges on the atoms are zero. The nonionic energy, EEAM , can then be viewed simply as the potential energy of the pure metal or pure oxygen systems, and its transferability to oxide systems is addressed by the additional charge transfer ionic interaction, ECTIP , as the system is progressively ionized. This potential for a metal and metal oxide heterostructure then requires two models to separately deﬁne EEAM and ECTIP . For the O−Al−Ni−Co−Fe system that will be investigated here, an EAM potential of the alloy type described above can be used for EEAM . A CTIP model was initially proposed by Rappe and Goddard [75] and Streitz and Mintmire [76]. However, the original CTIP models [75, 76] do not bound the charge transfer and this can lead to a violation of the classic concept of valency under some conditions. For instance, if the Streitz and Mintmire’s CTIP model [76] is coupled with an EAM potential [58,62,63], the simulations became divergent at small atomic separations because of nonphysical increases in charge transfer [72]. In addition, these CTIP models only give zero charges for single metal systems; they predict signiﬁcant (nonphysical) charges on the atoms in a metal alloy system [72]. Because of this, they have only been used to study oxygen-single metal (binary) systems. Recently, a modiﬁed CTIP models that incorporate the principle of valency have been proposed [72]. This modiﬁed CTIP can be combined with any EAM or other potential for stable simulations even at atomic spacings as small as 0.2 ˚ A. In addition, this modiﬁed CTIP model predicts zero charge and zero electrostatic energy for any locally metallic (either elemental metal or metal alloy) region. As a result, in metal regions energy value of EEAM + ECTIP from the EAM + CTIP model essentially equals the energy EEAM from the EAM model. In regions containing both oxygen and metals, it dynamically allows the ionization of oxygen and the metal atoms to create the anions and cations of the oxide and it accounts for their additional electrostatic energy contribution to the interatomic potential. This model enables the development of a O−Al−Ni−Co−Fe potential [77] suitable for direct MD simulation of the reactive growth of a MTJ multilayer. In this model, the CTIP energy is expressed as ECTIP =

N i=1

+

1 Vij (rij )qi qj 2 i=1 j=1 N

Xi qi +

N

N

ωS [−(qi − qi,min )](qi − qi,min )2

i=1

+

N

ωS(qi − qi,max )(qi − qi,max )2 ,

(14.19)

i=1

where qi and qj are the dynamically variable charges on atoms i and j, qi,min and qi,max are the lower and upper bounds for charges on atom i, S(x) is a

512

H. Wadley et al.

step function such that S(x) = 0 when x ≤ 0 and S(x) = 1 when x > 0, ω = 20 is a constant, and Xi and Vij are deﬁned as Xi = χi + kc

iN

Zj Pij (rij )

(14.20)

j=i1

and

iN (j)

Vij (rij ) = Ji δij + kc

Qik (rij ).

(14.21)

k=i1 (j)

Here the notation i1 , i2 , . . . , iN represents a list of i’s neighbors. For long range ionic interactions, the dimension of the computational cell may be small compared with the cutoﬀ distance of the potential. In such a case, the ith atom’s neighbors may include numerous image atoms introduced by periodic boundary conditions. The notation of i1 , i2 , . . . , iN concisely addresses this problem by including all image atoms in the list. The pair wise functions Pij (r) and Qij (r) depend on the charge parameters of atoms i and j, ξi and ξj . For ξi = ξj = ξ, 3 2 1 3 2 3 ξ + ξ r + ξ r exp(−2ξr), (14.22) Pij (r) = 8 4 6 11 3 1 1 1 1 + ξr + ξ 2 r2 + ξ 3 r3 exp(−2ξr), (14.23) Qij (r) = − r r 8 4 6 and for ξi = ξj , ξi ξj4 exp(−2ξi r) 1 ξj ξi4 exp(−2ξj r) exp(−2ξi r) + Pij (r) = − ξi + + r (ξi + ξj )2 (ξi − ξj )2 (ξj + ξi )2 (ξj − ξi )2 + Qij (r) =

(3ξi2 ξj4 − ξj6 ) exp(−2ξi r) (3ξj2 ξi4 − ξi6 ) exp(−2ξj r) + , r(ξi + ξj )3 (ξi − ξj )3 r(ξj + ξi )3 (ξj − ξi )3

(14.24)

ξi ξj4 exp (−2ξi · r) 1 ξj ξi4 exp(−2ξj r) − − r (ξi + ξj )2 (ξi − ξj )2 (ξj + ξi )2 (ξj − ξi )2 −

(3ξi2 ξj4 − ξj6 ) exp(−2ξi r) (3ξj2 ξi4 − ξi6 ) exp(−2ξj r) − . r(ξi + ξj )3 (ξi − ξj )3 r(ξj + ξi )3 (ξj − ξi )3

(14.25)

In (14.20) and (14.21), δij = 1 when i = j and δij = 0 when i = j, kc = −2 14.4 eV ˚ A e is the Coulomb constant (e represents the electron charge), Zi is an eﬀective charge of atom i, χi is its electronegativity [76], Ji (Ji > 0) is referred to as an “atomic hardness” [78] or a self-Coulomb repulsion [75], and the notation i1 (j), i2 (j), . . . , iN (j) means all the j atoms (i.e., j and its images) that are within the cutoﬀ distance from atom i. Vij (rij ) deﬁned in (14.21), (14.23), and (14.25) involves a summation of 1/rij . The direct summation of the slowly decaying function 1/r imposes a

14 Atomic Assembly of Magnetoresistive Multilayers

513

serious divergence problem. Note that the total contribution of these divergent terms to the system energy is N qi qj 1 . 2 i=1 j=i rij

N

i

1

It can be replaced by fast convergent Ewald summations [72,79,80] under the system neutral condition. The Ewald approach was therefore used to modify Vij to eliminate the divergence problem. Equation (14.19) is a function of both atom positions and atom charges. During simulations, charges are dynamically solved from the energy minimization conditions at each time step. Once charges are known, (14.19) becomes a function of atom positions only. Because charges are solved from energy minimization conditions, their derivatives have no eﬀects on forces or stresses. Equation (14.19) can then be used to calculate forces and stresses as if the charges were constant. Equation (14.19) is a quadratic type of potential with respect to qi . It has been demonstrated that the minimum ionic energy and N the equilibrium charges deﬁned by (14.19) for a neutral system i=1 qi = 0 can be eﬀectively solved using an integrated conjugate gradient technique and a Newton–Raphson method [72]. A relatively long cutoﬀ distance of 12 ˚ A was used for the potential. This cutoﬀ distance addresses the long range Coulomb interactions relatively well. It does not aﬀect the properties of the existing EAM potential [58, 62, 63] because (14.11) and (14.12) enable the potential to be virtually cutoﬀ at 7 ˚ A or below. All the charge parameters determined for the O−Al−Ni−Co−Fe system are listed in Table 14.2. Since the modiﬁed CTIP model has no eﬀect on the potential that describes the metal system, the existing EAM potential database [58, 62, 63] can in principle be used directly for metal alloys. To better ﬁt the experimental cohesive energies, lattice constants, elastic constants, and crystal structures of the four binary metal oxides: corundum Al2 O3 and Fe2 O3 , and B1 CoO and NiO, however, we have adjusted the EAM parameters for metals. The revised EAM parameters for the metals of interest here are shown in Table 14.3. In Table 14.3, F3 is split to F3 − and F3 + , the former is used when ρ ≤ ρe , and the latter is used when ρ > ρe . Compared with Table 14.1, relatively large Table 14.2. CTIP parameters for selected elements Element O Al Ni Co Fe

qmin (e) −2 0 0 0 0

qmax (e) 0 3 2 2 3

χ (eV e−1 ) 2.00000 −1.47914 −1.70804 −1.67765 −1.90587

J (eV e−2 )

−1 ξ (˚ A )

Z (e)

14.99523 9.07222 9.10954 8.65773 8.99819

2.144 0.968 1.087 1.055 1.024

0.00000 1.07514 1.44450 1.54498 1.28612

514

H. Wadley et al. Table 14.3. Revised EAM parameters for metals Element r e (˚ A) fe ρe ρs α β A (eV) B (eV) κ λ Fn0 (eV) Fn1 (eV) Fn2 (eV) Fn3 (eV) F0 (eV) F1 (eV) F2 (eV) F3 − (eV) F3 + (eV) η Fe (eV) μ ν

Al

Ni

Co

Fe

2.86392 1.20378 17.51747 19.90041 6.61317 3.52702 0.31487 0.36555 0.37985 0.75969 −2.80760 −0.30144 1.25856 −1.24760 −2.83 0 0.62225 −2.48824 −2.48824 0.78591 −2.82453 0.85 1.15

2.48875 2.21149 30.37003 30.37137 8.38345 4.47117 0.42905 0.63353 0.44360 0.82066 −2.69351 −0.07644 0.24144 −2.37563 −2.70 0 0.26539 −0.15286 4.58568 1.01318 −2.70839 0.85 1.15

2.50598 2.31544 31.89166 31.89166 8.67963 4.62913 0.42138 0.64011 0.5 1.0 −2.54180 −0.21942 0.73338 −1.58901 −2.56 0 0.70585 −0.68714 3.09213 1.07702 −2.56584 0.85 1.15

2.48199 2.31453 24.59573 24.59573 9.81827 5.23641 0.39281 0.64624 0.17031 0.34061 −2.53499 −0.05960 0.19306 −2.28232 −2.54 0 0.20027 −0.14877 6.69465 1.18290 −2.55187 0.85 1.15

adjustments are made to parameters F3 and η for Ni, Co, and Fe. These adjustments do not aﬀect the predictions of equilibrium properties of the elements as such parameters are only used in an electron density range signiﬁcantly higher than the equilibrium electron density, (14.16). The adjustments, however, are essential to improve the ﬁtting results. All the pair energies involving oxygen are expressed using (14.11). Instead of using the alloy EAM model, (14.13), (14.11) is also used to ﬁt the pair cross potential between aluminum and nickel to the experimental cohesive energy of the B2 phase of NiAl. All of the ﬁtted EAM pair energy parameters are summarized in Table 14.4. The electron density of oxygen is described using , fe exp −Γ rre − 1 f (r) = (14.26) 20 . 1 + rre − Ψ The corresponding parameters are listed in Table 14.5. A cubic spline is used to ﬁt the oxygen embedding energy so that it can smoothly describe the energy of four binary metal oxides: corundum Al2 O3

14 Atomic Assembly of Magnetoresistive Multilayers

515

Table 14.4. Parameters for EAM pair potentials between oxygen and oxygen, oxygen and all other metals, as well as between aluminum and nickel atoms Pair

r e (˚ A)

α

β

A (eV)

B (eV)

κ

λ

O−O O−Al O−Ni O−Co O−Fe Al−Ni

3.64857 2.98520 2.95732 2.59586 3.07992 2.71579

5.44072 8.49741 7.96528 8.25224 7.52309 8.00443

3.59746 4.52114 4.42411 4.37548 4.13330 4.75970

0.34900 0.09738 0.13521 0.25714 0.17108 0.44254

0.57438 0.38121 0.25332 0.34029 0.39869 0.68349

0.08007 0.18967 0.47077 0.37419 0.22335 0.63279

0.39310 0.95234 0.65524 0.50843 0.34380 0.81777

Table 14.5. EAM parameters for oxygen electron density function fe 1.39478

Γ

Ψ

2.11725

0.37457

Table 14.6. EAM parameters for the splined oxygen embedding energy function i 0 1 2 3 4

Fo,i (eV) −1.56489 −1.58967 −1.54116 −1.51798 −1.19082

F1,i (eV) −1.39123 1.30636 2.02821 2.30979 4.12936

F2,i (eV)

F3,i (eV)

ρe,i

ρmin,i

ρmax,i

1.77199 9.81033 6.56240 7.69582 10.32338

1.59833 0.00000 0.00000 0.00000 0.00000

54.62910 64.26953 66.21202 66.92391 74.23105

0 54.62910 65.24078 66.56797 70.57748

54.62910 65.24078 66.56797 70.57748 ∞

and Fe2 O3 , and B1 CoO and NiO. The cubic spline functions for the oxygen embedding energy have the form: F (ρ) =

3

Fi,j

i=0

ρ −1 ρe,j

i for ρmin,j ≤ ρ < ρmax,j ,

j = 0, 1, 2, 3, 4

(14.27) and the corresponding parameters are listed in Table 14.6. The EAM + CTIP potential is well ﬁtted to cohesive energies, lattice constants, and single crystal elastic constants of both metals and their oxides. 14.2.2 MD Model The atomic scale structure of a thin ﬁlm is the end result of many atomic assembly mechanisms. For instance, depending on the initial kinetic energy of the “adatoms” and the latent heat release during their condensation, a variety of impact induced assembly mechanisms occur, including thermal spike induced (athermal) atomic hopping [81], adatom biased skipping [81], resputtering [82], adatom reﬂection [82], and adatom-surface atom exchange [60,83]. These impact events are then followed by thermally activated diﬀusion. Here

