Porous Silicon Carbide and Gallium Nitride: Epitaxy, Catalysis, and Biotechnology Applications

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Porous Silicon Carbide and Gallium Nitride Epitaxy, Catalysis, and Biotechnology Applications

Randall M. Feenstra Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania, USA

Colin E.C. Wood Electronics Division, US Office of Naval Research, Arlington, Virginia, USA

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Porous Silicon Carbide and Gallium Nitride Epitaxy, Catalysis, and Biotechnology Applications

Randall M. Feenstra Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania, USA

Colin E.C. Wood Electronics Division, US Office of Naval Research, Arlington, Virginia, USA

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John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England Telephone (+44) 1243 779777

Email (for orders and customer service enquiries): [email protected] Visit our Home Page on www.wileyeurope.com or www.wiley.com All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except under the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1T 4LP, UK, without the permission in writing of the Publisher. Requests to the Publisher should be addressed to the Permissions Department, John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England, or emailed to [email protected], or faxed to (+44) 1243 770620. Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The Publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the Publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought. The Publisher and the Author make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of fitness for a particular purpose. The advice and strategies contained herein may not be suitable for every situation. In view of ongoing research, equipment modifications, changes in governmental regulations, and the constant flow of information relating to the use of experimental reagents, equipment, and devices, the reader is urged to review and evaluate the information provided in the package insert or instructions for each chemical, piece of equipment, reagent, or device for, among other things, any changes in the instructions or indication of usage and for added warnings and precautions. The fact that an organization or Website is referred to in this work as a citation and/or a potential source of further information does not mean that the author or the publisher endorses the information the organization or Website may provide or recommendations it may make. Further, readers should be aware that Internet Websites listed in this work may have changed or disappeared between when this work was written and when it is read. No warranty may be created or extended by any promotional statements for this work. Neither the Publisher nor the Author shall be liable for any damages arising herefrom. Other Wiley Editorial Offices John Wiley & Sons Inc., 111 River Street, Hoboken, NJ 07030, USA Jossey-Bass, 989 Market Street, San Francisco, CA 94103-1741, USA Wiley-VCH Verlag GmbH, Boschstr. 12, D-69469 Weinheim, Germany John Wiley & Sons Australia Ltd, 42 McDougall Street, Milton, Queensland 4064, Australia John Wiley & Sons (Asia) Pte Ltd, 2 Clementi Loop #02-01, Jin Xing Distripark, Singapore 129809 John Wiley & Sons Ltd, 6045 Freemont Blvd, Mississauga, Ontario L5R 4J3, Canada Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Library of Congress Cataloging-in-Publication Data Feenstra, Randall M. Porous silicon carbide and gallium nitride : epitaxy, catalysis, and biotechnology applications / Randall M. Feenstra and Colin E.C. Wood. p. cm. Includes bibliographical references and index. ISBN 978-0-470-51752-9 (cloth : alk. paper) 1. Silicon carbide. 2. Gallium nitride. 3. Semiconductors. I. Wood, Colin E.C. II. Title. TK7871.15.S56F44 2008 621.3815’2–dc22 2007046623 British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN 978-0-470-51752-9 Typeset in 10.5/13pt Sabon by Aptara Inc, New Delhi, India Printed and bound in Great Britain by TJ International, Padstow, Cornwall This book is printed on acid-free paper

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Contents Preface

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Porous SiC Preparation, Characterization and Morphology 1.1 Introduction 1.2 Triangular Porous Morphology in n-type 4H-SiC 1.2.1 Crystal Anodization 1.2.2 Description of the Porous Structure 1.2.3 Model of the Morphology 1.3 Nano-columnar Pore Formation in 6H-SiC 1.3.1 Experimental 1.3.2 Results 1.3.3 Discussion 1.4 Summary Acknowledgements References

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Processing Porous SiC: Diffusion, Oxidation, Contact Formation 31 2.1 Introduction 31 2.2 Formation of Porous Layer 32 2.3 Diffusion in Porous SiC 42 2.4 Oxidation 47 2.5 Contacts to Porous SiC 49 Acknowledgements 53 References 53

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Growth of SiC on Porous SiC Buffer Layers 3.1 Introduction 3.2 SiC CVD Growth

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3.3

Growth of 3C-SiC on Porous Si via Cold-Wall Epitaxy 3.3.1 Growth on Porous Si Substrates 3.3.2 Growth on Stabilized Porous Si Substrates 3.4 Growth of 3C-SiC on Porous 3C-SiC 3.4.1 Growth in LPCVD Cold-wall Reactor 3.5 Growth of 4H-SiC on Porous 4H-SiC 3.6 Conclusion Acknowledgements References 4

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Preparation and Properties of Porous GaN Fabricated by Metal-Assisted Electroless Etching 4.1 Introduction 4.2 Creation of Porous GaN by Electroless Etching 4.3 Morphology Characterization 4.3.1 Porous GaN Derived from Unintentionally Doped Films 4.3.2 Transmission Electron Microscopy (TEM) Characterization 4.4 Luminescence of Porous GaN 4.4.1 Cathodoluminescence (CL) of Porous GaN 4.4.2 Photoluminescence (PL) of Porous GaN 4.5 Raman Spectroscopy of Porous GaN 4.5.1 Characteristics of Raman scattering in GaN 4.5.2 Raman Spectra of Porous GaN Excited Below Band Gap 4.6 Summary and Conclusions Acknowledgements References Growth of GaN on Porous SiC by Molecular Beam Epitaxy 5.1 Introduction 5.2 Morphology and Preparation of Porous SiC Substrates 5.2.1 Porous Substrates 5.2.2 Hydrogen Etching

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MBE Growth of GaN on Porous SiC Substrates 5.3.1 Experimental Details 5.3.2 Film Structure 5.3.3 Film Strain 5.4 Summary Acknowledgements References 6

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GaN Lateral Epitaxy Growth Using Porous SiNx , TiNx and SiC 6.1 Introduction 6.2 Epitaxy of GaN on Porous SiNx Network 6.2.1 Three-step Growth Method 6.2.2 Structural and Optical Characterization 6.2.3 Schottky Diodes (SDs) on Undoped GaN Templates 6.2.4 Deep Level Transition Spectrum 6.3 Epitaxial Lateral Overgrowth of GaN on Porous TiN 6.3.1 Formation of Porous TiN 6.3.2 Growth of GaN on Porous TiN 6.3.3 Characterization by XRD 6.3.4 Characterization by TEM 6.3.5 Characterization by PL 6.4 Growth of GaN on Porous SiC 6.4.1 Fabrication of Porous SiC 6.4.2 GaN Growth on Hydrogen Polished Porous SiC 6.4.3 GaN Growth on Chemical Mechanical Polished Porous SiC Acknowledgements References HVPE Growth of GaN on Porous SiC Substrates 7.1 Introduction 7.2 PSC Substrate Fabrication and Properties 7.2.1 Formation of Various Types of SPSC Structure 7.2.2 Dense Layer 7.2.3 Monitoring of Anodization Process

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7.2.4

Vacancy Model of Primary Pore Formation 7.2.5 Stability of SPSC Under Post-Anodization Treatment 7.3 Epitaxial Growth of GaN Films on PSC Substrates 7.3.1 The Growth and Its Effect on the Structure of the PSC Substrate 7.3.2 Properties of the GaN Films Grown 7.4 Summary References 8

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Dislocation Mechanisms in GaN Films Grown on Porous Substrates or Interlayers 8.1 Introduction 8.2 Extended Defects in Epitaxially Grown GaN Thin Layers 8.3 Dislocation Mechanisms in Conventional Lateral Epitaxy Overgrowth of GaN 8.4 Growth of GaN on Porous SiC Substrates 8.5 Growth of GaN on Porous SiN and TiN Interlayers 8.5.1 GaN Growth on a TiN Interlayer 8.5.2 GaN Growth on a SiN Interlayer 8.6 Summary Acknowledgements References Electrical Properties of Porous SiC 9.1 Introduction 9.2 Resistivity and Hall Effect 9.3 Deep Level Transient Spectroscopy 9.3.1 Fundamentals of DLTS 9.3.2 Method of Solving the General Equation 9.4 Sample Considerations 9.5 Potential Energy Near a Pore 9.6 DLTS Data and Analysis Acknowledgements References

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Magnetism of Doped GaN Nanostructures 10.1 Introduction 10.2 Mn-Doped GaN Crystal 10.3 Mn-Doped GaN Thin Films 10.3.1 Mn-Doped GaN (1120) Surface 10.3.2 Mn-Doped GaN (1010) Surface 10.3.3 Mn and C Codoped in GaN (1010) Surface 10.4 Mn- and Cr-Doped GaN One-Dimensional Structures 10.4.1 Mn-Doped GaN Nanowires 10.4.2 Cr-Doped GaN Nanotubes 10.4.3 Cr-Doped GaN Nanohole Arrays 10.5 N-Doped Mn and Cr Clusters 10.5.1 Giant Magnetic Moments of Mnx N Clusters 10.5.2 N-induced Magnetic Transition in Small Crx N Clusters 10.6 Summary Acknowledgements References

SiC Catalysis Technology 11.1 Introduction 11.2 Silicon Carbide Support 11.3 Heat Effects During Reaction 11.4 Reactions on SiC as Catalytic Supports 11.5 Examples of SiC Catalyst Applications 11.5.1 Pt/β-SiC Catalyst for Catalytic Combustion of Carbon Particles in Diesel Engines 11.5.2 Complete Oxidation of Methane 11.5.3 SiC-Supported MoO3 -Carbon-Modified Catalyst for the n-Heptane Isomerization 11.5.4 Selective Oxidation of H2 S Over SiC-Supported Iron Catalysts into Elemental Sulfur

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Partial Oxidation of n-Butane to Maleic Anhydride Using SiC-Mixed and Pd-Modified Vanadyl Pyrophosphate (VPO) Catalysts (Case study) 11.6 Prospects and Conclusions References 11.5.5

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Nanoporous SiC as a Semi-Permeable Biomembrane for Medical Use: Practical and Theoretical Considerations 12.1 The Rationale for Implantable Semi-Permeable Materials 12.2 The Biology of Soluble Signaling Proteins in Tissue 12.3 Measuring Cytokine Secretion In Living Tissues and Organs 12.4 Creating a Biocompatible Tissue – Device Interface: Advantages of SiC 12.5 The Testing of SiC Membranes for Permeability of Proteins 12.6 Improving the Structure of SiC Membranes for Biosensor Interfaces 12.7 Theoretical Considerations: Modeling Diffusion through a Porous Membrane 12.7.1 Effective Medium Models for a Porous Membrane 12.7.2 Comparison with Experiment 12.8 Future Development: Marriage of Membrane and Microchip 12.9 Conclusions Acknowledgements References

Index

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291 291 292 294 295 296 299 301 302 304 305 307 307 308 311

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Preface Single crystal semiconductors can be etched electrochemically in an electrolyte such as dilute hydrofluoric acid. Illumination is often required to provide the positively charged holes necessary for oxidation. This process, known as photo-electrochemical (PEC) etching, can result either in a relatively featureless, two-dimensional (electro-polishing) or complex, three-dimensional porous morphology. Pore dimensions can range from nanometer to millimeter-scale by varying the etching conditions. PEC etching has allowed porous morphology in a variety of semiconductors. Perhaps the best known is porous silicon, which was studied intensely during the 1980s and 1990s [1]. When excited by an electric current or using incident blue light, porous silicon emits intense red light. In contrast, the 1.1 eV band gap of bulk (i.e. nonporous) silicon corresponds to a wavelength in the near infrared, and even at this energy, bulk silicon is a poor light emitter as it has an indirect band gap. Intense visible emission from porous silicon has attracted great interest. Despite much research, the precise mechanism for the light emission is still controversial. Moreover, persistent degradation effects in the emission intensity have hampered device development. Nevertheless, other applications have been successfully explored. Porous Si remains a very interesting prototypical porous semiconductor. This volume deals largely with the properties and application of porous silicon carbide (SiC), which, in single crystal form, has a relatively high bond strength. It has been commercially available in multi-centimeter diameter crystalline wafers and boules for only the past two decades. All the SiC polymorphs have large 3.0±0.3 eV band gaps, which together with high bond strength make them suitable for high power and/or high temperature applications. The very high thermal conductivity and close lattice match to gallium nitride (GaN), another wide band gap semiconductor, has recently

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prompted SiC usage as substrates for blue through UV optical emitters, and for very high frequency electronic applications (wireless communications, radar, etc.). It should be noted that GaN is not commercially available as a single crystal substrate. SiC can be made porous using PEC etching [2], although in contrast to silicon it is not an efficient light emitter. This volume describes various other applications of the material as explored during 2001–2006 under a Defense University Research Initiative on Nanotechnology (DURINT) program entitled ‘Nanoporous Templates for Large Defect Reduction in SiC and GaN, Nanocatalysis, Magnetic Clusters, and Biotechnology’. This program dealt with topics including the epitaxial growth of SiC and of GaN on porous SiC, utilizing the large surface area of porous materials for catalytic applications, and biotechnology applications in which free-standing porous SiC is used as a semi-permeable membrane for sampling proteins and other macromolecules. Chapter 1 deals with porous SiC formation mechanisms. A wide range of morphologies are found depending on etching conditions and dopant type and concentration of the initial SiC. One morphology explored extensively is a narrow columnar one with 10–100 nm diameter pores, normal to the surface, and depths of hundreds of micrometers. Such layers can be made free standing by separation from the underlying material through application of a current pulse. Processing steps required for application of porous SiC in electronic devices are described in Chapter 2, including doping via diffusion, thermal oxidation and contact deposition. Epitaxial growth of SiC on porous substrates, both SiC and Si, is discussed in Chapter 3. Pores may help reducing dislocations or strain, thereby improving the properties of epitaxial layers grown on porous substrates. The low cost and large area of porous silicon substrates make them attractive for SiC epitaxy. The porosity provides one mechanism of accommodating the lattice mismatch between the Si and the SiC. Porous GaN can be produced without using electrical excitation as described in Chapter 4. As for porous SiC, there is potential for using the porous GaN as a substrate for homo-epitaxial growth of GaN. Other applications with strong potential include chemical sensors, with the large surface area of the porous material providing enhanced sensitivity of such devices. Chapters 5–8 discuss uses of porous SiC, and porous intermediate layers of other materials, as substrates for GaN epitaxy. The lattice mismatch between GaN and SiC leads to dislocations in GaN films, and use of a porous template offers a mechanism for reducing the dislocation density.

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As for Ge on Si [3], growth conditions are chosen which favor nucleation only on regions between the pores. With further deposition threedimensional islands allow strain relaxation by elastic deformation, followed by island coalescence. The density of inter-island dislocations can be orders of magnitude less than in films grown on nonporous substrates. Prior studies of selected area GaN epitaxy with reduced dislocation densities employed lithographically patterned substrates [4]. In contrast, this book describes a nonlithographic nanoscale surface patterning process. Dislocation reduction in epitaxial GaN growth without lithography, using discontinuous SiNx thin interlayers [5] is covered in Chapter 6. Important electrical properties of porous SiC are discussed in Chapter 9. Not surprisingly, porous SiC has a higher specific resistivity than its host crystals. More significantly, pores appear to trap charge carriers, which renders p-SiC semi-insulating. Such effects strongly influence the use of porous material as electrical sensors. Chapter 10 presents theoretical work on the origin of magnetism in Mn- and Cr-doped porous GaN with promise towards a room temperature dilute magnetic semiconductor, an essential component for spintronic applications. The large surface areas of porous material allow very high concentration of surface-specific atomic arrangements to be formed. Extensive computations have been performed on (Ga,Mn)N and (Ga,Cr)N systems from zero-dimensional clusters to one-dimensional nanowires, nanotubes, and nanoholes, two-dimensional surfaces and thin films, and three-dimensional crystals. Chapter 11 presents and discusses porous SiC use in catalysis for which the large porous film surface areas are again clearly useful. SiC’s high chemical bond strength allows its use at high temperature and renders it resistant to oxidative erosion. Finally, Chapter 12 describes initial studies on biological applications of porous SiC. Free-standing porous membranes are explored as particlesize-selective semi-permeable membranes for filtering of macro (bio-) molecules. SiC’s hardness makes it chemically inert and bio-compatible (e.g. coating on stents [6]).

