Advances in Imaging and Electron Physics, Volume 143 (Advances in Imaging and Electron Physics)

ADVANCES IN IMAGING AND ELECTRON PHYSICS VOLUME 143 ELECTRON-BEAM–INDUCED NANOMETER-SCALE DEPOSITION EDITOR-IN-CHIEF ...

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ADVANCES IN IMAGING AND ELECTRON PHYSICS VOLUME 143 ELECTRON-BEAM–INDUCED NANOMETER-SCALE DEPOSITION

EDITOR-IN-CHIEF

PETER W. HAWKES CEMES-CNRS Toulouse, France

HONORARY ASSOCIATE EDITORS

TOM MULVEY BENJAMIN KAZAN

Advances in

Imaging and Electron Physics Electron-Beam–Induced Nanometer-Scale Deposition Edited by NATALIA SILVIS-CIVIDJIAN Department of Computer Science Vrije Universiteit Amsterdam, The Netherlands

CORNELIS W. HAGEN Delft University of Technology CJ Delft, The Netherlands

VOLUME 143

AMSTERDAM • BOSTON • HEIDELBERG • LONDON NEW YORK • OXFORD • PARIS • SAN DIEGO SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO Academic Press is an imprint of Elsevier

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CONTENTS

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Future Contributions . . . . . . . . . . . . . . . . . . . . . . . . . Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vii ix xv

Electron-Beam–Induced Nanometer-Scale Deposition

Natalia Silvis-Cividjian and Cornelis W. Hagen I. II. III. IV. V. VI.

Introduction. . . . . . . . . . . . . . . . . . . . Electron-Beam–Induced Deposition: A Literature Survey The Theory of EBID Spatial Resolution . . . . . . . The Role of Secondary Electrons in EBID . . . . . . Delocalization EVects in EBID . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . .

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Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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PREFACE

Deposition of matter at the scale of nanometres by means of electrons is the subject of this latest and very welcome example of a book-length contribution to theses Advances. With nanofabrication such an active research area, and likely to become even more busy, this study of the physics of what was originally regarded as (undesirable) contamination is timely and thorough. The authors first take us through the transitional years, in which the ‘benefits’ of contamination gradually became apparent. Instrumentation for electron beam–induced deposition is then described, followed by an account of experimental results – the list of achievements of the technique is impressive. Long sections are devoted to the underlying theory and such topics as secondary-electron scattering and delocalization have sections of their own. I am very pleased that Natalia Silvis-Cividjian and Cornelis W. Hagen agreed to prepare this text for publication here and am certain that such a full treatment of the subject will be found very useful. Peter W. Hawkes

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FUTURE CONTRIBUTIONS

G. Abbate New developments in liquid-crystal-based photonic devices S. Ando Gradient operators and edge and corner detection A. Asif Applications of noncausal Gauss-Markov random processes in multidimensional image processing C. Beeli Structure and microscopy of quasicrystals V. T. Binh and V. Semet Cold cathodes G. Borgefors Distance transforms A. Buchau Boundary element or integral equation methods for static and time-dependent problems B. Buchberger Gro¨bner bases T. Cremer Neutron microscopy H. Delingette Surface reconstruction based on simplex meshes A. R. Faruqi Direct detection devices for electron microscopy R. G. Forbes Liquid metal ion sources C. Fredembach Eigenregions for image classification S. Fu¨rhapter Spiral phase contrast imaging L. Godo and V. Torra Aggregation operators

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FUTURE CONTRIBUTIONS

A. Go¨lzha¨user Recent advances in electron holography with point sources M. I. Herrera The development of electron microscopy in Spain D. Hitz (vol. 144) Recent progress on high-frequency electron cyclotron resonance ion sources D. P. Huijsmans and N. Sebe Ranking metrics and evaluation measures K. Ishizuka Contrast transfer and crystal images J. Isenberg Imaging IR-techniques for the characterization of solar cells K. Jensen Field-emission source mechanisms L. Kipp Photon sieves G. Ko¨gel Positron microscopy T. Kohashi Spin-polarized scanning electron microscopy W. Krakow Sideband imaging R. Leitgeb Fourier domain and time domain optical coherence tomography B. Lencova´ Modern developments in electron optical calculations H. Lichte New deveopments in electron holography Z. Liu Exploring third-order chromatic aberrations of electron lenses with computer algebra W. Lodwick Interval analysis and fuzzy possibility theory

FUTURE CONTRIBUTIONS

L. Macaire, N. Vandenbroucke, and J.-G. Postaire Color spaces and segmentation M. Matsuya Calculation of aberration coefficients using Lie algebra S. McVitie Microscopy of magnetic specimens S. Morfu and P. Marquie´ Nonlinear systems for image processing M. A. O’Keefe Electron image simulation D. Oulton and H. Owens Colorimetric imaging N. Papamarkos and A. Kesidis The inverse Hough transform R. F. W. Pease Miniaturization K. S. Pedersen, A. Lee, and M. Nielsen The scale-space properties of natural images I. Perfilieva Fuzzy transforms E. Rau Energy analysers for electron microscopes H. Rauch The wave-particle dualism E. Recami Superluminal solutions to wave equations G. Ritter and P. Gader (vol. 144) Fixed points of lattice transforms and lattice associative memories J.-F. Rivest (vol. 144) Complex morphology P. E. Russell and C. Parish Cathodoluminescence in the scanning electron microscope

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FUTURE CONTRIBUTIONS

G. Schmahl X-ray microscopy J. Serra New aspects of mathematical morphology R. Shimizu, T. Ikuta, and Y. Takai Defocus image modulation processing in real time S. Shirai CRT gun design methods H. Snoussi Geometry of prior selection T. Soma Focus-deflection systems and their applications I. Talmon Study of complex fluids by transmission electron microscopy G. Teschke and I. Daubechies Image restoration and wavelets M. E. Testorf and M. Fiddy Imaging from scattered electromagnetic fields, investigations into an unsolved problem M. Tonouchi Terahertz radiation imaging N. M. Towghi Ip norm optimal filters D. Tschumperle´ and R. Deriche Multivalued diffusion PDEs for image regularization E. Twerdowski Defocused acoustic transmission microscopy Y. Uchikawa Electron gun optics C. Vachier-Mammar and F. Meyer Watersheds K. Vaeth and G. Rajeswaran Organic light-emitting arrays

FUTURE CONTRIBUTIONS

M. van Droogenbroeck and M. Buckley Anchors in mathematical morphology M. Wild and C. Rohwer Mathematics of vision J. Yu, N. Sebe, and Q. Tian (vol. 144) Ranking metrics and evaluation measures

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FOREWORD

At the end of the last century, we were trying to build a dual-beam instrument, in which a focused ion beam was brought onto the axis of a transmission electron microscope. The idea was to use the ion beam for the fabrication of sub-10 nm structures and do in situ inspection with the electron beam. Unfortunately, the project turned out to be too ambitious and it was decided to focus on nanofabrication with electron beams first. But soon we discovered that electron beam–induced processes usually result in structure sizes much larger than the probe size of the electron beam, and it was not really understood why. We were fascinated by this spatial resolution problem and started a detailed study, which finally led to the PhD-thesis of one of us (N.S.-C.). This book is based on a large part of her thesis. After a brief introduction (Section I), we present in Section II a literature survey on electron and ion beam induced deposition, which is probably not exhaustive but it identifies the problems of the techniques, in particular the spatial resolution problem. The theory of the spatial resolution, i.e., the physics of the interaction of electrons with matter, is treated in Section III, where many potential processes that influence the spatial resolution are also described. Only two of these were studied in more detail: (i) the spatial distribution of secondary electrons emitted from the substrate surface, using Monte Carlo techniques and taking the dissociation cross section of the precursor molecules into account (Section IV) and (ii) the delocalization of inelastic electron scattering (Section V). When we started this study there was not really a lot of interest in EBID as a nanofabrication technique, but in the last few years the situation has been changing and the field is receiving more attention. We hope that this book will contribute to that and serve the novice as an introduction into Electron Beam Induced Deposition (EBID), and also the specialist who is interested in the EBID spatial resolution problem. We are greatly indebted to Pieter Kruit for many valuable discussions and creating the nice environment to work on these issues, and to Annelies van Diepen for proofreading and preparing the manuscript with great devotion. Natalia Silvis-Cividjian and Cornelis W. Hagen Delft, July 2006 xv

ADVANCES IN IMAGING AND ELECTRON PHYSICS, VOL. 143

Electron‐Beam–Induced Nanometer‐Scale Deposition NATALIA SILVIS-CIVIDJIAN AND CORNELIS W. HAGEN

I. Introduction . . . . . . . . . . . . . . . . . . . . . . II. Electron‐Beam–Induced Deposition: A Literature Survey . . . . . . A. Historical Overview . . . . . . . . . . . . . . . . . . B. Motivation . . . . . . . . . . . . . . . . . . . . . C. Instrumentation and Techniques . . . . . . . . . . . . . . 1. Environment and Vacuum System . . . . . . . . . . . . 2. Probe Formation: Optical Focusing Columns . . . . . . . . 3. Patterning and Exposure Techniques . . . . . . . . . . . 4. Imaging Possibilities . . . . . . . . . . . . . . . . . 5. Specimens . . . . . . . . . . . . . . . . . . . . 6. Precursors and Gas Delivery Systems . . . . . . . . . . . 7. Conclusions . . . . . . . . . . . . . . . . . . . . D. Analysis of Experimental Results and Theoretical Models . . . . . 1. Electrical Properties . . . . . . . . . . . . . . . . . 2. Morphological Properties . . . . . . . . . . . . . . . 3. Chemical Structure Analysis . . . . . . . . . . . . . . 4. Geometric Parameters . . . . . . . . . . . . . . . . 5. Conclusions . . . . . . . . . . . . . . . . . . . . E. Applications and Achievements of EBID and IBID Deposition Methods 1. Mask Repair and Mask Fabrication . . . . . . . . . . . 2. Integrated Circuit Modification and Chip Surgery . . . . . . . 3. Shape Improvement for Scanning Probe Microscopy Tips . . . . 4. Field Emission Sources and Field Emitter Arrays . . . . . . . 5. Electrical Contacts for Molecules . . . . . . . . . . . . 6. Probing on Small Crystals . . . . . . . . . . . . . . . 7. Three‐Dimensional Artifacts, Nanostructures, and Devices . . . . 8. Conclusions . . . . . . . . . . . . . . . . . . . . F. Conclusions . . . . . . . . . . . . . . . . . . . . . III. The Theory of EBID Spatial Resolution . . . . . . . . . . . . A. The EBID Spatial Resolution: A General Statement of the Problem . . 1. Identifying Researchable Problems . . . . . . . . . . . . 2. Defining the Strategy. . . . . . . . . . . . . . . . . B. Relevant Interactions Between Electrons and Solid Matter . . . . . C. Monte Carlo Simulations for Secondary Electrons Emission . . . . 1. Input Data for an MCSE Program . . . . . . . . . . . . 2. Output Data of an MCSE Program. . . . . . . . . . . . D. Basic MCSE Procedure . . . . . . . . . . . . . . . . . E. Theoretical Models for Electron Scattering Simulation . . . . . . 1. Elastic Scattering . . . . . . . . . . . . . . . . . . 2. Inelastic Scattering . . . . . . . . . . . . . . . . .

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1 ISSN 1076-5670/06 DOI: 10.1016/S1076-5670(06)43001-9

Copyright 2006, Elsevier Inc. All rights reserved.

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3. Generation of Secondary Electrons . . . . . . . . . . . . . 4. Transport of Secondary Electrons Toward the Surface . . . . . . 5. Escape of Secondary Electrons into Vacuum . . . . . . . . . F. Compilation of Secondary Electron Emission Data Relevant for EBID Resolution . . . . . . . . . . . . . . . . . . . . 1. Results from SEM Imaging Analysis . . . . . . . . . . . . 2. Results from Resist‐Based Electron Beam Lithography . . . . . . 3. Results from EBID Studies . . . . . . . . . . . . . . . G. Relevant Interactions Between Electrons and Gaseous Precursors . . . 1. Introduction . . . . . . . . . . . . . . . . . . . . 2. Electronic Structure and Energy States of Atoms and Molecules . . . 3. Mechanisms of Electron Beam–Induced Molecular Degradation . . . 4. Electron Energy Loss in Electron Interaction with Gas Molecules . . 5. Cross Sections for Electron‐Induced Molecular Degradation . . . . 6. Electron‐Molecular Impact Data Available from Literature . . . . H. Relevant Surface Processes . . . . . . . . . . . . . . . . . 1. Adsorption . . . . . . . . . . . . . . . . . . . . . 2. Surface Diffusion of Precursor Molecules. . . . . . . . . . . 3. The Electric Field on the Surface . . . . . . . . . . . . . I. Conclusions . . . . . . . . . . . . . . . . . . . . . . IV. The Role of Secondary Electrons in EBID. . . . . . . . . . . . . A. Introduction. . . . . . . . . . . . . . . . . . . . . . B. The Model . . . . . . . . . . . . . . . . . . . . . . C. Secondary Electrons on a Flat Target Surface . . . . . . . . . . 1. A Monte Carlo Simulation Program for Secondary Electron Emission . 2. EBID Spatial Resolution Determined by the Secondary Electron on the Flat Surface . . . . . . . . . . . . . . . . . . . . . 3. Discussion . . . . . . . . . . . . . . . . . . . . . D. Role of Secondary Electrons Scattered in the Deposit. . . . . . . . 1. Introduction . . . . . . . . . . . . . . . . . . . . 2. Description of a Two‐Dimensional Profile Simulator for EBID . . . E. Conclusions . . . . . . . . . . . . . . . . . . . . . . V. Delocalization Effects in EBID . . . . . . . . . . . . . . . . A. Delocalization of Electron Inelastic Scattering: General Formulation of the Problem . . . . . . . . . . . . . . . . . . . . . B. Approaches for Quantitative Estimation of Electron Inelastic Scattering Delocalization . . . . . . . . . . . . . . . . . 1. The Classical Model 1 . . . . . . . . . . . . . . . . . 2. The Classical Model 2 . . . . . . . . . . . . . . . . . 3. The Semi‐Classical Approach . . . . . . . . . . . . . . . C. Delocalization of Secondary Electron Generation . . . . . . . . . 1. Introduction . . . . . . . . . . . . . . . . . . . . 2. The Spatial Extent of the Delocalization of Secondary Electrons Using the Semi‐Classical Approach . . . . . . . . . . . . . . . D. Delocalization of Surface Plasmon Generation . . . . . . . . . . 1. Surface Plasmons on a Flat Surface. . . . . . . . . . . . . 2. Surface Plasmons on a Spherical Gas Molecule. . . . . . . . . E. Conclusions . . . . . . . . . . . . . . . . . . . . . . VI. Conclusions . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . .

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I. INTRODUCTION Electron beam–induced deposition (EBID) is a technique to directly deposit structures on a target by the electron‐induced dissociation of adsorbed precursor molecules. Experiments have shown that the lateral size of structures made by EBID always exceeds the probe size of the electron beam. Until recently it was always believed that the secondary electron exit area of the substrate limits the lateral structure size to 15 nm. Only recently (2004– 2005) some experimental results appeared that demonstrated that sub–10 nm resolution is well possible to achieve using EBID. In this article we review the EBID work of the past 35 years and develop a theoretical model to estimate the EBID spatial resolution. We use Monte Carlo simulations to calculate the interactions between the electrons and the solid target and the gaseous precursor. The spatial resolution can be influenced by many factors, of which two are discussed: the secondary electrons and the delocalization of inelastic scattering. The results confirm the important role of the secondary electrons and show that the effect of delocalization is negligible. The model predicts that structures with minimum sizes between 0.2 nm and 2 nm can be made with a 0.2 nm electron beam. Dots of 1 nm diameter have actually been deposited using EBID, which demonstrates its potential as a nanofabrication technique.

II. ELECTRON‐BEAM–INDUCED DEPOSITION: A LITERATURE SURVEY A. Historical Overview The observation of electron beam–induced deposition (EBID) is not new. Probably everything started when microscopists observed that the electron beam on the specimen created dark brown films, commonly called contamination. Beam‐induced specimen contamination has been recognized as a problem from the infancy of electron microscopy. In the beginning, it was suspected that the poor vacuum inside the system resulting from oil diffusion pumps, O‐rings, grease, and so on was the main reason, which urged the construction of electron microscopes with better vacuum conditions (Ennos, 1954; Poole, 1953). Today the contamination problem in conventional electron microscopes can be satisfactorily controlled by the use of various anti‐contamination devices and good vacuum techniques. Typically the pressures around the specimen are as low as 105 Pa. However, contamination still occurs, but now by the hydrocarbons already deposited on the specimen and specimen

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holder during operation in the open air. It appears that an ultra‐high vacuum (UHV) alone does not completely solve the problem of contamination unless the specimen is prepared by cleaving, evaporation, or ion beam etching inside the UHV specimen chamber. The phenomenon of contamination under electron beam irradiation is not completely understood, but the current dogma holds that the growth occurs when adsorbed hydrocarbon contaminants, diffusing rapidly across the surface, are cracked and cross‐linked to the target surface under the influence of the electron beam. As a result, a carbon‐rich film, ring, or cone grows, depending on the beam diameter and exposure method. If the specimen is thin and the majority of electrons are transmitted, then contamination will grow not only on its top but also on its bottom side, as can be seen in Figure 1. When the electron beam is defocused, a ring is deposited, as shown in Figure 2. The morphological analysis of the contaminant films can be determined using energy‐dispersive X‐ray spectroscopy (EDS) and electron energy loss

FIGURE 1. TEM image of tilted contamination spots created by a focused electron beam coming from the left. From Harada et al. (1979).

FIGURE 2. TEM image of two contamination rings, created by a defocused electron beam for specimen temperatures of (a) 297 K and (b) 372 K. From Fourie (1976).

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FIGURE 3. Electron energy loss spectrum recorded from a contamination film. Reproduced with permission from Kislov and Khodos (1992). ß 1992, EDP Sciences.

spectroscopy (EELS) methods. A typical EELS spectrum from the deposits grown in a scanning transmission electron microscope (STEM) from pump oil vapor shows a volume plasmon peak at 20–25 eV, specific for carbon, indicating that the deposits contain carbon (Figure 3). This electron irradiation–induced carbon contamination is a significant barrier to high‐ resolution microstructural analysis. One of the most serious annoyances is the loss of spatial resolution, especially in the extreme case of a finely focused probe necessary in the scanning mode of a STEM (Hren, 1986). The degradation in resolution is caused by the beam spreading in the contaminant film or by the charging of the poorly conducting contaminant layer, followed by beam deflection. The contamination layer also affects the measurement of the local surface composition, both in EDS and EELS. The contamination rate is inversely proportional to the electron stopping power and the beam energy, making contamination a problem in low‐energy scanning electron microscopes (SEMs). Ion beam–induced deposition (IBID) of organic molecules also has been observed due to the effect of polymer buildup at the target of particle accelerators. Care must be taken to avoid contamination in some photon‐ and electron‐induced lithography processes. For these reasons much work has been done to look for methods to understand, prevent, and reduce the contamination buildup on specimen surfaces subject to electron or ion bombardment. However, contamination buildup is not always an undesirable process and can serve as a useful tool in electron beam lithography (EBL). The carbonaceous deposits resist

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subsequent removal by chemical etching or ion bombardment in the same way as photoresists used in solid‐state microfabrication. Christy (1960) was the first to mention the useful exploitation of contamination growth to fabricate thin insulating silicon films. Searching for new lithography methods, Broers et al. (1976) came up with the idea to use the electron beam–cracked hydrocarbon layer as a negative resist (protective mask) during reactive ion etching (RIE) lithography. The idea turned out to be successful, and for the first time 8 nm wide metal lines on a thin carbon film were fabricated in a STEM. Thus, the ugly duckling became a swan, the new technique received the name of contamination lithography, and it has now proved to provide high‐resolution structures. As a result of this success, metal‐bearing gases as well as various hydrocarbon mixtures started to be introduced as precursors on purpose into the focused‐beam columns, in order to study a promising lithography technique named electron beam–induced deposition. In the past 15 years, EBID obtained more technical importance, as a tool for ‘‘additive lithography’’ (Koops et al., 1994), being applied on a small scale in SEMs, transmission electron microscopes (TEMs), dedicated lithography systems, scanning tunneling microscopes (STMs), dual‐beam instruments, and image projection systems. Specimen contamination in electron microscopy can be interpreted as an EBID of structures from a precursor consisting of a mixture of hydrocarbons. The information accumulated about the physics of this phenomenon can be helpful in EBID studies. Contamination in electron microscopy and analysis has been reviewed by Hren (1986).

B. Motivation We decided to perform a literature review on the use of EBID in micro‐ and nanofabrication. The study of EBID started later than the study of contamination in electron microscopy; therefore a very extensive literature review on this subject has not been published yet. Koops et al. (1994) made a start in this direction. EBID has also been the subject of a doctoral dissertation by Weber (1997). We used these sources as a model to structure our review. Of course, a natural question arises on the usefulness of such an extensive effort: Why do a detailed review on this subject? The first reason is that we needed this review ourselves in order to know what has already been done, to establish the problems that remained to be solved, and to focus our efforts on what is really new. The second reason is that other readers also may benefit from this work. Who might further benefit from this review? First, a review is one of the most effective timesavers available. This review will allow readers to quickly

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acquire the know‐how in EBID and the theoretical and practical aspects necessary at different stages of the research. For example, outsiders reading about exciting EBID applications may consider using EBID for their purposes. The review is useful for novices who have already decided to use EBID but do not have an experimental setup yet. In this case, the review offers a set of possible precursors and constructive choices with their advantages and disadvantages. In addition, it will enable novices to become familiar with the prevailing knowledge and understanding of the topic. Some shaky points and still open problems in the theoretical modeling are identified, generating new ideas and approaches to follow for other researchers. Finally, more advanced and curious readers who still have questions on EBID can find some of the answers in this review. The EBID technique is sometimes used and reported under different names, which we mention, but to avoid confusion we will try to consequently use the most accepted terminology. For example, some authors refer to contamination lithography as electron beam–induced resist (EBIR) growth and the related metal deposition is called electron beam–induced metal formation (EBIM) (Ishibashi et al., 1991). Because it allows local patterning of small areas of the substrate, EBID is also called electron beam–induced selective chemical vapor deposition or just electron beam CVD (Matsui and Mori, 1986). The names electron beam–assisted direct‐write nanolithography, electron beam–assisted deposition (EBAD), electron beam–induced surface reaction, and electron beam–stimulated deposition also occur. Because etching also is possible as an effect of electron beam–induced surface reactions, by combining these two effects the method is also called electron beam– induced selective etching and deposition (EBISED) (Matsui et al., 1989; Takado et al., 1990). A new concept of environmental EBID (Folch et al., 1996) was introduced, in which an environmental SEM (ESEM) hosts the deposition process. Focused ion beam (FIB) machines are currently used for integrated circuit (IC) and mask repair, as well as for failure analysis of microdevices by milling and sputtering. By introducing gas in such a system, material deposition can also be obtained under ion irradiation, in competition with sputtering. The technique is named ion beam–induced deposition or sometimes ion beam–assisted deposition (IBAD) (Koh et al., 1991). Not only metals but also insulator material can be deposited for IC repair using IBID (Komano et al., 1989). If a reactive precursor is used, etching is observed under ion beam irradiation and a nanostructuring technique is obtained, named ion beam–induced etching or gas‐assisted etching (GAE). Nagamachi et al. (1998) introduced a new fabrication method named focused ion beam direct deposition (FIBDD). By maintaining a high vacuum (107 Pa) during deposition, it eliminates the contamination of the specimen

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with adsorbed gas molecules. By using very low beam energies, high current densities, and alloy ion sources, magnetic and superconducting materials have been deposited using this method. Even if it is not proper IBID according to our adopted definition, but rather an ion implantation method, we mention their results because they make a parallel analysis between IBID and FIBDD. During the past two to three decades, several research groups throughout the world have been using, experimenting, or modeling the EBID/IBID process. The research efforts usually were aiming for one or more requirements, such as high deposition rate, high fabrication resolution, and high deposit quality (low conductivity and high purity). We discuss the relevant work of the mentioned research groups, their results, and predictions (1980– 2005) in this literature review. Because we intended to study in detail the electron beam–induced direct writing processes, the interest in this review was mainly limited to reports about EBID, but because of similarities in phenomenology and modeling some IBID articles also are discussed. The sections about instrumentation (Section II.C) and deposit quality analysis (Section II.D) can also be integrally used for IBID. In modeling, the effect of material sputtering, which is much stronger for ion beams, should be taken into account. C. Instrumentation and Techniques This section presents typical experimental setups in which EBID and IBID are studied, as well as the options that the builder has at present. Experimental setups have been built to prove theoretical models, to appreciate the influence of different parameters on the deposition quality, or to show possibilities of new applications of these methods. Some essential hardware is needed to experimentally study EBID and IBID, starting with a vacuum chamber containing a position‐controlled focused particle beam, a specimen stage, and a gas delivery system with flow control facilities. If more complicated patterns are to be deposited, a pattern generator must be attached to the beam deflectors. Evaluation of the deposition results requires the addition of imaging, recording, and/or in situ analytical facilities to the experimental setup. Given these indispensable elements, the study of EBID began in modified electron microscopes, most often in SEMs due to their flexibility and availability, but also in STEMs, commercial EBL systems, dual‐beam instruments, or STMs, most of them with an added possibility to introduce gas in the specimen area. When the aim is not an application but the clarification of the fundamental mechanisms involved in EBID, special bakeable UHV setups have been built (Dubner and Wagner, 1989; Matsui et al., 1989; Scheuer et al., 1986). Their construction is simpler, containing only an electron gun, a gas

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FIGURE 4. EBID apparatus for studying fundamental characteristics. Reused with permission from Shinji Matsui, Journal of Vacuum Science & Technology B, 4, 299 (1986). ß 1986, AVS The Science & Technology Society.

inlet, and a multispecimen XYZ translational stage. However, they are largely supported by various in situ surface preparation and analysis equipment, as ion guns for cleaning, Auger spectrometers, diffraction analyzers, quadrupole mass spectrometers, quartz crystal microbalances, and so forth (Figure 4). When designing a gas injection system coupled to an UHV microscope column, care must taken to prevent the gas from leaking into the pressure‐ sensitive gun chamber (the Schottky electron gun requires pressures lower than 2 109 torr) and to reduce unwanted deposition in other places than on the specimen itself. The deposition system parameters are determined by the focused probe optics (beam acceleration voltage, probe current and probe size, and imaging performance), the specimen (material, temperature, treatment history, and electric potential), and the gas delivery system (precursor type, precursor temperature and vapor pressure, and pressure and molecular flux at the specimen). Several reported EBID experimental setups and their parameters are described in the next section. 1. Environment and Vacuum System High fabrication and imaging resolution requires very stable focused beams and specimen stages. For this reason, the deposition system can best be situated in an environment in which the temperature is maintained to within 0.1 C and which is shielded from the different environmental influences. For example, decoupling of floor vibrations can be realized by situating the

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entire system on a concrete cube with a large mass resting on three air springs with a designed eigenfrequency of 1 Hz. (Blauner et al., 1989; Hu¨bner et al., 2001). The ambient magnetic stray field must be restricted to below 0.2 mG at 50 Hz. The exhaust line of the vacuum pumps in case of precursors with a health hazard must be directed outside the laboratory space, and filters are necessary in some critical cases. Special safety measures for toxic precursors, with suitable manipulation and ventilation facilities, according to the maximum allowed concentrations (MAC) or threshold limit values (TLVs) (Sax, 1984), together with a hazard analysis are necessary in building an operational EBID experimental setup. A dry pumping system offers the best vacuum conditions. For this purpose ion getter pumps should be used, and the oil diffusion pumps usually present in the original microscope construction should be replaced by turbomolecular pumps. If this is not possible, then Fomblin pump oil must be used to avoid hydrocarbon contamination. Of course, in the case of contamination lithography, if the precursor is expected to come from the oil diffusion pump vapors and residual vacuum, these changes are not justified. A membrane pump instead of a rotary pump will produce fewer vibrations, increasing the specimen stage mechanical stability. In addition, a membrane pump is oil free and ensures an oil‐free combination with turbo/drag pumps. The construction of the vacuum pump must be compatible with the precursor vapors used to avoid corrosion problems. A turbopump is safer than a cryopump when potentially hazardous materials are used as precursors. The optical column should be differentially pumped using a double‐aperture construction to separate the gun chamber from the specimen chamber where gas at high pressure is introduced. Extra gauges must be mounted to monitor the gas inlet pressure and pressure changes in sensitive places in the column. 2. Probe Formation: Optical Focusing Columns Deposition can be induced by photon, electron, and ion beams, but photon beams are eliminated from the discussion at the outset because of their low achievable resolution. Electrons can be focused to a much smaller spot than ions and the current densities can be higher, compensating somewhat for their small reaction cross section. For ion systems, the resolution may be up to 20 times worse because of electrostatic lens aberrations and the large energy spread of the available liquid‐metal ion sources (LMIS). Another advantage of electron beams is that, compared with ion beams, they offer a smaller risk of implantation into the specimen and of simultaneous sputtering of the deposited material. Indeed, sputtering becomes a problem in case of high‐ resolution imaging with ion beams. Conversely, the deposition rate in IBID is

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much higher than in EBID due to the difference in mass between electrons and ions. As a result, the longer exposure time necessary for electron beam– induced surface reactions requires higher stability of the electron optical columns and their specimen stage. Ion beams are advantageous in IC surgery because, beside material deposition, they allow the removal of layers by sputtering in order to reveal buried defects. a. Electron Beam Columns. Electron beam columns usually are modified microscopes equipped with a thermionic gun (W or LaB6), a Zr/O/W thermal field emission gun (FEG), or a Schottky FEG as the electron source. A better electron source offers a higher reduced brightness and thus more current in a smaller probe, an essential feature in high‐resolution applications. The lenses used are magnetic, the gun lens is electrostatic. Probe sizes vary depending on the operation of the microscope. In commercial SEMs the beam diameter is 1 nm at best. In TEM/STEM‐based constructions the electron probes are much smaller, down to 0.2 nm. The advantage of a TEM/STEM is that the spot can be imaged at extremely high magnification, allowing the generation of an ideal beam regarding the spot diameter and astigmatism, a feature that is important in patterning. Figure 5 shows an example of an SEM modified to implement EBID.

FIGURE 5. An SEM modified to implement EBID. Reused with permission from H. W. P. Koops, Journal of Vacuum Science & Technology B, 6, 477 (1988). ß 1988, AVS The Science & Technology Society.

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The current density in the spot depends on the brightness of the source, on the focus, astigmatism and diffraction aberrations, and on the fixed chromatic and spherical aberrations of the objective lens. In systems without automatic alignment, current density depends on the skills of the operator, thus rendering reproducibility difficult. The beam current density distribution is usually supposed to be Gaussian, or otherwise it can be measured. A common method used to measure the beam density profile and diameter is to scan the beam over a sharp edge and apply synchronized detection of the current in a Faraday cup underneath (the transmitted signal) or of the secondary electrons (reflected signal), using the so‐called Rishton method (Rishton et al., 1984). The beam diameter is determined by reading the slope of the measured current between 15% and 85% of the total current change. The sharp edge can be the edge of a Faraday cup, an Ni mesh knife edge, or a cleaved edge of an Si wafer (Hiroshima et al., 1995; Kohlmann‐von Platen et al., 1993; Kunz et al., 1987; Matsui et al., 1992). In edge methods, the signal depends strongly on the nanostructure of the edge and the evaluation depends on the user’s skills. Weber et al. (1995b) argued that edge methods are not suitable for high‐resolution applications because they are slow and not reproducible. These authors have proposed a new, faster method to determine the beam current density distribution by analyzing the scanning force microscope (SFM) image of the deposited dot obtained in spot mode by EBID or contamination growth (i.e., the material response to the spot exposure). The probe size of the original microscope can be improved by using a special probe‐forming objective lens with lower aberration coefficients. The beam impact energies on the specimen usually vary between 30 and 120 keV, depending on the design of the microscope, but sometimes even lower energies are necessary for experimental reasons. The problem is that the performance of an electron beam column decreases with the beam energy, the low energy at the gun level increasing the spot size at the specimen. This inconvenience can be avoided if the beam is accelerated at high energy along the column and retarded between the final lens and the substrate by applying a negative bias on the specimen. In this way, operation down to zero energy is possible. In this regime, care must be taken with distances between the gas nozzle and specimen to avoid flashovers. Hoyle et al. (1996) experimented with EBID for landing energies ranging from 0.06 to 20 keV, drawing conclusions about the influence of landing energy on the deposition quality. However, high beam energies are preferable to reduce the chromatic aberration, diffraction, and beam broadening in a target by forward scattering. b. Ion Beam Columns. The FIB columns used for deposition are UHV chambers with an ion source, a condenser‐objective combination of

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electrostatic lenses, a specimen stage, and a gas delivery system. The ions are usually supplied by an LMIS or, less often, by a gas‐field ion source (GFIS). In most cases they are gallium (Gaþ) ions, but indium (Inþ), silicon (Siþ 2 ), þ gold (Auþ), hydrogen (Hþ ), and argon Ar ions are also used. Liquid‐alloy 2 ion sources are also available for conducting, superconducting, and magnetic materials. For example, Au‐Si, Au‐Cu, and Au‐Cu‐Si alloys are used as sources for conducting materials, Nb‐Au‐Cu alloy for superconducting Nb material, and Co‐Cu‐Nb‐Au alloy for Co magnetic material. A Wien mass filter must be inserted between the two lenses to separate different ion species when alloy sources are used. The host system can be a commercial FIB apparatus (Matsui et al., 2000) or a custom‐built system (Blauner et al., 1989). The beam accelerating energies can vary between 15 and 60 keV, and the probe sizes range from 7 nm to 250 nm. The final probe size depends on the spherical aberration in the high‐ current regime, on chromatic aberration in the intermediate regime, and mainly on the source size at the smallest currents. Higher resolutions can be obtained with special objective lenses designed to minimize the spherical aberration (Davies and Khamsehpour, 1996) or by insertion of energy filters to minimize the energy spread of the LMIS (usually 10 eV) and thus the chromatic aberration. Electrostatic octupoles can be used to correct the astigmatism due to mechanical misalignments (Blauner et al., 1989; Sawaragi et al., 1990). Figure 6 shows an example of an FIB system modified to implement IBID. Although it is customary to assume that the beam obtained by FIB columns has a Gaussian profile, deviations from this profile do exist. The ion beam current density distribution and diameter can be estimated in the same way as for electron beams—by scanning the beam across a sharp edge and measuring the resulting secondary electron signal as a function of beam displacement or by sputtering of thin films. The beam diameter is then defined by the distance between the 10% and 90% amplitude of this signal. c. Special EBID Setups. Less often encountered but nevertheless very interesting EBID host constructions and techniques are as follows:

The ESEM The STM Dual‐beam instruments FIBDD

The ESEM has the advantage that high pressures—up to 10 Pa—are allowed in the column (Folch et al., 1995, 1996; Ochiai et al., 1996), so that fewer precautions are needed when the precursor gas is introduced.

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FIGURE 6. An FIB modified to implement IBID. Reused with permission from Patricia G. Blauner, Journal of Vacuum Science & Technology B, 7, 609 (1989). ß 1989, AVS The Science & Technology Society.

The STM, without offering a focused beam, is an interesting research environment for low‐energy electron‐induced deposition. From a modeling point of view it is useful to separate low‐ and high‐energy electron excitations. In a SEM or a TEM this is not easy to realize. The STM is used for low‐energy deposition from organometallic or hydrocarbon precursors, the so‐called STM CVD. The main application is the improvement of the tip shape (McCord et al., 1988; Saulys et al., 1994). The visualization of fabricated structures can be realized in the same STM, or in an SEM with a higher resolution and speed. Such a combination STM‐SEM allowed structures of 10–100 nm to be deposited (Rubel et al., 1994). The low‐energy tunneling electrons decompose the precursor molecules adsorbed on the substrate and produce deposition. Two types of EBID can be performed in

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FIGURE 7. STM‐CVD microfabrication system. From Matsui et al. (1992). With kind permission of Springer Science and Business Media.

an STM. One is the growth of a structure (hillock, bump, or line) on the sample surface and another process grows a nanowire on the STM tip and improves its shape and imaging ability. These different effects are obtained by simply reversing the polarity of the tip. All experiments showed that no visible surface modifications occurred if the tip pulse was less than 3 V. The deposition in an STM also has a reverse effect: the molecular removal from the surface. This process also has a threshold at 3.5 eV. Etching of holes is possible only in air or when water vapor is adsorbed on the sample. In a vacuum environment no holes could be drilled. Holes with 4 nm diameter and 6 nm spacing could be drilled in a graphite substrate situated in air by applying a voltage pulse of 3–8 eV for 10–100 ms in the presence of water vapor (Albrecht et al., 1989). Figure 7 shows an example of an STM‐CVD system. In dual‐beam instruments, electron and ion beams are combined in one machine and a comparative analysis of electron‐/ion‐induced chemistry phenomena (deposition or etching) can be performed (de Jager, 1997; Lipp et al., 1996a; Sawaragi et al., 1990; Yavas et al., 2000). Another advantage offered by a dual‐beam system is that imaging can be realized in electron microscopy with less specimen damage. The two columns are oriented to aim at the same specimen and their optical axes usually intersect at an angle of 52 degrees. De Jager (1997) proposed another relative placement of columns where the ion and electron beams both are normally incident on

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FIGURE 8. Schematic of a dual‐beam instrument, combining FIB and EB columns and used for etching with Cl2. Reprinted with permission from Takado et al. (1990).

the specimen. Figure 8 shows an example of a dual‐beam instrument used for gas‐assisted etching. Nagamachi et al. (1998) introduced a new technique, FIBDD. In fact, it is an ion implantation technique and not IBID in our strict definition because it does not use a gaseous precursor. The FIB system has very low beam energies and high current densities, necessary for implantation, with an optimized lens system and a mass filter, maintaining a very low residual pressure, 2 107 Pa, during deposition. 3. Patterning and Exposure Techniques In order to deposit a certain pattern, the focused beam must be positioned and scanned while introducing the precursor gas at a constant rate. Deflection of the beam can be done manually or automatically by means of deflectors, which are usually magnetic for electron beams and electrostatic for ion beams. A blanking facility is necessary to avoid exposure during the return of the beam. A simple construction only requires two deflectors, in the orthogonal X and Y directions. The optimum construction is the double‐ deflector arrangement, which allows a normal beam incidence over the entire exposed area (telecentric beam path) by fixing a favorable pivot point in the back focal plane of the upper pole piece of the objective lens (Figure 9). The pattern is made of discrete points or pixels, and each pixel is exposed for a predefined time called dwell time (td). A delay must occur between successive visits of the beam to a certain pixel on the surface to provide time for replenishment with precursor molecules; this time is called the refresh or

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FIGURE 9. Telecentric beam path with Ko¨hler illumination. Reprinted from Hu¨bner et al. (1996). ß 1996, with permission from Elsevier.

loop time (tl). The loop time depends on the deposited area and on the exposure strategy: tl ¼

td L W ðD ð1 OLÞÞ2

;

ð1Þ

where D is the beam diameter, L and W are the length and width of the pattern, respectively, and OL is the overlap. The most common patterns to be deposited are dots, lines, and rectangles. They can be obtained by simply using the imaging scan generator available in any SEM to raster the beam. The deflection can also be made by a function generator with fast rastering, but with reduced patterning capabilities and

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no blanking. The maximum scanning rate (100 kHz) is limited by the response time of the magnetic deflector coils. In addition to these analog beam scanning modalities, modern systems use a digital beam scanning facility, assisted by a computer (Koops et al., 1994; Stark et al., 1992). If more complicated models are to be exposed, a scan generator is not flexible enough; then a pattern generator is necessary. A pattern generator can be a separate hardware module or a computer with a plugged‐in digital‐to‐analog conversion (DAC) card, controlled by a user interface and attached to the deflection coils. The pattern generator will generate the necessary signals to control the deflectors, according to the pattern given as input file. The scan field dimensions can vary from 50 mm 50 mm to more than 4 mm 4 mm. Exposure times per pixel (dwell time) vary from 1 ms to greater than 100 s. The refresh time depends on the exposure order and on the length of the pattern but typically is 10 ms. Exposure doses in EBID can vary from a low dose of 0.01 C/m2 to a high dose of 10,000 C/m2. Electrical noise and instabilities in the deflector signal reduce the achievable fabrication resolution. The same pattern can be exposed in different ways (timing, order, step) and it appears that the deposit properties and quality depend on these parameters. For example, the same line can be exposed by repeated fast scanning or by a single slow scanning; see Figure 10(a) and Figure 10(b), respectively. The following text subsections provide some recipes on ‘‘how to build’’ simple structures using EBID. In all cases it is assumed that the precursor gas supply in the irradiated substrate area is sufficient. a. Deposit a Dot, Tip, or Column. First, in the SEM picture or in the TEM defocused mode, locate the place where deposition is necessary. Switch the SEM to spot mode (focus the beam) and keep the beam in the same position for a certain time (Akama et al., 1990; Hu¨bner et al., 1992; Kohlmann‐von Platen et al., 1992). If dots are needed, then 10 seconds is enough, for tips 1 minute will be sufficient for a height of 1 mm. b. Deposit Lines (Wires). In low magnification localize the start or the center point of the needed segment, then focus the beam and scan it using the SEM line scanning mode or the imaging mode by deactivating one of the scan directions. Figure 11 shows example of lines and spaces deposited with EBID. c. Deposit Rectangles. Rectangles are useful to be deposited instead of lines to make the width and resistivity measurements easier and to reduce the influence of the beam drift. The simplest way is to use the scan generator in frame mode. When using a pattern generator, the rectangles should be deposited in meander (serpentine) pattern to avoid exposure during beam return (see Figure 10c). The step should be 10% of the measured spot size.

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FIGURE 10. Illustration of different scanning methods. (a) repeated fast scanning, (b) single slow scanning, and (c) meander pattern for rectangles.

d. Deposit Free‐Standing Structures (Nanowires, Rods, and Bridges Across a Hole in Membranes). Start by keeping the beam at the edge of a thin membrane until film nucleation is formed and then move the beam slowly in line scan toward the hole. The deposited layer also follows the slow‐moving electron beam outside the membrane, across the hole. If the beam sweep rate is too high, the growth cannot follow the beam and the process will be interrupted. In contrast, if the sweep rate is too slow, a thick sheet and not a rod will be formed. The solution is to start with high sweep rates and decrease them until the growth can follow the beam. The speed must be 1–5 nm/s (Albrecht et al., 1989; Bezryadin and Dekker, 1997; Kislov et al., 1996). Another method to deposit bridges across the hole is to keep the beam in the hole at a distance of a few nanometers from the edge and wait until the grown wire reaches the beam. This distance growth is explained by delocalization of molecular dissociation or by the tails of the beam current density distribution (Kislov et al., 1996).

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FIGURE 11. Gold lines deposited on Si substrate by EBID (4 106 C/cm2). Reused with permission from K. L. Lee, Journal of Vacuum Science & Technology B, 7, 1941 (1989). ß 1989, AVS The Science & Technology Society.

e. Deposit 3D Nanostructures. By controlling the x and y beam positions correlated with time, three‐dimensional (3D) structures can be deposited by EBID (Koops et al., 1994). A smaller penetration range of ions compared with electrons also enables the fabrication of complex 3D structures using IBID, pushing the application area to the fascinating world of nanostructure plastic art (Figure 12)! In Figure 13, the beam is scanned in digital mode. First a pillar is formed with the beam in position 1. The beam is then moved within the diameter of the pillar and fixed there until the terrace formed has a thickness exceeding the ion range a few tens of nm. This process is repeated to form 3D nanostructures. The key point is to adjust the beam scan speed and the vertical growth rate. 4. Imaging Possibilities Different signals can be used to form the specimen image in electron columns: the secondary electrons (SEs), the BSEs, the transmitted electrons, or the induced specimen current. In ion columns, imaging can be done also with

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FIGURE 12. Examples of 3D structures fabricated by IBID: (a) microcoil with a diameter of 0.6 mm and a linewidth of 0.08 mm (b) micro wineglass with an external diameter of 2.75 mm and a height of 12 mm. Reused with permission from Shinji Matsui, Journal of Vacuum Science & Technology B, 18, 3181 (2000). ß 2000, AVS The Science & Technology Society.

FIGURE 13. Procedure for the fabrication of 3D structures.

the secondary ions signal. The typical imaging chain consists of an imaging signal detector (scintillator, multichannel plate, Channeltron, semiconductor detector, isolated specimen holder, or Faraday cup), an amplifier, and the imaging monitor. The images can be recorded on conventional microscope plates, on high‐resolution videotape via a television camera system, on printers and plotters, and in an image file assisted by a computer and frame grabber. The central criteria for the choice of detector are the sensitivity, noise, electron detection capability, and lifetime. An excellent and widely used detector for SEs is the scintillator‐ photomultiplier combination, known as the Everhart–Thornley (E‐T) detector (Figure 14). The scintillator converts electrons to photons by cathodoluminescence and can be made of plastic (NE102A), phosphor powder (P47),

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FIGURE 14. Scintillator‐photomultiplier (E‐T detector) for SE signal recording. From Reimer (1998). With kind permission of Springer Science and Business Media.

or, the best and most modern, single crystals of cerium‐activated yttrium‐ aluminum garnet (YAG) (Autrata et al., 1992; Schauer and Autrata, 1979). The quality of an image signal detector can be described by the factor rn: S rn ¼ SN in > 1;

ð2Þ

N out

which is the measure of the increase in root‐mean‐square (RMS) noise amplification by the detector. For example, the E‐T construction with an NE102A plastic scintillator has a factor rn ¼ 2.5, whereas for a phosphor powder P47 scintillator rn ¼ 1.5 (Reimer, 1998). Alternatively, the quality can be described by the detector quantum efficiency (DQE), defined as: S 2 DQE ¼ N out : S 2

ð3Þ

N in

The top view of a deposited structure is most frequently imaged by detecting the secondary or BSEs in an SEM and, less frequently, by detecting the transmitted electrons in a TEM. The profile and cross‐sectional view of the deposited structures can be visualized both in TEM and SEM by tilting the specimen over 45 to 80 degrees or by using a scanning probe technique (atomic force microscope [AFM], STM) in case of small heights. Figures 15 through 18 show typical imaging possibilities of structures obtained with EBID or IBID.

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FIGURE 15. SEM image (top view and cross section) of a wire fabricated by IBID. Patricia G. Blauner, Journal of Vacuum Science & Technology B, 7, 609 (1989). ß 1989, AVS The Science & Technology Society.

In EBID, the imaging tools are also useful to observe the growth in situ, providing an important advantage with respect to standard lithography. For example, the secondary or Auger electron signals can be used as indicators of film formation. A conventional AES system can be modified by adding a gas system and a mass‐flow controller. Auger electrons are emitted and collected from the material when deposition starts, but the image resolution is rather poor (1 mm) (Matsui et al., 1989). In situ observation of deposition and growth has also been performed in a TEM (Ichihashi and Matsui, 1988; Matsui et al., 1989) using a real‐time television monitor system. With a resolution of 0.23 nm at 120 keV, sequential images could be obtained and recorded showing W atom rows in crystals, followed by clusters colliding and coalescing in a continuous film. The ultimate tool to study the fabrication resolution limits is not an SEM because of its poor imaging resolution. Only TEM or scanning probe imaging (AFM, STM) is able to image and analyze deposited structures of subnanometer size.

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W

1.5 nm

Sι FIGURE 16. TEM micrograph of a tungsten rod fabricated by EBID on a Si particle. Reused with permission from Toshinari Ichihashi, Journal of Vacuum Science & Technology B, 6, 1869 (1988). ß 1988, AVS The Science & Technology Society.

FIGURE 17. SEM tilted image of an array of platinum tips fabricated by EBID from CpPtMe3 with 10‐keV electrons. Reused with permission from H. W. P. Koops, Journal of Vacuum Science & Technology B, 13, 2400 (1995). ß 1995, AVS The Science & Technology Society.

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FIGURE 18. AFM image of a typical single wire fabricated by EBID, where the image area is 1 mm 1 mm and the deposit thickness is 6 nm. Reused from Komuro et al. (1998) with permission from IOP Publishing Limited.

5. Specimens a. Material. The substrate material used in EBID/IBID should have a certain minimum electrical conductivity to avoid charge‐up and the resulting beam deflection. The substrates can be made of bulk material, suitable for use in SEM or STM or thin film, more suitable for use in TEM. The bulk specimens are usually silicon (Si) wafers with an oxide (SiO2) layer of 100–300 nm grown on top, or semi‐insulating gallium‐arsenide (GaAs) wafers. Often 100 nm thick gold electrodes are pre‐evaporated on the substrate by conventional lithography methods to facilitate current‐voltage (I‐V) resistivity measurements of the subsequently deposited structures (Figure 19). The specimens used in TEMs are usually 3.05 mm diameter copper grids, blank or covered with 12–100 nm thin amorphous carbon or Si3N4 membranes (Hoyle et al., 1996; Koops et al., 1994; Lee and Hatzakis, 1989). Fine particles can be evaporated on the thin films as support for the deposition. For example, Ichihashi and Matsui (1988) used 60 nm diameter Si particles covered by SiO2 deposited on holey carbon film. In addition, micromachined substrates can be used, such as 200 100 mm2 Si3N4 windows in a 3 mm diameter silicon plate (Aristov et al., 1995). The substrate also can be quartz glass plates in the case of mask repair, or fused quartz fibers when studying

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FIGURE 19. Prefabricated electrodes for four‐probe resistivity measurement. Reused with permission from Yukinori Ochiai, Journal of Vacuum Science & Technology B, 14, 3887 (1996). ß 1996, AVS The Science & Technology Society.

different incidence angles of the beam (Xu et al., 1992). For beam‐induced etching, the substrates can be insulator material, SiO2, Si3N4, or polyimide (Winkler et al., 1996). As already mentioned, the use of EBID/IBID is not restricted to planar geometries, so that, for example, tip structures can also serve as substrate. By using EBID, the shape of scanning probe tips and thus their imaging performance can be improved by growing a sharper supertip on top. Good results have been obtained by applying EBID on STM tungsten tips, AFM Pt‐Ir tips, pyramidal Si3N4 tips, and field emitter arrays made by conventional lithography and thermal oxidation sharpening. b. Temperature. The substrates are usually kept at room temperature, but cooling and heating during or after deposition also has been used in experiments, following their implications in deposit growth and quality. For example, Koops et al. (1988) used a specimen stage that can be cooled or heated in the range of 40 C to 110 C and Scheuer et al. (1986) used EBID in the range of 130 C to 60 C, both measuring the temperature with a thermocouple. A temperature of 0 C represents the practical limit for cooling to avoid excessive hydrocarbon contamination and solid condensation of precursor vapors. Heating can be realized resistively with tantalum wire and cooling can be done with liquid nitrogen. The drift due to sample cooling with liquid nitrogen can be corrected by providing sufficient heat sinking to the SEM main chamber body. Thus the temperature can be kept stable within 1 C without drift in specimen position (Lee and Hatzakis, 1989). Another way to control the temperature is to use a Peltier element.

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c. Treatment. The specimens may undergo preparation and treatment before being ready for the deposition. Whereas for contamination lithography a dirty specimen is appreciated as extremely favorable for carbon film formation, in the case of metal deposition a clean specimen is the key to obtain high‐purity metal deposition characterized by a low resistivity. Various cleaning procedures have been developed over the years. Classical ways to clean a TEM thin carbon film are ex situ rinsing in methanol for 18 hours (Reimer and W€ achter, 1978), degreasing and rinsing in organic solvents (acetone, CCl4), followed by in situ slow heating and cooling between 25 C and 1325 C (Jackman and Foord, 1986), or annealing at 200 C for 1 hour in ambient atmosphere (Kislov et al., 1996). The methods described above are wet cleaning methods. Because wet cleaning cannot ensure highly conductive deposits with good reproducibility, dry cleaning methods are preferred. Examples are ex situ argon ion sputter cleaning (4 mA/cm2 for 2 min) (Scheuer et al., 1986) and O2 plasma cleaning (from 0.5 s to 10 min) followed by annealing in vacuum at 300 C for 1 hour. The cleaning procedure can continue in the deposition chamber. After air exposure, O2 is introduced in the EBID system and 200–400 V direct current (DC) voltage is applied (Hiroshima and Komuro, 1997; Hiroshima et al., 1999; Komuro et al., 1998) (Figure 20). In situ dry cleaning can also be performed, by including an Ar ion sputter cleaning facility in the deposition UHV system (Jackman and Foord, 1986; Matsui and Mori, 1986).

FIGURE 20. An UHV EB lithography system with a gas nozzle and plasma cleaning facilities. Reused from Hiroshima et al. (1999) with permission from the Institute of Pure and Applied Physics.

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d. Electrical Potential. The substrate is kept at ground potential during normal operation, except when the induced specimen current must be measured or a retarding bias potential has to be applied to the specimen. 6. Precursors and Gas Delivery Systems The precursor molecule must contain atoms of the material to be deposited. In the case of beam‐induced etching, a reactive gas is needed. An essential but not sufficient condition for the deposition to occur is that the precursor vapors adsorb on the substrate. The chemical bonding of the precursor on the surface and the beam impact on this bond are criteria determining if a precursor is suitable for deposition. The precursors commonly used in EBID were already known and synthesized in pyrolitic (CVD, molecular beam epitaxy [MBE], metal‐organic CVD) and photolitic (laserjet CVD) metal‐deposition techniques. Examples are WF6 for tungsten deposition and organometallic complexes (Fe(CO))5, trimethyl aluminum (TMA, Al(CH3)3) and copper bis‐hexafluoroacetylacetonate (Cu(hfac)2) for iron, aluminum, and copper deposition, respectively. For beam‐induced etching, gases from RIE processes, such as Cl2, I2, and XeF2 are used. For contamination lithography, the residual gases in the microscope (H2, O2, CO, H2O, and hydrocarbons) usually offer a sufficient precursor source. However, if necessary, other hydrocarbon vapors can be introduced in the system, such as styrene, benzene, toluene, liquid paraffin (a mixture of hydrocarbons from C12H26 to C18H38), or hexadecane (Behringer and Vettiger, 1986; Bezryadin and Dekker, 1997; Kislov et al., 1996; Vasile and Harriot, 1989). A current trend in the EBID field is the search for new precursors. Carbon contamination negatively affects the electrical properties of the deposit. Carbon impurities can come not only from the residual vacuum, a source that is difficult to avoid, but also from the precursor molecule, due to incomplete dissociation and chemisorption of carbon‐containing fragments. This effect can be diminished if low‐carbon–content metal clusters (Bedson et al., 2001) or carbon‐free precursors are used. For example, phosphines are metal‐bearing, carbon‐free precursors that are already in experimental use as alternatives for the commonly used precursors (Utke et al., 2000a,b). The precursors can be liquid, solid, or gaseous at room temperature and are usually kept in a small (50 cc) reservoir. Table 1 shows the vapor pressure of some precursors. Table 2 summarizes the names of these precursors. Because all precursors used have a vapor pressure in the range of 10–400 mtorr at room temperature, which is higher than the operating pressure in the vacuum deposition chamber, typically 106 torr, the gas molecules will

ELECTRON‐BEAM–INDUCED NANOMETER‐SCALE DEPOSITION

29

flow into the chamber down the pressure gradient. Important parameters for the EBID characterization are the gas flow rate (throughput) Q in the system, expressed in torrliters/s or Pa m3/s and the gas molecular flow on the substrate F, expressed in molecules/(s cm2 specimen area) or in molecules/(s m2). A necessary but not sufficient condition for the deposition is that the molecular flux is higher than the charged‐particle flux. Depending on the approach used to protect the pressure‐sensitive areas in the host column during gas introduction, three types of experimental deposition systems for EBID studies can be distinguished (Figure 21). In the case of contamination lithography, a complicated gas inlet system is usually not necessary because the precursor hydrocarbons will attach to the surface anyway, due to previous immersion in the atmosphere or in a vacuum system with high partial pressure of hydrocarbons, or because of arrival from the residual vacuum of the lithography system. Other simple ways to create a hydrocarbon source are in development, such as using an adhesive tape as a stable source of monomers (Yamaki et al., 1992). In the differentially pumped subchamber, built around the substrate (Figure 21a) (Koops et al., 1988; Lee and Hatzakis, 1989; Matsui and Mori, 1986), the gas is introduced into the system through a metering needle valve. The subchamber can be differentially pumped through a 1 mm aperture, keeping an operating pressure in the subchamber of 10–100 mtorr. Because in this construction the collection angle of secondary and backscattered electrons (BSEs) is too small, a movable shutter can be used in place of the differential aperture. The shutter opens to let the beam through for high‐ resolution imaging and the EBID process can continue when the shutter is closed. The disadvantage of this variant is the small field of exposure and imaging. When the reservoir is a box attached to the specimen holder, the movement of the specimen is restricted. Even if the subchamber is built around the specimen, only the area below the shutter can be exposed (see Figure 5). An advantage of the nozzle construction (Figure 21b) (Davies and Khamsehpour, 1996; Hoyle et al., 1994; Kohlmann et al., 1991) is that the gas is locally delivered in the beam‐irradiated specimen area, reducing the gas loading of the working chamber and thereby suppressing the pressure rise inside the optical column. Another advantage of this construction is that the beam can scan larger areas, creating larger imaging fields. The nozzle must be brought in close proximity to the sample surface where the electron beam is incident, such that the line of sight intercepts the beam at the surface of the device (Figure 22). The angle between the nozzle and the substrate usually is 45 degrees. The nozzle position above the specimen can be fixed or adjusted manually or automatically by means of an XYZ translation stage. Examples of gas

30

TABLE 1 PHYSICAL PROPERTIES OF EBID/IBID PRECURSORS

Deposit Al Au

Co Cr Cu

Vapor pressure at room temperature

Phase

AlCl3 Al(CH3)3 AuCl3 Me2Au(hfac)

700 mtorr

? Liquid ? Liquid

Me2Au(acac) Me2Au(tfac)

8 mtorr 40 mtorr

? ?