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complexities arise because each atom on the surface can exist in many diﬀerent local atomic conﬁgurations and hence a large number of diﬀerent diﬀusion paths and diﬀusion rates are encountered [56, 84]. The morphology, texture, grain size, and many of the defects within a ﬁlm are all dependent upon a combination of the impact events and the subsequent diﬀusion routes. In some applications, energetic inert gas ion impacts with the surface are utilized to modify the structure of the already deposited ﬁlm. Successful modeling and simulation methods of these deposition processes must accurately represent the transport of vapor atoms, their impact with surfaces, and their thermal diﬀusion under various environmental conditions. In a MD simulation, the positions and velocities of all the atoms are solved from Newton’s equations of motion. If high ﬁdelity interatomic potentials are used to calculate the interatomic forces, MD methods can accurately represent atomic events during vapor condensation, especially those associated with energetic impacts. Additionally, it allows the exploration of the relaxed nanostructure, and the calculation of the stress and strain. MD methods are therefore of great utility for exploring the growth of nanostructures. In principle, molecular dynamics allows the atomic environment dependent atom motion, the temperature, the defect content, and the stress states of the medium to be tracked. In a MD simulation of growth, a computational substrate is created by assigning positions of atoms according to equilibrium crystal, lattice constants, and crystallographic orientation of the substrate. Initial substrate temperature is introduced by assigning velocities to atoms based upon the Boltzmann distribution. To minimize the eﬀect of small systems that must be employed with practical computational resources, periodic boundary conditions are used in the two horizontal (e.g., x- and z-) coordinate directions. Free boundary conditions are used in the vertical (y-) coordinate direction. Growth of the top y surface is simulated by injecting adatoms into the top surface at an injection frequency that corresponds to the simulated growth rate. Newton’s equations of motion are then used to solve for the positions of both the substrate atoms and the adatoms as a function of time. To prevent a shift of the computational system due to the momentum imported by impact of the adatoms with the top surface, the positions of the bottom monolayer of atoms are ﬁxed during simulations. During growth, both the remote kinetic energy of adatoms and the latent heat release during adatom condensation onto the surface cause a continuous increase in system temperature. To mimic the isothermal growth conditions that are usually used in reality, an intermediate region that is above the ﬁxed region but several monolayers below the surface is maintained at a desired substrate temperature by adding Nose–Hoover dragging forces [85] to the atoms. This leaves a free surface zone that allows realistic simulations of events induced during adatom impacts. It also naturally introduces a heat conduction zone through which the energy created at the surface during impacts is transported to the temperature controlled region where it is then removed. This MD model of growth allows the study of eﬀects of adatom incident energy, adatom incident angle, and adatom species on the atomic scale

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structures of the multilayers. The approach has one signiﬁcant deﬁciency. An accelerated rate of deposition must be used since the real-time covered in the simulation is short (1–10 ns).

14.3 Growth of Metal Multilayers Using a 10 ˚ A thick Ni80 Fe20 substrate crystal containing 120 (22¯4) planes in the x-direction, and 16 (2¯ 20) planes in the z-direction (see Fig. 14.2b), a threedimensional MD model has been used to simulate the [108] direction growth A)/Cu(15 ˚ A)/Co90 Fe10 (40 ˚ A) multilayer unit at an adatom of a Co90 Fe10 (58 ˚ energy of 3.0 eV, a normal adatom incident angle, a substrate temperature of 300 K, and a deposition rate of 1 nm ns−1 . The multilayer stack employs similar materials to those used in experiment [86]. Because the intent is to explore the atomic scale structure of the interfaces, the layer thickness was somewhat arbitrarily chosen and the multilayer structure is not the one that would necessarily give rise to the best GMR properties. An adatom energy of 3.0 eV was used because a direct simulation Monte Carlo analysis indicated that this is the typical energy encountered during sputter deposition in chambers at pressures between 1 and 10 mTorr [51]. The use of normal adatom incidence and substrate temperature of 300 K also mimics the typical low temperature GMR sputter deposition processes where adatoms impact the growth surface with a cosine distribution peaking at normal incidence. The detailed atomic structure of the simulated multilayers is shown in Fig. 14.2b, where Ni, Fe, Co, and Cu atoms are marked green, yellow, blue,

Fig. 14.2. A comparison of (a) three-dimensional atom probe image and (b) a molecular dynamics simulation of the growth of permalloy/copper/permalloy multilayers on Ni80 Fe20 (111) substrates. (c) Example of a simulation where the atom impact energy is varied as the layers are deposited

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and red, respectively. It is interesting to note that the Cu-on-CoFe interface appears relatively sharp, whereas the CoFe-on-Cu interface is quite diﬀuse. A signiﬁcant number of Cu atoms are seen within the top CoFe layer, several atomic planes from the nominal CoFe-on-Cu interface. This indicates that Cu incorporation in the subsequently deposited CoFe layer is much greater than in the previously deposited CoFe layer. Atomic conﬁgurations like the one shown in Fig. 14.2b have also been directly measured using a three-dimensional atom probe (3DAP) approach [87]. Such a 3DAP technique has been used to obtain the atomic conﬁguration A)/Co90 Fe10 (40 ˚ A)/Cu(30 ˚ A)/Co90 Fe10 (40 ˚ A) multilayof the Ni82 Fe18 (50 ˚ ers [58]. The result of the 3DAP experiment for a ﬁlm grown under similar conditions to that simulated is shown in Fig. 14.2a. A remarkable similarity is found between the simulated and experimental images. For instance, the roughness (amplitude and wavelength) for both the Cu-on-CoFe interface and the CoFe-on-Cu interface seen in Fig. 14.2b is very close to that of the experiment in Fig. 14.2a. The experiment and simulation both indicate that the Cu-on-CoFe interface is relatively sharp while the CoFe-on-Cu interface is diﬀuse, and that Cu atoms are mixed in the subsequently deposited CoFe layer. Additional MD model simulations have been performed on a simple Ni/Cu system to establish the functional dependence of the interfacial roughness and interlayer mixing on the energy of the depositing atoms. Ni substrate crystals consisting of 120 (22¯ 4) planes in the x-direction, 3 (111) planes in the y-direction, and 16 (2¯ 20) planes in the z-direction were used. Alternative 20 ˚ A Cu and 20 ˚ A Ni was deposited on the substrate at diﬀerent adatom incident energies Ei between zero and 5.0 eV, but ﬁxed substrate temperature of 300 K, normal adatom incident angle, and deposition rate of 10 nm ns−1 . The simulations reveal a strong dependence of atomic scale structure upon the incident adatom energy. Figure 14.3 shows a typical set of results, where the Cu and Ni atoms are marked by light and dark spheres, respectively. It can be seen that at low incident energies (∼0.1 eV or less) typical of either thermal evaporation (e.g., MBE) or high pressure sputtering (e.g., diode sputtering), the interfaces exhibit both signiﬁcant roughness and Cu mixing in the subsequently deposited Ni layer. Interestingly, little mixing of Ni is seen in either of the deposited Cu layers. Increasing the incident energy from 0.1 to 5.0 eV signiﬁcantly reduces the roughness of both the Cu-on-Ni and the Nion-Cu interfaces. Examination of Fig. 14.3 reveals that the Ni-on-Cu interface appeared to be ﬂatter than the Cu-on-Ni interface at incident energies below 1.0 eV, but when the incident energy reached 3.0 eV, the roughness diﬀerence appears to be reversed. Increasing the incident energy from 0.1 to 1.0 eV also reduced the interlayer mixing of Cu in the Ni layer, but as the incident energy was increased to 3.0 eV and above, the mixing began again to increase. Again Cu atoms were dispersed in the subsequently deposited Ni layer much more signiﬁcantly than Ni atoms were dispersed in the subsequently deposited Cu layer.

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Fig. 14.3. Molecular dynamics simulations of the deposition of Cu/Ni/Cu layers on a (111) nickel substrate using diﬀerent vapor atom incident energies

Since both the amplitude and wavelength of interfacial roughness are expected to inﬂuence the GMR ratio, an interfacial roughness parameter, r1 , was deﬁned that depends both on the height and the width of a surface asperity [60]: n hil +hir r1 =

i=1

n

2

,

(14.28)

wi

i=1

where hil and hir are, respectively, the height measured from the left and right sides of the ith asperity, and wi is the width of this asperity (see Fig. 14.4). Summation is conducted over the n asperities in the x-direction. The value of r1 as a function of incident energy is plotted in Fig. 14.5a for both the Cu-on-Ni and the Ni-on-Cu interfaces. Figure 14.5a shows that the interfacial roughness initially decreased with increasing incident energy, reached a minimum between 2.0 and 3.0 eV for the Ni-on-Cu interface and at about 4.0 eV for the Cu-on-Ni interface, and then began to rise as the incident energy was increased beyond 4.0 eV. When surface roughness is experimentally measured by atomic force microscope, the average deviation from the mean height of local asperities, r2 , is usually obtained [88]. This deﬁnition ignores the (lateral) wavelength of

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Fig. 14.4. Deﬁnition of parameters used to deﬁne the surface roughness of a thin ﬁlm

asperities. However, for sinoidal asperities with an asperity wave length w, r2 , and r1 are simply related by wr1 . (14.29) r2 = π The r2 surface roughness parameter is also shown (on the right coordinate) in Fig. 14.5a. Kools [88] has experimentally measured the r2 surface roughness of Ni80 Fe20 /Cu/Ni80 Fe20 exchange-biased spin valve, and his results are shown in Fig. 14.5b. The samples used in Kools’ experiments were prepared by magnetron sputtering with a background Ar pressure between 1 and 10 mTorr and a (constant) target substrate distance of 109 mm. Using MD predictions of the energy spectrum of sputtered Cu and a binary collision model for Cu transport in an Ar atmosphere [51], the average incident atom energy was estimated to be about 0.1 eV at 10 mTorr and about 4.0 eV at 1 mTorr. These energies and the equivalent pressures are marked in Fig. 14.5. It can be seen that the decrease of roughness with incident energy in the low (thermal) energy range, the existence of a minimum roughness in the intermediate energy range, and an increase of roughness with incident energy in the high energy range were all also observed in the experiments. Since Cu mixing in the Ni layer is signiﬁcant, a parameter was deﬁned to quantify it. The approach used here is based upon an identiﬁcation of the atomic neighbors of each atom. If a Cu atom is isolated on a Cu/Ni interface, it must have at least three Cu nearest neighbors in order for it to be attached to a cradle from the Cu side of the interface. In an fcc structure, each atom has 12 nearest neighbors, and so a Cu atom located on a perfect (ﬂat {111}) Cu−Ni interface will have nine (or less) Ni nearest neighbors. The only way for a Cu atom to have more than nine Ni neighbors is for it to be dispersed in a Ni layer. A more strict criterion for identifying a Cu atom mixed in Ni is that it has more than ten Ni nearest neighbors. A mixing probability of Cu, p, can therefore be deﬁned as the number of the Cu atoms with at least ten Ni nearest neighbors divided by the total number of the Cu atoms deposited. The calculated mixing of Cu as a function of incident energy is shown in Fig. 14.6a. It can be seen that Cu mixing initially decreased with increasing

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Fig. 14.5. Comparisons between the simulated and experimentally measured surface roughness of NiFe/Cu/NiFe multilayers

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Fig. 14.6. Comparisons between simulated and experimentally deduced copper distributions in a NiFe overlayer

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incident energy, reached a minimum at an incident energy between 1.0 and 2.0 eV, and then increased signiﬁcantly with increasing incident energy. Serious Cu mixing (p = ∼1.7%) occurred when the incident energy approached 5.0 eV. A direct experimental measurement of the Cu mixing probability, p, has not been made. However, in Kools’ experiments with exchange-biased spin valve based upon Ni80 Fe20 /Cu multilayers [88], the extent of Cu mixing into a Ni rich permalloy layer was related to a thickness, td , within which the permalloy lost its magnetism due to Cu contamination. Values of 2td were measured as a function of Ar background pressure [88] and are reproduced in Fig. 14.6b, where the Ar pressure range has been converted into an estimated incident energy range as described above. The predicted trend of Cu mixing with incident energy is clearly seen in the 2td data of Kools’ experiment. In particular, the existence of a minimum mixing at a pressure of about 8 mTorr (near 1 eV) is in good agreement with the simulations. The experimental data in Fig. 14.6b also indicate that the degree of mixing after high energy deposition is signiﬁcantly greater than after a low energy deposition as seen in the MD simulations. It is clear from Fig. 14.3 that Cu mixing was caused by the migration of previously deposited Cu atoms into subsequently deposited Ni layers. Earlier Monte Carlo calculations and a variety of experiments [89–92] have shown a strong tendency for Cu to segregate on the surface of Cu−Ni alloy. This is understandable because the surface energy of Cu is lower than that of Ni [93] and the larger atomic size of Cu releases the surface “tension” stress. Both eﬀects favor the segregation of Cu onto a growth Ni surface. These segregated Cu atoms can be gradually trapped in the Ni layer, resulting in regions of mixing near the Ni-on-Cu interface. This process is signiﬁcant for low deposition rate, high substrate temperature deposition where atomic hopping is dominant. However, during the low temperature, high rate deposition simulated, thermally activated atomic hopping was kinetically constrained, and a purely thermal diﬀusion mechanism was unable to signiﬁcantly disperse Cu into a Ni layer. Also a purely thermal diﬀusion mechanism is unable to rationalize the observed dependence of mixing upon the impact energy of atoms (Fig. 14.6). As a result, the surface segregation cannot fully account for the Cu mixing observed. Stop-action MD simulations indicated that the mixing of Cu in subsequently deposited Ni layers resulted from the ejection of Cu atoms from a Cu layer during energetic Ni atom impacts [60]. The probability of this exchange mechanism increases with the adatom energy, and decreases with the perfection of the surface. It has been found that the probability for a Ni adatom to exchange with a Cu surface atom is always much higher than that for a Cu adatom to exchange with a Ni surface atom. MD simulation indicated that when the surface element has a low cohesive energy and a large lattice interstice, it is more likely that the impacting atom can penetrate the surface and