REFERENCES [1] A.G. Cullis, L.T. Canham, and P.D.J. Calcott, The structural and luminescence properties of porous silicon, J. Appl. Phys., 82, 909 (1997). [2] J.S. Shor, I. Grimberg, B.-Z. Weiss, and A.D. Kurtz, Direct observation of porous SiC formed by anodization in HF, Appl. Phys. Lett., 62, 2836–2838 (1993).

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[3] S. Luryi and E. Suhir, New approach to the high quality epitaxial growth of latticemismatched materials, Appl. Phys. Lett., 49, 140 (1986). [4] D. Zubia, S. H. Zaidi, S. R. J. Brueck, and S. D. Hersee, Nanoheteroepitaxial growth of GaN on Si by organometallic vapor phase epitaxy, Appl. Phys. Lett., 76, 858 (2000). [5] H. Lahr`eche, P. Venn´egu`es, B. Beaumont, and P. Gibart, Growth of high-quality GaN by low-pressure metal-organic vapour phase epitaxy (LP-MOVPE) from 3D islands and lateral overgrowth, J. Cryst. Growth, 205, 245 (1999). [6] C. Harder, A. Rzany, and M. Schaldach, Coating of vascular stents with antithrombogenic amorphous silicon carbide, Prog. Biomed. Res., 1, 71 (1999).

Randall M. Feenstra Department of Physics, Carnegie Mellon University, USA Colin E.C. Wood Electronics Division, US Office of Naval Research, USA

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1 Porous SiC Preparation, Characterization and Morphology Y. Ke1 , Y. Shishkin2 , R.P. Devaty1 and W.J. Choyke1 1

Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260, USA 2 Caracal, Inc., 611 Eljer Way, Ford City, PA 16226, USA

1.1

INTRODUCTION

The production and investigation of porous semiconductors began in the 1950s at Bell Laboratories with work by Uhlir Jr [1] and Turner [2] on Si and Ge and at the Westinghouse Research Laboratories by Faust Jr [3] for SiC. Technological interest began with the discussion of the process of insulation by porous oxidized Si in the 1970s [4]. Interest in porous Si exploded in 1990 when Canham [5] at RSRE in the UK discovered that highly porous layers of Si excited by a blue laser emit readily visible red light at room temperature. The origin of this above band gap luminescence was a topic of heated controversy for several years. We became interested in the possibility of blue shifted luminescence into the ultraviolet (UV) in porous SiC, and began to collaborate with Joseph Shor and colleagues, who were actively investigating electrochemical etching

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of SiC at Kulite Semiconductor products and Columbia University [6]. They successfully fabricated porous SiC [7,8], but initial cathodoluminescence results [9] in 1994 did not convincingly reveal the desired effect. Further low temperature photoluminescence and cathodoluminescence measurements did not resolve this issue. However, we [10] found a dramatic effect of porosity on the reststrahl band of thick p-type 6H-SiC layers observed using room temperature infrared (IR) reflectance. A simple effective medium model, chosen to incorporate the porous morphology, accounted for the observed spectral features. Subsequently, these effects have been observed in several other porous polar semiconductors and explained using similar models. Spanier and Herman [11] published further work on the IR reflectance of porous SiC. We ceased our optical investigations of porous SiC in 1995. Our interest in porous SiC was renewed in 2000, based on some interesting work in the intervening years, which has been reviewed by Saddow et al. [12]. We set up a laboratory for fabricating porous SiC by (photo)electrochemical etching. We discovered (or rediscovered, in some cases) about ten distinct morphologies in 4H-, 6H- and 3C-SiC, as well as GaN layers [13]. This chapter focuses on the two morphologies we have investigated most thoroughly: the layered triangular and the nanocolumnar morphologies. For each case, we discuss the fabrication and characterization, followed by discussion of the formation mechanism.

1.2

TRIANGULAR POROUS MORPHOLOGY IN n-TYPE 4H-SiC

The ‘triangular’ porous morphology may be manufactured from highly doped hexagonal Si-face 4H-SiC by photoelectrochemical etching (PECE) [14]. A small number of Si-face 6H-SiC samples was also studied and revealed no significant difference from 4H-SiC. The observed morphology is explained based on the crystallography and a model for the semiconductor/electrolyte interface.

1.2.1

Crystal Anodization

The electrochemical etching, with the intent of making the etched semiconductor porous, is performed in the anodic regime, so that positive charge is collected at the semiconductor–electrolyte interface. In order to increase the speed of the anodization process, electrical bias is applied to the sample through ohmic contacts. To protect the ohmic contacts on the

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back as well as the edges during the anodization procedure, the samples are masked using Apiezon black wax. The experiments described here were performed in aqueous 5 % HF solution mixed with ethanol in the ratio HF:ethanol = 1:1 (measured by weight). There are two ways to produce a substantial anodic current. One way is to apply a large positive, or reverse, bias so that dielectric breakdown occurs and electrons from the ions in the electrolytic solution tunnel into the semiconductor. Voltages may range from 10 up to 100 V. The resultant structures are dendritic, sinuous, and columnar. The other way is to apply a moderate reverse bias, from 1 to 3 V, accompanied by UV light illumination (from which the term photoelectrochemical etching originates). The UV light of above photon band gap energy generates electron–hole pairs. The electrons are swept away by the electric field into the bulk of the semiconductor, while the holes rush to the surface where they participate in the electrochemical reaction. To make porous 4H-SiC of triangular morphology, we employed the second approach. As a UV light source one can use a Hg arc lamp. Filters and dichroic mirrors are recommended to attenuate visible and IR components of the radiation from the source. The UV light intensity was ∼160 mW/cm2 as measured by a thermopile-type power meter. The electrochemical etching is conducted in a three-electrode cell where the SiC crystal serves as the working electrode. The current is controlled either potentiostatically (constant potential) or galvanostatically (constant current) with a potentiostat/galvanostat. In the potentiostatic mode, the voltage applied to the cell should not exceed 3 V. When the galvanostatic mode was used, the fixed current density ranges from 1 to 5 mA/cm2 so that the corresponding applied voltage would not exceed about 3 V in order to minimize breakdown effects. After anodization, samples are carefully removed from the bath and cleaned in acetone to remove the black wax mask. As an alternative, trimethylchloroethylene may be used. Plan-view and cross-sectional imaging is performed by scanning electron microscopy (SEM). The 8-bit gray scale [intensity ranges from 0 (black) to 255 (white)] digital SEM pictures are then processed by imaging software to obtain the pore size and porosity. The porosity is estimated from cross-sectional images by integrating the area occupied by the pores.

1.2.2

Description of the Porous Structure

Figure 1.1 shows a series of cross-sectional SEM images of porous 4HSiC (n ∼ 6 × 1018 cm−3 ) taken at different depths from about 5 to 55 μm

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Figure 1.1 Sequence of cross-sectional images of a 56 μm thick porous vicinal Siface 4H-SiC sample of triangular morphology. In the sequence, (a) corresponds to the top of the film, (e) to the bottom. The distance d from the front surface and the corresponding porosity P are: (a) d = 5 μm, P = 0.28; (b) d = 15 μm, P = 0.23; (c) d = 30 μm, P = 0.16; (d) d = 40 μm, P = 0.12; (e) d = 55 μm, P = 0.08. Reproduced from Y. Shishkin et al., J. Appl. Phys., 96(4), 2311–2322. Copyright (2004), the American Institute of Physics

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below the surface. The morphology seen on Figure 1.1 was obtained in 8◦ -offcut Si-face 4H-SiC porous samples made by UV-photoassisted electrochemical etching at a voltage of +3 V. The particular surface exposed to the imaging by fracturing the sample is the (1210) plane. The sample is organized into a stack of planar layers. When viewed from the 1210 direction, a tilt of about 8◦ of the layered structure relative to the normal to the front surface is seen (image not shown). A similar layering of pores is seen also in 3.5◦ -offcut 6H-SiC. In photoelectrochemically etched n-type crystals, the porosity is rarely uniform throughout the porous layer. The porosity is largest at the surface and gradually decreases with depth. This is illustrated in Figure 1.1. As can be seen, not only the porosity changes but also there is a distinctive development of the triangular pore shape. Figure 1.1(e), taken near the interface between the porous layer and the substrate, shows that small oblong channels form in an orderly fashion. They are arranged in an array with rows separated by about 30 nm with the distance between pores also about 30 nm on average. The pore width at this stage is 5–10 nm. A porous film produced under similar conditions for 2 min, whose thickness was later measured to be 3 μm, exhibited only structure resembling Figure 1.1(e). This indicates that Figure 1.1(e), taken at the bottom of a 56 μm thick porous film (etched for 5 h), portrays the initial stage of the triangular pore development. In order to estimate the porosity, the pixels of the gray-scale images are thresholded so that those corresponding to a pore on the image are assigned the value 0 (black), and the pixels corresponding to the solid the value 1 (white). The total area occupied by the black pixels Sblack can be calculated [15]. Then the porosity P is estimated by taking the ratio of Sblack to the total area of the cross-sectional image. Here, it is assumed that the areal porosity for a particular cross-section equals the volume porosity for the channel pore structure. For Figure 1.1(e), the porosity P obtained by this method is 0.08. As the anodization process continues, the channels quickly pierce the crystal in directions perpendicular to the c-axis. The non-basal plane walls of every channel begin to flatten out [Figure 1.1(d)] to follow crystallographic planes tilted at about 60◦ relative to the basal plane. One can clearly distinguish triangular shapes. Figure 1.1(b) and Figure 1.1(c) represent the continuing pore development as the channel walls become more distinct quasi-equilateral triangles. Their characteristic shape suggests anodization anisotropy, i.e. not all the directions in the crystal are equivalent in terms of the PECE. The tendency of the pores not to propagate normal to the [0001] direction suggests that the (0001) basal plane

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Figure 1.2 Plan view image of a 4H-SiC Si-face sample, off-cut 8◦ towards [1210], photoelectrochemically etched to obtain the triangular porous morphology. About 2 μm of material was removed by RIE prior to imaging. The exposed channels apparently propagate preferably along 1210 directions. Reproduced from Y. Shishkin et al., J. Appl. Phys., 96(4), 2311–2322. Copyright (2004), the American Institute of Physics

possesses an etch-stop character. The largest triangles are on Figure 1.1(a) corresponding to the top of the porous film. Here, the porosity P is estimated to be about 0.28. At this point we note that the experiments have shown so far no, or very little, porosity gradient in p-type SiC in which the etching is performed without light assistance [16]. Figure 1.2 is a plan view SEM image of a porous sample similar to the one shown in Figure 1.1 but processed for 15 min by reactive ion etching (RIE) with SF6 plasma to perform the plan view SEM analysis. Figure 1.2 shows how a vicinal basal plane appears with roughly 2 μm removed by RIE. Compared with the non-RIE surface, which had just occasional circular openings, one can now see channels which tend to propagate parallel to the basal plane. The channels branch out, wriggle, and occasionally intersect each other. There seems to be a slight preference in the channel propagation along 1210 directions, which are indicated by the arrows in Figure 1.2. The particular [1210] direction towards which the 8◦ miscut was made is indicated. If the C-face (0001) is anodized, conical pores with triangular crosssections are observed, but the pores are not arranged into arrays of planes (images not shown). The conical pores intersect, forming an overall spongy network. Even though their typical size is very similar to that

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Figure 1.3 Plan view of a (1100)-oriented porous 4H-SiC sample. ‘Triangles’ on the surface are about the same size as the ‘triangles’ seen on cross-sectional SEM images of the vicinal (0001) samples. Reproduced from Y. Shishkin et al., J. Appl. Phys., 96(4), 2311–2322. Copyright (2004), the American Institute of Physics

of the triangular channels, it is clear that Si-terminated and C-terminated surfaces etch differently. The observed differences in the etching of (0001) and (0001) crystal faces suggest etching experiments on non-basal planes. In these cases the electric field is applied parallel to the basal plane. Figure 1.3 shows an example of a front surface of a (1100) 4H-SiC sample after UV photoassisted anodization. The front surface of an etched (1210) sample looks similar within the resolution limits of the SEM. The surface morphology is described by layered triangular pits of average size of 30–40 nm observed all over the surface. The fact that the surface pits have a defined geometrical shape as well as their self-regulating character again point out anodization anisotropy. The non-basal samples were also sectioned for analysis. Figure 1.4 shows an example for which a 4H-SiC (1100) oriented sample has been fractured to expose the (1210) plane. The crystal is seen to be divided into 35–50 nm thick layers. Each layer contains triangular cavities 30–40 nm in size. When the image in Figure 1.4 is rotated 90◦ clockwise, a similarity to the cross-sectional images of the (0001) etched samples can be seen. The size and the shape of the triangular pores and their general planar layout on the fractured surface are identical. The similarity is striking given the fact that during etching the electric field is applied parallel to the basal plane and consequently perpendicular to the field applied to etch the sample in Figure 1.1.

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Figure 1.4 Cross-sectional image of a porous (1100) 4H-SiC sample. The surface shown in the image is a {1210} plane. When rotated, it resembles the cross-sectional images of vicinal Si-face samples. Reproduced from Y. Shishkin et al., J. Appl. Phys., 96(4), 2311–2322. Copyright (2004), the American Institute of Physics

Figure 1.5 shows an example for which a 4H-SiC (1100) oriented sample has been fractured to expose a basal plane. The channeled structure of the pores can still be discerned. The arrows next to the figure show the 1210 directions. There are no (or very few) channels aligned with 1100, suggesting that 1210 are the primary directions along which

Figure 1.5 Cross-sectional image of a porous (1100) 4H-SiC sample. The surface shown in the image is a basal plane. Compare the wormy character of the pore channels with Figure 1.2. Reproduced from Y. Shishkin et al., J. Appl. Phys., 96(4), 2311–2322. Copyright (2004), the American Institute of Physics

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the pores prefer to propagate. Comparing the result with Figure 1.2, where we were able to look at the basal plane by means of RIE etching off the top layer, we again conclude that pores do not propagate well along the c-axis. Moreover, the direction of the electric field applied during the experiment does not seem to be a factor in the pore formation in the investigated voltage/current regime.