PF3AuCl C8H8 or C6H5CH2 2¼CH2

10–25 torr

Gas ?

10 torr 0.004 mbar 420 torr 0.2 mbar 0.1 mbar 1.3 mbar

Liquid ? Liquid Liquid Liquid Liquid Liquid Gas ? Liquid Gas Gas ? ? ?

C12H26 to C18H38 C16H10 C3H4O2 C3H6O2 C2H4O2 CH2O2 C8H8 C2H4 Co2(CO)8 Cr(CO)6 Cu(hfac)2 Cu(hfac)(VTMS) Cu(hfac)(MHY) Cu(hfac)(VTMS) Cu(hfac)(DMB)

Reference Shimojo et al. (2005) Gamo et al. (1984), Ishibashi et al. (1991) Shimojo et al. (2005) Blauner et al. (1989), Du¨bner and Folch et al. (1995, 1996), Shedd et al. (1986), Wagner (1989), Weber et al. (1995a) Shimojo et al. (2005), Weber et al. (1995a) Bruckle et al. (1999), Floreani et al. (2001), Koops et al. (1988), Lee and Hatzakis (1989), Scho¨ssler et al. (1996) Utke et al. (2000a,b) Davies and Khamsehpour (1996), Harriot and Vasile (1988) Bezryadin and Dekker (1997) Yasaka et al. (1991) Bret et al. (2005) Bret et al. (2005) Bret et al. (2005) Bret et al. (2005) Bret et al. (2005) Guise et al. (2004a) Lau et al. (2002), Utke et al. (2004) Kislov et al. (1996), Matsui and Mori (1986) Luisier et al. (2004), Weber et al. (1995b) Ochiai et al. (1996) Luisier et al. (2004) Luisier et al. (2004) Luisier et al. (2004)

SILVIS-CIVIDJIAN AND HAGEN

C

Precursor molecular formula

Fe

Ga

Os Pd Pt

Fe(C5H5)2 Ga(CH3)/AsH3 D2GaN3 Mo(CO)6 Ni(CO)4 Ni(C5H5)2 Os3(CO)12 Pd(OOCCH3)2 Pd(C3H5)(C5H5) (CH3)3(C5H5) Pt or C5H5PtMe3 or CpPtMe3 (CH3C5H4)(CH3)Pt

Re Rh

Pt(PF3)4 Re2(CO)10 [RhCl(PF3)2]2

Ru Si SiO2 SiOx W

[RhCl(CO)2]2 Ru3(CO)12 SiH2Cl2 Si(C2H5O)4 Si(OCH3)4 W(CO)6

3 torr

Gas/Liquid

54 mtorr

? ? ? Gas Solid ? ? ? ? Gas

54 mtorr

Gas

55 mtorr

? ? Solid

78 mtorr 10 torr 17 mtorr

0.25 Pa

1.5 torr 420 torr 17 mtorr

? ? ? ? Liquid Gas

Solid

WCl6

?

31

WF6

Folch et al. (1996), Kunz et al. (1987), Takeguchi et al. (2004), Shimojo et al. (2004) Welipitya et al. (1996) Takahashi et al. (1992) Crozier et al. (2004) Weber et al. (1995a) Rubel et al. (1994), Wang et al. (1997) Jiang et al. (2001) Scheuer et al. (1986) Saulys et al. (1994) Saulys et al. (1994) Bruckle et al. (1999), Floreani et al. (2001), Hu¨bner et al. (2001), Koops et al. (1995), Lipp et al. (1996), Takai et al. (1998), Weber et al. (1995a) Morimoto et al. (1996), Puretz and Swanson (1995), Tao et al. (1990) Wang et al. (2004) Kislov et al. (1996) Cicoira et al. (2004), Marchi et al. (2000), Szkutnik et al. (2000) Cicoira et al. (2005) Scheuer et al. (1986) Ichihashi and Matsui (1988), Matsui et al. (1989) Kunz and Mayer (1987), Young and Puretz (1995) Komano et al. (1989) Micrion FIB Han et al. (2004), Hoyle et al. (1996), Kohlmann‐von Platen et al. (1993), Koops et al. (1988), Liu et al. (2004, 2005), McCord et al. (1988), Petzold and Heard (1991), Sawaragi and Mimura (1990), Shimojo et al. (2005), Stewart et al. (1989, 1991), Takeguchi et al. (2004), Song et al. (2005), Tanaka et al. (2005) Hiroshima and Komuro (1997), Ichihashi and Matsui (1988) Shimojo et al. (2005)

ELECTRON‐BEAM–INDUCED NANOMETER‐SCALE DEPOSITION

Mo Ni

Fe(CO)5

32

SILVIS-CIVIDJIAN AND HAGEN TABLE 2 CHEMICAL FORMULAS AND CORRESPONDING NAMES FOR EBID/IBID PRECURSORS

Material Al

Au

C

Co Cr Cu

Fe GaAs Ga Mo Ni Os Pd Pt

Re Rh Ru Si

Precursor chemical formula

Precursor name

Al(CH3)3 or AlMe3 Al(C4H9)3 AlCl3 (CH3)2Au(hfac) or Me2Au(hfac) Me2Au(acac) Me2Au(tfac) AuCl3 PF3 AuCl C2H4 C8H8 or C6H5CH2 2CH2 C16H10 C16H34 C12H26 to C18H38 CH2O2 C2H4O2 C3H4O2 C3H6O2 C5H8O2 Co2(CO)8 Cr(CO)6 Cu(hfac)2 Cu(hfac)(DMB) Cu(hfac)(MHY) Cu(hfac)(VTMS) Fe(CO)5 Fe(C5H5)2 Ga(CH3)/AsH3 D2GaN3 Mo(CO)6 Ni(CO)4 Ni(C5H5)2 Os3(CO)12 Pd(OOCCH3)2 Pd(C3H5)(C5H5) (C5H5)Pt(CH3)3 or CpPtMe3 (CH3C5H4)Pt(CH3)3 Pt(PF3)4 Re2(CO)10 [RhCl(CO)2]2 [RhCl(PF3)2]2 Ru3(CO)12 SiH2Cl2

Trimethyl aluminum, TMA Tri‐isobutyl aluminum Aluminum trichloride Dimethyl gold hexafluoroacetylacetonate, DMG(hfac) Dimethyl gold acetylacetonate Dimethyl gold trifluoroacetylacetonate Gold trichloride Gold trifluorophosphine chloride Ethylene Styrene Pyrene Hexadecane Liquid paraffin Formic acid Acetic acid Acrylic acid Propionic acid Methyl methacrylate (MMA) Dicobalt octacarbonyl Chromium hexacarbonyl Copper bis‐hexafluoroacetylacetonate DMB ¼ dimethylbutene MHY ¼ 2‐methyl‐1‐hexen‐3‐yne VTMS ¼ vinyltrimethylsilane Iron pentacarbonyl Ferrocene or biscyclopentadienyl iron Trimethyl gallium/arsine Perdeuterated gallium azide Molybdenum hexacarbonyl Nickel tetracarbonyl Nickelocene Triosmium dodecacarbonyl Pd‐Ac, palladium acetate Palladium allylcyclopentadienyl Cyclopentadienyl trimethyl platinum Methylcyclopentadienyl trimethyl platinum Trifluorophosphine platinum Dirhenium decacarbonyl Di‐m‐chloro‐tetracarbonyl‐dirhodium Di‐m‐chloro‐tetrakis‐trifluorophosphine‐dirhodium Triruthenium dodecacarbonyl Dichlorosilane (Continues)

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TABLE 2 (Continued) Material SiO2 SiOx W

Precursor chemical formula Si(C2H5O)4 Si(OCH3)4 W(CO)6 WF6 WCl6

Precursor name Tetraethoxysilane (TEOS) Tetramethoxysilane (TMS) Tungsten hexacarbonyl Tungsten hexafluoride Tungsten hexachloride

FIGURE 21. Different gas deposition system constructions. (a) Differentially pumped subchamber, (b) capillary injection nozzle, and (c) gas cell in an environmental SEM.

injector systems can be found in FEI Company’s FIB tools such as the FIB200 and FIB500 series and are produced and commercialized on a small scale by, for example, NaWoTec Gmbh (Hu¨bner et al., 2001; Koops et al., 2001). The positioning of the nozzle can be performed during SEM imaging with low magnification or under video camera monitoring. Sometimes the precursor vapor is introduced in the system together with another carrier gas (e.g., O2) (Komano et al., 1989). The molecular flow rate (throughput) of the precursor in the system, Q, can be controlled in three ways: (1) with a variable leak valve, (2) by choosing the dimensions and position of the nozzle, and (3) by controlling the precursor reservoir temperature. The only restriction imposed on the optimization of the molecular flow is that the pressure in the working chamber, P, may not exceed 105 torr. Usually the nozzle is a nonmagnetic steel or tantalum capillary with a circular cross section of 0.2–5 mm diameter. Some authors tried to optimize the form of the nozzle section to maximize the molecular flow (Davies and Khamsehpour, 1996; Kohlmann et al., 1991). For example, Kohlmann et al. (1991) calculated the effect of nozzle geometry on deposition

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FIGURE 22. Schematic of a nozzle‐based gas delivery system in an IBID machine. Reused with permission from L. R. Harriot, Journal of Vacuum Science & Technology B, 6, 1035 (1988). ß 1988, AVS The Science & Technology Society.

parameters and found an optimal inner diameter at the end of the nozzle of 80 mm with conically increasing diameter. As an example, a molecular flux on the specimen of 1018 molecules/cm2 can be obtained with a nozzle of 0.8 mm inner diameter suspended 0.2 mm above the substrate, with a vapor pressure of the dimethyl gold (DMG) complex precursor of 350 mtorr (Blauner et al., 1989). Typical nozzle parameters are illustrated in Figure 23 and the molecular fluxes obtained on the specimen have been collected in Table 3. The vapor molecular flow rate into the system, Q, can be calculated as a function of the upstream pressure in the precursor reservoir Pgas, the nozzle length L and diameter d, and the pressure in the specimen chamber P (Davies and Khamsehpour, 1996) or can be determined by solving the simple pumping speed relationship: P ¼ P0 þ

Q ; S

ð4Þ

where P0 is the base pressure in the deposition chamber measured before gas introduction, S is the pumping speed for the gas, and P is the pressure

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35

FIGURE 23. Illustration of nozzle construction parameters.

TABLE 3 TYPICAL PARAMETERS FOR THE GAS FEED NOZZLE Nozzle d [mm]/L[mm]

Vertical h[mm]

Gas flow [molec/(cm2s)]

Precursor

0.8 0.254/13

0.2 1

1018

DMG C8H8

0.300 0.250/10 3 4 0.2 1.6 0.080 0.7 0.5 0.2 0.260

0.250 0.100 5 5 0.5 3 0.05–0.250 0.4 1 0.2 4.2

1.4 1016 3 1019

W(CO)6 C8H8 WF6 W(CO)6 Si(OCH3)4 WF6 W(CO)6 C5H5Pt(CH3)3 W(CO)6 Cl2 WF6

1019 8 1017 8 1015

Reference Blauner et al. (1989) Davies and Khamsehpour (1996) Hoyle et al. (1996) Harriot and Vasile (1988) Ichihashi and Matsui (1988) Koh et al. (1991) Komano et al. (1989) Matsui et al. (1989) Kohlmann et al. (1991) Lipp et al. (1996a,b) Petzold and Heard (1991) Takado et al. (1989) Hiroshima et al. (1999)

reading in the chamber after the gas flow is switched on and equilibrium is reached. The pressure in the precursor reservoir Pgas can be sensed with a capacitance manometer. The pressure at the specimen cannot be measured exactly and usually is sensed at some distance from the gas delivery point, by an ionization gauge. In some setups the pressure at the specimen can be

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SILVIS-CIVIDJIAN AND HAGEN

measured more accurately, for example, by replacing the sample holder with a stagnation tube connected to a capacitance manometer (Blauner et al., 1989). The first pressure tests can be done safely with N2 instead of the real precursor. The pumping speed specified in the pump manual is given for water in case of cryogenic pumps and for N2 in case of turbomolecular types. The correction for a specific precursor gas is calculated by this equation: sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ MN2 Sprecursor ¼ SN2 ; ð5Þ Mprecursor where M is the molecular weight. A typical result of the N2 test is shown in Figure 24 for an EBL system modified to implement EBID. Note that in the situation shown the pressure in the gun and the stage mechanism chambers remains practically unchanged during gas introduction in the specimen chamber. The molecular flow can also be enhanced by resistively heating the precursor reservoir. A heat shield can be built around the reservoir to reduce the radiant heating of the specimen (Scheuer et al., 1986; Stewart et al., 1989).

FIGURE 24. Variation of pressures in the deposition instrument during gas introduction. Reused with permission from H. Hiroshima, Journal of Vacuum Science & Technology B, 13, 2514 (1995). ß 1995, AVS The Science & Technology Society.

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By varying the reservoir temperature, control over the vapor pressure is obtained and thus the influence of the molecular flux on the deposition rate can be studied (Kohlmann et al., 1991; Stewart et al., 1989; Weber et al., 1995b). When considering the option of heating the gas delivery system, care should be taken to avoid condensation in colder places in the gas line. Temperatures for the connection lines to the specimen chamber, the nozzle, and the specimen must be carefully maintained well above the temperature of the gas reservoir to avoid condensation (Nambu et al., 1995; Scheuer et al., 1986). In some cases, the deposition yield does not depend strongly on the precursor delivery pressure, as in the case of gold deposition from a DMG complex by IBID (Blauner et al., 1989). In this case, heating the gas delivery system would not be especially effective. In gas delivery constructions with a subchamber (Figure 21a) and with a nozzle (Figure 21b) modifications to the specimen chamber have to be made, which can be a technical inconvenience and a limitation in the normal functioning of the host microscope. Portable gas or wet cells should be designed to avoid these irreversible mechanical interventions. To study EBID, Folch et al. (1996) built a small 3.5 mm diameter cell containing the liquid Fe(CO)5 precursor and the specimen between two TEM apertures and the entire ‘‘sandwich’’ could be mounted on the specimen holder (Figure 21c). The gas escapes through the apertures and eventually adsorbs on the specimen. An additional purpose was to isolate the specimen from the residual vacuum, thus reducing the carbon contamination of the deposit. An environmental SEM was used (1–3 torr pressure) to avoid the vacuum constraints, but previously a conventional SEM has also been used; the authors believe that the reactive‐gas cell also can be used with precautions in normal SEMs. Together with this experiment, a new concept of ‘‘environmental EBID’’ was introduced. More sophisticated and flexible gas‐cell constructions with variable apertures to control the gas flow will be necessary in the future. 7. Conclusions EBID is most frequently studied in modified SEMs and EBL machines. Less often hosts such as TEMs, STMs or dual‐beam instruments are encountered. IBID is used and studied in commercial or home‐built FIB systems with lower optical resolution than the electron columns, but compensated by a higher reaction rate and more facilities necessary for IC surgery. The most widely used gas delivery system at this moment is based on the nozzle injector, with perspectives toward environmental gas cells. The precursors commonly used are the organometallic compounds assimilated from CVD technology. An actual trend is the search for new carbon‐free precursors.

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D. Analysis of Experimental Results and Theoretical Models The use of direct electron‐ or ion‐induced deposition for growing structures is an encouraging step, but in most cases it is insufficient. In some situations, the deposited structure must be characterized. Its analysis is required to evaluate the performance of the experiment and to present arguments for promoting or rejecting the chosen approach. In other situations, a theoretical model that can explain the obtained experimental results would be welcome. Both the analysis results and the theoretical models create the environment necessary for understanding EBID. The analysis regards the electrical properties of deposited material, its microstructure, its chemical structure, or its basic geometrical parameters such as thickness, growth rate, and lateral size. For each of these properties, our literature review uses the following scheme. First, ideal values required by a high‐quality EBID are given. Then the methods and instruments used to measure the deposit properties are summarized. Relevant experimental results and numerical values encountered by different authors are detailed. Major theoretical models developed to explain and support these experimental results are also described. The EBID/IBID models operate with three basic entities: the substrate, the precursor vapors, and the focused charged‐ particle beam. A complicated triangle of interactions among precursor, beam, and substrate governs the deposition process. The details of IBID and EBID are still not completely understood. First, the particle‐induced dissociation mechanism is complex and difficult to model because of the huge number of excitation channels possible even for small molecules. The presence of the substrate complicates the problem, because it creates new molecular dissociation paths and surface processes such as diffusion, migration, desorption, and so on. Modeling of IBID is even more complicated, because sputtering by ion beams occurs simultaneously with material deposition. It is difficult to identify the primary causes of molecular dissociation among the electronic or vibrational excitations, the SEs, or the primary electrons. That is why no analytical solution for the modeling problem is possible without gross approximations. However, partially working models have been developed based on experimental observations. 1. Electrical Properties Because EBID and IBID are expected to be mainly used for device manufacturing and wiring, it is necessary to produce deposits with low resistivity, as close as possible to the bulk metal values. For example, these values are for pure gold 2.2 m cm, for copper 2.05 m cm, for tungsten 5.5 m cm, and for platinum 10.6 m cm. For the deposition of insulator

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39

material, a resistivity value higher than 1 m cm and a breakdown voltage higher than 10 V are required. The electrical resistivity r ¼ R A/L can be determined by depositing lines or rectangles between pre‐evaporated metal contacts (Au, W, Al, or NiCr) (Figure 25), and by measuring their electrical resistance R, length L, and cross section A. The latter can be determined by cleavage of the deposit. The resistance can be measured using an I‐V method in a two‐ or four‐probe arrangement (Figure 26). The two‐probe arrangement is sufficiently accurate when measuring resistances much larger than the resistance of an ohmic contact. However, for lower resistances (<0.1 ), the voltage drop on the

FIGURE 25. Prefabricated contacts for resistance measurement. From Hiroshima et al. (1999) with permission from the Institute of Pure and Applied Physics.

FIGURE 26. Arrangement schemes for (a) two‐probe and (b) four‐probe resistance measurements.

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contacts cannot be neglected without considerable measurement errors. In this case, the four‐probe arrangement is recommended as a more accurate resistance measurement method. Results that are more reliable can be obtained if the film resistivity can be measured in situ by avoiding possible changes in conductance because of exposure to the atmosphere (Hoyle et al., 1996). The following text presents a few resistivity results obtained by different authors using EBID and IBID. Gold, tungsten, copper, platinum, rhodium, cobalt, and contamination lines have been deposited to study their electrical properties. The first effect observed in all cases is that the resistivity of deposited lines is higher than the bulk value. The resistivity of tungsten film deposited by IBID from W(CO)6 is 600–800 m cm (Koh et al., 1991) and 150–200 m cm (Stewart et al., 1991). These values are larger than the bulk tungsten value but sufficient for IC repair. Good STM images also can be obtained with contamination grown tips (Akama et al., 1990). This means that, although not being a tragedy for some applications, the high resistivity is a drawback of the direct deposition method. Gold has been deposited by IBID from DMG hexafluoroacetylacetonate (DMG(hfac)) with resistivities of 500–1500 m cm, also much higher than the bulk resistivity of pure gold (Blauner et al., 1989). Koops et al. (1988, 1994) used EBID to deposit tungsten from W(CO)6. The tungsten deposits, bars of 2 mm length and 400 nm width, had a resistivity measured in four‐ point measurement of 0.02 cm, more than four orders of magnitude larger than that of bulk tungsten. Utke et al. (2002a,b) found a resistivity of 50 m cm for deposition of cobalt from Co(CO)8, which is also nearly four orders of magnitude more than for bulk cobalt. They reduced the resistivity by applying a voltage over the newly grown line while writing. A potential of 5 V improved the conductance by a factor of 3 between two scans over the line. Ex situ heating of the lines at 300 C increased the resistivity because separated cobalt grains appeared. In contrast, Komuro et al. (1998) reduced the resistivity of tungsten deposits from WF6 by an order of magnitude by post‐annealing at 500 C for 60 minutes under hydrogen gas flow. Lau et al. (2002) found a better resistivity than Utke et al. (2002b) for the Co(CO)8 precursor; they achieved 45 m cm in an ESEM. They wrote arches spanning the distance between the electrodes instead of lines lying on the substrate, a geometry that also might have influenced the resistivity. In a similar geometry, Madsen et al. (2003) measured a resistivity in the order of 0.1 m cm for lines deposited from dimethyl gold acetylacetonate (DMG(acac)).

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Morimoto et al. (1996) measured the resistivity of platinum tips grown on SiO2 wafers and obtained a value of 30 m cm, three times higher than the bulk platinum value. They observed that the situation improved by modest substrate heating, which resulted in the resistivities reaching the bulk values. The influence of substrate heating was also noticed by Utke et al. (2000a). Koops et al. (1996) found for deposits from dimethyl gold trifluoroacetylacetonate (DMG(tfac), Me2Au(tfac)) that substrate heating from room temperature to 80 C increased the conductivity, which they attributed to the higher metal content at higher temperatures. Scho¨ssler et al. (1996) observed that by annealing Pt‐containing resistors, their resistivity reduced by three orders of magnitude and their value stabilized. Gopal et al. (2004) also found the same behavior for platinum‐ containing structures. Koops et al. (1996) found that annealing at 180 C decreased the resistivity of deposits from both gold and platinum precursors by two or three orders of magnitude. Both materials were found to have a negative temperature coefficient for the resistivity. When the same precursor is used, structures deposited by IBID have a lower electrical resistivity than when deposition is done with an electron beam. Gopal et al. (2004) found a resistivity of a factor 10 better (2004). Some authors observed that lower resistivity values could be obtained at higher exposure currents. Kohlmann‐von Platen et al. (1992) found this for W(CO)6. Ochiai et al. (1996) formulated the same dependence in a slightly different way: a low resistivity can be obtained with a high current density. We believe this is a more correct formulation. Ochiai et al. (1996) deposited copper lines using EBID from copper hexafluoroacetylacetonate vinyltrimethylsilane (Cu(hfac)(VTMS)) in an ESEM and the lowest resistivity reported was 3.6 m cm, only two times larger than the bulk copper value. This result is explained by the very high current density exposure of 1270 A/cm2, created by a 1 nA beam focused in a 10 nm spot. Lau et al. (2002) found a similar relationship when depositing cobalt between two electrodes. Tao et al. (1990) used IBID to deposit platinum films and the resistivities were in the range of 70–700 m cm, decreasing with higher current densities. Experiments done by Bruk et al. (2005) with Fe3(CO)12 confirm this dependence of resistivity on beam current. When the beam current increased by a factor of two, the resistivity decreased by four orders of magnitude, with the best value for the resistivity being 4 102 cm. All deposited lines showed a decreasing resistance with increasing temperature, indicating nonmetallic conduction. The reason for this dependence on the beam current density has not been discovered yet. The resistivity of the deposited lines also depends on the beam scanning conditions—the exposure dose per pixel (C/m2) and the dwell and loop

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times. The electrical properties of tungsten lines deposited from W(CO)6 using EBID have been measured by Hoyle et al. (1993, 1994). The resistance was measured with the two‐probe arrangement, depositing a line in the 10–20 mm gap between two gold contacts predeposited on semi‐insulating GaAs substrate pads. The measurements showed resistivities of 3000 m cm obtained with a 5 kV electron beam, 1 nA probe current, and fast scanning, whereas resistivities 40 times smaller could be obtained from slow scanning conditions, proving that fast rastering is not suitable for low‐resistivity interconnects. Hiroshima and Komuro (1997) used EBID in a 50 kV SEM to deposit tungsten from WF6 and studied the influence of the scanning conditions on deposit resistivity, with the same conclusion as Hoyle et al. (1993, 1994) that slow scanning decreases the deposit resistivity. Conducting wires have been fabricated with a width of 10–20 nm with a lowest resistivity of 600 m cm. Another conclusion is that three times higher doses improve the conductivity by up to five orders of magnitude. In a later study, the resistivity was reduced to 300 m cm by annealing the sample at 300 C for 1 hour, followed by 10 minutes of O2 plasma cleaning before fabricating the structures (Hiroshima et al., 1999). Hoyle et al. (1996) reduced the resistivity of deposits from W(CO)6 by increasing the dose. The initial dependence on dose is nonlinear. Increasing the dose from 0.5 nC/m2 initially leads to increasing resistance, after which it drops to a minimum level that is about a factor of 3 lower than the starting value. The influence of beam energy on electrical resistivity is unclear. Kohlmann‐von Platen et al. (1992) found for W(CO)6 that lower resistivities are obtained at lower impact energies. Hoyle et al. (1994, 1993) found similar results. For example, the decomposition of W(CO)6 by a 1 keV primary beam produces material with a four times lower resistivity than decomposition by a 20 keV beam. The lowest value, 600 m cm, is obtained for an impact energy of 0.25 keV, still two orders of magnitude larger than the bulk tungsten resistivity (Hoyle et al., 1993, 1994). These experiments are contradicted by results found by Gopal et al. (2004). For lines deposited from a platinum precursor, the resistivity decreased by a factor of 3 for beam energies increasing from 2.5 to 12.5 kV, to remain constant from 12.5 to 20kV. An accepted explanation for the high resistivity of deposited materials blames the carbon impurities included during deposition. Because one of the sources of contamination seems to be the specimen itself, a condition requisite to obtain a deposit of low resistivity is careful treatment and cleaning of the sample. Experiments using FIBDD can provide much better results in the deposition of Au, Cu, and Al films with low resistivities; these are only 1.2–2.2 times larger than the bulk values, due to a very low residual pressure.

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This result also underscores the importance of a clean environment in obtaining low resistivities (Nagamachi et al., 1998). Folch et al. (1996) succeeded in reducing the carbon content by building a gas cell that includes both the specimen and the liquid precursor Fe(CO)5. The precursor is isolated by two TEM apertures so that contaminant residual gases cannot easily reach and adsorb on the specimen. Komuro et al. (1998) found that an O2 plasma etch for 5 seconds before deposition reduced the effect of contamination noticeably and increased the conductivity by three orders of magnitude. Currently the precise mechanism is not yet understood since a longer plasma etch again caused a deterioration of the conductance. Another method to obtain pure deposits with low resistivity is the use of carbon‐free precursors. This is the approach taken by Utke et al. (2000a), using the inorganic precursor PF3AuCl, with which they could deposit gold lines using EBID with a resistivity as low as 22 m cm. No special care was taken to prevent hydrocarbon contamination. They found that the deposited lines consisted of individual interconnecting gold grains and that an increase in dose led to better conduction due to better contact between the grains. The use of another carbon‐free precursor, Rh[Cl(PF3)2]2, did not lead to good conductance (Utke et al., 2000b). Deposited lines consisted of Rh crystals in an amorphous phosphorus/carbon matrix, the carbon being due to contamination in the microscope. The conductance was 10 cm. The electrical conductivity is also influenced by a proximity effect. When depositing lines from a platinum precursor at spacings decreasing from 20 to 5 mm, Gopal et al. (2004) noticed that the resistance decreased exponentially from 100 G to 100 k. Using time‐of‐flight secondary ion mass spectrometry (TOF‐SIMS) they were able to show that adjacent lines became connected by platinum deposition between the lines. They explain these results by broadening due to secondary electron‐assisted decomposition and thermally assisted diffusion of the deposited platinum. A more likely explanation might be that primary electrons are scattered from the growing line and cause further deposition in the region around the line. 2. Morphological Properties The structure of the deposit may have an impact on the ultimate achievable fabrication resolution. For example, if the material is crystalline, the minimum obtainable feature size will be limited by the size of the nanocrystals. The most common techniques used to determine the microstructure or morphology of the deposited material are high‐resolution electron microscopy (HREM) and electron diffraction analysis in a TEM. In order to be inspected in a TEM, the structures usually are deposited on a thin 3‐mm

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diameter TEM carbon or Si3N4 membrane or they are grown as free‐standing structures in open space, across holes in membranes or blank TEM meshes. Contamination growth is an old topic in microscopy. Ennos (1954) studied this phenomenon in the 1950s, but even today the precise chemical composition is a subject of research. It has been confirmed by TEM diffraction analysis that contamination growth usually deposits amorphous material (Akama et al., 1990). Bret et al. (2005) performed compositional analysis on deposits from styrene, acrylic acid, propionic acid, acetic acid, and formic acid. It appears that the composition is close to C9H2O, regardless of the chemical composition of the precursors. The structures resulting from metal EBID in general consist of metal crystallites embedded in an amorphous carbon matrix. TEM images in general show small polycrystallites of less than 5 nm diameter, for instance, in the case of aurum (Lee and Hatzakis, 1989). Dubner et al. (1991) applied diffraction analysis to the results of IBID using DMG(hfac) and found that gold islands of 30–40 nm are formed, randomly oriented in a carbon matrix. Koops et al. (1994) used EBID to deposit gold from DMG(tfac) and DMG(acac) in an SEM. They discovered a new class of nanocrystalline compound materials. The morphological information about these materials was obtained by TEM at 100–400 kV and revealed metal or metal carbide crystallites of a few nanometers, immersed in an amorphous carbonaceous matrix (Figure 27). The packing of the crystallites became tighter at a higher beam current (1000 pA), while the size of the crystallites decreased. Furthermore, a larger dwell time per pixel resulted in the formation of larger crystallites. A more detailed analysis can be obtained by imaging the lattice planes of the deposited nanocrystallites. The lattice planes of the crystallites have a lattice period of 0.233 nm, compared with 0.235 nm for gold single crystals. The difference in structure obtained from the two different gold precursors was found to be negligible. Diffraction patterns of deposits from DMG(tfac) show a face‐centered cubic (fcc) structure. The elementary lattice cell of the crystallites is 0.401 nm, while the base cell unit for gold is 0.408 nm. This implies that the crystallites are mainly gold and the amorphous material in which they are embedded is carbon. Koops et al. (1996) also used EBID to deposit platinum from cyclopentadienyl trimethyl platinum (CpPtMe3) and used the same two analysis methods, TEM and diffraction analysis. The lattice spacing was found to be 0.231 nm for (111) and 0.196 nm for (200) planes. This is in good agreement with the platinum bulk values from the literature. The diffraction analysis shows an fcc structure of the elementary cell, with a lattice constant of 0.392 nm, compared with 0.3924 nm for bulk platinum. This agreement confirms that the deposit contains Pt nanocrystals.

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FIGURE 27. High resolution TEM image of a tip grown by EBID that reveals the nanocrystallinity of the material (gold in carbon matrix). Reused with permission from C. Schoessler, Journal of Vacuum Science & Technology B, (1997). ß 1997, AVS The Science & Technology Society.

In situ observation of the EBID process may suggest a possible deposition mechanism. For example, Ichihashi and Matsui (1988) performed an in situ TEM observation of EBID from WF6 and SiH2Cl2. This host microscope allowed the recording of successive electron micrographs of the deposit during beam exposure, suggesting the following mechanism. First, the beam impact causes the adsorbed WF6 to dissociate into W and F2. The deposition starts when clusters are formed, consisting of 3 nm b‐W crystals. After a while the clusters coalesce into a film. The same WF6 adsorbed on fine Si particles on carbon film produces larger clusters of a‐W. Diffraction analysis showed that a Si layer formed from SiH2Cl2 is amorphous, probably because Cl atoms destroy the crystallinity. It is possible that other, chlorine‐free precursors such as SiH4 or Si2H6 would deposit crystalline Si. Deposits do not always have the morphology of small crystallites in an amorphous carbon matrix; the deposit can also be amorphous or crystalline, depending on the exposure conditions. Hoyle et al. (1993, 1994) studied EBID from W(CO)6 in a TEM. Micrographs and diffraction patterns showed that the structure of a 10 nm thick tungsten film is continuous and depends on the exposure dose used. A low dose of 5 C/m2 results in an amorphous structure (Figure 28a), whereas a higher dose of 10,000 C/m2 deposits a polycrystalline structure, with crystals of less than 3 nm in diameter (Figure 28b). The crystals are probably a high‐temperature crystalline b‐phase of tungsten carbide,

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FIGURE 28. Transmission electron diffraction pattern of film deposited with (a) a dose per scan of 5 C/m2 and (b) a dose per scan of 10,000 C/m2. Reused with permission from P. C. Hoyle, Journal of Vacuum Science & Technology B, 14, 662 (1996). ß 1996, AVS The Science & Technology Society.

b‐WC1‐x. The continuous structure differs from that of films produced by IBID from the same W(CO)6, which were reported to have a discontinuous island structure with a thickness of up to 23 nm. Kislov et al. (1996) grew self‐standing wires from W(CO)6, Cr(CO)6, and Re(CO)10. The rhenium deposits consisted of several individual fibers aligned in parallel, while the tungsten and chromium deposits consisted of nanocrystals in an amorphous matrix. The formation of the rhenium fibers could indicate an autocatalytic decomposition for the rhenium precursor. Takeguchi et al. (2004) found nanocrystals of 2 nm in diameter in an amorphous matrix when writing self‐standing deposits from W(CO)6. Annealing did not lead to a change in this morphology. Free‐standing deposits from Fe(CO)5 also consisted of nanocrystals in an amorphous matrix and although the crystal size could not be defined precisely, the crystals are larger than in the case of the tungsten deposits. Upon annealing, the deposits transformed into single‐crystal or polycrystalline phases with a stoichiometry of Fe3C. The phases found were a‐Fe, Fe3C, Fe5C2, Fe7C3, and Fe2C. The a‐Fe phase was found only in the free‐standing rod, not in dots written on the carbon substrate. Utke et al. (2004) have studied structures grown from Co2(CO)8. In the initial growth stages, tip deposits show a smooth surface and consist of Co crystals of 1–2 nm embedded in a carbon‐rich matrix. With increasing tip length or beam current, a transition to a rougher, corrugated and polycrystalline surface is observed. The same change in surface morphology was seen

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for deposits from Cu(hfac)(VTMS), Co(CO)3NO (Rothschild, 1990), and Mo(CO)6 (Weber et al., 1995a). Since the tip apex temperature was found to be proportional to the beam power and tip length for small diameters in a first approximation, the authors correlated the morphology of structures to heating effects. Jiang et al. (2001) have found that for nickelocene (Ni(C5H5)2) deposition results depend strongly on the ratio of the precursor partial pressure during deposition to equilibrium vapor pressures at different substrate temperatures. Depositions were performed at substrate temperatures between 25 C and 103 C and pressures between 3 106 and 3 08 torr. Uniform and continuous deposits were achieved when the partial pressure was below the vapor pressure at the deposition temperature, whereas nonuniform, porous deposits were obtained when the partial pressure was above the vapor pressure corresponding to the temperature during deposition. The electron dose was varied at a temperature of 85 C and a partial pressure of 5 108 torr, with the partial pressure being above the vapor pressure at that temperature. At low dose, the deposited material formed a network with relatively large openings. As the electron dose was increased, the deposit became more uniform and continuous. Structures deposited at 58 C and 5 108 torr partial pressure consisted of crystalline grains of a few nanometers in diameter embedded in an amorphous matrix (Jiang et al., 2001). The lattice fringe spacing of 0.206 0.004 nm closely corresponds to the bulk value of Ni of 0.203 nm. The morphology also depends on the environment in which deposition takes place. Mølhave et al. (2003) have deposited structures from DMG(acac) in an ESEM with an additional background gas of nitrogen and water. Tips deposited in 1 torr nitrogen consisted of 3–5 nm gold crystals spaced at 1–2 nm in an amorphous deposit, similar to tips fabricated in a traditional SEM. Tips deposited in water pressures above 0.4 torr consisted of a central polycrystalline gold core surrounded by a crust. The crust was of the same morphology as the tips deposited in N2, whereas the core consisted of grains with significantly larger diameter. Similar behavior was found for deposited lines. Tip height and core diameter decreased with decreasing water pressure and no core was observed below the threshold pressure of 0.4 torr. Deposition with a background gas of hydrogen and oxygen (with an amount of H and O in the chamber corresponding to 0.8 torr water) did not yield the core–crust structure. The core diameter increased proportional to the square root of the electron beam current. The authors suggested as possible explanation for the core–crust formation that both irriadiation and the presence of water can influence the diffusivity of gold clusters.

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3. Chemical Structure Analysis Once the deposit has been formed, it is also interesting to determine its chemical composition, to see how much metal it contains, and to determine what causal relation exists between a certain composition and the conditions at which it was deposited. A high‐quality deposition process must create highly pure crystalline material. The deposition from organometallic compounds has to create a high percentage of metal and a low percentage of carbon. The information about the composition can also offer some clues for a better understanding of step‐by‐step deposition mechanisms. In order to detect different elements in the composition of the deposit, a number of spectroscopic methods are currently available, such as AES, X‐ray microanalysis (XMA), energy dispersive X‐ray analysis (EDX), Raman spectroscopy (RS), secondary ion mass spectrometry (SIMS), X‐ray photoelectron spectroscopy (XPS), and so forth. Because the spatial resolution of these microprobe analysis methods is 1 mm, lower than the fabrication resolution in SEM and TEM, the deposited structures to be analyzed must be large enough to be detected. For this purpose, rectangles must be deposited instead of small dots or lines, and in case of the inspection of small tips, a wide band of tip material must be mounted on a substrate and then analyzed. Tips grown by contamination in an SEM or FIB apparatus, using the residual vacuum as precursor, have been analyzed by AES, showing carbon and oxygen, as expected from residual gases present in the microscope. Raman spectroscopy revealed amorphous carbon a‐C with sp3 and sp2 hybrids, corresponding to the bonding structure of diamond and graphite, respectively (Figure 29) (Ishibashi et al., 1991; Matsui et al., 2000). This has been confirmed by Djenizian et al. (2003) from AES measurements on lines written in contamination. Castagne` et al. (1999) obtained a mass spectrum of carbon supertips grown in an SEM from residual vacuum, which showed carbon, oxygen, and silicon atoms, but also atomic hydrogen and complex carbon hydride molecules (12C2, 12CH, 12C2H, 13C, 12C) with no evidence of nitrogen or metal doping. Guise et al. (2004b) have deposited carbon from ethylene on Si (100) using AES and XPS to determine the composition. The authors argue that during irradiation, the adsorbed ethylene partially dehydrogenates to C2H4, with x < 4. These unsaturated species will produce a polymeric structure consisting of a carbon–carbon bonded structure with remaining C–H bonds, making a CxHy polymer. Upon continued irradiation, C–H bonds are removed. From this amorphous hydrogenated carbon film, hydrogen can be desorbed when heating to 450 C and the carbon becomes SiC at temperatures above 900 C. It was found that EBID yields a more stable carbon

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FIGURE 29. Raman spectra of a diamondlike amorphous carbon film deposited by IBID. The decomposed bands are shown in G (graphite) and D (diamond) in solid lines. Reused with permission from Shinji Matsui, Journal of Vacuum Science & Technology B, 18, 3181 (2000). ß 2000, AVS The Science & Technology Society.

structure with a greater fraction of higher‐order carbon–carbon bonds (C¼C and CC) compared with films made by thermal decomposition. In a similar study, Bret et al. (2005) have studied five different carbon precursors: styrene, acrylic acid, propionic acid, acetic acid, and formic acid. The composition was close to C9H2O for deposits from all precursors, quite independent of the precursor stoichiometry. A large part of the carbon– carbon bonds consisted of sp2 bonds, and most of the remaining sp3 C was bonded to H atoms. This result seems consistent with results found for contamination growth. Deposition rates appeared to be dependent on the polarity of the precursor molecules, with polar molecules with high vapor pressures favorable for high deposition rates. Deposits from tungsten precursors have been analyzed by Auger and X‐ray analysis. The deposits formed using EBID from W(CO)6 contained tungsten carbide and up to 75% W, but typically 55% W, 30% C, and 15% O (Hoyle et al., 1996; Kislov et al., 1996; Koops et al., 1994). The deposits

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þ obtained by Hþ 2 and Ar irradiation from the same precursor contained more tungsten, typically 75% W, 11% O, and 14% C (Figure 30). The disadvantage of IBID is the gallium implantation in the deposit. When Gaþ ions were used, the deposit contained 70–75% W, 10% C, 10% Ga, and 5–10% O (Stewart et al., 1989). These results may suggest a possible mechanism of EBID. For example, it is known from organometallic chemistry that in the W(CO)6 molecule, the bond energy between the W atom and the CO ligand is smaller than that between the C and O atoms in the carbonyl group. Because the measured contents of C and O in the deposits are equal, the C and O atoms probably come from the incomplete decomposition of the precursor and not from the ambient atmosphere. The suggested decomposition products of W(CO)6 are W(CO)6–x and (CO)x (x ¼ 1, 2, . . . 6), which partially desorb from the surface.

þ FIGURE 30. Auger spectra for films deposited by IBID with Hþ 2 and Ar ions. Reused with permission from Y. B. Koh, Journal of Vacuum Science & Technology B, 9, 2648 (1991). ß 1991, AVS The Science & Technology Society.

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The XPS data from the deposited and bulk tungsten are quite the same. Different precursors containing the same metal can produce deposits of different metal purity. For example, a deposit of higher purity may be obtained by choosing a different tungsten precursor. Deposition from WF6 during Auger analysis was performed by Matsui and Mori (1986, 1987). The W Auger signal increased exponentially as the exposure time increased, until the signal saturated after 10 minutes because the deposit thickness reached the escape depth of the Auger electrons (the growth rate was only 0.1 nm/min). The composition after 15 minutes exposure time was 85 at. % W, 7.5 at.% F, and 7.5 at.% O. The O is believed to originate from residual oxygen in the specimen chamber. When the temperature of the SiO2 substrate was varied, different beam‐induced behavior was observed. When the temperature was increased from 110 C to 25 C, the deposited thickness decreased by a factor of 4 103. The W Auger signal of deposits fabricated at 25 C was higher than of deposits fabricated at 110 C. When the temperature is increased to above 50 C, etching occurs instead of deposition. The etching rate increased when the temperature was increased further to 160 C. AES measurements indicate that the tungsten remains on the etched surface, the contents being 66 at.% W, >1 at.% F, 30 at.% C. and 4 at.% O. An explanation for this behavior might be that the electron bombardment produces elemental Si at the SiO2 surface, which forms a volatile product with the F from the dissociated WF6. However, Shimojo et al. (2005) have found lower tungsten contents when experimenting with WCl6 compared with values mentioned previously for W(CO)6. Deposits contained 58 at.% W, 16 at.% Cl, 8 at.% C, and 18 at.% O, which indicates that more parameters influence deposit purity than just precursor chemistry. This has been confirmed by other experiments. The use of inorganic precursors can lead to pure metal deposition, as is shown for AuClPF3 (Utke et al., 2000a). Without special precautions to prevent hydrocarbon contamination, nanostructures consisting of gold grains with varying size (up to 60 nm in diameter) could be deposited. In contrast, the inorganic precursor [RhCl(PF3)2]2 yields a deposit consisting of 60 at.% Rh, 20 at.% P, and 20 at.% Cl, O, and N combined, surrounded by a carbon contamination layer (Cicoira et al., 2004). This composition was nearly constant for beam energies ranging from 2 to 25 kV and beam currents from 1 to 10 nA. The Rh and Cl content for structures deposited from [RhCl(CO)2]2 was similar at 56 at.% Rh, 34 at.% C, 5 at.% Cl, and 5 at.% O and N (Cicoira et al., 2005). Unexpected behavior similar to that found by Matsui and Mori (1986, 1987) was observed by Shimojo et al. (2005), who performed EBID with AlCl3 and AuCl3 on carbon and silicon substrates. When moving the beam from the silicon substrate into vacuum in the presence of AlCl3 to

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fabricate self‐standing lines, silicon rods containing small amounts of carbon and oxygen were formed. No aluminum or chlorine signal was detected by EDS measurements. Similar behavior was observed for AlCl3 on carbon and AuCl3 on silicon and carbon. A possible explanation is that SiCl4 or CCl4 are formed after dissociation of the original precursors and are re‐decomposed to volatile species and nonvolatile silicon and carbon, respectively. When depositing on thin membranes, a deposit grows both on the entrance and on the exit side of the substrate. Liu et al. (2004a) have observed in high‐angle angular dark‐field (HAADF) images that in the very early stages of growth (from W(CO)6) on a thin membrane, the deposit on the exit side is much brighter than the deposit on the entrance side. This indicates that the bottom structure contains more tungsten than the top one. A precise explanation has not yet been given. Weber et al. (1995b) have determined the composition of deposits from CpPtMe3, Mo(CO)6, DMG(acac), DMG(tfac), and DMG(hfac) by EDX. The metal content increases for all precursors with increasing beam current and lower primary electron energies. The metal content for deposits from the gold precursors reaches the stoichiometric composition of the precursor above beam currents of 900 pA at 20 kV. For Mo(CO)6 deposits, the metal content does not reach the corresponding value of the precursor molecule. Metal contents are 13 at.% for CpPtMe3 and about 40 at.% for Mo(CO)6. Upon heating, the metal content for deposits from DMG(tfac) increases up to 73 at.% at 45 C, with no remaining carbon in the deposit (only elements with Z 6 were measured). Deposition from Mo(CO)6 shows an inverse relationship with temperature, with a decreasing metal content at higher temperatures. In contrast to the experiments performed by Koops et al. (1994), Folch et al. (1995) have not found a dependence on beam current or energy when measuring the composition of DMG(hfac) deposits with AES. The metal content could be improved when allowing a second gas into the specimen chamber during writing. A mixture of 10 torr of argon and oxygen increased the gold content up to 50%, whereas pure argon did not influence the composition significantly. Allowing water into the chamber increased the metal content up to 20% at 3 torr partial pressure. Gold contents below 12.5% were systematically observed when the pressure of the reactive gas was decreased to below 0.1 torr. Lee and Hatzakis (1989) used EBID from DMG(tfac) by 30 keV electron irradiation and obtained a content of 75% Au and 25% C. The film composition was similar for different beam energies: 2 keV, 5 keV, and 30 keV. The reason for the difference between these measurements and those for the same precursor by Koops et al. (1994) remains unclear.

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Ishibashi et al. (1991) have studied the growth from TMA. Although deposition times were long (in the range of 20 minutes for lines), pure aluminum was deposited. The copper precursor Cu(hfac)(VTMS) used in EBID gives a copper content of 10–20%, with a percentage ratio in the deposit of Cu:C:O:Si:F ¼ 1:5:0.5:3:<0.1. This ratio is different from the percentage ratio in the precursor, which is 1:10:2:1:6. Comparing these results, it appears that the C, O, and F contents decrease, whereas the Si percentage increases. A possible explanation could be that the SiO2 substrate also decomposes under electron beam irradiation (Ochiai et al., 1996). Luisier et al. (2004) have compared four different copper precursors— Cu(hfac)2, Cu(hfac)(MHY), Cu(hfac)2(VTMS), and Cu(hfac) dimethylbutene (DMB). Composition analysis was performed by AES and showed a Cu content of 14 at.%, 13 at.%, 20 to 45 at.%, and 25 to 60 at.%, respectively. The large fluctuations for the latter two precursors may be due to selective etching during the sputtering cycle of the Auger measurements. The authors argue that decomposition of the first two precursors is more complete, since the large variations in etching rates are not observed. Assuming for the latter two precursors that the minimum values are closest to the original EBID decomposition values, the Cu content in deposits seems to be governed primarily by the electron‐to‐precursor flux ratio and precursor stability rather than by precursor stoichiometry. Kislov et al. (1996), using EBID followed by annealing from chromium and rhenium carbonyls, analyzed the deposits in the diffraction mode and found that Cr rods contained some unidentified phases in addition to the metal phase, but the rhenium deposits contained only one crystalline metal phase. Therefore Re(CO)6 has been promoted as an attractive precursor material for microengineering. For the cobalt carbonyl Co2(CO)8 precursor, the composition varied from 12 to 80 at.%, depending on the beam current (Utke et al., 2004). At a beam current of 20 pA, the deposit composition corresponded to the precursor stoichiometry, while at currents above 10 nA almost pure cobalt tips were deposited (taking the offset values for the substrate background signal into account). For the same precursor, Lau et al. (2002) have found a cobalt content of 35 at.% at 1.6 nA to 50 at.% at 10.7 nA. A much lower metal content (8 at.% Co, 72 at.% C, 20 at.% O) was found for small islands that were formed in the vicinity of grown pillars. Apparently, a high current density is beneficial for obtaining high‐purity deposits. The authors suggest two possible mechanisms. A local temperature rise can result from electron beam heating, or the increase in electron flux relative to the gas flux leads to a higher

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probability that a molecule interacts with an electron and is converted to the final product. The carbon‐to‐oxygen ratio was roughly 3:1 for all deposits. A slight decrease in metal content from 45 at.% to 35–40 at.% Co was observed for an increase in beam energy from 15 to 25 kV. Furthermore, it was observed that the shape of the deposits did not have a significant influence on the material composition. A trial to deposit platinum from CpPtMe3 resulted in tips with 21.5% Pt, 73% C, and 5.5% O (Morimoto et al., 1996). Platinum films deposited by a Gaþ FIB were amorphous and their Auger analysis showed 46% Pt, 24% C, 28% Ga, and 2% O (Tao et al., 1990). Performing EBID with Pt(PF3)4 yielded 15 at.% Pt, 57 at.% P, 18 at.% C, and 9 at.% O (Wang et al., 2004). The authors attribute the presence of C and O in the deposit to dissociation of the background gases water and carbon monoxide. The Pt/P ratio of 0.26 in the deposit is equal to that in the precursor, within the experimental uncertainty. This ratio could be increased to 0.63 by allowing oxygen in the specimen chamber during deposition, but this also led to a larger concentration of O in the deposited film. By increasing the temperature from 25 C to 120 C, the P content could also be reduced to a Pt/P ratio of 3. GaAs:C lines and dots have been fabricated by Takahashi et al. (1992) from trimethyl gallium and AsH3 (cracked at 1000 C). Atomic concentrations determined by AES were 30% Ga, 40% As, and 25% C, the carbon originating from the Ga precursor. Electron probe microanalysis (EPMA) measurements showed that the carbon content decreased to less than 10% when the substrate temperature during fabrication was increased from room temperature to 300 C, while Ga and As were present in equal concentrations. Crozier et al. (2004) have deposited GaN from perdeuterated gallium azide (D2GaN3) onto SiOx, a precursor especially designed to have the correct Ga–N concentration. EELS measurements on deposited dots showed that the near‐edge fine structure of the nitrogen K‐edge is nearly identical to that found in bulk GaN, indicating that the deposit is pure GaN. EELS measurements across a self‐standing rod fabricated from Fe(CO)5 showed that Fe and C are distributed evenly over the rod, while O is present only near the surface of the rod (Takeguchi et al., 2004). Analysis in combination with high‐resolution TEM indicated that the surface is covered by Fe oxide crystals, the oxide probably due to exposure of the specimen to air between fabrication and analysis. The shape of the carbon edge in the EELS spectrum is identical to that of amorphous carbon. After heating the specimen to 600 C, the oxidized surface layer had disappeared and the amorphous carbon present in the rod had been converted to a carbide.

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4. Geometric Parameters a. Thickness and Growth Rate. The growth rate or deposition rate is defined as the time gradient of thickness and is usually expressed in EBID/ IBID studies in nanometers per second. As a convention, a positive rate is adopted in case of net deposition and a negative rate is adopted for etching. For a deposition method to be qualified for industrial processes a high throughput, expressed in wafers per hour, is important. Here, this requirement is translated to a high deposition rate. The thickness of a deposited film can be measured in an SEM by tilting the sample more than 75 degrees (Koops et al., 1988; Petzold and Heard, 1991), by stylus profilometry (Harriot and Vasile, 1988; Hoyle et al., 1993; Koh et al., 1991; Koops et al., 1988; Lee and Hatzakis, 1989; Matsui and Mori, 1986), or by scanning probe profilometry. Structures lower than 20 nm can be imaged by scanning probe techniques such as AFM (Hiroshima and Komuro, 1998; Komuro and Hiroshima, 1997a,b; Weber et al. 1992). In case of etching, the depth is the equivalent of thickness and can be measured with a diamond stylus moved over the sample surface (Takado et al., 1989). Another way to measure the thickness of the deposit is by using the Auger signal from the deposited film. Matsui et al. (1989) give a relation between the Auger signal intensity and the deposited film thickness. The normalized Auger intensity IAuger, detected from a film when applying a cylindrical mirror analyzer (CMA) as Auger electron detector, is given by: IAuger ¼ 1 e0:75l ; d

ð6Þ

where d is the deposited film thickness and l is the electron mean escape depth. The deposited thickness d is proportional to the electron dose, which is proportional to the exposure time t if the current is maintained constant. Therefore, the deposited film thickness d becomes: d ¼ Rt;

ð7Þ

where R is the EBID growth rate. Substituting, the relation becomes: lnð1 IAuger Þ ¼

R t: 0:75l

ð8Þ

Values for the electron mean escape depth l and empirical equations have been reported. Therefore, the EBID growth rate R can be determined by measuring a relation between the normalized Auger intensity and the electron beam exposure time. The growth rate for EBID typically ranges from 1 to 10 nm/s. For example, Hu¨bner et al. (2001) obtained a growth rate of 8.4 nm/s in an

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SEM with a platinum precursor. FIBs provide higher growth rates compared with EBID, as large as 20 nm/s for small areas, as reported by Petzold and Heard (1991) for W(CO)6. The relation between the growth rate and the deposition parameters has been experimentally and theoretically investigated by many authors. An obvious parameter of influence on the growth rate is the electron dose, but it is not easy to find a clear and generally valid relationship. Christy (1960) found a linear increase of deposited contamination with dose, and the same observation was made for various precursors by Matsui and Mori (1986), Lee et al. (1989), Ishibashi et al. (1991), Ochiai et al. (1996), Hoyle et al. (1996), Hu¨bner et al. (2001), and Takai et al. (2003). However, a decreasing growth rate with dose was observed by Ichihashi et al. (1988), Lau et al. (2002), Hoffmann et al. (2002), Johnson et al. (2002), and Djenizian et al. (2004). Koops et al. (1988, 1993) have found that the deposition rate is linear for some precursors but nonlinear for others. This was also found by Hiroshima and Komuro (1997), who observed that the growth is linear for deposition of WF6 but nonlinear again for the highest beam current. So, merely measuring the height of deposits and calculating the total dose supplied does not provide real insight. For example, parameters of interest are the dose per scan and the dwell and loop times in the case of line depositions (the loop or refresh time being the period until a particular point is revisited). Hoyle et al. (1993) have studied this and have found a relationship that was not so easy to interpret. Lines were deposited with a constant total dose, but with varying doses per scan and a corresponding number of scans per line. Saturation of the thickness at a maximum value for a small dose per scan and a minimum value for a large dose per scan was observed. Unfortunately, in their setup the dwell and loop times both scale linearly with the dose per scan, so that it is not possible to distinguish between effects caused by the increased dose and effects caused by the increased loop time. Kohlmann et al. (1992) have studied the influence of dwell and loop times separately. The deposition yield decreased with increasing dwell time at constant loop time, whereas the deposition yield increased with increasing loop time at constant dwell time. Experiments by Lipp et al. (1996b) and Amman et al. (1996) confirm these results, indicating that the replenishing of the point of irradiation by new precursor molecules is an important parameter for increasing the growth rate. Petzold and Heard (1991) researched the deposition rate for IBID and found that the curves show a maximum as a function of both dwell and loop time (Figures 31 and 32). Yet these are not the only parameters that can influence growth rates. This has been proven by Hiroshima and Komuro (1998), who found that repeated scanning produces a line of half the height of a wire fabricated by a single

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FIGURE 31. Deposition rate in IBID versus dwell time. Reused with permission from H. ‐C. Petzold, Journal of Vacuum Science & Technology B, 9, 2664 (1991). ß 1991, AVS The Science & Technology Society.

3.5 Current = 40 pA 3

gf = 4.1017/cm2s

45 ⬚C

Dwell time = 0.8 ms

Rate [nm/s]

2.5 2

Focus = 0.0105 mm2

1.5 1 0.5

0

100

200

300

400

500

600

Loop time [ms] FIGURE 32. Deposition rate vs. loop time. Reused with permission from H.‐C. Petzold, Journal of Vacuum Science & Technology B, 9, 2664, (1991). ß 1991, AVS The Science & Technology Society.