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cause the exchange. The impact of a Ni atom on a Cu surface is then much more likely to eject a Cu atom than vice versa. The exchange mixing mechanism can be used to now rationalize the dependence of mixing upon incident energy observed in Fig. 14.6. At low incident energies, the growth surfaces are rough and defective, and exchanges are therefore able to occur relatively easily. As a result, Cu mixing was moderately high at low incident energies. As the incident energy increases, the surface roughness decreases, and the Cu intermixing was reduced. This trend continued until the incident energy reached 2.5 eV. Above this energy, further surface ﬂattening was small. However, the probability of exchange continued to increase with incident energy, and so the Cu mixing began to increase with energy. The atomistic scale calculations above have indicated that high energy depositions promote ﬂat interfaces, but this is achieved at the expense of mixing by an exchange mechanism. Figures 14.5 and 14.6 indicate that the incident energy for the best combination of interfacial roughness and intermixing lies between 1.5 and 2.5 eV. This appears to be one reason why energetic sputter deposition processes have produced better GMR ﬁlms than those grown by MBE where the atoms have low energies during impact with surface. Youssef et al. studied the eﬀects of sputtering pressure on the GMR properties of RF diode sputtered [Co(11 ˚ A)/Cu(9 ˚ A)]25 multilayers [30]. Their results indicated that the GMR ratio is relatively low at both low and high pressures, and the highest GMR ratio occurred at an intermediate pressure. In addition, their results also indicated that the lowest saturation ﬁeld was obtained at an intermediate pressure. These results are in good agreement with simulations. Simulations also indicated that during RF diode sputtering, a fraction of high energy inert gas ions may reach the substrate surface and also promote interlayer mixing [49, 51, 94]. They also indicate that heavier Xe ions usually cause more signiﬁcant damage (exchange) than Ar ions at a given ion energy. This suggests that during RF diode or magnetron sputtering of GMR multilayers, the use of Ar instead of Xe is preferential. Gangopadhyay et al. [86] explored the eﬀects of sputtering inert gases on the GMR properties of the [CoFe(15 ˚ A)/Cu(dCu )]8 multilayers deposited using DC magnetron sputtering and found that the GMR ratio obtained using Ar sputtering gas was signiﬁcantly higher than that obtained using the Xe sputtering gas. This result is again corrugates the insights gained from simulations. These studies emphasized the need to reduce high energy inert gas ion ﬂux at the substrate. It can be achieved by optimizing RF power, chamber pressure [51], or the substrate bias voltage. In an IBD process, the adatom energy increases with ion beam gun voltage that accelerates the inert gas ions used for sputtering. Saito et al. [95] measured the GMR ratio of [Ni80 Fe20 (20˚ A)/Cu(50 ˚ A)/Co(10 ˚ A)/Cu(50 ˚ A)]10 multilayers at diﬀerent Ar acceleration voltages. Their results indicate that the GMR ratio is indeed highest when an intermediate Ar acceleration voltage of 700 eV was used. Direct molecular dynamics simulation of high energy

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inert gas ion impact on the target has shown that both the energy and ﬂux of reﬂected neutrals are lower for Xe ions than for the Ar ions [49]. Since the high energy reﬂected neutrals can signiﬁcantly damage the multilayer, the simulations predict that the use of Xe instead of Ar should produce better GMR multilayers during IBD deposition. Schmeusser et al. [53] measured the GMR properties of the IBD deposited [Co(10 ˚ A)/Cu(dCu )]16 multilayers using Ar and Xe as the working gases. Their results indicate that the saturation ﬁeld of the multilayers deposited using Xe gases is in general signiﬁcantly lower than that deposited using Ar gas which again, appears in good agreement with the simulations. The detailed atomistic picture that has emerged from the analyses above enables the exploration of other deposition strategies that might further better both roughness and intermixing. Since ﬂat surfaces are promoted by high energy deposition, high impact energies should be used to terminate the growth of a metal layer (e.g., Ni or Cu). Because mixing decreases as the incident atom energy is reduced, the use of a very low energy to deposit the ﬁrst few monolayers of a new metal (Cu or Ni) avoids mixing by the exchange mechanism. Once complete coverage by 4–5 monolayers has been achieved, the subsequent deposition of the energetic atoms needed to ﬂatten the layer is much less likely to cause interlayer mixing. It should then be possible to use intralayer energy modulation during growth to promote ﬂatness without inducing interlayer mixing between diﬀerent metal layers. To test this notion, growth of the multilayers shown in Fig. 14.2b was simulated using the modulated energy scheme. The calculated atomic structure and modulated energy scheme are shown in Fig. 14.2c. It can be seen that the structure is indeed signiﬁcantly improved. The experiments by Hylton et al. [96] may have come closest to achieving energy modulation deposition for published work to date. In their experiments, diﬀerent chamber pressures were used to deposit the NiFe and the Ag layers of the NiFe(40 ˚ A)/Ag(40 ˚ A) multilayers using magnetron sputtering. They found that at a constant high pressure of about 25 mTorr, the multilayers had the lowest GMR ratio. Because a low adatom energy was obtained at a high pressure due to background gas scattering, the multilayers thus produced were likely to have a high interfacial roughness. The GMR ratio was signiﬁcantly increased when the multilayers were deposited at a constant lower pressure of 3 mTorr. This occurred because the low pressure resulted in a relatively high adatom energy, which ﬂattened the interfaces. However, the highest GMR ratio was obtained when a low adatom energy (high pressure) was used to deposit the NiFe layer on Ag surface and a high adatom energy (low pressure) was used to deposit the Ag layer on NiFe surface. As will be discussed below, the NiFe(40 ˚ A)/Ag(40 ˚ A) system is special in that Ag has a very strong tendency for surface segregation and the deposition of NiFe on Ag is associated with a very high probability for the exchange. The use of a low energy to deposit NiFe on Ag becomes critical in reducing the mixing of

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Ag into the subsequently deposited NiFe layer. This experiment can certainly be well explained by the simulations. While GMR eﬀects were ﬁrst discovered for simple A/B/A systems [7, 8], signiﬁcant improvement has been achieved by introducing additional elements in the multilayers [31]. Hyperthermal impacts may ﬂatten the interfaces, but its use is limited by the interlayer mixing. If there is a third element C that can always segregates on to the surface of the A/B/C system and the A and B elements deposited on C can always be reconstructed to ﬂat conﬁgurations, then an addition of C to the system may signiﬁcantly reduce the interfacial roughness of the multilayers. An element C that has such an eﬀect is called here a surfactant. To explore this idea, the MD approach was used to simulate multilayer dispositions with the addition of elements that might act as surfactants. The NiCo/Cu multilayer system was chosen for study because this simple system has practical applications as spin valves. The same crystal geometry shown in Figs. 14.2 and 14.3 was used to simulate the growth of the Ni75 Co25 /Cu/Ni75 Co25 multilayers in the [108] direction. A substrate temperature of 300 K and hyperthermal adatom energy of 1.0 eV typical of sputtering deposition processes were used. Simulations were ﬁrst carried out at a normal incident atom angle of 0◦ . The resultant atomic structure is shown in Fig. 14.7a. It can be seen that the use of moderate hyperthermal energy deposition at normal incidence results in interfaces in the Ni75 Co25 /Cu/Ni75 Co25 multilayers that are relatively smooth. However, the adatom incident angles in real sputtering deposition processes are hardy all normal. They typically satisfy a cosine angular distribution where a signiﬁcant fraction of adatoms makes impact at oblique incident angles. To induce signiﬁcant interfacial roughness so that the surfactant eﬀects can be clearly revealed, we simulated growth of the same multilayers using an oblique adatom incident angle of 45◦ . The

Fig. 14.7. (a) Molecular dynamics simulation of a Cu/NiCo/Ni multilayer on a NiCo substrate. The atoms impacted at normal incidence to the surface with an impact energy of 1.0 eV. (b) Atomic structures of simulated multilayers grown using oblique deposition. The strong ﬂattening eﬀect associated with the addition of a small number of silver atoms can be clearly seen in (c)

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resulting atomic conﬁguration is shown in Fig. 14.7b. It can be seen that both the Cu-on-Ni75 Co25 and Ni75 Co25 -on-Cu interfaces are rougher than the ones in Fig. 14.7a. The roughness is even more signiﬁcant on the Cu surface. This is caused by shadowing eﬀects during oblique angle deposition. We have explored the eﬀects of adding Ag and Au into the system. The growth of the Ni75 Co25 /Cu80 Ag15 Au5 /Ni75 Co25 multilayers under the oblique incident angle condition is shown in Fig. 14.7c. It indicates that the roughness of the interfaces and the free surface is dramatically reduced. Interestingly, it can be seen that the Ag has segregated to the surface. No Au surface segregation is seen in Fig. 14.7c. More detailed simulations with Ag and Au added separately have veriﬁed that the surface ﬂattening eﬀect of Au is minor compared to that resulting from Ag. Magnetron sputtering has been used to deposit Co/Cu multilayers with and without Ag by Yang et al. [97] and with and without Au by Egelhoﬀ et al. [98]. In the experiments by Yang et al., in situ X-ray photoelectron spectroscopy (XPS) indicated that Ag atoms ﬂoat out to the surface during successive growth of Co and Cu layers. Their TEM analysis further indicated that Ag leaves behind smooth interfaces without pinholes. These eﬀects resulted in an order of magnitude increase in GMR ratio compared to Ag-free samples [97]. In the experiments by Egelhoﬀ et al., no Au surface segregation was observed and Au was shown to slightly reduce the GMR ratio [98]. We have also experimentally explored the eﬀects of surfactants. A Randex Model 2400-6J diode sputtering system was used to deposit Cu and Cu80 Ag15 Au5 ﬁlms on silicon wafers at an Ar pressure of 20 mTorr and a plasma power of 175 W. The AFM surface morphology as a function of ﬁlm thickness for two typical samples with and without the addition of Ag and Au are shown, respectively, in the left and the right columns of Fig. 14.8. The ﬁlms with Ag and Au added are seen to be smoother. The RMS surface roughness for the two samples was measured and the results are shown in Fig. 14.9. It can be seen that the surface roughness increased as the ﬁlm thickness increased. However, over the entire ﬁlm thickness range explored, the surface roughness was always signiﬁcantly lower for the ﬁlms grown with the Ag-Au surfactant. Detailed AFM analysis of a surface proﬁle along a cross section going through the black dots in Fig. 14.8d indicated that these black dots are pinholes with an average depth possibly well above 40 ˚ A. Scanning Auger microscopy has been used to analyze the surface compositions of the ﬁlms. A focused ion beam technique was used to etch the sample to diﬀerent thickness so that a surface composition vs. ﬁlm thickness proﬁle could be obtained. Figure 14.10 shows the Cu, Ag, and Au composition proﬁles along the thickness of a Cu80 Ag15 Au5 ﬁlm. Figure 14.10 clearly shows a very strong Ag surface segregation eﬀect. The signiﬁcant interfacial roughness in the Ni75 Co25 /Cu/Ni75 Co25 multilayers shown just above is anticipated to cause a signiﬁcant deterioration of the GMR properties. Pinhole formation in Cu layers seen in the simulation would also allow the two adjacent ferromagnetic layers to be connected which in turn

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Fig. 14.8. Surface roughness maps for Cu thin ﬁlms grown on silicon substrates with and without Ag−Au surfactant additions

would prevent the magnetic moment of either magnetic layer from being easily rotated. To investigate these suppositions, both Ni75 Co25 /Cu/Ni75 Co25 and the Ni75 Co25 /Cu80 Ag15 Au5 /Ni75 Co25 multilayers were deposited using RF diode sputtering and their GMR properties were measured. The GMR ratio and saturation ﬁeld as a function of the number of GMR sandwich repeats are shown in Fig. 14.11a, b for the two types of multilayers. Figure 14.11 veriﬁes that the addition of Ag and Au in the Cu layer signiﬁcantly improves the GMR properties, due to the improved interfacial structures and the elimination of pinholes in the Cu layers. Simple two-dimensional EAM calculations of the energetics of the Cu−Ag−Au system suﬃciently helped better understanding of the mechanisms responsible for strong surfactant eﬀects [59]. These calculations indicate that the exchange between a Ag atom on a Cu surface and an underlying Cu atom resulted in an increase of energy. The exchange of an Au atom on a Cu surface with an underlying Cu atom, however, decreased energy. As a result,