1.2.3 1.2.3.1

Model of the Morphology Pore Dimensions and Porosity

One of the arguments used in the porous silicon literature to explain the typical dimension of the structures states that the pore formation is governed by the width of the space charge region formed near the semiconductor/electrolyte junction (see, for example, [17]). The argument seems to be very plausible as it works well for the mesoporous structures (10–100 nm pore size) obtained from n-type Si. The model has also been proposed for porous SiC [18] and elaborated in Shishkin et al. [14]. The width of the space charge (or, depletion) layer Lsc (cm) is determined by solving the Poisson equation with appropriate boundary conditions. For the case of an n-type semiconductor with a planar surface, such that n ≈ Nd , and Nd  Na , the charge density is approximated as ρ ≈ en. One obtains:  Lsc =

2εsc ε0 φsc . en

(1.1)

At the potential φ sc = 3 V, the width of the space charge region when the free carrier concentration is n = 6 × 1018 cm−3 is calculated to be Lsc ∼ 30 nm (ε sc is assumed ∼10). As we showed in Figure 1.1(e), the average distance between the newly formed channels in the triangular pore structure obtained by PECE is 30–35 nm. The calculated value for Lsc then may be interpreted as a typical distance which determines the selfregulatory character of the lateral (i.e. parallel to the basal plane) pore formation process. Piercing the crystal, the channels align themselves into a network in such a way that for each given channel the onset of another channel next to it occurs at a distance where the electric field produced by the band bending vanishes, i.e. where the depletion layer ends. Such pore initiation-alignment processes happen both vertically and horizontally.

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Depleted of charge carriers, the interpore spacing of a newly formed porous structure exhibits semi-insulating properties with the Fermi level of the semiconductor pinned to the surface energy levels close to the middle of the band gap [18]. Such pinning results in a different distribution of the potential at the interface as compared with a planar semiconductor/electrolyte junction without surface states. In particular, a substantial potential drop in the so called Helmholtz region of the electrolyte occurs, which has a few nanometers thickness and is adjacent to the sample surface. The field in the semiconductor then is expected to become lower, decreasing the band bending at the surface and slowing down the charge transfer through the interface. In this regard, the stages of the pore formation can be deduced indirectly from the current versus time dependence recorded over the course of the PECE experiment. In Figure 1.6, the etching starts in the mA cm−2 range, which is due to the rapid pore initiation process which manifests itself in the fact that one can obtain a porous film a few micrometers thick in 1 min. The cross-sectional SEM image of such a film shows small ‘shapeless’ channels similar to what is seen in Figure 1.1(e). A rough estimate gives the total internal surface area of the pores at this stage to be 50–60 times larger than the front surface area of the sample. This turns out to be enough to substantially increase the number of collected holes. The current density quickly rises to a value

Figure 1.6 Current density vs time for an n-type 4H-SiC sample etched at 3 V for 2 h. The sample area is ∼0.45 cm2 . Integration of the curve provides the total charge transferred during the course of the reaction leading to the estimate of porosity P ∼ 0.2. Reproduced from Y. Shishkin et al., J. Appl. Phys., 96(4), 2311–2322. Copyright (2004), the American Institute of Physics

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an order of magnitude higher than its initial value on a flat (nonporous) surface. As seen in Figure 1.6, the current density reaches its maximum value of about 3 mA cm−2 in approximately 30 min, and then gradually drops, indicating a decreasing rate of dissolution. Such a decrease in the anodic current density for SiC has also been reported in the literature [8,19]. Despite the noisy character, the current density j(t) dependence in Figure   1.6 may be used to calculate the integrated charge Qint = i(t)dt = A j(t)dt transferred during the course of the reaction. Knowledge of Qint allows one to estimate the average porosityP = Vp /V. The total volume of the semiconductor V is simply the product of the front surface area A and the film thickness d. The total ‘void’ volume produced by dissolution is Vp = N · V0 where N is the number of Si-C pairs dissolved and V0 is the volume of a single Si-C pair in the SiC crystal lattice. V0 is obtained from ˚ c/4 = 2.52 A ˚ [20]. N is the lattice constants of 4H-SiC: a = 3.081 A, Qint /eγ , where γ is the number of holes required to dissolve one Si-C pair. Combining all the terms, we write  V0 j(t)dt Vp V0 Qint /eγ = = . P= V Ad edγ

(1.2)

The gravimetric measurements for 4H n-type SiC show that γ is very close to 7, within 1% accuracy [14]. When the j(t) curve (see Figure 1.6) is integrated, one gets roughly 22.3 C cm−2 . Once the porous film thickness is determined from the cross-sectional SEM measurement (d ∼16 μm for the sample in Figure 1.6), one can obtain the value of the average porosity for the porous planar/triangular morphology obtained in n-type 4H-SiC using Equation (1.2). After inserting all the numbers, the estimated average porosity is P = Vp /V ≈ 0.20. SEM images have also been obtained for the above sample at 1, 4, 7, 10, 14 and 16 μm from the front surface. The resultant dependence of P as a function of depth d is shown in Figure 1.7. This 16 μm thick sample has a clear porosity gradient which is reflected by the decreasing values of P with the increasing of d. If fitted to an exponential, P(d) = P0 + ae−bd ,

(1.3)

the constant b can be determined (values of the offset P0 are negligible.). For the sample in Figure 1.7, b = 880 cm−1 . Making a similar analysis

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Figure 1.7 The porosity as a function of distance from the front surface of the sample. The porous layer was obtained in the run shown in Figure 1.6. The values of porosity are extracted from digital analysis of the SEM images. The solid line is a fit to Equation (1.3), which gives P = 21 % for the average porosity. Reproduced from Y. Shishkin et al., J. Appl. Phys., 96(4), 2311–2322. Copyright (2004), the American Institute of Physics

for samples etched for shorter times (so that the photo-electrochemical action proceeds closer to the original, ‘starting’, surface) results in larger values of b. For longer etching times used to produce thicker films, the collection of holes, on average, takes place at larger depths where the longer wavelengths of the UV light, associated with lower absorption coefficient, penetrate more efficiently. Therefore, b is a representative coefficient which takes into account the range of UV lines participating in the etching process. The integration of the P(d) function given by Equation (1.3) gives the average porosity of the porous layer. A value of 0.21 is obtained from the data in Figure 1.7 when integration is done from 0 to dmax = 16 μm. Thus, the porosity estimated from SEM images is in good agreement with the average porosity calculated using the charge transfer (P ∼ 0.20). 1.2.3.2

Model for the Pore Shape

The base of each ‘triangle’ always lies in the basal plane whereas its sidewalls are oriented about 60◦ relative to the base. This pore shape implies some etching relationship to the crystallographic planes of the original SiC single crystal. Our SEM cross-sectional images show that the etching rate, defined as the thickness of a porous layer etched per unit time, is a factor of

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two larger for a {1210} plane than for a {1100} plane under identical conditions. This fact supports our observation deduced from Figure 1.2 that the {1210} surface is less resistant to electrolytic attack. Qualitatively, this can be explained by the fact that, in hexagonal polytypes, {1210} surfaces have a higher surface energy than the {1100} surfaces [21]. It is reasonable to assume that those directions will be chosen for the pore growth which are easier to etch. The surfaces of low energy are the ones which ‘survive’ the etching and the channel pore patterns are formed. Even though the etch rate difference between an a-face {1210} and a p-face {1100} provides the possibility for the channel formation, it is not sufficient to explain the triangular shape. Pores form by an oxidation of the surface silicon and carbon atoms with the immediate removal of the oxidized species into the electrolytic solution. Therefore, in order to investigate the issue of a particular plane’s etching inertness, one has to make an assumption that the oxidation is substantially weaker on Si-rich surfaces of SiC as compared with the C-rich ones. The basis for this statement depends upon experiments on the oxidation of the Si- and C-faces of SiC, in which the polar character of the silicon–carbon bond [22] was first suggested to be responsible. Muelhoff et al. [23] reported different oxidation rates for (0001) and (0001), i.e. Si-rich and C-rich, surfaces for thermally oxidized SiC. The oxidation of a Si-terminated surface proceeds at a much slower rate. Although the oxidation chemistry in aqueous environment is likely somewhat different from that reported in Muelhoff et al. [23], in which dry oxygen was used, the rate of oxidation for the (0001) surface is still larger by at least a factor of two than that of the (0001) surface when water vapor is used for oxidation. Consequently, the pore shape in a SiC crystal is greatly affected by the surface polarity. Since we have already shown the etch-stop character of the (0001) plane, a silicon-terminated surface, we propose that the surfaces which make up the sidewalls of our triangular channels are silicon-rich etch-stop surfaces also. Let us now examine the lattice structure of 4H- and 6H-SiC polytypes. Having established the preference for triangular pore propagation along 1210 directions, the logical thing to do would be, looking along a 1210 direction, to find those surfaces which are terminated with silicon atoms. Figure 1.8 shows a schematic view of a 4H-SiC crystal lattice as seen from a 1210 direction. The zigzagged lines connecting silicon atoms (lighter shaded dots) make up the surfaces of the walls forming a triangle. Two of the thick solid lines represent the (1102) and (1102) planes. We propose that, like the (0001) surface, the (1102)and (1102)

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Figure 1.8 Schematic of the projection of the 4H-SiC crystal lattice as viewed from a 1210 direction. The planes comprising the walls of the imaginative triangular channel are indicated. Light dots, silicon atoms; black dots, carbon atoms. Reproduced from Y. Shishkin et al., J. Appl. Phys., 96(4), 2311–2322. Copyright (2004), the American Institute of Physics

surfaces are also nominally terminated with silicon atoms. The counterparts (1102) and (1102) are then terminated with carbon atoms. An oxidation experiment conducted on 6H-SiC using (1103) and (1103) surfaces, which are somewhat similar to the respective (1102) and (1102) surfaces in 4H-SiC, confirms the model [24]. Despite the lack of data on 4H-SiC, we are confident that silicon termination makes the (1102) and (1102) surfaces behave like etch-stops under anodization conditions, similar to the (0001) face. Therefore, the sides of each triangle are made of surfaces corresponding to the {1102} family of planes. This fact plus preferential pore propagation along the 1210 directions create the necessary environment for the observed triangular-channeled structural pore shape. Next we determine the angle of inclination θ of the triangular sides of the pores, assuming the {1102} planes to be the walls of these triangles. One way of doing this is to determine the components of the reciprocal ˆ y, ˆ lattice vector 1102 in terms of the basis vectors of the real space x, and zˆ [14]: 4π 4π 1102 = 1 · b 1 − 1 · b 2 + 2 · b 3 = − √ yˆ + zˆ . c a 3

(1.4)

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Based on the components of the vector in the reciprocal lattice space the angle θ is found as: √ √ 4π/a 3 tan θ = = c/a 3 = 1.889 4π/c which gives θ = 62.1◦ . The inclination of the {1102} plane is indeed very close to 60◦ , explaining why we observe the pore cross-sections as almost equilateral triangles. This result plus preferential pore propagation along the 1210 directions, discussed earlier, create the necessary environment for the observed triangular-channeled pore structure. Since it has been proposed that this surface is terminated with silicon atoms, it would be logical to assume that the surfaces corresponding to the {1102} family of planes are terminated with carbon atoms. Nonbasal planes corresponding to pore surfaces are interesting candidates for boule growth experiments, electrical properties studies, and surface science investigations [24–26]. Already, low-energy electron diffraction (LEED) and Auger electron spectroscopy (AES) have revealed differences in the composition of the (1102)and (1102) surfaces of 4H-SiC [26].

1.3

NANO-COLUMNAR PORE FORMATION IN n-TYPE 6H-SiC

The achievements of making controllable self-organized columnar porous alumina, porous Si and porous InP [27–32] raise the question whether we can obtain a similar porous structure in SiC by controlling the etching conditions. This section focuses on the fabrication of columnar porous SiC. The necessary etching conditions and formation mechanisms are also discussed.

1.3.1

Experimental

The experimental set-up and technique to fabricate columnar porous SiC are similar to the set-up used for triangular porous SiC. But, since we need to apply a high voltage (>10 V) and use a relatively concentrated HF electrolyte, the PECE experiments are conducted in a two-electrode cell where a SiC crystal is used as the anode. Aqueous 10% HF mixed with 5 % ethanol (measured by weight) electrolyte is used. Voltage is applied

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across the two electrodes using a PAR 2273 Potentiostat/Galvanostat. Since front side illumination is needed to increase the hole concentration in the n-type semiconductor, a 1000 W Oriel Hg Xe Arc Lamp combined with optical filters is used to produce a flux of UV photons with intensity about 600 mW cm−2 as measured by a thermopile-type light power meter. Up to now, both 6H- and 4H-SiC samples from single crystal, on axis, n-type nitrogen doped (range from 3 × 1017 to 3 × 1018 cm−3 ) wafers have been used for making the nano-columnar porous structure with the proper selected etching conditions. In this section, we focus on the etching of n-type 6H material doped about 1 × 1018 cm−3 . For comparison of porous structures, we set the etching times at 1 h in all experiments, unless specifically stated otherwise. A Sartorius MC21S microbalance is used to measure the mass loss of the sample due to the PECE. Planar and cross-sectional scanning electron microscope imaging is then performed using a Philips XL30 FEG microscope at an operating voltage of 15 kV. The thickness of the porous structure is determined by the cross-sectional SEM measurement. To reveal the structure at some depth from the top surface, we use a Plasma-Therm 790 RIE system to remove a known thickness of the porous structure. In the RIE etching process, 20 mTorr SF6 gas is used with 250 W power applied.

1.3.2

Results

Initial attempts to produce columnar porous SiC were performed on the Si-face by applying larger voltage (>50 V) or current density (>50 mA cm−2 ). The columnar pore growth under these high field conditions is unstable, and the result was either a columnar macroporous (∼1 μm diameter) structure or a hybrid partial columnar structure (low volume fraction of large diameter columns penetrating dendritic nanoporous SiC) [33]. In addition to the fact that the pore size is difficult to adjust, the macrocolumnar porous structure has high porosity (>0.9) and thus is too fragile to be generally useful for practical applications. Our research on the triangular porous morphology in 6H-SiC indicates that the Si-face is an electrochemical etching resistant plane. Therefore, attempting columnar porous growth on the Si-face of SiC is essentially etching through an unfavorable crystalline face. Etching the Si-face therefore tends to favor branching rather than the development of long, straight columns. Unless an avalanche breakdown etching

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Figure 1.9 SEM images [34] of (a) original porous SiC surface after PECE, (b) early stage formation of columnar pore in cross-section, (c) porous surface structure 20 μm below the original surface after 90 min of RIE (the inset shows the Fourier transform of a larger area of this picture), and (d) the self-ordered columnar porous structure below the cap layer in cross-section. Reproduced from Y. Ke, R.P. Devaty and W.J. Choyke, Self-ordered nanocolumnar pore formation in the photoelectrochemical etching of 6H SiC, Electrochem. Solid-State Lett., 10(7), K24–K27 (2007). Copyright 2007, with permission from The Electrochemical Society

condition (even locally) is achieved, the columnar pore growth will not happen. To achieve controllable columnar pore growth, electrochemical etching should be done on ‘non-etch stop’ faces. The fact that the C-face oxidizes much faster than the Si-face in wet oxidation [23] suggests that in another kind of oxidation – the photo-electrochemical etching process – the C-face is less likely to be an etch stop than the Si-face. This suggests that etching the C-face of a SiC crystal may favor the columnar pore formation. When 20 V etching voltage is applied to a C-face SiC sample, a uniform nano-columnar porous structure forms. Figure 1.9 shows SEM images of the formed columnar porous structure. From these images we can see that the pore morphology in the porous SiC is similar to those seen in porous Si, Al2 O3 and InP [27–32]. From our cross-sectional SEM images [Figure 1.9(d)], we estimate that the pore diameter is about 20 nm and the pore wall thickness is about 40 nm. Within our SEM resolution, no detailed structure is seen on the pore walls. The pore walls are smooth. The 200 μm long nano-columnar pores are generally straight and parallel. The planar SEM image [Figure 1.9(a)] shows that the columnar pores do not form right at the surface. The cross-sectional SEM image of the ambient/porous interface [Figure 1.9(b)] indicates a ∼10 nm thick initial low porosity ‘skin layer’. The surface pore nucleation tends to follow the scratch marks left by mechanical polishing and shows no particular order [35]. The areal density of the surface pores is far less than that of the columnar pores formed deeper in the bulk. The subsequent porous growth initiates from the surface pores. The pores are neither regular nor straight, and keep branching without following any particular crystalline

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direction. The regularity of the columnar pore lattice improves with increasing depth. An ordered columnar porous structure can be recognized about 10 μm below the skin layer. For convenience, we call this ∼10 μm thick transition porous structure the ‘cap layer’. To reveal the columnar porous structure and check the regularity of the porous pattern below the cap layer, we RIE the sample for 90 min and remove roughly 20 μm of the porous structure from the top. A planar-view SEM image of the freshly exposed surface shows a semi-selforganized porous pattern [Figure 1.9(c)]. The Fourier transform inset shows a multiple ring structure. This suggests that the columnar pores fabricated so far do not have an orientational long range order. The columnar pores are, however, uniformly distributed in space and possess some short range regularity as a hexagonal pore lattice. The diameter of the pores is about 30 nm instead of 20 nm as seen on the cross-sections [Figure 1.9(d)]. We believe that the RIE process widens the openings of the columnar pores. Based on the weight loss during the PEC process measured using the microbalance, the porosity is estimated to be 0.1. Because the columnar pores are generally uniform throughout the porous layer, it is reasonable to assume that the columnar porous structure we obtain is comparable with a perfect hexagonal packed cylindrical pore lattice. For such a pore lattice, the porosity P can be calculated using: 2π  r 2 P=√ 3 D

(1.5)

where r is the radius of the columnar pore and D is the distance between adjacent pore centers. According to the SEM images, the estimated values are r ≈ 10 nm and D ≈ 60 nm, and the calculated porosity P = 0.1, which agrees with the gravimetric porosity. This value is also similar to the porosity of self-organized porous alumina [30]. The reason for this particular porosity is discussed for the porous alumina, but remains unclear for columnar porous SiC. Nevertheless, the mechanical strength associated with this low porosity makes this nano-columnar porous SiC a potentially useful nano-material for practical applications.