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slow scan. Since a lower supply efficiency of precursor molecules would be expected for the single slow scan, the increased height must be due to a higher deposition efficiency. The authors explain this by the fact that the angle of incidence of primary electrons is different in repeated scanning compared with a single scan. For repeated scanning, the angle of incidence is constantly normal to the line surface, while the angle is larger in the case of a single slow scan. Since the region of line growth is always oblique in the latter case, the number of SEs emitted from the surface is larger and hence the deposition rate becomes larger. The effect of precursor supply should become observable when the growth rate is studied as a function of the beam current when experiments are performed in the precursor‐limited regime. This appears to have been demonstrated by experiments by Christy (1960) for contamination and Scheuer et al. (1986) for deposition from Ru3(CO)12, where the growth rate decreased with increasing current density. Experiments by Matsui and Ichihashi (1988), where deposition was performed at beam currents of 1, 10, and 100 A/cm2, seem to indicate similar behavior. The growth rate remained constant at a low beam current, but decreased during growth at the higher beam currents. However, this dependence has not been confirmed experimentally by Scheuer et al. (1986) or Mølhave et al. (2003). Scheuer et al., when measuring deposition rates for Os3(CO)12, found a linear relationship with the beam current density even though the precursor flux was lower than for the Ru3(CO)12 precursor. Mølhave et al. found a nonlinear relationship that is even more difficult to interpret, an initial increase for low beam currents until a certain maximum and decreasing again for the highest beam current. The reported values are currents instead of current densities and a background gas of 0.8 torr H2O was present in addition to the gold precursor, which makes the interpretation of the result more complex. Results on the variation of the beam energy are more consistent. Lee et al. (1989), Kohlmann et al. (1993), Hoyle et al. (1994), Lipp et al. (1996b), and Takai et al. (2003) have all found that upon increasing the beam energy from 0.5 kV, the deposition rates decrease. This is consistent with the fact that secondary electron generation yields decrease with increasing primary electron energy. Hoyle et al. found that the deposition rate had an optimum value around 0.1 kV, below which the deposition rates decreased also. Takai et al. (2003) and Ueda and Yoshimura (2004) observed that the deposition rates do not change significantly between 10 and 30 kV. The same consistency is true for results from varying the precursor pressure around the specimen; experiments indicate that the deposition yield is approximately proportional to the pressure (Figure 33). Tanaka et al. (2004) have studied this dependence to the extreme limit and performed depositions in UHV conditions, with precursor pressures in the range of 106 Pa. When

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FIGURE 33. The deposition yield of IBID as a function of DMG(hfac) gas pressure and specimen temperature. Reused with permission from D. Dubner, Journal of Vacuum Science & Technology B, 7, 1950 (1989). ß 1989, AVS The Science & Technology Society.

decreasing the precursor pressure from 1 105 Pa to 2 106 Pa, the dot size decreased from 5 to 2.4 nm in diameter. Below a precursor pressure of 1 106 Pa, deposition was never found to occur regardless of the beam intensity. This suggests that there is a critical gas pressure for dot fabrication, although the possibility that the dots were too small to distinguish was not excluded. The temperature is a complex parameter to vary for deposition experiments. The substrate temperature influences both the residence time of precursor molecules at the surface and the diffusion rates across the surface. It may even influence the dissociation cross section of the adsorbed molecules. This being the case, results from experiments by different groups are mostly consistent in showing that an increase in substrate temperature during deposition decreases the vertical growth rate. In the temperature range of 20 to 100 C (Christy, 1960; Ishibashi et al., 1991; Matsui et al., 1989; and Scho¨ssler et al., 1997), or even up to 400 C (Takahashi et al., 1992) the growth rates decrease with higher temperature. A surprising discrepancy has been reported by Kohlmann et al. (1993), who found the opposite relationship for W(CO)6. When increasing the temperature from 52 to 59 C, the growth rate increased. Matsui and Mori (1986) observed that above 50 C etching of the SiO2 substrate occurred when using WF6, whereas deposition occurred below that temperature. Finally, Kunz et al. (1987) obtained interesting results for Fe(CO)5. At a substrate temperature of 125 C, the deposition can become as high as 50 atoms per incident electron, while virtually no growth occurred in

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the absence of the beam. Thermal decomposition did not occur until the temperature reached 250 C. EBID growth need not necessarily occur in the upward direction (opposite to the incident electron direction), but can also occur in the downward direction (in the incident electron direction). When depositing on a thin membrane, electrons can dissociate precursor molecules on the exit surface as well as on the entrance surface. Liu et al. (2004a) have observed that on a 100 nm carbon membrane growth rates at the exit surface exceed those at the entrance surface in the very first stage of growth (for 200 keV electrons). The effect disappears as soon as the deposit on the entrance surface becomes significantly high. The same behavior was observed for self‐supporting tungsten wires, which had an elongated cross section along the incident electron direction (Liu et al., 2004b). The deposition efficiency or the deposition yield, defined as the number of deposited atoms per incident ion/electron, depends on the substrate, the type and energy of the incident particle, and the nozzle position. Ochiai et al. (1996) obtained a high deposition efficiency of copper, equal to 2 102 atoms/ electron, while Koops et al. (1988) achieved a tungsten deposition from W(CO)6 with a yield of 5 102 atoms/electron. FIBD with a gold precursor gives deposition yields of 4–5 atoms/ion with 15 keV Gaþ ions, 1 atom/ion with 0.75 keV Arþ ions, and 8–16 atoms/ion with 50 keV Siþ ions (Shedd et al., 1986). IBID with 25 keV Gaþ with W(CO)6 has a deposition efficiency of 1–2 W atoms per incident ion. Du¨bner et al. (1987) have published a list with IBID yields. For example, from WF6, 0.75 keV Arþ ions with a current density of 0.0004 A/cm2 produced a yield of 5 atoms/ion. Blauner et al. (1989) deposited gold using IBID on SiO2 with a yield of 5.8 atoms/ion and a growth rate of 1.1 nm/s. The current density was 180 mA/cm2. Information on the development of tip growth can possibly be obtained by monitoring the sample current during deposition, as performed by Bret et al. (2003). When deposition starts, the absolute value of the detected current drops due to increased emission of backscattered and SEs from the growing tip. After a first‐order–like decay the current saturates to a constant value. This behavior can be correlated with the tip growth behavior. The growth of a tip starts with a rounded cone, which eventually develops into a cylinder‐shaped tip with a conical top. The saturation of the current is reached once the cone has been formed completely. Once the growth of the cylinder begins, the current remains constant. Correlation of these results with Monte Carlo simulations of emitted backscattered and SEs shows that the current drop is caused mainly by scattered primary electrons and SEs emitted at the cone edges.

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FIGURE 34. Illustration of surface processes in EBID modeling.

The theory of the growth rate is supported by a number of models based on the one proposed by Scheuer et al. (1986). They developed a phenomenological model of the growth process in a flood beam EBID system, assuming that only one monolayer of gas molecules is adsorbed on the surface and that only the molecules adsorbed in the beam‐irradiated area will decompose. Figure 34 illustrates the processes on the surface. The adsorption rate of the precursor gas molecules on the substrate surface is given by the rate equation: dN N N ¼ gF 1 sdiss NJ dt N0 t

ð9Þ

and the growth rate of the layer, R is given by: R ¼ VNsdiss J;

ð10Þ

where N is the density of adsorbed molecules or the surface molecular coverage (#/cm2), N0 is the density of available adsorption sites in one monolayer (#/cm2), g is the sticking coefficient of gas precursor on the target, F is the precursor molecular flux (#/cm2/s), t is the mean life time of adsorption (s), sdiss is the molecular dissociation cross section under

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electron impact (cm2), J is electron flux on the surface (cm2/s), and V is the volume occupied by a dissociated molecule or its fragment (cm3). The first term in Eq. (9) governs the precursor adsorption on the surface, the second term represents the loss by spontaneous thermal desorption in the gas phase with the time constant t, and the third term corresponds to the electron‐induced dissociation rate of adsorbed molecules. The steady‐state growth equation will be reached for dN/dt ¼ 0, when the density of adsorbed molecules at equilibrium will be: N ¼ N0

g NF0 g NF0 þ 1t þ sdiss J

;

ð11Þ

and the growth rate at steady‐state R can be determined by: R ¼ VN0

g NF0 sdiss J g NF0 þ 1t þ sdiss J

:

ð12Þ

From Eq. (12), we can see that the growth rate is the result of a competition between two fluxes: the electron flux J and the molecular gas flux F, such that two situations are possible: the growth is limited by the gas flux or the growth is limited by the beam current. The growth rate depends on the residence time of molecules on the substrate, t. This confirms the experimental observations by Stewart et al. (1989) in IBID, which showed that cooling the specimen increases the growth rate. The maximum obtainable rate for any given electron flux is proportional to the current density on the surface: Rmax ¼ VN0 sdiss J:

ð13Þ

If the deposited mass can be measured, then based on Eq. (9) other deposition or precursor parameters can be determined. Scheuer et al. (1986) measured the deposited material mass and thus the growth rate R and determined other unknown parameters, such as the mean relaxation time for Os and Re carbonyls, t ¼ 1.4 1 s and a deposition yield of 1/280 atoms/electron. Koops et al. (1988) used the same model to optimize the EBID growth rate and give a numerical example for the W(CO)6 precursor. For a specimen temperature of 20 C and a precursor pressure in the subchamber of 2 mtorr, the molecular flux F ¼ 2.2 1017 molecules/(cm2s). Some typical values were assumed for the sticking coefficient g ¼ 1, the dissociation cross section of W(CO)6 sdiss ¼ 2 1017 cm2, and the volume of a deposited tungsten carbide molecule V ¼ 7.3 103 nm3. At these conditions, the maximum growth rate obtained from Eq. (12) is R ¼ 82 nm/s, which requires an

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63

electron flux J ¼ 1.5 1020 electrons/s, (i.e., a current density of 24 A/cm2, which is a feasible value). The model of Scheuer et al. (1986) can also be used for IBID if an extra term, the sputtering yield YS is added, which takes into account the effect of sputtering of substrate atoms (Blauner et al., 1989; Dubner et al., 1991). The amount of deposited material then results from competition between deposition and sputtering, and the net deposition yield YD, expressed in atoms/ incident ion is: YD ¼ Nsdiss YS :

ð14Þ

The first term in Eq. (14) depends on the gas pressure, substrate temperature, and the gas‐substrate interaction; the second term depends on the ions energy and mass and on the ion‐substrate interaction. Using the density of adsorbed molecules at equilibrium from Eq. (11), we obtain an ion‐induced deposition yield at steady‐state conditions: YD ¼

1 N0 sdiss

1 YS : J þ gF s1diss t þ gF

ð15Þ

The deposition yield YD can be determined if the deposited mass is measured, for example, using a quartz crystal microbalance (QCM). The sputtering yield YS can also be measured. Using the model described above, other ambiguous deposition parameters, such as the molecular dissociation cross section sdiss, can be determined. Du¨bner and Wagner (1989) determined this cross section for the gold precursor DMG as equal to 2 1013 cm2 for IBID with 5 keV Arþ ions. In the same article they reported that the measured deposition yield increases with increasing gas pressure and decreasing substrate temperature (see Figure 33). In an earlier steady‐state model of IBID presented by Ru¨denauer et al. (1988), sputtering is neglected and the growth rate for IBID is calculated as a function of beam energy, gas pressure, and current density. Petzold and Heard (1991) and Harriot (1993) extended the Scheuer model for scanned beam FIB deposition systems and modeled the growth rate as a function of dwell time and refresh time. Edinger and Kraus (2000) improved the Petzold model by considering a Gaussian beam current density distribution instead of a uniform one. The etching rate is expressed as a function of the dwell and refresh times, and the model was tested for GAE of Si with Cl2 and I2. Hoyle et al. (1993) developed the intermediate‐product model for EBID. They used the Petzold model adapted for EBID and divided the precursor conversion process in two main stages, with two different products, having different carbon contents and resistivities. The first step is the dissociation of

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SILVIS-CIVIDJIAN AND HAGEN

W(CO)6 into an intermediate product with high resistivity, and the second step is the conversion of this intermediate product into a final product of low resistivity. From this model, a faster scan produces higher volume rates, but the resulting material has higher resistivity, not suitable for the production of electrical interconnects. This conclusion corresponds with the experimental observations of many authors (see Section II.D.1). The two growth rates R1 and R2 are calculated as a function of the dwell and loop times. By fitting the model with the measured thickness of the deposit, values for the sticking coefficient of W(CO)6, g ¼ 0.32 and the electron‐induced dissociation cross section of W(CO)6 molecules in the intermediate product s1 ¼ 2.2 1018 cm2 and s2 ¼ 1.5 1018 cm2 were calculated. b. Lateral Size and Fabrication Resolution. Especially now, when the miniaturization process is developing so rapidly, it is important to estimate the lateral size of the deposited structure (i.e., the resolution of the fabrication process). Although EBID is not a fast method or an extremely high‐ purity deposition method, it can gain credibility if it demonstrates a high fabrication resolution. Values that are considered promising at this moment are in the 1–20 nm range, where conventional beam‐induced lithography methods encounter difficulties. The experimental resolution is usually described by the diameter of a singular dot, grown by a stationary focused electron probe or by the width of a singular line deposited by a scanned probe. For nanolithography applications, the line width and the line spacing are the most important features. In conventional polymethyl methacrylate (PMMA) resist‐based electron lithography, the smallest center‐to‐center distance obtained is 30 nm and isolated features of 5 nm have been produced, although the smallest useful structures were closer to 20 nm. The lateral sizes in EBID are most frequently measured by HREM imaging of the tilted specimen in an SEM or TEM. Another way to measure the lateral size is to image the profile of a structure with an AFM. To eliminate ambiguities generated by the finite apex radius of the tip, it is necessary to deposit more sets of lines and average the profile data. There are two ways to obtain high resolution in EBID: (1) to use it in an STEM with high beam energies and thin specimens, or (2) to use it in an STM with low‐energy electrons. EBID and contamination growth have been investigated in STMs in which it was possible to fabricate very small individual dots and narrow lines. For example, Uesugi and Yao (1992) used an STM with an electron beam size from the negatively biased tip estimated as 0.4 nm. They obtained holes in graphite of 2.5 nm diameter and 0.7 nm depth in the center, using a bias voltage of 5 to 10 V in air. The probable

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65

reaction occurring during hole drilling is the removal of carbon atoms from the target: CðgraphiteÞ þ O2 ! CO2 or CðgraphiteÞ þ H2 O ! CO þ H2 Organic molecules have been introduced in STMs to produce nanoscale carbon structures (Dujardin et al., 1992). Contamination deposition from a mixture of acetone and hydrogen produced an individual carbon dot of 0.8 nm in diameter and 0.7 nm in height, with a pulse of 4 V during 50 ms applied to the tip (Figure 35) (Uesugi and Yao, 1992). Organometallic precursors have been used to deposit a number of metals in STMs (W, Ni, Au, and Rh). Wang et al. (1997) used STM‐assisted CVD with Ni(CO)4 to fabricate Ni nanowires with a base width of 18 nm (9 nm at full width half maximum [FWHM]), a length of 6 mm, and a height of 4.5 nm on an H‐passivated silicon Si (111) surface. The beam diameter was approximately 10 nm, depending on the radius of curvature of the tip. The SEs did not play an important role because the electron beam from the tip lacked sufficient energy to excite them. This is an interesting observation because it implies that structures with the same diameter as the primary beam are obtained if no SEs are emitted to laterally enlarge the structure. Szkutnik et al. (2000) performed STM‐assisted CVD with [RhCl(PF3)2]2 and very sharp, optimized tips, with radii between 2 and 4 nm, enabling a very small space between adjacent deposited dots. Depending on the size of the tip and its shape, nanometer‐scale rhodium islands with a spacing of down to 1.5 nm were obtained. Figure 36 shows 3 nm wide islands aligned with a separation of about 4 nm (Figure 36a) and 1.5 nm (Figure 36b).

FIGURE 35. STM image of a carbon contamination dot of 0.8‐nm diameter and 0.7‐nm height. Reprinted from Uesugi and Yao (1992). ß 1992, with permission from Elsevier.

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SILVIS-CIVIDJIAN AND HAGEN

FIGURE 36. Results of STM‐assisted CVD. (a) Rhodium dots on an Au‐covered mica surface, separated by 3.3 nm, and (b) rhodium dots on an Au‐covered mica surface, separated by 1.5 nm (bottom) and line profile across the dots (top). Reprinted from Szkutnik et al. (2000). ß 2000, with permission from Elsevier.

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67

Marchi et al. (2000) used STM‐assisted CVD with [RhCl(PF3)2]2 to deposit Rh on gold‐coated mica substrates. The dot diameter was measured as 3 nm and the spacing was 4 nm. The same experiment on a silicon surface resulted in a rhodium line of 17 nm wide and 5 nm high. The best resolution result of EBID in STM is obtained in the deposition of magnetic material, whereby 5 nm FWHM and 2 nm high lines could be deposited from Fe(C5H5)2 (Pai et al., 1997). Surface oxidation induced by an SFM tip is also possible. The first report of tip‐induced oxidation of silicon was of an STM study by Dagata et al. (1990). Oxidation induced by an AFM tip has also been observed and GaAs oxide nanowires with a width of 10 nm could be fabricated (Matsuzaki et al., 2000). The AFM configuration offers important advantages over tunneling‐ based instruments, because the topographic viewing of the substrate does not induce exposure of the resist. In conclusion, low‐energy electron deposition in STMs can produce very small structures (1–10 nm), but with very small heights (1–10 nm). It is impossible to accurately measure the diameter of the electron beam in STM. STM images provide an idea of the topology of small structures, but it is not possible to discern their composition or crystalline phase. Another conclusion is that when electron beam deposition is induced by relatively high‐energy beams (thus excluding STM), the lateral size of the structures exceeds the primary beam diameter. In a first approximation, the lateral size of the deposited structures is determined by the probe diameter and there has been some research into the precise relationship. Hu¨bner et al. (1992) have measured the feature width as a function of beam diameter for beam energies between 2 and 30 kV. Beam diameters ranged from 7 to 2 nm. They have found that there is a constant ratio of 2:5 between beam diameter and tip diameter. On the other hand, Takai et al. (2003) have observed that the tip diameter decreases nonlinearly from about 540 nm for a 10 nm beam diameter to about 50 nm for a 2 nm beam. However, it has been well established that the tip diameter is not constant with electron dose. Initially the dot diameter increases very fast and upon continued irradiation, it reaches a saturation value (Figure 37). This has been confirmed by Kohlmann et al. (1993, 50–350 nm), Tanaka et al. (2004, 2–10 nm), Hu¨bner et al. (2001, 50–150 nm), Matsui et al. (1988), Lau et al. (2002), Perentes et al. (2004), Djenizian et al. (2004), Liu et al. (2004a), and Guise et al. (2004a). Table 4 shows some experimental results from which the ratio between the electron probe diameter and the obtained lateral size of the deposit can be appreciated. The table shows that over an extended period little progress was made in improving the fabrication resolution. In 10 years, the minimum feature size was reduced by a factor of 3, and some authors were skeptical about the future. Only recently has the resolution been improved dramatically.

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FIGURE 37. Experimentally determined evolution of the dot diameter in time. Reused with permission from K. T. Kohlmann‐von Platen, Journal of Vacuum Science & Technology B, 11, 2219 (1993). ß 1993, AVS The Science & Technology Society.

Compared with the deposition rate and chemical quality studies, the spatial evolution during EBID has not been sufficiently investigated and the theoretical modeling is rather poor. There is a discrepancy between the many experimental results and the theoretical explanations and models. This is due to the many approximations the present models accept. One of the most flagrant mistakes is that the only ‘‘player’’ taken into account during quantitative modeling of the deposition process has been the incident beam, either electrons or ions. However, in reality the situation is more complicated, because the adsorbed molecules can be decomposed or vanish as a result of more interactions, such as:

The direct impact of incident electrons/ions The interaction with a sputtered ion or atom in the case of IBID The impact with the SEs emitted upon primary particle impact Thermal spikes caused by the momentary temperature rise on the surface at the point of primary impact Surface diffusion and desorption induced by the beam irradiation. The next degree of complexity to be introduced in EBID/IBID modeling is the specimen mediation in the deposition process. At this moment, questions such as the following will appear: ‘‘Which factors are responsible for the growth (vertical and lateral) and to what degree?’’ and ‘‘What are the limiting factors for vertical/lateral growth?’’ Modeling of specimen mediation requires simulation of electron interactions with both solid matter and precursor molecules. Modeling of electron impact with solid matter can be done by

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69

analytically solving the Boltzman transport equation or by Monte Carlo–type methods. Only recently these issues haven been addressed (Mitsuishi et al., 2005; Silvis‐Cividjian, 2002; Silvis‐Cividjian et al., 2002). Depending on the growth condition and the growth stage, different tip diameters can be observed. In the saturation stage, a diameter of a few hundred nanometers can be expected. If the growth is terminated in the very first stage, smaller features are obtainable. Sub–10 nm features have been achieved by various groups, nearly all using STEMs. Of course, Broers et al. (1976) have deposited 8 nm wide contamination lines that were used as a positive resist. In more recent years, Jiang et al. (2001) have written 8 nm wide metal‐containing lines, and Silvis‐Cividjian et al. (2003) have fabricated lines of 4.3 nm at FWHM and arrays of dots with an average estimated dot diameter of less than 2 nm by contamination growth. Crozier et al. (2004) have deposited 4 nm dots, and Shimojo et al. (2005) have also written sub– 10 nm dots and self‐standing features of different materials. Tanaka et al. (2004) have observed in a transmission microscope that the evolution of the dot diameter in the early stages of growth develops approximately linearly with electron dose, with the minimum obtainable feature size 1.5 nm. Van Dorp et al. (2005) have deposited arrays of dots (Figure 38) from W(CO)6 with an average diameter of 1.0 nm (Figure 39), with the smallest dot in the array having a diameter of 0.7 nm at FWHM. The smallest line width they achieved was 1.9 nm. Although STEMs are used most frequently for the deposition of sub–10 nm structures, modern SEMs are also capable of reaching this fabrication resolution. This has been shown by Fujita et al. (2003), who produced a 5 nm wide carbon self‐standing pillar and by Guise et al. (2004a), who achieved a minimum feature size of 3.5 nm at FWHM, if corrections for the finite radius of the AFM tip were taken into account. Liu et al. (2004b) have studied the growth behavior of self‐standing features for different scan speeds for deposits from W(CO)6. Nanowires grow as the beam is moved away from the substrate and into the vacuum. The width of the nanowires is 65 nm at a scan speed of 0.4 nm/s and decreases quickly with increasing scan speed. The wire width eventually saturates at 7 to 10 nm for scan speeds of 15 to more than 70 nm/s. The lateral fabrication size depends on the probe current: a lower current deposits narrower lines. Unfortunately, results from different studies do not show similar results. Both Kohlmann et al. (1993) and Mølhave et al. (2003) observed that the diameter increases linearly with the square root of the beam current. The same relationship can (approximately) be derived from measurements by Perentes et al. (2004). Conversely, Kohlmann et al. (1992) have found almost no influence of beam current on lateral deposit size. Miura et al. (1997b) used contamination growth in a 30 kV SEM to measure

70

TABLE 4 EXPERIMENTAL EBID LATERAL RESOLUTION COMPARED WITH THE PROBE DIAMETER*

Precursor

System

Beam energy and current

Al Al Au Au Au Au Au Au Au C C C C C C C C Cu Fe

TMA AlCl3 AuCl3 Me2Au(acac) Me2Au(tfac) Me2Au(tfac) Me2Au(tfac) Me2Au(tfac) Me2Au(tfac) C16H34 pump oil pump oil AN styrene acetone contamination contamination Cu(hfac)(VTMS) Fe(CO)5

SEM STEM STEM STEM SEM SEM SEM SEM STM SEM SEM SEM SEM SEM STM STEM SEM ESEM SEM

6 keV/10 pA 200 keV/500 pA 200 keV/500 pA 200 keV/500 pA 35 keV/6 pA 20 keV/80pA 25 keV/1 nA 30 keV/50 pA 6 V/300 nA 30 keV 35 keV/6 pA 15 keV/100 pA 6 keV /10 pA 50 keV/100 pA 4V 200 keV/5 pA 20 keV/340 pA 30 keV/600 pA 3 keV

Probe diameter (nm) 8 0.8 0.8 0.8 2 100 <10 1 2 2 8 5 0.4 1 1 20 100

Lateral resolution (nm) 20 <100 <100 <10 16–26 20 200 30 30 10 8–15 20–30 20 14 0.8 <2 3.5 100 150

Reference Ishibashi et al. (1991) Shimojo et al. (2005) Shimojo et al. (2005) Shimojo et al. (2005) Go¨rtz et al. (1995) Koops et al. (1994) McCord et al. (1988) Lee and Hatzakis (1989) Bruckle et al. (1999) Bezryadin and Dekker (1997) Go¨rtz et al. (1995) Go¨rtz et al. (1995) Ishibashi et al. (1991) Matsui et al. (1992) Uesugi and Yao (1992) Silvis‐Cividjian et al. (2003) Guise et al. (2004a) Ochiai et al. (1996) Kunz et al. (1987)

SILVIS-CIVIDJIAN AND HAGEN

Deposit

Fe(CO)5 Fe(CO)5 Fe(C2H5)2 D2GaN3 Ni(CO)4 Ni(CO)4 Ni(C5H5)2 (C5H5)Pt(CH3)3 (C2H5)Pt(CH3)3 (C5H5)Pt(CH3)3 [Rh(PF3)2Cl]2 W(CO)6 W(CO)6 W(CO)6 W(CO)6 W(CO)6 WF6

SEM STM STM STEM STM STM STEM SEM SEM DBI STM SEM SEM STEM STEM STEM SEM

1 keV/70 pA 15 V/50 pA 10 V 200 keV/20 pA 15 V 15 V/1–2 nA 100 keV 30 keV/70–100 pA 20 keV/400pA 30 keV/70–100 pA 6V 25 keV/10 nA 5 keV/1 nA 200 keV/500 pA 200 keV 200 keV/40 pA 50 keV/100 pA

W W

WF6 WF6

TEM SEM

120 keV/7 pA 50 keV/100 pA

300

0.3 10 1 3 3 150 400 0.8 0.8 0.3 3 3 3

300 7 5 4 35 18 8 40 20 40 17 250 3.5 1.5 1.0 13 15 13–20

Kunz et al. (1987) Kent et al. (1993) Pai et al. (1997) Crozier et al. (2004) Rubel et al. (1994) Wang et al. (1997) Jiang et al. (2001) Morimoto et al. (1996) Koops et al. (1994) Takai et al. (1998) Marchi et al. (2000) Koops et al. (1988) Hoyle et al. (1993) Shimojo et al. (2005) Tanaka et al. (2005) Van Dorp et al. (2005) Hiroshima and Komuro (1997, 1998), Hiroshima et al. (1995) Ichihashi and Matsui (1988) Komuro and Hiroshima (1997a,b), Komuro et al. (1998)

*The table also shows the material deposited, the precursor, the description of the host system used, and the reference. Columns 5 and 6 reveal the discrepancy between the electron beam size and the lateral size of the deposited structure.

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Fe Fe Fe Ga Ni Ni Ni Pt Pt Pt Rh W W W W W W

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FIGURE 38. Annular dark field (ADF) STEM‐image of a 10 10 array of dots deposited from W(CO)6 on a SiN membrane. The average diameter of the dots is 1 nm. Reprinted with permission from van Dorp et al. (2005). ß 2005, American Chemical Society.

FIGURE 39. Three‐dimensional representation of the ADF‐STEM image of the average tungsten‐containing dot in the array of Figure 38, obtained by averaging over 100 dots (left) and the radial intensity of the average dot, showing a radius at half maximum of 0.5 nm.

the relationship and found nonlinear behavior. They obtained narrow wires of 30 nm width with a high aspect ratio for less than 40 pA current exposure, as shown in Figure 40. The information in this graph is quite poor and ambiguous because the time necessary to grow these lines is not clear. The width grows in time until it reaches saturation and it is important to mention at what time the measurement was done.

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FIGURE 40. The dependence of the width of a carbonaceous wire on the electron beam current. Reprinted from Miura et al. (1997a). ß 1997, with permission from Elsevier.

Does the fabrication resolution depend on the beam energy? Experiments (Lee and Hatzakis, 1989) with different beam energy have been performed to observe its influence on the resolution. In depositing vertical tips with the same electron beam of 10 nm spot diameter, it was observed that by increasing the beam energy, the width and cone apex radius of the grown tip decrease by approximately 10% at each 10 kV increment in beam voltage. This implies that the tip shape is determined by forward‐scattered electrons at the apex of the deposited material. Experiments by Hu¨bner et al. (1992), Kohlmann et al. (1993), and Bauerdick et al. (2003) also confirm that the lateral resolution is rather independent of acceleration energy. Conversely, Lau et al. (2002) state that higher beam energies lead to wider columns, because primary electrons of higher energy have a larger penetration depth in the already grown column. Secondary electron emission from a greater depth along the column leads to more deposition along the column and hence a larger diameter. The spacing between deposits depends on the so‐called proximity effect, which is low when the electron energy is low or when the specimen is thin and the electron energy very high. Gopal et al. (2004) have observed an interesting phenomenon related to the proximity effect. Deposition was not entirely localized to the electron beam raster area but also occurred micrometers away. Time‐of‐flight secondary ion mass spectroscopy on structures fabricated from a platinum precursor showed that platinum was detected beyond 10 mm micrometer distance from a deposited tip, which is larger than

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the secondary electron excitation area. Although the authors mention thermally assisted diffusion of deposited platinum as a possible cause, it is perhaps more likely that primary electrons are scattered from the growing tip and redeposit precursor molecules around the tip. Another type of proximity effect was observed by Lau et al. (2002). When depositing tips in the direct vicinity of neighboring tips (i.e., a few hundred nanometers), additional deposition occurred on the latter as well. Apparently, electrons scattered from the growing tip also caused deposition on the already existing tips. The thickness of the substrate does not appear to play an important role in the lateral resolution. Lee and Hatzakis (1989) obtained gold features of 30 nm width and 50 nm spacing, using EBID with a beam size smaller than 10 nm at 30 kV. Lines have been deposited both on thin Si3N4 membranes and thick bulk Si specimens and their widths were the same. Mitsuishi et al. (2003) have not found a significant difference in dot diameter between thin and thick specimens. Apparently, the BSEs do not play an important role in the resolution limitation. Low‐energy electrons with energies in the 0–20 eV range are expected to play a major role in the decomposition of adsorbed molecules via the processes of dissociative attachment and dipolar dissociation. A series of experiments have confirmed the important role of SEs in deposition. The strategy used by several authors is to measure the deposition rate for different incident energies and compare it with the secondary electron yield dependence on the incident energy. Lipp et al. (1996a) and Kunz and Mayer (1987) compared the deposition rate with the secondary emission yield and found that the curves are similar. Kunz and Mayer have also tilted the specimen to 60 degrees during deposition and found an increase of nearly a factor of 2 for both the secondary electron emission and the deposition rate. Hence, the general conclusion is that the chemical reactions induced by electron beam irradiation are mainly caused by the generated SEs. 5. Conclusions Currently the resistivity of deposited materials (W, Au, Cu, Pt, Al, and Fe) using both EBID and IBID is still two to three times larger than the values for the bulk metal. The materials grown by contamination lithography are sufficiently conductive for scanning probe imaging. The resistivity obtained with IBID is lower than that with EBID. Experiments showed that high current densities, low impact energies, slow scanning, and post annealing can produce lower resistivities of the deposits. It would seem likely that the conductivity is related to the carbon impurity content and to the packing between the nanocrystals, although carbon‐free

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precursors do not necessarily yield low‐resistivity films. High current densities seem more important, and the highest conductivity has been obtained with a carbon‐containing precursor. The result of contamination growth is amorphous carbon with properties of diamond or graphite. Deposition from organometallic complexes grows metal nanocrystallites embedded in an amorphous carbonaceous matrix. The crystallite size is a few nanometers and is influenced by the dwell time and the probe current. The presence of reactive gases during deposition can improve the metal content considerably. The growth rate generally increases with increasing exposure dose and current density and decreases with increasing substrate temperature and beam energy. Typical growth rates are 1–10 nm/s for electron excitation and 10–20 nm/s for ion excitation and a current density of 4 mA/cm2. The average deposition yield for electron beams is 102 atoms/electron and for ions 4–10 atoms/ion. The ion‐induced deposition yield can be 50–100 times larger than the electron‐induced yield. The deposits from all currently used organometallic precursors contain C and O, and 75% metal at maximum. The ratio of atoms in the deposit is not always the same as the ratio in the precursor molecule, suggesting that the substrate can also decompose under beam irradiation, that some atoms adhere better to the substrate than others, or that residual components from the background vacuum are incorporated in the structure. The ratio between the metal content and the rest of the elements in the deposit can yield information about the decomposition paths. The step‐to‐step mechanism of decomposition is not known, but it is believed that the precursor does not always decompose totally to form pure metal atoms. At present, the state of the art in fabrication resolution using EBID is as follows: Carbon dots with a diameter of 3.5 nm have been deposited by

contamination in an SEM.

Dots with an average size of 1.0 nm have been fabricated; the smallest

dot was 0.7 nm at FWHM (Van Dorp et al., 2005).

Metal‐containing lines with a lateral size of 2 nm at FWHM have

been obtained on thin membranes (Van Dorp et al., 2005).

Self‐standing nanowires of 7 nm width have been fabricated (Liu

et al., 2004b).

Individual dots with a diameter between 1 and 10 nm and a height of

1–150 nm and lines of 5 nm width and 2 nm height have been deposited by low‐energy electrons (5–10 V) in an STM (McCord et al., 1988; Pai et al., 1997; Uesugi and Yao, 1992).

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The theoretical modeling of the spatial evolution of EBID has not been

developed sufficiently yet. To model the EBID fabrication resolution and the structure growth, Monte Carlo simulations, based on secondary electron generation in the substrate and the dissociation of adsorbed precursor molecules, are beginning to be developed now.

E. Applications and Achievements of EBID and IBID Deposition Methods Most applications of EBID and IBID are found in mask and IC repair and in the nanofabrication of contacts and prototype devices. The limited number of applications is caused by the high content of carbon in the deposits, the small exposed areas, and the low reaction rates. Small beam diameters mean low current and longer times necessary to deposit complicated, massive patterns. We describe the most valuable and interesting application areas for each group, pointing out the achieved performance, the encountered problems, and predictions for the future. 1. Mask Repair and Mask Fabrication a. Photomask Repair. The generation of patterns used in semiconductor microcircuits by optical lithography relies on the use of chromium‐on‐glass photomasks. Two types of photomask defects are encountered: defects in the form of excess chromium (opaque defects) and absence of chromium (clear defects). The mask‐repair procedure must be simple and fast and if possible is a one‐step process. In conventional chromium‐glass photomask repair, the opaque defects can be removed by an FIB in commercial tools or by laser zapping (i.e., laser‐induced thermal vaporization). To repair submicron clear defects (pinholes), gas‐assisted IBID can be used if a number of conditions are imposed on the process. For example, the deposited film must be opaque, must adhere to both glass and metal surfaces, and must be chemically and physically resistant to the mask‐cleaning procedures. Furthermore, the deposition must be faster than sputtering induced by the ion beam. A study of carbon deposition from a set of potential organic compound precursors (benzene, toluene, methylmethacrylate, and styrene) revealed that all except styrene deposited thin, translucent, and noncontinuous masks, making styrene the only suitable precursor for the repair of open mask defects by ion‐beam‐induced contamination growth (Harriot and Vasile, 1988).

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Clear defects in silicon transmission masks can be repaired by contamination writing, using the so‐called darning method by building bridges across the pinholes. These bridges serve as a support layer for ulterior gold deposition. The gold layer will fill the hole and the contamination layer will be removed later by O2 plasma (Behringer and Vettiger, 1986). b. X‐Ray Mask Repair. X‐ray lithography has been the subject of much research and development interest because of its ability to produce patterns with critical dimensions below the 0.25 mm limit achievable with optical and deep ultraviolet (DUV) techniques. The mask produced consists of a gold layer of 0.5 mm thickness on a 2 mm thick membrane of silicon or silicon nitride (Prewett, 1992). Compared with the photomask repair, which is now routinely done by means of laser systems or FIB, the repair of X‐ray masks is significantly more critical because of the small dimensions and higher aspect ratios. Opaque defects can be repaired by FIB milling. However, repair of clear defects requires a very well localized deposition of high‐Z material that offers a high X‐ray opacity at the defect site. The deposited layer must attenuate the X‐rays by at least a factor of 8. Focused‐ beam deposition can be used for this purpose. The advantage of using an FIB is that both clear and opaque defects can be repaired. However, the sputtering and gallium implantation in the mask are problematic. The use of EBID does not suffer from this problem, but the growth rate has to be maximized to improve the throughput in the repair of clear defects of X‐ray masks using EBID. c. Mask Fabrication. EBID and contamination lithography have been used occasionally and on a small scale for mask fabrication in an RIE process. Using such a mask, made by contamination growth, Craighead and Mankiewich (1982) obtained arrays of 7 nm diameter silver and 10 nm diameter gold‐palladium structures using a 2 nm probe. Kohlmann‐von Platen et al. (1992) fabricated a stable etching mask with a thickness of less than 200 nm by deposition of tungsten from W(CO)6. Hoyle et al. (1996) used the same method to obtain a mask for CF4 plasma etching of Si, while Koops et al. (1988) used this method for the fabrication of a high‐resolution mask for oxygen RIE of polyimide with a 57:1 selectivity. 2. Integrated Circuit Modification and Chip Surgery IBID is currently used in IC failure analysis and debugging because it can mill layers to reach a specified interface or discontinuity and deposit conductive metal films and wires to restore the damaged functionality. The resistivity of the material used in chip surgery must be as low as possible.

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3. Shape Improvement for Scanning Probe Microscopy Tips Scanning probe microscopes (STM, AFM) are profiling instruments that form images by scanning a sharp probe (tip) over the sample surface. In the case of an STM, the image is given by the current that flows between the surface and a small atomic cluster on the apex of the tip. In an AFM, the image signal is given by the force between the cantilever tip and the target surface. The probe is one of the most crucial parts of the instrument, because the resulting topographic image is a convolution between the tip shape and the analyzed surface morphology. In imaging with high, even atomic resolution of flat surfaces, almost any tip can be used. Usually this is a conventional tip obtained by electropolishing of a metal (Pt‐Ir, Au, Pt, or W). However, for imaging of non‐flat structures with a high aspect ratio or very steep edges, deep grooves, and depressions with vertical side walls, more rigorous requirements are imposed, not only on the tip but also on the whole tip geometry. The classical tip will produce a deformed topographic image if its diameter is larger than the diameter of the groove/hole. The tip must be thin, sharp, long, with low resistivity, and still mechanically stable. The conventional electrochemically etched tips, with a radius of 10–50 nm at the apex, cannot fulfill this requirement. EBID can be used to add supertips to the commercial SPM tips, improving their radius and aspect ratio. Figure 41 shows an example of a tip with very high aspect ratio, grown by EBID. Since the groove width in large‐scale integration (LSI) fabrication is approaching 0.05 mm, tips with 50 nm diameter will be urgently needed for future topographic measurement of micropatterns. a. STM Tips. Akama et al. (1990) fabricated a long and straight microtip with submicron diameter on the top of a Pt‐Ir STM tip by using contamination lithography. The tip is amorphous, contains C and O, and is smooth, with a diameter of 100 nm that is uniform along the tip. The problem in growing tips is that the longer the tip grows, the more the beam is defocused. If this effect can be compensated, even smaller diameters can be realized. Successful STM experiments have been performed to test the improvement in the imaging quality of the new tip. The shape of a conventional Pt‐Ir STM tip has been improved by using contamination lithography in an SEM (Hu¨bner et al., 1992). With an electron beam diameter of 2–5 nm and a growth rate of 0.1–1 mm/min, a tip with a shank diameter below 200 nm was obtained. The radius of the tip was 10 nm, independent of beam acceleration voltage. Tunneling experiments have shown sufficient conductivity of the deposited tip.

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FIGURE 41. Tip with high aspect ratio fabricated by EBID. The scale marker indicates 1 mm. Reprinted from Hu¨bner et al. (1992). ß 1992, with permission from Elsevier.

An interesting way to increase the STM imaging resolution by sharpening the existing tip can be performed in situ using EBID with an organometallic palladium precursor and negative sample bias. A secondary, much sharper tip is grown (Saulys et al., 1994). b. AFM Tips. AFM can be used to investigate the morphology and roughness of surfaces. Pyramidal tips are appropriate for surfaces with shallow relief or widely spaced features, but more slender tips are needed for narrow and steep features. EBID is used to improve the shape of commercially available pyramidal Si3N4 tips by depositing carbon or gold supertips. The improved tips are mechanically stable and show no damage of the apex after a few scans, surviving days of continuous use (Antognozzi et al., 1997; Go¨rtz et al., 1995; Keller and Chih‐Chung, 1992). Starting from a commercial pyramidal AFM tip with end radius of 50–100 nm and opening angle of 114 degrees, a contamination tip is fabricated in SEM spot mode with an end diameter of 30 nm and conical end angle of 10–20 degrees (Figure 42). Because the carbon tips are very durable, other tiny machine tools for milling samples on a small scale could be fabricated by the same method (Keller and Chih‐Chung, 1992).

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FIGURE 42. SEM images of AFM supertips fabricated by EBID. Reprinted from Keller and Chih‐Chung (1992). ß 1992, with permission from Elsevier.

High‐resolution electron beam deposition is particularly suitable for the fabrication of AFM tips where different conventional lithography methods are difficult to implement. In AFM, a tip with low spring constant is imposed for force detection sensitivity. The best tip achieved so far has a radius of 15 nm, with a shaft diameter of 100 nm and a length of 1000 nm (Hu¨bner et al., 1992). Miura et al. (1997b) also used contamination growth in an SEM to improve the shape of an AFM tip. First, a Pt‐Pd alloy was deposited on the Si3N4 tip by radiofrequency (RF) sputtering to make the surface electrically conductive. Then, a 1 mm long carbon conical structure was deposited

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on the top of an AFM tip, with a diameter of 40 nm. Improvements in planar resolution of AFM tip images were demonstrated. Castagne` et al. (1999) have grown carbon (diamond) supertips on the top of a silicon AFM probe in a 30 kV SEM, with an electron spot size of 8 nm and a probe current of 100 pA. The tips were included in a photon scanning tunneling microscopy (PSTM) experiment and used as near‐field converters in the infrared range of wavelengths. c. Magnetic Force Microscopy Tips. Utke et al. (2002b) have fabricated high‐aspect ratio magnetic tips on top of batch fabricated scanning force microscopy tips. Depositions were done with a cobalt precursor, Co2(CO)8, and the magnetic properties were characterized using tracks of magnetic transition written in recording media of hard disks. The resolution of the transitions that could be discriminated was 45 nm and the magnetic properties of the tips are stable for more than a year in air. The ultimate limit is expected to be determined by the size of individual Co clusters, which was 2 to 5 nm. 4. Field Emission Sources and Field Emitter Arrays a. Field Emission Tips. In 1994, Koops et al. (1994) used EBID to deposit an integrated structure consisting of a tip and an extractor anode on two Au islands, and tested the field emission from this construction. The IV characteristic is given in a Fowler‐Nordheim plot and shows the presence of field emission. A resistor could also be deposited to stabilize the emission current. Later Scho¨ssler et al. (1996) and his colleagues fabricated supertips using EBID with MeAu(tfac) and CpPtMe3 on top of an etched tungsten tip. An increased field enhancement factor was observed when nanocrystallites protruded from the tip itself. Current‐voltage characteristics of these supertips were measured. The base tungsten tip was spot‐welded to a hairpin or a carbon vice to elevate its temperature, and a supertip was grown on its top by EBID. The field emission from the supertips was measured in excess of 100 mA at 22 V extraction voltage. The emission was observed on a phosphor screen placed in front of the tip and was recorded by a charge‐coupled device (CCD) camera. Deposited supertips provided cold, single‐emission site field emitters with a brightness four times higher than that of conventional tips. Scho¨ssler and Koops (1998) went a step further and fabricated a nanostructured integrated reliable high‐brightness field emission electron source. EBID was used to fabricate the emitter, the resistor, and the extractor. The deposited tip had a radius of 10 nm and a total height of 100 nm. A 200 kV TEM micrograph showed gold nanocrystals immersed in an amorphous carbon matrix. The protrusions were acting as supertips, on which the

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simulation of emission showed an increased extracting field. The emission was tested in a field emission microscope in a hairpin construction. A total emission of up to 10 mA was observed for several hours. A comparison with the reduced brightness of a Philips ultrasharp Schottky W‐Zr‐O field emitter (Br ¼ 3 105 A/(cm2 srV)) showed that the deposited supertip has at least the same brightness (Fransen et al., 1996). In conclusion, the authors show that an integrated field emission source can be fabricated by combining conventional lithography and EBID from an Au precursor. They even state that the deposited field emitter supertips using EBID exceed all conventional electron field emitters in brightness. In 1997 a microtriode with field emission for operation in air with a water Taylor cone has been built by Koops et al. (1997). b. Field Emitter Arrays. Field emitter arrays (FEAs) belong to the most important electron sources for vacuum microelectronics, for example for emissive flat panel displays (FPDs) with high intensity, fast response, and wide viewing angle. One of the problems in FEA fabrication is that not all the tips have the same shape and thus inhomogenities in the emission behavior occur. FEAs can be fabricated by EBID according to the following procedure: First, a 10 10 Si FEA array is fabricated by conventional methods (RIE and thermal oxidation sharpening) and introduced in the EBID chamber. Pt tips are deposited on the top of each Si tip by EBID from a CpPtMe3 precursor, with a beam diameter of 3 nm at 30 kV. The Pt columns are 1 mm high and have a 20 nm radius sharp tip. The field emission is tested after Pt deposition, and a maximum current of 10 mA per tip is obtained with a stability of 20% over the operation time of 24 hours (Morimoto et al., 1996). The combination of EBID and FIB can be used to fabricate prototype FEAs or to repair damaged emitters. FIB etching is used to fabricate the gate hole and EBID to deposit the Pt tip. Takai et al. (1998) used a dual‐ beam machine that combines focused EB and FIB to build a 10 10 FEA. The gate opening and an overetched Si emitter were made by GAE with 30 kV Gaþ ions and a I2 precursor. Using EBID with a 3 nm spot size at 30 kV a sharp Pt tip, with a radius of 20 nm and a length of 1 mm, was deposited in the gate opening (Figure 43). The Pt tips contain 21.5% Pt, 73% C, and 5.5% O, as analyzed by Auger spectroscopy. The resistivity of the deposited material is 30 m cm, three times higher than that of bulk Pt. The I‐V characteristic was measured and field emission was demonstrated. In conclusion, EBID combined with FIB etching can be a fast prototyping method for nanometer‐sized FEAs. At this moment, Gaþ impurities are still a problem due to the leakage currents. A better control of the process is necessary in the future.

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FIGURE 43. SEM view of a field emitter array after gate opening by FIB and platinum tip fabrication by EBID. Reprinted from Takai et al. (1998). ß 1998, with permission from Elsevier.

5. Electrical Contacts for Molecules Tiny electrical contacts are necessary to characterize the electron transport through a single molecular chain. Two problems occur when measuring the transport through single molecules. First, conducting electrodes must be fabricated, separated by a distance smaller than the molecule’s length. The molecules of interest are smaller than the resolution of conventional EBL; for example, the conjugated oligomers usually have a length of 5 nm. Second, a contact must be established between the outside‐world electrodes and these molecules. EBID could be an alternative to approaches based on scanning probe techniques. Bezryadin and Dekker (1997) used contamination lithography in an SEM to fabricate two free‐standing horizontal carbon nanowires of 5–20 nm in diameter, oriented toward each other with a gap in between of 3–5 nm (Figure 44). This gap is small enough to trap a molecule between the electrodes by electrostatic trapping (ET). For example, by applying a potential difference of 1 V between the electrodes, an electric field of 108 V/m is created, which can attract the polarized molecule. A thin metal layer is sputtered on top of the grown electrodes to improve their conductivity. ET has also been used for trapping of carbon nanotubes. The most recent application of EBID for fabrication of electrical contacts to single molecules (microtubules) has been reported by Fritzsche et al. (1999). Microtubules are intercellular proteinaceous elements with essential functions in cell architecture and cellular transport with dimensions of micrometers (length) and nanometers (diameter). Some MT are adsorbed on an oxidized Si pad with gold‐prestructured electrodes. A contamination

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FIGURE 44. (a) Free‐standing amorphous carbon wire of 10 nm grown by contamination lithography, and (b) two free‐standing carbon nanowires grown toward each other by EBID and separated by 4 nm. Reused from A. Bezryadin, Journal of Vacuum Science & Technology B, 15, 793 (1997). ß 1997, AVS The Science & Technology Society.

line is deposited in situ between the existing gold electrodes and the MT biomolecule of interest. This line is used afterwards as etching mask and golden bridges between the prestructured contacts and the molecule are obtained. In situ SEM imaging is used to choose the right orientation of the lines. Our suggestion is that directly depositing a metal line should improve the situation. Nobody has made metal nanowires to contact molecules yet, using EBID. In the case of MT experiments, a four‐wire resistance measurement scheme should also bring improvement. Using the two‐wire scheme, Fritzsche et al. (1999) measured not only the resistance of the trapped molecule, but also the resistance of the connecting gold electrodes. 6. Probing on Small Crystals In the research of new materials, the measurement of their electric properties can be important. However, when the sample is too small to directly attach probe electrodes and it is too frail to fabricate probe electrodes by metal deposition and photolithography, then beam‐induced deposition can be a unique technique to fabricate probe electrode patterns for such small samples. 7. Three‐Dimensional Artifacts, Nanostructures, and Devices EBID and IBID have occasionally been used to fabricate metal, dielectric, and carbonaceous artifacts, such as wires, sensors, and transducers on nanometer scale (flow sensors), resistors in arch form, lens systems, Fresnel

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lenses, X‐ray lenses, and free‐standing nanometer structures and bridge wires across a hole (Koops et al., 1994). The deposited wires are very rigid and chemically inert to solvents and acids. Dot arrays can be deposited in small, deformed areas for the metrology of mechanical properties of micromechanically designed and fabricated parts. Diamond‐like carbon microsystem parts, such as microcoils, microdrills, and microbellows, have recently been deposited by IBID from aromatic hydrocarbons and the application area can even be extended toward microstructure plastic arts (for example, a micro–wine glass with 2.75 mm external diameter and 12 mm height has been grown; see Figure 12; Matsui et al., 2000). Single‐electron transport (SET) devices for future ICs such as high‐density memory and logic have attracted great interest. To realize device operation at high temperature, many attempts have been made to fabricate nanometer‐ scale Coulomb islands using Si/SiO2 and metal/insulator/metal (MIM) systems. To realize single‐electron devices operating at higher temperature, nanometer‐scale dot arrays and low resistivity deposits will be needed to maintain low resistance even at high temperature. Komuro and Hiroshima (1997a,b) and Komuro et al. (1998) reported the fabrication of single‐tunnel junctions for single‐electron devices using EBID from WF6. A single‐electron transistor composed of three EBID dots with 20 nm spacings, connected to wires with a gate electrode, exhibited clear Coulomb oscillation at 230 K. Miura et al. (1997a) used contamination growth in an SEM to deposit 40 nm diameter minute carbon dots. The dots were arranged in series between fine metal electrodes to form a device with multiple tunnel junctions. Single‐electron charging effects, such as the Coulomb blockade and the Coulomb staircase, were clearly observed at 9.4 K. 8. Conclusions Electron beam–induced direct deposition can be applied with success in a few situations—for example, in rather rare occasions when structures are needed on nonplanar substrates that cannot be created otherwise (such as long tips or when a fast result on a small area is needed and the time needed for the resist‐based process would not be justified). Another appropriate situation is when a local microrepair is needed as soon as it is seen. Ions are better in this case than electrons due to their higher deposition rate. The most exciting application is the deposition of nanometer‐size lines and spaces, with a higher resolution than other conventional lithography methods can currently achieve. In this case, electrons are more favorable than

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ions. Being resistless, EBID might be the key to break the resolution limit of 10 nm achieved in resist‐based lithography.

F. Conclusions At the end of each section in this literature review already specific conclusions have been presented for the interested reader. Here we present some general conclusions on the present status of EBID. 1. In the majority of cases, EBID is performed in a more or less modified SEM. Occasionally, EBID is performed in a (S)TEM, STM, dual‐beam instrument, or EBL machine. The deposit analysis is done by SEM, TEM, AFM, Auger, EDX, and profilometry. 2. Most researchers usually aim for either high deposition rate or high fabrication resolution, or high quality (purity, resistivity, hardness, and opacity). 3. For a long time (i.e., until 2002), the best EBID resolution results obtained in an SEM, with a 2–3 nm diameter beam, were linewidths of 15– 20 nm at 50 kV on bulk silicon (Hu¨bner et al., 2001; Komuro et al., 1998). In a TEM, 14 nm rods could be fabricated on fine Si particles (Ichihashi and Matsui, 1988). In an STM, using a beam of very low energy (5–10 eV), individual dots of 0.8 nm diameter and 0.7 nm height could be fabricated (Uesugi and Yao, 1992), and lines with a minimum width of 5 nm and a height of 2 nm (Pai et al., 1997). By using ingenious tricks, small spaces could be created between EBID structures. For example, spaces as small as 4 nm were obtained by growing two wires toward each other (Bezryadin and Dekker, 1997). It was intriguing that the sizes of EBID structures always exceeded the beam diameter in SEM and TEM hosts. However, since 2002 the EBID resolution has been improved dramatically. Carbon dots with a diameter of 3.5 nm have been deposited by contamination in an SEM (Guise et al., 2004a). In an STEM, self‐standing nanowires of 7 nm width were grown by Liu et al. (2004b). Very recently, van Dorp et al. (2005) have fabricated, on thin membranes in an STEM, dots with an average size of 1.0 nm, the smallest dot being 0.7 nm at FWHM, as well as metal‐containing lines with a lateral size of 2 nm at FWHM. 4. The deposition process is not completely understood. It is obvious that until now only simple theoretical models have been provided, especially for the deposition rate. It is suspected that SEs play a role, but a quantitative analysis has not been done yet. Many discrepancies still remain between calculated and measured lateral sizes and thicknesses, and quantitative

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growth models are hampered by the fact that the electron‐induced dissociation cross sections for adsorbed precursor gases, as a function of impact energy, are barely known. 5. The application area of EBID is growing, extending to the life sciences. There is a growing interest and need for electrical contacts (2–5 nm) to single molecules and nanocrystals. Small dots of less than 20 nm diameter are necessary for single‐electron devices to operate at room temperature. The following sections will focus on the theoretical understanding of the EBID fabrication resolution; we will use Monte Carlo simulations to predict the ultimate resolution.

III. THE THEORY

OF

EBID SPATIAL RESOLUTION

A. The EBID Spatial Resolution: A General Statement of the Problem An intriguing question in the field of EBID is: what is the smallest structure that can be produced with this technique? For a long time, the smallest reported structures had lateral sizes of 13–20 nm (Hu¨bner and Plontke, 2001; Komuro et al., 1998; Matsui et al., 1989), although the electron beams used were always much smaller. Only recently also smaller structures have been fabricated (van Dorp, 2005) using a sub‐namometer electron beam in an STEM. Now that such electron beams with diameters even down to 0.2 nm are available, the question is: what determines the fabrication limit? The typical answer found in literature is the generation of SEs in the target, with a range exceeding the primary beam diameter. According to some authors the range of SEs in the target limits the EBID minimum feature size to 15–20 nm (Hiroshima and Komuro, 1997; Hu¨bner and Plontke, 2001), but our belief is that this broadening effect can be minimized. Before beginning a discussion about fabrication resolution, we should first define this important EBID characteristic. The resolution of a method is usually defined as the smallest value that can be obtained without errors. So, let us assume that the finest electron beam is focused on a specimen and used to deposit dots by the EBID method. Obviously, the EBID fabrication resolution will be defined as the characteristic size of the smallest deposited dot (Figure 45). Which size exactly should be considered is still a controversial matter. Here, we present different definitions as used in related fields, such as imaging in SEM, microanalysis in a TEM, or EBL. The EBID fabrication resolution can be defined as determined by the FWHM of the radial density distribution of the deposited dot (Figure 46a). Another definition considers the FW50% of the integral of the radial distribution. This

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FIGURE 45. Illustration for the definition of EBID fabrication resolution.

I(r) (a)

1

FWHM = 2 R0

0.5

r 0

R0 NΣ(r)

(b)

1

0.5 50% FW50% = 2 R0 r 0

R0

FIGURE 46. Different possibilities to define the EBID fabrication resolution. (a) FWHM of the radial density distribution of the deposited dot I(r), and (b) FW50% of the normalized integral function of the deposited dot, NS(r).