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Fig. 14.9. Surface roughness of copper thin ﬁlms grown with and without the presence of a Ag−Au surfactant

Fig. 14.10. Compositional proﬁles for a copper ﬁlm grown using a Ag−Au surfactant. Strong surface segregation exits at the top face surface (right) of the ﬁlm

Ag atoms tend to stay on the surface while Au atoms are easily buried in the bulk. While it appeared that lower surface energy materials can segregate to the surface, further analysis of the atomic structures has indicated that other factors could aﬀect surface segregation. For instance, embedding a bigger atom into a lattice composed of smaller atoms was found to be energetically unsta-

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Fig. 14.11. Eﬀect of surfactant additions to the GMR transport properties of permalloy/Cu/permalloy multilayers

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ble. If the bigger atom was embedded at a near surface site, it could be easily exchanged with an atom on the surface. Ag has a size signiﬁcantly bigger than that of Cu, Ni, and Co, Ag hence segregates to the surface. For atoms of the same size, the critical factor for surface segregation was found to be the cohesive energy of the atoms. During energetic impact, the incoming atom more easily penetrates a lattice of lower cohesive energy atoms. This then results in an exchange between the incoming atom and an underlying atom, leaving the lower cohesive energy atom at the surface. Thermodynamically the surface segregation of lower cohesive energy atoms on the surface (breaking some bonds) also incurs less of an energy penalty than that of more strongly bonded atoms. Ag and Au are of the same size, but Ag has a much lower cohesive energy [93], it should surface segregates. Likewise, Ni and Cu have about the same size, but since Cu has a much lower cohesive energy [93], so Cu segregates to the surface of Ni [89–92]. Compared with Cu, Au, Ni, and Co, Ag has a lower cohesive energy and relatively big size, so Ag has a strong tendency to surface segregate. These results suggest that during the deposition of multilayers, Ag atoms continuously segregate to a surface. Other metal atoms deposited on this Ag-rich surface can then quickly exchange with Ag atoms. These calculations also indicated that Ag atoms have lower energy barriers for surface diﬀusion than Cu, Ni, or Co atoms. As a result, Ag atoms can rapidly migrate to lower energy ledge, kink and pit sites on a surface. The presence of these Ag atoms was found to reduce the Schwoebel barriers for other atoms on top of the terrace and to greatly increase the rate at which they could hop down to the ledge sites. Consequently, Ag promoted the step ﬂow growth that resulted in much smoother surfaces. Furthermore, the energetic impact induced ﬂattening more easily occurs on a surface composed of more mobile atoms. The hyperthermal energy processing conditions that can lead to smooth growth are readily accessible if an Ag-rich surface is formed during deposition. The eﬃcient smoothing of local surface asperities also greatly reduces the probability of surface shadowing during oblique deposition which synergistically enhances the eﬀects of the surfactant. Experiments show that multilayers using Ag as the spacer do not exhibit good GMR properties [99]. This is at ﬁrst surprising since Ag is highly conductive. The results discussed above suggest that this anomaly might be a consequence of Ag segregation to the surface as other materials are deposited on it. This would make the thickness of an Ag spacer extremely diﬃcult to control during multilayer deposition. Extensive mixing of Ag into the subsequently deposited magnetic layer is also likely to occur. In the worst case, this results in a thin layer of the magnetic layer near the interface completely losing its ferromagnetism, forming the so-called “dead layer.” While Ag is a good surfactant candidate, it does not appear to be a good choice for the spacer layer material. Good surfactants must be able to both segregate to the surface and to reconstruct surface asperities into ﬂat conﬁgurations. Ideally, their presence

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at the surface and in the interior of the layers should not aﬀect transport properties. Atomistic simulations have shown that mobile materials present on the surface are likely to ﬂatten the growth surface. These materials usually have a low surface energy, a low bonding energy, and a low melting temperature. Elements that have relatively large atomic sizes also favor segregation to a surface to reduce the energy. Roughly speaking, elements with low melting temperature and relatively large size may be the most promising surfactants candidates. This includes metals such as Ag, Pb, Sb, Ga, etc.

14.4 Ion-Assisted Growth of Metal Multilayers When multilayers are grown with many layers, it becomes increasingly diﬃcult to keep an atomically ﬂat growth surface during deposition. Ion-assisted deposition is often used to resolve this problem. During RF diode sputtering, a substrate bias voltage can be applied to induce low energy inert gas ion impacts with the growth surface while in IBD, a secondary ion beam gun can be used to inject inert gas ions toward the substrate surface. Atomistic simulations have been applied to explore ion assistance schemes for growing Ni/Cu [100–102], Co/Cu [103–105], and Ta/Cu [106] multilayers. MD analysis of inert gas ion impact eﬀects during the growth of Ni/Cu/Ni multilayers [100–102] indicates that the energy of the assisting ions must be very low (<20 eV) to avoid mixing of the diﬀerent layers. However, the ion energy must also be high enough to induce ﬂattening eﬀects. We can deﬁne a critical ion energy for ﬂattening and a critical ion energy for mixing so that ﬂattening and mixing start to become signiﬁcant when the ion energy exceeds the critical values. The critical ion energies for ﬂattening and mixing depend on ion species, ion incident angle, and the type of surface. In general, weakly bound atoms can be most easily ﬂattened during impacts, and smaller atoms are more likely to penetrate a lattice with large lattice interstices. This suggests that during the deposition of relatively weakly bonded, larger atoms on a surface composed of relatively strongly bonded, smaller atoms, the critical ion energy for ﬂattening will be low and the critical energy of mixing high. In such a case, it is easy to deﬁne an appropriate ion energy that can ﬂatten the surface without causing intermixing. However, deposition of relatively strongly bonded smaller atoms on a surface composed of relatively weakly bonded larger atoms is likely to be more challenging especially if the gap between the critical ion energy for mixing and the critical ion energy for ﬂattening is small or even negative. For the Co/Cu/Co sandwich used in the middle part of a spin valve, the most diﬃcult interface to grow is the Co-onCu interface. MD simulations can be used to explore strategies to control the Co-on-Cu interface using low energy ion-assisted deposition. Cu crystals containing 72 (22¯4) planes in the x-direction, 8 (111) planes in the y-direction, and 42 (2¯ 20) planes in the z-direction were used to simulate the predeposited Cu surface (Fig. 14.12a). To explore the eﬀects of inert ion

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Fig. 14.12. The eﬀect of Xe ion energy upon the surface structure of a Co-on-Cu interface

impact on the reconstruction of a “rough” surface, the deposited Co atoms were artiﬁcially formed into arrays of hillocks on the underlying surface. Inert ion impact was simulated by injecting inert gas ion species (He, Ne, Ar, and Xe) toward the top (y) surface from random locations far above. The evolution of surface structures following impacts was then calculated. After the thermal spike induced by the previous ion impact was dissipated, another ion was injected to repeat the same procedure. Simulations were carried out at a substrate temperature of 300 K, various ion incident angles and various ion incident energies below 30 eV. For each ion impact condition a total up to −2 3,000 ion impacts (corresponding to a maximum ﬂuence of 1.0 impact ˚ A ) were simulated. The eﬀect of ion energy upon the atomic scale structure of the model system after bombardment with 1,500 Xe ions at a normal ion incident angle (θ = 0◦ ) can be seen in Fig. 14.12. At a low ion energy of 2 eV (Fig. 14.12b),

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a relatively large fraction of the Co atoms remained in two Co monolayers or more above the Cu surface. This occurred even though most of the Co atoms had experienced several Xe ion impacts. The fraction of the Co atoms remaining in or above the second monolayer was reduced as the ion energy was increased to 4 eV (Fig. 14.12c). It is also evident that below this energy, almost no intermixing occurred in the copper surface layer. Increasing the ion energy to 6 eV resulted in fully ﬂattened Co clusters (Fig. 14.12d). However, some Co atoms had penetrated into the Cu layer and four Cu atoms were ejected onto the top surface. This intermixing became more signiﬁcant as the ion energy was increased to 10 eV (Fig. 14.12e). A normalized roughness, R can be deﬁned as the fraction of Co atoms remaining more than one monolayer above the Cu surface, and an intermixing parameter, M can be deﬁned as the fraction of Co atoms present in the Cu layer. The eﬀects of ion energy and ion species on roughness and intermixing metrics are shown in Fig. 14.13a, b. It can be seen that the energies required for ﬂattening and mixing, as well as the energy gap between mixing and ﬂattening, are all increased when light ions are used. For each ion species, an optimum energy can be identiﬁed where both roughness and intermixing are low. For Xe, this energy is about 5 eV whereas for He, this optimum energy is around 18 eV. The roughness and intermixing parameters are shown in Fig. 14.14a, b as a function of ion ﬂuence at selected ion energies and a normal ion incident angle for several ion species. From the 3 eV ion energy data shown in Fig. 14.14a we can see that the roughness parameter decreases with increasing ion ﬂuence for all ion species, albeit the rate of decrease is lower for the lighter ions. The 15 eV ion energy data shown in Fig. 14.14b, on the other hand, indicates that increasing the ﬂuence causes an increase in intermixing, but again the rate of increasing is lower for light ions. A critical ion energy for ﬂattening can now be deﬁned as the lowest ion energy to completely ﬂatten the surface (deﬁned as R < 0.02) after a des−2 ignated high ion irradiation ﬂuence of 0.5 ions ˚ A . Likewise, a critical ion energy for mixing can be deﬁned as the lowest ion energy for the initial onset −2 of mixing (M > 0.02) after a high ion ﬂuence of 0.5 ions ˚ A . It should be pointed out that values of the ﬂattening and mixing critical energies depend on the designated ﬂuence, but this dependence is relatively weak when the −2 ﬂuence is 0.5 ions ˚ A or above. The eﬀects of ion incident angle have been explored in detail. To uniquely deﬁne the incident angle, the impact ions were assumed to move in the (1¯10) plane and the angle θ was measured from the [¯1¯1¯1] direction. To examine the role of incident ion angle, critical energies for ﬂattening and mixing were calculated as a function of the ion incident angle for the diﬀerent ion species and the results are shown in Fig. 14.15 for both ﬂattening and intermixing. It is evident from Fig. 14.15 that it is relatively more diﬃcult to ﬁnd an ion energy that can cause ﬂattening without mixing when ions strike

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Fig. 14.13. The eﬀects of ion impact energy upon the surface roughness and intermixing of a Co-on-Cu interface

the surface at a normal incident angle. Flattening without mixing can be more easily achieved when a higher ion incident angle is used. The results described above assume that the ion assistance occurs concurrently with deposition of Co on Cu. During this simultaneous ion assistance, it is diﬃcult to avoid mixing. Better ion assistance strategies are possible. One is to use modulated ion assistance where the ﬁrst half of a new material layer is grown without ion assistance while the remainder of that layer is grown with ion assistance. Because the interface is already buried below the surface, the ion impacts are less likely to cause mixing. Another strategy is sequential ion assistance, where the entire layer is grown without ion assistance. Upon the completion of a layer, ion irradiation is then introduced to ﬂatten the surface

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Fig. 14.14. The eﬀect of ion ﬂuence upon the surface roughness and intermixing at a Co-on-Cu interface

before another layer is deposited. This strategy is even less likely to result in mixing. Direct MD simulations of the Ar ion-assisted growth of the Cu/Co/Cu multilayers were carried out to explore the three ion assistance strategies. The model system analyzed consisted of a Cu substrate made up of 72 (22¯4) planes in the x-direction, eight (111) planes in the y-(growth) direction, and 42 (2¯ 20) planes in the z-direction. A Co layer and then a Cu layer were sequentially deposited onto the surface at a substrate temperature of 300 K, a deposition rate of 1 nm ns−1 , an adatom energy of 0.5 eV, and an adatom incident angle of 40◦ . An oblique rather than normal adatom incident angle was used to promote the formation of a rough surface so that the eﬀects of ion assistance could be revealed. Ion/adatom ﬂux ratios of two and four were used for simulations of simultaneous and modulated energy ion assistance schemes, −2 respectively. An ion ﬂuence of 0.5 ions ˚ A was used to assess sequential ion assistance scheme. The atomic conﬁgurations obtained from the three

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Fig. 14.15. The eﬀect of the ion incident angle upon the surface ﬂattening and intermixing critical energies

deposition strategies are shown in Fig. 14.16, where Cu, Co, and Ar are marked by white, gray, and black spheres, respectively. Figure 14.16a shows that without ion assistance (ion energy of zero), the Cu-on-Co interface is very rough. When 8 eV, normally incident Ar ion assistance was used (Fig. 14.16b), the interfacial roughness was significantly reduced. However, when the Ar ion energy was increased to 20 eV (Fig. 14.16c), signiﬁcant interlayer mixing occurred at the Co-on-Cu interface and some mixing even occurred at the Cu-on-Co interface. Our simulations over a wide variety of ion incident energies and incident angles indicate that the lowest combination of roughness and mixing occurs at an ion energy of 10 eV and an ion incident angle of 50◦ .