1.3.3

Discussion

After the fabrication of the columnar porous structure, to gain a deeper insight into the formation mechanism, we performed the following three

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comparison PECE experiments: EXP. 1: C-face SiC etched under 20 V constant voltage conditions. EXP. 2: Si-face SiC etched under 20 V constant voltage conditions. EXP. 3: C-face SiC etched under 30 mA cm−2 constant current conditions. To evaluate the photoelectrochemical reactions in these PECE processes, it is useful to calculate and compare the average number of holes ‘γ ’ needed to etch away a single SiC pair. The agreement among different experiments points to a similar electrochemical process. γ is calculated using the following expression: 

γ = Nholes NSiC

Q = e



Vp Q = V0 e



m QρV0 . = ρV0 em

(1.6)

Here, Q is the total electric charge flowing through the sample during the experiment (Q is estimated by integrating the current–time curves), e is the unit electric charge (1.6 × 10−19 C), Nholes = Q/e is the total number of holes that flowed, m is the mass loss and ρ is the SiC mass density (3.21 g cm−3 ). V p , the pore volume, which is the total volume of SiC pairs removed by the PECE process, is then m/ρ. V0 is the volume of a SiC pair and can be calculated (V0 = 20.7 × 10−24 cm3 ) using 6H-SiC lattice constants [20]. In all three experiments, about seven holes (7.3 in EXP. 1; 6.9 in EXP. 2; 7.1 in EXP. 3) on average are needed for a single SiC pair to be removed. These results are also consistent with the hole number calculated for triangular porous SiC formation and the PECE reported by Shor and Kurtz [8]. This implies that all the photoelectrochemical reactions are similar, at least in the number of holes needed to etch each SiC pair. The different porous morphologies obtained here are unlikely to be related to different chemical reactions. Further comparison of EXP. 1 vs 2 and EXP. 1 vs 3 shows that two etching conditions are necessary for the columnar structure formation: the C-face of 6H-SiC rather than the Si-face must be used, and an appropriate constant etching voltage has to be maintained. 1.3.3.1

EXP. 1 vs EXP. 2

Figures 1.10 and 1.11 show SEM images and etching curves, respectively, from the three experiments. In EXP. 1 [Figure 1.10(a–d)], we observe

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Figure 1.10 Planar and cross-sectional SEM images [34] of (a)–(d) C-face porous SiC in EXP. 1; (e)–(h) Si-face 6H porous SiC in EXP. 2; (i)–(l) C-face 6H porous SiC in EXP. 3. Reproduced from Y. Ke, R.P. Devaty and W.J. Choyke, Self-ordered nanocolumnar pore formation in the photoelectrochemical etching of 6H SiC, Electrochem. Solid-State Lett., 10(7), K24–K27 (2007). Copyright 2007, with permission from The Electrochemical Society

the formation process of a self-ordered columnar porous structure as described earlier. In EXP. 2 [Figure 1.10(e–h)], even though an identical condition is applied to the Si-face sample, no columnar pore growth is observed. The ‘dendritic’ pores grow approximately parallel to the c-axis with ‘branch’ diameters of about 20–50 nm. The etching current– time (I–t) curves of Figure 1.11(a) and Figure 1.11(b) both record a rapid nonexponential drop. After an initial interval, the current density becomes linear on a double log scale and can be fitted to the equation: I = Ct β .

(1.7)

For the C-face sample in EXP. 1, we have C ≈ 510 and β ≈ −0.40, while for the Si-face sample in EXP. 2, C ≈ 415 and β ≈ −0.43. The values of β are essentially the same within experimental error. The etching on the C-face has a larger constant C, corresponding to a larger current density than the etching on the Si-face, but a similar current decay rate.

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Figure 1.11 I–t curves [34] in (a) EXP. 1 and (b) EXP. 2; (c) V–t curve in EXP. 3. Reproduced from Y. Ke, R.P. Devaty and W.J. Choyke, Self-ordered nanocolumnar pore formation in the photoelectrochemical etching of 6H SiC, Electrochem. SolidState Lett., 10(7), K24–K27 (2007). Copyright 2007, with permission from The Electrochemical Society

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A higher current density usually reflects a larger electrochemical reaction rate. For the C-face columnar pore growth, the pore geometry and distribution is uniform. As explained earlier, the two-dimensional areal porosity of a columnar porous layer is almost constant below the first few microns of etching. The effective etching area is therefore roughly a constant throughout. Consequently, the high electrochemical reaction rate here indicates a high growth rate of the porous layer thickness at the beginning of the etching process compared with the rate at the end. This behavior is confirmed by etching a C-face sample at constant voltage for 1 min. The resulting 23 μm thick columnar porous layer suggests that the average rate of increase of the porous layer thickness for the 1 min etching is about seven times the rate for 1 h PECE. However, the reason for this specific etching rate decrease is not clear. If we compare the current densities at the same etching time in the two experiments, it is found that the current density on the C-face is in general higher than that on the Si-face, which suggests that the reaction rate is higher for the C-face SiC experiment under the same etching conditions. Current–voltage scan (I–V) measurements were performed on both the C-face and the Si-face of 6H-SiC to examine the electrolyte and semiconductor junction properties (Figure 1.12). The results show that, for both the C-face and Si-face, UV illumination in general enhances the current density remarkably. (The ‘abnormal’ behavior between ∼7 V and ∼15 V for the C-face SiC scan is not understood.) There are two distinct steps in

Figure 1.12 I–V scans [34] on the (a) Si-face and (b) C-face of 6H-SiC in 10% HF, 5% ethanol electrolytic solution at 1 V s−1 scan rate. Note that in order to better distinguish the curves recorded with and without UV illumination, the I–V curve without UV illumination is lowered by 100 mA cm−2 . UV intensity is 600 mW cm−2 . Reproduced from Y. Ke, R.P. Devaty and W.J. Choyke, Self-ordered nanocolumnar pore formation in the photoelectrochemical etching of 6H SiC, Electrochem. SolidState Lett., 10(7), K24–K27 (2007). Copyright 2007, with permission from The Electrochemical Society

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the curves with UV illumination at which the current increases abruptly. These steps are separated by a plateau ( Si for the Si-face scan and C for the C-face in Figure 1.12). Beyond this plateau, the I–V curve for the C-face SiC shows a larger and more rapidly increasing current density than that for the Si-face. The clear difference between the Si-face and C-face I–V curves confirms the dissimilar interface junction properties of the two crystalline faces in a photoelectrochemical process. The larger current density on the C-face provides a faster electrochemical etching rate or oxidation rate than the rate on the Si-face, which is in agreement with the result from wet oxidation experiments [23]. Moreover, the ratio of the porous layer thickness in EXP. 1 to that in EXP. 2 along the c-axis is 2.5. This suggests that the PECE more strongly prefers to proceed in the [0001] direction for the C-face than in the [0001] direction for the etching of the Si-face. Therefore, to achieve controllable columnar pore growth (without using avalanche breakdown conditions), PECE must be done in etch preferred directions, in our case, on C-face SiC.

1.3.3.2

EXP. 1 vs EXP. 3

In EXP. 1, in the linear plot [Figure 1.11(a)], after the rapid current density drop at the beginning, the current density stabilizes around 30 mA cm−2 during most of the etching interval. To check whether this quasiconstant current flow is responsible for the columnar pore formation, we conducted a constant current density experiment (EXP. 3) at 30 mA cm−2 with all other experimental conditions unchanged. The result shows that the constant current density does not lead to a uniform columnar porous morphology and the resulting porous structure [Figure 1.10(i–l)] is believed to be correlated with the compliance voltage [Figure 1.11(c)], which is applied to maintain the desired current. In the early stage, the porous morphology is triangular [Figure 1.10(j)]. Below this layer, irregular columnar pores are observed. It is only towards the latter stage of etching, when the voltage approaches 20 V, that a relatively ordered and straight columnar porous structure is observed, which resembles the structure fabricated by constant voltage etching in EXP. 1. This result indicates that an appropriate voltage is crucial to form the ordered nano-columnar porous structure. This could also suggest that a specific electric field at the electrolyte/solid interface is necessary to the columnar pore formation, if we assume that the major voltage drop is across the interface during the complete etching process.

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Further comparison of EXP. 1 and 3 on C-face samples shows that the mass loss and the total charge flow are practically identical. However, under the constant voltage condition, the porous layer thickness is about 50 μm larger. The constant current condition is a charge supply limited process and the thinner porous structure suggests that the constant voltage etching is likely to be a mass transfer rate limited process. The rate of etching depends on the concentrations of the chemicals and the mass transfer rates of the ions in the electrolyte at the columnar pore tips. These mass transfer rates of the reactant and product ions balance with the hole supply rate from the semiconductor (anodic current) in order to maintain the columnar pore formation. The concentrations of chemicals at the pore tips decrease as the columnar pores become longer. This would explain why columnar pores form much faster at the beginning of the etching. In EXP. 3, columnar pore growth is optimized when the voltage is around 20 V. A series of SEM images is shown in Figure 1.13 to compare the pore formation when the voltage is lower or higher than 20 V. Figure 1.13(e–h) shows the SEM images of an optimized columnar porous structure under 20V as discussed earlier. If 10 V is applied [Figure 1.13(a–d)], the porous structure close to the surface has a layered morphology filled

Figure 1.13 Planar and cross-sectional SEM images of (a)–(d) 10 V, (e)–(h) 20 V and (i)–(l) 30 V constant voltage etching on C-face 6H-SiC. (m) Cross sectional image shows the inhomogeneous porous layer thickness of a columnar porous structure fabricated by applying 30 V voltage

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with triangular shaped pores [Figure 1.13(b)]. The relationship between the underlying pore growth and the surface pores is not obvious. Below this layer, for most of the porous layer, we find a very irregular columnar pore structure. The pore morphology can hardly be recognized as columnar. The sinuous pores go in and out of the cleaved SiC plane and do not show a connected porous network in the SEM cross-sectional image. The final porous structure thickness is about 210 μm and the average porosity is 0.1. Comparing with the 20 V etching, the porous layer thickness and the overall porosity are both similar. The 30 V etching destroys the columnar porous structure in another way. In Figure 1.13(i–l), we can see that the porous structure close to the ambient/porous interface is quite similar to the 20 V etched porous structure. In the middle of the porous layer, the columnar pores are straight and ordered. The pores are 20 nm in diameter but the pore density is higher. However, towards the porous/bulk interface, the porous structure becomes irregular. Therefore the columnar porous etching has a depth limitation under 30 V etching. Most importantly, the thickness of the porous structure is inhomogeneous [Figure 1.13(m)]. The thinnest part of the structure is about 70 μm thick whereas the thickest part is about 200 μm. It is interesting to see that the maximum thickness remains close to the values obtained in 10 V and 20 V etching. However, some part of the porous growth is slower or even stopped at some point. The reason for this large variation of the thickness is not clear. Because of this thickness variation, the porosity of the porous structure can not be evaluated. The recorded current density–time curves for three different voltages are shown in Figure 1.14. In all three curves we observe a linear decay

Figure 1.14 Current density vs time curves recorded during constant voltage etching of n-type 6H SiC under the voltage (A) 10 V, (B) 20 V and (C) 30 V. Note that to better distinguish the curves (A) and (B) in the linear plot, curve (A) is lowered by 20 mA cm−2 . The inset shows the log–log plot of the same curves

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section in the log–log plot. If we fit the data using Equation (1.7), we have C ≈ 545 and β ≈ −0.43 for 10 V etching, C ≈ 510 and β ≈ −0.40 for 20 V etching. For 30 V etching, there are two linear sections. For the first 500 s, C ≈ 893 and β ≈ −0.43, while for the rest of the curve, C ≈ 388 and β ≈ −0.37. It is interesting to see that the current density curves (A) and (B) overlap after the initial 100 s. The curve fitting results for these two curves are also very close. However, the very different pore morphology suggests that the initial high current flow is important for the columnar pore growth. The curve (C) under 30 V etching shows a larger current density. The curve has a similar decay constant in the first 500 s, after which the decay rate becomes slower. Finally, the seemingly necessary constant voltage condition for columnar pore formation might suggest a space-charge-region depletion mechanism for pore wall passivation, which determines the pore wall thickness. The idea that the thickness of the pore walls between two pores is about twice the space-charge-region width is attractive. If we assume that the 20 V voltage drop is mainly across the space-charge-region of the semiconductor, the width of this space-charge-region is estimated to be about 60 nm at the cylindrical pore walls, which would suggest an inter-pore wall thickness of about 120 nm. The observed 40 nm pore wall is not consistent with this estimate. Although we believe that the pore wall is completely depleted, its thickness is apparently not defined by the space-charge-region width. The reasons for the observed 40 nm inter-pore distance and 20 nm pore diameter remain unclear and subject to further study.

1.4

SUMMARY

In summary, we have succeeded in fabricating porous 6H- and 4H-SiC with various morphologies, among which we have most intensively studied the triangular and the columnar porous morphologies. Through the investigation of triangular porous SiC, we find that in the PECE of (0001), (1100), and (1210) surfaces of 4H-SiC using low current densities (up to 5 mA cm−2 ), the shape and the size of the pores remain substantially the same, and the overall macroscopic porous structure is retained. A proposed model accounts for the observed triangular channel pore morphology. The foremost result of the investigation of the planar/triangular porous morphology is the discovery of a new surface which corresponds to the {1102} family of planes in 4H-SiC.