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value is given by the diameter of the circle that contains 50% of deposited atoms (Figure 46b). In the particular case of a Gaussian distribution of the dot spatial profile, these two definitions coincide. We present both the FWHM and FW50% results. A somewhat different definition is given in the practical assessment of the SEM imaging resolution, where no flat surfaces but fine heavy metal particles on light substrates are observed. The SEM edge‐to‐edge resolution is then defined as the minimum distance observable between two edges (Ding and Shimizu, 1989). The definition of spatial resolution in TEM analysis is given by a relation between the beam spread in a thin film b, and the incident beam diameter d (Williams and Carter, 1996). The beam diameter d is defined as the area where 90% of the electrons enter the specimen. The beam spread b has been the subject of extensive theoretical and experimental work. The single‐ scattering model states that the beam spread in a thin film is given by (Reed, 1982): b ¼ 7:21 105

Z r 1=2 3=2 t ; E0 A

ð16Þ

where t is the film thickness (cm), Z the atomic number, A the atomic weight (g/mol), r the density (g/cm3) of the target, and E0 is the electron beam energy (keV). This definition comprises 90% of the electrons emerging from the specimen. When the specimen has a more complicated geometry, Monte Carlo (MC) simulations can be used and the diameter of a disk at the exit surface of the specimen that contains 90% of the emerging electrons gives the beam spread. The spatial resolution is defined by adding b and d in quadrature: pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ R ¼ b2 þ d 2 : ð17Þ For a long time, this equation remained the standard definition. In the particular case of X‐ray spatial resolution, based on the Gaussian model and experimental measurements, Michael et al. (1990) proposed that the definition of R be modified so as not to present the worst case but to define R midway through the foil: R¼

d þ Rmax ; 2

ð18Þ

where Rmax is given by Eq. (17). Another definition is given in the modeling of resist‐based EBL. In this case, the fabrication resolution is given by the contour of the opening in the resist, made by the smallest electron beam after exposure and development,

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the so‐called dot exposure or beam response (Greenich and van Duzer, 1973). A simple resist‐solubility model is usually used—the threshold energy density model. Studying the energy deposited on the surface and comparing it to a threshold value provides the spatial fabrication resolution (Hawryluk et al., 1974). 1. Identifying Researchable Problems Figure 47 shows a chart with the achievable EBID resolution. Curve 1 shows the ideal situation, in which the deposited dot sizes are equal to the diameter of the primary electron (PE) beam. Curve 2 contains some reported experimental data, showing the structure sizes plotted versus the beam diameter used to deposit them. Regular sizes of 20–200 nm have been obtained with probe sizes between 2 and 100 nm. For example, a 30 nm electron beam deposits a 250 nm diameter dot (Kohlmann‐von Platen et al., 1993), a beam of 10 nm yields a dot of 100 nm diameter (Ochiai et al., 1996), and a 2 nm beam diameter yields a 20 nm diameter tip (Hu¨bner et al., 2001). However, sub–10 nm features also have been achieved by several groups. For instance, Broers et al. (1976) made 8 nm wide lines with a 1 nm probe, Jiang et al. (2001) also made 8 nm lines with a 1.2 nm probe, 3.5 nm was achieved with a 1 nm probe by Guise et al. (2004a), 1.5 nm dots with a 0.8 nm probe by Tanaka et al. (2004), 4 nm dots by Crozier et al. (2004) with a 0.3 nm probe, and 1 nm dots made with a 0.3 nm probe by van Dorp et al. (2005). A few challenging questions arise when analyzing this chart. First: what is the functional relation between the diameter of the electron probe and the size of the deposited structure? This is not a trivial problem, because the chart shows that this size is not directly given by the diameter of the PE beam. The current understanding of the EBID process often suggests that the main influence factors are the SEs emitted at the target surface (Hoyle et al., 1996; Hu¨bner et al., 2001; Lipp et al., 1996a). For a simple check of this assumption, the spatial range of the SEs are drawn on the target surface on the same chart (curve 3 in Figure 47). Actually, a cloud of SE ranges can be plotted because of the disagreement between different simulations (Ding and Shimizu, 1989; Joy, 1984a, 1985; Kotera, 1989). The guide to the eye through these points is closer to curve 1 than to curve 2, except at small beam sizes. So, a discrepancy still exists. The second challenging question is what is the ultimate feature size, or how close can one get to the primary beam size? The theoretical modeling of EBID is a rather poorly explored field; this lack of fundamental results has generated different and sometimes contradictory predictions of the ultimate resolution. Some authors observed that in the particular case of tip growth, the fabrication resolution seems to be limited only by the

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FIGURE 47. The achievable EBID resolution chart. Curve 1 is an ideal situation: dot size ¼ diameter of primary electron (PE) beam. Curve 2 is a guide to the eye through some experimental EBID feature sizes (Hu¨bner et al., 2001; Kohlmann‐von Platen et al., 1993; Ochiai et al., 1996, Broers et al., 1976; Jiang et al., 2001; Guise et al., 2004a; Tanaka et al., 2004; Crozier et al., 2004; van Dorp et al., 2005); Curve 3 is a guide to the eye through values of the calculated SE range on the target surface (Ding and Shimizu, 1989; Joy, 1984a, 1985; Kotera, 1989).

primary beam diameter, so they promised tips of higher resolution, provided that a finer focused beam could be obtained (Hu¨bner et al., 1992; Kohlmann‐von Platen et al., 1993). However, this promise can only be valid as long as the beam diameter is larger than the range of the SEs. It is possible that even if a finer primary beam could be achieved due to improvements of the electron optics, the emitted SEs with their large spatial range would limit the size of the ultimate EBID structure. This is the current situation in SEM imaging. The same prediction has been given for PMMA conventional resist‐based EBL. In that case, the ultimate fabrication resolution is fixed at 10 nm for beam energies from 20 keV to 120 keV (Broers et al., 1996). The left‐hand side of curve 2 in Figure 47 shows that much recent progress has been made to make very small structures, but so far there was no good theoretical model available to explain these results. A third interesting question is why deposition with a 0.3 nm probe can sometimes result in dots with diameters of 1 nm (van Dorp et al., 2005) and sometimes of 4 nm (Crozier et al., 2004). If we succeed in answering these questions and develop an acceptable theoretical model of EBID, then we can contribute to the dispute concerning the future of the EBID resolution. The future evolution of the EBID curve 2 (Figure 47), where the PE probe size approaches 0.2 nm (as in

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today’s state‐of‐the‐art TEMs, e.g., the FEI Tecnai 20 series), is still an open question. Will the EBID resolution curve be limited in the same way as the SEM imaging resolution, or can it be forced to meet the primary beam size? The answer is not trivial because EBID differs from SEM, having two more active participants: the PE and the precursor. EBID is also a resist‐less technique and these differences could be exploited to create a path to a higher fabrication resolution. These questions generate two problems: the theoretical prediction and the experimental demonstration of the EBID resolution limits. Here we deal with the first problem only—estimating theoretically the spatial profile of the deposited dot for given electron beam, precursor, and target parameters. 2. Defining the Strategy The problem of predicting the profile of the deposited dot is similar to that of surface topography evolution during classical beam‐assisted lithography techniques (CVD, sputtering, etching). The surface profile simulators developed for this purpose are using, as mathematical background, string algorithms, level‐set methods, or cellular automata (Adalsteinsson and Sethian, 1995; Neureuther et al., 1980). After a review of these methods, we have concluded that regardless which spatiotemporal technique we might choose, to predict the time evolution of the dot profile from initial moment t0 to the final moment tn, we need to know the deposition rate R(x) at any point on the surface (Figure 48). The deposition rate R(x) is influenced by a number of factors. We have adopted the following strategy, summarized in Figure 49. We start with an assumption, noted A, and we then calculate the profile of the smallest dot based on this assumption. The theoretically estimated size (T ) is compared with existing experimental data (E ) and more factors are introduced one by one, correcting the previous assumption until an agreement has been achieved within an acceptable accuracy (E T ).

FIGURE 48. The time evolution of the deposited dot boundary.

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FIGURE 49. The strategy adopted in solving the EBID resolution evaluation problem.

For example, we start with the assumption that the primary role in EBID is played by the electrons on the target and dot surface. Because we neglect the migration of molecular fragments, the deposited dot is formed in the precursor area exposed by the electron beam. If we assume that the interaction of electrons is localized (i.e., only with adsorbed molecules situated on their trajectory) and that the angle of incidence is not important, then the exposed area is given by the spatial distribution of the electrons on the surface, convolved with their ‘‘power’’ of dissociation. The deposition rate R(x) under the action of an electron beam of energy E0 at distance x from the beam central point of incidence can be expressed (in molecules/unit area/s) and is given by (Kunz et al., 1987): E ð0

RðxÞ ¼

f ðx; EÞsdiss ðEÞN dE;

ð19Þ

0

where f(x,E ) is the flux of electrons passing through the surface as a function of the position and energy (electrons/unit area/s; Figure 50), sdiss(E ) is the electron‐induced dissociation cross section of the precursor molecule (unit area) as a function of the incident electron energy, and N is the surface density of adsorbed precursor molecules (molecules/unit area).

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FIGURE 50. Illustration of the definition of deposition rate R(x).

The deposition rate can also be expressed in volume per unit area per second and is given by (Scheuer et al., 1986): ð f ðx; EÞsdiss ðEÞNV dE; ð20Þ RV ðxÞ ¼ all energies

where V is the volume occupied by a dissociated molecule. As seen from Eqs. (19) and (20), the following data are necessary to predict the deposited dot profile evolution. First, the total electron flux through the surface in the vicinity of the primary beam incidence point (spatial and energy distributions), f(x,E ). Because there is enough experimental evidence that not only PEs determine the structure size, both PE and SE surface distributions will be necessary. Further, the electron impact molecular dissociation cross section as a function of the electron energy, sdiss(E ) will be needed for the given precursor. In our case, the precursor is an organometallic compound or a hydrocarbon complex. Unfortunately, only rather precarious information is available about the electron impact dissociation cross sections of different gases. More experimental data exist for electron impact ionization than for dissociation, usually for H2, N2, CO, CH4, in general for gases abundantly present in the interstellar medium and planetary atmospheres. For some hydrocarbons (CxHy), the cross sections have been measured or calculated. Recently collections of recommended data have been published for gases used in plasma processing in microengineering, as well as for hydrocarbons (Christophorou et al., 1996). If the first results show that the influence of electrons is not so strong that it can be solely held responsible for the broadening of the deposited structure, we will need to evaluate in detail the influences of other parameters on

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FIGURE 51. Illustration of the possible effects of delocalization of electron inelastic scattering.

EBID resolution. For example, we might have to consider the fact that a swift electron can interact with a target atom or a precursor molecule situated some distance away from its trajectory (Muller and Silcox, 1995) (Figure 51). The magnitude of this effect, known as delocalization of electron inelastic scattering, is still in dispute, but all authors agree that it must be considered, especially in the case of fine electron probes (Joy and Pawley, 1992; Reimer, 1998). The problem of surface excitation, in which an electron can excite an SE when it is still in vacuum before entering the target, also requires more research (Ding and Shimizu, 2000). For this reason, an extra analysis step is introduced, estimating the eventual degradation of EBID resolution due to the delocalization of the electron inelastic scattering. Another deviation from the reality in our initial model is that migration of fragments created after electron‐molecule impact is neglected. In reality, the ionized or dissociated fragments of precursor molecules can obtain enough energy to hop on the surface before definitely sticking onto a surface site and forming a deposit. An analysis of the influence of the migration of molecular fragments on the surface might be necessary. Depending on the result of these correction steps, other parameters of influence, such as surface plasmon decay, clustering of atoms, electrons under the surface, charging effects, and so forth might also need to be considered In summary, we will focus on the EBID fabrication resolution. We have localized an interesting problem, viz. the theoretical estimation of EBID resolution and its fundamental limits. Building an appropriate EBID model for the specimen‐mediated electron beam interaction with the precursor (Figure 52) requires an extended theoretical study in the following domains: The interactions between electrons and the adsorbed precursor

molecules,

The interactions between electrons and the solid matter, and The interactions between the precursor and the target surface.

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FIGURE 52. The EBID model based on specimen‐mediated electron beam‐precursor interactions.

Because the contamination problem in HREM and EBID fabrication phenomena are similar, the results of this study will be useful for both direct electron beam deposition and electron microscopy. B. Relevant Interactions Between Electrons and Solid Matter A typical study of the electron‐solid matter interaction starts with the incident electron beam, consisting of the so‐called PEs. The simplest representation of the PEs is the pinpoint, zero‐diameter, monoenergetic beam, usually incident normally to a solid target. This is not a realistic approximation, but it is a convenient simplification for the further study of the electrons scattering in the target. In this case, the primary current density distribution (or flux distribution) on the surface is a delta function. In reality, the beam incident on the surface is two dimensional and the current density distribution in the spot on the surface is usually modeled by a Gaussian (or normal) function. The current‐density I(r), expressed in units of electrons per unit area per unit time, is defined by the number of electrons striking the surface per second, at a radial distance r from the center of incidence: Ntotal r2 IðrÞ ¼ exp ; ð21Þ 0:38pd 2 0:38d 2 where Ntotal is the total number of electrons crossing the surface per second. The diameter of the Gaussian beam distribution d is usually defined as the diameter at FWHM, which in the 2D case is also the circle that contains half of the total current (FW50%). Comparing this with the Gaussian beam standard deviation s, then d ¼ 1.67s. Figure 53 shows the surface flux of the primary incident electron beam in the case of a Gaussian beam of 2 nm diameter. When the PE beam hits a solid target covered with precursor molecules, a complex interaction scheme is generated, as shown in Figure 54. Let us analyze

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FIGURE 53. The normalized spatial distribution for a Gaussian primary beam of diameter d ¼ 2 nm.

FIGURE 54. Typical EBID electron‐target‐precursor interaction scheme.

this typical EBID scheme and move ‘‘in the shoes’’ of the adsorbed precursor gas molecules. They can be dissociated by many kinds of electrons, which happen to circulate in their proximity. First, the incident PEs can interact with the adsorbed gas molecules and trigger their dissociation. Further, the inelastically scattered PEs produce secondary electrons (SE1) in the target, which eventually emerge on the surface. The primary beam also generates BSEs, which also scatter in the substrate and produce supplementary secondary electrons (SE2). This labeling of SEs, used by Joy (1991), is of course artificial, taking as criteria their energy and exit position. From the scheme in Figure 54 it is obvious that in addition to the PE (zone 2), the BSEs and secondary electrons SE1 (zone 3) and SE2 (zone 4) can also induce decomposition of

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adsorbed precursor molecules, each kind of electron with a different cross section and contribution to the shape of the deposited structure. C. Monte Carlo Simulations for Secondary Electrons Emission The second usual suspect among the parameters that can influence the EBID resolution are the SEs emitted from a target bombarded by the primary beam. Information about this secondary emission can be obtained by studying the electron scattering in the target. The problem of the electron‐solid interaction should ideally be solved experimentally, by measuring the relevant physical quantities resulting from the primary beam bombardment. However, the interaction process remains partially unknown, due to the limitations of current experimental techniques. In such a situation, simulations become the most powerful theoretical method, as an idealized replacement of experiments. The subject of SE emission has been treated extensively in the past, primarily supporting the developments in SEM. Three elements are necessary to simulate the SEs: their generation, their transport, and their escape from the target. Theories of secondary emission caused by electron bombardment can be divided in four levels of approximation. The first approximation uses a simple empirical equation for SE emission and uses adjustable parameters for each material. A second one assumes an analytical model for the geometry of electron diffusion and yields the spatial or energy distribution of SE emission. For example, Chung and Everhart (1974) used a simple exponential decay law and quantum theory to obtain the energy distribution of SE. The third approach analytically or numerically solves the Boltzmann transport equation (Amelio, 1970; Devooght et al., 1987; Rez, 1983; Ro¨sler and Brauer, 1981a,b; Wolff, 1954). The fourth approximation uses probability distributions to express each phenomenon in the production and propagation of SEs and by MC simulations obtains the electron’s trajectory in three dimensions (Koshiwaka and Shimizu, 1974). After calculation of a large number of trajectories, the results are summed to obtain various physical quantities of the SEs. The theories become progressively more general in going from first to fourth. Our main interest goes to the MC‐type of simulations, because they have lately been used very widely and can be performed by computer using relatively simple mathematics. MC electron trajectory simulation techniques have previously been studied by Koshikawa and Shimizu (1974), and have constantly been improved by Ding and Shimizu (1996, 2000), Ding et al. (2001), Hovington et al. (1997a,b), Joy (1984b, 1988, 1995a), Kotera (1989), Kotera et al. (1989), Murata et al. (1981), Reimer (1998), Shimizu and Ding (1992), Shimizu and Ichimura (1983), and others. The method has been

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applied with success to EPMA, electron spectroscopy, SEM, and electron‐ and ion beam lithography. The existing MC programs are of a half‐ commercial type, their use being restricted to a certain research group or institute. Usually authors publish their results in graphical form and only partial descriptions of the MC procedures are given. A very elementary book on MC methods in general was written by Sobol (1994). A mathematical discussion on MC methods is provided by James (1980). A primer for the MC method applied in electron microscopy is the book by Joy (1995a), whereas a description of the procedures and useful equations for MC in EPMA is given by Scott et al. (1995) and by Henoc and Maurice (1991). MC methods used for secondary emission have been reviewed by Shimizu and Ding (1992). A very detailed description of an MC program for low‐energy electrons is given by Hovington et al. (1997a,b). Another series of MC programs have been written for high‐energy (100 keV–1 MeV) electron scattering in accelerators (Kijima and Nakase, 1996; Kijima et al., 1995). They use the same models as in EPMA but are corrected for relativistic velocities. Some of these programs are for public use (e.g., ETRAN, ITN). This section presents the most widely used simulation technique for SE emission: the MC method. Some existing MC programs are described, together with some of their results relevant for the EBID case. Some theoretical models and typical calculation procedures are given for a physicist interested in SE emission and doing his or her own programming. The description of a typical Monte Carlo simulation for secondary electrons emission (MCSE) program can be divided in two parts. The first part treats the data transfer between the computer program and its user. The second part is more programmer oriented and treats the MC procedures and the physical background of the electron‐ target interaction. 1. Input Data for an MCSE Program The typical electron–solid matter program considers a pinpoint (zero‐diameter) electron beam incident on a target situated in vacuum (Figure 55). The necessary input data usually are the energy of the PE beam E, the angle of incidence y, the target thickness h and the target material, the number of simulated trajectories, and the required calculation accuracy. Quantitative modeling of the electron‐solid interactions using MC techniques is possible only if there are sufficient experimental data on which to base the model and against which to test its predictions. The accuracy of the method depends, among other things, on the accuracy of these parameters. That is why, transparent for the user but of great importance for the programmer, information sources are needed, such as databases with target properties, dielectric functions, scattering or ionization cross sections, energy

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FIGURE 55. Typical input parameters for a MCSE program.

loss spectra, SE yields, electron‐stopping powers, and mean ionization potentials. There have been efforts to build these kinds of databases. For example, a typical database for electron‐solid interactions is described by Joy (1995b). However, a need still exists for more detailed and comprehensive sets of relevant data presented to the researcher in an accurate and convenient form. The targets are bulk materials (typically 200–500 nm thick), usually metals like copper, aluminum, silver, gold, or materials from the semiconductor IC industry (silicon, silicon oxide, PMMA resist). In electron lithography, the target is multilayered, a substrate of Si of different thicknesses, and a typically 100 nm thick resist layer. The primary beam energies are specific to SEM applications, typically 5–30 kV. For lower primary beam energies the development of a new generation of MC programs is in progress (Hovington et al. 1997a,b; Kuhr and Fitting, 1999a,b). 2. Output Data of an MCSE Program While the MCSE program is running, very often a graphical display of PE and SE trajectories in the target is provided. This display has the disadvantage that it slows down the computation, but it can be very useful as a test for the programmer and as a visual tool for the user to estimate, for example, the electron interaction volume. The display can be made in the target cross section, projected in a plane parallel to the initial trajectory of the incident beam (YZ ), or by showing the emission sites on the surface, clustered around the beam incidence point (XY ). Examples of both types of these direct visual assessment displays are shown in Figure 56. In modern programs, the screen displays with electron trajectories can be saved in bitmap image files. If the MC procedure considers a pinpoint PE beam normally incident on the target, then the emerging SEs will have a symmetric radial distribution around the incidence position. The target surface in the XY plane is then

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FIGURE 56. Examples of typical MCSE graphical displays. (a) The emission sites on the target surface XY plane (Reprinted (Figure 1) with permission from H. Li, Z. Ding and Z. Wu (1995). Phys. Rev. B, 51, 13554. ß 1995, by the American Physical Society). (b) The SE trajectories in the target YZ plane (Reused from Joy (1988) with permission from IOP Publishing Limited). The primary electrons are incident along the Z‐axis.

divided in concentric circles centered around the incidence point, having a distance dr between them. The direct results from MC simulation are the number of SEs emitted from a ring between the circle of radius r and the next circle of radius r þ dr, expressed in the number of SEs emitted per incident PE (Figure 57). Let us denote this number by N(r) where r ¼ 0, dr, 2dr, 3dr, . . .. We will try to clearly specify the format in which these data can be processed and graphically presented. Different plots are usually shown in articles, which do not always clearly specify what type of results they represent, making a comparison difficult or even impossible. An example of cumulated radial distributions of SE spatial distributions is shown in Figure 58.

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FIGURE 57. The geometry used by MC methods.

1.0 NΣ (r)

0.5

N(r) I(r) 0.0 Radial position r FIGURE 58. Example of cumulated SE spatial distributions on the target surface; N(r) ¼ the normalized radial distribution of outgoing SE current; I(r) ¼ the normalized radial intensity distribution of SE; NS(r) ¼ the normalized SE current from a circle of radius r. Reprinted from Ding and Shimizu (1989) with permission from Blackwell Publishing.

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a. Radial Distribution of Outgoing Secondary Electron Current, N(r). N(r) represents the number of SEs emitted in a ring between r and r þ dr per incident PE, which is the direct result from the MC simulation. Here r is the distance of emergence of the SEs with respect to the entrance point of the primary beam. If determined by numerical MC simulations, N(r) is a discrete function. Sometimes N(r) is plotted normalized. b. The Radial Intensity Distribution of the Secondary Electrons, I(r). The radial intensity distribution of SEs on the surface, I(r), is the most frequently shown result of MCSE, sometimes under the simple name of spatial distribution. It represents the number of SEs emitted per unit area from a surface ring [r, r þ dr] situated at a distance r from the incidence point. It is expressed as the number of SEs per unit area per incident PE and is defined by: IðrÞ ¼

NðrÞ ; AðrÞ

ð22Þ

where A(r) is the area of the ring between a circle of radius r and a circle of radius r þ dr: AðrÞ ¼ pð2r þ drÞdr 2prdr

ð23Þ

NðrÞ NðrÞ

pð2r þ drÞdr 2prdr

ð24Þ

IðrÞ ¼

If analytically determined, I(r) is continuous and has a singularity in r ¼ 0. c. Secondary Electron Current Emitted Inside a Circle of Radius r, NS(r). NS(r) is the number of SEs emitted from within a circle of radius r per incident PE, expressed in number of SEs per unit length per incident PE: NS ðrÞ ¼

r X

Nðr0 Þ

ð25Þ

r0 ¼0

The curve NS(r) is asymptotic to the total number of emitted SEs, equal to the SE yield or NS(1). The curve can also be plotted normalized and then is asymptotic to 1. d. Lateral Distribution of Secondary Electrons on the Surface, D(x). The lateral distribution shows the number of SEs emitted from a unit length, obtained by integration of the radial distribution I(r) in one direction parallel to the surface. For example, if this direction is x, then the lateral distribution on the surface D(x) expressed in number of SEs per unit length per incident PE is:

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DðxÞ ¼

Ið

pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ x2 þ y2 Þ dx:

ð26Þ

1

If the SE radial distribution I(r) is a Gaussian function, it does not change by integration and the lateral distribution is the same as the radial intensity distribution. D. Basic MCSE Procedure We now present the typical information necessary to complete an MCSE program. After reading this chapter, a beginner will be able to understand the language used by MC authors in their articles. Passing through the target, the electron will lose energy by excitation of plasmons, phonons, X‐rays, SEs, and so on and will suffer a series of deflections as a result of close encounters with atomic nuclei. In MC programs, these processes are usually treated as entirely independent. MC simulation programs consider two possible types of electron scattering events: elastic and inelastic, while between two processes the electron moves linearly (Figure 59). Elastic scattering is assumed to result only in the electron deviating from its trajectory, without energy loss. Inelastic scattering occurs as a result of electron interaction with the electrons from the target atoms and deviates the electron, while also leading to energy loss. This energy loss can result in the generation of one or more so‐called internal SEs. These electrons scatter in the target and are eventually emitted from the surface, thus being registered as SEs and contributing to the results of the MC simulation. A typical MCSE procedure consists of tracing the electron between two successive scattering events. Before each collision, an electron is defined by its energy, position, and direction, given by the cosines of angles with the axes of a three‐dimensional (3D) coordinate system. The essential problem

FIGURE 59. Typical electron scattering events in the target; elastic scattering.

▪ inelastic scattering;

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of an MCSE program is to calculate the energy and direction of travel for each electron after it suffered a collision, based on the previous values. In this way, the path of the electron can be traced until it emerges from the sample or until it has lost so much energy that no other secondary particles can be generated. Let us start, as the majority of MCSE programs do, with a PE normally incident on a target. First, a number of input parameters are needed, such as the energy of the electron Ep, the thickness and material of the target, and the number of simulated trajectories. The influence of the surface barrier is the same as the light refraction at the interface of two media. The PE penetrating the surface from vacuum modifies its energy to: E ¼ Ep þ U0 ¼ Ep þ EF þ W ;

ð27Þ

where Ep is the energy measured from the vacuum level and E is its energy measured from the bottom of the conduction band of the target material. U0 is the inner potential and is equal to the sum of the Fermi energy of the target material EF and the target work function W. The usual MC procedure traces the PE step by step between two scattering events until it reaches a target boundary or has lost all of its energy. We can assume that the path between two events is short, so that the electron moves linearly without losing energy and only one event takes place at a time. This is the so‐called single‐scattering model. Figure 60 shows a widely used geometry in simulating the electron trajectory in the solid. The XYZ coordinate system is attached to the specimen and it is chosen such that the Z‐axis is normal to the specimen surface and directed toward the specimen, the X‐axis is parallel with the tilt axis of the specimen holder, and X‐Y is the plane of the untilted sample (Joy, 1988). After each event, a coordinate system X0 Y0 Z0 connected with the electron is generated from XYZ by rotation with angles y and f. The next scattering angles will then be defined with respect to the X0 Y0 Z0 system. Let us consider the scattering event 1 (see Figure 60). The previous event is 0 and the next scattering event will be denoted by 2. Before a scattering event 1, each electron is characterized by an energy E, a position (X1,Y1,Z1), and a direction given by the direction cosines of the trajectory segment 0–1 with respect to the XYZ axes (cx01,cy01,cz01), First, we must decide whether scattering event 1 is elastic or inelastic. Second, after scattering event 1 has occurred, a number of calculation steps are necessary. If event 1 was elastic, we need the new PE direction, given by its scattering angles (polar y and azimuthal f). The new direction cosines cx12,cy12,cz12 can also be calculated using the set of Eqs. (28)–(34).

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FIGURE 60. Typical geometry used to simulate the electron scattering in the target.

cx12 ¼ cx01 cosðyÞ þ V1 V3 þ cy01 V2 V4

ð28Þ

cy12 ¼ cy01 cosðyÞ þ V4 ðcz01 V1 cx01 V2 Þ

ð29Þ

cz12 ¼ cz01 cosðyÞ þ V2 V4 cy01 V1 V4

ð30Þ

V1 ¼ AM sinðyÞ

ð31Þ

V2 ¼ AN AM sinðyÞ

ð32Þ

V3 ¼ cosðfÞ; V4 ¼ sinðfÞ

ð33Þ

AN ¼

cx01 1 , AM ¼ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ cz01 1 þ AN 2

ð34Þ

If event 1 was inelastic, an SE has been generated. The energy and scattering angles for both the PE and the SE must be determined. The new direction cosines can be calculated for both electrons using Eqs. (28)–(34). The energy, position, and direction data for the new SE are stored in

ELECTRON‐BEAM–INDUCED NANOMETER‐SCALE DEPOSITION

107

memory. The simulation of the PE continues with a new step until the next event 2. The new electron position given by (X2, Y2, Z2) is calculated using Eqs. (35)–(37). X2 ¼ X1 þ step cx12

ð35Þ

Y2 ¼ Y1 þ step cy12

ð36Þ

Z2 ¼ Z1 þ step cz12

ð37Þ

This sequence is repeated until the PE reaches a specimen boundary and escapes on the surface or its energy drops below the lower limit of the chosen energy window. When the PE simulation is finished, the information about the stored SEs is recalled and the trajectories are simulated in the same way as for the PE. This time, the transport of each generated SE is simulated until it exits on the surface or comes to rest within the sample. The essential problem is to determine the step length between one scattering event and the next, which is related to the mean free paths for elastic and inelastic scattering, the energy loss, and the scattering angles. For all these quantities, existing theoretical models give us the scattering cross sections s(x), but we need an algorithm that can sample these parameters in conjunction with these cross sections. From statistics, it is well known that random numbers x that are distributed according to a certain function s(x) can be obtained from a uniform distribution of random numbers R between zero and unity, according to Ðx R¼

xmin xÐmax

sðxÞ dx :

ð38Þ

sðxÞ dx

xmin

With this relation and knowing the cross sections s(x), we can sample each scattering parameter x using a uniform random number R. If the cross sections have a simple form, then analytical equations relating x to R can be obtained. In more difficult cases, when no analytical solutions exist, only numerical integration can solve the problem. In those cases, look‐ up tables must be generated that will allow one to pick a value x when a uniform random number R is generated. This approach requires substantial memory, but it has the advantage of shorter computing time, because no on‐line calculations are needed.

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E. Theoretical Models for Electron Scattering Simulation After an electron enters a solid target, a complicated cascade multiplication of electrons is generated. Usually the secondary generation is simulated with a classical binary collision approximation, in which only one SE is generated after each inelastic scattering event, so that the cascade process can be simulated by the programmer with a binary tree data structure (Figure 61). Solving the full‐cascade collisions tree generated in the target is a titanic work, both for the computer and for the programmer. If one considers that the distance between two events may be as small as 0.1–1 nm, while the specimens may be up to 1000 nm thick, one can imagine how many levels in the tree would need to be tracked to simulate just one electron trajectory. Furthermore, only a representation obtained from a large number of computed trajectories is a good approximation to experimental reality. The relative error of an MC simulation varies with N, where N is the number of trajectories computed. Because a large number of trajectories need to be calculated, the method becomes time consuming, and to avoid this, various approximations were used in the past. Until recently the computing time and memory capacity have been an impediment for the simulation of the full interaction scheme. Today’s high‐speed computers, supercomputers, and high‐memory capacities facilitate fast progress toward the implementation of more complete models in MC simulations. However, the computing time is not the only problem. Even if we have enough time, it is unknown how exactly the electron scatters in the target. MC simulations of electron transport in a solid solve this problem by a stochastic description of the scattering process. The techniques use random numbers as a means of predicting the magnitude of various events (scattering angles, loss of energy by the electron) as well as to select between

FIGURE 61. Electron trajectories in the target can be simulated by a binary‐tree data structure.

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109

FIGURE 62. The flow chart for SE theoretical models.

different scattering options. With the present state of the art, it is particularly important to pay close attention to these simplifications, which are often introduced in the model by neglecting the unknown distributions or in order to reduce the complication of calculations. Approximative models for MCSE have been generated as time savers and as replacement for the unknown scattering phenomena. It must be understood that there is not one single MC approach, but a large number of models that differ by more or less arbitrary simplifications of the real process. The development of MC modeling of electron‐solid interactions is a history of improvements to the approximations adopted to describe elastic and inelastic scattering, in which a compromise has to be found between the accuracy needed and the time available. A safe start for an MC programmer is to build simple programs using rough approximations, progressively introducing more realistic models, until the accuracy satisfies the requirements of the application. Various approximations have been reported to simplify the MCSE simulations. The following sections present some of these approaches organized according to the flow chart shown in Figure 62. 1. Elastic Scattering A very simple approximation is based on the assumption that PEs only scatter elastically in the target. Then the electron trajectory is a chain of linear segments between two elastic events (Figure 63). The first unknown is the elastic mean free path lel as a function of the energy of the electron. After each elastic scattering event, the future direction

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FIGURE 63. The primary electrons only scatter elastically.

of the electron, given by the elastic‐collision scattering angles y and f, needs to be determined. For this there are two options, given by the Rutherford and Mott cross sections. The Rutherford total cross section, corrected for relativistic effects and screening of the nucleus by inner shell electrons, is given by (Joy, 1995a; Newbury, 1986): 2 2 E þ mc2 4p 21 Z Ruth sel ¼ 5:21 10 ½cm2 ; ð39Þ 2 2 að1 þ aÞ E E þ 2mc where E is the electron energy in keV, a is the screening parameter, and mc2 is the rest energy of the PE (511 keV). The screening parameter a takes into account the diminution of the net charge of the atom due to the effect of the atomic electrons, and can be calculated using the relation (Henoc and Maurice, 1991): a¼

3:4 103 Z 2=3 : E

ð40Þ

The polar scattering angle y for a particular elastic collision can be found using (Henoc and Maurice, 1991): cosðyÞ ¼ 1

2aR ; 1þaR

ð41Þ

where R is a random number uniformly distributed between 0 and 1. The azimuthal angle f can be assumed to be uniformly distributed because scattering in the radially symmetric field of the atom exhibits cylindrical symmetry: f ¼ 2pR; where R is another uniform random number between 0 and 1.

ð42Þ

ELECTRON‐BEAM–INDUCED NANOMETER‐SCALE DEPOSITION

111

The elastic mean free path (in cm) between two elastic events can then be calculated as: lel ¼

A ; NA rsel

ð43Þ

where NA is Avogadro’s number (¼ 6.0221367 1023 mol1). The step between two elastic events can be expressed as a function of a random number: step ¼ lel ln ðRÞ

ð44Þ

Since the Mott cross section is more satisfactory in the case of low‐energy electrons than the Rutherford cross section (Shimizu and Ichimura, 1983), the use of the Mott cross section in the keV and sub‐keV energy regions is now popular. The relativistic representation of the Mott differential elastic cross section is expressed as: dsel ¼ j f ðyÞj2 þ jgðyÞj2 ; ð45Þ d Mott where the element‐of‐solid angle d ¼ 2p sin d. The total Mott relativistic screened elastic cross section can be found by integrating Eq. (45) over the range 0 p. The functions f() and g() are the scattering amplitudes obtained from the partial wave expansion solution of Pauli‐Dirac equation instead of the Schro¨dinger equation used by Bethe. The partial wave method (PWM) can be used to calculate f() and g(). There is no analytical solution to this problem, but tabulated values with Mott coefficients are available for a few materials from the authors (Czyzewski et al., 1990; Reimer and Lodding, 1984) upon request. However, the data set for tabulated Mott cross sections is large and computations tend to be slow, due to the need to interpolate between data points. Browning et al. (1994) and Gauvin and Drouin (1993) have proposed empirical equations for the total elastic cross section as substitute for the tabulated Mott cross sections. The proposed form is very similar to the Rutherford screened cross section, except for some correction coefficients (g and b): pﬃﬃﬃ 2 2 2 4pg 1 eb E Z E þ mc sMott ½cm2 ¼ 5:21 1021 2 ð46Þ el að1 þ aÞ E E þ 2mc2 Usually graphics showing the ratio >() ¼ (sel)Mott/(sel)Ruth between the two types of elastic cross sections are given for each scattering angle . An example from Bongelier et al. (1993) is shown in Figure 64.

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(a)

(b)

2.0

5.0

C

E = 1 keV 24 10 4.0 100

0

0

60⬚

120⬚ Θ

2 4 6 8 10 20 50 100

r(q)

1.0

0 0

E = 1 keV

3.0

2 4 6 10 20 30 50 100

E = 1 keV 2.0

AI

2.0

180⬚

Cu

r(q)

r(q)

1.0

60⬚

120⬚ Θ

180⬚

1.0

0

0

60⬚

120⬚ Θ

180⬚

Mott Ruth FIGURE 64. The curves () ¼ sel /sel for different materials and energies. From Bongeler et al. (1993). Reprinted from Scanning (1993, 15, 1–18) with permission from the Foundation for Advances of Medicine and Science, Inc.

The Rutherford equation has been widely used because of its simplicity. It results from the Coulomb screened potential treated by means of the first Born approximation. The theory is useful for the determination of spatial profiles of SEs for light‐element targets and high acceleration voltages (beyond several keV), but less effective for determining the energy distribution of SE and heavy‐element targets, particularly in the low‐energy region, where the Born theory breaks down. In these situations the Mott cross sections should be used. 2. Inelastic Scattering In reality, the electron loses energy via inelastic scattering through interaction with the electrons of the target atoms. A widely used model that takes into consideration these interactions is the so‐called continuous‐slowing‐ down approximation (CSDA) (Figure 65). It assumes that the electron is continuously losing energy, slowing down as it travels through the target. In this way, the effect of all individual inelastic scattering events that occur between two elastic events is simulated.

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113

FIGURE 65. Illustration of the continuous‐slowing‐down approximation (CSDA).

In the case of high energies (>10 kV), the stopping power, defined as the rate at which the energy of the electron is lost, can be expressed very accurately using the Bethe equation (Shimizu and Ding, 1992): dE 2pe4 NA Zr 1:166E ¼ ln ; ð47Þ ds EA I where s is the electron path length (cm), E the energy of the incident electron (kV), I the mean ionization potential of the target material (kV), and e is the electron charge. I can be found analytically using the empirical equation (Joy, 1988; Kotera, 1989; Luo and Joy, 1990): I ¼ 9:76Z þ 58:5Z 0:19 :

ð48Þ

Rao‐Sahib and Wittry (1974) proposed a relation that uses the Bethe equation for energies E > 6.338 I and an extrapolation for energies lower than the mean ionization potential, E < 6.338 I: dE 2pe4 NZ pﬃﬃﬃﬃﬃﬃ : ¼ ds 1:26 IE

ð49Þ

A semi‐empirical stopping power for electron energies above 50 eV was recently proposed by Luo and Joy (1990) and is very widely used by MC programmers. Luo and Joy modified the Bethe equation and corrected it for energies lower than the ionization potential as follows: dE Z 1:166ðE þ kIÞ ¼ 78500r ln ; ð50Þ ds AE I where k is a variable whose value depends on the material. k is always close to, but less than unity. For example, k ¼ 0.851 for Au, 0.852 for Ag, 0.83 for Cu, and 0.851 for Al (Luo and Joy, 1990).

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The energy lost by the electron between two elastic events situated at distance step then is: DE ¼ step

dE : ds

ð51Þ

Evidently, the Bethe CSDA lacks physical background. Nevertheless, MC simulations based on the conventional model, which uses the Rutherford differential cross section for elastic scattering and the Bethe equation (CSDA) for inelastic scattering, have been successfully used to solve difficult problems in EBL and electron beam microanalysis (Ho et al., 1991). However, when the primary energies become a few kV or lower, the model cannot be used anymore. The lower the electron energy, the lower the accuracy of the Bethe approach. At low electron energies, the stopping power can be computed from the imaginary part of the dielectric function, obtained by measurement of the EELS or by optical measurement of the refractive index. Until now, we could get an idea about the scattering of PEs in the target but we still do not know anything about the SEs. The next model uses a stricter theory, which replaces the global energy loss between two elastic events, based on the CSDA, with individual inelastic scattering events. As a result of these inelastic collisions, so‐called internal SEs can be generated. These SEs can scatter in the target and eventually emerge on the target top surface, registered by the MC program as SEs (Figure 66). Conventionally, the true SEs are those with energies between 0 and 50 eV at the surface. In this model, PEs can suffer two types of possible events: elastic or inelastic scattering. The PE trajectory in the target is a chain of linear segments between two successive interactions. The length of the linear segments (i.e., the step between the events) has a Poisson distribution and can be sampled using a uniform random number:

FIGURE 66. The generation of secondary electrons.

ELECTRON‐BEAM–INDUCED NANOMETER‐SCALE DEPOSITION

step ¼ lT lnðRÞ;

115 ð52Þ

where lT is the total mean free path, which is related to the corresponding elastic (lel) and inelastic (linel) mean free paths through (Shimizu and Ding, 1992): 1 1 1 ¼ þ : lT lel linel

ð53Þ

The interaction sampling (i.e., the type of event [elastic/inelastic]) will also be determined using a random number as follows. If R is a random number between 0 and 1, the interaction will be elastic if R < lT/lel, and inelastic otherwise. The new unknown, linel, the inelastic mean free path (IMFP) for electron‐ electron scattering, can play a crucial role in the spatial results of the simulation, and therefore we pay special attention to this parameter. linel(E ) is the IMFP of an electron with energy E in the solid (i.e., the distance it can travel between two inelastic collisions). This quantity also depends on the target material and can be calculated or measured but is still a subject of discussion. Some authors use an average value for this parameter in their MC programs, for example, 0.5 nm for Cu targets (Koshikawa and Shimizu, 1974). In reality, however, the IMFP varies with the electron energy. The ideal situation for MCSE would be a universal predictive equation valid for a large number of materials and energies. Early calculations of electron IMFPs were based on the ‘‘jellium model’’ for a solid. The only parameter in this model was the valence electron density, often expressed in terms of rs, the average interelectron spacing. For example, in the beginning of SE emission studies, Chung and Everhart (1974) used such a relation, proposed by Quinn (1962) and Kanter (1970), valid for metallic targets: 1:47ðEF bÞ3=2 EðE EF Þ2

pﬃﬃﬃ pﬃﬃﬃ ½nm ðm Þ1=2 tan1 1= b þ b=ð1 þ bÞ 0 11=3 0 1 0 11=3 ; 4 r 3 s with b ¼ @ pA @ Aand rs ¼ @ pna30 A 9 4 p

linel ðEÞ ¼

ð54Þ

where E is the electron energy (eV), EF the Fermi energy of the target material (eV), rs is the radius of the volume element per electron, measured in units of the first Bohr radius a0 (0.0529 nm), and m* is the effective mass of the electron, measured in units of the free electron mass. Later, Seah and Dench (1979) published a compilation of electron IMFP values measured for a large number of solid targets. Based on this collection of data, they also proposed some still very widely used empirical equations,

116

SILVIS-CIVIDJIAN AND HAGEN

valid for electron energies between 1 and 10,000 eV. According to Seah and Dench, the inelastic mean free path for elements is: ! 538 1=2 linel ðEÞ ¼ am þ 0:41ðam ðE EF ÞÞ ½nm ð55Þ ðE EF Þ2 for anorganic compounds: linel ðEÞ ¼ am

2170 ðE EF Þ2

! þ 0:72ðam ðE EF ÞÞ

1=2

½nm

ð56Þ

and for organic compounds: 106 linel ðEÞ ¼ r

49 ðE EF Þ2

! þ 0:11ðE EF Þ1=2 ½nm;

ð57Þ

where am (¼ 107 (A/(nANA))1/3 ) is the average thickness of a monolayer (nm), E is the energy of the electron with respect to the bottom of the conduction band (eV), and nA is the number of atoms in a compound molecule. Figure 67 shows the IMFP for a carbon target (EF ¼ 20 eV), calculated using Eq. (55). The IMFP can also be indirectly calculated from the

FIGURE 67. The inelastic mean free path (IMFP) of electrons in a carbon target as a function of the electron energy E, measured with respect to the bottom of the conduction band.

ELECTRON‐BEAM–INDUCED NANOMETER‐SCALE DEPOSITION

117

measured EELS or the experimentally obtained dielectric function. The results usually agree with the empirical Seah and Dench equation [Eq. (55)]. The theoretical treatment of SE emission is based on the concept of a three‐stage mechanism consisting of the generation, transport, and escape into the vacuum. 3. Generation of Secondary Electrons Secondary electrons are generated as a result of electron inelastic scattering in the target. Inelastic scattering produces excitation of atomic electrons in the jellium and an energy loss of the incident electron. The SEs can be created as a result of different electron‐induced processes in the target, artificially divided into single‐electron excitations (valence or conduction electrons, core electrons) and collective plasma excitations (decay of a volume or surface plasmon), each process occurring with a specific cross section. Usually it is assumed that each inelastic scattering event generates an SE and the energy of this SE is the energy lost by the PE. Thus, in each inelastic scattering two electrons are involved: the PE and the generated SE. To implement this model in an MC simulation, for the PE we need its energy after scattering EPE ¼ E DE and its scattering angles (, )PE, and for the SE we need its initial energy ESE ¼ DE and initial direction (, )SE (Figure 68). We present different approaches to solve this problem. a. The Direct Model. The direct method artificially treats each type of excitation individually and defines a cross section for each type of excitation. The total cross section then is the sum of the partial cross sections based on an observation by Ritchie et al. (1969), who found that the stopping power described by Bethe’s equation is the sum of the stopping powers for each excitation mechanism. The direct method can be applied for high‐energy incident electrons.

FIGURE 68. A secondary electron is generated in an inelastic scattering event.

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SILVIS-CIVIDJIAN AND HAGEN

For metal targets, the main mechanism for SE generation is the excitation of conduction electrons. Most existing simulations only consider SEs generated by this excitation process. More detailed models also consider other generation mechanisms, such as ionization of inner shell (core) electrons, plasmon decay, and so forth, with corresponding cross sections. The type of particular excitation is sampled again using a uniform number R. For metals bombarded by electrons, Streitwolf (1959) has given the differential cross section for conduction electron excitation (Amelio, 1970; Ho et al., 1991; Shimizu and Ichimura, 1983): dsc ðESE Þ e4 N A p ¼ dðESE Þ EðESE EF Þ2

ð58Þ

The total energy loss cross section sc (ESE) can be obtained by integrating the Streitwolf differential cross section between the lower energy limit EF þ W and the upper energy limit Ep, by using a random number R, between 0 and 1 and the inversion equation, Eq. (38). The obtained relation samples the energy of the SE with the random number R (Koshikawa and Shimizu, 1974; Kotera, 1989): ESE ðRÞ ¼ A¼

RE F AðEF þ W Þ RA

ð59Þ

EP EF EP EF W

ð60Þ

This relation is ready to be used in MC simulation programming. This kind of relation is what the programmer needs and sometimes it takes much work to obtain it starting from the theoretical expression of the differential inelastic scattering cross section dsinel/d(ESE). In this equation, all the energies are calculated from the bottom of the conduction band. Figure 69 shows the excitation function for SEs as a function of a uniform random number R between 0 and 1 for different incident electron energies, as given by Eqs. (59) and (60), with all energies calculated with respect to the Fermi energy level. Once the energy of the SE upon generation, which is equal to the energy lost by the PE, is known, the next question is how the two electrons are oriented in space. The simplest approximation, the isotropic approximation, assumes that after each inelastic event no deviation occurs to the high‐energy electrons (PEs) and that the low‐energy electrons (SEs) are generated isotropically. This means that after an inelastic event the PE does not change its direction (PE ¼ 0, PE ¼ 0), an approximation valid especially for high‐ energy electrons incident on thin films. The SEs are generated isotropically

ELECTRON‐BEAM–INDUCED NANOMETER‐SCALE DEPOSITION

119

FIGURE 69. The SE energy ESE in the direct model, as a function of a random number R between 0 and 1, for two different primary‐beam energies Ep. The energies are given with respect to the Fermi energy level.

(i.e., all the directions of motion of an excited internal SE are equally probable), which is a reasonable approximation for electrons with energies below 100 eV. The direction of the electron can be specified by a unit vector from the origin, whose endpoint lies on the surface of the unit sphere. The phrase ‘‘all directions are equally probable’’ means that the endpoint is a random point uniformly distributed on the surface of a sphere (Figure 70). In the spherical coordinates (, ) on the sphere, for the polar scattering angle of the SE we have: cosðySE Þ ¼ 2R1 1

ð61Þ

and the azimuthal angle of the SE is: fSE ¼ 2pR2 ; where R1 and R2 are two different random numbers between 0 and 1.

ð62Þ

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SILVIS-CIVIDJIAN AND HAGEN

FIGURE 70. A random direction in space.

More accurate results can be obtained if the classical binary collision approximation is used, which results from conservation of energy and momentum. The azimuthal angle is again assumed to be isotropic. For the incident electron, we then have: rﬃﬃﬃﬃﬃﬃﬃ DE ð63Þ sinðyPE Þ ¼ E fPE ¼ 2pR;

ð64Þ

where DE is the energy lost by the incident electron. For the SE the scattering angles can be calculated as follows: sinðySE Þ ¼ cosðyPE Þ

ð65Þ

fSE ¼ p þ fPE

ð66Þ

b. The Fast Secondary Electron Model. The isotropic approximation holds for so‐called slow internal SE with energies lower than 100 eV. Slow electrons are ejected from the conduction or valence bands of the atoms in the specimen. Sometimes, however, high‐energy electrons can be generated, receiving a large fraction of the beam energy, up to E/2. These high‐energy electrons are named fast secondary electrons (FSEs). The FSE model starts from the free‐electron model and the Coulomb interaction between the incident electron and the free electrons of the target atoms. In this approach, the generation process is not isotropic, as previously assumed, but predominantly at relatively high angles to the beam direction (Joy, 1984a).

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121

The FSEs will broaden the spatial distribution of the SEs obtained in the isotropic approximation and thus degrade the spatial resolution in microanalysis in electron microscopy and in EBL (Murata et al., 1981). Joy (1984a) used this model and obtained results situated in the middle of the range of numerical values spanned by other formulations and thus gives a good estimation of SE spatial distribution. The differential cross section per electron for the FSE excitation process is: ! ds pe4 1 1 ¼ þ ; ð67Þ dðESE Þ E 2 e2 ð1 eÞ2 where E is the PE energy and ESE ¼ eE is the energy of the generated SE. Integrating Eq. (67) between 0.001 E and 0.5 E, the energy of the FSE can be sampled by using a random number R between 0 and 1 according to (Joy, 1995a): ESE ¼ eE ¼

1 E; 1000 998R

ð68Þ

where all energies are measured with respect to the vacuum level. To compare different approaches, in Figure 71 the energy excitation function for the FSEs given by Eq. (68) is shown, where all the energies are calculated with respect to the Fermi energy level. Knowing the FSE energy, from the conservation of energy and momentum, the scattering angles for PE and SE can be obtained, the same way as in the binary collision approximation. The polar scattering angle of the PE after the collision is: sin2 ðyPE Þ ¼

2ð1 eÞ ; 2 þ te

ð69aÞ

where t ¼ E/mc2. The polar scattering angle of the FSE after its generation is: sin2 ðySE Þ ¼

2e : 2 þ t te

ð69bÞ

c. The Dielectric Function Model. Until now, all the models for SE generation needed fitting coefficients to obtain the correct SE yields. Therefore, a unified treatment of electron inelastic scattering and SE generation is quite necessary. The best approach is based on the dielectric function, which characterizes an excitation process specific for the sample. The Bethe stopping‐ power theory is not necessary anymore if the dielectric function approach is used. The dielectric function e(o, q) describes a dielectric response of a material to an external perturbation such as an electromagnetic wave or an incident

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FIGURE 71. The fast SE energy ESE in the FSE model, as a function of a random number R between 0 and 1, for two different primary beam energies Ep. The energies are given with respect to the Fermi energy level.

electron. It is an attractive approach because it uses a measurable feature of the target material and thus includes almost all excitation mechanisms (valence‐electron excitations, conduction, plasmons, but not core‐ionizations). Ding and Shimizu (1996, 2000) showed that very good results can be obtained if the cascades of SEs are included. The dielectric function is very useful for MC simulations of electron inelastic scattering, the best simulation for SEM applications. Ding and Shimizu (1996, 2000) and Ding et al. (2001) presented a very good model based on dielectric theory with which SE yields that agree with experiments have been obtained. The theoretical formulation of inelastic scattering of an incident electron in a solid has been well established in terms of the dielectric function, in which the differential cross section for inelastic scattering is given by: dl1 1 1 1 inel ; ¼ Im eðo; qÞ q dðDEÞdq pa0 E

ð70Þ

ELECTRON‐BEAM–INDUCED NANOMETER‐SCALE DEPOSITION

123

where q is the momentum transfer from an incident electron of energy E to the solid, causing an energy loss of DE ¼ ho, and Im(–1/e(o, q)) is the energy loss function (ELF). The ELF completely determines the probability of an inelastic scattering event, the energy loss distribution, and the scattering angle distribution necessary for MC simulation. The ELF can be obtained from optical measurements or from EELS. Optical data have been compiled for a number of materials giving the optical constants n and k, the real and imaginary part of the refractive index, respectively. The optical ELF corresponding to q ¼ 0 can then be determined as: eðo; 0Þ ¼ ðn þ ikÞ2

ð71Þ

From the optical dielectric function e(o, 0) a dispersion relation is needed to obtain e(o, q). For example, Penn (1987) has suggested the bulk plasmon pole approximation: oq ¼ op þ hq2/2m. Then the ELF for other q 6¼ 0 is given by: 1 o hq2 =2m 1 Im Im ¼ ð72Þ eðo; qÞ o eðo hq2 =2m; 0Þ The energy of the SE as well as its scattering angle can be sampled by integrating Eq. (70) and using random numbers. At this moment, no analytical inversion equation exists that can be used for all materials. This is a disadvantage compared with the Streitwolf and FSE equations [Eqs. (58) and (67)]. Numerical integration of the inelastic cross section is needed for each material and it involves time‐consuming procedures. An inversion algorithm that builds look‐up tables seems to be the only alternative (Ding and Shimizu, 1996; Fitting et al., 1991; Kuhr and Fitting, 1999a,b). As an example, we used the dielectric model (Ding and Shimizu, 1996) to calculate the energy of SEs as a function of a random number R for a copper target. We started with the optical dielectric function e(o, 0), where n(o) and k(o) were taken from a handbook of optical data (Palik, 1998). A bulk plasmon‐pole approximation dispersion relation was used to obtain the extrapolated dielectric function e(o, q) for q 6¼ 0. The inelastic cross section was numerically integrated. Figure 72 shows the dependence of the energy of the SE on the random number R between 0 and 1 for two incident beam energies, as given by the dielectric function approach. All the energies were calculated with respect to the Fermi energy level. If we compare this result with the other two models, specific for slow and fast electrons, respectively, we notice that in the dielectric function approach, the SE have a probability to receive all energies ranging from W

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FIGURE 72. The SE energy ESE in the dielectric function model, as a function of a random number R between 0 and 1 for different primary beam energies Ep. All energies are given with respect to the Fermi energy level.

up to the energy of the PE, making this model the most realistic one and free of approximations. However, as expected, most of the SEs have energies between 0 and 50 eV. A disadvantage of this approach is that it can be used only for materials of known dielectric constant. It can be used for so‐called free electron materials, but is hardly applicable to heavy and noble metals. However, recent rapid progress in synchrotron radiation facilities enables the provision of databases of optical dielectric constants e(o, 0) for a wide range of materials. Even the dielectric function approach is complicated, because surface plasmons can be generated close to the surface, so the dielectric function should be a function of the depth in the material. Pijper and Kruit (1991) showed that surface plasmons play a significant role in SE emission. 4. Transport of Secondary Electrons Toward the Surface Now that we know the energy of the generated SE and its initial direction, we will track its transport in the target. The straight‐line‐approximation (SLA) model is a very simple transport model, proposed by Chung and Everhart (1974). It assumes that after generation the SE moves in a straight line to the surface. It is further assumed that upon scattering in the electron gas of the solid the scattered SE is absorbed completely and not counted anymore. This assumption is realistic for low‐energy SE, but as the energy of the excited electron increases, the assumption becomes more approximative.

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In the SLA, the absorption effect of the target via scattering by the lattice and energy losses in collisions with conduction electrons is quantified by p(E, z0), the probability that an SE of energy E, generated at depth z0, moving in a direction , will reach the surface unscattered (Figure 73): pðE; z0 Þ ¼ exp

z0 : linel ðEÞcosy

ð73Þ

This is the so‐called exponential decay. A compromise approach can be used to improve this approximation, if we assume that SEs scatter only elastically until the surface is reached, resembling a diffusion‐like transport (Figure 74). In reality, the exponential decay is the statistical result of a cascade process. The SLA can be improved using a more complete model, which takes into account the cascades produced by the internal SEs on their way to the surface. This way, we are getting closer to the complete scheme proposed in the beginning of Section III.E. In fact, the scattering of excited SEs does not result in absorption of all of these SEs. Secondary electrons generate cascade multiplications (Figure 75). These cascades become important for low‐energy internal SE (<100 eV).

FIGURE 73. In the SLA, the secondary electron propagates linearly toward the surface.

FIGURE 74. The SEs scatter elastically on their way to the surface.

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FIGURE 75. The cascade multiplication of secondary electrons in the target.

A classical cascade model was proposed by Koshikawa and Shimizu (1974) and was later used by almost all authors. This model is based on the classical binary collision approximation. It assumes that the scattered SE suffers an inelastic collision with the target atom and thus two SEs are generated: the old one, with energy E0 and the new one, with energy E00 According to this model, which neglects the binding energy of the atomic electron, the energy of the incident electron after collision is: E 0 ¼ Ecos2 ðy0 Þ;

ð74Þ

where 0 is the old electron scattering angle (see Figure 76). On the other hand, assuming spherical symmetric scattering in the center of mass system, Wolff (1954) showed that the average electron energy after scattering E0 is related to the electron energy before scattering E as follows: pﬃﬃﬃﬃ E0 ¼ E R ð75Þ where R is a uniform random number.