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Fig. 14.16. Atomic structures of Cu−Co−Cu multilayers grown in (a) without ion assistance. (b) and (c) show the eﬀect of increasing the ion energy during deposition. The structure shown in (d) was made by using ion assistance during only the last half of each layer. The structure shown in (e) used an ion treatment to smooth each layer after its deposition was complete

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Fig. 14.17. The eﬀects of ion energy upon the structure of copper ﬁlms deposited on Ta using simultaneous ion assistance

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Fig. 14.18. The eﬀects of ion energy upon the structure of copper ﬁlms grown on Ta using modulated and sequential ion assistance schemes

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The multilayer structure shown in Fig. 14.16d was obtained using modulated ion assistance, where the ﬁrst ﬁve atomic layers of Co were deposited without ion assistance, and the remainder of the Co layer was deposited using an ion assistance at 20 eV. Flat interfaces without mixing were obtained. The multilayer structure shown in Fig. 14.16e was obtained using sequential ion assistance, where complete metal layers were ﬁrst deposited without ion assistance, and then ion impacts with a relatively high energy of 30 eV were used −2 to ﬂatten the ﬁnished metal surfaces at an ion ﬂuence of 0.5 ions ˚ A . The results show that the sequential ion assistance scheme resulted in a multilayer structure with planar interfaces and little interfacial mixing even when a moderately high ion energy of 30 eV was used. The above analysis applies to Co/Cu system. MD simulations were also used to study the growth of low energy Ar ion-assisted deposition of Cu on Ta [106]. Here both metals and ions were assumed to impact the growth surface at an incident angle of 45◦ . The eﬀects of ion energy and ion to metal ratio on ﬁlm packing density, surface roughness, and Cu/Ta intermixing are shown in Fig. 14.17 for simultaneous ion assistance scheme. Figure 14.18 shows ﬁlm density, surface roughness, and interlayer mixing as a function of argon ion energy for modulated energy and sequential ion assistance schemes. During the modulated energy ion assistance simulations, the ﬁrst half of the Cu layer was deposited without ion assistance and the remainder was deposited using an ion/metal ﬂux ratio of 6. During the sequential ion assistance simulations, −2 an ion ﬂuence of 1.0 ions ˚ A was applied after completion of deposition of the Cu layer. These results indicate that increasing the ion energy and ion to metal ratio can increase the ﬁlm density and reduce the growth surface roughness, but it causes an increase in interlayer mixing. The modulated energy and sequential ion assistance schemes delay the occurrence of the intermixing to higher ion energy levels. As a result, higher ion energies can be used to improve ﬁlm density and surface smoothness without causing signiﬁcant mixing. Several groups have tried to explore low energy ion-assisted deposition approaches and have shown signiﬁcant ion assistance eﬀects upon thin ﬁlm structures [107]. We utilized the above simulations to recently help develop a biased target ion beam deposition (BTIBD) system [108,109] and have used it to explore the low energy ion-assisted growth of model Ta/Cu bilayer ﬁlms at room temperature. The BTIBD system utilized a similar low energy ion source consisting of an end-Hall ion source and a hollow cathode electron source for both sputtering and ion assistance. These ion sources reliably produce a high density, very low ion energy (up to 100 eV) inert gas ion beam [110]. When a negative bias voltage is applied to the sputtering target, the inert gas ions are attracted and make a near-normal incidence with the target surface. An advantages of this technology is that it enables an easily controlled low sputtering energy and it creates a low ﬂux of reﬂected neutrals.

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Fig. 14.19. Eﬀect of argon ion energy upon the roughness and resistivity of copper ﬁlms deposited on a Ta surface

Model 5 nm Ta/30 nm Cu ﬁlms were deposited on 6-in. silicon wafers using the three ion assisting methods (simultaneous deposition with ion assistance, modulated ion assistance, and sequential ion assistance). An oblique incident angle of θ = 45◦ was used for the assisting argon ions. All samples were grown at a base pressure of 3×10−8 Torr, an Ar working pressure of about 4.5×10−4 Torr, and a target bias voltage of 300 V. Diﬀerent assisting ion energies and ion ﬂuxes were investigated. The surface roughness and in-plane electrical resistivity of ﬁlms grown using simultaneous ion assistance at an ion to metal ratio of about four are shown as a function of the assisting ion energy in Fig. 14.19a, b. It can be seen from Fig. 14.19a that the ﬁlm surface roughness initially decreased as the ion energy was increased from 0 to 7 eV, and then remained constant with further increases in ion energy. This is in good agreement with simulations (Fig. 14.17b). Figure 14.19b shows that the ﬁlm electrical resistivity at ﬁrst decreased as the ion energy was increased from 0 to 10 eV but then started to increase as the ion energy was further increased. Many studies [111, 112]

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Fig. 14.20. Eﬀect of ion ﬂux upon the surface roughness and resistivity of Cu ﬁlms deposited on Ta surfaces

have shown that the resistivity of thin ﬁlms increases due to defects such as vacancies and voids [113], or impurity atoms [114] like those introduced by intermixing at ﬁlm interfaces. Surface and interfacial roughness can also contribute to increases in resistivity [114–118]. It is therefore anticipated that the resistivity changes observed in the experiments are related to changes in surface (and interfacial) roughness, the ﬁlm’s packing density (vacancy and void content), and alloy scattering due to interlayer mixing. The initial drop in resistivity is consistent with a decrease in roughness while the subsequent resistivity rise may be a manifestation of mixing at the Cu on Ta interface. The measured ﬁlm roughness and resistivity as a function of the assisting ion ﬂux at an assisting ion energy of 10 eV, are shown in Fig. 14.20. It can be seen from Fig. 14.20a that an increase of ion to atom ratio from 0 to 8 resulted in an ∼50% reduction in surface roughness. The roughness then reached a near plateau as the ﬂux ratio was increased above 10. This is again in good agreement with the simulation studies. Figure 14.20b shows that the ﬁlm resistivity initially decreased as the ﬂux ratio was increased to around 6. A further increase in the ion ﬂux then caused an increase in ﬁlm resistivity.

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Fig. 14.21. Copper concentration proﬁles at a Cu on Ta interface for ﬁlms grown with various ion assistance strategies

The initial decrease in resistivity is believed to result from impact ﬂattening which is accompanied with reduction in defects (Fig. 14.12). The subsequent increase can again be explained by the increase in intermixing. To further verify that intermixing indeed occurs, Auger electron spectrometry was used to measure the ﬁlm composition as a function of depth for samples grown using the simultaneous ion assistance scheme. The results are shown in Fig. 14.21 for three ion assistance conditions: (a) no ion assistance, (b) an ion energy of Eion = 10 eV and an ion to metal ﬂux ratio of 5, and (c) an ion energy of Eion = 20 eV and an ion to metal ﬂux ratio of 14. The data reveal that the sharpest interface with a minimal combination of interfacial roughness and interlayer mixing was obtained using an intermediate ion energy of 10 eV and an ion to atom ratio of 5. Direct TEM observations of the structures grown above (Fig. 14.22) also indicate that the sample grown with 10 eV ion assistance had the sharpest interface. The prediction that the low energy ion-assisted deposition can improve the interfacial structures has also been experimental veriﬁed in other experiments. A group at Veeco investigated the eﬀects of ion assistance on the transport properties of GMR stacks [119]. They found that ion energies in the range 10– 60 eV signiﬁcantly improved the GMR ratio of their ﬁlms. Kools also found that slight increases in kinetic energy (>5 eV) could lead to biased diﬀusion and the suppression of defect formation [120]. Another example is the growth of X-ray mirror multilayers that involve many repeats (400) of Cr/Sc bilayers with the thickness of the layers similar to that of GMR multilayers (around 10 ˚ A) [121]. Flat sharp interfaces are critical for a high reﬂectivity X-ray mirror. Low energy ion-assisted deposition was found to signiﬁcantly improve the quality of such multilayers [121]. The ion energy for the best performance device was reported to be around 9 eV [121].

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Fig. 14.22. Transmission electron micrographs of Cu ﬁlms grown on Ta surfaces using various low energy, ion assistance strategies. Film (b) had the highest quality interface

14.5 Dielectric Layer Deposition The computational substrates used for oxidation are similar to those used for vapor deposition. However, instead of injecting adatoms toward the growth surface, oxidation is simulated by introducing an atomic oxygen vapor above the metal surface. The oxygen vapor is maintained at a constant pressure and a constant temperature. To maintain a constant vapor pressure, the number of oxygen atoms in the vapor zone is monitored. Once oxygen atoms are found to have condensed on the metal surface, they are reﬁlled in the vapor zone. The growth of an AlOx tunnel barrier layer on a fcc Ni65 Co20 Fe15 substrate can be simulated using the MD methods with a charge transfer potential approach described earlier. An initial fcc Ni65 Co20 Fe15 single crystal substrate was made from 120 (22¯ 4) planes in the x-direction, 3 (111) planes in the ydirection, and 16 (2¯ 20) planes in the z-direction. It was created using the equilibrium (bulk) lattice parameter (a = 3.604 ˚ A) for fcc Ni65 Co20 Fe15 . The usual MD simulation approach was then used ﬁrst to deposit approximately six atomic layers of Ni65 Co20 Fe15 on the initial (111) substrate surface. This

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Fig. 14.23. Atomic structures showing the eﬀect of aluminum metal layer thickness upon morphology of reactively grown AlOx layers (a, b). (c) Shows the formation of a hole in the aluminum oxide layer and its self-healing as oxidation progresses

was followed by the deposition of aluminum layers of various thickness. The metal vapor atoms were injected perpendicular to the growth surface, the substrate temperature was maintained at 300 K, and the deposition rate was 10 nm ns−1 as ﬁlms were grown at various adatom energies between 0.1 and 5.0 eV. The geometry of the system can be seen in Fig. 14.23a, b. Examples of aluminum ﬁlms grown on Ni65 Co20 Fe15 crystals can be seen on the left of Fig. 14.23a, b. They were obtained by depositing the Ni65 Co20 Fe15 layer at a 4.0 eV adatom energy and the aluminum layer at a 0.2 eV adatom energy. Increasing the adatom energy during deposition of the permalloy layer resulted in much smoother Ni65 Co20 Fe15 surfaces consistent with earlier ﬁndings with metal/metal multilayers [58, 60]. Relatively smooth aluminum surfaces were always obtained regardless of its adatom energy. Further analysis indicates that this occurs because aluminum has a low Schwoebel barrier [122] facilitating the step ﬂow mode of growth. In addition, aluminum has a relatively low cohesive energy (3.58 eV) compared to Ni (4.45 eV), Co (4.41 eV), and Fe (4.29 eV). As a result, the binding between aluminum and the underlying Ni, Co, Fe atoms (with higher cohesive energies) is stronger than the binding between the aluminum atoms themselves. This also promotes wetting of aluminum on the Ni65 Co20 Fe15 surface. However, epitaxial

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aluminum growth was complicated by the large lattice mismatch (∼15%) between aluminum and Ni65 Co20 Fe15 . Misﬁt dislocations are formed in the bilayer system by mechanisms similar to those recently analyzed in detail for the (111) gold/permalloy system [123, 124]. Oxidation was initiated by introducing an atomic oxygen atmosphere above the Al/Ni65 Co20 Fe15 multilayer. To ensure that a suﬃciently thick oxide layer formed within the real time simulated (∼1 ns), both a high oxygen −3 vapor temperature (8,000 K) and vapor density (0.0003 oxygen atoms ˚ A ) were used. This corresponds to a vapor pressure of ∼12 atm. of pure (atomic) oxygen. The heat of the Al + O reaction [125] released about 8.4 eV per atomic oxygen atom that reacted with the aluminum crystal. The thermostatically temperature controlled molecular dynamics algorithm [85] conducted this thermal energy away from the surface and maintained a surface temperature close to 330 K during oxidation even though the heat of reaction and atomic oxygen collision rate with the solid surface were both very high. The atomic conﬁgurations of two typical oxidized aluminum layers whose thickness prior to oxidation was about 12 and 2.5 ˚ A are shown on the right of Fig. 14.23a, b. The formation of amorphous aluminum oxide layers was observed in all the simulations as expected from experimental observations [126]. The composition of the AlOx oxide layer increased from x = 0 before oxidation to x = 1.55 ± 0.05 by the time oxidation ceased. The surface morphology of the AlOx layers was found to be highly sensitive to the aluminum layer thickness prior to oxidation. It can be seen from Fig. 14.23a that the oxidation of the thicker aluminum layer resulted in the formation of a compositionally uniform, continuous and ﬂat AlOx ﬁlm. However, when the aluminum layer thickness was reduced to 2.5 ˚ A (Fig. 14.23b), the AlOx ﬁlm became discontinuous, and in some places much thicker than anticipated even though the aluminum layer prior to oxidation had been continuous in thickness and relatively smooth. Oxidation of the thin aluminum ﬁlm clearly results in the formation of holes in the AlOx layer, exposing areas of the underlying Ni65 Co20 Fe15 crystal. The AlOx oxide layer roughness could be quantiﬁed by taking the maximum diﬀerence in the layer thickness and dividing it by the average layer thickness. This relative roughness was calculated for many simulations and is shown in Fig. 14.24 as a function of the average aluminum layer thickness (prior to oxidation). When the aluminum layer thickness exceeded 6 ˚ A, the AlOx oxide layer roughness was low. It can be seen that as the aluminum layer thickness was decreases below 6 ˚ A, the AlOx oxide layer roughness increases rapidly, which corresponds to the formation of pin holes in the AlOx layer. Further simulations using diﬀerent random number seeds to initiate the runs indicated that at an aluminum layer thickness of between 6 and 10 ˚ A, holes were formed with a probability that increased as the aluminum layer thickness was reduced. For all the simulations carried out at aluminum layer thicknesses above 10 ˚ A,