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The successful fabrication of a self-ordered, low porosity (0.1), columnar porous SiC structure with a pore diameter of about 20 nm provides a practical porous morphology for potential applications. To control columnar pore growth, voltage rather than current is the decisive etching condition. A proper voltage must be applied to obtain columnar pore formation. Rather than the differences in the photoelectrochemical reactions, it is the fact that the C-face does not act as an etch stop that avoids the problem of branching and favors the formation of straight columnar pores under controllable etching conditions. The further improvement of the pore lattice regularity and control of the pore diameter are challenging as long as the mechanism determining the inter-pore spacing and pore diameter remains unclear. Further understanding of the growth process is challenging. More experimental parameters must be studied in order to model this process.

ACKNOWLEDGEMENTS We gratefully acknowledge Albert Stewart, associated with the Materials Micro-Characterization Laboratory of the Department of Mechanical Engineering and Materials Science, for assistance with the electron microscopy conducted during this study. We thank Chris Bowman, supervisor of the clean room at Carnegie Mellon University, for kindly allowing us to use the RIE apparatus and A. Sagar for his help with RIE processing. We also thank CREE, Inc. and II-VI, Inc. for providing us with high quality 4H- and 6H-SiC single crystal wafers. This work is supported by the ONR-DURINT grant N00014-01-1-0715.

REFERENCES [1] A. Uhlir, Jr, Electrolytic shaping of germanium and silicon, Bell Sysem. Tech. J., 35, 333–347 (1956). [2] D.R. Turner, Electropolishing silicon in hydrofluoric acid solutions, J. Electrochem. Soc., 105, 402–408 (1958). [3] J.W. Faust, Jr, The etching of silicon carbide, in Silicon Carbide: A High Temperature Semiconductor, J.R. O’Connor and J. Smiltens (Eds), Pergamon, Oxford, 1960, pp. 403–419. [4] Y. Watanabe, Y. Arita, T. Yokoyama and Y. Igarashi, Formation and properties of porous silicon and its application, J. Electrochem. Soc., 122, 1351–1355 (1975). [5] L.T. Canham, Silicon quantum wire array fabrication by electrochemical and chemical dissolution of wafers, Appl. Phys. Lett., 57, 1046–1048 (1990).

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[6] J.S. Shor and R.M. Osgood, Jr, Broad-area photoelectrochemical etching of n-type beta-SiC, J. Electrochem. Soc., 140, L123–L125 (1993). [7] J.S. Shor, I. Grimberg, B.-Z. Weiss and A.D. Kurtz, Direct observation of porous SiC formed by anodization in HF, Appl. Phys. Lett., 62, 2836–2838 (1993). [8] J.S. Shor and A.D. Kurtz, Photoelectrochemical etching of 6H-SiC, J. Electrochem. Soc., 141, 778–781 (1994). [9] J.S. Shor, L. Bemis, A.D. Kurtz, I. Grimberg, B.Z. Weiss, M.F. MacMillan and W.J. Choyke, Characterization of nanocrystallites in porous p-type 6H-SiC, J. Appl. Phys., 76, 4045–4049 (1994). [10] M.F. MacMillan, R.P. Devaty, W.J. Choyke, D.E. Goldstein, J.E. Spanier and A.D. Kurtz, Infrared reflectance of thick p-type porous SiC layers, J. Appl. Phys., 80, 2412–2419 (1996). [11] J.E. Spanier and I.P. Herman, Use of hybrid phenomenological and statistical effective-medium theories of dielectric functions to model the infrared reflectance of porous SiC films, Phys. Rev. B, 61, 10437–10450 (2000). [12] S.E. Saddow, M. Mynbaeva and M.F. MacMillan, Porous SiC technology, in Silicon Carbide: Materials, Processing and Devices, Zhe Chuan Feng and Jian H. Zhao (Eds), Taylor and Francis, New York, 2004, Chapter 8, pp. 321–385. [13] Y. Shishkin, Y. Ke, R.P. Devaty and W.J. Choyke, A short synopsis of the current status of porous SiC and GaN, Mater. Sci. Forum, 483–485, 251–256 (2005). [14] Y. Shishkin, W.J. Choyke and R.P. Devaty, Photoelectrochemical etching of n-type 4H silicon carbide, J. Appl. Phys., 96, 2311–2322 (2004). [15] E.J. Garboczi, D.P. Bentz and N.S. Martys, Digital images and computer modeling, in Methods in the Physics of Porous Media, Po-zen Wong (Ed.), Experimental Methods in the Physical Sciences 35, Academic Press, San Diego, 1999. [16] Y. Shishkin, Y. Ke, R.P. Devaty and W.J. Choyke, Fabrication and morphology of porous p-type SiC, J. Appl. Phys., 97, 044908 (2005). [17] M.I.J. Beale, N.G. Chew, M.J. Uren, A.G. Cullis and J.D. Benjamin, Microstructure and formation mechanism of porous silicon, Appl. Phys. Lett., 46, 86–88 (1985). [18] A.O. Konstantinov, C.I. Harris and E. Janz´en, Electrical properties and formation mechanism of porous silicon carbide, Appl. Phys. Lett., 65, 2699–2701 (1994). ¨ ¨ [19] O. Jessensky, F. Muller and U. Gosele, Microstructure and photoluminescence of electrochemically etched porous SiC, Thin Solid Films, 297, 224–228 (1997). ¨ ¨ [20] A. Bauer, J. Kraußlich, L. Dressler, P. Kuschnerus, J. Wolf, K. Goetz, P. Kackell, J. ¨ Furthmuller and F. Bechstedt, High-precision determination of atomic positions in crystals: the case of 6H- and 4H-SiC, Phys. Rev. B, 57(5), 2647–2650 (1998). [21] E. Rauls, J. Elsner, R. Gutierrez and Th. Frauenheim, Stoichiometric and nonstoichiometric (1-100) and (11–20) surfaces in 2H-SiC: a theoretical study, Solid State Commun., 111, 459–464 (1999). [22] E. Burstein and P.H. Egli, The physics of semiconductor materials, in Advances in Electronics and Electron Physics, L. Marton (Ed.), Academic Press, Inc., New York, 1955, Vol. VII, p. 43. [23] L. Muelhoff, M.J. Bozack, W.J. Choyke and J.T. Yates, Jr, Comparative oxidation studies of SiC(000-1) and SiC(0001) surfaces, J. Appl. Phys., 60, 2558–2563 (1986). [24] Y. Shishkin, E. Oborina, A. Maltsev, S.E. Saddow and A.M. Hoff, Oxide of non-basal quasi-polar 6H-SiC surfaces, J. Phys. D: Appl. Phys., 39, 2692–2695 (2006). [25] Y. Shishkin and O. Kordina, Bulk growth of 6H-SiC on non-basal quasi-polar surfaces, J. Cryst. Growth, 291, 317–319 (2006).

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[26] U. Starke, W.Y. Lee, C. Coletti, S.E. Saddow, R.P. Devaty and W.J. Choyke, SiC pore surfaces: Surface studies of 4H-SiC(1–102) and 4H-SiC(-110-2), Appl. Phys. Lett., 88, 031915 (2006). ¨ Fast pore etching, Phys. [27] S. Frey, M. Kemell, J. Carstensen, S. Langa and H. Foll, Status Solidi A, 202(8), 1369–1373 (2005). ¨ M. Christophersen, J. Carstensen and G. Hasse, Formation and application [28] H. Foll, of porous silicon, Mater. Sci. Eng. R 39, 93–141 (2002). [29] H. Masuda and K. Fukuda, Ordered metal nanohole arrays made by a two-step replication of honeycomb structures of anodic alumina, Science, 268, 1466–1468 (1995). ¨ [30] K. Nielsch, J. Choi, K. Schwirn, R. Wehrspohn and U. Gosele, Self-ordering regimes of porous alumina: the 10% porosity rule, Nano Lett, 2(7), 677–680 (2002). ¨ Single crys[31] S. Langa, M. Christophersen, J. Carstensen, I.M. Tiginyanu and H. Foll, talline 2D porous arrays obtained by self organization in n-InP, Phys. Status Solidi A, 197(1), 77–82 (2003). ¨ S. Langa, J. Carstensen, M. Christophersen, and I.M. Tiginyanu, Pores in [32] H. Foll, III-V semiconductors, Adv. Mater. 15(3), 183–198 (2003). [33] Y. Ke, F. Yan, R.P. Devaty and W. J. Choyke, Columnar pore growth in n-type 6H SiC, Mater. Sci. Forum, 527–529, 739–742 (2006). [34] Y. Ke, R.P. Devaty and W.J. Choyke, Self-ordered nanocolumnar pore formation in the photoelectrochemical etching of 6H SiC, Electrochem. Solid-State Lett., 10 (7), K24–K27 (2007). [35] Y. Ke, C. Moisson, R.M. Feenstra, R.P. Devaty and W.J. Choyke, A comparison of various surface finishes and the effects on the early stages of pore formation during high field etching of SiC, Mater. Sci. Forum, 527–529, 743–746 (2006).

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2 Processing Porous SiC: Diffusion, Oxidation, Contact Formation S.I. Soloviev1 and T.S. Sudarshan2 1 2

GE Global Research Center, Niskayuna, NY 12309, USA University of South Carolina, Columbia, SC 29208, USA

2.1

INTRODUCTION

Porous SiC material, to be used for various device applications, requires additional processing steps which are common for the fabrication of electronic devices. These steps include cleaning, etching, doping, oxidation, metallization, film deposition, annealing, etc. Such treatments of the porous layer can modify the properties of the porous layer and, moreover, the kinetics of the processes in porous material might be different from similar processes in nonporous substrates of the same material. In this chapter we will summarize our initial research efforts covering some key processing steps in device technology such as doping via diffusion, thermal oxidation and contact deposition with respect to porous SiC. In addition, working on preparation of porous SiC samples we found significant variations in pore morphology as a function of

Porous Silicon Carbide and Gallium Nitride: Epitaxy, Catalysis, and Biotechnology Applications Edited by Randall M. Feenstra and Colin E.C. Wood  C 2008 John Wiley & Sons, Ltd

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many parameters such as current density, operation voltage, electrolyte solution, and resistivity of SiC substrate. Thus, at the beginning of the chapter we will discuss different porous SiC structures used in this research, their formation and characterization in order to specify initial porous structures which were then subject to processing steps.

2.2

FORMATION OF POROUS LAYER

Among many key parameters which affect the pore morphology (such as current density, voltage, time of anodization, composition of electrolyte, etc.) substrate doping concentration (or resistivity) plays a particularly significant role. However, not much data related to the effect of SiC substrate resistivity on the formation of a porous layer has been published so far. In this work, we discuss surface and pore morphology of SiC and explore its correlation with substrate doping concentration. The chemical aspects of the electrochemical etching process in SiC are consistent with the behavior of the anodic etching of Si, where dissolution occurs via two reactions: silicon dioxide formation and oxide removal in the electrolyte [1]. Moreover, reaction of oxidation occurs in the presence of positively charged carriers, holes. Thus, the hole concentration must be sufficient in order to initiate the pore etching process. One of the ways to generate the required concentration of holes in n-type SiC is ultraviolet (UV) illumination. Also, a fairly high concentration of electron–hole pairs can be generated in the depletion layer when the electric field is high enough to initiate impact ionization, resulting in an avalanche breakdown in the semiconductor. The mechanism of breakdown depends on many factors, which include doping concentration and material of the semiconductor. For instance, tunneling effect in Si might occur when the voltage Ut ≤ 4Eg /q (where Eg is the band gap energy and q is the electron charge) and doping concentration is higher than ∼2–5 × 1017 cm−3 [2]. Since the probability of tunneling breakdown significantly reduces for wide band gap materials with the same doping concentration, one should expect that the tunneling mechanism of the breakdown in SiC will be dominant at higher doping concentrations compared with Si. Our calculation has shown that in 6H-SiC (Eg = 3.09 eV) tunneling is the most possible mechanism of breakdown if the doping concentration exceeds ∼1019 cm−3 , while the avalanche breakdown is dominant in lower doped substrates. Figure 2.1 shows the theoretical curve of breakdown voltage in 6H-SiC vs substrate

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Breakdown voltage (V)

500 Experimental data Theoretical curve

400

300

200

100

0 10

17

10

18

19

10

Doping concentration (cm−3)

Figure 2.1

Breakdown voltage vs substrate doping concentration

doping concentration calculated using the equation:  U(Nd ) =

2 EM

2εε0 qNd

 (2.1)

where ε, εo are the dielectric constants, q is the electron charge, Nd is the doping atom concentration, and E M is the maximum breakdown field. Experimental values of voltages at which breakdown occurred during anodization of the substrate with different doping concentration are also presented in Figure 2.1. In our research, porous silicon carbide (por-SiC) samples were prepared using n-4H-SiC wafers from CREE Research Inc. These wafers were nitrogen doped and had a resistivity varying from 0.01 to 0.50  cm. Electrochemical etching was performed on both the polished silicon- and carbon-terminated faces of the samples using a mixture of hydrofluoric acid (HF) and ethanol (1:1) as electrolyte for a time period of 2–60 min with and without the assistance of a 150 W mercury lamp. Prior to turning on the current, the sample arrangement in the Teflon cell was kept under the Hg lamp for 1 min. The counter electrode was a platinum wire positioned about 1 cm from the sample (Figure 2.2). The applied current density varied between 10 mA cm−2 and 80 mA cm−2 . Por-SiC samples were analyzed after ultrasonic cleaning in methanol for 10–20 min. Thicknesses of the porous layers were measured by the cylindrical grove technique.