FIGURE 76. Illustration of a cascade multiplication.

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The energy loss then is DE ¼ E E 0 ¼ Eð1

pﬃﬃﬃﬃ RÞ

ð76Þ

From here we can determine the scattering angle of the old electron: rﬃﬃﬃﬃﬃﬃﬃ! rﬃﬃﬃﬃﬃ E0 DE y ¼ arccos ¼ arcsin E E 0

ð77Þ

The energy of the new electron is E00 ¼ DE þ EF and the scattering angle of the new electron then is: rﬃﬃﬃﬃﬃﬃﬃ! rﬃﬃﬃﬃﬃ E0 DE y ¼ arcsin ¼ arccos E E 00

ð78Þ

5. Escape of Secondary Electrons into Vacuum Once it has arrived at the surface, in order to escape into the vacuum the SE has to overcome the surface barrier, that is, E > EF þ W

ð79Þ

Therefore, the angle of incidence with the surface must be lower than a critical value so that the electron is not reflected back into the specimen. The probability for an SE with energy E at the surface to be transmitted into the vacuum is (Luo and Joy, 1990; Luo et al., 1987): rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ rﬃﬃﬃﬃﬃﬃ EF þ W U0 TðEÞ ¼ 1 ¼1 : E E

ð80Þ

In metals, most of the excited electrons cannot escape since they have energies lower than the work function. For large‐gap insulators nearly all excited electrons can escape into vacuum since they have energies higher than the vacuum level in accordance with the energy band theory. The surface barrier is important to obtain the correct absolute SE yield. According to calculations for SEs with energies <50 eV the average T(E ) ¼ 0.1 and the reflection coefficient at the metal‐vacuum interface is 0.9 (Luo and Joy, 1990; Luo et al., 1987). The energy of SEs is considered relative to the bottom of the conduction band. The energy of PEs is calculated with respect to the vacuum level. Each time an SE escapes into vacuum, its energy is reduced with EF þ W.

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F. Compilation of Secondary Electron Emission Data Relevant for EBID Resolution One of our main objectives is to theoretically estimate the role of SEs in the EBID spatial resolution. During the past years much theoretical work has been done to simulate the SE emission from a target bombarded with an electron beam. From this enormous sea of information, we needed to extract a number of systematic results, which could serve as a reliable reference and guidance for future work. The relevant results should concern the spatial resolution and the energy and angular distributions of SEs. A compilation of the results concerning the resolution in SEM imaging, resist‐based EBL, and EBID are presented. When necessary we also present results obtained using other methods than MC (Monte Carlo) simulation (e.g., analytical approaches). 1. Results from SEM Imaging Analysis The theoretical estimation of the imaging resolution in a SEM can be defined by referring to a certain spatial distribution of SEs. We consider it very important to specify relative to which profile this is defined. The most popular way to define the SEM spatial resolution is by using the FWHM of the SE radial distribution I(r) obtained as response to the primary beam. In case this beam is zero‐dimensional, the delta function response will define the ultimate SEM resolution. The drawback of this definition is that for the zero‐diameter beam used in MC simulations the width of the I(r) peak depends on the choice of the step dr (Kotera, 1989). However, for a 2D beam with Gaussian distribution, the convolution between the delta response and the beam profile yields a more realistic distribution, and then FWHM can be better defined. For example, Kotera (1989) has presented the MC results convolved with a Gaussian beam of 0.1 nm diameter, while Allen et al. (1988) and Kunz et al. (1987) have done the same with a beam of 100 nm. In cases where the I(r) profile is very narrow in the center and has wide tails, the peak contains only a small percentage of the total number of emitted SEs. In this case, another approach becomes more realistic, which defines the resolution by the FW50% of the integral of the radial intensity distribution (i.e., the diameter of the circle that contains 50% of all emitted SEs). In our opinion, this definition is also more suitable for material deposition characterization. To determine the FW50%, we need the normalized integral function of the radial density distribution—the number of SEs emitted inside a circle of radius r, NS(r). Many authors observed that for the SE emission the FW50% is usually larger than the FWHM, for example, 3–4 nm instead of 0.8 nm for gold targets (Ding and Shimizu, 1989).

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When scanning along a line, a common situation in SEM imaging, the lateral distribution is more important due to the emphasis on the change of information along a special direction and its relation to the practical contrast. Some authors believe that the lateral distribution of SEs on the surface in practice determines the ultimate resolving power of the SEM. The FWHM of the lateral distribution is larger than that of the radial distribution, for example, 0.423 nm versus 0.157 nm for copper targets (Kotera, 1989). Using an analytical approach, Wells and Boyde (1974) concluded that half the FWHM of I(r) for a zero‐diameter beam is of the order of the average electron IMFP in the target material. Using MC calculations, Shimizu and Murata (1971) pointed out that the ultimate resolution of SEM was restricted by the IMFP. The results of a simple diffusion calculation (Everhart and Chung, 1972) and another MCSE in cascade processes (Koshikawa and Shimizu, 1974) agreed with this observation. Koshikawa and Shimizu (1974) obtained a value of 1 nm for the FWHM of the SE lateral distribution for copper targets. Shimizu and Murata (1971) calculated the lateral distributions for copper and aluminum using a very simple model. The conclusion was that BSEs have a low contribution to the lateral distribution. The FWHM of the lateral distribution of SEs is almost completely determined by the yield due to PEs and depends on the IMFP of the target material. The values of IMFP as given by Seah and Dench (1979) and calculated and tabulated by Powell (1984, 1989) and Powell and Jablonski (1999a,b, 2000) vary between 0.5 nm and 2 nm for metals and are several times larger for insulating materials. From optical design, the minimum probe size in SEM has been predicted to be 0.6 nm. Taking into account this probe size, the general consensus could be that the ultimate resolution of SEM is 1–2 nm. However, it has been shown experimentally that an edge‐to‐edge resolution of 0.8 nm can be obtained (Ding and Shimizu, 1989). Ding and Shimizu showed that the edge‐to‐edge resolution can extend beyond the ultimate resolution of 1–2 nm by image processing and improvement of the signal‐to‐noise ratio in the edge image. Ding and Shimizu (1989) simulated the scattering of 10 keV and 30 keV electrons incident on a 10 nm gold substrate on the edge of the specimen. The I(r) and NS(r) curves were similar to the simple calculation made earlier by Everhart and Chung (1972). The FWHM of I(r) provides an estimation of the resolution of 0.8 nm. However, because only 8% of the SE current is contained in this FWHM peak, a more reasonable radial resolution is recommended, the FW50%, estimated to be 3.4 nm for 30 keV and 4.4 nm for 10 keV electrons. The FWHM of the lateral distribution is 2.2 nm. Joy (1984a,b) implemented the FSE model with no tertiary electrons considered. The calculated FWHM of the FSE spatial distribution (not clear whether radial or lateral) is 2–3 nm for copper and carbon targets bombarded by a pinpoint electron beam of 20–30 keV. Joy’s general conclusion

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is that the spatial extent of FSE is 2–3 nm for a 20 kV electron beam irradiating a metal target. Kotera (1989) and Kotera et al. (1989) used a hybrid model, which divides the internal SEs into fast and slow electrons, according to their initial energy. They neglected the plasmons and the Auger electrons. The fast electrons (>100 eV) were treated with the single‐scattering model and the slow SEs (<100 eV) were treated including their cascades. The treatment of cascades and the calculation of the IMFP were done following the model of Koshikawa and Shimizu (1974). Later Kotera et al. (1990) also included the plasmons and Auger electron excitation mechanisms. They presented the lateral distribution for copper and alumina in the 0–10 nm range and in the radial distribution in the 0–0.5 nm range. For example (Kotera, 1989), for a 10 kV and 0.1 nm diameter primary beam on a copper target, the FWHM of the SE radial distribution is 0.157 nm. The FWHM of the SE lateral distribution is larger, 0.423 nm for a 10 kV beam on copper. We believe that the result is so small compared with the results of Joy (1984a,b) because the cascades of SEs were included. Luo and Joy (1990) also considered the SE cascades and the core electron excitations, but to our knowledge did not present the spatial distributions, so we cannot compare those with the case when the cascades were neglected. It can be concluded that when the multiplication cascades are also included, a sharper SE spatial distribution is obtained. This is an encouraging result. 2. Results from Resist‐Based Electron Beam Lithography Murata et al. (1981) used MC simulations to determine the resolution in PMMA resist‐based EBL. In this type of application, the spatial distribution of the energy dissipation in the resist is the most important quantity. The slow electrons are not very important, because they cannot travel far from the incidence point. Interesting are the fast electrons with keV energy and their effect on the spatial resolution of energy deposition in the polymer film, because FSEs travel almost perpendicular to the path of the PEs. The SEs they generate can create a spatial spread of the exposed area of the resist. The contribution of SEs to the energy deposition will be dominant on the surface. Joy (1983) also calculated the role of FSE in resist exposure. The resolution limits in lithography are given by the absorbed energy profiles in the PMMA resist. The values predicted by MC simulations for the line width using a threshold model are in excellent agreement with the results of Broers (1988) and show that a fundamental limit exists to this type of lithography. It is determined by the inelastic scattering of electrons in the substrate and the sensitivity of the resist to exposure to low‐energy electrons.

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Samoto and Shimizu (1983) developed MC simulations of SE emission for the theoretical study of the ultimate resolution in EBL. They calculated energy dissipation profiles in PMMA resist. Their calculations showed that blurring due to SEs at the surface of PMMA resist on a silicon substrate is of the order of 10 nm for a 20 keV electron beam. 3. Results from EBID Studies Very few attempts to use MCSE emission in EBID studies have been undertaken until now. Allen et al. (1988) used an approach very similar to the one we follow. Their application is the selective deposition of iron from an Fe(CO)5 precursor using a low‐energy electron beam. They have written an MCSE emission from the target surface in case of a primary beam with an energy ranging from 250 eV to 2 keV. They used the elastic Mott cross section for the low‐energy electrons and the Streitwolf excitation function for the treatment of the electron inelastic scattering. The cascades of SEs were modeled with the classical binary collision approximation. They calculated the BSE and SE yield per unit area and the SE flux as a function of the radial distance. They also applied these simulations for deposition but did not couple the MC results to the dissociation cross section of the iron pentacarbonyl precursor. For a different purpose but also in an EBID study, Weber (1994) performed MC simulations of electron scattering in tip structures grown by EBID to investigate whether electron‐induced tip heating can explain the growth. Weber used the Rutherford cross section for the elastic scattering and the dielectric‐function approach for IMFP determination, but the isotropic approximation for the calculation of angles in inelastic scattering. G. Relevant Interactions Between Electrons and Gaseous Precursors 1. Introduction An important step in the understanding of EBID is to develop an appreciation of the electronic structure and bonding of the precursor molecules and knowledge of the principles of electron beam–induced surface chemistry of these molecules. In addition to being a central problem in the understanding of EBID, the electron‐gas interaction is also important for other fields, such as astrophysics, plasma‐assisted microtechnology, and ESEM. Electron impact phenomena play a major role in two naturally occurring atmospheric phenomena, viz. the SE emission in the earth’s ionosphere and the auroral emissions in the earth’s polar atmosphere. Here is where abundant information can be found.

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During the EBID process, the precursor molecules adsorbed on the target are exposed to a ‘‘shower’’ of electrons: the monoenergetic PEs, with high energies (40–200 kV), and the SEs emerging from the surface, with a whole spectrum of energies peaking at low values (2–5 eV). These electrons can stimulate many processes in the adsorbed molecular layer, such as molecular excitation, dissociation, and ionization, and also surface processes such as desorption, adsorption, and migration. We focus only on the interactions between electrons and gas molecules that might be interesting for the EBID spatial resolution. Data of the electron impact dissociation cross section versus the electron kinetic energy are needed to estimate the role of SE and PE in the deposition. Knowledge of the electron energy loss during the interaction with gas molecules is also necessary for the estimation of the localization of the energy transfer. Because the behavior under electron irradiation is different for each species, and because the existing experimental data are so vast and diverse, we focus gradually on precursors relevant for EBID, following the path: gases in general ! organometallic complexes ! metal carbonyls ! tungsten hexacarbonyl. A first example of electron impact data available in literature is given for the hydrogen molecule H2. This molecule is of minor relevance for EBID, but it is the simplest and the most frequently studied molecule, with an almost complete set of data available. Because of the similarities between the EBID process and specimen contamination in electron microscopy, special attention is given to hydrocarbon complexes CxHy, which are easy to find in the microscope vacuum systems. Further, some information about organometallic precursors is given. 2. Electronic Structure and Energy States of Atoms and Molecules Although atoms are composed of three types of subatomic particles—protons, neutrons, and electrons—the chemical behavior of the atom is governed only by the behavior of the electrons. In the case of a one‐electron atom or the so‐ called hydrogen‐like atom, the Schro¨dinger wave equation for the electron is: Hc ¼ Ec;

ð81Þ

where H ¼ the Hamiltonian operator and E ¼ the energy of the electron. The solution of the equation is the wave function c, and its characteristics are essential for an understanding of the chemical bonding. The characteristics of the wave function c are as follows: 1. It describes the probable location of electrons; it is not capable of predicting exactly where an electron is at a given time. 2. For any atom there are more solutions to the wave equation. Each solution (wave function) describes the motion of an electron in an orbital of the atom.

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3. c is a mathematical description of a region of space (an atomic orbital) that can be occupied by up to two electrons. 4. The square of the wave function, c2, evaluated for a given set of coordinates (x,y,z) is a direct measure of the probability density of the electron in that point (the probability that an electron will be at that point). 5. The mathematical expression of c incorporates quantum numbers that are related to the size, energy, and shape of atomic orbitals (Table 5). An electron bonded in an atom has the states noted by s, p, d, f according to the angular momentum number l, as follows: l ¼ 0 ! s (ground state), l ¼ 1 ! p , l ¼ 2 ! d, l ¼ 3! f. The symbols stand for sharp, principal, diffused, and fundamental, referring to the order of appearance in the spectrum. In a many‐electron atom, the Schro¨dinger equation can be set up but it cannot be evaluated exactly. In a first approximation, each electron is assigned a set of quantum numbers. However, there is a strong interaction between the electrons so that this approximation is not realistic. The interactions are not easy to describe, but the behavior of real atoms can be approximated with a situation called the LS or Russell‐Saunders coupling scheme. The LS coupling scheme uses two quantum numbers: L, the total orbital angular momentum of all the electrons, and S, the total spin angular momentum of all the electrons. Two electrons can interact by coupling their angular momenta l and their spins s, giving the total L and S for the configuration. Because of electron‐electron repulsion in many‐electron atoms, it is possible that one electronic configuration (L,S) results in several atomic energy states, or terms. The most convenient classification of atomic energy states is in terms of L, S, and J, where J is defined as the total angular momentum and can take all values J ¼ L þ S, L þ S 1, . . ., |L S|, in total 2S þ 1 different values. In this way, one electron configuration (L,S) can yield 2S þ 1 different energy states (terms). The value 2S þ 1 is called the multiplicity of the term. Each energy state can be assigned a term symbol: multiplicity state J or 2Sþ1 state LþS, LþS1, LþS2, . . . TABLE 5 QUANTUM NUMBERS OF THE ELECTRON IN THE HYDROGEN‐LIKE ATOM Symbol

Name

Possible values

Description

n l ml ms

Principal Angular momentum Magnetic Spin

1, 2, 3, . . .7 0, 1, 2, 3 0, 1, 2 ½, –½

Size and energy of orbitals Shape of orbitals Orientation of orbital Electron spin in orbital

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The atomic states notation employs capital letters S, P, D, corresponding to the total electronic orbital angular momentum quantum number L: L ¼ 0123456 SPDFGHI

This notation agrees with the corresponding lower‐case letters that are used to designate the quantum number l, the angular momentum of electrons in individual orbitals. Molecules are formed when more atoms are bonded together. Even for a diatomic molecule the Schro¨dinger equation cannot be solved analytically. To overcome this difficulty, the Born‐Oppenheimer approximation is usually used. The nuclei are considered static and the equation is solved only for the electrons. Different arrangements of the nuclei may be adopted and then the calculations are repeated. Thus an approximate solution of the wave equation for a molecule can be obtained by solving the wave equation for the electrons alone, with the nuclei held in a fixed configuration. The set of solutions allows building the molecular potential energy curve for a diatomic molecule. The Born‐Oppenheimer approximation is reliable for ground electronic states but becomes less reliable for excited states. The electronic structure and binding in molecules can be calculated by molecular quantum mechanics, which tries to solve the Schro¨dinger equation for the electrons in a molecule. All the techniques applied in solving this equation make heavy use of computers. There are two main approaches. In ab initio calculations, a model is chosen for the electron wave function and the calculations are made based only on fundamental constants and atomic numbers of nuclei. The model tries to predict the properties of atomic and molecular systems. Examples of ab initio methods are the self‐consistent field (SCF) method, the density functional theory (DFT), the Møller‐Plesset perturbation theory (MPPT), and the self‐consistent field Xa‐Dirac scattered‐wave (DSW) molecular orbital method. For large molecules accurate ab initio calculations are computationally expensive and semi‐empirical methods have been developed in an attempt to treat a larger number of chemical species. A semi‐ empirical method makes use of a simplified form for the Hamiltonian as well as adjustable parameters with values obtained from experimental data. Examples of semi‐empirical methods are the Hu¨ckel molecular orbital theory (HMO) and the Pariser‐Parr‐Pole method (PPP). In both cases, it is a challenging task to compute chemically accurate energies, that is, energies calculated within about 0.01 eV of the exact values (Atkins and Friedman, 1997). Sophisticated software packages have been developed over the past three decades to perform electronic‐structure calculations using the existing ab initio and semi‐empirical methods. These packages are widely available and are becoming increasingly easy to use. Some of the packages are

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commercially available like Gaussian (Foresman and Frisch, 1996; Frisch and Frisch, 1998), GAMESS, CADPAC, and MOPAC; others are used in only one research group, like ADF, the Amsterdam density functional program. 3. Mechanisms of Electron Beam–Induced Molecular Degradation An energetic electron passing through a volume of gas molecules loses most of its energy through excitations and ionizations of these molecules. The interaction between an electron e and a molecule AB can generate one of the following molecular reactions: Excitation (electronic, vibrational, rotational): e þ AB ! ðABÞ þ e Dissociative electron attachment (DEA): e þ AB ! ðABÞ ! A þ B Dissociation into neutrals: e þ AB ! A þ B þ e Dipolar dissociation (DD): e þ AB ! Aþ þ B þ e Ionization: e þ AB ! ðABÞþ þ 2e Dissociative ionization (DI): e þ AB ! A þ Bþ þ 2e Dissociative recombination: e þ ðABÞþ ! A þ B One of the most frequently encountered mechanisms for the electron impact dissociation is the electronic excitation of the molecule to a repulsive molecular state. However, in the region very close to the dissociation threshold, these states are hardly accessible. In this case, the resonance mechanism involving the formation of the negative‐ion state may be more important. The excited states can decay and result in dissociation of neutrals. If the energy of the electron is greater than a critical value, some molecules in the gas target will be ionized. As the energy of the electron beam increases, the abundance and variety of ionized species will increase. Some of the ionized molecules will dissociate if the electron energy is sufficiently large. Ionization can occur via several channels:

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single ionization, double ionization, multiple ionization, dissociative ionization, and ion pair formation. Here it is relevant that ionized molecules can later dissociate, through so‐called dissociative ionization. Dissociation can also occur when an already ionized molecule captures an electron and dissociates via recombination. In conclusion, there are many pathways possible for a molecule to dissociate under electron impact. The more complicated the molecule, the more pathways are possible. The main mechanisms for molecular dissociation under electron impact are as follows: Dipolar dissociation. DD is a nonresonant process. It occurs above the threshold energy and corresponds to the inelastic electron scattering process resulting in a molecular excitation followed by dissociation to both positive and negative ions. Dissociative ionization. DI involves dissociation via an ionized species. The dependence of the probability of this process on the electron kinetic energy does not have a maximum. Dissociative electron attachment. DEA is a resonant process that involves the formation of a negative ion due to electron capture and occurs when the excited state is dissociative in a particular vibrational coordinate. The DEA process is results from the transfer of an electron to an anti‐bonding s* orbital of the adsorbate molecule (i.e., an electron transfer between the substrate and the adsorbate). The DEA mechanism can be explained by the resonance theory (Srivastava, 1987). First, an electron attaches itself to the parent molecule and forms a temporarily molecular negative ion. Then this state either decays to the parent state (autoionization) or it dissociates into a stable negative ion and a neutral.

Within the energy range of SEs (0–20 eV), DEA and DI are believed to be the major processes leading to molecular dissociation. For higher impact energies, DD and DI mechanisms play the most important role. 4. Electron Energy Loss in Electron Interaction with Gas Molecules Let us suppose that an electron collides with an atom and excites it to an excited state at an excitation energy DE, measured from the ground state. The kinetic energy of the electron will be reduced with DE, which may be called the energy loss for the incident electron or the energy transfer to the target atom. The theoretical treatment of electron inelastic scattering with atoms and molecules can be conveniently classified into two types: those dealing with fast electrons and those dealing with slow ones. The criterion used in this classification is the mean orbital velocity of the electrons situated in the shell

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of the target atom that takes part in the interaction. The PEs in EBID can be considered as fast electrons and the SEs can be considered as slow electrons. a. The Fast Electrons. Fast incident electrons have velocities higher than the velocities of bound target electrons. Their influence on the target can be considered as a sudden and small external perturbation. The Bethe theory provides the general framework for discussing inelastic scattering of fast electrons. The theory was conceived for free atoms, but it can also be applied for solids. The Bethe theory uses the Born approximation. Inokuti (1971) gives a very detailed discussion. For fast incident electrons, the energy loss due to the target ionization and excitation represents the so‐called collision losses (Figure 77) and can be modeled using the CSDA and the Bethe stopping power. The relativistic Bethe stopping power is defined as the energy loss of the projectile per unit distance traveled (Knoll, 1979): 0 1 " qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ dE A 2pe4 NZ mv2 E 2 2 @ 2 1 b 1 þ b ln 2 ¼ ln dx 2I 2 ð1 b2 Þ ð4pe0 Þ2 mv2 c ð82Þ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ2 # 1 2 2 1 1b þ 1b þ ; 8 where b is the velocity of the PE divided by the velocity of light (¼ v/c) light, m is the rest mass of the electron, and I is the mean ionization or excitation potential of the absorber target. Electrons differ from other charged particles in that the energy may be lost by radiative processes as well as by Coulomb interactions. These radiative losses take the form of ‘‘bremsstrahlung.’’ The linear specific energy loss through this radiative process is (Knoll, 1979): dE NEZðZ þ 1Þe4 2E 4 ¼ 4 ln : ð83Þ dx r ð4pe0 Þ2 137m2 c4 mc2 3

FIGURE 77. Different pathways for an electron to lose energy in an interaction with a gas molecule.

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The radiative losses are most important for high electron energies and absorber materials of large atomic number. The ratio between the radiative and collision losses is EZ/700, where E is the electron energy in MeV. Radiative losses are only a small fraction of the collision losses. The total linear stopping power of the electron is the sum of its collision and radiative losses: dE dE dE ¼ þ : ð84Þ dx dx c dx r The most important nontrivial quantity in the Bethe stopping‐power equation is the mean excitation potential, I. It summarizes the properties of the target in terms of energies and oscillator strength of transitions, and is defined as X ln I ¼ fn ln En ; ð85Þ n

where fn is the oscillator strength of a transition from the ground state to a state of energy En. Its direct evaluation requires the knowledge of atomic wave functions for ground and excited states. Such direct calculations are feasible only for a few atoms with low Z. In the case of hydrogen, I ¼ 15 eV. Usually, the mean excitation potential is an experimentally determined parameter for each material. Ahlen (1980) gives a table with mean excitation potentials for many elements. For compound targets, the Bragg‐Kleeman rule can be used (with sometimes 10%–20% error), which assumes that the stopping power per atom is additive. The generalized oscillator strength fn, or GOS, is the central notion of the Bethe theory and is a function of both energy transfer and momentum transfer. The calculation of the GOS for many‐electron atoms is obstructed by the lack of sufficiently accurate wave functions. The oscillator strength for molecules has been calculated only in a few cases, like H2 and other diatomic molecules such as N2 ,O2, and CO. Another way to obtain the energy loss spectrum for the high‐energy primary beam is from photochemistry using the photoabsorbtion spectrum, because at such high energies only optically allowed transitions are possible, where the dipole approximation can be used. High‐energy electrons are ideal photon sources or pseudophotons. The total loss in inelastic scattering (the collision losses) can also be measured by EELS. b. The Slow Electrons. In the case of slow electrons incident on a molecule, the relative and absolute magnitude of each interaction process is different from that for the equivalent reactions produced by the fast PEs.

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The Bethe approximation is not valid, and the combined system of incoming electron and target must now be considered. The molecular orbitals are strongly perturbed by the slow electrons and forbidden transitions are favored, while phenomena such as electron resonance also occur. Electron resonance can lead to vibrational and electronic excitation and dissociative attachment. The impact of low‐energy electrons with gas molecules has been extensively treated by Sanche (1989, 1990, 1997). The experimental determination of the energy loss spectrum for slow electrons incident on molecular targets is much more difficult. The only solutions are theoretical calculations. In the case of He, the Bethe approximation is valid only for electron energies higher than 500 eV. The energy loss in helium for slow electrons has been calculated by Ashankar (1976, 1977) for energies from 50 eV up to 10 keV as the sum of ionization and excitation energy losses. At energies below the dissociation threshold, only dissociative attachment and elastic scattering are allowed. The SEs lose a considerable amount of their energy by exciting phonon modes and vibrational levels of individual molecules of the irradiated solid. DEA and DI are the major processes leading to dissociation. In some cases the SEs play only a minor role in molecular dissociative attachment, like in the case of cyclopropyl on copper. The peak is at 10 eV above the SE maximum energy (Martel and McBreen, 1997). c. The Fate of the Energy Lost by the Incident Electron. The equations presented until now can be used to determine the total energy lost by an electron during its inelastic scattering on a target molecule, DEtotal. But how is this energy divided over the molecule? Which energy fraction is lost by the electron for the dissociation of the molecule? This is a difficult problem. The solution starts from the fact that the total electron energy loss is the sum of the energy loss for molecular ionization and the energy loss for molecular excitation. A fraction of both losses eventually results in molecular dissociation. DEtotal ¼ DEioniz þ DEexcit

ð86Þ

The electron energy loss for ionization DEioniz is a quantity that can be obtained directly from a coincidence measurement between the electron energy loss spectrum and all ions produced. The electron energy loss for molecular ionization can be deduced indirectly from photoelectron spectra. However, the availability of such spectra is rather limited to spectra at a few selected photon energies, such as the resonance line of He‐I (or He‐II). In the photoelectron spectrum experiment, a photon of energy EHe ¼ 21.2 eV (He‐I resonance) is incident on the molecule, and the electron resulting from the molecular ionization is collected. The measured photoelectron spectrum is the probability P(EHe, E ) that the emitted electron has an energy E. The probability that a photon of arbitrary energy En will

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create an electron of energy E can be obtained from the helium resonance line photoelectron spectrum according to Meisels et al. (1972): PðEn ; EÞ ¼ PðEHe ; EÞ

. EnðE0

PðEHe ; EÞ dE;

ð87Þ

E¼0

where E0 is the onset energy for ionization. Another method to determine the energy lost for ionization is by using the photoionization cross section of the gas molecule sioniz(En), a known quantity for many molecules: PðEn Þ ¼

Eðmax sioniz ðEn Þ . sioniz ðEn Þ dEn : En En

ð88Þ

I

In conclusion, there are a number of ways to determine the electron energy loss for molecular ionization. The energy lost for excitation DEexcit can then be determined as the difference between the total electron energy lost and the energy lost for ionization [Eq. (86)]. Figure 78 shows the curves for the impact of a 33 eV electron on a N2 molecule (Mi and Bonham, 1998). The energy losses in the excitation of molecular vibration and rotation are relatively small compared with the energy lost to electronic transitions. For

FIGURE 78. The total inelastic energy loss, the energy loss for ionization and their difference responsible for the excitation; 33 eV electron impact with N2 molecule. The dotted curve is the total inelastic scattering; the solid curve on the right is the ion coincidence data. The solid curve on the left is the difference between the former two curves and represents the contribution from the sum of neutral dissociation and excitation. Reused with permission from L. Mi (1998), J. Chem. Phys. 108, 1904. ß 1998, American Institute of Physics.

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the low‐energy SEs, most energy loss goes to vibrational excitation when the energy lies within the range of resonance. The energy loss for dissociation is much more difficult to estimate or measure. 5. Cross Sections for Electron‐Induced Molecular Degradation The results of electron collision experiments are usually expressed in terms of quantities called cross sections. They can be defined as a transition probability per unit time per unit target scatterer and per unit flux of the incident particles with respect to the target. Total cross sections have the dimensions of area. Since in atomic units (a.u.) the unit of length is the first Bohr radius a0, it is convenient to express the atomic cross sections in units of pa02 ¼ 2.801021 m2. Another unit is also frequently used, the barn; 1 barn ¼ 1024 cm2. A typical ionization cross section dependence on the electron energy is shown in Figure 79. a. The Cross Sections for Electron Impact Excitation of Molecular States sexcit. Electrons are very effective in molecular vibrational excitation, especially at low energies via a resonant mechanism. The largest cross section is for the electronic excitations associated with optically allowed transitions at intermediate energies. The value of the excitation cross section increases 5 e− on CH4

4

Rapp Orient Duric

s i (10−20 m2)

Schram BEB (Adiab.)

3

BEB (Vert.) 2

1

0 101

104 103 Electron energy E (eV) FIGURE 79. Example of the ionization cross section of methane during electron impact; energy range from 10 eV to 20 keV. Reused with permission from Y.‐K. Kim (1997). J. Chem. Phys. 106, 1026. ß 1997, AVS The Science & Technology Society. 102

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gradually with the impact energy from the threshold to 10 times the threshold energy and then slowly decreases at high energies. At low impact energies (within a few eV of the threshold value) the forbidden transitions dominate the energy loss spectra and represent an important cross section. The cross sections for spin‐forbidden processes rise steeply near the threshold, reach their maximum within a few eV from the threshold value, and then decrease sharply with increasing energy. Trajmar and Cartwright (1984) give summarized sources of experimental data. Most experimental work has been done on the N2 molecule. The motivation was the very important role of the eN2 process in a variety of atmospheric phenomena and the fact that the molecule is easy to handle experimentally. With the exception of N2, only fragmentary data exist for electron impact excitation of molecules. Theoretical models for electronic excitation by electrons are difficult to develop. The difficulty arises from computational problems associated with the accurate representation of many‐electron electronic and nuclear force fields experienced by the incident and the scattered electron. The Born‐ Oppenheimer approximations are better for high‐energy electrons. Most theoretical work has been done on the H2 molecule because of its simple electronic structure. b. The Cross‐Sections for Electron Impact Molecular Ionization sioniz. The electron impact ionization cross sections are needed in applications such as modeling of fusion plasmas in tokamaks; modeling of radiation effects for material and medical research; astrophysics research; and atomic, molecular, and plasma physics. There is more quantitative information about these cross sections than about the dissociation cross sections. Because of the great need for reasonable estimates of ionization cross sections and the present scarcity of accurate data, a number of empirical equations to calculate ionization cross sections have been published. During the past years, many equations have been reported for the ionization cross sections of the most popular molecular species. A set of such equations can be found in Younger and M€ark (1985). For fast electron collisions, the ionization cross section equation consists of two different factors, one involving the properties of the incoming electron and the other dealing with the properties of the target molecule (i.e., the GOS). This picture is used by the Born approximation and a general equation is given by Inokuti (1971): 4pa20 Ry 2 4ci E sioniz ¼ Mi ln ; ð89Þ Ry E where Mi2 and ci are constants related to the oscillator strength fn and Ry is the Rydberg energy (13.61 eV).

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For slow collisions, the combined system of incoming electron plus target molecule must be considered. Other equations (empirical, semi‐empirical, classical, and semi‐classical quantum mechanical) and summarized data sources can be found in M€ark (1984). We consider as most interesting a model for calculation of the electron impact ionization cross section of atoms and molecules, which is free from adjustable parameters, published by Kim et al. (1997). This model uses the binary‐encounter Bethe (BEB) model. It provides reliable electron impact ionization cross sections using very simple input data for the ground state, all of which can be obtained from standard molecular wave function codes. The model predicts the total ionization cross section as the sum of the ionization cross sections for ejecting one electron from each of the molecular orbitals. The equation is valid from the first ionization threshold up to several keV incident electron energies. The BEB model is a simpler version of the binary‐encounter dipole (BED) model for the electron impact ionization of atoms and molecules. The BED model combines the binary‐ encounter theory with the Bethe theory. At high energies, the two theories coincide. According to the BEB model, the total ionization cross section per molecular orbital is: 2 0 3 1 S lnt 1 1 ln t 4 @1 A þ 1 5 sioniz ðEÞ ¼ tþuþ1 2 t2 t tþ1 4pa20 NR2y E U with t ¼ ;u ¼ ; and S ¼ : Eb Eb Eb2

ð90Þ

N is the occupation number of the orbital, U is the kinetic energy of the orbital in the initial state, usually the ground state of the target, and Eb is the electron binding energy. U can be calculated by any molecular wave function software package. Kim et al. (1997) give the U, N, and Eb values for 11 atmospheric molecules determined by using the GAMESS package. The term associated with the first logarithm function represents the distant collisions at large impact parameter, dominated by the dipole interactions, and the rest of the terms on the right‐hand side represent the close collisions at small impact parameters. The summation over all orbitals gives the total ionization cross section. Figure 80 shows the cross section for ionization of methane, calculated using Eq. (90).

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FIGURE 80. The electron‐impact ionization cross section for CH4 calculated using Eq. (90).

c. Cross Sections for Electron‐Induced Molecular Dissociation sdiss. Dissociative processes play a major role in the physics and chemistry of planetary and cometary atmospheres and in many industrial applications using gaseous discharges or laser systems. A comprehensive set of accurate cross‐ section values is of great importance. Nearly complete cross‐section sets for major diatomic molecules and polyatomic molecules of planetary and cometary importance (H2, D2, O2, N2, NO, CO, CO2, and NH3) have been measured. The dissociation mechanisms depend on the impact energy and, in general, all the curves have the same shape, starting with a threshold followed by a maximum in the 10–100 eV range and a decay at high impact energies. Sometimes, however, the curve can have another form. The general dependence of the dissociation cross section on the energy of the incident electron can be written as (Hall et al., 1977): sdiss ðEÞ

K E ln ; E B

ð91Þ

where K and B are constants. Different equations have been constructed in the last years to facilitate the numerical calculations of dissociation cross sections for O2 and N2. For example, Zipf (1984) gives the following equation: b 4pa20 R2y fn ½1 ðW =EÞa 4EC þe ; ð92Þ ln sdiss ðEÞ ¼ W EW where Ry is the Rydberg energy, W is a parameter that influences the low‐ energy shape of the cross section and is usually close to the energy loss Wj

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associated with excitation of the j‐th state, fn is the optical oscillator strength, C is a factor determined from the high‐energy behavior of the cross section, e is the base of the natural logarithm, and a and b are adjustable parameters. d. The Dissociative Electron Attachment (sDEA) and the Dissociative Ionization (sDI) Cross Sections. Rigorous theoretical calculations of DI cross sections are not possible, except perhaps for molecular hydrogen. Experimentally more information is available. Parikh (1975) developed a theoretical model to calculate DI cross sections for diatomic molecules using the binary‐ encounter model. For DI, the threshold behavior is not too different from a power law dependence xy, where y ¼ 1.0 1.127 (Parikh, 1975). The magnitude of the DEA cross sections might be unknown, but the general form peaks over a very narrow energy region, as can be seen in Figure 81 for CF4. 6. Electron‐Molecular Impact Data Available from Literature In our EBID study, we are searching for electron impact data for possible gas precursors such as organometallic molecules or hydrocarbons. The data we need to know as accurately as possible are the dissociation cross section versus the electron energy sdiss(E ) and the electron energy loss invested in

FIGURE 81. Dissociative electron‐attachment cross section for CF4. Open circles: normalized total attachment cross section from single collision experiment; Solid line: swarm‐unfolded attachment cross section. Reproduced with permission from Christophorou et al. (1996).

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the molecular dissociation EELdiss(E ). Our conclusion after an extensive literature search is that there is only precarious information available about the electron impact properties of the gases we need. Nearly complete experimental and theoretical data exist only for H2, N2, CO, CH4, in general for the gases abundantly present in the interstellar medium and planetary atmospheres, and for some hydrocarbons (CxHy). Recently collections of recommended electron impact data have been published for the gases used in plasma processing in microengineering (e.g., carbon tetrafluoride, CF4; Christophorou et al., 1996). We present as a first example the most simple and extensively studied molecule, hydrogen, for which most data exist. Further, we have collected in a systematic manner all the information on electron impact we could find for some precursors used in EBID (hydrocarbons and organometallic complexes Mx(CO)y). a. The Hydrogen Molecule Under Electron Impact. A good example of the quantitative description of electron‐induced molecular dissociation is difficult to find because the information is far from complete for most molecules. Maybe the best example is the hydrogen molecule, the most simple gas molecule found in nature. Even for such a simple molecule, more than one dissociation path is possible, as can be seen from the potential energy diagram in Figure 82. Consider a H2 molecule that is initially in the ground state X1Sþ g . Under electron impact, the molecule can dissociate via two processes with different products: H2 ! H 2 ! Hð1sÞ þ Hð1sÞ

ð1Þ

H2 ! H 2 ! Hð1sÞ þ Hð2sÞ

ð2Þ

The excited state H*2 in process (1) can result via a direct excitation to the repulsive state b3Suþ (1a), but also via an excitation to a higher state (1b) followed by a cascade de‐excitation to the same repulsive state (1b0 ) . The 3 þ excited state in process (2) may be any of the four states B0 1Suþ, E1Sþ g , e Su , 3 þ a Sg , all of which are bound states. Dissociation results only from excitation to continuum levels of these states above the dissociation limit. The energy loss spectra of H2 in coincidence with the dissociation process (1) were measured by Odagiri et al. (1995). Despite being the simplest dissociation process, only a few theoretical calculations of high‐energy electron impact dissociative excitation cross sections from the ground state have been done until now. Chung et al. (1975) made the first steps with an ab initio calculation of the dissociation cross section of H2 under electron impact.

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FIGURE 82. Potential energy curves of H2 illustrating different mechanisms of dissociation under electron impact. Reprinted (Figure 1) with permission from S. Chung, C. C. Lin and E. T. P. Lee (1975). Phys. Rev. A 12, 1340–1349. ß 1975, by the American Physical Society.

Since then, efforts have been made to determine the electron impact dissociation cross section for the H2 molecule more accurately. At electron energies higher than 100 eV, the contribution due to the excitation via state B0 1Suþ accounts for more than 95% of the total dissociation. Liu and Hagstrom (1994) give a very accurately deduced equation for the dissociation cross section only for excitations to the state B0 1Suþ, process (2), resulting in the production of H(1s) and H(2s). They calculated the potential energy curves for both ground and excited states using the Le Roy method. The equation is valid for very high projectile energies, since it uses the Born‐Bethe approximation. Thus, the cross section for dissociation into neutrals from the excited states is: sdiss ¼

i 4pa20 h 0:0317 ln EðRy Þ þ 0:0006 ; EðRy Þ

ð93Þ

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where E(Ry) is the energy of the incident electron in Rydberg units (Ry ¼ 13.61 eV). The excitation cross section (dissociative and nondissociative) is: i 4pa20 h 0:1054 ln EðRy Þ þ 0:1461 sexcit ¼ ð94Þ EðRy Þ Using these equations, we calculated the electron impact dissociation and excitation dissociation cross‐sections for H2 versus the electron energy, as shown in Figure 83. The cross section of dissociation into neutrals resulting from excited states represents 20% of the total excitation (dissociative and nondissociative) cross section (Figure 84). An empirical equation for the ionization of the H2 molecule by a fast particle of velocity v is given by (Tilinin, 1986): sioniz ¼

4p v2 0:58 ln v2 0:046

ð95Þ

The binary‐encounter model developed by Kim and Rudd (1994) yields the electron impact ionization cross section for H2 shown in Figure 85. The ionization cross section for high impact energies has been calculated by Saksena et al. (1997) for electrons with 100 keV to 3 MeV kinetic energy for hydrogen and other molecules, as shown in Figure 86.

FIGURE 83. The electron‐impact dissociation (solid line) and excitation (dashed line) cross sections for H2.

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FIGURE 84. The ratio between the electron‐impact dissociation and total excitation cross section for H2.

FIGURE 85. Electron‐impact ionization cross section for H2. Reprinted (Figure 7) with permission from Y. K. Kim and Rudd M. E. (1994). Phys. Rev. A 50, 3954–3967. ß 1994, by the American Physical Society.

Process (1) is considered to be a direct scattering process, pictured schematically as: e þ H2 ðX1 Sgþ ; v ¼ 0Þ ! e þ H2 ðb3 Sgþ Þ ! e þ Hð1sÞ þ Hð1sÞ The threshold energy for this process is approximately 8 eV and the cross section is of the order of 1021 m2. Significant cross sections for dissociation

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FIGURE 86. Electron‐impact ionization cross section for H2, N2, O2, and H2O in the energy range of 0.1 to 3 MeV. Reprinted from Saksena et al. (1997). ß 1997, with permission from Elsevier.

at lower impact energies are not observed experimentally under normal laboratory conditions. A new effect is observed due to resonant scattering—an enhancement of dissociation caused by trapping of an electron in a temporary anion state of H2. More dissociation resonant channels are opened due to the temporary excitation of the two lowest lying resonant 2 þ 2 þ anion states of H 2 : X Su ,B Sg . b. The Hydrocarbon Complexes CxHy Under Electron Impact. We have collected information about the electron impact–induced degradation of hydrocarbon molecules of importance for the study of contamination in

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electron microscopy. Usually the absolute total dissociation cross sections are virtually unknown. Partial dissociation cross sections can be measured experimentally by detecting the fragments. The difficulty consists in measuring the number of neutral fragments created in electron‐molecule collisions. Using the experimental data, and, eventually scaling algorithms, extensions to other similar gases can be theoretically obtained. The electron impact–induced molecular dissociation of hydrocarbons plays an important role not only in contamination growth studies but also in plasma, atmospheric, interstellar, and radiation chemistry. Recently cross‐ section sets for different gases necessary in industrial applications have been published. A very systematic and complete set of electron impact data can be found in a review article on CF4 by Christophorou et al. (1996). CF4 is one of the most widely used feed‐gas components in plasma‐assisted material processing applications. Unfortunately, CF4 is also a greenhouse gas with a high global warming potential. To assess the behavior of this gas in the atmosphere and in many applications, especially in the semiconductor industry, it is necessary to have accurate basic information on its fundamental properties and reactions. Christophorou et al. (1996) have assessed and synthesized the available information on the cross sections and rate coefficients for collisional interactions of CF4 with electrons. We can follow the same division to arrange the data we found about other precursors of interest. For the case of hydrocarbons, we believe the general empiric equations proposed by Alman et al. (2000) for the electron impact ionization and dissociation cross sections of 16 hydrocarbon molecules are useful. Based on the experimental electron impact data for simple hydrocarbons, Alman et al. have presented a general equation that allows extension to heavier hydrocarbons. The electron impact ionization cross section sioniz(E ) versus the electron kinetic energy E is: 8 0; E <1Eth > 0 > > > > > ðEmax EÞ2 A > > ; Eth < E < Emax < smax @1 ðEmax Eth Þ2 sioniz ðEÞ ¼ ; 0 1 > > > > E Emax A > > ; E Emax smax exp@ > > : l

ð96Þ

where Eth is the threshold energy for ionization, Emax is the energy where the cross section peaks, smax is the maximum value achieved by the cross section, and l is a constant that determines the rate of decay of the cross‐ section beyond Emax. Emax does not vary much from molecule to molecule and a value of Emax between 70 eV and 90 eV is considered reasonable.

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A relation for Emax is given for each hydrocarbon, using the number of H and C atoms in the molecule: Emax ¼ 7:71C þ 1:31H þ 67:0 ½eV:

ð97Þ

The maximum cross section shows a more definite dependence on the C and H number in the molecule. The fit relationship is: smax ¼ ð2:36C þ 0:413H 0:631Þ102 ½nm2 :

ð98Þ

The decay constant l increases with the number of C and H atoms in the molecule. The recommended approximative fit relation is: l ¼ 64:3739C þ 35:3963H þ 668:358½eV:

ð99Þ

Alman et al. (2000) have published tables with values for Eth, Emax, and l for a series of hydrocarbons. In the case of electron impact dissociation, the measured data are available only for the CHy family. This information is used to extrapolate to heavier hydrocarbons. The shape of the curve for electron impact dissociation is the same as that for electron impact ionization. The same functional form can be used to describe the cross‐section curve in terms of the four parameters Eth, Emax, smax, and l: 8 0; E <1Eth > 0 > > > > > ðEmax EÞ2 A > > smax @1 ; Eth < E < Emax < ðEmax Eth Þ2 ð100Þ sdiss ðEÞ ¼ ; 0 1 > > > > E Emax A > > ; E Emax smax exp@ > > : l where Eth, Emax, smax, and l are the same parameters as in Eq. (96) but now for dissociation. The threshold energy for dissociation is always 10 eV. The same graph shape as for methane is obtained, but the graph is scaled up or down with different values of smax. The maximum is 80% of the ionization cross‐section maximum. smax ¼ ð1:89C þ 0:330H 0:505Þ 102 ½nm2

ð101Þ

Values for Emax and l are given by Alman et al. (2000) for many dissociation channels. For instance, for C2H5 ! C2 þ H4 þ H: Emax ¼ 25 eV and l ¼ 77 eV; for C2H5 ! C2 þ H3 þ 2H: Emax ¼ 18 eV and l ¼ 11.4 eV. In the vacuum system of an electron microscope the following hydrocarbon molecules can be found: C2H5, C3H7, and C4H5 (Yoshimura et al., 1983). By using the values from Alman et al. (2000) and the above scaling rules for smax we obtained curves for the ionization and dissociation cross sections as a function of the electron energy for C2H5 in the gas phase (Figure 87).

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FIGURE 87. The electron‐impact ionization (solid line) and dissociation (dashed line) cross sections versus the electron energy for C2H5.

c. Organometallic Compounds Under Electron Impact. Because the main application of EBID is expected to be in the IC industry, where deposition of conductive material is required, a basic condition for the chosen precursor molecule is to contain metal atoms. This is why organometallic complexes are widely used in EBID. Metallic complexes in general are molecules containing metal atoms and ligands. If the molecule contains a carbon‐metal bond, it is called an organometallic compound. Depending on the ligand, the molecule has specific names, such as carbonyl if the ligand is CO. Examination of the interactions between metal orbitals and orbitals of the ligand can provide valuable insight in how organometallic molecules form and react. Several books have been published on organometallic chemistry and photochemistry (Geoffroy and Wrighton, 1979; Lukehart, 1985; Spessard and Miessler, 1997). The commonly known carbonyls of transition metals are six‐coordinate octahedral complexes M(CO)6, where M ¼ Cr, Mo, or W (Figure 88 and Table 6). This geometry has been confirmed by X‐ray and electron diffraction studies. These studies also confirmed the linearity of the M–C¼O chain. The electronic structure and geometry of hexacarbonyls M(CO)6 have been measured or calculated using software packages by many authors. Measurements of the electronic structure have been performed by electron and X‐ray diffraction (Beach and Gray, 1968; Brockway et al., 1938). Calculations have been made using the Dirac scattered‐wave (DSW) method (Arratia‐Perez and Yang, 1985), density functional theory (DFT), Møller‐ Plesset second‐order perturbation theory (Jonas and Thiel, 1995), and DFT with relativistic corrections (Rosa et al., 1999). Electron impact dissociation cross‐sections are practically unknown for organometallic complexes.

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FIGURE 88. The geometry of a transition‐metal hexacarbonyl molecule M(CO)6.

TABLE 6 GEOMETRY OF METAL HEXACARBONYL MOLECULES

No. of terminally bonded CO Terminal distance M2 2C (nm) Terminal distance C2 2O (nm) Terminal M2 2C2 2O angle (degrees)

W(CO)6

Mo(CO)6

Cr(CO)6

Fe(CO)5

Ni(CO)4

6 0.2049–0.207 0.116 180

6 0.206 0.1156–0.1164 180

6 0.192 0.117 180

5 0.183 0.115 —

4 0.182 0.115 —

H. Relevant Surface Processes 1. Adsorption Gas molecules strike the surface from an arbitrary direction. Some are reflected back by elastic collisions. Others undergo inelastic collisions, thus binding to the surface for a period of time. The molecules encounter an attractive potential that ultimately will bind them to the surface under proper circumstances and trap them in a potential barrier. This phenomenon is called adsorption. The length of time the molecules stay on the surface depends on factors such as the type of surface and molecule, the temperature of the surface, and so on. Once the molecule is bonded to the surface, its mobility across the surface depends on interaction of the adsorbed molecule with the surface and with other adsorbed molecules. The resultant adsorbed layer, the density of which depends on the pressure, is usually treated as a monolayer. Even at high pressures the adsorbed material may be no more than a few atomic layers.

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Adsorption is likely to occur if the incident atom or molecule has a kinetic energy that is smaller than the well depth of the attractive surface potential. An atom with higher kinetic energy may first be trapped in the surface potential and then slide along the surface before desorbing again into the gas phase, since it has enough kinetic energy left to escape. Adsorption is an exothermic process. The enthalpy of adsorption, DHads has a negative sign, the heat of adsorption, DHads is positive. The residence time t of an adsorbed atom is given by: DHads t ¼ t0 exp ; ð102Þ RT where t0 is correlated with the surface‐atom vibration times of the order of 1013 to 1012 s, T is the temperature, and R is the gas constant. It is customary to distinguish two classes of adsorption, namely physical adsorption (or physisorption) and chemical adsorption (chemisorption). The physisorption equilibrium is very rapidly attained and is reversible. The adsorbate‐surface interaction is termed weak if it leads to heats of adsorption of less than 40 kJ/mol. Then the adsorbate‐adsorbate and adsorbate‐ surface interactions are of the same order of magnitude. If the residence time is several vibration periods, it becomes reasonable to consider that adsorption occurs. The equilibrium surface concentration of adsorbed atoms and molecules is achieved through surface diffusion. 2. Surface Diffusion of Precursor Molecules The role of surface diffusion in specimen contamination under electron bombardment has been emphasized by Amman et al. (1996), Hart et al. (1970), Mu¨ller (1971a,b), Reimer and W€ achter (1978), and Wall (1980). A simple proof that surface diffusion plays a role in contamination is the deposition of a dot inside and outside a labyrinth frame. The height of the dot, and therefore the amount of contamination, decreases with the number of frame walls (Amman et al., 1996). The crucial parameters are the surface density of precursor molecules n and the diffusion constant Ds. Let us consider the irradiation of a substrate by a pulsed electron beam and a delay time td between two successive exposures. Because the molecules are continuously cross‐linked during one exposure, the density of molecules on the surface is out of equilibrium, with a minimum in the irradiated area. To regain the equilibrium density, the hydrocarbons must be transported from outside into the irradiated area, down the density gradient. The molecules can arrive in the vicinity of the irradiation area by two mechanisms: over the specimen surface by diffusion, or from the vacuum. If it is assumed that there is sufficiently low vacuum, then only surface diffusion is important.

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A finite time is needed for the molecules to reach the interaction place and replenish the irradiated area, tfill. This time is dictated by the mechanism of contaminant transport across the surface. The cross‐sectional profile of the deposited structure depends on the relation between td and tfill. If the delay time between two successive exposures is shorter than the time necessary for the molecules to travel from the source to the place of electron impact, then the zone is completely depleted of molecules and crater‐type dots are grown (Figure 89) (Amman et al., 1996). If the delay time is large enough, then the growth is proportional to the exposure. The peak height in the center of the irradiated area decreases with decreasing delay time. This simple model has been proved experimentally. The surface density n(x, t) of mobile hydrocarbon molecules at time t and distance x from the center of the irradiated area can be described by the following diffusion equation: @nðx; tÞ ¼ Ds r2 nðx; tÞ: @t

ð103Þ

Given the distribution after a particular exposure n(x, t ¼ 0), the distribution at the start of the second exposure can be determined by solving Eq. (103). For a dot geometry, appropriate initial conditions are: nr if 0 < r < d nðr; t ¼ 0Þ ¼ : ð104Þ n0 if r > d The time dependence of the density in the center of the beam can be calculated as the solution of the diffusion Eq. (103) assuming the initial conditions of Eq. (104): d2 nðr ¼ 0; t ¼ td Þ ¼ nr þ ðn0 nr Þexp ; ð105Þ 4Ds td where 2d is the effective size of the exposed circular region and polar coordinates x ¼ (r, ) have been used. The solution can be plotted as a function of the dimensionless delay time 4Dstd/d2 (Figure 90). By comparing this curve with an experimental curve obtained by examining contamination dots grown with different delay times, Amman et al. (1996) obtained a value of 3 s for the diffusion time parameter d2/4Ds on a GaAs substrate for a beam of 40 keV and a current of 100 nA. Mu¨ller (1971a,b) assumed that surface diffusion of molecules toward the irradiated area is the main mechanism of contamination. He calculated the dependence of the contamination rate on the beam diameter and current density and explained the crater formations.

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FIGURE 89. AFM images and cross‐sectional profiles of electron beam written contamination lines using various delay times: (a)(d) decreasing delay time, (e) cross‐sectional profile of the lines ad. Reused with permission from M. Amman (1996). J. Vacuum Sci. Technol. B, 14, 54. ß 1996, AVS The Science & Technology Society.

The steady‐state rate of transport of molecules diffusing from a source of radius re to a sink of radius r0 can be determined as (Figure 91): dn 2pDs n0 ¼ ; dt ln rr0e where dn/dt is the number of molecules reaching r0 per unit time.

ð106Þ

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FIGURE 90. Normalized carbon surface density plotted as a function of the dimensionless delay time for the dot geometry. Reused with permission from M. Amman (1996). J. Vacuum Sci. Technol. B, 14, 54. ß 1996, AVS The Science & Technology Society.

FIGURE 91. A hydrocarbon molecule diffuses from a source of radius re to a sink of radius r0.

If the beam current is not sufficient to immediately cross‐link the molecule when it reaches the periphery r0, then the contamination rate will decrease. Hart et al. (1970) introduced a correction factor to take this into account: dn 2pDs n0 re ; ¼ 1 dt ln r 1 þ Ds

ð107Þ

0

where D is the exposure dose, in electrons per unit area and s is the cross section for formation of a cross link. Multiplying this expression by the volume of a molecule n and noting that nn0 ¼ h0, the effective thickness of the diffusing layer, we obtain:

ELECTRON‐BEAM–INDUCED NANOMETER‐SCALE DEPOSITION

dV dn 2pDs h0 r ; ¼n ¼ 1 dt dt 1 þ Ds ln re

159 ð108Þ

0

where dV/dt is the volume of contaminant deposited per unit time. From Eq. (108) it can be seen that for high doses (Ds >> 1) the number of molecules deposited per unit time is almost independent of the beam size. For low doses (Ds << 1), the amount of contamination obtained by the integral of Eq. (108) is proportional to the dose. When Ds ¼ 1, the contamination rate is 50% of the maximum rate. The interpretation of r0 is not really the half diameter of the beam, as a result of the larger volume of interaction for inelastic scattering in the substrate of 2 nm. For small beams r0 should be replaced with (r02 þ (2 nm)2)1/2. For larger beams the contamination may not be deposited uniformly over the beam cross section. The magnitude of this effect can be estimated using the Einstein equation: hx2 i ¼ 4Ds t; where x is the mean distance traveled by a molecule in time t. Ds depends on the temperature according to the relation: Es Ds ¼ Ds0 exp ; kT

ð109Þ

ð110Þ

where Es is the activation energy for diffusion and Ds0 is a constant pre‐factor. Wall (1980) measured the activation energy and found a value of 0.97 eV, compared with 0.6 eV measured by Hart et al. (1970). 3. The Electric Field on the Surface When a specimen is bombarded by an electron beam in SEM, TEM, or other microprobe analysis techniques, the specimen becomes electrically charged because PEs may be absorbed and SEs are emitted. Depending on the acceleration energy, which controls the SE yield, the material becomes positively or negatively charged. These excess charges are accumulated in the specimen. If the specimen has a conductive path to a sink or reservoir, the excess charges will always be neutralized and the specimen will remain at its initial potential. However, if this path does not exist, these charges will accumulate and will cause the potential on the specimen to change. The difference between metals and dielectrics is that a dielectric does not have sufficient conduction electrons to quickly restore the neutrality of the specimen. The electrical field can be a danger if the specimen is isolated in the specimen holder or if the specimen is an insulator. The charging of the specimen gives rise to an electrical field that can produce a breakdown in

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the insulator and electrostatic deflection of the primary beam or the low‐ energy SEs. In SEM, charging is observed by bright zones charged negatively and dark zones charged positively. Maybe the most spectacular effect is the mobile‐ion migration in glass materials (Naþ, Cl, etc.). We are interested in whether the electric field created on the substrate surface can produce the migration of ionized molecular fragments away from the irradiated area. If they will get fixed at some distance from the irradiated area, then this electric field might negatively influence the EBID spatial resolution. Cazaux (1986, 1995) provides analytical equations for the radial field intensity Er and the potential Vr on a dielectric surface irradiated by a focused electron beam for different specimen geometries. The general relations for the radial field intensity are: 2 0 1 0 13 rd 2a 4 @ r A r J1 J2 @ A 5 ; r < a Er ðrÞ ¼ 2e pr a a 2 0 1 0 13 rd 2 4 @aA a ¼ J1 J2 @ A 5 ; 2e p r r

;

ð111Þ

r>a

where J1(k) and J2(k) are the elliptic integrals: p

ð2 J1 ðkÞ ¼ 0

dc ð1

k2 sin2 cÞ1=2

ð112Þ

p

ð2 J2 ðkÞ ¼ ð1 k2 sin2 cÞ1=2 dc:

ð113Þ

0

For a thin film in vacuum, the relations are (see Figure 92): qr ; 0a ¼ 2ped r

Er ðrÞ ¼

ð114Þ

where d is the film thickness (m), a is the beam radius (m), e ¼ ere0, e0 is the permittivity of vacuum (8.8541878171012 Fm1), and q is the accumulated charge in the target (C). If the film is thin, then the negative charge is zero, because all electrons are transmitted.