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Fig. 14.24. Eﬀect of aluminum layer thickness upon roughness of a reactively formed AlOx layer

Fig. 14.25. The eﬀect of the preoxidized aluminum layer thickness upon the magnetoresistance change of a magnetic tunnel junction

smooth oxide layers were obtained and no holes were observed. As a result, we conclude that for the crystal surfaces analyzed here, the critical aluminum layer thickness for smooth oxidation is around 10 ˚ A. This ﬁnding appears to be consistent with the experimental observation of the loss of TMR when the preoxidation aluminum layer thickness was decreased below ∼8 ˚ A, Fig. 14.25 [42], and with other experimental studies [43]. To explore the mechanism of hole formation, an initial Ni65 Co20 Fe15 substrate crystal containing 54 (22¯4) planes in the x-direction, 3 (111) planes in the y-(growth) direction, and 32 (2¯20) planes in the z-direction was assembled. About six additional atomic layers of the Ni65 Co20 Fe15 alloy were deposited on the initial substrate using an incident atom energy of 4 eV, a growth temperature of 300 K, and a deposition rate of 10 nm ns−1 . Between two and three

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˚) of aluminum were then atomic layers (corresponding to a thickness of ∼6 A deposited on the Ni65 Co20 Fe15 surface using an incident atom energy of 0.2 eV, a growth temperature of 300 K, and a growth rate of about 1.5 nm ns−1 . Oxidation of the aluminum surface was simulated by exposing the surface at a substrate temperature of 300 K to a high pressure (12 atm.) atomic oxygen vapor held at a high vapor temperature of 8,000 K. Time-resolved atom position images obtained during MD simulation of oxidation are shown in Fig. 14.23c to enable the detailed mechanisms of the oxide layer formation to be examined. It can be seen that after 40 ps of oxidation, oxygen vapor atoms had reacted with the aluminum surface to form aluminum oxide. The initial oxidation was not uniform and an aluminum depleted region developed near the center of the simulated region. This arises because the cohesive energy (eV atom−1 ) in oxides (such as Al2 O3 ) is much higher (more negative) than that of either pure aluminum or pure oxygen [72, 77], and the ﬁrst nucleated oxide regions then grow by drawing in nearby aluminum atoms. This results in the depletion of aluminum in the nearby surface, leading to exposure of the underlying Ni65 Co20 Fe15 . To access the stability of the aluminum depleted zone, the oxygen vapor was removed and the system was annealed at 600 K for 100 ps as shown in Fig. 14.23c. It can be seen that at least within the simulated timescale, the hole formed was quite stable and changed little during annealing. Oxidation was then resumed. As can be seen, after another 20 ps oxidation at 300 K, the aluminum depleted zone began to shrink. After a total of 80 ps of oxidation, the aluminum depleted zone had completely disappeared and the nickel alloy substrate was more or less covered by the aluminum oxide. To quantify the observations, the surface oxide layer of the system shown in Fig. 14.23c was divided into a 14 × 14 grids. If a grid element contains neither an oxygen nor an aluminum atom, the substrate area beneath the element was considered to be uncovered by either (the unreacted) aluminum or AlOx . The fraction of the grid elements that contained either aluminum or oxygen atoms can then be determined and is referred to as the coverage parameter. An oxygen fraction for a grid element can also be deﬁned as the ratio of the number of oxygen atoms to the total number of oxygen and aluminum atoms in the grid. Let the oxygen fraction for grid element i be XO,i (i = 1, 2, . . . , ng , where ng is the total number of grids containing either aluminum or oxygen atoms). The overall state of oxidation can be represented by the average oxygen fraction ng 1 ¯ XO,i . XO = ng i=1

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The uniformity of the oxide can then be represented by the standard deviation of the oxygen fraction . / ng ¯ O 2 / 1 XO,i − X . σ=0 ¯O ng X i=1

¯ O , and the standard deviation of the oxygen The average oxygen fraction, X fraction, σ, are shown in Fig. 14.26a as a function of oxidation time. The corresponding surface coverage parameter is shown in Fig. 14.26b. Figure 14.26a indicates that during oxidation, the oxygen fraction in the oxide layer gradually increased, eventually approaching a value of 0.7 (corresponding to AlO2.33 ). Formation of this highly oxidized state is consistent with highly reactive oxygen vapor conditions used for the simulation. Figure 14.26a also shows that the deviation in oxygen fraction was greatest early in the oxidation process and decreased with elapsed oxidation time. It indicates that the oxide formed during the earliest stages of oxidation was the least uniform. This occurs at a stage when holes have their highest nucleation probability. Figure 14.26b indicates that the initially fully aluminum covered Ni65 Co20 Fe15 surface gradually became locally uncovered once the oxidation began. This was associated with the formation of holes in the oxide layer such as that in Fig. 14.23c. However, the surface coverage parameter began to recover after an oxidation time of about 50 ps. The surface was once again fully covered (now by AlOx ) after about 90 ps of oxidation, consistent with the healing of the holes. Because the structure changed little during annealing, the rapid elimination of holes such as those shown in Fig. 14.23 appears to be a consequence of continuous oxidation rather than atom diﬀusion. Unlike annealing, continued oxidation caused increases in both thickness and oxygen composition of the oxide layer. Once oxidation starts, local regions with rich oxygen concentrations randomly form on the aluminum surface due to the random arrival of oxygen atoms on the surface. As has been discussed in the above, these oxygen-rich regions can attract nearby aluminum atoms to form expanding oxide nuclei because aluminum in the oxide has a much lower energy than aluminum alone. When the aluminum layer is very thin, this process can easily cause aluminum depleted zones around the oxygen-rich regions. As a result, holes are most likely to form at the earliest stage of the oxidation. The observation that holes begin to shrink in the fully oxidized layer can be easily rationalized by surface energy arguments. Suppose a round hole with a radius r forms in an AlOx layer with a thickness h, Fig. 14.27. The formation of such a hole results in (1) the creation of additional oxide surface area (on the interior of the hole), (2) the elimination of an oxide surface area (at the top of the hole), and (3) the creation of a Ni alloy surface area and the

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Fig. 14.26. Variation of average oxygen fraction (a) and AlOx coverage (b) with time during the reactive oxidation of aluminum to form an AlOx tunnel barrier on permalloy

elimination of some Ni alloy/oxide interface area (at the bottom of the hole). The resulting energy change, ΔE, can be written as ΔE = 2πrhγAlOx + πr2 (γNi65 Co20 Fe15 − γAlOx /Ni65 Co20 Fe15 − γAlOx ), (14.30) where γAlOx and γNi65 Co20 Fe15 are the surface energies of AlOx and Ni65 Co20 Fe15 , respectively, and γAlOx /Ni65 Co20 Fe15 is the interface energy

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Fig. 14.27. Model circular hole in an AlOx ﬁlm on a permalloy substrate

between AlOx and Ni65 Co20 Fe15 . Equation (14.30) indicates that holes with small radius, r, and large thickness, h, have a positive energy increase, ΔE. They are therefore unstable and can be healed. This is driven by a competition between the area increases of the aluminum oxide–nickel alloy interface and the area reductions of the aluminum oxide and nickel alloy surfaces. Under the accelerated oxidation conditions required for the short timescale simulations, the transient hole phenomenon was found to occur within a very short time (80 ps) (Fig. 14.23). This means that during experiments where the timescale is signiﬁcantly longer, the phenomenon is not likely to be constrained by kinetics. As a result, holes are expected to always form during the early stage of oxidation of very thin (say, 6 ˚ A thick) aluminum layer under conditions commonly used in experiments. The healing of the holes is expected to occur when the aluminum layer is relatively fully oxidized. This suggests that the transient holes never form during oxidation of thick aluminum layers because the surface aluminum is always fully oxidized before any aluminum region is completely depleted to initiate a hole. The simulations also suggest that holes cannot be healed during prolonged oxidation of very thin aluminum layers because when the aluminum is quickly fully oxidized, the driving force for the hole healing is saturated and therefore the hole ceases to further shrink. A direct experimental observation of the atomic scale structure of the AlOx -on-Ni65 Co20 Fe15 system has not been found in literature. However, Petford-Long et al have carried out extensive high resolution transmission electron microscopy (HRTEM) and 3DAP experiments to examine atomic scale structure of the AlOx oxide formed from oxidation of 6 ˚ A thick aluminum layer on Co90 Ni10 [127]. Their experiments indicated that with under-oxidation conditions, the AlOx layer exhibits discontinuous islands with signiﬁcant areas of the Co90 Ni10 surface uncovered. This phenomenon closely corresponds to the formation of big holes in the oxide layer in the under-oxidized samples seen above. Annealing of these under-oxidized samples was found to cause the AlOx islands to spread to form a network along the grain boundaries. Note that

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the experimental annealing involved further oxidation. These experimental observations appear similar to the results of the simulations. The experiments further indicated that more complete oxidation of the aluminum surface produces a more continuous AlOx layer. However, these as-grown ﬁlms still contained holes on the scale of roughly 10 nm. The oxygen composition in the AlOx layer, on the other hand, was found to be still far below the one deﬁned by the fully oxidized AlO1.5 (Al2 O3 ). These holes were eliminated and a continuous AlO1.5 layer ﬁnally formed when the samples were annealed. This suggests that oxygen may have diﬀused from further away to complete the oxidation and that the layer then laterally spread to ﬁll the holes. Dewetting of a very thin metal layer on another metal surface due to the oxidation is clearly a very potent and perhaps quite widespread phenomenon. Low energy electron microscopy (LEEM) and diﬀraction (LEED) experiments have been used to study the oxidation of 1–2 ﬂat monolayer’s of chromium deposited on a (100) tungsten surface [128]. The results indicate that the chromium oxide layers become unstable and form three-dimensional islands as the Cr2 O3 was formed at elevated temperatures, T ≥ 790 K.

14.6 Ion-Assisted Reactive Growth of Dielectric Layers The various simulations and experiments discussed above indicate that inert ion impacts with the rough surface of a thin ﬁlm are highly eﬀective at redistributing the material contained in asperities leading to formation of a ﬂatter surface. This occurs because high energy inert gas impacts break the bonds between the atoms forming the asperities, and when this is performed during deposition, it reduces the probability of island nucleation and the signiﬁcance of ﬂux shadowing. Because highly constrained kinetic conditions are used in the deposition of metallic multilayers, the broken surface asperities are also slow to reform through thermally activated diﬀusion, even when these structures are thermodynamically more favorable. There has been signiﬁcant speculation that ion assistance during the reactive formation of dielectric tunneling barriers might be advantageous. However to our knowledge, little has been reported on the beneﬁts of inert gas ion assistance during the reactive growth of tunnel barrier layers used in TMR structures. It is possible that the idea has not been pursued because of concern that the ion assistance used to ﬂatten the surface of a very thin aluminum oxide layer will also cause damage to the underlying interface. This stems in part from a realization that the cohesive energy of Al2 O3 is about 6.5 eV [72, 77], which is much higher than those of the underlying metals (Al: 3.58 eV, Ni: 4.45 eV, Co: 4.41 eV, and Fe: 4.29 eV). This implies that ion energies suﬃcient to break the Al2 O3 bonds are likely to cause signiﬁcant mixing at the underlying Al2 O3 –metal interface since the Al2 O3 layer is very thin. We have also seen that, there is

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a strong tendency for the holes to form when the aluminum oxide thickness is between 10 and 20 ˚ A. In this regime, it is likely that even if the assisting ion impacts ﬂatten the oxide layer without causing damage to the underlying interface, a rough oxide layer surface is likely to quickly reform as the process is driven by energetic considerations and not signiﬁcantly impeded by kinetic’s at ambient or perhaps even cryogenic temperatures. The simulation methods developed in this chapter allow the beginning of a quantitative assessment of these speculations. The MD approach used to simulate the oxidation of the single-layer aluminum sample shown in Fig. 14.23b can be used for this assessment except that an additional xenon ion ﬂux is injected toward the growth surface translating an ion energy of 8.0 eV. The xenon energy and the xenon to oxygen ﬂux ratio can be easily varied but only results for a ﬂux ratio of 6.67 are discussed here. The atomic conﬁgurations obtained before and after the ion-assisted oxidation are shown in Fig. 14.28a, b, respectively. If these are compared with the nonassisted results in Fig. 14.23b it can be seen that a rough AlOx layer has still formed even with an ion assisting energy of 8.0 eV. This is consistent with the very strong dewetting phenomena present in very thin oxide layers. Careful comparisons of Figs. 14.28 and 14.23 indicate that the ion impacts have had some eﬀect and appear to have slightly reduced the height of the AlOx regions and reduced the underlying metal surface area that has been exposed. It should be pointed out that the dewetting eﬀect is most severe for the very thinnest oxide layers. As a result, the observation here does not

Fig. 14.28. Ion-assisted reactive growth of an AlOx layer on a permalloy substrate. Ion assistance has failed to modify the dewetting phenomenon driving the transient hole formation during the oxidation of thin aluminum layers

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exclude the possibility that ion-assisted deposition could be used to more eﬀectively ﬂatten thicker aluminum oxide or other reactively formed ﬁlms that have a lesser tendency for dewetting. The ﬂattened islands on these thicker ﬁlms are also less likely to reform under appropriately constrained kinetic growth conditions. An additional advantage for thicker oxide ﬁlms is that higher ion energies could be used without risk of damaging the underlying oxide–metal interface.