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−

Pt-electrode

O-ring

+

Teflon cell

SiC sample Figure 2.2

Schematic of the anodization cell

It should be noted that the effect of UV illumination on the gain in current during anodization was not significant (∼0.1 mA) due to the low density of UV light (∼50 mW cm−2 ). Typical I–V characteristics of SiC substrates with different doping concentrations, immersed in the electrolyte at a reverse bias, are shown in Figure 2.3. According to Equation (2.1) the substrates with different doping concentrations should exhibit different breakdown voltages. The curve H corresponds to the high doped (8 × 1018 cm−3 ) substrate, while curves M and L correspond to moderately (1 × 1018 cm−3 ) and low doped (3 × 1017 cm−3 ) SiC substrates, respectively. As it can be seen from the 20 18

Current (mA)

16

Operating points

14 12 10 8 6

H

4

M

L

2 0

0

20

40

60

80

100

120

Voltage (V) Figure 2.3 Reverse biased I–V curves of electrolyte/SiC substrate with different doping concentrations

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I–V curves, the formation of porous SiC was performed in the avalanche breakdown mode. For heavily (H) doped samples an operating current point of 10 mA was at the voltage of 7 V, while for moderately (M) and low (L) doped samples the operating voltage points for the same current were established at 48 and 125 V, respectively. The transient period of time during which the current approached this operating point of 10 mA was 10 s for each experiment, following which, the anodization current was constant for a period of time. SEM analysis of an ‘as-formed’ porous SiC surface could not reveal any characteristic pattern on it. This might be explained by the fact that the openings of the pores that propagate through the por-SiC layer have diameter on the surface of the order of 20 nm or less [3]. Similar structure of a porous layer is also observed in porous Si [4]. A very thin surface layer exists with a thickness less than 0.1 μm and pore diameter in the order of 5–10 nm, which could barely be observed by scanning electron microscopy (SEM). These pores increase in diameter up to several hundreds of nanometers as they extend from surface to bulk. This led us to the idea of stripping off the skin layer to observe the bulk pore morphology. After removal of the surface layer of about 0.3 μm thick using reactive ion etching (RIE), the characteristic pattern of a porous structure could be observed. An SEM image of the porous SiC sample (current density of 40 mA cm−2 for 5 min) after the removal of a thin layer from half of the surface is shown in Figure 2.4. This image is taken from the boundary region where the porous surface with removed layer is on the left side and the ‘as-formed’ porous surface is on the right side. Note that the SEM electron accelerating voltage was 30 kV. This allowed the electrons to penetrate deeper into the substrate and reveal the porous structure, which is beneath the thin surface layer (see shadow on the right side of Figure 2.4). As can be seen, the pore openings have irregular shapes with feature sizes varying from 0.3 to 0.7 μm. There is also a very narrow region at the edge of the removed layer where the pore openings have a circular shape with diameter of less than 0.1 μm. Obviously, the thickness of the removed layer in this transition region was less than that in the region which is far enough from the boundary. It indicates that pore size enlarges with depth from several nanometers on the surface to several hundreds of nanometers at a depth of around 0.3 μm. Figure 2.5(a) shows a SEM image of a heavily doped sample H after skin layer removal. The grain-like surface is indicative of very small diameter formed pores. The mean grain size calculated using AFM Nonoscope III software was 60 nm. A transmission electron microscopy (TEM) image of a sample from the same H group is shown in Figure 2.5(b). This

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Acc-V Spot Magn 30.0 kV 3.0 5000x

5 µm

Det WD Exp SE 4.2 1

Figure 2.4 SEM image of porous SiC after 0.2 μm surface layer removal from half of the surface (on the left side). Reproduced from S. Soloviev et al., Electrochemical and Solid-State Letters 6, G22–G24. Copyright (2003), with permission from the Electrochemical Society

cross-section of the porous layer cut parallel to the [1120] face shows that pores have an average size of 20–25 nm while the surrounding crystalline walls have feature size of 50–60 nm, which is in excellent correlation with the mean gain size measured by atomic force microscopy (AFM). It should be noted that the size of these pores and their direction

0.1um

bulk

Acc-V Spot Magn Det WD Exp 30.0 kV 3.0 56000x SE 5.4 1

(a)

USC EM Center

500 nm

(b)

Figure 2.5 SEM image (a) and cross-section TEM image (b) of the porous layer formed in a heavily doped SiC substrate

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bulk

Surface Acc-V Spot Magn 5.00 kV 2.0 5000x

(a)

Det SE

WD Exp 5.4 0

USC EM Center

5 µm

500 um

(b)

Figure 2.6 SEM image (a) and cross-section TEM image (b) of the porous layer formed in a moderately doped SiC substrate

(perpendicular to the surface) do not change through the entire thickness of the porous layer. The SEM image of the porous layer formed in a moderately doped SiC substrate and the TEM image of the cross-section of the same sample are shown in Figure 2.6(a) and (b), respectively. As in case of the porous SiC formed in high-doped substrate the SEM analysis could not reveal any pore openings on the surface without the skin layer removal. After 0.1 μm of the skin layer was etched off, the diameter of the pore openings varied from approximately 100 to 600 nm. From the TEM cross-section analysis of the same sample one could see that the pore morphology has a bush-like structure with ‘root’ location at the surface. The pore diameter enlarges with pore propagation into the bulk of the substrate and at a depth of about 2 μm the pores overlap. This pore enlargement explains the light rings around the pores in the SEM picture, which appears due to the charge crowding effect at the sharp edges on the surface corresponding to pore openings. Figure 2.7(a) shows the SEM image of a low-doped 6H-SiC sample anodized for 5 min. A characteristic etch pit pattern appears in the anodized sample, since in this case the pore nucleation occurs mostly at dislocations and dislocation walls. Similar to the other two types of substrates, the pore openings on the surface could not be observed neither under the optical microscope nor under the SEM without the skin layer removal. The SEM image of the cross-section of the cleaved sample demonstrates that pores increase in diameter with depth and might reach a size of several micrometers [Figure 2.7(b)]. Moreover, the pore density for the low-doped samples is relatively low compared with those in the high and

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Mag WD HV Det Pressure 3/7/2002 ... 2:44:25 PM 2600x 7.3mm 30.0kV ETD

20.0µm USC EM Center

(a)

Det ot Magn 0 16000x SE

WD 4.7

Exp 1

USC EM Center

2 µm

(b)

Figure 2.7 Surface SEM image (a) and cross-section SEM image (b) of the porous layer formed in a low-doped SiC substrate

moderately doped samples; the pore overlapping did not take place even after increasing the anodization time from 5 to 20 min. However, usage of voltage pulse mode with a single pulse of 1 min long resulted in complete pore overlapping and formation of a uniform structure after 12 pulses with a peak current density of 40 mA cm−2 (Figure 2.8). It should be noticed that the shape of the pore openings has transformed with time into irregular voids with a feature size up to 1 μm while the feature size of the remaining crystalline walls decreased down to 0.2–0.3 μm. The SEM picture of a cleaved low-doped porous sample is shown in Figure 2.8(b). A ‘branch’-like porous layer propagating into bulk crystal up to 15 μm is formed. The trunk of such a porous structure is highlighted

Acc-V Spot Magn 30.0 kV 3.0 6564x

(a)

Det WD Exp SE 5.4 1 USC EM Center

5 µm

Acc-V Spot Magn 30.0 kV 3.0 2000x

Det WD Exp SE 4.9 1

USC EM Center

10 µm

(b)

Figure 2.8 Surface SEM image (a) and cross-section SEM image (b) of the porous layer formed in a low-doped SiC substrate with voltage in pulse mode. Reproduced from S. Soloviev et al., Materials Science Forum, 389–393, 1113–1116. Copyright (2002), with permission from Trans Tech Publications

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Pore diameter (nm)

1000

100

Space charge layer width Variation in pore diameter

10 10

18

10

19

Doping concentration (cm−3)

Figure 2.9

Pore diameter vs SiC substrate doping concentration

in the right part of the picture. One can notice that there are a number of small pores surrounding the trunk. The diameter of these pores varied from 50 to 200 nm and their density decreased from the surface to the bulk of the substrate. The observed dependence of pore diameter on the SiC substrate doping concentration has a similar trend found for porous Si [5], although in our experiments, we observed uniform pore propagation only in heavily doped samples. Considering only the pore opening on the surface, the range of pore diameters vs substrate doping concentration is presented in Figure 2.9. On average, the pore diameter increase with decrease of the doping concentration might be explained by the dependence of space charge layer width on the substrate resistivity. The calculated curve of space charge layer width as a function of the substrate doping concentration exhibited good fit with the measured pore diameters (see dashed line in Figure 2.9). Therefore, a higher dopant concentration will lead to the formation of smaller pores as well as a smaller spacing between the pores, because a smaller radius of curvature on the pore bottom is required for stable pore propagation. The pore depth penetration in the high-doped samples was about 15 μm after 5 min of anodization at 40 mA cm−2 , while the moderately and low-doped sample had pore depth penetrations of ∼3 and ∼1 μm, respectively. Since the porous layers were formed at the same conditions, i.e. the same total charge was applied to the samples, the amount of

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C-face Si-face

14

Thickness (µm)

Thickness (µm)

35 30 25 20 15 10

10 8 6 4

5 0

C-face Si-face

12

2 0

(a)

10

20

30

40

Time (min)

50

60

2

(b)

4

6

8

10

Time (min)

Figure 2.10 Thickness of porous layer as a function of time for current density of 10 mA cm−2 (a) and 40 mA cm−2 (b). Reproduced from S. Soloviev et al., Electrochemical and Solid-State Letters 6, G22–G24. Copyright (2003), with permission from the Electrochemical Society

etched substrate material per sample was the same during anodization. Thus, larger pore diameters and thinner porous layers are observed in substrates with lower doping concentration. The effect of anodization time on thickness of the formed porous layers was investigated for heavily doped SiC substrate. Figure 2.10 shows the measured porous silicon carbide film thicknesses as a function of anodization time for both silicon (Si)- and carbon (C)-faces at current densities of 10 and 40 mA cm−2 . Each data point in these plots has been taken from the thickness measurements of different por-SiC samples processed under the same conditions but with anodization time as the only variable. The anodization time was varied from 5 to 60 min and from 2 to 10 min at a current density of 10 and 40 mA cm−2 , respectively. We limited the time of anodization to 10 min at current densities more than 40 mA cm−2 because peeling of the porous layer occurs in these cases. It is clear that a por-SiC film grows linearly for these current densities during the first 10 min. After that the growth rate becomes lower and the film thickness as a function of time might be interpolated by a parabolic curve. Based on the fact that the process of porous layer formation consists of two main reactions (oxidation and the oxide etching) we may assume that the mechanism of anodization is similar to the kinetics of oxidation. During the initial period of anodization when the thickness of the porous layer is fairly thin, the limiting process of the porous layer growth is the reaction at the interface between the substrate and the porous layer. However, when the thickness of the porous layer becomes higher, then the growth rate is limited by the diffusion of electrolyte

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through the porous layer leading towards the interface. It leads to the lowering of the porous layer growth rate. Moreover, it is known that the oxidation rate of the Si-face is significantly less than that of the C-face of a SiC crystal [6]. This explains the formation of thinner porous layer on the Si-face compared with the C-face at the same conditions. The anodization rate appeared to be directly related to the current density used in these experiments. For the initial period (up to 10 min), the growth rate increases from 0.3 to 1.1 μm min−1 for the Si-face and from 0.8 to 1.5 μm min−1 for the C-face when the current density is increased from 10 to 40 mA cm−2 . It should be noted that the anisotropic properties of SiC appear more clearly at lower current densities because the difference between the porous layer growth rate of Si- and C-faces is several times greater at current density of 10 mA cm−2 than at 40 mA cm−2 . No significant variation in pore diameter was observed in moderately doped SiC substrates with an increase in current density from 10 to 60 mA cm−2 . However, the pore density increased by more than one order of magnitude. The lowest pore density of 3 × 107 cm−2 was obtained at the anodization current density of 10 mA cm−2 (Figure 2.11). An increase of the current density to 20 mA cm−2 led to an increase of the pore density to 1 × 108 cm−2 . A further doubling of the current density (up to 40 mA cm−2 ) formed a porous network with a pore density of 1.5 × 108 cm−2 , and then, the pore density does not depend on current density significantly.

18

Pore density, x 107 (cm−2)

16 14 12 10 8 6 4 2 0 10

20

30

40

50

60

Current density (mA cm −2)

Figure 2.11 density

Pore density in the moderately doped SiC substrate vs etching current

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Summarizing the obtained results we may conclude that the resistivity of SiC substrate has the most significant impact on morphology of the forming porous layer. Thus, further processing the porous layer for use in the device applications must take into account the resistivity of SiC substrate as well as other parameters of the anodization process.

2.3

DIFFUSION IN POROUS SiC

It is known that diffusion coefficients of doping impurities in SiC are very low even at temperatures above 1800 ◦ C. For this reason, using traditional technology to form deep doped layers in SiC requires diffusion of doping impurities at very high temperatures for a long time. An attractive approach is to use the large surface areas of porous crystals for very efficient and fast dopant in-diffusion. High temperature diffusion of aluminum and boron atoms into porous SiC single crystal substrates will be discussed in this chapter The samples for diffusion were moderately doped n-type 6H-SiC substrates with porous layers 2–10 μm thick. The diffusion was carried out at temperatures varying from 2000 to 2200 ◦ C in argon ambient in a graphite crucible. A vertical double wall water-cooled quartz chamber with inductive heating was used to perform the diffusion process. The samples were glued to the top of the lid of the crucible face down. Prior to use, the samples were cleaned by the standard procedure to remove organic and ionic impurities from the wafer surface. Blanket thermal diffusion of aluminum and boron was implemented from the vapor phase as schematically illustrated in Figure 2.12. Aluminum and boron atoms in vapor were generated by evaporating from solid impurity sources such as elemental boron and Al4 C3 . Since the diffusion process was conducted

sample

Al

crucible source powder

Figure 2.12

Crucible for dopant diffusion into porous SiC

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1021 Anodization:

Atom concentration (cm−3)

10 min at 5 mA cm−2 1020

1019

1018

Boron, 2200°C diffusion Boron, 2000°C Aluminum, 2200°C

1017 0

Aluminum, 2200°C 1

2 Depth (µm)

3

Figure 2.13 SIMS profiles of aluminum and boron atoms in porous SiC layer after diffusion at different temperatures for 10 min

above 2000 ◦ C, which is already beyond the sublimation point of SiC, source materials were mixed with the SiC powder in the crucible to form a SiC equilibrium vapor ambient for avoiding evaporation of SiC from the substrate. Once the equilibrium condition is established inside the crucible, the velocity of sublimation and condensation will be equal, and simultaneously, the impurities of Al/B will be diffused into the substrate. The aluminum and boron depth distributions after diffusion at different temperatures are analyzed using secondary-ion mass spectrometry (SIMS) data. Figure 2.13 shows SIMS profiles of the boron and aluminum atoms at different temperatures (2000 and 2200 ◦ C) after diffusion for 10 min into porous SiC layer with a thickness of 2.7 μm. It is clearly seen that the distribution of aluminum atoms in a porous layer is practically uniform and constant for both temperatures, while the distribution of boron atoms is uniform only for the lower temperature of diffusion. At the higher temperature, the maximum concentration of boron atoms is greater near the surface than that after diffusion at lower temperature, and yet it gradually decreases within the porous layer. Note that the concentration of aluminum in the porous layer is the same for both temperatures of diffusion, while the concentrations of boron atoms fit their values for different temperatures only at the interface porous layer–substrate. Once

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the impurity atoms reach the depth of the porous layer, their distribution in the nonporous substrate is described by regular diffusion – greater temperature, deeper atom penetration. Slight decrease in the doping concentrations for both impurities at the surface of the porous layer apparently is associated with the out-diffusion process, which was also observed during diffusion of the same impurities into nonporous SiC substrates [7]. Such uniform dopant distribution in the porous layer was observed in all SiC samples in which the thicknesses of porous layers varied from 2 to 10 μm in our experiments on diffusion. This can be explained by the fact that diffusion of dopant atoms in a porous layer occurs not only via diffusion through the SiC walls of porous layer but also through gas-phase transport within pore openings and surface diffusion. Figure 2.14 shows SIMS profiles of boron and aluminum atoms after diffusion at 2200 ◦ C for 10 min into porous substrates with different thicknesses of the porous layers. These porous layers were formed at the same current densities of anodization but for different periods of time. This resulted in identical atom profiles in both substrates but shifted by ∼0.2 μm as the depth of the porous layer in the second substrate was shallower by 0.2 μm.