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FIGURE 92. Illustration of the charging effect of an insulator bombarded by an electron beam of radius a.

The electric potential at a radial distance r from the center of the beam on the surface, with the condition Vr(r0) ¼ 0 is 2 3 q 4 r2 r0 5 1 2 þ 2 ln ; 0
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FIGURE 93. Typical electric field intensity distribution on a surface irradiated by an electron beam of radius a ¼ 1 nm.

acts on the molecular dipole. The drift force on polarized molecules in an electric field Er is given by: F ¼ aEr

dEr : dr

ð116Þ

Figure 93 shows a typical electric field intensity distribution on a surface irradiated with a beam with a radius of 1 nm, calculated using Eq. (114). For distances r > a, molecules will be attracted toward the illuminated region and for r < a, they will be deflected in the opposite direction. So, at the perimeter of the beam the concentration of molecules increases. The idea of Fourie (1975, 1979, 1981), supported by Cazaux (1986, 1995) but criticized by Reimer and W€ achter (1978), is that the electric field enhances the diffusion of molecules to the periphery of the radiated area, explaining the rings formed for a defocused beam. In microbiology, the fact that an electric field can induce migration of polarizable cells is known as diaphoresis. I. Conclusions The following steps must be taken to obtain a good theoretical EBID resolution model that agrees with experimental results. First, the role of the SEs in EBID must be theoretically evaluated. For this purpose, MC methods can be used to simulate the SE emission and the deposited profile evolution. A compilation of MC results shows that the radial distribution of SEs on the surface has a typical minimum FWHM of

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TABLE 7 SPATIAL DISTRIBUTION OF SECONDARY ELECTRONS ON THE TARGET SURFACE* Radial distribution (nm) FW50% 4.4 3.4

FWHM 0.8 0.8

0.125 0.157 0.1

Lateral distribution (nm) FW50% FWHM 2.3 2

2.2 2.2 3 3 0.491 0.423 1

Substrate Au, 10 nm Au, 10 nm Al, 5 nm C Cu Cu Al Cu

Beam Beam energy diameter (keV) (nm) 10 30 20 30 1 10 1 1

0 0 0 0 0.1 0.1 0 0

Reference Ding et al. (1988) Ding et al. (1988) Joy (1984b) Joy (1984b) Kotera (1989) Kotera (1989) Kotera et al. (1990) Koshikawa and Shimizu (1974)

*Typical MC simulation results reported by different authors.

0.1–2 nm and the radial distribution has a FWHM of 0.5–2 nm for metal targets. Table 7 summarized some relevant SE spatial data determined using MC simulations by different authors. The spatial distribution of SEs is not a final result for us, but it provides an estimation of the maximum extent of the influence of SEs in EBID. The results are only interesting in conjunction with the spatial extent of the SE energies in the exit point. The same conclusion was obtained in the case of resist‐based EBL. For further discussion on the effect of SEs on the ultimate resolution in EBL, the MC calculations combined with a resist‐development model are needed (Samoto and Shimizu, 1983). Numerous MC simulation programs for SE emission have already been generated. Therefore, an obvious question is why we should produce yet another simulation program instead of using the existing tools. We propose a number of arguments for that: 1. We believe that there is no unanimous opinion about the spatial distribution of SEs. The results are quite different, so we can talk only about a range of scattered results. 2. The existing programs have been written for SEM applications. Therefore, they accept as input only electron energies up to 30 keV. We can extend this range to TEM applications for 100–200 keV with relativistic corrections. 3. For the same reason, the specimens are usually bulk, 1–1000 mm thick, which require a long calculation time for each simulated trajectory. Although many programs have been written, they all used many simplifications in modeling in order to save time. We can restrict the program to thin‐foil targets of 10–50 nm and afford more complex theoretical models.

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4. The MC simulations for SEM provide the SEs as a global signal for image formation. The output data are given as a spatial profile, which is good for us, but the energy is presented as a cumulated spectrum. The data are not classified by position and energy. We need energy spectra of the SEs in each position on the surface, to couple these to the dissociation cross sections of different precursors. In resist EBL modeling, only the threshold model of resist solubility is used. The real dissociation cross section for a gas precursor, however, is far from a step function. 5. The calculation of the absolute SE yield is still a challenging task. All simulation methods used until a few years ago needed an empirical fit parameter to scale the yield curve for each element. For us, the SE yield is very important if we want to compare the role of PEs and SEs in dissociation. Only the dielectric‐function approach can calculate this yield (Ding and Shimizu, 1996; Ding et al., 2001). This attractive approach in MC simulations is relatively new—it can be used only since optical data and measured EELS data have become accessible and fast computers have become available. 6. Our own program affords us flexibility and all the advantages of an accessible source code. For example, a more complex computer simulation customized for EBID can be built. It should have more modules—the MC simulation of electron trajectories, a profile simulator to trace the boundary evolution of a deposited dot on‐line, a module for migration influences, and so on. The spatial distribution of SEs obtained by MC simulations has to be further combined with the electron impact dissociation cross section, specific for the given precursor. An accurate expression for this cross section is difficult to find for most gases. Other effects, even less investigated than the SEs but which may affect the EBID resolution, must be quantified as well, like the delocalization of electron inelastic scattering, migration of electron beam–induced fragments and electric field–induced molecular displacement.

IV. THE ROLE

OF

SECONDARY ELECTRONS

IN

EBID

A. Introduction The spatial resolution of EBID is determined by many factors, such as the electron transport to the surface, the parameters of the precursor gas, the target and its environment, various surface processes, delocalization effects, and so on. Most EBID models consider only the parameters of the PE beam (Scheuer et al., 1986). However, there is abundant experimental evidence

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that the lateral size of dots and lines, fabricated by EBID with high‐energy electrons, considerably exceeds the diameter of the electron beam writing tool (Kohlmann‐von Platen et al., 1993; Komuro and Hiroshima, 1997a,b; Schiffmann, 1993). From the EBID literature survey we noticed that many authors assume that this lateral broadening is mainly caused by the low‐ energy SEs, emitted from the substrate as a result of the irradiation by the PE beam. This assumption is based on the fact that the electron impact molecular dissociation, the main process in EBID, has cross sections peaking at low kinetic energies. EBID performed in an STM also indicates that dissociation is induced by low‐energy electrons. The diameter of the structures grown in STM are similar to the beam diameter, which might be explained by the absence of SEs. However, a complete theoretical model that explains the lateral broadening based on the role of SEs, offering results in agreement with experiments, has not been published yet. Our objective is to fill this gap and quantify the role of the SEs in EBID spatial resolution. Our model uses MC methods for the simulation of electron scattering in the solid and for the prediction of the deposit growth under the influence of SEs. We present the results of these simulations, which are in good agreement with experimental observations.

B. The Model Let us consider a typical EBID process, in which a finely focused electron beam is kept stationary on a target covered by precursor molecules. After a short time, a conical structure starts to grow on the target, localized in the electron‐irradiated area. This process is also well known from contamination growth in electron microscopes. The diameter of the cone, measured at its base or at half maximum height, grows steeply and after some time reaches a saturation value, which always exceeds the diameter of the electron probe at the target. Typically encountered values range from 20 to 500 nm for beam diameters of 2–10 nm on both thin and bulk specimens. The exact time behavior of the diameter is difficult to determine, as it depends on many parameters—the settings of the electron optics, the partial pressure of the precursor gas, the surface diffusion of the precursor molecules, the cleanliness of the specimen, and so on. Qualitatively the diameter versus time curve is sketched in Figure 94, in which the following regimes can be distinguished: the nucleation stage (marked 0‐A in Figure 94) when no significant growth is observed, an intermediate regime (A‐B) characterized by a fast growth of the structure diameter, and the saturation regime (B‐C) where the diameter attains a more or less constant value.

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FIGURE 94. A typical curve showing the evolution of the cone diameter.

We model this behavior by assuming that it is the result exclusively of the SEs emitted as a result of primary beam bombardment. The model we propose describes the growth process as follows. After some time following the start of the electron beam exposure, the nucleation is completed (point A in Figure 94). The PEs hit the flat substrate surface and generate SEs in the substrate, which are partly emitted from the flat substrate, from an area larger than the beam diameter. Both types of electrons, primary and secondary, dissociate the adsorbed molecules and a dot begins to be deposited, its diameter determined by the exit area of SEs on the target surface (Figure 95a). Although this scenario has been suggested by many authors as an explanation for the growth of structures broader than the size of the primary beam, we will show from MC simulations that experimentally observed structure sizes cannot be explained this way at all. Therefore, we extended this model by including electron scattering in the freshly grown structure. While the tip‐like structure grows in vertical direction, the PEs entering the apex of the tip may scatter in the tip, generating SEs that can exit the tip from its side walls. These SEs dissociate the precursor molecules adsorbed on the tip flanks and thus contribute to an extra lateral broadening (Figure 95b). Saturation occurs when the SEs are no longer able to exit the side flanks. This moment is determined by the escape depth (i.e., the inelastic mean free path) of the SEs in the deposit (5–15 nm) (Reimer, 1998). The next step is development of a model based on this scenario. The problem is thus reduced to the prediction of the spatial profile of a cone grown by the SEs between times A and B. We first describe the general procedure followed to solve this problem.

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FIGURE 95. Illustration of the role of the SEs at different growth moments: (a) in the beginning, (b) after a tip structure has grown.

The dissociation rate RSE (x) produced by SEs is given by: E ðp

RSE ðxÞ ¼

fSE ðx; EÞsdiss ðEÞNdE:

ð117Þ

0

Some authors tried to extend the fabrication resolution analysis by including the role of SEs (Allen et al., 1988; de Jager, 1997; Dubner and Wagner, 1989; Joy, 1983). They all started with an MC simulation or an analytical approach and determined the spatial and energy distributions of the SEs on the target surface, fSE(x,E ). However, they encountered difficulties with the dissociation cross section sdiss(E ), which, in general, is unknown for the precursors used in the EBID process. The reactions of the authors confronted with this challenge differed. Some used a simplified model, as did Dubner and Wagner (1989) for IBID, Joy (1983) for resist EBL and de Jager (1997) for ion beam–induced chemistry—the so‐called threshold model. Others considered another available dissociation cross section of a known gas, for example CO, and made a simple speculation about the real W(CO)6 precursor (Koops et al., 1995). Some authors stopped and did not finish the exercise (e.g., Allen et al., 1988). We use the same general procedure to improve the models of these authors by including a more accurate dissociation cross section for a specific precursor. We use MC methods for the simulation of electron scattering in solid targets and SE emission. The MC simulations provide the energy distribution of SEs and a spatial distribution for a zero‐diameter primary beam. This result is convolved with a primary beam with Gaussian distribution and will yield the spatial and energy distribution of the SEs on the surface fSE(x,E ). This distribution is used in conjunction with the electron precursor impact

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properties. The result is the molecular dissociation rate R(x) due to SEs emitted from the flat target surface. The EBID fabrication resolution can be defined as the FWHM of the radial intensity distribution of the dissociated molecules Idiss(r) or as the FW50% of its integral function Ndiss,tot(r) (i.e., the radius of the circle that contains 50% of the dissociated molecules). According to our model, the spatial profile of the deposited cone is determined by the SEs generated and propagating in two different materials, initially the flat substrate (Figure 95a) and later the already deposited tip (Figure 95b). If we define the EBID resolution as the smallest lateral structure size that can be deposited, then the ultimate resolution will be determined only by the SEs emitted from the flat target surface and is obtained at point A in Figure 94. This is achieved only for very small primary beam diameter and very shortly after the growth has started. A more realistic lateral resolution, which can be routinely achieved, will be obtained at point B in Figure 94 and is determined by the SEs emitted from the more complicated shape of the grown tip. The following text sections investigate the role of SEs at these two moments in EBID. C. Secondary Electrons on a Flat Target Surface 1. A Monte Carlo Simulation Program for Secondary Electron Emission In the past, many MC programs have been written for the simulation of the SE emission from targets irradiated with electron or ion beams. In most cases, these programs have been applied in the image analysis in SEM or studies of proximity effects in resist‐based EBL. Following the arguments and the programmers’ guide presented in Sections III.D and III.E, we developed a new 3D MC simulation program for SE emission under electron bombardment of flat surfaces. The simulation has been customized for high‐spatial‐resolution EBID performed in an STEM, that is, the thin‐film targets (1–100 nm) and high electron kinetic energies (10–200 keV), necessary to obtain a finely focused probe in practice. The SE emission output data are organized in a more complex way than in a classical MCSE simulation used for SEM imaging analysis. Thus, the SEs emitted from the surface are classified not only by their radial exit position with respect to the beam incident point, but also by their energy. This additional information is necessary because the results must be further coupled to the dependence of the dissociation cross section on the electron energy. Our MC program, named SEEBID, has been designed as an interactive Windows NT application, developed in the programming environment Delphi 5.0. The Windows‐based programming environment allows almost

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169

unlimited memory sizes, facilitating a high resolution for the position and energy results, as well as good calculation accuracy, offered by the large number of simulated trajectories. The user can interactively introduce the energy of PEs Ep (keV), the specimen thickness, and the number of simulated PE trajectories PEmax as input data. Figure 96 shows the screen capture of the SEEBID main page. The general scheme of the program follows the electron scattering in the target, according to the flow chart presented in Figure 97. When a programmer wants to treat elastic and inelastic scattering of the electrons in the target, choices must be made. Section III.E presented a number of existing theoretical approaches—some very simple and widely used, some more accurate—but only recently has it been possible to implement these latter approaches due to the amazing progress in the computing hardware. We treated the elastic scattering with Rutherford equations because they are simple and very suitable in the high‐energy range of the PEs. For elastic

˚ (50 FIGURE 96. The main page of the SEEBID program. The SE trajectories in a 500 A nm) thick Cu target are shown in the Y‐Z plane and their exit sites on the top surface are marked in the X‐Y plane.

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FIGURE 97. The general flow chart for the MC program for SE emission simulation.

scattering of the SEs, it would be better to use the Mott cross section, but we leave that as a future exercise. The options are very diverse for the simulation of electron inelastic scattering. We chose to make a comparative analysis of a number of approaches in the case of EBID. We compare three models with different degrees of complexity and computational demands:

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1. The SLA used by Chung and Everhart (1974), Dwyer and Matthew (1985), and Koshikawa and Shimizu (1974) 2. The FSE model with no tertiary electrons (Joy et al., 1982; Murata et al., 1981) 3. The FSE model with cascades included. The simulations run in the 3D coordinate system of the microscope (XYZ). The Z‐axis is normal to the target surface; the Y‐axis is parallel with the tilt axis of the specimen holder (see Figure 60). Two types of graphical displays are produced when running the program: the electron trajectories in the plane Y‐Z and the emission sites distribution on the target surface in the plane X‐Y. The user can select the complexity of the information displayed on the screen. The selection offers the PE and/or the SE trajectories to be displayed with or without the cascades. An example of only the PE trajectories, displayed in the Y‐Z plane in a copper target, is shown in Figure 98. In Figure 96, the trajectories of the SEs are displayed in the Y‐Z plane, and their exit sites on the target surface are marked by circles in the X‐Y plane. Both displays Y‐Z and X‐Y can be saved as bitmap images at the end of the simulation.

FIGURE 98. Graphical display of the SEEBID program during PE simulation. 1000 PE ˚ (50 nm) thick Cu target irradiated by a zero‐diameter, trajectories are shown in a 500 A 20 keV beam.

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The values of two counters—the counter for the simulated trajectory number and the counter for the emitted SEs—are displayed when the program is running:. The numerical output of the SEEBID program is the zero‐diameter primary beam response and is organized in two matrices noted N [r], one‐ dimensional, counting the number of SEs emitted at the top surface from a ring [r, r þ dr], centered around the beam incidence point, and NE [r, E ], two‐dimensional, counting the number of electrons of energy E emitted in each ring [r, r þ dr]. All data are written in ASCII files on the disk and can be processed off‐line by using an appropriate scientific engineering package (Mathcad or Maple) to obtain the spatial and energy distributions of the SEs on the target surface. Some results from our simulation program, showing the spatial and energy distribution of the SEs for thin copper targets, are presented in Section IV.C.2. 2. EBID Spatial Resolution Determined by the Secondary Electron on the Flat Surface As an example, we consider a 10 nm thick copper target, covered with C2H5 hydrocarbon precursor molecules and irradiated by an electron beam accelerated at 20 keV. We chose a copper target because it has been widely used in existing MC simulations and many results are available for comparison. We chose a hydrocarbon molecule as the precursor because the electron impact dissociation cross section for this type of molecule is better known than for any organometallic complex. In this way, we actually simulate electron beam–induced contamination growth, a particular case of EBID. We calculate the rate of dissociation produced by the SEs emitted from the target surface (i.e., the profile of the dot at the very beginning of the deposition) when the surface is still flat. We use our MC simulation program SEEBID to obtain information about the SEs emitted from the flat target surface. The relevant result of this simulation is the spatially dependent energy distribution of SEs on the flat target surface, fSE(r,E ) for a zero‐diameter electron beam, resulting directly from NE [r,E ]. This distribution must be combined with the electron impact dissociation cross‐section dependence on the electron energy, sdiss(E ), of a hydrocarbon precursor. The final result is the SE‐induced dissociation rate RSE(x) at each point situated at a radial distance x from the beam incidence point [obtained by using Eq. (117)]. If we assume that each molecule is fixed to the surface exactly where it dissociates, and that the PEs always enter the substrate at level z ¼ 0, then the FW50% of the

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173

FIGURE 99. The dissociation cross section sdiss(E ) for C2H5 adsorbed on the target surface.

obtained profile RSE(x) will provide the EBID resolution in the very beginning (point A on the curve in Figure 94). The electron impact dissociation cross section for the hydrocarbon molecule C2H5, sdiss(E ) is plotted versus the electron energy in Figure 99. This curve has been obtained by adapting a similar curve valid for the precursor in the gas phase. The data for this precursor in the gas phase, taken from Alman et al. (2000) had a dissociation threshold at an electron energy of 10 eV. We adapted these data for the case of an adsorbed molecule, knowing from STM literature that the threshold for the dissociation of adsorbed hydrocarbon molecules is 3.5 eV. The cross section obtained with this method is shifted toward lower energies, so that the threshold becomes 3.5 eV. The following sections apply different degrees of approximation in the MCSE simulation of electron scattering in the target. Three models are used, in order of increasing complexity, and are later compared regarding the compromise between calculation accuracy and computation time. a. Slow Electrons and the Straight Line Approximation. A simple model is a trade‐off. It offers a fast way to get the right feeling, but it has to accept rough approximations. We start with a simple model that combines different approximations used in the SE studies by Chung et al. (1975), Joy (1995a), and Koshikawa and Shimizu (1974). As a first assumption, for sufficiently thin targets we can neglect the energy loss of the PE during its passage through the target. We assume that

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FIGURE 100. Illustration of the straight‐line‐approximation (SLA) model.

the SEs are generated at random depths z0, ranging between Zmin ¼ 0 and Zmax ¼ 10 nm according to the algorithm used by Koshikawa and Shimizu (1974) for a similar situation (Figure 100). We restrict ourselves to the SEs generated by conduction electron excitations, where the excitation function (energy distribution) is given by the Streitwolf equation [Eq. (59)]. The initial polar angle y of the SEs with respect to the target surface normal is considered to be uniformly and randomly distributed in space, thus assuming isotropic generation of SEs. This assumption holds especially for slow SEs. The azimuthal angle f is randomly distributed on a circle. After generation, the SEs are transported linearly to the surface without scattering. This approximation, which neglects the SE angular deflection and considers each scattered electron to be absorbed, is known as the straight‐ line approximation, a term used by Dwyer and Matthew (1985) and Joy (1995a), or exponential attenuation. In this model, the probability that an electron with energy E and generated at depth z will reach the surface unscattered is: z p1 ðE; zÞ ¼ exp : ð118Þ linel ðEÞcosy For the IMFP of the SEs, linel(E ), we used the empirical equation given by Seah and Dench (1979). Each time an SE reaches the target top surface, the radial electron counter is incremented with the product of the probability p1(E, z) of the SE to reach the surface and the probability p2(E ) of the SE to cross the surface barrier: rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ EF þ W p2 ðESE Þ ¼ 1 : ð119Þ ESE

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175

Each time an SE escapes into the vacuum, its energy is reduced with the surface barrier energy (EF þW) and the 2D array containing the energy information of the SE, correlated with its exit position, is incremented in the same way. We implemented the SLA model in our MC program. As an example, Figure 101 shows a copy of the screen during the program running; 1000 SE trajectories in an 80 nm thick copper target, bombarded by a 20 keV electron beam, are shown. The direct results of MCSE noted N(r), are further processed using the Mathcad package to determine the radial intensity distribution I(r) and the integral function of the outgoing SE current Ntot(r). Figure 102 shows for a 20 keV PE beam incident on a 10 nm thick copper target the normalized plots of the SE outgoing current N(r), the SE intensity

FIGURE 101. Graphical display of the SEEBID program during the SE simulation using ˚ (80 nm) Cu target, irradiated by a the SLA model; 1000 SE trajectories are shown in a 800 A zero‐diameter, 20 keV electron beam.

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FIGURE 102. Cumulated plot of the SE normalized spatial distribution on the surface, according to the SLA model (20 keV beam on a 10 nm Cu target). N(r) ¼ total outgoing SE current, I(r) ¼ SE intensity distribution on the surface, Ntot(r) ¼ number of SE emitted within a circle of radius r.

distribution I(r), and its integral function, that is, the total number of SE emitted within a circle of radius r, Ntot(r). For this example, we simulated 50,000,000 PE trajectories. The normalized SE energy spectra at different radial distances from the point of primary beam incidence are plotted in Figure 103. The electrons that exit closer to the beam center have a broader energy peak, also containing higher energy values. Combining these results with a Gaussian primary beam distribution and with the dissociation cross section for a hydrocarbon molecule, we can obtain the spatial profile of the structure initially deposited on the target surface. Figures 104 and 105 show the normalized density distribution of the dot initially deposited by the SEs, Idiss(r), and its integral function, showing the number of molecules dissociated within a circle of radius r, Ndiss,tot(r), for two incident beam diameters: 2 nm and 0.2 nm. According to the SLA model, for a zero‐diameter, 20 keV primary beam, normal incident on a 10 nm copper target, the FW50% of the outgoing SE current on the surface, defined as the diameter of the area from where 50% of the SEs are emitted, is 0.5 nm.

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FIGURE 103. Normalized SE energy spectra at different radial distances from the center of beam incidence.

FIGURE 104. Spatial distribution of molecules dissociated by the SE emitted by a 2 nm diameter electron beam (20 keV beam on a 10 nm Cu target). Idiss(r) ¼ normalized density distribution of the deposited atoms, Ndiss,tot(r) ¼ number of deposited atoms within a circle of radius r.

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FIGURE 105. Spatial distribution of dissociated molecules by the SE emitted by a 0.2 nm diameter electron beam (20 keV beam on a 10 nm Cu target). Idiss(r ) ¼ normalized density distribution of the deposited atoms, Ndiss,tot(r) ¼ number of deposited atoms within a circle of radius r.

The spatial extent of the single dot initially deposited by the SEs on the flat surface yields the following values. For a 0.2 nm beam diameter, 50% of the molecules dissociated by the SEs are contained in a circle with a diameter equal to 0.23 nm. For a 2 nm beam diameter, 50% of the molecules dissociated by the SEs are found within a circle of 2.1 nm diameter. It is interesting to compare the profile of SEs on the surface and the profile of the deposited dot. This comparison should give an indication of the influence of the dependence of the dissociation cross section on the electron energy. Our results show that for a broad beam, for example with a diameter of 2 nm, there is almost no difference between the profile of the SEs on the surface and the profile of the molecules they dissociated. In the case of a narrower beam, for example 0.2 nm, the FW50% of the dissociated profile is 25 % smaller than the FW50% of the SE profile—0.23 nm instead of 0.31 nm. b. The Fast Secondary Electron Model. Fast SEs are SEs with energies up to E/2. Some authors have been preoccupied with the role that fast SEs might play in resolution limitations in SEM imaging, microanalysis, and EBL. Because when generated, they start almost normal to the direction of the PEs, they are thought to determine the limit of SEM imaging resolution (Murata et al., 1981). Joy (1995a) calculated the accumulated energy on the surface due to fast SEs but did not classify them by energy and position, Gauvin and Le´sperance (1992) simulated their role in X‐ray generation. According to Murata et al. (1981) these fast SEs establish the lateral resolution limit in EBL.

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We are concerned with the role of fast SEs in EBID spatial resolution. We implemented the FSE model in our SEEBID simulation program. The program displays the electron‐scattering picture during simulations. Figure 106 shows some FSE trajectories. In this example, a 200 keV zero‐ diameter electron beam normal incident along the Z‐axis on a 80 nm thick copper target was used. During the passage through the target, the PE is scattered elastically and inelastically. The step between two events depends on the elastic and inelastic mean free path of the electron. In our simulation, elastic scattering of PEs is treated with the Rutherford screened cross section. Inelastic scattering is treated according to the FSE model. Each inelastic scattering event generates a fast SE (Figure 107a). After each inelastic scattering event, the energy and scattering angles for both the parent PE and the new fast SE are calculated. During the simulation of each PE trajectory, all information about the fast SE that is generated is stored in memory for later use. When the PE trajectory simulation is terminated, because it has reached a boundary of the specimen or has lost its energy, the fast SEs are retrieved from the memory and tracked in the target until they leave the specimen or are thermalized. For the simulation of FSE scattering in the target, the conventional Rutherford‐Bethe model was used. The elastic scattering of fast SEs is modeled using the screened Rutherford cross section, and the inelastic scattering of the fast SEs is modeled using the CSDA approximation (Figure 107b). The electron inelastic mean free path is given by Seah and Dench’s (1979) empirical equation. The tracing of fast SEs stops when the electron exits the surface or when its energy falls below EF þ W. In this approach, in order to save time, no tertiary electrons are considered. We now consider the same example as in the SLA approximation, a 20 keV primary beam normal incident on a 10 nm thick copper target. Three situations were analyzed: (1) the zero‐diameter electron beam, (2) the 2 nm diameter beam (a typical situation in SEM), and (3) the 0.2 nm diameter beam (the smallest probe size in a modern STEM). The MC program gives the zero‐ diameter beam response. The other two cases are obtained by convolving the MC results with Gaussian primary beam current density distributions. The number of primary trajectories simulated was 50,000,000. The spatial distribution of the exit sites of fast SEs on the top surface of the target is shown in Figure 108. The cumulative results for the spatial distribution of fast SEs on the target surface for a zero‐diameter PE beam are shown in Figure 109. For a zero‐ diameter beam, 50% of the fast SEs are emitted from a circle with a diameter of 2.8 nm. For a 2 nm diameter Gaussian primary beam, the area from which 50%

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FIGURE 106. Graphical display of the SEEBID program, showing 1000 trajectories of FSE ˚ (80 nm) Cu target by a zero‐diameter, 200 keV electron beam. generated in a 800 A

of the fast SEs are emitted has a diameter of 0.2 nm. For a 0.2 nm diameter Gaussian beam, the area containing 50% of the emitted fast SEs has a diameter of 0.23 nm. These results agree quite well with other simulations of FSE (Ding and Shimizu, 1989; Joy, 1995a). The profile of the dot deposited by the fast SEs emitted from the flat target surface is obtained by combining the spatial and energetic FSE data with the dissociation cross section of the C2H5 molecule. Figure 110 shows the normalized radial intensity distribution Idiss(r) and the number of deposited atoms contained in a circle of radius r, Ndiss,tot(r) for a 2 nm diameter beam. Figure 111 shows the same curves for a 0.2 nm beam. Our results show that fast SEs have a larger influence on the spatial evolution of the dot grown

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FIGURE 107. Illustration of the FSE model. (a) FSE generation. (b) FSE propagation inelastic scattering event. towards the surface. elastic scattering event;

▪

by finely focused beams. For the 0.2 nm beam diameter the FW50% of the dot is 0.28 nm, while for the 2 nm beam diameter the dot FW50% is practically unchanged, equal to the primary beam diameter. c. Including the Cascades of Secondary Electrons. We concluded from the MC literature that taking into account the cascade multiplication of the generated fast SEs improves the spatial resolution on the target surface. The present FSE model can be improved if the cascades are also included and higher‐order electrons are generated. We used the classical binary collision scattering model for the treatment of the FSE cascades. The higher‐order generation electrons are stored in memory and when the FSE trajectory is terminated, they are retrieved and followed during their scattering in the target. New electrons are generated and the process continues until the memory store is empty. In this way, we simulate the complete binary interaction tree presented in the beginning of Section III. We implemented the cascade model in our MC simulation SEEBID. The distribution of the emission sites on the surface in the X‐Y plane is shown in Figure 112. It can be seen from this figure that the fast SEs are emitted more clustered around the beam center, which agrees with the expectations.

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FIGURE 108. The spatial distribution of the FSE exit sites on the top surface of the target, marked in the X‐Y plane. The primary beam is zero‐dimensional, accelerated at 20 keV and the target is 10 nm thick Cu.

FIGURE 109. Cumulated plot of the spatial FSE distributions. The beam is zero diameter, accelerated at 20 keV, the target is 10 nm thick Cu. N(r) ¼ total outgoing SE current, I(r) ¼ SE intensity distribution on the surface, Ntot(r) ¼ number of SE emitted within a circle of radius r.

We calculated the profile of the dot deposited by the SEs emitted from the surface. This profile was almost identical to the one obtained when no cascades were included. Our conclusion is that even if the spatial distribution of fast SEs on the surface becomes sharper, the influence of the introduction of cascades on the dot spatial extent is negligible.

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FIGURE 110. Normalized plots of the radial intensity distribution Idiss(r) and its integral function Ndiss,tot(r) for a single dot deposited by FSE on the top surface of the target. The beam diameter is 2 nm, the beam energy 20 keV, the Cu target is 10 nm thick.

FIGURE 111. Normalized plots of the radial intensity distribution Idiss(r) and its integral function Ndiss,tot(r) for a single dot deposited by FSE on the top surface of the target. The beam diameter is 2 nm, the beam energy 20 keV, the Cu target is 10 nm thick.

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FIGURE 112. The spatial distribution of FSE exit sites on the top surface of the target when cascades are included.

3. Discussion According to our calculations, the FW50% (the area containing 50% of the deposited atoms) for a single dot arising only from SEs emitted from the target surface is similar to the beam diameter if the beam diameter is 2 nm and it is enlarged to 0.28 nm when the beam diameter is 0.2 nm. Even though we do not yet have experimental results for the 0.2 nm beam to compare with our theoretical prediction, we can conclude that this result does not agree with the values reported from EBID practice with a 2 nm diameter beam (see Figure 47). There still is a discrepancy between these experimental values and our calculations. This can mean two things: the SEs are not the only important influence in EBID, or the experimentally measured results we use for comparison are always taken at point B rather than at point A on the curve in Figure 94. In Section IV.D, we investigate the latter option and extend the simulation to include the tip growth toward point B. If the resulting cross‐sectional shapes of the tip agree with the experimental results, then we will have provided strong evidence that SEs play the most important role in the deposit shapes and sizes in EBID. D. Role of Secondary Electrons Scattered in the Deposit 1. Introduction At the very beginning of the deposition process after nucleation has started, the SEs emitted from the flat target govern the spatial extent of the structure. In Section IV.C we estimated the size of this SE exit area on the target surface

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and obtained a FWHM of around 1 nm for a pinpoint incident beam. This value is still smaller then the experimentally measured saturation value. We will attempt to prove that broadening occurs because of the SEs generated in the freshly grown tip structure and emitted from its side flanks. For this purpose, an MC profile simulator has been written that evaluates the border of the tip structure as determined by the SEs each time a new PE is simulated. 2. Description of a Two‐Dimensional Profile Simulator for EBID The methods used to simulate the profile evolution during deposition or etching processes fall under two categories: geometric methods and cellular automata (CA) methods. In the geometric method the substrate is treated as a continuous entity. The string and set‐level methods (Adalsteinsson and Sethian, 1995; Neureuther et al., 1980) belong to this group. In the CA method the target is represented by a large number of cells that reside in the substrate. We used the CA method to build a simulator for the spatial evolution of a dot grown by EBID in the spot mode of an electron microscope. We considered a simplified case, in which a carbon contamination dot is grown by a zero‐diameter beam on a thin carbon foil covered by C2H5 molecules, to avoid complicated interface effects. This situation can be nearly achieved in practice at high‐acceleration voltage (100–300 kV) in a modern high‐ resolution STEM. In this way the simulation results can be easily compared with experimental results. The space of interest is represented with an array of discrete square cells with a lateral size of 0.5 nm (Figure 113). This value is the average of the size of a precursor molecule and the diameter of a deposited atom. The simulated space is 801 cells long in the Y direction and 151 cells wide in the X direction. The origin of the coordinate system coincides with the impact point of the beam. The substrate together with the already deposited structure form one object (OBJ), permanently covered by a monolayer of gas molecules (Figure 114). This is an ideal situation, when the diffusion time necessary for a gas molecule to reach the irradiated area from the sink is assumed to be zero. Each discrete cell in the mesh is described by its occupational state. The occupational flag can assume three states, codified as: 0 if it is empty, 1 if it is occupied by a molecule that might be dissociated and create a deposited atom (border), and 2 if it is occupied. We use the MC method to simulate the SEs generated in the solid object on the trajectory of the PE. The PE enters the object OBJ in the center of the deposit and scatters inside, generating SEs during inelastic scattering. It moves linearly between two inelastic scattering events (see Figure 114). The step between inelastic scattering events can be sampled using a uniform

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FIGURE 113. The simulated space divided in discrete cells.

random number R. The interaction sampling—the type of event (elastic/ inelastic)—will also be determined using a random number. If R is a uniform random number, the interaction will be elastic if R < lT/lel, and inelastic otherwise. We neglect the elastic scattering because of the high energy and thin substrate. We assume that SEs are generated isotropically in space. A 3D simulation is time consuming and for this reason 2D simulations are often preferred. In the 2D simulation we observe only the SEs emitted from a narrow band situated in the X‐Y plane (shaded in Figure 115). We build a shape grown by these SEs seen as a one cell thick wall, parallel to the X‐Z plane. The result is a cross section of the 3D dot grown in reality. The SEs emerged on the narrow band are uniformly generated on a one cell thick ring. The polar scattering angle y of the SEs is: 1 y ¼ p 2pR; 2 where R is a random number between 0 and 1.

ð120Þ

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FIGURE 114. The geometry used in growth simulation. PE ¼ primary electrons, SE ¼ secondary electrons; substrate þ tip ¼ OBJ.

FIGURE 115. The 3D2D transformation.

▪ inelastic scattering event.

The energy of the SE, ESE is given by the excitation function of the conduction electrons, given by the Streitwolf equation [Eq. (59)]. After its generation, at depth z, the SE propagates linearly in the given direction. With small steps it is checked whether the cell it crosses on its way is full (2), in the border (1) or empty (0). The propagation continues as long as the encountered cells are full and until the SE hits a border cell (see Figure 114). When the SE reaches the surface, its energy ESE is corrected with the exponential probability p1(z) that it will reach the surface and the probability to escape into vacuum p2(ESE), and finally reduced with the surface barrier. The reason for these corrections can be found in Section III.

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ESE ¼ ðESE0 W EF Þp1 1 ðzÞp2 ðESE Þ p1 ðzÞ ¼ exp@

path A ; p2 ðESE Þ ¼ 1 linel ðESE Þ

sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ EF þ W : ESE

ð121Þ

The energy of the SE is combined with the dissociation cross section of the C2H5 precursor, given in Section III.C.2. The probability that the emerging SE will dissociate the molecule on the border is equal to the dissociation cross section divided by the area seen by SE: pdiss ðESE Þ ¼

sdiss ðESE Þ : 55

ð122Þ

Using another random number we decide, according to this probability, whether the molecule situated in the exit cell will be dissociated or not. In our program, a dissociated molecule is translated to a ‘‘shot’’ cell. When a cell (X,Z) is shot, its state changes to ‘occupied,’ by switching its occupancy flag to 2, and its neighbors with the coordinates (X,Zþ1), (X,Z1), (Xþ1,Z), (X1,Z) are included in the border (Figure 116). A cell needs to have at least one side in common with a filled cell in order to be declared candidate for deposition and be included in the border. When the simulation of one PE is terminated, the border of OBJ is adjusted and the entrance point of the beam is set in the top of the grown tip. If the foil is thin, the tip grown on its bottom side is also shown and is also part of OBJ. The simulation process can continue according to the flow chart in Figure 117, where only one time quantum equivalent with the effect of one PE is shown. The cross‐sectional shapes are saved in bitmap files at regular exposure intervals for later processing. Figure 118 shows the time evolution of the shape of a tip grown by SEs generated by a 20 keV primary beam incident on a 10 nm thick carbon target. Each 200,000 PE a profile is plotted. If we

FIGURE 116. The neighbors of the shot cell.

ELECTRON‐BEAM–INDUCED NANOMETER‐SCALE DEPOSITION

FIGURE 117. The flow chart of the 2D profile simulator programming.

189

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FIGURE 118. A sequence of profiles of a single tip deposited by SE generated by a zero‐ diameter 20 keV beam incident on a 10 nm carbon target.

assume that the probe current is 5 pA, the time step between two profiles is estimated as 6 ms. The last profile shown is grown in 39 ms, giving a vertical growth rate of 1.6 nm/ms. We observe that the shapes obtained by the simulations agree with those obtained experimentally. Figure 119 shows the result of the simulation of a series of tips grown from the beginning until a height of 150 nm is obtained. It is observed that the diameter at the base of the tips tends to saturate at a value of 15–20 nm, a situation also confirmed experimentally. We also observe that according to the simulations, if the exposure time is very low, structures with a lateral size of 1 or 2 nm should be possible to fabricate. E. Conclusions A model has been presented to explain the shape and the lateral size of tips, experimentally grown using EBID in the spot mode of an electron microscope. The model confirms the major role played by the SEs emitted under electron beam irradiation. The role of SEs in EBID spatial resolution has

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191

FIGURE 119. A sequence of tips deposited at the same conditions as in Fig. 118 by a 20 keV zero‐diameter beam. It can be seen that the diameter at the base tends to saturate. At each 400,000 PE, a profile was plotted.

been estimated by combining the results of our MCSE simulation with an accurate dissociation cross section for a specific hydrocarbon precursor. We used three theoretical models of increasing complexity for the SE simulation and concluded that, at least for a thin target (<10 nm) the three models yield similar results. The SEs emitted from the substrate surface play a key role in the very beginning of the growth process and establish the ‘‘theoretical’’ ultimate EBID resolution at 2 nm. Building such small structures is quite a challenge because they are also very thin, making the visualization difficult and ambiguous in an SEM or STEM system. What happens after the very beginning has for the first time been successfully modeled by taking into account electron scattering in the grown structure. This leads to a broadening of the structures caused by SEs generated in the deposit, dissociating adsorbed molecules on the side flanks of the deposit. This broadening is in agreement with experimental observations. Visible tips with heights greater than 50 nm already have diameters of 10–20 nm, even for a zero‐diameter primary beam. Because of similarities between EBID and specimen contamination in electron microscopes, the proposed model can be also very useful for high‐resolution electron microscopy.

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V. DELOCALIZATION EFFECTS

IN

EBID

A. Delocalization of Electron Inelastic Scattering: General Formulation of the Problem Electron inelastic scattering in matter is a delocalized process, in a degree inversely proportional to the electron energy loss. As a result, all processes initiated by this energy loss, especially when the energy loss is small, such as in the generation of SEs or the degradation of gas molecules, are also delocalized. A loss of resolution in inelastic dark‐field images due to inelastic scattering delocalization has been observed experimentally in a high‐ resolution STEM (Colliex, 1985; Isaacson et al., 1974). A quantitative comparison with theoretical results is difficult because of the weakness of the signals involved and uncertainties in the specimen shape and in the electron probe positioning. However, subnanometric resolution plasmon maps can occasionally be achieved, and recent measurement of the delocalization of the EELS signal by Muller and Silcox (1995) showed a localization as good as 0.5 nm. Difficulties in theoretical modeling of delocalization are imposed by the unknown elements in electron scattering in a solid or a gas. Until now, only very simple models have been used to quantify the delocalization effects, mainly in studies of SEM or STEM imaging resolution. The results of different approaches sometimes differ drastically, leading to pessimistic as well as optimistic predictions. For example, the delocalization of the generation of SEs is expected to be as large as 0.05–70 nm (Joy, 1991; Joy and Pawley, 1992; Reimer, 1998) but in practice the degree of localization will fall somewhere between these extremes (Joy, 1991). This predicted range approaches, in the order of magnitude, the smallest electron beam diameter currently obtainable in an STEM, 0.2 nm. That is why it is feared that the delocalization of electron inelastic scattering imposes a fundamental resolution limit on any analysis technique performed in an electron microscope, as well as any electron beam–induced fabrication process in general and EBID in particular. One of the few attempts to study the localization of energy transfer in EBL between electrons and PMMA resist has been made recently by Han and Cerrina (2000). They calculated that the range of interaction between a 1 keV electron and the PMMA molecules is of the order of 2.0 nm. In this section, we take a first step to quantify the role that the electron inelastic scattering delocalization plays in EBID resolution. First, we identify the important EBID events that could be affected by the delocalization of electron inelastic scattering (Figure 120).

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FIGURE 120. Illustration of the different effects of delocalization of inelastic scattering in EBID. (a) Generation of secondary electrons is delocalized, (b) electron‐induced precursor dissociation is delocalized, (c) and (d) molecular dissociation can be induced by surface plasmons (SP), whose generation is a delocalized phenomenon. (c) represents an SP on the gas molecule and (d) an SP on the target surface interacting with a molecule.

Because the inelastic scattering in the solid substrate is delocalized, an SE may be generated away from the incident electron path, so that its exit point on the surface is not exactly where it is expected from the MC simulations described in Section IV (Figure 120a). The effect will be a broadening of the spatial profile of SEs on the target surface. Because the energy transfer between the electron and the precursor molecules is also delocalized, a molecule adsorbed on the surface at a certain distance away from the electron trajectory may be excited and eventually dissociate (Figure 120b). The resulting effect will be a deposited dot profile larger than the one given by the SEs only. We will attempt to quantify the impact of the electron scattering delocalization on the spatial resolution of EBID, studying these cases, which are both single‐electron excitation processes. Because the idea exists that the precursor molecules can be dissociated as a result of collective excitations, such as SP decay, another useful result would be the estimation of delocalization of SPs generated by an electron in EBID. Two cases will be analyzed: the generation of an SP directly on the precursor molecule (Figure 120c) and the generation of an SP on the flat substrate surface, which may transfer its energy to an adsorbed precursor molecule (Figure 120d). Both events can lead to molecular dissociation.

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B. Approaches for Quantitative Estimation of Electron Inelastic Scattering Delocalization Let us consider the case of an electron with energy E, which interacts with an atom or molecule, losing some energy, DE. The electron can also excite atoms situated away from its trajectory, at a certain distance b, called the impact parameter. In the latter case, the interaction is designated as delocalized. The degree of delocalization is inversely proportional to the energy loss of the incident electron and can be described by the impact parameter b. During the past years, several approaches have been formulated to evaluate the degree of delocalization. Their complexity grows from an almost straightforward one, the classical model, to a semi‐classical one, and it ends with a very complicated quantum mechanical approach. We describe only the first two models because we do not expect to use the quantum mechanical model. According to Ritchie (1981), electrons with energies between 10 keV and 100 keV behave as classical point charge particles, and quantum corrections are negligible. 1. The Classical Model 1 The classical model treats the electron as a point charge with energy E, passing next to an atom A and losing some energy DE. The impact parameter b, also known as the Bohr cutoff radius, is defined as the radius of a sphere inside which the electron must pass for the interaction to really happen. The magnitude of the impact parameter can be estimated straightforwardly from the wave nature of the electron and the Heisenberg uncertainty principle DxDp h, where Dx represents the impact parameter b and Dp ¼ hDq, where Dp is the momentum change and Dq is the change in the wave vector q. If the momentum change is small, then the electron can pass at a distance away from an atom and still ionize it. The minimum momentum transfer for an energy loss DE for a zero scattering angle is given by Dqmin ¼ DE/ hv. The maximum impact parameter is then given by: bmax ¼

hv ; DE

ð123Þ

where h is the Planck constant h divided by 2p, v is the velocity of the incident electron, and DE is the energy lost by the incident electron. The same result can be obtained from another formulation of the Heisenberg uncertainty principle, DEDt ﬃ h, where the accuracy of the energy measurement DE is connected with the time interval Dt required for this measurement (Colliex, 1985). Taking the interaction and measurement time equal to b/v we obtain:

ELECTRON‐BEAM–INDUCED NANOMETER‐SCALE DEPOSITION

bmax ¼ vDt ¼

hv : DE

195 ð124Þ

The energy of the electron can be expressed as: E¼

hc hv ¼ ; l lb

ð125Þ

where b is the electron velocity v divided by the velocity of light c, and l is the wave length of the incident electron. By substituting the electron velocity in Eq. (123) another expression can be obtained for the impact parameter: bmax ¼

El h lE b¼ b: DE h 2pDE

ð126Þ

By denoting with E ¼ DE/2E the characteristic scattering semi‐angle for an energy loss DE, the radius of the interaction sphere is: bmax ¼

l b: 4pyE

ð127Þ

The diameter of localization given by the diameter of the interaction sphere will then be: d ¼ 2bmax ¼

l b: 2pyE

ð128Þ

Some authors (Buseck et al., 1988; Cheng, 1987; Jackson, 1975; Joy, 1991) obtained an equation similar to Eq. (123) by using the Heisenberg principle with h instead of h. In this case, the radius of the interaction sphere is: bmax ¼

hv E l ¼ lb ¼ b; DE DE 2yE

ð129Þ

and the diameter of localization in this approach is given by: d ¼ 2bmax ¼

l b: yE

ð130Þ

From Eq. (123) we can estimate, for example, that an electron with an energy of 100 keV and a velocity v ¼ 0.5 c can lose an energy of DE ¼ 5 eV within an impact parameter bmax of 20 nm and can lose an energy DE ¼ 25 eV within an impact parameter bmax of 4 nm. In Figure 121, the classical dependence of the impact parameter is plotted as function of the electron energy according to Eq. (123). Pennycook (1988) gives an expression for the ionization impact parameter as a function of the electron energy loss, considered equal to the ionization energy Ei:

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FIGURE 121. The classical dependence of the impact parameter on the energy loss, bmax(DE ), for a 100 keV electron.

brms

v h 4E 1=2 ¼ ln Ei Ei

ð131Þ

2. The Classical Model 2 In this approach, the energy loss when passing through matter is modeled by the Coulomb interaction between the incident swift electron and an electron in the target atom. From classical electrodynamics, the energy lost by a swift electron with a velocity v in interaction with the atom electron is (Jackson, 1975):

DE ðbÞ ¼

e4 1 2 ðin cgs systemÞ: mv2 b

ð132Þ

This expression is valid if we consider the electron in the target atom as free. For very distant collisions, the result of this approach is in error, because of the binding of electrons. The energy transfer to a harmonically bound charge then is:

ELECTRON‐BEAM–INDUCED NANOMETER‐SCALE DEPOSITION

0 12 3 2e4 @ 1 A4 2 2 1 2 2 5 x K1 ðxÞ þ 2 x K0 ðxÞ DE ðbÞ ¼ 2 g mv b2 o0 b with x ¼ gv

;

197

ð133Þ

where o0 is the characteristic frequency of the binding, and ho0 is the ionization potential of the atom. K0(x) and K1(x) are the modified Bessel functions of the second kind. 3. The Semi‐Classical Approach If the classical model was correct, then a dissociation process, which needs an energy loss of 5 eV, could give EBID features, limited in resolution by the delocalization process to 20 nm. This is not really the situation we observed experimentally in a high‐resolution STEM. This is a reason to continue the study with a model better than the classical one. Semi‐classical models treat the incident electron as a classical point charge with a well‐defined straight linear trajectory and constant velocity. The interaction with the target is treated quantum mechanically. The classical relation between the impact parameter and the energy loss DE(b) is no longer correct, because in quantum mechanics only a certain probability of interaction makes sense. A new quantity is thus introduced, P(b,E ), the probability for a swift electron to lose a discrete energy E in an interaction with a target atom situated at a distance b. For a large number of collisions the average energy loss at b will be P(b,E )E quantum mechanically and DE(b) classically. The two values must be equal for regions where the electron can be treated as a classical particle. Because this model is valid for distances larger than the atomic radius, where a linear trajectory can be assumed, and because the electron as a point charge causes the function P(b,E ) to diverge in the origin, a cutoff radius of a0 must be introduced. The origin of coordinates is considered in the center of mass of the target atom, its nucleus. The nearest approach at the impact parameter b is at the moment t ¼ 0 (Figure 122). For simplicity, a hydrogen‐like atom is considered, with only one electron. The impact vector b and velocity vector v are mutually perpendicular vectors. The trajectory of the incident electron can be expressed as: RðtÞ ¼ b þ vt;

ð134Þ

where R is the coordinate vector of the incident electron. The Hamiltonian characterizing the interaction between the fast electron and the target atom is given by (Ritchie, 1981):

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FIGURE 122. The Feynman diagram of electrontarget interaction.

V ðtÞ ¼

e2 ; jb þ vt rj

ð135Þ

where r is the coordinate vector of the electron in the excited atom. The atom is considered in its ground state until the moment t ¼ 0, when the swift electron field is suddenly ‘‘switched on.’’ During the interaction, the incident electron loses an energy E, by transferring it to the target atom, situated at a distance b. The result of this energy transfer is that the atom makes a transition from its initial ground state (i) to a final higher energy state ( f ) (see Figure 122). These states of the target atom are described by the wave functions ’i and ’f, respectively. The calculation of these wave functions is a very difficult and time consuming, and sometimes an even impossible operation. For this reason, usually only hydrogen‐atom‐like wave functions are used. Time‐dependent perturbation theory gives the probability that the atom experiences a transition i ! f under the influence of the Coulomb field of a classical point electron, traveling with a constant velocity v along a path specified by the impact parameter b (Ritchie, 1981):

Pi!f

1

ð 2

iðEf Ei Þt 1

¼ 2 h’i jV ðtÞj’f i exp dt

; h i h

ð136Þ

1

where the energy transfer necessary for the transition is E ¼ ho ¼ Ef Ei. The dimensions of the target atoms and molecules are small. Because the origin of r is in the center of the atom, the exponentials eiot ¼ eikr can be expanded as a power series, since this series will converge very rapidly: eikr ¼ 1 þ k r iðk rÞ2 þ . . .

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The classical analog of this expansion of the exponential is a multipole expansion of the charges that interact with the radiation field. The transitions that are due to the first term of the expansion are called electric dipole transitions, and the transitions due to the second term are known as magnetic dipole and electric quadrupole transitions (Hameka, 1965). Very widely used is the so‐called dipolar approximation, which takes into account only the electric dipole transitions. The dipole moment operator is defined as er. The matrix element of the electric dipole moment operator between the target states i and f is responsible for the electric dipole transitions between the two states i and f and is known as the transition moment between the two states (Moss, 1973). Time‐dependent perturbation theory in dipolar approximation gives the probability that the atom electron will be excited from the ground state i to the state f (Bolton and Brown, 1990): 2 1 l0 Pi!f ¼ ½ðrfi ev Þ2 K02 ðb=bmax Þ þ ðrfi eb Þ2 K12 ðb=bmax Þ; ð137Þ p2 b2max a0 where l0 ¼ h/mv is the nonrelativistic de Broglie wavelength of the incoming electron, ev and eb are the unit vectors of the v and b directions, rfi ¼ h’f jrj’i i is the dipole matrix element of target electron coordinate operator r, and bmax ¼ v h/Efi is the Bohr cutoff parameter. The unknown quantities in this expression are the dipole matrix elements rfi , which are difficult to calculate. Using the approximation suggested by Fano (1970) and Hameka (1965) we can assume that the atoms in the target are randomly oriented in the coordinate system related to the electron microscope with respect to the radiation wave. In this approximation, the components of the dipole matrix elements are equal to one another and can be expressed in terms of the oscillator strength ffi, according to the relation: ðrfi Þ2v ¼ ðrfi Þ2b ¼

2 h ffi : 2mEfi

ð138Þ

Replacing these dipole matrix elements in Eq. (137) we obtain the transition probability: 2 2 1 l0 h Pðb; Efi Þi!f ¼ ffi ½K02 ðb=bmax Þ þ K12 ðb=bmax Þ; ð139Þ p2 b2max a0 2mEfi where ffi is the oscillator strength for the transition between initial and final states i ! f, a property of the target material that quantifies its response to an electromagnetic perturbation. In order to plot the transition probability P(b,E) we can simplify its expression by taking ffi ¼ 1, an assumption valid for a bound electron that

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oscillates harmonically in three dimensions (Atkins and Friedman, 1997). In STEM calculations, the oscillator strength is often modeled simply as unity up to a cutoff angle, and zero for larger collection angles (Pennycook, 1988). Figure 123 shows two curves for P(b,E) for different energy losses, E ¼ 25 eV and E ¼ 100 eV, for a 100 keV electron, assuming that the oscillator strength is equal to unity. In reality, the oscillator strength is a function of both the energy loss E and the momentum transfer q, f (E, q), and it is known as the generalized oscillator strength (GOS). The theoretical calculation of the GOS

FIGURE 123. The probability of losing energy E at the impact parameter b for a 100 keV electron, P(b,E) (semi‐classical approach; the oscillator strength is assumed equal to unity). The solid line represents P(b, 25), the dashed line shows P(b, 100).

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for many‐electron atoms is obstructed by the lack of sufficiently accurate wave functions. For q ¼ 0, the GOS is reduced to the optical dielectric oscillator strength valid for photon‐induced excitations. In the case of electron beam– induced excitations, f ﬃ 1 for the allowed dipole transitions (q ¼ 0) and f 1 for forbidden transitions (q 6¼ 0) (Atkins and Friedman, 1997). All target materials have the same form for the probability of excitation P(b,E) curve, the difference being established only by the oscillator strength ffi. If we analyze the curves in Figure 123, two variation regimes can be distinguished, separated by the Bohr cutoff parameter bmax. In the first region, b < bmax and P(b,E) / 1/b2 and in the second region, b > bmax and P(b,E) / exp(–2b/bmax) (Muller and Silcox, 1995). The indetermination that occurs inqﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ the origin of the P(b,E) plot can be ﬃ –1 2 2 , where b eliminated if b is replaced with þ b b min ¼ (qyc(E)) , min pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ q ¼ 2mEp = h and yc ¼ E=Ep , where Ep is the kinetic energy of the incident electron. This idea has been suggested by Muller and is also found in Classical Electrodynamics (Jackson, 1975). A plot of P(b,E) after this correction, showing the two distinguishable regions, is presented in Figure 124. The impact parameter is already much smaller than in the classical approach for the same energy loss. C. Delocalization of Secondary Electron Generation 1. Introduction Our results from Section IV show that the SEs are the main cause for the dissociation of the precursor molecules in EBID. Secondary electrons are generated as a result of inelastic scattering of PEs in the irradiated material. Usually in simulations of SE emission, as well as in our estimation of the SE spatial extent in EBID obtained in Section IV, it is assumed that their generation occurs exclusively where the inelastic scattering takes place. However, because the energy transfer in an inelastic scattering event is not perfectly localized, a non‐zero probability exists for an SE to be generated at some distance from the PE scattering center. The ultimate spatial resolution of a SE image formed by scanning a subnanometer probe across a surface is limited by the delocalization of the generation process. The FWHM of the SE localization profile for a 100 keV zero‐diameter electron beam is estimated from the measurements to be 2 nm (Drucker and Scheinfein, 1993). Even though the necessity for a quantitative evaluation of this delocalization effect in high‐resolution SEM imaging has been signaled by some authors (Joy, 1991; Reimer, 1998), no convincing response has been issued yet and the different results available do not agree with each other.