14.7 Conclusions Atomistic simulation approaches capable of accurately predicting atomic scale structures of vapor deposited metal and metal oxide multilayers have been developed. Simulations using these approaches revealed fundamental insights determining the quality of GMR metal multilayers and TMR metal/metal oxide multilayers. Increasing adatom energy is found to both ﬂattens the interface and causes interlayer mixing. As a result, a low roughness/mixing combination is obtained at an intermediate adatom energy. The use of modulated energy deposition, where low energy is used to deposit the ﬁrst a few monolayers of a new layer to minimize mixing and a high energy is used to complete that layer to ﬂatten the ﬁnished surface, is found to further minimize interfacial roughness and interlayer mixing. Surfactants can also reduce interfacial roughness. Low energy ion-assisted deposition is additional means to reduce interfacial roughness. To minimize inert gas impact induced mixing, modulated ion assistance and sequential ion assistance can be used. Due to a strong dewetting phenomenon, pin holes always form during growth of tunneling barrier layers provided that the barrier layer thickness is below ∼6–10 ˚ A. These pin holes cannot be avoided using ion assistance. Smooth uniform barrier layers can be grown when the barrier layer thickness is increased beyond 10 ˚ A.

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Index

β-alumina, 375 Absorption coeﬃcient, atoms, 312 Ag-based delafossite materials, 424 All-TCO p–n junction diode, 444 delafossite based I–V characteristics, 442 transparency of, 444 spinel based I–V curve, 441 lattice mismatch, 442 ZnO epitaxial layer, 442 Ambipolar diﬀusion, HiPIMS, 330 Amorphous semiconductors, 442 Analytical and experimental models, 81 discharge voltage, 82 ionization distribution vs. plasma emission distribution, 81 Apatite, 388 Apatite structure, 371 Ar-N2 gas mixture, emission spectrum in, 308 Argon neutral emission, 329 Asymmetrical bipolar discharge, 255, 268 electron temperature, 260 insulating dielectric ﬁlms, 255 potential drop, 270 target potential and plasma potential, 268 Atomistic simulations, 505 advantages of the approach, 555 analyses results, 525

energy modulation deposition experiments, 525 interatomic potentials, 505 charge transfer ionic potential (CTIP), 510 CTIP and EAM parameters, 513, 514 embedded atom method (EAM) potential, 505, 508 inert gas impacts and ionic interactions, 507 ionic energy, calculations, 510 oxygen electron density, 514, 515 molecular dynamics (MD) model, beneﬁts of, 515 surfactant eﬀects, 526 Ag atoms surface diﬀusion and inﬂuence, 531 compositional proﬁles, 527, 529 experimental approach with Au-Ag, 527–529 mechanisms responsible, 528 molecular dynamics approach, 526 Aurivilius phase structure, 371 Barium cerate, 390–392 Bipolar pulsed dual magnetron discharges, 350, 358 charge carrier density and electron temperature, 350 CME and plasma properties of, 350 ITO ﬁlm properties and CME, 358 optical emission intensity of, 352 Brownmillerite structure, 370

562

Index

Carbon nitride, RF sputtering and deposition of, 273 Cathode poisoning, 319 CCE, see Cross corner eﬀect Ceramic Na+ conductors, 375 Cerates, 390 Ceria based electrolytes, dopant and ionic conductivity of, 384 Charge carrier density, 264, 349 and electron temperature, 349 spatial distribution of, 262, 264 unipolar and bipolar pulsed single magnetron discharges, 349, 350 Charge carrier density and deposition rate, ratio of, 360 Chemical Modulation, p-type conductivity, 450 Chromogenic building skins, energy eﬃciency, 486 Coating densiﬁcation and stack integrity, 380 Computation illustrations, 103 calculation process, 105 collision rates, 109 electric ﬁeld, 107, 108 electron and Ar+ ion densities, 108 ion ﬂux bombarding the cathode, 114, 115 mean energy and energy probability function, 111 operating conditions and simulation data, 103 potential distribution, 105, 106 sheath architecture, 107 Computational load allieviation, 99 sorting, 102 subcycling, 100 superparticle (SP) weight determination, 103 variable time step, 101 weighting optimization, 101 Computer simulation codes, 2 molecular dynamic (MD) types, 4 Monte Carlo (MC) types, 2 Construction of GMR structures, sputtering methods, 504 Copper aluminum oxide (p-CuAlO2 thin ﬁlms), 459 delafossite structure, 469

direct bandgap of, 465 Fermi level and Fermi energy, 471 ﬁeld emission property, research into, 475 ﬁlm orientation, 459 future research topics, 475 Hall coeﬃcient of, 468 I–V characteristics of, 466 percentage of excess oxygen in, 461 residual stress, 460 Seebeck coeﬃcient (SRT) of, 468 strain and particle size determination of, 461 strain broadening, 460 synthesis by reactive DC sputtering, 457 polycrystalline nature, 474 reﬂectance and transmittance measurement, 457 target preparation and ﬁlm deposition, 457 temperature variation of conductivity, 467 thermoelectric properties, enhancement, 469 transmittance, reﬂectance and absorption coeﬃcient, 462, 463 Cross corner eﬀect, 337, 339 asymmetry of, 339 E × B drift, 340 in literature, 337 ionisation points, 342 magnets, size and shape of, 341 prevention, 344 Cross magnetron eﬀect, twin or dual magnetron, 346 Cu-based delafossite materials, 424 CuAlO2 thin ﬁlm, deposition parameters of DC sputtering, 428 D10 -based delafossite materials, 424 Cu-based and Ag-based, 424 space group, 424 Delafossite materials, 416, 417 applications, 417 defect reaction for, 451 ion exchange method, 432 temperature variation of conductivity of doped and undoped, 453

Index ternary and quaternary metal oxides, 416 thermoelectric properties, research, 475 Delafossite structure, 416 Dissociated oxygen, 360 atomic oxygen and total ﬂuxes, ratio of, 361 deposition process and jO− /jtot values, 361 Doppler broadening, 313 Double probes, 257 Electrical probes, plasma-processing discharges, 256 Electrically ﬂoating surface and plasma potential, 270 Electrochemical stability, 393 Electrochromic display, 400 Electrochromic foils, 490 applications, present and future, 490, 492 properties, 490, 491 Electrochromic materials, 399 deposition of, 400 optical properties, 399 Electrochromics, 487 devices, 487 materials in EC devices, 488 present state and future promise, 493 technological progress, 488 ﬁlm porosity, need for, 489 non-conventional technologies, 488 Electron drift velocity and magnetic ﬁeld, 340 Electron emission, 43 electron transport, 46 electron yields, 46 angular distributions, 48 clean and contaminated surface areas, 48, 49 ion velocity dependence, 47, 50 oxidation eﬀects on, 57 excitation mechanisms, 44 kinetic electron emission (KEE), 45 minimum energy, U , 44 potential electron emission (PEE), 45 separation of PEE and KEE, 46

563

factors inﬂuencing, 46 research directions, 58 Electron energy distribution functions (EEDF), 259, 261, 262 Electron temperature and pulse frequencies, 259, 260 Electronic collisions, 323 Emissive probe, plasma potential, 258 Encapsulation layer, 392 Energy-resolved mass spectrometry, 272 Excitation spectrum, LIE, 322 Excited level 3, creation terms and loss terms for, 323, 324 Film forming particles, total ﬂux of, 361 Film thickness distribution, targets, 354, 355 Film transparency and deposition process, 337, 354 Fluorescence spectrum, LIE, 322 Fluorite structure, 369 Gadolinia doped ceria (GDC), 385 coating deposition by DC sputtering, 385 deposition on YSZ membranes, 385 gadolinium doping, 385 ionic conductivity, 385 Gas temperature measurement, 313 Giant magnetoresistive eﬀect, 497 micro electronic devices, 497 tecnological developments, 497 Giant magnetoresistive multilayers, 498 construction of GMR structures, 504 magnetron sputtering methods, 504 vapor deposition methods, 504 discovery and use, 498 magnetic tunnel junctions devices, 500 perpendicular or parallel current ﬂow, 499 spinvalve devices, 501 magnetotransport properties sensitivity, 503 performance optimization, 501 TMR eﬀects, 503 tunneling magnetoresistance (TMR) eﬀect, 501 Glow discharges

564

Index

1D hybrid model simulation, 50, 51 discharge conditions, 52 eﬀective electron yield, 54 electron recapture, 54 incidence angle dependence, 52 sputter deposition, 53 chemisorption of the cathode, 56 discharge voltage change, 56 electron emission yield discrepancies, 57 ion-induced electro emission, role of, 50 GMR materials, sputtering pressure, 524 IBD process, 524 ion beam deposition process, 524 simulations vs experiment, 524 GMR properties, multilayer types, 527 Half-intensity broadening of Ti lines, 317 High-Power Impulse Magnetron Sputtering, 327 dissociation rate for, 332 electric impulsions production, 327 emission spectra, 328 HiPIMS, see High-Power Impulse Magnetron Sputtering Hollow cathode lamp, 311 pulsing, 311 spectrum, 317 Homo-junctions and lattice matching, 445 Indium tin oxide (ITO), 354 CCE and CME eﬀects on, 355 incorporation of oxygen in, 360 Inorganic electrochromic thin ﬁlms, 399 Instrumental broadening, 460 Ion energy distribution functions, 274 eﬀective stopping potential, 274, 277, 278 of argon, oxygen and titanium species, 274 pulse frequency eﬀects on, 276 time-resolved measurements of, 278, 279 Ionisation collisions, 261

Ionisation points, spatial distribution of the, 343 ITO ﬁlms, 355 FWHM values and lattice spacing of, 359, 360 optical absorption and electrical resistivity of, 355–358 K2 NiF4 structure, 374 KH2 PO4 (KDP) structure, 374 La-Si coatings, 389 LAMOX (Lanthanum-Molybdenum Oxide) structure, 372 LAMOX coatings, 388 Lanthanum molybdate coatings, 387 Lanthanum silicates, 388 Large bandgap spinels, 415 Laser beam energy density, 325 Laser excitation, 325 Laser-induced ﬂuorescence (LIF), 293, 320 experimental set-up for, 326 physical principle of, 320, 322 uses of techniques, 293, 295 Li+ conductor elecrolytes, 377 LIF, see Laser-induced ﬂuorescence LiNbO3 , 402 LISICON fast ionic conductors, 393 Lithium all solid state sputter deposited microbattery, 392 Lithium conductor electrolytes, 393 Low-pressure magnetron plasma, 307 Magnetic ﬁeld distribution, target, 339 Magnetic ﬁeld tuning, see Cross corner eﬀect Magnetically shielded anode, eﬀects of, 351 Magnetron and plasma density distribution, 342 Magnetron discharge modeling analytical approach evaluation, 123 future research scope, 124 industrial challenges, 76 accuracy, 78 geometry issues, 77 pulsed sputtering, 77 laboratory challenges, 75

Index electron recapture, 76 electron transport issues, 76 secondary electron emission yield γ, 75 planar semi-analytical model, 78 Coulomb collisisons and Bohm diﬀusion, 81 discharge current calculation, 80 ionization model, 79 self-consistent model, 79 Magnetron discharge modeling approaches analytical models, 65, 66 disadvantages, 67 model types and their uses, 66 Boltzmann equation, use of, 68 ﬂuid models, 67 hybrid models, 71 features and uses, 71 validity limitations, 71 Monte Carlo (MC) simulations, 69 advantages, 70 types and their contribution, 70 PIC-MCC simulations, 65, 72 disadvantages, 73 features and advantages, 72 requirements in the model, 65 Magnetron discharge simulations, 62 discharge model, 63 electrons and discharge gas particles, 65 ion bombardment, 63 magnetic ﬁeld, 62 sputtered particle transport, 64 Magnetron plasmas, 301, 311, 346 emission spectroscopy of, 302 laser-induced ﬂuorescence of, 326 optical emission spectroscopy, 301 resonant absorption spectroscopy of, 311 time dependent optical emission of, 346 Magnetron source, 347 Magnetron sputtering, 61, 200, 229 biaxially aligned thin ﬁlms, 223 deposition pressure inﬂuence, 224 in-plane alignment, 223 binary collision Monte Carlo code, 218