1021 Diffusion at 2200°C for 10 min Atom concentration (cm−3)

1020

1019

1018 Boron, 10 min anodization

n

Aluminum, 10 min 1017

Aluminum, 8 min Boron, 8 min

1016

0

1

2 Depth (µm)

3

Figure 2.14 SIMS profiles of aluminum and boron atoms after diffusion into porous layers with different thicknesses

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Atom concentration (cm−3)

1021

1020

Diffusion at 2100°C Anodization for 6 min

1019

1018

Boron, 8 mA cm−2 AI, 8 mA cm−2

1017

Boron, 10 mA cm−2 AI, 10 mA cm−2

1016 0.0

0.5

1.0

1.5

2.0 2.5 Depth (µm)

3.0

3.5

4.0

Figure 2.15 SIMS profiles of aluminum and boron atoms after diffusion into porous SiC layers formed at different current densities

It was shown that the pore density in the formed porous layer increased with an increase in current density. Dopant diffusion into porous SiC layers formed at different current densities resulted in slightly different maximum doping concentrations of both aluminum and boron atoms in the porous layers (Figure 2.15). The porous layer with larger pore size (higher current density used) exhibited greater maximum doping concentration. This suggests that the gas-phase transport mechanism is, probably, dominant during diffusion in the porous layer since with a greater number of pores, more impurity atoms penetrate through the porous layer and, thus, their doping concentration in the porous layer is higher. Porous layer formed with a lower current density was thicker since anodization time was longer (15 min), and, thus, dopant penetration was deeper. Diffusion of impurity atoms in bulk substrate under the porous layer is fairly different from diffusion of the same species in nonporous crystals. Figure 2.16 shows boron atom profiles in bulk substrate under the porous layer (formed at the same conditions) after diffusion at different temperatures. Coordinate x = 0 corresponds to the interface porous layer–bulk substrate. The diffusion profile of boron atoms in nonporous SiC substrate after diffusion at the same conditions (2000 ◦ C, 10 min) is also presented in this plot for comparison. It is seen that the maximum concentration of boron atoms diffused from the porous layer into bulk

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Boron concentration (cm−3)

Boron 2000°C Boron 2200°C 1019

Boron 2000°C, nonporous

1018

1017 0. 0

0.5

1.0

Depth (µm)

Figure 2.16 SIMS normalized boron profiles after diffusion from the porous layer at different temperatures for 10 min

substrate is less than that in the nonporous substrate. We believe that this can be explained by the fact atom site density in the porous material is less due to porosity and, thus, the total number of impurity atoms per volume unit would be also less than the one in nonporous crystal. Note this statement is based on the assumption that the solubility of boron atoms in crystalline walls of porous layer is the same as in nonporous crystal at a given temperature. Although the higher temperature of diffusion resulted in deeper atom penetration under the porous layer (up to ∼0.4 μm at 2200 ◦ C vs ∼0.2 μm at 2000 ◦ C for 10 min), boron atoms in nonporous substrates penetrate up to 0.8 μm at 2000 ◦ C for the same period of time. This suggests that the diffusion coefficient of boron atoms in SiC substrate under the porous layer is significantly less than that in nonporous substrate. The origin of such a difference in diffusion coefficients is not clear, however, we can speculate that a stress field in the region close to the porous layer caused by different thermal expansion coefficients of porous and nonporous material might affect the diffusivity of the impurity atoms. In contrast to boron atoms, diffusion of aluminum atoms under the SiC porous layer occurs with a greater coefficient of diffusion. Moreover, the maximum concentration of aluminum atoms in the porous layer is higher than the maximum concentration of aluminum in a SiC nonporous substrate (Figure 2.17) after diffusion at the same temperature. Apparently,

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Aluminum concentration (cm−3)

Al 2000°C 1020

Al 2200°C Al 2000°C, nonporous

1019

1018

1017

0.0

0.1

0.2

0.3

0.4

Depth (µm)

Figure 2.17 SIMS normalized aluminum profiles after diffusion from the porous layer at different temperatures for 10 min

such a high concentration of aluminum in the porous layer is associated with precipitation of the atoms on the surface of the pores, since, in contrast to boron atoms in the porous layer, maximum concentration of aluminum atoms in the porous layer did not depend on the temperature of diffusion. However, additional investigation is required to clarify this statement.

2.4

OXIDATION

Oxidation of a porous surface might not only change the optical and electrical characteristics of the surface but the oxidation followed by oxide removal could also modify the pore morphology. In this section we will discuss the kinetics of thermal oxidation of SiC substrates with porous layers formed on both carbon and silicon terminated faces. Anodization of moderately doped n-SiC samples (with resistivity of 0.018  cm) was carried out in the dark mode at current densities from 10 to 60 mA cm−2 in 2.5% HF solution for 2–10 min as described at the beginning of this chapter. The resulting layer had porosity of about 90%. After anodization, the samples were rinsed in deionized water and

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Oxide thickness (nm)

200

Porous Si-face Porous C-face C-face Si-face

150

100

50

0 40

80

120 160 Time of oxidation (min)

200

Figure 2.18 Silicon dioxide thickness vs time of oxidation of 4H-SiC substrate with porous layer on it. Reproduced from S. Soloviev et al., Materials Science Forum, 389– 393, 1113–1116. Copyright (2002), with permission from Trans Tech Publications

dried in nitrogen ambient. After RCA cleaning, oxidation of the porous samples was performed in wet oxygen at 1000 ◦ C for 60–180 min. The thickness of the grown oxide layers both on the porous and nonporous regions were measured by Dektak profilometer and by Rudolph ellipsometer. Also, the steps between porous and nonporous regions before and after the oxide removal were measured on each face to obtain data on the oxide propagation into por-SiC. The surface morphology of porous silicon and carbon faces before and after oxidation was analyzed by means of AFM. Figure 2.18 shows the dependence of oxide thickness grown on both porous and nonporous SiC substrate vs oxidation time for the oxidation temperature of 1000 ◦ C. The oxidation rate of porous substrate on both the faces is less than the plain carbon face but higher than the plain silicon face. This difference in the oxidation rates results in a thicker oxide layer grown on a nonporous C-face than on the porous C-face and Si-face, and a thinner oxide layer grown on a nonporous Si-face than on the porous C-face and Si-face. Measurements of an oxide step by the stylus Dektak profilometer performed on the same sample allowed us to conclude that the interface between the oxide layer and a porous substrate is always below the corresponding interface for nonporous substrates in both Siand C-faces (Figure 2.19). In order to explain this we may assume that the mechanism of oxidation of the porous SiC layer apparently consists

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SiO2/SiC

SiO2/por-SiC

por-SiC

SiO2/por-SiC

por-SiC

Si-face SiC-substrate

C-face SiC-substrate

(a)

(b)

Figure 2.19 Schematic of silicon dioxide penetration into porous and nonporous SiC substrate regions for Si-face up (a) and C-face up (b). Reproduced from S. Soloviev et al., Materials Science Forum, 389–393, 1113–1116. Copyright (2002), with permission from Trans Tech Publications

of three phases which occur simultaneously: penetration of oxygen atoms through the pores into the bulk region; oxidation of pore walls; oxidation of the face which is parallel to the substrate surface (‘regular’ surface). Based on the fact that the oxidation rate of the SiC face, which is parallel to the c-axis (a-face), is higher than that of the Si-face and less than that of the C-face [7,8], we can conclude that oxidation of the pore walls (in a-face) is a dominant process rather than oxidation of a ‘regular’ surface (c-face). This might be a reason why the thickness of a porous oxide layer in our experiment is always thicker than that on the nonporous Si-face, and thinner than that on the nonporous c-face. Obviously, for the porous material, the total surface area of the a-face is significantly larger than that of the c-face. Hence a much larger a-face area is subjected to oxidation. Further, if the above c-face happens to be the C-face, then its oxidation rate will be higher than if it is the Si-face. This explains the higher oxide rate of the porous C-face vs the porous Si-face seen in Figure 2.18. The AFM images shown in Figure 2.20 were taken from porous C-face before oxidation [Figure 2.20(a)] and after oxidation and subsequent removal of the oxide layer [Figure 2.20(b)]. It is seen clearly that after oxidation of the porous C-face the surface peaks become sharper. This result is in good agreement with the anisotropic mechanism of oxidation of a porous layer that is discussed above.

2.5

CONTACTS TO POROUS SiC

In this section, we will discuss our studies on the electrical properties of nickel contacts formed on porous SiC layer via current–voltage (I–V) and capacitance–voltage (C–V) characterization.

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120.000 nm

100.000 nm

50

19:36

µ.m

µ.m 1.5

1.5 0.1

0.1

(a)

(b)

0.5

0.5

Figure 2.20 AFM images of porous C-face before oxidation (a) and after oxidation and subsequent oxide removal (b). Reproduced from S. Soloviev et al., Materials Science Forum, 389–393, 1113–1116. Copyright (2002), with permission from Trans Tech Publications

Samples of low doped (resistivity of 0.13  cm) n-SiC used in this study were anodized under UV illumination of 150 W Hg lamp at current densities of 10 to 60 mA cm−2 in HF: ethanol (1:1) solution for 2–10 min as described above. On the exposed circular area (7 mm in diameter), uniform porous layers with a thickness of 1–15 μm have been formed. After ultrasonic cleaning in ethanol and rinsing in deionized water, the samples were dried on a hot plate at 100 ◦ C for 2 h. The morphology of the formed porous SiC layers was shown in Figure 2.8. Nickel Schottky contacts with a diameter of 300 μm and a thickness ˚ were deposited on the porous SiC by magnetron deposition of 1500 A followed by photolithography patterning. A blanket ohmic contact was formed by Ni deposition on the backside and rapid thermal annealing at 1000 ◦ C was done prior to anodization. The schematic cross-section of the formed structure is shown in Figure 2.21. Note, nickel contacts were deposited on a porous substrate with the skin layer which is characterized by low porosity and pore diameters of <20 nm. Thus, the effect of contact Ni contact Deposited SiO2 Nanoporous skin layer (0.1 µm) Microporous SiC layer (15 µm) n-SiC substrate Ni ohmic contact

Figure 2.21

Schematic cross-section of the formed structure

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0.006 Nonporous Porous

Current (A)

0.004

0.002

0.000

−0.002 −1200

−800

−400

0

400

800

Voltage (V)

Figure 2.22

I–V characteristics of Ni/por-SiC/n-SiC structures at room temperature

area increase due to the metal penetration into pores is negligible. This is also confirmed by C–V measurements using a Hg probe when no mercury penetration into pores occurs. In the latter case, the carrier concentration profile is similar to the one obtained using Ni contacts. The I–V characteristics of the formed structures are shown in Figure 2.22. The I–V curve of a Schottky diode fabricated on the nonporous region of the same substrate is also shown in Figure 2.22 for reference. Due to the high leakage current of the Schottky diode formed in the nonporous region, its breakdown voltage is less than 50 V while a breakdown voltage of more than 1100 V has been observed for the Ni/por-SiC/ SiC structure. The leakage current of this structure, on porous SiC is very low (less than 10−9 A) and it remains relatively stable up to 200 V. An increase in the reverse bias results in the rise of the leakage current till it reaches its saturation value of about 10−6 A, which corresponds to a current density of ∼10−3 A cm−2 . At 1100 V, catastrophic breakdown occurs. Considering the thickness of the porous layer, which was measured on a cleaved sample, to be 15 μm, the electrical breakdown field was 7.3 × 105 V cm−1 . It is interesting to note that the forward bias I–V curve of the Ni/porSiC/SiC structure shows a negative resistance region starting from 60 V, where the I–V characteristic has a current peak of ∼17 mA. The current decays as the forward voltage increases to ∼250 V, after which, the current remains practically constant (∼8 mA) up to 500–550 V, where a forward breakdown takes place.

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−3

0.010

1x10−4 0.008

1x10−6

Current A

Current (A)

1x10−5

1x10−7 1x10

−8

1x10−9 1x10

200°C 150°C Room temperature

−10

−11

10

10−12 −1200

0.006 0.004 Room temperature 100°C 250°C

0.002 0.000

−1000 −800 −600 −400 −200

0

0

200

400

600

800

1000

1200

Voltage (V)

Voltage (V)

(b)

(a)

Figure 2.23 Reverse (a) and forward (b) I–V characteristics of Ni/por-SiC/n-SiC structures at different temperatures

The nature of this negative resistance is not clear but most probably this effect is associated with charge traps in the developed surface of the porous SiC substrate. The negative resistance region disappears when measurements are taken at elevated temperatures (more than 100 ◦ C as shown in Figure 2.23). In this case, forward current approaches its maximum of 5 mA and remains constant till the forward breakdown, which occurs at 375–400 V for 100 ◦ C. The typical C–V characteristic of the Ni/por-SiC/SiC structure and its carrier concentration profile obtained based on that measurement are shown in Figure 2.24(a) and (b), respectively. It can be seen that the carrier concentration gradually decreases from a value of ∼1017 cm−3 1x1017 Carrier density (cm−3)

Capacitance (pF)

50 40 30 20 10 0

1x1016

1x1015 0

2

4

6

8

10

0.2

Voltage (V)

(a)

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Depth (µm)

(b)

Figure 2.24 C–V characteristic (a) and effective carrier density profile (b) of Ni/porSiC/SiC structure. Reproduced from S. Soloviev et al., Materials Science Forum, 389– 393, 1113–1116. Copyright (2002), with permission from Trans Tech Publications

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at the surface to a value of less than 1015 cm−3 at 1.5 μm. The higher carrier density at the surface (skin layer still present) is explained by the lower pore density in the thin, near surface ‘skin layer’ which is commonly created during anodization. Going towards the bulk substrate, the porosity of the electrochemically etched layer increases. This results in the reduction of charge carriers per unit volume. This explains why a porous layer exhibits semi-insulating properties, which also explains the high breakdown voltage at the reverse bias.

ACKNOWLEDGEMENTS The authors are grateful to Dr D. Cherednichenko for fruitful discussions and suggestions. Also, the authors are grateful to Dr J. Baker for SIMS measurements, which were carried out in the Center for Microanalysis of Materials, University of Illinois, partly supported by the US Department of Energy under grant DEFG02-96-ER45439, and to Dr J. Bai and Dr P.I. Gouma for TEM analysis.

REFERENCES [1] J.S. Shor, Z.G. Zhang and R.M. Osgood, J. Electrochem. Soc., 139, 1213 (1992). [2] S.M. Sze, Physics of Semiconductor Devices (2nd Edn), Wiley-Interscience, New York (1981). [3] S. Zangooie and H. Arwin, J. Electrochem. Soc., 148, G297 (2001). [4] X.G. Zhang, J. Electrochem. Soc., 138, 3750 (1991). [5] V. Lehmann and U. Gruning, Thin Solid Films, 297, 13 (1997). [6] S. Soloviev, T. Das and T.S. Sudarshan, Mater. Sci. Forum, 389–393, 1113–1116 (2002). [7] Y. Gao, S. I. Soloviev and T. S. Sudarshan, J. Appl. Phys., 90, 5646 (2001). [8] J.N. Shenoy, M.K. Das, J.A. Cooper, M.R. Melloch and J.W. Palmour, J. Appl. Phys., 79, 3042 (1996).