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FIGURE 124. The probability P(b,E) for a 100‐keV electron to lose an energy E ¼ 25 eV (solid line) and E ¼ 100 eV (dashed line) by exciting an atom situated at a distance b, plotted at two different scales.

One of the frequent mistakes leading to pessimistic estimations in evaluating the SE delocalization is the use of the classical expression, Eq. (123), with the kinetic energy of the SEs after being emitted into the vacuum)—the energy measured with respect to EF þ W(4 eV) instead of

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203

the higher energy lost by the PE at the moment of internal SE generation (25 eV) (Joy, 1991). Our goal is to quantify the role of delocalized SE generation in EBID. This problem is reduced to the estimation of the probability for an SE to be generated by exciting a target atom situated at a distance b from the PE inelastic scattering center, denoted PSE(b) (see Figure 120a). As a case study, we consider EBID performed in an STEM, with a finely focused electron beam accelerated at 100 keV and passing through a thin carbon film. To resolve the problem of delocalization, we must choose one of the theoretical approaches described in Section V.B. The classical approach seems too simple and yields results that do not agree with experimental observations. We further rely on the statements by Ritchie (1981) indicating that the fast electrons at 10–100 keV behave like classical particles and quantum corrections are expected to be negligibly small. The semi‐classical approximation has been used with success by Muller and Silcox (1995) to calculate the localization of the EELS signal and the results agreed with the experimentally obtained signal in the case of large collection angles. These considerations lead us to believe that the semi‐classical approach is a right choice to solve the problem of the role of SE delocalization in EBID. 2. The Spatial Extent of the Delocalization of Secondary Electrons Using the Semi‐Classical Approach We start from the theoretical model described in Section V.B. According to the semi‐classical approach, the probability that an atom will transit from an initial state 0 to final state n as result of the incident PE passage at distance b, is:

P0!n

2 1 l0 h2 fn0 ½K02 ðb=bmax Þ þ K12 ðb=bmax Þ; ¼ p2 b2max a0 2mDE

ð140Þ

where fn0 is the oscillator strength for the transition 0 ! n and DE is the energy lost by the swift electron. We can further transform Eq. (140) by replacing bmax using Eq. (123):

P0!n ¼

DE l0 2 1 fn0 ½K02 ðbDE= hvÞ þ K12 ðbDE=hvÞ p2 v2 a0 2m

ð141Þ

If we assume that the excitation of the target atom from state 0 to state n will generate an SE with an energy E ¼ DE, then the probability that an SE is generated causing an electron energy loss DE at distance b is:

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PSE ðb; EÞ ¼

E l0 2 1 ½K 2 ðbE= hvÞ þ K12 ðbE=hvÞ fSE ðEÞ p2 v2 a0 2m 0

ð142Þ

From Eq. (142) we observe that the probability PSE(b,E ) is a product of a kinematic component, dependent on the incident electron motion, which can be easily evaluated, and a component dependent on the material, fSE(E ). This is a practically unknown quantity, a kind of oscillator strength for the SE generation or the target probability of absorbing a quantity of energy in order to produce a SE. The integrated probability that an SE will be generated and cause an energy loss E for the incident PE can be obtained by integrating Eq. (142) over all possible b values, assuming that only one atom is excited upon each interaction (Inokuti, 1971): 1 ð

sSE ðEÞ ¼ 2pN

Pðb; EÞbdb:

ð143Þ

0

As a first approximation, we can assume that fSE(E) ¼ 1, as in many microscopy calculations (Muller and Silcox, 1995; Pennycook, 1988), and we obtain an approximate probability that an SE will be generated with an electron energy loss E. sSE(E) is plotted versus the electron energy loss E in Figure 125. An experienced eye can see that the shape of the curve in Figure 125 is not specific for the electron energy loss in inelastic scattering events. It would be useful to check this dependence against a correct energy distribution at least for one particular scattering case. The physics of secondary emission under electron irradiation has been studied for a long time. Still a very intriguing question is how the energy lost by the incident electron is distributed after the inelastic scattering in the material. It is known that after inelastic scattering SEs are generated internally and that they eventually escape into the vacuum. Much less is known about the mechanisms of SE generation, because a number of excitation channels and steps are possible, such as interband transitions, excitation of valence electrons, ionization of core electrons, and plasmon decay. Modern EELS enables measuring the total energy lost by the PE passing through a target, but what is needed now is the distribution of energy losses that produced an SE (i.e., the energy invested by PEs only in SE generation). Solutions can be found by simulations using MC methods, where by simulating a huge number of collisions, one hopes to approach the real situation provided that the correct cross sections for each excitation channel are known. The most reliable answer can be obtained by experimentally measuring the correlation between the secondary emission and the incident electron energy

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205

FIGURE 125. The energy loss distribution sSE(E) for an SE generated by a 100 keV primary electron ( fSE ¼1).

loss events. A few attempts have been made in this direction, contributing to the clarification of the internal mechanisms of SE generation. (Drucker and Scheinfein, 1993; Drucker et al., 1993; Mullejans et al., 1993; Pijper and Kruit, 1991; Voreades, 1976). Figure 126 shows a measured EELS–SE coincidence spectrum, obtained by combining the data reported by Drucker and Scheinfein (1993) and Pijper and Kruit (1991). It is obvious that the energy loss distribution curves from Figures 125 and 126 do not agree with each other; the reason for the discrepancy is the assumption that we made in the calculation of sSE(E), that fSE ¼ 1. At this moment we are able to correct this simplification, and determine the function fSE(E) as a correction factor necessary to fit the calculated to the measured curves. Figure 127 shows the correction factor fSE(E) determined in this way. Returning to Eq. (142), we can now correct the expression of PSE(b,E) for each energy loss E. Figure 128 shows the probability PSE (b,E) to generate an SE with an energy loss of 25 eV at a distance b, corrected using the EELS– SE coincidence experimental data. The final answer to our problem is the SE delocalization profile, obtained by integrating the generation probability PSE (b,E) over all possible energy losses:

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FIGURE 126. The coincidence rates between the electron energy loss and the SE generation events in a 10 nm carbon film irradiated by a 100 kV electron beam. Data from Drucker et al. (1993) and Pijper and Kruit (1991).

FIGURE 127. The dependence fSE(E) determined as a correction parameter between the curves of Figure 125 (calculated) and Figure 127 (measured).

1 ð

PSE ðbÞ ¼

PSE ðb; EÞdE

ð144Þ

0

Figure 129 shows the normalized probability PSE(b) that an SE is generated within an impact radius b from the PE inelastic scattering center.

ELECTRON‐BEAM–INDUCED NANOMETER‐SCALE DEPOSITION

(a)

207

10−3 10−4

P(b, 25 eV)

10−5 10−6 10−7 10−8 10−9 10−10 0

2

4 6 Impact parameter b (nm)

8

10

(b) 5 × 10−4

P(b, 25 eV)

4 × 10−4

3 × 10−4

2 × 10−4

1 × 10−4

0 0.0

0.1 0.2 Impact parameter b (nm) FIGURE 128. The probability PSE(b,E) that an SE is generated causing an energy loss of E ¼ 25 eV within an impact parameter b (corrected using the measured EELS‐SE coincidence spectra). (a) b up to 10 nm, (b) b up to 0.2 nm.

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FIGURE 129. (a) Normalized probability that an SE will be generated within an impact parameter b (100 kV electron incident on a 10 nm carbon foil). (b) Integral function of this probability: the probability that an SE will be generated in a circle of radius b.

Even though a non‐zero probability exists that an SE is generated at a distance of 1 nm, we see from Figure 129 that the probability decreases very sharply in the region 0–0.05 nm. From the plot of the integral function NS(x), we have estimated the FW50% of the SE delocalization profile to be 0.04 nm and the FW90% to be 0.32 nm.

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D. Delocalization of Surface Plasmon Generation The previous section analyzed the delocalization of single‐electron excitation events. This section analyzes the delocalization of collective excitations, generated in a medium by the passage of a fast electron. A particle approaching a polarizable body can induce collective excitations, including SPs, surface optical phonons, and surface excitons. Plasmons are collective oscillations of the valence (conduction) sea of electrons in a material. Two types of plasmons can be distinguished: volume (bulk) plasmons (VPs) and SPs. Volume excitation is only possible when the beam penetrates the target, whereas surface excitation can also occur if the beam passes near the surface. The intensity of SPs is roughly proportional to the area of the excited object and depends on the object shape. In the study of plasmons, the free‐electron theory has been applied with success for metals and semiconductors. For dielectrics this theory must be replaced with the dielectric response theory. A detailed study of plasmons can be found in Raether’s book (1980). Sernelius (2001) treats the SPs for different object configurations. The eigenfrequencies oS (SPs) and oP (bulk or volume plasmons) and the corresponding energies of the plasma oscillations ES ¼ hoS and EP ¼ hoP are known for a large number of materials, from measurements or calculations. The bulk plasmon eigenfrequency oP can be calculated using the Drude model that considers the electrons as free and not bound to the atoms. eðoÞ ¼ 1

o2P ; oðo þ iGÞ

ð145Þ

where e(o) is the dielectric function of the target material, and G is the damping due to frictional forces proportional to electron velocity. The resonance excitation of the volume occurs when e(o) ¼ 0. The energy ES of the SP on a flat target is (Egerton, 1996; Wang, 1996): pﬃﬃﬃ pﬃﬃﬃ ES ¼ ho S ¼ ho P = 2 ¼ E P = 2: ð146Þ For example, for amorphous carbon the SP is at 17.7 eV and the volume plasmon is at 20–25 eV. Figure 130 shows the energy loss function for surface and bulk plasmons in the case of carbon. The dielectric function was calculated using the optical data from Arakawa et al. (1977). EELS is usually used to measure the plasmon losses defined as the charge oscillations in a thin film irradiated by an electron beam. Currently EELS with a very fine beam can also register the loss spectra when the beam passes outside or inside a nanoparticle. The charge oscillations associated with plasmons can reach the entire medium even if the excitation source is a fine

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FIGURE 130. The energy loss function for carbon calculated from optical data from Arakawa et al. (1977). The solid line shows the surface plasmon, and the dashed line shows the bulk plasmon.

electron probe. The plasmon excitation therefore is a long‐range excitation and a delocalized scattering process. The plasmons decay, creating SEs or transferring part of their energy to the precursor gas molecules, and that is why they might influence the EBID resolution. We will attempt to estimate the implications that the plasmon delocalization might have in EBID. EBID involves an electron beam passing through a thin target and a gaseous precursor adsorbed on the target. Many types of plasmons can be generated and interact with each other, making this case very complicated to study. Because this is a first step in such an analysis, we will try to simplify the problem and reduce it to cases already solved and available in the literature. Therefore, let us analyze a simpler, practically assessed case, which considers an electron beam passing outside the target. A long‐range contamination growth at some distance from the electron trajectory can easily be observed in any electron microscope. The effect has been observed and modeled by Aristov et al. (1992) and Kislov and Khodos (1992). Contamination rods could be grown starting from the edge of a holey carbon foil even when the beam passed through a hole. This effect is also used in electron microscopy as a method of determining the horizontal contamination rate by measuring the time necessary to close a hole of given diameter. The EEL spectrum measured during the long‐range growth provides information about the mechanism of electron‐induced processes. The EEL spectrum of the passing 80 keV electron (Figure 131), recorded when a contamination rod was grown outside the beam trajectory (position 2), shows a carbon SP peak (17.7 eV). A different spectrum was recorded during

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211

FIGURE 131. The EELS spectra of PE passing through the rod (1, solid line) and outside the rod (2, dashed line). From Aristov et al. (1992). ß 1992, EDP Sciences.

the growth within the beam area (position 1), when the carbon volume plasmon peak (25 eV) appeared. This means that the long‐range growth can be explained by the electron interaction with the precursor molecule or the target via the SPs. We consider the SPs as an additional cause for the dissociation of molecules. In this context, a complete study of EBID resolution requires an estimation of the delocalization of SP generation. To obtain a first feeling of the dimension of the localization of plasmon generation by fast electrons, we can use a simple classical approach, proposed by Cheng (1987). A plasma is treated as a system containing many relatively mobile, charged particles. The excitation of a plasma is a coherent motion of a very large number of electrons, leading to small density fluctuations as a wave propagates through plasma. Consider a wave moving with a certain velocity, which decays in a certain time, then the localization distance can be defined as: L ¼ vg t;

ð147Þ

where vg is the group velocity and t is the relaxation time determined from the Heisenberg principle. The localization distance then is: L¼

6 h2 EF k ; 5 m Eplasmon DE1=2

ð148Þ

where Eplasmon is the plasmon energy, k is the average wave vector of the electron, and DE1/2 is the half width of the plasmon peak in the energy loss spectrum.

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For example, in the case of an aluminum target, the delocalization of a 15 eV plasmon generated by a 100 keV electron is 0.4 nm, a value also obtained from the experiments of Isaacson et al. (1974). Now the question is how an SP can induce a molecular dissociation. The electron can transfer energy and excite a precursor molecule situated some distance away via two channels. One of these is by direct‐resonant collective excitation of the valence electrons in the gas molecule (i.e., the excitation of SPs on the surface of the molecule; see Figure 120c). The situation is similar with the excitation of SPs on small metal spheres situated at some distance from the electron trajectory. The second process is an indirect one and involves the SP generated on the target edge parallel to the electron trajectory (see Figure 120d). This SP can transfer part of its energy to a nearby molecule. Both types of energy transfer may result in the dissociation of the molecule. Unfortunately, the specific cross sections for both processes are practically unknown. The direct excitation of the molecule probably has a larger cross section in deposition than the indirect process, because the SP generated on the target can also enhance gas desorption, which is a process counterbalancing adsorption and deposition. Let us first solve the problem of the localization of the generation of SPs. We can separate two types of SP‐mediated electron–molecule interactions: 1. The generation of a SP on the vertical edge of the thin target, treated as a single planar surface (see Figure 120c) 2. The generation of an SP on the molecule, treated as a nonplanar spherical surface (see Figure 120d). Both interaction processes are delocalized and have a certain probability of occurring, depending on the distance of the electron passage. We will treat these two cases separately. The eigenfrequencies of surface modes depend on the geometric shape of the excited object. For flat objects modeled as a plane‐bounded medium, a vast literature exists, whereas for spherical or cylindrical symmetric bodies the literature is less extensive. 1. Surface Plasmons on a Flat Surface The flat interface is the most important type of interface. Let us consider an electron moving parallel to the z‐axis at a distance x from a flat surface. Depending on the distance x, the electron may (or may not) cross the target (Figure 132). The plasmon generation on the flat edge (semi‐continuous medium) can occur at a certain distance from the electron trajectory with a probability given by (Howie, 1983; Marks, 1982; Wang, 1996):

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213

FIGURE 132. An incident PE passing through or outside of a target.

d 2 PðxÞ e2 2 2ox ¼ Im K 0 dodz 1þe v 2pe0 hv2

ð149Þ

if the electron passes parallel to and outside the surface (x > 0) and by: 1 0 11

0 10 0

d 2 PðxÞ e2 2ox

@1A@ @2pkc vA AA ¼ 2 ln K0 @

Im dodz e o v 2p e0 hv2 0 1 0 1

2 2ox AK 0 @ A

þ Im@

1þe v

ð150Þ

if the electron penetrates into the crystal (x < 0). In the first case, only SPs can be excited, as these have an electric field that is non‐zero outside the material. The first term in Eq. (150) describes the excitation of the VP and the second term describes the excitation of SPs. We now consider the case when the electron passes outside the surface (x > 0). Integrating the expression for the probability that a SP with energy ho will be generated at distance x over all possible frequencies, Aristov et al. (1992) obtained the full excitation probability of a plasmon on a flat surface at distance x along the electron path z: ze2 oG2 PS ðxÞ ¼ 2 S2 2p e0 hv

1 ð

K0 o0

2ox odo ; 2 v ðoS o2 Þ þ G2 o2

ð151Þ

where v is the velocity of the electron, G is the damping factor, experimentally determined experimentally from EELS to be equal to the width of the SP peak (1.5 1016 s–1), z is the length of the electron path at a distance x

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FIGURE 133. The calculated probability PS(x) for surface plasmon excitation on a 50 nm long edge of a carbon thin film as a function of electron impact parameter x. The energy of the incident electron is 100 keV.

from the surface (the target thickness), and hoS (¼ 17.7 eV) is the energy of the SP loss peak for amorphous carbon. If we use a simple threshold model for the precursor dissociation cross section, only the SPs with an energy exceeding the dissociation energy of hydrocarbon molecules (3 eV on average) are interesting. The lower limit of integration is chosen as o0 ¼ 5.331 1015 s–1. Figure 133 shows the calculated probability plot for SP generation at a distance x. We notice that the SP excitation also occurs when the beam passes at a distance of 1 nm outside the surface. The excitation probability drops quickly when the beam is far from the surface but is still non‐zero even when the beam is further than 2 nm from the edge. This result should be coupled to a cross section of SP‐induced dissociation to be able to give a quantitative estimate of the contribution of SP delocalization to the EBID rate. 2. Surface Plasmons on a Spherical Gas Molecule We may assume the gas molecule to be a dielectric sphere. The generation of a SP on the molecule can be treated similarly as the energy loss of an electron passing near a dielectric spherical particle. Currently, several theories exist that treat the particular case of dielectric spheres held in vacuum, and other

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215

FIGURE 134. An electron moving at impact parameter b > a near a dielectric sphere.

more general cases. The study of the more complicated case of supported particles is in rapid development. If the beam passes through the target, SPs will interact with volume plasmons, which makes the situation very difficult to model. Ouyang and Isaacson (1989a,b) developed a formalism that can deal with supported particles of any shape and dielectric constant. Usually simpler situations are analyzed, with particles in vacuum and subtracting the effect of the substrate. Let us consider a dielectric nanosphere of radius a, situated in vacuum and a fast electron passing with velocity v near this sphere at distance b from its center (Figure 134). The passing electron will induce a time‐dependent electrostatic field. While approaching the object, this field will excite polarization fields in the medium. The polarization‐induced electrical forces are given by Echenique and Howie (1987). During the time when the electron passes at a distance b from the molecule (10–17 s for a 100 keV electron), it can cause the collective displacement of the molecule valence electrons, without changing the position of its atomic nuclei. These excitations of the valence electrons are SPs, and they can cause the breaking of bonds or the ionization of the molecule. In a spherical geometry, the excited surface modes are quantified as a function of their angular momentum l. For spheres, the well‐defined SP modes have eigenfrequencies given by: 0sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ1 o2P l A ol ¼ @ ½1=s; ð152Þ 2l þ 1 where oP is the VP frequency. For an organic molecule, the typical plasmon loss can be calculated using the free‐electron theory: pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ hoP ¼ 4pNZe2 =me ; ð153Þ where me is the electron mass.

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The result is around hoP ¼ 20–25 eV (Aristov et al., 1992; Kislov and Khodos, 1992), for air at NTP: hoP ¼ 21 eV, for graphite: hoP ¼ 25 eV (Jackson, 1975). The main dipolar mode is associated with l ¼ 1 and most calculations are restricted to this term (Colliex, 1985; Schmeits, 1981). The dipole‐ approximation equivalent for spherical objects is the solution of electrodynamics for a uniformly moving charge and a harmonically bound charge. Little work has been done for the general case. Ache`che et al. (1986) have identified the contribution of higher l modes. Schmeits (1981) used the free‐ electron gas model for dipolar and a few superior l values. Ferrell and Echenique (1985) proposed a dielectric model that includes all multipole contributions. In general, the probability Ql for excitation of the l mode of an SP at distance b on a sphere of radius a has a maximum at r ¼ a, and for r >> a only the dipole mode can be excited. The governing factor is a transition factor with the radial dependence (Colliex, 1985): fl ðbÞ ¼ ðb=aÞl ; b=a < 1 : ða=bÞlþ1 ; b=a > 1

ð154Þ

The probability for excitation of the mode l of a SP on a dielectric sphere with radius a, by an electron passing at a distance b from the sphere center is given by Ferrell and Echenique (1985) and Schmeits (1981), using the free‐electron gas model: 1 X l o a2l o b ae2 X l l Pol ðbÞ ¼ Alm ol Km2 ; v v 2pe0 hv2 l¼0 m¼0

ð155Þ

where Alm ¼

ð2 d0m Þ ðl þ mÞ!ðl mÞ!

ð156Þ

and d0m is the Kronecker delta operator and Km ¼ the Bessel function of order m. The dipole approximation l ¼ 1 is valid only when oa/v 1, for a 100 keV electron implying that the radius of the sphere is a < 1 nm (Echenique et al., 1987). In many experimental situations, however, b a and oa/v 1, and therefore the study needs to include many l values, especially for electrons passing close to the sphere. Then again, a gas molecule usually has a radius smaller than 1 nm, so in a first approximation we can accept only the dipolar contributions.

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217

FIGURE 135. Probability of exciting the first mode of a surface plasmon (ol¼1 ¼ 14.4 eV) on a hydrocarbon molecule with radius a ¼ 0.5 nm at the reduced impact parameter B ¼ b a (nm) for a 100‐keV electron.

We can calculate the delocalization of the generation of the first mode SP (l ¼ 1) at a distance b from the sphere: o a3 o b a 1 1 2 2 o1 b Pol ðbÞ ¼ o1 K0 þ K1 ð157Þ 2pe0 v v h v2 v pﬃﬃﬃ The frequency of the first mode is ol¼1 ¼ oP/ 3 ¼ 14.4 eV. The probability of exciting an SP on a typical hydrocarbon molecule by a 100 keV electron is shown in Figure 135 as a function of the reduced impact parameter B ¼ b a. E. Conclusions The SEs play the most important role in EBID spatial resolution. By using the semi‐classical approach we estimated that the delocalization of the generation of SEs cannot enlarge their spatial profile with more than 0.5 nm. Another path used by the PEs to dissociate molecules is via SPs. We performed a simple calculation of the localization of SP‐induced dissociation, considering the case when the substrate is eliminated. A beam of fast electrons, at some distance away from the edge of a target with adsorbed gas

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molecules, can generate SPs on the surface of the gas molecules or on the edge of the target. The probability for generation of a SP in these two ways has a FW50% of 1 nm. At distances larger than 2 nm the probability of SP generation drops drastically. The same conclusions have been obtained by Aristov et al. (1992) and by Han and Cerrina (2000). Because of the lack of accurate cross sections for the dissociation of the precursor molecules due to these processes it is difficult to draw quantitative conclusions on the contribution of Plasmon‐induced processes to the EBID resolution.

VI. CONCLUSIONS Section II provided an extensive overview of EBID results achieved recently and in the past, showing that in the past few years great progress has been made in EBID lateral structure sizes. The smallest dots, written with a 0.3 nm STEM probe, have an average diameter of only 1 nm (van Dorp et al., 2005). Lateral structure sizes always exceed the diameter of the electron beam, and many authors suspected that the SEs generated in the EBID process play a role in the spatial evolution of structures grown by EBID, but they never really quantified this. In Section III, we described the theory of the EBID spatial resolution. This resolution is influenced by many factors, two of which we have quantified: the SEs and the delocalization of inelastic scattering. We treated the generation of SEs by the primary electron beam using MC simulations. We have not just calculated the exit points of the SEs at the target surface, as many others have done, for instance to estimate SEM imaging resolution, but also the energy distribution at each point of the surface. This information was used, together with the energy‐dependent cross section for the dissociation of adsorbed precursor molecules, to calculate the deposit size. We also described the relevant interactions between electrons and the precursor molecules, as well as some surface processes that may influence the spatial resolution, such as surface diffusion and surface electric fields. Section IV describes an MC program used to calculate the spatial resolution in EBID and a profile simulator based on cellular automata to model the growth of a single dot in the spot mode of an electron microscope. The ultimate resolution calculated for a zero‐diameter electron beam and a very thin (10 nm) target, according to our model, is 0.23 nm (FW50). However, the SEs generated in the freshly grown structure impose a larger limit on the spatial resolution of EBID. This limit is 2 nm as soon as the height of the structures exceeds a few monolayers. When taller structures are grown, our

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model predicts that the width saturates as dictated by the range of the SEs generated in the deposit, in agreement with experimental observations. Section V estimated the effect of the delocalization of inelastic scattering, and we conclude that it does not impose a fundamental limit to the EBID resolution. Recently parts of Sections III, IV, and V have also been published elsewhere (Silvis‐Cividjian et al., 2005). Much work still remains to be done to better understand the EBID process. For instance, little is known about the actual precursor dissociation process, the surface migration of partially decomposed fragments, or how to improve the purity of the deposits. However, the fact that the lateral resolution of EBID is 1 nm offers a very promising perspective for the fabrication of sub–10 nm structures. In nanoscience, the possibility to routinely create structures between 1 and 10 nm hopefully generates as much interesting physics as has been the case when 10–100 nm structures became available through microfabrication techniques. In the long run, EBID also may very well play a role in the semiconductor industry, as a writing tool for the sub–10 nm details of ICs.

ACKNOWLEDGMENTS We gratefully acknowledge Willem F. van Dorp for his contributions to Section II, Pieter Kruit for numerous discussions on EBID and many valuable suggestions, and Annelies E. van Diepen for careful proofreading and preparation of the manuscript for publication.

REFERENCES Ache`che, M., Colliex, C., Kohl, H., Nourtier, A., and Trebbia, P. (1986). Theoretical and experimental study of plasmon excitations in small metallic spheres. Ultramicroscopy 20, 99–105. Adalsteinsson, D., and Sethian, J. A. (1995). A level set approach to a unified model for etching, deposition, and lithography. I: Algorithms and two‐dimensional simulations. J. Comput. Phys. 120, 128–144. Ahlen, S. P. (1980). Theoretical and experimental aspects of the energy loss of relativistic heavily ionizing particles. Reviews of Modern Physics 52, 121–173. Akama, Y., Nishimura, E., Sakai, A., and Murakami, H. (1990). New scanning tunneling microscopy tip for measuring surface topology. J. Vac. Sci. Technol. A 8, 429–433. Albrecht, T. R., Dovek, M., Kirk, D. M., Lang, C. A., Quate, C. F., and Smith, D. P. E. (1989). Nanometer‐scale hole formation on graphite using a scanning tunneling microscope. App. Phys. Lett. 55, 1727–1729.

220

SILVIS-CIVIDJIAN AND HAGEN

Allen, T. T., Kunz, R. R., and Mayer, T. M. (1988). Monte Carlo calculations of low‐energy electron emissions from surfaces. J. Vac. Sci. Technol. B 6, 2057–2060. Alman, D.A, Ruzic, D. N., and Brooks, J. N. (2000). A hydrocarbon reaction model for low temperature hydrogen plasma and an application to the Joint European Torus. Phys. Plasmas 7, 1421–1432. Amelio, G. F. (1970). Theory for the energy distribution of secondary electrons. J. Vac. Sci. Technol. 7, 593–604. Amman, M., Sleight, J. W., Lombardi, D. R., Welser, R. E., Deshpande, M. R., Reed, M. A., and Guido, L. J. (1996). Atomic force microscopy study of electron beam written contamination structures. J. Vac. Sci. Technol. B 14, 54–62. Antognozzi, M., Sentimenti, A., and Valdre`, U. (1997). Fabrication of nano‐tips by carbon contamination in a scanning electron microscope for use in scanning probe microscopy and field emission. Microsc. Microanal. Microstruct. 8, 355–368. Arakawa, E. T., Wiliams, M. W., and Inagaki, T. (1977). Optical properties of arc evaporated carbon films between 0.6 and 3.8 eV. J. Appl. Phys. 48, 3176–3177. Aristov, V. V., Kasumov, A. Y., Kislov, N. A., Kononenko, O. V., Matveev, V. N., Tulin, I. I., Khodos, I. I., Gorbatov, Y. A., and Nikolaichik, V. I. (1995). A new approach to fabrication of nanostructures. Nanotechnology 6, 35–39. Aristov, V. V., Kislov, N. A., and Khodos, I. I. (1992). Direct electron‐beam‐induced formation of nanometer‐scale carbon structures in STEM. I. Nature of ‘‘long‐range’’ growth outside the substrate. Microsc. Microanal. Microstruct. 3, 313–322. Arratia‐Perez, R., and Yang, C. Y. (1985). Bonding in metal hexacarbonyls. J. Chem. Phys. 83, 4005–4014. Ashankar, D. (1976). Construction of energy loss function for low‐energy electrons in helium. Physica C 81, 409–414. Ashankar, D. (1977). Electron energy deposition in helium. Physica C 85, 219–222. Atkins, P. W., and Friedman, R. S. (1997). Molecular Quantum Mechanics, 3rd ed. Oxford: Oxford University Press. Autrata, R., Hermann, R., and Muller, M. (1992). An efficient single crystal BSE detector in SEM. Scanning 14, 127–135. Bauerdick, S., Burkhardt, C., Rudorf, R., Barth, W., Bucher, V., and Nisch, W. (2003). In‐situ monitoring of electron beam induced deposition by atomic force microscopy in a scanning electron microscope. Microelctron. Eng. 67–68, 963–969. Beach, N. A., and Gray, H. B. (1968). Electronic structures of metal hexacarbonyls. J. Am. Chem. Soc. 90, 5713–5721. Bedson, T. R., Palmer, R. E., and Wilcoxon, J. P. (2001). Electron beam lithography in passivated gold nanoclusters. Microelectron. Eng. 57–58, 837–841. Behringer, U. F. W., and Vettiger, P. (1986). Repair techniques for silicon transmission masks used for submicron lithography. J. Vac. Sci. Technol. B 4, 94–99. Bezryadin, A., and Dekker, C. (1997). Nanofabrication of electrodes with sub‐5 nm spacing for transport experiments on single molecules and metal clusters. J. Vac. Sci. Technol. B 15, 793–799. Blauner, P. G., Ro, J. S., Butt, Y., and Melngailis, J. (1989). Focused ion beam fabrication of submicron gold structures. J. Vac. Sci. Technol. B 7, 609–617. Bolton, J. P. R., and Brown, L. M. B. (1990). Imaging surface states in the electron microscope: A semiclassical model. Proc. R. Soc. London A 428, 291–305. Bongeler, R., Golla, U., Kassens, M., Reimer, L., Schindler, B., Senkel, R., and Spranck, M. (1993). Electron specimen interactions in low voltage scanning electron microscopy. Scanning 15, 1–18.

ELECTRON‐BEAM–INDUCED NANOMETER‐SCALE DEPOSITION

221

Bret, T., Utke, I., Bachmann, A., and Hoffmann, P. (2003). In situ control of the focused‐ electron‐beam‐induced deposition process. Appl. Phys. Lett. 83, 4005–4007. Bret, T., Mauron, S., Utke, I., and Hoffmann, P. (2005). Characterization of focused electron beam induced carbon deposits from organic precursors. Microelectron. Eng. 78–79, 300–306. Brockway, L. O., Ewens, R. V. G., and Lister, M. W. (1938). An electron diffraction investigation of the hexacarbonyls of chromium, molybdenum and tungsten. Trans. Faraday Soc. 34, 1350–1357. Broers, A. N., Molzen, W. W., Cuomo, J. J., and Wittels, N. D. (1976). Electron‐beam ˚ metal structures. Appl. Phys. Lett. 29, 596–598. formation of 80‐A Broers, A. N. (1988). Resolution limits for electron beam lithography. IBM J. Res. Develop. 32, 502–513. Broers, A. N., Hoole, A. C. F., and Ryan, J. M. (1996). Electron beam lithography—Resolution limits. Microelectron. Eng. 32, 131–142. Browning, R., Li, T. Z., Chui, B., Ye, J., Pease, R. F. W., Czyzewski, Z., and Joy, D. C. (1994). Empirical forms for the electron/atom elastic scattering cross sections from 0 to 30 keV. J. Appl. Phys. 76, 2016–2022. Bruckle, H., Kretz, J., Koops, H.W, and Reiss, G. (1999). Low energy electron beam decomposition of metalorganic precursor with a scanning tunneling microscope at ambient atmosphere. J. Vac. Sci. Technol. B 17, 1350–1353. Bruk, M. A., Zhikharev, E. N., Grigor’ev, E. I., Spirin, A. V., Kal’nov, V. A., and Kardash, I. E. (2005). Focused electron beam‐induced deposition of iron‐ and carbon‐ containing nanostructures from triiron dodecacarbonyl vapor. High Energ. Chem. 39, 65–68. Buseck, P. R., Cowley, J. M., and Eyring, L. (1988). High‐Resolution Transmission Electron Microscopy and Associated Techniques. Oxford: Oxford University Press. Castagne´, M., Benfedda, M., Lahimer, S., Falgayrettes, P., and Fillard, J. P. (1999). Near field optical behaviour of C supertips. Ultramicroscopy 76, 187–194. Cazaux, J. (1986). Some considerations on the electric field induced in insulators by electron bombardment. J. Appl. Phys. 59, 1418–1430. Cazaux, J. (1995). Correlations between ionization radiation damage and charging effects in transmission electron microscopy. Ultramicroscopy 60, 411–425. Cheng, S. C. (1987). Localization distance of plasmons excited by high‐energy electrons. Ultramicroscopy 21, 291–292. Christophorou, L. G., Olthoff, J.K, and Rao, M. V. V. S. (1996). Electron interactions with CF4. J. Phys. Chem. Ref. Data 25, 1341–1388. Christy, R. W. (1960). Formation of thin polymer films by electron bombardment. J. Appl. Phys. 31, 1680–1683. Chung, M. S., and Everhart, T. E. (1974). Simple calculations of energy distribution of low‐ energy secondary electrons emitted from metals under electron bombardment. J. Appl. Phys. 45, 707–709. Chung, S., Lin, C. C., and Lee, E. T. P. (1975). Dissociation of the hydrogen molecule by electron impact. Phys. Rev. A 12, 1340–1349. Cicoira, F., Leifer, K., Hoffmann, P., Utke, I., Dwir, B., Laub, D., Buffat, P. A., Kapon, E., and Doppelt, P. (2004). Electron beam induced deposition of rhodium from the precursor [RhCl(PF3)2]2: morphology, structure and chemical composition. J. Cryst. Growth 265, 619–626. Cicoira, F., Hoffmann, P., Olsson, C. O. A., Xanthopoulos, N., Mathieu, H. J., and Doppelt, P. (2005). Auger electron spectroscopy analysis of high metal content micro‐structures grown by electron beam induced deposition. Appl. Surf. Sci. 242, 107–113. Colliex, C. (1985). An illustrated review of various factors governing the high spatial resolution capabilities in EELS microanalysis. Ultramicroscopy 18, 131–150.

222

SILVIS-CIVIDJIAN AND HAGEN

Craighead, H. G., and Mankiewich, P. M. (1982). Ultra‐small particle arrays produced by high resolution electron‐beam lithography. J. Appl. Phys. 53, 7186–7188. Crozier, P. A., Tolle, J., Kouvetakis, J., and Ritter, C. (2004). Synthesis of uniform GaN quantum dot arrays via electron nanolithography of D2GaN3. Appl. Phys. Lett. 84, 3441–3443. Czyzewski, Z., O’Neil MacCallum, D., Romig, A., and Joy, D. C. (1990). Calculations of Mott scattering cross section. J. Appl. Phys. 68, 3066–3072. Dagata, J. A., Schneir, J., Harary, H. H., Evans, C. J., Postek, M. T., and Benett, J. (1990). Modification of hydrogen‐passivated silicon by a scanning tunneling microscope operating in air. Appl. Phys. Lett. 56, 2001–2003. Davies, S. T., and Khamsehpour, B. (1996). FIB machining and deposition for nanofabrication. Vacuum 47, 455–462. Devooght, J., Dubus, A., and Dehaes, J. C. (1987). Improved age‐diffusion model for low‐ energy electron transport in solids. I. Theory. Phys. Rev. B 36, 5093–5109. Ding, Z. J., and Shimizu, R. (1989). Theoretical study of the ultimate resolution of SEM. J. Microsc. 154, 193–195. Ding, Z. J., and Shimizu, R. (1996). A Monte Carlo modeling of electron interaction with solids including cascade secondary electron production. Scanning 18, 92–113. Ding, Z. J., and Shimizu, R. (2000). Monte Carlo simulation study of secondary electron emission and surface excitation. Inst. Phys. Conf. Ser. No. 165: Symposium 8, 2nd Conf. Int. Union Microbeam Analysis Societies, Kailua‐Kona, Hawaii, 9–13 July 2000. London: IOP Publishing Ltd., p. 279. Ding, Z. J., Shimizu, R., Sekine, T., and Sakai, Y. (1988). Theoretical and experimental studies of N(E) spectra in Auger electron spectroscopy. Appl. Surf. Sci. 33–34, 99–106. Ding, Z.J, Tang, X. D., and Shimizu, R. (2001). Monte Carlo study of secondary electron emission. J. Appl. Phys. 89, 718–726. Djenizian, T., Macak, J., and Schmuki, P. (2003). Selective titanium oxide formation using electron‐beam induced carbon deposition technique. Mater. Res. Soc. Symp. Proc. 741, J.4.5.1–J.4.5.5. Djenizian, T., Santinacci, L., and Schmuki, P. (2004). Factors in electrochemical nanostructure fabrication using electron‐beam induced carbon masking. J. Electrochem. Soc. 151, G175–G180. Drucker, J., and Scheinfein, M. R. (1993). Delocalization of secondary‐electron generation studied by momentum‐resolved coincidence‐electron spectroscopy. Phys. Rev. B 47, 15973–15975. Drucker, J., Scheinfein, M. R., Liu, J., and Weiss, J. K. (1993). Electron coincidence spectroscopy studies of secondary and Auger electron generation mechanisms. J. Appl. Phys. 74, 7329–7339. Dubner, A.D, Shedd, G. M., Lezec, H., and Melngailis, J. (1987). Ion‐beam‐induced deposition of gold by focused and broad‐beam sources. J. Vac. Sci. Technol. B 5, 1434–1435. Dubner, A.D, and Wagner, A. (1989). Mechanism of ion beam induced deposition of gold. J. Vac. Sci. Technol. B 7, 1950–1953. Dubner, A. D., Wagner, A., Melngailis, J., and Thompson, C. V. (1991). The role of the ion‐ solid interaction in ion‐beam‐induced deposition of gold. J. Appl. Phys. 70, 665–673. Dujardin, G., Walkup, R. E., and Avouris, Ph. (1992). Dissociation of individual molecules with electrons from the tip of a scanning tunneling microscope. Science 255, 1232–1235. Dwyer, V. M., and Matthew, J. A. D. (1985). A comparison of electron transport in AES/PES with neutron transport theory. Surf. Sci. 152–153, 884–894. Echenique, P. M., and Howie, A. (1987). Image force effects in electron microscopy. Ultramicroscopy 16, 269–272.

ELECTRON‐BEAM–INDUCED NANOMETER‐SCALE DEPOSITION

223

Echenique, P. M., Howie, A., and Wheatley, D. J. (1987). Excitation of dielectric spheres by external electron beams. Philos. Mag. B 56, 335–349. Edinger, K., and Kraus, T. (2000). Modeling of focused ion beam induced surface chemistry. J. Vac. Sci. Technol. B 18, 3190–3193. Egerton, R. F. (1996). Electron Energy‐Loss Spectroscopy in the Electron Microscope, 2nd ed. New York: Plenum. Ennos, A. E. (1954). The sources of electron‐induced contamination in kinetic vacuum systems. Br. J. Appl. Phys. 5, 27–31. Everhart, T. E., and Chung, M. S. (1972). Idealized spatial emission distribution of secondary electrons. J. Appl. Phys. 43, 3707–3711. Fano, U. (1970). The formulation of track structure theory, in Charged Particle Tracks in Solids and Liquids, edited by L.H. Gray and G.E. Adams. London: Institute of Physics, p. 1. Ferrell, T. L., and Echenique, P. M. (1985). Generation of surface excitations on dielectric spheres by an external electron beam. Phys. Rev. Lett. 55, 1526–1529. Fitting, H. J., Hinkfoth, C., Glaefeke, H., and Kuhr, J.‐Ch. (1991). Electron scattering in the keV and sub‐keV range. Phys. Status Solidi A 126, 85–99. Floreani, F., Koops, H. W. P., and Els€aßer, W. (2001). Operation of high power field emitters fabricated with electron beam deposition and concept of a miniaturised free electron laser. Microelectron. Eng. 57–58, 1009–1016. Folch, A., Servat, J., Esteve, J., and Tejada, J. (1996). High vacuum versus ‘‘environmental’’ electron beam deposition. J. Vac. Sci. Technol. B 14, 2609–2614. Folch, A., Tejada, J., Peters, C. H., and Wrighton, M. S. (1995). Electron beam induced deposition of gold nanostructures in a reactive environment. Appl. Phys. Lett. 66, 2080–2082. Foresman, J. B., and Frisch, A. (1996). Exploring Chemistry with Electronic Structure Methods. Pittsburgh: Gaussian. Fourie, J. T. (1975). The controlling parameter in contamination of specimens in electron microscopy. Optik 44, 111–114. Fourie, J. T. (1976). A model for contamination phenomena in electron microscopes, in Proceedings of the VIth European Congress on Electron Microscopy, Jerusalem, pp. 396–398. Fourie, J. T. (1978). High contamination rates from strongly adsorbed hydrocarbon molecules and a suggested solution. Optik 52, 91–95. Fourie, J. T. (1979). A theory of surface origination contamination and a method for its elimination, in Scanning Electron Microscopy, Vol. II, Chicago: SEM Inc., pp. 87–102. Fourie, J. T. (1981). Electric effects in contamination and electron beam etching, in Scanning Electron Microscopy, edited by O. Johari. Vol. I, Chicago: SEM Inc., pp. 87–102. Fransen, M. J., Damen, E. P. N., Schiller, C., van Rooy, T. L., Groen, H. B., and Kruit, P. (1996). Characterization of ultrasharp field emitters by projection microscopy. Appl. Surf. Sci. 94–95, 107–112. Frisch, A., and Frisch, M. J. (1998). Gaussian 98 User’s Reference. Pittsburgh: Gaussian. Fritzsche, W., Ko¨hler, J. M., Bo¨hm, K. J., Unger, E., Wagner, T., Kirsch, R., Mertig, M., and Pompe, W. (1999). Wiring of metallized microtubules by electron‐beam‐induced structuring. Nanotechnology 10, 331–335. Fujita, J., Ishida, M., Ichihashi, T., Ochiai, Y., Kaito, T., and Matsui, S. (2003). Carbon nanopillar laterally grown with electron beam‐induced chemical vapor deposition. J. Vac. Sci. Technol. B 21, 2990–2993. Gamo, K., Takakura, N., Samoto, N., Shimizu, R., and Namba, S. (1984). Ion beam assisted deposition of metalorganic films using focused ion beams. Jpn. J. Appl. Phys. 23, L293–L295. Gauvin, R., and Drouin, D. (1993). A formula to compute total elastic Mott cross sections. Scanning 15, 140–150.

224

SILVIS-CIVIDJIAN AND HAGEN

Gauvin, R., and Le´sperance, G. (1992). A Monte Carlo code to simulate the effect of fast secondary electrons on kAB factors and spatial resolution in the TEM. J. Microsc. 168, 153–167. Geoffroy, G. L., and Wrighton, M. S. (1979). Organometallic Photochemistry. New York: Academic Press. Gopal, V., Stach, E. A., Radmilovic, V.R, and Mowat, I. A. (2004). Metal delocalization and surface decoration in direct‐write nanolithography by electron beam induced deposition. Appl. Phys. Lett. 85, 49–51. Gopal, V., Radmilovic, V. R., Daraio, C., Jin., S., and Yang, P. (2004). Rapid prototyping of site‐specific nanocontacts by electron and ion beam assisted direct‐write nanolithography. Nano Lett. 4, 2059–2063. Go¨rtz, W., Kempf, B., and Kretz, J. (1995). Resolution enhanced scanning force microscopy measurements for characterizing dry etching methods applied to titanium masked InP. J. Vac. Sci. Technol. B 13, 34–39. Greeneich, J. S., and van Duzer, T. (1973). Model for exposure of electron‐sensitive resists. J. Vac. Sci. Technol. 10, 1056–1059. Guise, O., Ahner, J., Yates, J., and Levy, J. (2004a). Formation and thermal stability of sub‐ 10‐nm carbon templates on Si(100). Appl. Phys. Lett. 85, 2352–2354. Guise, O., Marbach, H., Levy, J., Ahner, J., and Yates, J. T., Jr. (2004b). Electron‐beam‐ induced deposition of carbon films on Si(100) using chemisorbed ethylene as a precursor molecule. Surf. Sci. 571, 128–138. Hall, J. T., Hansma, P. K., and Parikh, M. (1977). Electron beam damage of chemisorbed surface species: A tunneling spectroscopy study. Surf. Sci. 65, 552–562. Hameka, H. F. (1965). Advanced Quantum Chemistry; Theory of Interactions between Molecules and Electromagnetic Fields. Reading: Addison‐Wesley. Han, G., and Cerrina, F. (2000). Energy transfer between electrons and photoresist: Its relation to resolution. J. Vac. Sci. Technol. B 18, 3297–3302. Han, M., Mitsuishi, K., Shimojo, M., and Furuya, K. (2004). Nanostructure characterization of tungsten‐containing nanorods deposited by electron‐beam‐induced chemical vapour decomposition. Philos. Mag. A 84, 1281–1289. Harada, V., Tomita, T., Watabe, T., Watanabe, H., and Etoh, T. (1979). Reduction of contamination in analytical electron microscope, in Scanning Electron Microscopy, edited by O. Johari. Vol. II, pp. 103–110. Chicago: SEM Inc. Harriot, L. R. (1993). Digital scan model for focused ion beam induced gas etching. J. Vac. Sci. Technol. B 11, 2012–2015. Harriot, L.R, and Vasile, M. J. (1988). Focused ion beam induced deposition of opaque carbon film. J. Vac. Sci. Technol. B 6, 1035–1038. Hart, R. K., Kassner, T. F., and Maurin, J. K. (1970). The contamination of surfaces during high‐energy electron irradiation. Phil. Mag. 21, 453–467. Hawryluk, R. J., Hawryluk, A. M., and Smith, H. I. (1974). Energy dissipation in a thin polymer film by electron beam scattering. J. App. Phys. 45, 2551–2566. Henoc, J., and Maurice, F. (1991). A flexible and complete Monte Carlo procedure for the study of the choice of parameters, in Electron Probe Quantitation, edited by K.F.J. Heinrich and D.E. Newbury. New York: Plenum Press, pp. 105–143. Hiroshima, H., and Komuro, M. (1997). High growth rate for slow scanning in electron‐beam‐ induced deposition. Jpn. J. Appl. Phys. 36, 7686–7690. Hiroshima, H., and Komuro, M. (1998). Fabrication of conductive wires by electron‐beam‐ induced deposition. Nanotechnology 9, 108–112. Hiroshima, H., Okayama, S., Komuro, M., Ogura, M., Nakazawa, H., Nagagawa, Y., Ohi, K., and Tanaka, K. (1995). Nanobeam process system: An ultrahigh vacuum electron beam lithography system with 3 nm probe size. J. Vac. Sci. Technol. B 13, 2514–2517.

ELECTRON‐BEAM–INDUCED NANOMETER‐SCALE DEPOSITION

225

Hiroshima, H., Suzuki, N., Ogawa, N., and Komuro, M. (1999). Conditions for fabrication of highly conductive wires by electron‐beam‐induced deposition. Jpn. J. Appl. Phys. 38, 7135–7139. Ho, Y., Tan, Z., Wang, X., and Chen, J. (1991). A theory and Monte Carlo calculation on low‐ energy electron scattering. Scanning Microsc. 5, 945–951. Hoffmann, P., Utke, I., and Cicoira, F. (2002). Limits of 3‐D nanostructures fabricated by focused electron beam (FEB) induced deposition. Proceedings of the 10th International Conference on Nanoscience and Technologies, St. Petersburg, 2002, pp. 5–11. Hovington, P., Drouin, D., and Gauvin, R. (1997a). CASINO:A new Monte Carlo Codein C language for electron beam interaction—Part I: Description of the program. Scanning 19, 1–14. Hovington, P., Drouin, D., Gauvin, R., Joy, D. C., and Evans, N. (1997b). CASINO: A new Monte Carlo Code in C language for electron beam interaction—Part III: Stopping power at low energies. Scanning 19, 29–35. Howie, A. (1983). Surface reactions and excitations. Ultramicroscopy 11, 141–148. Hoyle, P. C., Cleaver, J. R. A., and Ahmed, H. (1994). Ultralow‐energy focused electron beam induced deposition. Appl. Phys. Lett. 64, 1448–1450. Hoyle, P.C, Cleaver, J. R. A., and Ahmed, H. (1996). Electron beam induced deposition from W(CO)6 at 2 to 20 keV and its applications. J. Vac. Sci. Technol. B 14, 662–673. Hoyle, P. C., Ogasawara, M., Cleaver, J. R. A., and Ahmed, H. (1993). Electrical resistance of electron beam induced deposits from tungsten hexacarbonyl. Appl. Phys. Lett. 62, 3043–3045. Hren, J. (1986). Barriers to AEM: contamination and etching, in Principles of Analytical Electron Microscopy, edited by D. Joy, A. Romig, and J. Goldstein. New York: Plenum, p. 353. Hu¨bner, B., Koops, H. W. P., Pagnia, H., Sotnik, N., Urban, J., and Weber, M. (1992). Tips for scanning tunneling microscopy produced by electron‐beam‐induced deposition. Ultramicroscopy 42–44, 1519–1525. Hu¨bner, B., Jede, R., Specht, I., and Zengerle, R. (1996). E‐beam lithography by using an STEM with integrated laser interferometer stage. Microelectron. Eng. 30, 41–44. Hu¨bner, U., Plontke, R., Blume, M., Reinhardt, A., and Koops, H. W. P. (2001). On‐line nanolithography using electron beam‐induced deposition technique. Microelectron. Eng. 57–58, 953–958. Ichihashi, T., and Matsui, S. (1988). In situ observation on electron beam induced chemical vapor deposition by transmission electron microscopy. J. Vac. Sci. Technol. B 6, 1869–1872. Inokuti, M. (1971). Inelastic collisions of fast charged particles with atoms and molecules—the Bethe theory revisited. Rev. Mod. Phys. 43, 297–348. Isaacson, M., Langmore, J. P., and Rose, H. (1974). Determination of the non‐localization of the inelastic scattering of electrons by electron microscopy. Optik 41, 92–96. Ishibashi, A., Funato, K., and Mori, Y. (1991). Electron‐beam‐induced resist and aluminium formation. J. Vac. Sci. Technol. B 9, 169–172. Jackman, R. B., and Foord, J. S. (1986). Electron beam stimulated chemical vapor deposition of patterned tungsten films on Si(100). Appl. Phys. Lett. 49, 196–198. Jackson, J. D. (1975). Classical Electrodynamics. New York: Wiley. de Jager, P. (1997). Design of the ‘‘Fancier,’’ an Instrument for Fabrication and Analysis of nanostructures combining Ion and Electron Regulation. Delft: Delft University of Technology. James, F. (1980). Monte Carlo theory and practice. Rep. Prog. Phys. 43, 1145–1189. Jiang, H., Borca, C. N., Xu, B., and Robertson, B. W. (2001). Fabrication of 2‐ and 3‐dimensional nanostructures. Int. J. Mod. Phys. B 15, 3207–3213. Johnson, S. D., Hasko, D. G., Teo, K. B. K., Milne, W. I., and Ahmed, H. (2002). Fabrication of carbon nanotips in a scanning electron microscope for use as electron field emission sources. Microelectron. Eng. 61–62, 665–670.

226

SILVIS-CIVIDJIAN AND HAGEN

Jonas, V., and Thiel, W. (1995). Theoretical study of the vibrational spectra of the transition metals carbonyls M(CO)6 [M¼Cr, Mo, W], M(CO)5 [M¼Fe, Ru, Os], and M(CO)4 [M¼Ni, Pd, Pt]. J. Chem. Phys. 102, 8474–8484. Joy, D. C. (1983). The spatial resolution limit of electron lithography. Microelectron. Eng. 1, 103–119. Joy, D. C. (1984a). Beam interactions, contrast and resolution in the SEM. J. Microsc. 136, 241–258. Joy, D. C. (1984b). Monte Carlo studies of high resolution imaging, in Microbeam Analysis, edited by A. Romig and J. Goldstein. San Francisco: San Francisco Press, p. 81. Joy, D. C. (1985). Resolution in low voltage scanning electron microscopy. J. Microsc. 140, 283–292. Joy, D. C. (1988). An introduction to Monte Carlo simulations. Inst. Phys. Conf. Ser. 93, 23–32. Joy, D. C. (1991). The theory and practice of high‐resolution scanning electron microscopy. Ultramicroscopy 37, 216–233. Joy, D. C., and Pawley, J. B. (1992). High‐resolution scanning electron microscopy. Ultramiscopy 47, 80–100. Joy, D. C. (1995a). Monte Carlo Modeling for Electron Microscopy and Microanalysis. New York: Oxford University Press. Joy, D. C. (1995b). A database on electron‐solid interactions. Scanning 17, 270–275. Joy, D. C., Newbury, D. E., and Myklebust, R. L. (1982). The role of fast secondary electrons in degrading spatial resolution in the analytical electron microscope. J. Microsc. 128, RP1–RP2. Kanter, H. (1970). Slow electron mean free paths in Al, Ag and Au. Phys. Rev. B 1, 522–536. Keller, D. J., and Chih‐Chung, C. (1992). Imaging steep, high structures by scanning force microscopy with electron beam deposited tips. Surf. Sci. 268, 333–339. Kent, A. D., Shaw, T. M., von Molna´r, S., and Awschalom, D. D. (1993). Growth of high aspect ratio nanometer‐scale magnets with chemical vapor deposition and scanning tunneling microscopy. Science 262, 1249–1252. Kijima, T., Kotera, M., Suga, H., and Nakase, Y. (1995). Monte Carlo calculations on the passage of electrons through thin films irradiated by 300 keV‐electrons. Trans. IEICE (C) E78, 557–563. Kijima, T., and Nakase, Y. (1996). Monte Carlo calculations of the behavior of 300 keV electrons from accelerators. Radiation Measurements 26, 159–168. Kim, Y.‐K., and Rudd, M. E. (1994). Binary‐encounter‐dipole model for electron‐impact ionization. Phys. Rev. A 50, 3954–3967. Kim, Y.‐K., Hwang, W., Weinberger, N. M., Ali, M.A, and Rudd, M. E. (1997). Electron‐ impact ionization cross sections of atmospheric molecules. J. Chem. Phys. 106, 1026–1033. Kislov, N. A., and Khodos, I. I. (1992). Direct electron‐beam‐induced formation of nanometer‐ scale carbon structures in STEM. II. The growth of rods outside the substrate. Microsc. Microanal. Microstruct. 3, 323–331. Kislov, N. A., Khodos, I. I., Ivanov, E. D., and Barthel, J. (1996). Electron‐beam‐induced fabrication of metal‐containing nanostructures. Scanning 18, 114–118. Knoll, G. F. (1979). Radiation Detection and Measurement. New York: Wiley. Koh, Y. B., Gamo, K., and Namba, S. (1991). Characteristics of W films formed by ion beam assisted deposition. J. Vac. Sci. Technol. B 9, 2648–2652. Kohlmann, K. T., Thiemann, M., and Bru¨nger, W. H. (1991). E‐beam induced X‐ray mask repair with optimized gas nozzle geometry. Microelectron. Eng. 13, 279–282. Kohlmann, K. T., Buchmann, L.‐M., and Bru¨nger, W. H. (1992). Repair of open stencil masks for ion projection lithography by e‐beam induced metal deposition. Microelectron. Eng. 17, 427–430.