565

deposition proﬁles comparison, 219 material ﬂux simulation, 220, 222 sputter sources, 218 cost reduction needs, 61 energy and angular distribution of particles, 201 alternate analytical models, 204 analytical models and experiments, 206 collision cascade regimes, 201 comparitive merits of models, 208, 209 numerical method, 207 Sanders and Roosendaal model, 205 Sigmund-Thompson theory, 201 simulation model development, 207 sputter yield calculation, 201 energy deposited on substrate, 229, 231 electrical eﬀects, 236 energy exchange parameters, 230 integral energy ﬂux, factors, 232, 234 magnetron power, 235 measurement, 231 particles’ inﬂuence, 229 per atom basis, 237, 238 probe and plasma potentials, 236, 237 target distance, 235 temperature determination techniques, 231, 233 energy model representation, 239 electron density, 243, 244 electron temperature, 244 ions and electrons contribution, 243 plasma radiation contribution, 242 reﬂected neutrals contribution, 241 shield temperature, 245, 246 sputtered particle contribution, 240 thermal radiation eﬀects, 244 energy model results, 246 per atom basis, factors, 248 plasma, power and pressure eﬀects, 250 reactive vs elemental deposition, 249 total energy ﬂux, 246, 247

566

Index

ﬁlm structure, role of energy deposited, 251 gas particle collision, 209 attractive potential, 214 Born–Mayer potential, 216 collision cross section, σ, 210 combined potential, 217 hard sphere approximation, 211 mean free path, 210 repulsive potential, 214 scattering interaction geometry, 211, 212 screening functions, 215 sputtered atom direction, 213, 214 Thomas-Fermi-Dirac interaction potential, 216 gas rarefaction, 217 radial distribution of particles, 200 simulation process inputs, 61 simulation vs experiment results, 224 virtual sputter magnetron, 62 Metal multilayer growth, 532 atomic layer structure, HRTEM experiments, 552 dielectric layer deposition, 545 aluminum ﬁlm growth, 546 aluminum layer thickness eﬀect, 547, 548 mechanism of hole formation, 548, 550 quantiﬁcation of oxidation, 549, 551 ion assisted deposition, 532 Auger electron spectrometry results, 544 ﬂat growth of surface, 532, 533 in-plane electrical resistivity, 542, 543 ion incident angle eﬀect, 534, 537 low energy approaches, 539–541, 544 model system analysis, comparison, 536, 538 rough surface reconstruction, 533 roughness and intermixing parameters, 534–536 ion assisted dielectric layer growth, 553 formation of a ﬂatter surfaces, 553, 554

MD approach to simulation, 554 molecular dynamics simulation, 516 atomic conﬁgurations, 517, 518 copper (Cu) mixing, 520, 522 exchange mixing mechanism, 524 incident adatom energy, 518, 519 interfacial roughness, amplitude and wavelength, 519 surface roughness, 519–521 micro accumulator, 392 electrolyte (LIPON), 393 positive electrode, 394 Microbatteries, 392 Mixed conductors, 377 Monochromator, 303 Monte Carlo collision (MCC) model, 95 features and beneﬁts, 95 null collision method, 96 collision sampling procedure, 98 merits and drawbacks, 96 Monte Carlo simulation, magnetron system, 340 NASICON (Sodium (Na) Super Ionic Conductor), 375 NASICON sputter deposition, 398 Neodymium cobaltite thin ﬁlms, 399 Ni-based spinel ﬁlms (NiCo2 O4 ), deposition of, 421 Ni/R, see Charge carrier density and deposition rate, ratio of O− and O− 2 negative ions, energy distribution of, 280–281 OES, see Optical emission spectroscopy Optical depth and absorption coefﬁcient, relationship between, 312 Optical diagnostics, 301 Optical emission line, 382 Optical emission measurement, 347 Optical emission spectroscopy (OES), 286 plasma emission monitoring (PEM), 287 reactive sputter processes, characterisation of, 286 sputter gas argon, emission lines of, 288

Index Optical imaging, 292, 293 Optical thickness kσ0 L, 312 Oxygen partial pressure (pO2 ), powering modes, 363 Oxygen partial pressure and substrate, 361 P-TCO thin ﬁlms, 424 copper gallium oxide and copper indium oxide, 424 deposition parameters and electrooptical parameters of DC-reactive sputtered, 440 deposition parameters of delafossite, 428 doping concentrations, 426 fabrication and characterization, 475 optical and electrical properties of spinel and delafossite, 435 P-type transparent conducting oxides delafossite structure based, 422, 424 deposition parameters, 428 electro-optical properties of, 420, 425 oxygen intercalation in, 453 pulsed laser deposition (PLD) of, 427 reactive sputtering of, 436 space group, 424 materials, 420 p-type conductivity, causes of, 448, 451 reactive sputtered, 432 spinel structure based, 420 conductivity and transparency, 420 deposition of, 421 structural requirement for designing, 450 substitutional doping of, 453 Particle-in-cell (PIC) model, 83 approximations and computational cycle, 84 charge assignment, 86, 88 external circuit incorporation, 89 force interpolation digital ﬁltering, 93 leap-frog algorithm, 85 Poisson’s equation, cyclic reduction method (CRM), 87 stability and accuracy, 93

567

Particle-size broadening, 459, 460 Perovskite structure, 370 Perovskites, 398 PIC-MCC model extension computation illustrations, 115, 119 electron density proﬁle, 121, 122 erosion proﬁle, 122, 123 gas temperature distribution, 120 description, 116 numerical procedure, 116 species included, 116 Plasma broadening, 313 Plasma density, decay of, 266 Plasma emission monitoring (PEM), 287 Plasma mass spectrometry, 270 Plasma potential measurements, 266 PLD, see Pulsed laser deposition Potential drop, substrate and plasma, 270 Probe techniques, plasma-processing discharges, 257 Proton conductors, 389 Pulsed laser deposition, delafossite p-TCO thin ﬁlms, 427 Pulsed magnetron discharges, 258, 264 electrical probes, 258 target voltage waveforms, 262, 264 Pyrochlore phase, cathode and YSZ ﬁlm, 381 Pyrochlore structure, 370 Radiative deexcitation, 323 Reactive magnetron sputtering, 255, 367 laboratory set-up for, 271 trends to control, 367 unipolar and bipolar modes, 255 Reactive magnetron sputtering process, 131, 153, 240 aluminium oxide deposition, 153 discharge voltage, 156, 157 hysteresis behaviour and experiment, 153–155 parameters inﬂuencing, 156 Berg’s model, 133, 153 complete model, 186 comparison with Berg’s model, 192 deposition proﬁle inﬂuence, 186, 188

568

Index

erosion proﬁle inﬂuence, 189 plasma chemistry implementation, 186 rotating cylindrical magnetron, 191 energy of reaction, 240, 241 experiment conclusions, comparison validity, 166 gas addition eﬀects, 131 ion induced electron emission (ISEE), 155 material properties and process conditions, 141 electron emission and ion implantation, 150 pumping speed and sputtering yield, 141, 142, 156 reactive co-sputtering, 147 sticking coeﬃcient α, 141 target size and mixtures, 143 two reactive gases, 145, 147 mathematical treatment, 134, 135 oxygen exposure, discharge voltage, 157, 158 plasma oxidation, 158 diﬀerence from oxygen exposure, 160 discharge voltage, 159 experiments with other materials, 162, 164 relative discharge voltage, 160, 161 total sputter yield, 160 poisoning of target, mechanisms and eﬀects, 161 reactive gas ﬂow calculated χ2 and the experimental error, 183 experimental trends, 184, 185 parameters involved, 182 reactive gas partial pressure calculation, 174 reactive gas ﬂow, 173 reactive ion implantation, with chemisorption chemisorption inﬂuence, 171 erosion rate and target sputter yield, 170, 171 knock-on eﬀect, 181 oxidation level dependence, 176, 177 target condition, 176

target surface condition, 180, 181 reactive ion implantation, without chemisorption, 175 experiment vs. model, 175, 176 implanted ion concentration, 167 mole fraction calculation, 178, 179 reaction rate constant, k, 179, 180 time-dependent concentration, 169 stability experiment, 164–166 steady state equations, 136 assumptions of conditions, 136 deposition rate D, 138 derivation of equations, 136 reactive gas ﬂow vs. compound fractions, Rm and D, 138, 140 Reactive sputtering technique, 473 applications to p-type thin ﬁlms, 473 bandgap CuAlO2 thin ﬁlms, 474 research needs, 474 conductivity increase, 474 cost-eﬀective fabrication, 475 spinel and delafossite oxide ﬁlms, 474 Reactively DC sputtered YSZ-based sensor fabrication process, 396 RF coil and magnetron cathode, 303 samaria doped ceria (SDC), 385 Secondary electron emission coeﬃcient γ, 265 Silver cobalt oxide thin ﬁlm, 425 direct bandgap of, 422 optical transmission of, 427 XRD pattern of, 430 Silver nitride, 175 Sine wave driven dual magnetron, deposition rate of, 364 Sine wave powering, 351 Single probes, 266 SOFC, see Solid oxide fuel cells Solid electrolytes, 369 H + Carriers, 374 O2− Carriers, 369 ionic transport properties, 369 Li+ Carriers, 377 Na+ Carriers, 375 Solid oxide fuel cells, 377 Solid state electrochemical gas sensors, 394 amperometric sensors, 395

Index magnetron sputtering considerations, 396 potentiometric gas sensors, 395 Source broadening, 313 Space charge sheath formation, 257, 269 Spinel materials, 414 binary, ternary and quaternary metal oxides, 415 large bandgap spinels, 415 Spinel structure cations, 415 fcc array of anions, 414 Sputtering processes, 1 angular distribution of sputtered atoms, 23 low and high incident-energy, 21, 22 Sigmund-Thompson theory, 201, 204 sputtering mechanism, 24, 25 atomically rough surface, 28, 29 compound materials, 2 computer codes, 1, 6 diﬀerential yields, 2 direct and indirect knock-out process, 12, 14 energy spectrum of sputtered atoms, 16 inelastic and elastic energy loss, 20 light-ion bombardment, 17, 18 Thompson formula, 16 incident energy Bohdansky formula, 8 sputtering mechanisms, 5 Thomas-Fermi potential, 8 Yamamura formula, 5, 9 incident-angle energy, density distribution, 9, 14, 15 low energy sputtering, randomization, 28 modeling of surfaces, 11 multi-component material surface ion-ﬂuence dependence, 30, 35 Monte Carlo simulation codes, 33 multiple component target theory, 32 radiation-induced diﬀusion, 35 spectroscopies used, 30 surface composition, understanding of, 31

569

surface segregation, 30 time constant of kinetic process, 37 preferential ejection angle βp , 26 surface roughness eﬀects, 2 Stimulated emission, 324 Strain broadening, 460 Strontium zirconate, 391 Substitutional doping and p-type conductivity, 453 Substrates, heat load of, 353 Tantalum pentoxide (Ta2 O5 ) ﬁlms, 401 Target erosion inhomogeneity, 337 and homogeneous target erosion, 342 plasma density distribution, 342 rectangular magnetron’s, 338 Target potential and plasma potential, 268 TCO, see Transparent conducting oxides Ternary metal oxide crystal structure, 414 Thin ﬁlm growth techniques, 427 Thin ﬁlms, 420 electrical conductivity and optical transmittance of ZnRh2 O4 , 420, 422 resistivity of Ni−Co−O, 420 Ti and Ti+ energy levels, 303, 304 Titanium oxynitride thin ﬁlms, 272 Transparent conducting oxides, 417 bandgap designing for, 418, 419 characteristics and applications of, 417, 418 p-type, 418 delafossite structure based, 422 spinel structure based, 420 Transparent electronics, 418 p-TCO materials for, 420 transparent ﬁeld-eﬀect transistors (TFET), fabrication of, 447 Tungsten oxide ﬁlms, 400 properties of, 400 sputtering, 400 Unipolar pulsed single magnetron discharges, 349 CCE and plasma properties of, 349 ITO ﬁlm properties, 356

570

Index

Vacuum chamber, 302 Valence band edge, metal-oxygen bondings, 449 Y doped barium cerate coatings, 390 YSZ, see Yttrium stabilized zirconia YSZ ceramic ﬁlms, deposition methods of, 379 YSZ coatings, 380 deposition rate and emission line, 382 RF sputtered, 380 Yttrium stabilized zirconia, 379 coatings on large area substrates, 382

deposition rates of, 381 properties, 379 sputtering deposition parameters, eﬀects of, 397 thin-ﬁlm morphology, 384 Zirconia based electrolytes, 378 dopant concentration, 378 vacancies rate, 378 Zn-based spinel p-TCO ﬁlms, deposition of, 422 Zr-Y metallic alloys, sputter-deposition rates of, 382

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