ELECTRON‐BEAM–INDUCED NANOMETER‐SCALE DEPOSITION

227

Kohlmann‐von Platen, K. T., Buchmann, L.‐M., Petzold, H.‐C., and Bru¨nger, W. H. (1992). Electron beam induced tungsten deposition: Growth rate enhancement and applications in microelectronics. J. Vac. Sci. Technol. B 10, 2690–2694. Kohlmann‐von Platen, K.T, Chlebek, J., Weiss, M., Reimer, K., Oertel, H., and Bru¨nger, W. H. (1993). Resolution limits in electron beam induced tungsten deposition. J. Vac. Sci. Technol. B 11, 2219–2223. Komano, H., Ogawa, Y., and Takigawa, T. (1989). Silicon oxide formation by focused ion beam (FIB)‐assisted deposition. Jpn. J. Appl. Phys. 28, 2372–2375. Komuro, M., and Hiroshima, H. (1997a). Fabrication and properties of dot array using electron‐beam‐induced deposition. Microelectron. Eng. 35, 273–276. Komuro, M., and Hiroshima, H. (1997b). Lateral junction produced by electron‐beam‐induced deposition. J. Vac. Sci. Technol. B 15, 2809–2815. Komuro, M., Hiroshima, H., and Takechi, A. (1998). Miniature tunnel junction by electron‐ beam‐induced deposition. Nanotechnology 9, 104–107. Koops, H. W. P., Weiel, R., Kern, D. P., and Baum, T. H. (1988). High‐resolution electron‐ beam induced deposition. J. Vac. Sci. Technol. B 6, 477–481. Koops, H. W. P., Kretz, J., Rudolph, M., and Weber, M. (1993). Constructive three‐dimensional lithography with EBID of quantum effect devices. J. Vac. Sci. Technol. B 11, 2386–2389. Koops, H. W. P., Kretz, J., Rudolph, M., Weber, M., Dahm, G., and Lee, K. L. (1994). Characterization and application of materials grown by EBID. Jpn. J. Appl. Phys. 33, 7099–7107. Koops, H. W. P., Kaya, A., and Weber, M. (1995). Fabrication and characterization of platinum nanocrystal material grown by EBID. J. Vac. Sci. Technol. B 13, 2400–2403. Koops, H. W. P., Scho¨ssler, C., Kaya, A., and Weber, M. (1996). Conductive dots, wires, and supertips for field electron emitters produced by electron‐beam induced deposition on samples having increased temperature. J. Vac. Sci. Technol. 14, 4105–4109. Koops, H. W. P., Dobisz, E., and Urban, J. (1997). Novel lithography and signal processing with water vapor ions. J. Vac. Sci. Technol. B 15, 1369–1372. Koops, H. W. P., Reinhardt, A., Klabunde, F., Kaya, A., and Plontke, R. (2001). Vapour manifold for additive nanolithography with electron beam induced deposition. Microelectron. Eng. 57–58, 909–913. Koshikawa, T., and Shimizu, R. (1974). A Monte Carlo calculation of low‐energy secondary electron emission from metals. J. Phys. D 7, 1303–1315. Kotera, M. (1989). A Monte Carlo simulation of primary and secondary electron trajectories in a specimen. J. Appl. Phys. 65, 3991–3998. Kotera, M., Ijichi, R., Fujiwara, T., Suga, H., and Witry, D. B. (1990). A simulation of electron scattering in metals. Jpn. J. Appl. Phys. 29, 2277–2282. Kotera, M., Kishida, T., and Suga, H. (1989). A simulation of secondary electron trajectories in solids. Scanning Microsc. 3, 993–1001. Kuhr, J.C, and Fitting, H. J. (1999a). Monte‐Carlo simulation of low energy electron scattering in solids. Physica Status Solidi A 172, 433–450. Kuhr, J. C., and Fitting, H. J. (1999b). Monte Carlo simulation of electron emission from solids. J. Electron Spectrosc. Relat. Phenom. 105, 257–273. Kunz, R. R., Allen, T. E., and Mayer, T. M. (1987). Selective area deposition of metals using low‐energy electron beams. J. Vac. Sci. Technol. B 5, 1427–1431. Kunz, R., and Mayer, T. (1987). Surface reaction enhancement via low energy electron bombardment and secondary electron emission. J. Vac. Sci. Technol. B 5, 427–429. Lau, Y. M., Chee, P. C., Thong, J. T. L., and Ng, V. (2002). Properties and applications of cobalt‐based material produced by electron‐beam‐induced deposition. J. Vac. Sci. Technol. A 20, 1295–1302.

228

SILVIS-CIVIDJIAN AND HAGEN

Lee, K. L., and Hatzakis, M. (1989). Direct electron‐beam patterning for nanolithography. J. Vac. Sci. Technol. B 7, 1941–1946. Li, H., Ding, Z., and Wu, Z. (1995). Multifractal behavior of the distribution of secondary‐ electron‐emission‐sites on solid surfaces. Phys. Rev. B 51, 13554. Lipp, S., Frey, L., Lehrer, C., Demm, E., Pauthner, S., and Ryssel, H. (1996a). A comparision of focused ion beam and electron beam induced deposition processes. Microelectron. Reliability 36, 1779–1782. Lipp, S., Frey, L., Lehrer, C., Frank, B., Demm, E., Pauthner, S., and Ryssel, H. (1996b). Tetramethoxysilane as a precursor for focused ion beam and electron beam assisted insulator (SiOx) deposition. J. Vac. Sci. Technol. B 14, 3920–3924. Liu, J. W., and Hagstrom, S. (1994). Dissociative cross sections of H2 by electron impact. Phys. Rev. A 50, 3181–3185. Liu, Z. Q., Mitsuishi, K., and Furuya, K. (2004a). The growth behavior of self‐standing tungsten tips fabricated by electron‐beam‐induced deposition using 200 keV electrons. J. Appl. Phys. 96, 3983–3986. Liu, Z. Q., Mitsuishi, K., and Furuya, K. (2004b). Features of self‐supporting tungsten nanowire deposited with high‐energy electrons. J. Appl. Phys. 96, 619–623. Liu, Z. Q., Mitsuishi, K, and Furuya, K. (2005). Three‐dimensional nanofabrication by electron‐beam‐induced deposition using 200‐keV electrons in scanning transmission electron microscope. Appl. Phys. A 80, 1437–1441. Lukehart, C. M. (1985). Fundamental Transition Metal Organometallic Chemistry. Monterey, CA: Brooks/Cole. Luo, S., and Joy, D. C. (1990). Monte Carlo calculations of secondary electron emission. Scanning Microsc. Suppl. 4, 127–146. Luo, S., Zhang, Y., and Wu, Z. (1987). A Monte Carlo calculation of secondary electrons emitted from Au, Ag and Cu. J. Microsc. 148, 289–295. Luisier, A., Utke, I., Bret, T., Cicoira, F., Hauert, R., Rhee, S.‐W., Doppelt, P., and Hoffmann, P. (2004). Comparative study of Cu precursors for 3D focused electron beam induced deposition. J. Electrochem. Soc. 151, C535–C537. Madsen, D. N., Mølhave, K., Mateiu, R, Rasmussen, A. M., Brorson, M., Jacobsen, C. H. J., and Boggild, P. (2003). Soldering of nanotubes onto microelectrodes. Nano Lett. 3, 47–49. Marchi, F., Tonneau, D., Dallaporta, H., Pierrisnard, R., Bouchiat, V., Safarov, I., Doppelt, P., and Even, R. (2000). Nanometer scale patterning by scanning tunneling microscope assisted chemical vapour deposition. Microelectron. Eng. 50, 59–65. M€ ark, T. D. (1984). Ionization of molecules by electron impact, in Electron‐Molecule Interactions and Their Applications, edited by L. G. Christophorou. Orlando, FL: Academic Press, Vol. 1, p. 251. Marks, L. D. (1982). Observations of the image force for fast electrons near an MgO surface. Solid State Commun. 43, 727–729. Martel, R., and McBreen, P. H. (1997). Dissociative resonance activation of cyclopropane monolayers on copper: Evidence for CH and CC bond scission. J. Chem Phys. 107, 8619–8626. Matsui, S., and Ichihashi, T. (1988). In situ observation on electron beam induced chemical vapor deposition by transmission electron microscopy. J. Vac. Sci. Technol. B 6, 1869–1872. Matsui, S., Ichihashi, T., and Mito, M. (1989). Electron beam induced selection etching and deposition technology. J. Vac. Sci. Technol. B 7, 1182–1190. Matsui, S., Ichihashi, T., Ochiai, Y., Baba, M., Watanabe, H., and Sato, A. (1992). Nanostructure technology developed through electron‐beam‐induced surface reaction, in Nanostructure Science and Technology of Mesoscopic Structures, edited by S. Namba, C. Hamaguchi, and T. Ando. Tokyo: Springer‐Verlag, pp. 334–352.

ELECTRON‐BEAM–INDUCED NANOMETER‐SCALE DEPOSITION

229

Matsui, S., Kaito, T., Fujita, J., Komuro, M., Kanda, K., and Haryama, Y. (2000). Three dimensional nanostructure fabrication by focused‐ion‐beam chemical vapor deposition. J. Vac. Sci. Technol. B 18, 3181–3184. Matsui, S., and Mori, K. (1986). New selective deposition technology by electron‐beam induced surface reaction. J. Vac. Sci. Technol. B 4, 299–304. Matsui, S, and Mori, K. (1987). In situ observation on electron beam induced chemical vapor deposition by Auger electron microscopy. Appl. Phys. Lett. 51, 646–648. Matsuzaki, Y., Yamada, A., and Konagai, M. (2000). Improvement of nanoscale patterning of heavily doped p‐type GaAs by atomic force microscopy (AFM)‐based surface oxidation process. J. Crystal Growth 209, 509–512. McCord, M. A., Kern, D. P., and Chang, T. H. P. (1988). Direct deposition of 10‐nm metallic features with the STM. J. Vac. Sci. Technol. B 6, 1877–1880. Meisels, G. G., Chen, C. T., Giessner, B. G., and Emmel, R. H. (1972). Energy‐deposition functions in mass spectroscopy. J. Chem. Phys. 56, 793–800. Mi, L., and Bonham, R. A. (1998). Electron‐ion coincidence measurements: The neutral dissociation plus excitation cross section for N2. J. Chem. Phys. 108, 1904–1909. Michael, J. R., Williams, D. B., Klein, C. F., and Ayer, R. (1990). The measurement and calculation of the X‐ray spatial‐resolution obtained in the analytical electron microscope. J. Microsc. 160, 41–53. Mitsuishi, K., Shimojo, M., Han, M., and Furuya, K. (2003). Electron‐beam‐induced deposition using a subnanometer‐sized probe of high‐energy electrons. Appl. Phys. Lett. 83, 2064–2066. Mitsuishi, K., Liu, Z. Q., Shimojo, M., Han, M., and Furuya, K. (2005). Dynamic profile calculation of deposition resolution by high‐energy electrons in electron‐beam‐induced deposition. Ultramicroscopy 103, 17–22. Miura, N., Ishii, H., Shirakashi, J., Yamada, A., and Konagai, M. (1997a). Electron beam‐ induced deposition of carbonaceous microstructures using scanning electron microscopy. Appl. Surf. Sci. 113–114, 269–273. Miura, N., Numaguchi, T., Yamada, A., Konagai, M., and Shirakashi, J. (1997b). Single‐ electron tunneling through amorphous carbon dots array. Jpn. J. Appl. Phys. 36, L1619–L1621. Mølhave, K., Madsen, D. N., Rasmussen, A. M., Carlsson, A., Appel, C. C., Brorson, M., Jacobsen, C. J. H., and Boggild, P. (2003). Solid gold nanostructures fabricated by electron beam deposition. Nano Lett. 3, 1499–1503. Morimoto, H., Kishimoto, T., Takai, M., Yura, S., Hosono, A., Okuda, S., Lipp, S., Frey, L., and Ryssel, H. (1996). Electron‐beam‐induced deposition of Pt for field emitter arrays. Jpn. J. Appl. Phys. 35, 6623–6625. Moss, R. E. (1973). Advanced Molecular Quantum Mechanics.. London: Chapman and Hall. Mullejans, H., Bleloch, A. L., Howie, A., and Tomita, M. (1993). Secondary electron coincidence detection and time of flight spectroscopy. Ultramicroscopy 52, 360–368. Muller, D. A., and Silcox, J. (1995). Delocalization in inelastic scattering. Ultramicroscopy 59, 195–213. Mu¨ller, K. H. (1971a). Speed controlled electron microrecorder. I. Optik 33, 296–311. Mu¨ller, K. H. (1971b). Speed controlled electron microrecorder. II. Optik 33, 331–343. Murata, K., Kyser, D. F., and Ting, C. H. (1981). Monte Carlo simulation of fast secondary electron production in electron beam resists. J. Appl. Phys. 52, 4396–4405. Nagamachi, S., Ueda, M., and Ishikawa, J. (1998). Focused ion beam direct deposition and its applications. J. Vac. Sci. Technol. B 16, 2515–2521. Nambu, Y., Morishige, Y., and Kishida, S. (1995). High speed laser direct writing of tungsten conductors from W(CO)6. Appl. Phys. Lett. 56, 2581–2583.

230

SILVIS-CIVIDJIAN AND HAGEN

Neureuther, A. R., Ting, C. H., and Liu, C. Y. (1980). Applications of line‐edge profile simulation to thin film deposition processes. IEEE Trans. on Electron Devices ED‐27, 1449–1455. Newbury, D. E. (1986). Electron beam specimen interactions in the analytical electron microscope, in Principles of Analytical Electron Microscopy, edited by D.C. Joy, A.D. Romig, Jr., and J.I. Goldstein. New York: Plenum, p. 1. Ochiai, Y., Fujita, J., and Matsui, S. (1996). Electron‐beam‐induced deposition of copper compound with low resistivity. J. Vac. Sci. Technol. B 14, 3887–3891. Odagiri, T., Uemura, N., Koyama, K., Uksai, M., Kouchi, N., and Hatano, Y. (1995). Electron energy‐loss study of superexcited hydrogen molecules with the coincidence detection of the neutral dissociation. J. Phys. B 28, L465–L470. Ouyang, F., and Isaacson, M. (1989a). Accurate modeling of particle‐substrate coupling of surface plasmon excitation in EELS. Ultramicroscopy 31, 345–349. Ouyang, F., and Isaacson, M. (1989b). Surface plasmon excitation of objects with arbitrary shape and dielectric constant. Philos. Mag. B 60, 481–492. Pai, W. W., Zhang, J., Wendelken, J. F., and Warmack, R. J. (1997). Magnetic nanostructures fabricated by scanning tunneling microscope‐assisted chemical vapor deposition. J. Vac. Sci. Technol. B 15, 785–787. Palik, E. D. (1998). Handbook of Optical Constants of Solids III. San Diego, CA: Academic Press. Parikh, M. (1975). Calculation of dissociative ionization cross section of diatomic molecules. Phys. Rev. A 12, 1872–1880. Penn, D. R. (1987). Electron mean‐free‐path calculations using a model dielectric function. Phys. Rev. B 35, 482–486. Pennycook, S. J. (1988). Delocalization corrections for electron channeling analysis. Ultramicroscopy 26, 239–248. Perentes, A., Bachmann, A., Leutenegger, M., Utke, I., Sando, C., and Hoffmann, P. (2004). Focused electron beam induced deposition of a periodic transparent nano‐optic pattern. Microelectron. Eng. 73–74, 412–416. Petzold, H.‐C., and Heard, P. J. (1991). Ion induced deposition for X‐ray mask repair: Rate optimization using a time‐dependent model. J. Vac. Sci. Technol. B 9, 2664–2669. Pijper, F. J., and Kruit, P. (1991). Detection of energy‐selected secondary electrons in coincidence with energy‐loss events in thin carbon foils. Phys. Rev. B 44, 9192–9200. Poole, K. M. (1953). Electrode contamination in electron optical systems. Proc. Phys. Soc. (London) B66, 542–547. Powell, C. J. (1984). Inelastic mean free paths and attenuation lengths of low energy electron in solids, in Scanning Electron Microscopy, edited by O. Johari. Vol. IV, Chicago: SEM Inc., p. 1649. Powell, C. J. (1989). Cross sections for inelastic electron scattering in solids. Ultramicroscopy 28, 24–31. Powell, C. J., and Jablonski, A. (1999a). Consistency of calculated and measured electron inelastic mean free paths. J. Vac. Sci. Technol. A 17, 1122–1126. Powell, C. J., and Jablonski, A. (1999b). Evaluation of calculated and measured electron inelastic mean free paths near solid surfaces. J. Phys. Chem. Ref. Data 28, 19–62. Powell, C. J., and Jablonski, A. (2000). Evaluation of electron inelastic mean free paths for selected elements and compounds. Surf. Iinterface Anal. 29, 108–114. Prewett, P. D. (1992). Focused ion beams in microfabrication. Review of Scientific Instruments 63, 2364–2366. Puretz, J., and Swanson, L. W. (1995). Focused ion beam deposition of Pt containing films. J. Vac. Sci. Technol. B 10, 2695–2698.

ELECTRON‐BEAM–INDUCED NANOMETER‐SCALE DEPOSITION

231

Quinn, J. J. (1962). Range of excited electrons in metals. Phys. Rev. 126, 1453–1457. Raether, H. (1980). Excitation of Plasmons and Interband Transitions by Electrons. Berlin: Springer. Rao‐Sahib, T.S, and Wittry, D. B. (1974). X‐ray continuum from thick element targets for 10–50‐keV electrons. J. Appl. Phys. 45, 5060–5068. Reed, S. J. B. (1982). The single‐scattering model and spatial resolution in X‐ray analysis in thin foils. Ultramicroscopy 7, 405–409. Reimer, L. (1998). Scanning Electron Microscopy. Berlin: Springer. Reimer, L., and Lodding, B. (1984). Theory of secondary electron emission II. Scanning 6, 128–151. Reimer, L., and W€achter, M. (1978). Contribution to the contamination problem in transmission electron microscopy. Ultramicroscopy 3, 169–174. Rez, P. (1983). A transport equation theory of beam spreading in the electron microscope. Ultramicroscopy 12, 29–38. Rishton, S. A., Beamont, S. P., and Wilkinson, C. D. W. (1984). Measurement of the profile of finely focused beams in a scanning electron microscope. J. Phys. E 17, 296–303. Ritchie, R. H. (1981). Quantal aspects of the spatial resolution of energy‐loss measurements in electron microscopy. I. Broad‐beam geometry. Philos. Mag. A 44, 931–942. Ritchie, R. H., Garber, F. W., Nakai, M. Y., and Birkhoff, R. D. (1969). in Advances in Radiation Biology, edited by L.G. Augenstein, R. Mason, and M. Zelle. New York: Academic, Vol. 3, p. 1. Rosa, A., Baerends, E. J., van Gisberen, S. J. A., van Lenthe, E., Groeneveld, J. A., and Snijders, J. G. (1999). Electronic spectra of M(CO)6 (M ¼ Cr, Mo, W) revisited by a relativistic TDDFT approach. J. Am. Chem. Soc. 121, 10356–10365. Ro¨sler, M., and Brauer, W. (1981a). Theory of secondary electron emission. I. General theory for nearly‐free‐electron metals. Phys. tatus Solidi B 104, 161–175. Ro¨sler, M., and Brauer, W. (1981b). Theory of secondary electron emission. II. Application to aluminum. Phys. Status Solidi B 104, 575–587. Rothschild, M., Sedlacek, J. H. C., Shaver, D. C., Ehrlich, D. J., Bittenson, S. N., Edwards, D., and Economou, N. P. (1990). Mater. Res. Soc. Symp. Proc. 158, 79–84. Rubel, S., Trochet, M., Ehricus, E. E., Smith, W. F., and de Lozanne, A. L. (1994). Nanofabrication and rapid imaging with a scanning tunneling microscope. J. Vac. Sci. Technol. B 12, 1894–1897. Ru¨denauer, F. G., Steiger, W., and Schrottmayer, D. (1988). Localized ion beam induced deposition of Al‐containing layers. J. Vac. Sci. Technol. B 6, 1542–1547. Saksena, V., Kushwaha, M. S., and Khare, S. P. (1997). Electron impact ionisation of molecules at high energies. Int. J. of Mass Spectrom. Ion Processes 171, L1–L5. Samoto, N., and Shimizu, R. (1983). Theoretical study of the ultimate resolution in electron beam lithography by Monte Carlo simulation, including secondary electron generation: Energy dissipation profile in polymethylmethacrylate. J. Appl. Phys. 54, 3855–3859. Sanche, L. (1989). Investigation of ultra fast events in radiation chemistry with low energy electrons. Radiat. Phys. Chem. 34, 15–33. Sanche, L. (1990). Low‐energy electron scattering from molecules on surfaces. J. Phys. B 23, 1597–1624. Sanche, L. (1997). Les electrons secondaires en chimie et biologie sous rayonnement. J. Chim. Phys. 94, 216–225. Saulys, D. S., Ermakov, A. V., Garfunkel, E. L., and Dowben, P. A. (1994). Electron beam induced patterned deposition of allycyclopentadyenil palladium using STM. J. Appl. Phys. 76, 7639–7641.

232

SILVIS-CIVIDJIAN AND HAGEN

Sawaragi, H., Mimura, R., Kasahara, H., Aihari, R., Thompson, W., and Hassel Shearer, M. (1990). Performance of a combined focused ion and electron beam system. J. Vac. Sci. Technol. B 8, 1848–1852. Sax, N. I. (1984). Dangerous Properties of Industrial Materials. New York: Van Nostrand Reinhold. Schauer, P., and Autrata, R. (1979). Electro‐optical properties of a scintillation detector in SEM. J. Miscrosc. Spectrosc. Electron. 4, 633–650. Scheuer, V., Koops, H., and Tschudi, T. (1986). Electron beam decomposition of carbonyls on silicon. Microelectron. Eng. 5, 423–430. Schiffmann, K. I. (1993). Investigation of fabrication parameters for the electron‐beam‐induced deposition of contamination tips used in atomic force microscopy. Nanotechnology 4, 163–169. Schmeits, M. (1981). Inelastic scattering of fast electrons by spherical surfaces. J. Phys. C 14, 1203–1216. Scho¨ssler, C., Kaya, A., Kretz, J., Weber, M., and Koops, H. W. P. (1996). Electrical and field emission properties of nanocristalline materials fabricated by electron‐beam induced. Microelectron. Eng. 30, 471–474. Scho¨ssler, C., Urban, J., and Koops, H. W. P. (1997). Conductive supertips for scanning probe applications. J. Vac. Sci. Technol. B 15, 1535–1538. Scho¨ssler, C., and Koops, H. W. P. (1998). Nanostructured integrated electron source. J. Vac. Sci. Technol. B 16, 862–865. Scott, V. D., Love, G., and Reed, S. J. B. (1995). Quantitative Electron‐Probe Microanalysis, 2nd ed. New York: Horwood. Seah, M. P., and Dench, W. A. (1979). Quantitative electron spectroscopy of surfaces: A standard data base for electron inelastic mean free paths in solids. Surface and Interface Analysis 1, 2–11. Sernelius, B. E. (2001). Surface Modes in Physics. Berlin: Wiley‐VCH. Shearer, M. (1990). Performance of a combined focused ion and electron beam system. Journal of Vacuum Science and Technology B 8, 1848–1852. Shedd, G. M., Lezec, H., Dubner, A. D., and Melngailis, J. (1986). Focused ion beam induced deposition of gold. Appl. Phys. Lett. 49, 1584–1586. Shimizu, R., and Ding, Z. J. (1992). Monte Carlo modelling of electron‐solid interactions. Rep. Prog. Phys. 55, 487–532. Shimizu, R., and Ichimura, S. (1983). Direct Monte Carlo simulation of scattering processes of kV electrons in aluminum; comparison of theoretical N(E) spectra with experiment. Surf. Sci. 133, 250–266. Shimizu, R., and Murata, K. (1971). Monte Carlo calculations of electron sample interactions in the scanning electron microscope. J. Appl. Phys. 42, 387–394. Shimojo, M., Takeguchi, M., Tanaka, M., Mitsuishi, K., and Furuya, K. (2004). Electron beam‐induced deposition using iron carbonyl and the effects of heat treatment on nanostructure. Appl. Phys. A 79, 1869–1872. Shimojo, M., Bysakh, S., Mitsuishi, K., Tanaka, M., Song, M., and Furuya, K. (2005). Selective growth and characterization of nanostructures with transmission electron microscopes. Appl. Surf. Sci. 241, 56–60. Shimojo, M., Mitsuishi, K., Tanaka, M., Song, M., and Furuya, K. (2005). Electron beam‐ induced nano‐deposition using a transmission electron microscope. Mater. Sci. Forum 480– 481, 129–132. Silvis‐Cividjian, N. (2002). Electron beam induced nanometer scale deposition. Ph.D. thesis, Delft, The Netherlands: Delft University of Technology.

ELECTRON‐BEAM–INDUCED NANOMETER‐SCALE DEPOSITION

233

Silvis‐Cividjian, N., Hagen, C. W., Leunissen, L. H. A., and Kruit, P. (2002). The role of secondary electrons in electron‐beam‐induced‐deposition spatial resolution. Microelectron. Eng. 61–62, 693–699. Silvis‐Cividjian, N., Hagen, C. W., Kruit, P., van der Stam, M. A., and Groen, H. B. (2003). Direct fabrication of nanowires in an electron microscope. Appl. Phys. Lett. 82, 3514–3516. Silvis‐Cividjian, N., Hagen, C. W., and Kruit, P. (2005). Spatial resolution limits in electron‐ beam‐induced deposition. J. Appl. Phys. 98, 084905. Sobol, I. M. (1994). A Primer for the Monte Carlo Method. Boca Raton, FL: CRC Press. Song, M., Mitsuishi, K., Tanaka, M., Takeguchi, M., Shimojo, M., and Furuya, K. (2005). Fabrication of self‐standing nanowires, nanodendrites, and nanofractal‐like trees on insulator substrates with an electron‐beam‐induced deposition. Appl. Phys. A 80, 1431–1436. Spessard, G. O., and Miessler, G. L. (1997). Organometallic Chemistry. Upper Saddle River, NJ: Prentice Hall. Srivastava, S. K. (1987). Present status of the measured dissociation attachment cross sections, in American Institute of Physics Conference Proceedings, Vol. 158, pp. 69–82. Stark, T. J., Mayer, T. M., Griffis, D. P., and Russell, P. E. (1992). Formation of complex features using electron‐beam direct‐write decomposition of palladium acetate. J. Vac. Sci. Technol. B 10, 2685–2689. Stewart, D. K., Stern, L. A., and Morgan, J. C. (1989). Focused‐ion‐beam induced deposition of metal for microcircuit modification, in Electron‐Beam, X‐ray, and Ion‐Beam Technology, edited by A.W. Yanof, Proc. SPIE 1089, pp. 18–25. Stewart, D. K., Morgan, J. A., and Ward, B. (1991). Focused ion beam induced deposition of tungsten on vertical sidewalls. J. Vac. Sci. Technol. B 9, 2670–2674. Streitwolf, H. W. (1959). Zur Theorie der Sekundarelektronenemission von Metallen. Ann. Phys., Lpz 3, 183–196. Szkutnik, P. D., Piednoir, A., Ronda, A., Marchi, F., Tonneau, D., Dallaporta, H., and Hanbu¨cken, M. (2000). STM studies: Spatial resolution limits to fit observations in nanotechnology. Appl. Surf. Sci. 164, 169–174. Takado, N., Ide, Y., and Asakawa, K. (1990). Electron beam excited GaAs maskless etching using Cl2 nozzle installed FIB/EB combined system, in Multichamber and in‐situ Processing of Electronic Materials, edited by R.S. Freund, Proc. SPIE 1188, pp. 134–139. Takahashi, T., Arakawa, Y., Nishioka, M., and Ikoma, T. (1992). MOCVD selective growth of GaAs: C wire and dot structures by electron beam irradiation. J. Cryst. Growth 124, 213–219. Takai, M., Kishimoto, T., Morimoto, H., Park, Y. K., Lipp, S., Lehrer, L., Frey, H., Ryssel, A., Hosono, A., and Kawabuchi, S. (1998). Fabrication of field emitter array using focused ion and electron beam induced deposition. Microelectron. Eng. 41–42, 453–456. Takai, M., Jarupoonphol, W., Ochiai, C., Yavas, O., and Park, Y. K. (2003). Processing of vacuum microelectronic devices by focused ion and electron beams. Appl. Phys. A 76, 1007–1012. Takeguchi, M., Shimojo, M., Mitsuishi, K., Tanaka, M., and Furuya, K. (2004). Nanostructures fabricated by electron beam induced chemical vapor deposition. Superlattices Microstruct. 36, 255–264. Tanaka, M., Shimojo, M., Han, M., Mistuishi, K., and Furuya, K. (2005). Ultimate sized nano‐ dots formed by electron beam‐induced deposition using an ultrahigh vacuum transmission electron microscope, Surf. Interface Anal. 37, 261–264. Tanaka, M., Shimojo, M., Mitsuishi, K, and Furuya, K. (2004). The size dependence of the nano‐dots formed by electron‐beam‐induced deposition on the partial pressure of the precursor. Appl. Phys. A. 78, 543–546. Tao, T., Ro, S., Melngailis, J., Xue, Z., and Kaesz, H. D. (1990). Focused ion beam induced deposition of platinum. J. Vac. Sci. Technol. B 8, 1826–1829.

234

SILVIS-CIVIDJIAN AND HAGEN

Tilinin, I. S. (1986). Energy and angular distributions of secondary electrons induced by fast charged particles in the near surface layer of solid molecular hydrogen. Phys. Chem. Mech. Surf. 4, 1350–1364. Trajmar, S., and Cartwright, D. C. (1984). Excitation of molecules by electron impact, in Electron‐Molecule Interactions and Their Applications, edited by L.G. Christophorou. New York: Academic Press, p. 151. Ueda, K, and Yoshimura, M. (2004). Fabrication of nanofigures by focused electron beam‐ induced deposition. Thin Solid Films 464–465, 331–334. Uesugi, K., and Yao, T. (1992). Nanometer‐scale fabrication on graphite surface by scanning tunneling microscopy. Ultramicroscopy 42–44, 1443–1445. Utke, I., Hoffmann, P., Dwir, B., Leifer, K., Kapon, E., and Doppelt, P. (2000a). Focused electron beam induced deposition of gold. J. Vac. Sci. Technol. B 18, 3168–3171. Utke, I., Dwir, B, Leifer, K, Cicoira, F., Doppelt, P., Hoffmann, P., and Kapon, E. (2000b). Electron beam induced deposition of metallic tips and wires for microelectronics applications. Microelectron. Eng. 53, 261–264. Utke, I., Cicoira, F., Jaenchen, G., and Hoffmann, P. (2002a). Focused electron beam induced deposition of high resolution magnetic scanning probe tips. Mater. Res. Soc. Symp. Proc. Boston 706, 307–312. Utke, I., Hoffmann, P., Berger, R., and Scandella, A. (2002b). High‐resolution magnetic Co supertips grown by a focused electron beam. Appl. Phys. Lett. 80, 4729–4794. Utke, I., Bret, T., Laub, D., Buffat, Ph., Scandella, L., and Hoffmann, P. (2004). Thermal effects during focused electron beam induced deposition of nanocomposite magnetic‐cobalt‐ containing tips. Microelectron. Eng. 73–74, 553–558. Van Dorp, W. F., van Someren, B., Hagen, C. W., Kruit, P., and Crozier, P. A. (2005). Approaching the resolution limit of nanometer‐scale electron beam‐induced deposition. Nano Lett. 5, 1303–1307. Vasile, M. J., and Harriot, L. R. (1989). Focused ion beam stimulated deposition of organic compounds. J. Vac. Sci. Technol. B 7, 1954–1958. Voreades, D. (1976). Secondary electron emission from thin carbon films. Surface Science 60, 325–348. Wall, J. S. (1980). Contamination in the STEM at ultra high vacuum, in Scanning Electron Microscopy, edited by O. Johari. Chicago: SEM Inc., Vol. I, pp. 99–106. Wang, Z. L. (1996). Valence electrons excitations and plasmon oscillations in thin films, surfaces, interfaces and small particles. Micron 27, 265–299. Wang, X.‐D, Rubel, S. E., Purbach, U., and de Lozanne, A. L. (1997). Resistance of Ni nanowires fabricated by STM‐CVD, in Micromachining and Imaging, edited by T. A. Michalske and M.A. Wendman, Proc. SPIE 3009, pp. 2–6. Wang, S., Sun, Y.‐M., Wang, Q., and White, J. M. (2004). Electron‐beam induced initial growth of platinum films using Pt(PF3)4. J. Vac. Sci. Technol. B 22, 1803–1806. Weber, M. (1994). Scattering of non‐relativistic electrons in tip structures. J. Phys. D 27, 1363–1369. Weber, M. (1997). Der Prozess der Elektronstrahlinduzierten Deposition. Darmstadt: Technische Hocheschule Darmstadt. Weber, M., Koops, H. W. P., and Go¨rtz, W. (1992). Scanning probe microscopy of deposits employed to image the current density distribution of electron beams. J. Vac. Sci. Technol. B 10, 3116–3119. Weber, M., Koops, H. W. P., Kretz, J., Rudolph, M., and Schmidt, G. (1995a). New compound quantum dots materials produced by electron‐beam induced deposition. J. Vac. Sci. Technol. B 13, 1364–1368.

ELECTRON‐BEAM–INDUCED NANOMETER‐SCALE DEPOSITION

235

Weber, M., Rudolph, M., Kretz, J., and Koops, H. W. P. (1995b). Electron‐beam induced deposition for fabrication of vacuum field emitter devices. J. Vac. Sci. Technol. B 13, 461–464. Welipitya, D., Green, A., Woods, J. P., Dowben, P. A., Robertson, B. W., Byun, D., and Zhang, J. (1996). Ultraviolet and electron radiation induced fragmentation of adsorbed ferrocene. J. Appl. Phys. 79, 8730–8734. Wells, O. C., and Boyde, A. (1974). Scanning Electron Microscopy. New York: McGraw‐Hill. Williams, D. B., and Carter, C. B. (1996). Transmission Electron Microscopy: A Textbook for Materials Science. New York: Plenum. Winkler, D., Zimmermann, H., Mangerich, M., and Trauner, R. (1996). E‐beam probe station with integrated tool for electron beam induced etching. Microelectron. Eng. 31, 141–147. Wolff, P. A. (1954). Theory of secondary electron cascade in metals. Phys. Rev. 95, 56–66. Xu, X., Della Ratta, A. D., Sosonkina, J., and Melngailis, J. (1992). Focused ion beam induced deposition and ion milling as a function of angle of ion incidence. J. Vac. Sci. Technol. B 10, 2675–2680. Yamaki, M., Miwa, T., Yoshimura, H., and Nagayama, K. (1992). Efficient microtip fabrication with carbon coating and electron beam deposition for atomic force miscroscopy. J. Vac. Sci. Technol. B 10, 2447–2450. Yasaka, A., Yamaoka, T., Kaito, T., and Adachi, T. (1991). Experimental study on the influence of liquid metal ion source energy distribution on focused ion beam induced deposition. J. Vac. Sci. Technol. B 9, 2642–2647. Yavas, O., Ochiai, C., Takai, M., Park, Y. K., Lehrer, C., Lipp, S., Frey, L., Ryssel, H., Hosono, A., and Okuda, S. (2000). Field emitter array fabricated using focused ion and electron beam induced reaction. J. Vac. Sci. Technol. B 18, 976–979. Yoshimura, N., Hirano, H., and Etoh, T. (1983). Mechanism of contamination build‐up induced by fine electron probe irradiation. Vacuum 33, 391–395. Young, R. J., and Puretz, J. (1995). Focused ion beam insulator deposition. J. Vac. Sci. Technol. B 13, 2576–2579. Younger, S. M., and M€ark, T. D. (1985). Semi‐empirical and semi‐classical approximations for electron ionization, in Electron Impact Ionization, edited by T.D. M€ark and G.H. Dunn. New York: Springer‐Verlag, p. 24. Zipf, E. (1984). Dissociation of molecules by electron impact, in Electron‐Molecule Interactions and Their Applications, edited by L. Christophorou. Orlando, FL: Academic Press, p. 335.

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Index

Binary-encounter dipole (BED) model, 142 Binary-encounter model, 148–149 Bohr cutoV radius, 194 Born-Bethe approximation, 147 Born-Oppenheimer approximation, 133 Bragg-Kleeman rule, 138 Bridges, 19 BSE. See Backscattered electrons

A Acetic acid, 49 Acrylic acid, 49 ADF. See Annular dark field Adsorption, 154–155 AES, 23, 48 Annular dark fields (ADF), 72 Argon ion sputter cleaning, 27 Artifacts, 84–85 Atomic force microscope (AFM), 22, 23, 25, 26, 55, 67, 69, 78 for electron-beam-written contamination lines, 156 shape improvement for tips, 79–81 supertips, 80 Atoms, energy states of, 132–134 Auger electron excitation mechanism, 129 Auger spectra, 50

C Capillary injection nozzles, 33 Carbon energy loss function for, 210 precursors, 49 targets, 116 wire, 84 Carbonaceous wire, 73 Cascade multiplication illustration of, 126 of secondary electrons, 125 CCD. See Charge-coupled devices Cellular automata, 185 C-H bonds, 48 Charge-coupled devices (CCD), 81 Charging eVect, 161 Chemical structure analysis, EBID/IBID, 48–54 Chip surgery, 77 Chromium-glass photomask repair, 76 Classical binary collision approximation, 125 Classical cascade model, 125 Cleanliness, 43 Cobalt, 40 Cobalt carbonyl, 53

B Backscattered electrons (BSE), 29 Beam energy electrical resistivity and, 42 variation of, 58 Beam impact energies, 12 Beam-assisted lithography, 92 BEB model. See Binary-encounter Bethe model BED model. See Binary-encounter dipole model Bethe equation, 113 Bethe stopping power, 137 Binary tree data structures, electron trajectories and, 108 Binary-encounter Bethe (BEB) model, 142, 143 237

238 Columns, 18 Cone diameter, 165 curve, 166 Contamination, 3–4, 75 electron-beam-written, 156 explanations for, 4 growth tips, 40 morphological analysis of, 4–5 TEM image of, 4 tips grown by, 48 Contamination lithography, 6, 29 Continuous slowing-down approximation (CSDA), 112 illustration of, 113 Copper, precursors, 53 Copper hexafluoroacetylacetonate vinyltrimethylsilane, 41 Coulomb interactions, 137 Cross-sectional shapes, 188 Crystalline structures, 44–45 CSDA. See Continuous slowing-down approximation Cu(hfac)(MHY), 53 Cu(hfac)(VTMS), 53 CVD. See Electron beam-induced selective chemical vapor deposition Cyclopentadienyl trimethyl platinum, 44 Cylindrical mirror analyzer (CMA), 55

D DAC. See Digital-to-analog conversion DD. See Dipolar dissociation de Broglie wavelengths, 199 DEA. See Dissociative electron attachment Delocalization in EBID, 192–217 eVects, 95, 193 of secondary electron generation, 201–208

INDEX

spatial extent of, 203–208 of surface plasmon generation, 209–217 Density-functional theory (DFT), 134 Deposited dot boundaries, time evolution of, 92 Deposited dot profile evaluation, 94 Deposition environment, 47 process, 86–87 Deposition eYciency, factors varying, 60 Deposition rate, 93–94 definition of, 94 in IBID, 57 loop time v., 57 Deposition yield, 63 factors varying, 60 of IBID, 59 Deposits, secondary electrons scattered in, 184–190 Detector quantum eYciency (DQE), 22 Devices, 84–85 DFT. See Density-functional theory DI. See Dissociative ionization Diameter v. time curve, 165 Diaphoresis, 162 Dielectric Function Model, 121–124 Dielectric nanospheres, 215 DiVerentially pumped subchambers, 29, 33 DiVraction patterns, transmission electron, 45 Digital-to-analog conversion (DAC), 17 Dimethyl gold triflouracetylacetonate, 41 Dipolar dissociation (DD), 135 Dipolar modes, 216 Dirac scattered wave (DSW), 134 Discrete cells, 185 simulated space divided in, 186 Dispersion relations, 122 Dissociation into neutrals, 134

INDEX

of precursor molecules, 193 Dissociative electron attachment (DEA), 134, 145 cross section, 144 Dissociative ionization (DI), 135 cross section, 144 Dissociative recombination, 135 DMG(acac), 47, 52 DMG(hfac), 44, 52 DMG(tfac), 44, 52 Dose per scan, 56 Dots, 18 diameter, 68 DQE. See Detector quantum eYciency DSW. See Dirac scattered wave Dual-beam instruments, 14–15 schematic of, 15

E EBAD. See Electron beam–assisted deposition EBID. See Electron beam–induced deposition EBIM. See Electron beam–induced metal formation EBIR. See Electron beam–induced resist EBISED. See Electron beam–induced selective etching and deposition EBL. See Electron beam lithography Edge-to-edge resolution, 89 EDS. See X-ray spectroscopy EDX. See Energy dispersive X-ray analysis EELS. See Electron energy loss spectroscopy Eigenfrequencies, 209 Elastic scattering, 109–112, 169 of primary electrons, 110 Electric dipole transitions, 199 Electric field, 159–162 Electric quadrupole transitions, 199

239 Electrical conductivity, 43, 74–75 Electrical contacts for molecules, 83–84 Electrical properties, EBID/IBID, 38–43 Electrical resistivity, 39, 42–43, 74–75 beam energy and, 42 Electron beam columns, probe formation and, 11–12 Electron beam lithography (EBL), 5–6 Electron beam–assisted deposition (EBAD), 7 Electron beam–induced deposition (EBID), 37, 61, 210, 218–219 applications of, 76–87 chemical structure analysis of, 48–54 delocalization and, 192–217 electrical properties, 38–43 electron-target-precursor interaction scheme, 97 experimental results and theoretical models, 38 fabrication resolution, 64–74, 87 geometric parameters, 55–74 gold lines deposited by, 20 historical overview of, 3–6 instrumentation and techniques, 8–9 introduction to, 3 mask repair/fabrication and, 76–77 MCSE and, 130–131 model for, 165–168 morphological properties of, 43–47 motivation behind studies on, 6–8 precursor properties, 30–31 profile simulator for, 185–190 resolution chart, 91 resolution of, 86 role of secondary electrons in, 162–163, 164–191 secondary electron emission and, 127–131 SEM implementation of, 11 spatial resolution problems, 87–96 special setups, 13–16 specimens used in, 25

240 Electron beam–induced metal formation (EBIM), 7 Electron beam–induced molecular degradation, mechanisms of, 134–136 Electron beam–induced resist (EBIR), 7 Electron beam–induced selective chemical vapor deposition (CVD), 7 Electron beam–induced selective etching and deposition (EBISED), 7 Electron beam–induced surface reaction, 7 Electron beam–stimulated deposition, 7 Electron energy loss, 136–140 inelastic, 140 pathways for, 136 secondary electron generation and, 206 Electron energy loss spectroscopy (EELS), 4–5, 54, 122, 203, 204, 205, 209–210 of primary electrons, 211 Electron energy loss spectrum, 5 Electron impact, hydrogen molecule under, 145–149 Electron impact dissociation, 153 Electron impact excitation of molecular states, 140–141 Electron impact ionization, 153 Electron impact ionization cross section, 143, 150, 151 Electron impact molecular ionization, cross sections for, 142–143 Electron probe microanalysis (EPMA), 54, 99 Electron probes, diameter of, 90 Electron scattering events, 104 geometry used in, 106 theoretical models for, 108–127 Electron trajectory binary-tree data structures and, 108 geometry in, 105

INDEX

Electron-impact dissociation, 148 Electron-impact excitation, 148 Electron-induced molecular degradation, cross sections for, 140–144 Electron-induced molecular dissociation, 143–144 Electron-molecular impact data, from literature, 144–154 Electrons fast, 136–138 gaseous precursors and, 131–164 incident, 139–140 slow, 138 solid matter and, 96–98 Electron-target interaction, 198 Electron-target-precursor interaction scheme, 97 Electrostatic approach, 161 Electrostatic trapping (ET), 83 ELF. See Energy loss function Energy dispersive X-ray analysis (EDX), 48 Energy loss function (ELF), 122 for carbon, 210 Energy states, of atoms and molecules, 132–134 Energy-loss distribution, 205 Environment and vacuum system, 9–10 Environmental SEM (ESEM), 7 EPMA. See Electron probe microanalysis ESEM. See Environmental SEM ET. See Electrostatic trapping E-T detector. See Everhart-Thornley detector Everhart-Thornley (E-T) detector, 21 Excitation, 134 electron impact, of molecular states, 140–141 Exponential decay, 124 Exposure techniques, probe formation and, 16–20

241

INDEX

F

G

Fabrication resolution, 64–74, 87 EBID, 87 Faraday cups, 12 Fast electrons, 136–138 Fast secondary electron (FSE) model, 120–121, 129 spatial distribution of, 184 FEG. See Field emission guns Feynman diagram, 198 FIBDD. See Focused ion beam direct deposition Field emission guns (FEG), 11 Field emission sources, 81–82 Field emission tips, 81–82 Field emitter arrays, 81–82 SEM view of, 83 Flat panel displays (FPDs), 82 Flat surface, surface plasmons on, 212–214 Flat target surface, secondary electrons on, 168–184 Focused ion beam (FIB), 12–13, 33, 46, 48, 76, 77, 82 IBID and, 14 Focused ion beam direct deposition (FIBDD), 7, 8, 16, 60 Formic acid, 49 Four-probe resistance measurements, 39 FPDs. See Flat panel displays Free-standing amorphous carbon wire, 84 Free-standing structures, 19 FSE model. See Fast secondary electron model Full width half maximum (FWHM), 65, 67, 69, 86, 87, 88, 89, 127, 128, 129, 162, 163 Full-cascade collisions tree, 108 FWHM. See Full width half maximum

GAE. See Gas-assisted etching Gallium azide, 54 Gas cells, 33 Gas delivery systems, 28–37 constructions, 33 nozzle-based, 34 pressure variation in, 36 Gas feed nozzles, parameters for, 35 Gas field ion source (GFIS), 13 Gas injection systems, 9 Gas-assisted etching (GAE), 7 Gaseous precursors, 131–164 Gaussian primary beam, 97 Generalized oscillator strength (GOS), 200 Geometric methods, 185 Geometric parameters, 55–74, 104 in electron scattering, 106 GFIS. See Gas field ion source Gold, 44 precursors, 60 GOS. See Generalized oscillator strength Growth rate, 55–64, 75 secondary electrons and, 167

H HAADF. See High-angle annular dark-field Heisenberg uncertainty principle, 194 High-angle angular dark-field (HAADF), 52 High-resolution electron microscopy (HREM), 43–44 HMO. See Hu¨ckel molecular orbit theory HREM. See High-resolution electron microscopy

242 Hu¨ckel molecular orbit theory (HMO), 134 Hydrocarbon complexes, 149–152 molecule diVusion, 158 polarization of, 161 Hydrogen, 47 under electron impact, 145–149 electron impact dissociation, 148 electron impact excitation, 148 potential-energy curves of, 146 Hydrogen-likeatoms, quantum numbers of, 132

I IBAD. See Ion beam-assisted deposition IBID. See Ion beam-induced deposition IC. See Integrated circuit Imaging, 20–24 IMFP. See Inelastic mean free path Impact parameters electrons moving at, 215 on energy loss, 196 Incident electron, 139–140 Inelastic energy loss, 140 Inelastic mean free path (IMFP), 115, 128 electron values, 115–116 of electrons, 116 Inelastic scattering, 112–117, 169 delocalization of, 193 quantitative estimation of, 194–201 secondary electron generation in, 117 Insulators, 161 Integrated circuit (IC), 7 modification, 77 Intermediate-product model, 63–64 Ion beam columns, probe formation and, 12–13 Ion beam-assisted deposition (IBAD), 7

INDEX

wire fabricated by, 23 Ion beam-induced deposition (IBID), 5, 7, 8 applications of, 76–87 chemical structure analysis of, 48–54 deposition rate in, 57 deposition yield, 59 electrical properties, 38–43 experimental results and theoretical models, 38 fabrication resolution, 64–74 FIB modified, 14 geometric parameters, 55–74 lateral size, 64–74 mask repair/fabrication and, 76–77 morphological properties of, 43–47 precursor properties, 30–31 specimens used in, 25 structures fabricated by, 21 Ion beam-induced etching, 7 Ion implantation, 16 Ionization, 135

K Kronecker delta operators, 216

L Large-scale integration (LSI), 78 Lateral distribution, of secondary electrons, 103 Lateral resolution, probe diameter and, 70–71 Lateral size, 64–74 Le Roy method, 147 Lines, 18 resistivity of, 41 Liquid-metal ion sources (LMIS), 10, 13 LMIS. See Liquid-metal ion sources Loop time, deposition rate v., 57 Low-energy electron deposition, 67 LSI. See Large-scale integration

243

INDEX

M M(CO)6, 152 geometry of, 153, 154 MAC. See Maximum allowed concentrations Magnetic dipoles, 199 Magnetic force microscopy, shape improvement for tips, 81 Mask fabrication, 76–77 Mask repair, 76–77 photo, 76–77 Materials, 25–26 Maximum allowed concentrations (MAC), 10 MCSE. See Monte Carlo Secondary Electron programs Meander pattern scanning, 19 Metal targets, 118 Methane, 141 Mo(CO)6, 52 Molecular flow rate, 33–36 Molecules energy states of, 132–134 formation of, 133 Møller-Plesset perturbation theory (MPPT), 134 Monte Carlo Secondary Electron programs (MCSE), 98–99, 128, 191 basic procedure, 104–107 EBID studies and, 130–131 graphical displays, 101 ideal situation for, 115 input data for, 99–100 output data for, 100–104 Monte Carlo simulations, 3, 69, 128, 167, 185–186, 218–219 flow chart for, 170 geometry used by, 102 for secondary electron emission, 168–172 for secondary electrons, 98–104 Morphological properties, EBID/IBID, 43–47

Mott cross sections, 111 MPPT. See Møller-Plesset perturbation theory

N Nanocrystals, 45 Nanospheres, 215 Nanostructures, 84–85 Nanowires, 19 NE102A, 21, 22 Nickelocene, 47 Normalized carbon surface density, 158 Nozzle construction, 29, 34 parameters, 35

O O2 plasma cleaning, 27 Optical focusing columns, 10–16 Organometallic compounds, 152–154 Organometallic precursors, 65, 75 Oxygen, 47

P Pariser-Parr-Pole method (PPP), 134 Partial wave method (PWM), 111 Patterning, probe formation and, 16–20 Pauli-Dirac equation, 111 PE. See Primary electron Peltier elements, 26 Petzold model, 63 Photolitic metal-deposition techniques, 28 Photomask repair, 76–77 Plasmons, 129 defined, 209 generation of, 209–217 Platinum, 44 precursors, 54 Platinum tips, SEM tilted image of, 24 PMMA. See Polymethyl metacrylate

244 Polymethyl metacrylate (PMMA), 64, 91 PPP. See Pariser-Parr-Pole method Precursor molecules dissociation of, 193 surface diVusion of, 155–159 Precursors, 28–37 carbon, 49 chemical formulas for, 32 cobalt carbonyl, 53 copper, 53 gas molecules, 61–62 gaseous, 131–164 gold, 60 new, 28 organometallic, 65, 75 platinum, 54 pressure, 58–59 properties of, 30–31 supply of, 58 tungsten, 49–50 vapor pressure of, 28–29 Prefabricated electrodes, 25, 39 Primary electron (PE), 91, 94, 95, 105, 106–107, 118, 166 EELS of, 211 in growth simulation, 187 passing through targets, 213 scattering of, 110 simulations of, 188 Probe current, 69–70 Probe diameter, 90 lateral resolution and, 70–71 Probe formation, 10–16 electron beam columns and, 11–12 gas delivery systems and, 28–37 ion beam columns and, 12–13 patterning and exposure techniques, 16–20 precursors and, 28–37 special EBID setups and, 13–16 specimens, 25–28 Probing, small crystal, 84 Propionic acid, 49 Proximity eVects, 74 Pulsed electron beams, 155

INDEX

PWM. See Partial wave method Pyrolitic metal-deposition techniques, 28

Q Quantitative estimation, 194–201 classical model 2 for, 196–197 classical model I for, 194–196 semi-classical, 197–201 Quantum numbers, of electrons in hydrogen-like atoms, 132 Quartz crystal microbalance (QCM), 64

R Radial distribution, of outgoing secondary electron current, 103 Radial intensity distribution, secondary electron, 103 Raman spectroscopy (RS), 48, 49 Random directions in space, 119 Reactive ion etching (RIE), 6 Rectangles, 18 Repeated fast scanning, 19 Resistance measurement, 39 Resist-based electron beam lithography, of secondary electrons, 130 Rhenium, 45 Rhodium, dots, 66 Rishton method, 12 Rods, 19 Rutherford equations, 169–170 Rutherford total cross section, 110

S Scaling algorithms, 150 Scanning electron microscopes (SEM), 5, 8, 14, 48 EBID implementation and, 11 of field emitter array, 83 of platinum tips, 24

INDEX

probe size in, 129 of secondary electron emission, 127–129 specimens used in, 25 of wire fabricated by IBID, 23 Scanning methods meander pattern for rectangles, 19 repeated fast, 19 single slow, 19 Scanning probe microscopy tips, shape improvement for, 78–81 Scanning transmission electron microscopes (STEM), 5, 8, 64, 69, 197, 203, 218 ADF, 72 Scanning tunneling microscopes (STMs), 6, 14, 64, 65 shape improvement for tips, 78–79 Scheuer model, 63 Schro¨dinger equation, 111, 133 Scintillator-photomultiplier combination, 21–22 SE. See Secondary electrons Secondary electrons (SE), 95, 97, 105, 166, 204 cascade multiplication of, 125 delocalization of, 201–208 Dielectric Function Model, 121–124 direct model of, 117–120 in EBID, 162–163, 164–191 EBID resolution and, 127–131 electron energy loss and, 206 energy of, 123 on flat target surface, 168–184 flow chart for emissions, 170 flow chart for theoretical models, 109 FSE model, 120–121 generation of, 114, 117–124, 186 at growth moments, 167 in growth simulation, 187 in inelastic scattering events, 117 lateral distribution of, 103 model for, 165–168 Monte Carlo simulations for, emissions, 168–172

245 Monte Carlo simulations of, 98–104 normalized probability of generation of, 208 radial distribution of, 103 radial intensity distribution of, 103 resist-based electron beam lithography of, 130 scattered in deposit, 184–190 spatial distribution, 102 spatial extent of delocalization of, 203–208 from substrate surface, 191 surface movement of, 125 on target surface, 163 tips deposited by, 190 transport of, 124–126 in vacuums, 126–127 Secondary emission, under electron irradiation, 204 Secondary ion mass spectrometry (SIMS), 48 SEEBID, 167–168 graphical display of, 171 main page of, 168 Self-consistent field, 134 SEM. See Scanning electron microscopes SET. See Single-electron transport Shape improvement, for scanning probe microscopy tips, 78–81 Shot cells, 188 neighbors of, 188 SIMS. See Secondary ion mass spectrometry Single slow scanning, 19 Single-electron transport (SET), 85 Single-scattering model, 129 SLA model. See Straight-lineapproximation Slow electrons, 138 Small crystals, probing, 84 Solid matter, electrons and, 96–98 Space, random direction in, 119

246 Spatial distribution secondary electron, 102 of secondary electrons on target surface, 163 Spatial evolution, 68 Spatial resolution EBID, 172–184 problems, 87–96 researchable problems, 90–92 strategy for working with, 92–96 Special EBID setups, probe formation and, 13–16 Specimen electrical potential, 28 materials, 25–26 temperature, 26–27 treatment, 27 Specimen-mediated electron beam-processor interactions, 96 Spherical gas molecules, surface plasmons on, 214–217 Spherical symmetric scattering, 126 Steady-state growth equations, 62 Steady-state model, 63 STEM. See Scanning transmission electron microscopes Step lengths, 107 STMs. See Scanning tunneling microscopes Straight-line-approximation (SLA) model, 124 Streitwolf equation, 187 Styrene, 49 Surface density, normalized carbon, 158 Surface diVusion, of precursor molecules, 155–159 Surface excitation, 95 Surface oxidation, 67 Surface plasmon generation delocalization of, 209–217 exciting, 217 on flat surface, 212–214 on spherical gas molecule, 214–217 Surface processes adsorption, 154–155 diVusion, 155–159

INDEX

in EBID modeling, 61 electric field, 159–162

T Target surfaces, spatial distribution of secondary electrons on, 163 Telecentric beam paths, with Ko¨hler illumination, 17 TEM. See Transmission electron microscopy Temperature, 26–27 in deposition experiments, 59–60 Thermionic guns, 11 Thickness, 55–64, 74 3D nanostructures, 20 fabrication of, 21 IBID and, 21 Threshold limit values (TLVs), 10 Time evolution, of deposited dot boundaries, 92 Time-dependent perturbation theory, 198, 199 Time-of-flight secondary ion mass spectrometry (TOF-SIMS), 44 Tips, 18 diameter, 67, 69 field emission, 81–82 grown by contamination, 48 growth of, 60 high aspect ratio, 79 profiles of, 190 scanning probe microscopy, 78–81 sequences of, 191 TEM of, 45 TLVs. See Threshold limit values TOF-SIMS. See Time-of-flight secondary ion mass spectrometry Transition moments, 199 Transmission electron diVraction patterns, 46 Transmission electron microscopy (TEM), 6, 23, 44 spatial resolution in, 89

247

INDEX

specimens used in, 25 of tilted contamination spots, 4 of tips, 45 of tungsten rod, 24 Tungsten, 51 lines, 42 precursors, 49–50 rods, 24 2D Profile simulators, 185–190 flow chart of, 188 Two-probe resistance measurements, 39

U UHV. See Ultra-high vacuum Ultra-high vacuum (UHV), 4, 9, 27

V Vacuum systems, 9–10 Vacuums, secondary electrons in, 126–127

W W Auger signals, 51 W(CO)6, 50, 51, 56, 62, 69 WCl6, 51 Wires, 18 carbon, 84 carbonaceous, 73

X XMA. See X-ray microanalysis XPS. See X-ray photoelectron spectroscopy X-ray mask repair, 77 X-ray microanalysis (XMA), 48 X-ray photoelectron spectroscopy (XPS), 48, 51 X-ray spectroscopy (EDS), 4

Y YAG. See Yttrium-aluminum garnet Yttrium-aluminum garnet (YAG), 22

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