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3 Growth of SiC on Porous SiC Buffer Layers S.E. Saddow, R.L. Myers-Ward1 and Y. Shishkin2 Electrical Engineering Department, University of South Florida, Tampa, FL 33620, USA 1 Current address: Naval Research Laboratory, Code 6882, 4555 Overlook Ave. SW, Washington, DC 20375, USA 2 Current address: Caracal., 611 Eljer Way, Ford City, PA 16226, USA

3.1

INTRODUCTION

Porous SiC technology relevant to this chapter dates to the early 1990s and has been discussed in a book chapter published on SiC materials, processing, and devices. A summary to the research outlined in this chapter is essentially an extension of the comprehensive work published in Saddow et al. [1]. Based on the pioneering work of M. Mynbaeva and S.E. Saddow in the late 1990s involving the epitaxial growth of SiC on porous SiC, the US Office of Naval Research (ONR) initiated a program called the Defense University Research Initiative on Nanotechnology (DURINT). At the time of the original work in Saddow et al., there were many unanswered questions such as what the optimum structure of the porous SiC network should be to achieve the desired improvement in SiC epitaxial film quality. Much was left to do to answer this question and the past 5 years have been spent to do just that. Along the way this work has been

Porous Silicon Carbide and Gallium Nitride: Epitaxy, Catalysis, and Biotechnology Applications Edited by Randall M. Feenstra and Colin E.C. Wood  C 2008 John Wiley & Sons, Ltd

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extended to many other areas of technology and hence, this book was born. In order to produce SiC material of the level of quality required for device applications, chemical vapor deposition (CVD) is currently used as the primary growth technique for SiC epitaxy [2]. Due to the continuous improvements in commercial substrate quality, the presence of micropipes in SiC epilayers is not the device yield limiting issue as it was a decade ago. However, the epitaxially grown SiC films still suffer from other extended defects such as basal plane and threading edge dislocations as well as point defects. The vision of growing SiC on porous SiC was to reduce the concentration of these defects and thus improve the epitaxial layer quality for device applications. The most important outcome of the work presented in Saddow et al. [1] was the demonstration that the number of defects can be reduced by epitaxy on porous substrates. It has been shown that CVD growth of SiC on porous SiC and Si substrates is feasible [3–5] and, in fact, may help in the reduction of the dislocation density in epitaxial layers [3,4]. The motivation for this work is clear, especially in the case of SiC on porous Si. Low-cost, high-quality Si substrates are highly attractive for the development of power electronics. If porous Si could be used to mitigate the effects of a large lattice mismatch between 3C-SiC and Si (20 %, see for example Madelung [6]), then a leap forward in SiC technology would result. While the outcome of this preliminary work did not produce any significant breakthroughs in this regard, significant progress was made and the results indicate possible research and development paths that others may take to move the technology forward. Indeed it is the sincere hope of the authors of this chapter that such a result comes about due to the disclosure of this work here. A significant amount of effort and expense was made and is documented in this chapter – let us hope that future progress can be accelerated by what follows and the ultimate promise of low-cost, high-quality 3C-SiC films on large-area Si substrates or hexagonal polytype SiC films on porous SiC substrates is finally achieved. Of particular interest from the early work reported in Saddow et al. [1] pertains to the intensity of the L1 defect line, which appears in the low temperature photoluminescence (LTPL) spectra of 4H-SiC CVD films at ∼2.901 eV and which is considered to be a measure of intrinsic defects [7]. In this early work it was noted that this defect was substantially reduced by using porous SiC substrates [8]. It is also worth mentioning that GaN layers have also been grown on both substrates of porous SiC [9] and GaN [9,10]. It was demonstrated that the dislocation density of

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plasma assisted molecular beam epitaxy (PAMBE) GaN grown on porous 6H-SiC could be reduced by an order of magnitude when compared with GaN grown on standard nonporous 6H-SiC substrates. Inoki et al. [11] have shown that five to ten times fewer dislocations can be obtained for GaN films overgrown by metal-organic chemical vapor deposition (MOCVD) on porous GaN seed layers. The films were also found to be more strain-relaxed than those grown on nonporous GaN. This information is provided as a means to round out the body of knowledge for the reader as we will focus exclusively in this chapter on the growth of SiC epitaxial layers on porous SiC and Si buffer layers.

3.2

SiC CVD GROWTH

The most common technique used to grow epitaxial SiC is CVD. The standard gas chemistry used is hydrogen–propane–silane, or H2 -C3 H8 -SiH4 , respectively. In this chemistry, C3 H8 is the carbon growth precursor while SiH4 is the silicon precursor. By the type of reactor heating configuration, the reactors are divided into cold-wall and hot-wall types. ‘Cold-wall’ refers to the fact that the boundary of the reaction vessel (a quartz tube in this case) is actively cooled (Figure 3.1), whereas there is no outer cooling jacket in a hot-wall reactor (Figure 3.2). In the hot-wall reactor, the walls of the growth zone are actively heated, resulting in a fairly uniform temperature profile. The typical growth rate of 10–30 μm h−1 is achieved in hot-wall reactors due to efficient cracking of the growth reactants (i.e. precursors for growth), and thus this technique is viewed to be more economical than the coldwall method, which only has a growth rate typically of ∼3–4 μm h−1 . RF coil

Cooling water jacket

Gas flow

Quartz boat SiC coated susceptor

Figure 3.1 Cross-section view of cold-wall reaction tube used in the initial experiments reported in this chapter [12]

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Susceptor

Inlet

Outlet

Foam

SiC substrate

SiC polyplate

Figure 3.2 Schematic drawing of the horizontal hot-wall reactor [13,14] hot zone used in the experiments. A SiC polycrystalline plate is used for loading samples. A growth rate of greater than 30 μm h−1 has been demonstrated with this system using standard process chemistry

3.3

GROWTH OF 3C-SiC ON POROUS SI VIA COLD-WALL EPITAXY

The cubic polytype of SiC, namely 3C-SiC, is the only form that can be grown hetero-epitaxially on Si substrates. However, there exists a 20 % lattice mismatch between these two crystal systems and the hope was that growth on a porous buffer layer might provide a means to reduce the defect density. This section presents preliminary research performed with this goal in mind. The first 3C-SiC deposition experiments were performed using the LPCVD cold-wall reaction system introduced in Section 3.2. The porous Si samples (10–15 % porosity) were processed at the University of Pittsburgh from n-type Si (100). The samples were then cleaned using the standard RCA cleaning method [15] before the epitaxial deposition took place. Two types of cold-wall experiments were performed: the first on asreceived porous Si and the second on oxidized porous Si in an attempt to limit the modification of the porous network during growth.

3.3.1

Growth on Porous Si Substrates

Initially, a carbonization step, carried out at atmospheric pressure, was used to convert Si into SiC by introducing the C3 H8 precursor (100 sccm, 3 % C3 H8 in H2 ) during the temperature ramp up to the growth temperature, during which the C atoms attach to the Si dangling bonds of

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the substrate to produce a thin layer of SiC. An attempt was made to use hydrogen etching to remove the Si native oxide prior to the Si conversion to SiC [16]. This was found to be deleterious in that the hydrogen etch step actually created preferentially etched pits on the substrate surface along the (111) crystal planes. Three-dimensional (3D) nucleation was then observed during the 3C-SiC growth over the etch pits. After the H2 etch step was removed from the growth process, the effect of 3D nucleation was virtually eliminated. One minute after the growth temperature had been reached, the pressure was reduced to 150 Torr and silane introduced into the gas stream. The propane flow was simultaneously reduced to achieve a Si/C ratio of 0.31. Growth took place from this point until the desired run time was reached. This process will be called the cold wall growth process schedule from this point on. Plan-view scanning electron microscopy (SEM) micrographs of a 3CSiC epitaxial film grown on bulk Si are shown in Figure 3.3 in order to provide a baseline for the hetero-epitaxial growth-on-porous process. The film morphology was smooth, with a minimal amount of particles observed on the surface as seen in the low magnification image (100×). At the higher magnification (5000×), minor anti-phase domain boundaries are observed. The hetero-epitaxial growth of 3C-SiC on porous Si substrates was investigated using the process flow for growing SiC on bulk (001) Si, as described above. Plan-view SEM micrographs of a porous Si substrate prior to growth are shown in Figure 3.4. The micrograph at the lower magnification [Figure 3.4(a)] shows a diagonal line across the substrate. The lower half of the line is the porous Si zone, while the top half is the non-porous ‘standard’ (001) Si zone. At the higher magnifications (a)

(b)

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Figure 3.3 Plan-view SEM micrographs of 2 μm thick 3C-SiC layer grown on bulk (001) Si: (a) 100× magnification; (b) 5000× magnification

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(b)

porous Si#13 20.0kV x2000 5μm

porous Si#13 20.0kV x12000 1μm

Figure 3.4 Plan-view SEM micrograph of porous Si (001) substrate at: (a) 2000× magnification; (b) 12 000× magnification. In (a), the porous structure is at the bottom of the diagonal line; top section is standard Si

[Figure 3.4(b)], it can be seen that the pores are square in nature. The pores are not evenly spaced across the surface and there seems to be no particular pattern of these pores. Note that the pores also vary in size. A hetero-epitaxial 3C-SiC film was grown on this porous surface with a few modifications to the growth schedule described above. The process included a hydrogen etch step prior to the carbonization and growth. The etch step was performed in order to evaluate whether pore enlargement was beneficial to growth on porous Si. The etching took place at 1000 ◦ C for 10 min at 150 Torr, with a hydrogen flow rate of 9 slm. The pressure was maintained at 150 Torr through the entire experiment. The temperature was reduced for 5 min between the hydrogen etch step and the carbonization step. The growth took place for 3 h at the Si/C ratio of 0.33, resulting in a film thickness of 10 μm. A cross-sectional view SEM micrograph of this 10 μm thick film is shown in Figure 3.5(a). Notice that the porous Si network is present in the top 10 μm of the Si substrate surface. The pores are not continuous at the surface and they vary in size. Figure 3.5(b) shows a plan-view SEM image at the porous/nonporous interface after the 3C-SiC epitaxial growth, whereby the porous surface is on the left and the standard region on the right. The surface morphology of the film on the standard Si surface is smooth and specular, while that on the porous surface is slightly textured. After growth, the film was studied using plan- and cross-section SEM and the sample quality evaluated using low-temperature photoluminescence (LTPL) at 2 K, performed by the group of W.J. Choyke at the University of Pittsburgh. For comparison, and to serve as a reference, ˚ shift in each experiment contained a standard Si substrate region. A 1 A wavelength towards the blue part of the spectrum was observed, likely indicating a slight stress relief in the 3C-SiC film grown on porous Si.

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(a)

(b)

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Figure 3.5 (a) Cross-section and (b) plan-view SEM micrographs 10 μm thick 3C-SiC on porous Si (001) [12]

However, no other dramatic improvement in film quality was observed indicating that these initial experiments require further refinement. In an effort to more directly assess the microstructure of the grown 3CSiC on Si and porous Si films, the samples were analyzed using transmission electron microscopy (TEM) by T. S. Kuan of the State University of New York (SUNY) at Albany. Figure 3.6 shows a cross-section TEM micrograph of the 3C-SiC on porous Si sample, whereby the porous Si layer is the white portion at the bottom of the image and the film surface is above this. Due to the 20 % lattice mismatch between 3C-SiC and Si, it is common to see the defect structure shown in this image, with a highly defective layer present at the Si/SiC interface and anti-phase boundary (APB) and twin boundary (TB) defects observed propagating along the (111) planes. Note that the film quality improves with thickness which is

Epitaxial 3C-SiC

Porous Si

2 μm

Figure 3.6 Cross-section TEM micrograph of a 10.9 μm thick 3C-SiC film on porous Si (001) substrate. Data used with permission from T. S. Kuan, SUNY at Albany.

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also as expected. Defects include APBs, partial dislocations of 1/6112 type, and stacking faults (SF). The defect density is ∼2 × 107 cm−2 in the top (epitaxial) layer. Selective area diffraction (SAD) pattern (not shown) indicated a SiC/Si lattice difference of 24.8 %. The high temperature required for the hetero-epitaxial growth of 3C-SiC, is close to the Si melting temperature of 1410 ◦ C, which most likely alters the porous Si substrate structure during growth. Therefore, further analysis of the porous substrates was performed to determine whether the pores could be stabilized before attempting hetero-epitaxial growth.

3.3.2

Growth on Stabilized Porous Si Substrates

It has been reported that during SiC growth on porous 6H- and 4H-SiC buffer layers, the porous structure is modified due to the high temperature processing in a hydrogen carrier gas [1]. This causes large voids to form in the porous layer that may add stress to the film grown on top. In Si technology, when the porous Si network was stabilized prior to epitaxial growth, the resulting Si films grown on porous Si were of high quality [17,18]. Borrowing from this idea, oxidation of porous Si samples was conducted and 3C-SiC growth performed in the cold-wall reactor to determine if this approach would reduce the level of pore modification. The experiments started out with cleaving the porous Si samples in two halves. The samples were then RCA cleaned and dry oxidation at 1000 ◦ C ˚ Following was performed, yielding a total oxide thickness of ∼500 A. ◦ oxidation, a thermal anneal at 950 C for 2 min was performed and a light etch of the oxide (to remove the surface oxide but leave oxide in the porous network) was conducted by immersing the samples in a 10:1 solution of buffered oxide etch. Following this procedure, which we called ‘stabilization of porous Si’, the hydrogen etching, carbonization, and the SiC growth took place in the cold-wall reactor at the same time as that for the non-stabilized porous sample shown in Figure 3.5. Figure 3.7(a) shows a cross-section SEM micrograph of a 10 μm thick 3C-SiC layer hetero-epitaxially grown on stabilized porous Si sample. The interface of the porous/standard film is shown, with the left side of the image being the porous structure, while the right is the standard Si reference substrate. The interface in the epitaxial layer can clearly be seen in the image. Note the original 10 μm thick porous structure was more than likely altered during the hydrogen etching step. Figure 3.7(b) shows the border between the epitaxial layer on the standard (left) and porous (right) Si substrate. The surface morphology on the

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(a)

(b)

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Figure 3.7 (a) Cross-section and (b) plan-view SEM micrographs of 3C-SiC on stabilized porous Si substrate

porous substrate is highly mosaic, while that on the standard portion of the susbstrate was smooth. ˚ shift in wavelength towards the The LTPL analysis revealed a 5 A blue part of the spectrum as compared with the one obtained for the ‘non-stabilized’ porous Si substrate (LTPL spectra not shown). This again indicates a slight stress relief of 3C-SiC on the stabilized porous Si but, unfortunately, the film morphology was poor. However, it must be noted that a high net carrier concentration in all of the films studied, approximately mid 1018 cm−3 , was estimated from the LTPL analysis. This inhibits the determination of the exact peak position due to the broadened peaks affected by the high doping level. In order to assess the microstructure of the grown 3C-SiC on stabilized porous Si films, the samples were again analyzed using TEM by T.S. Kuan of the SUNY at Albany. Figure 3.8 shows a cross-section TEM

Epitaxial 3C-SiC

Porous Si

2 μm

Figure 3.8 Cross-section TEM micrograph of 3C-SiC film grown on stabilized porous Si showing a film thickness of 10.6 μm. TEM data used with permission from T. S. Kuan, SUNY at Albany

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micrograph of the 3C-SiC layer grown on top of the stabilized porous Si surface. It is common to see the defect structure shown in this image, with a highly defective layer present at the SiC/Si interface and APB and TB defects observed propagating along the (111) planes. Note that the film quality improves with thickness which, again, is expected. Besides APBs and TBs, other defects such as partial dislocations of 1/6112 type and stacking faults are observed. The defect density is ∼2 × 107 cm−2 in the epitaxial (top) layer.

3.4

GROWTH OF 3C-SiC ON POROUS 3C-SiC

Free-standing 3C-SiC substrates [19] were provided by H. Nagasawa (Hoya Corporation) and converted to porous 3C-SiC by Y. Shishkin of the group of W.J. Choyke (University of Pittsburgh). 3C-SiC substrates were anodized in aqueous solution at current densities of 15, 30 and 60 mA cm−2 to yield 46, 52 and 72 μm thick porous 3C-SiC layers, respectively. A portion of each porous 3C-SiC substrate was then processed by reactive ion etching (RIE) prior to growth to enlarge the pores. The samples were then cleaned using the RCA method prior to deposition.

3.4.1

Growth in LPCVD Cold-wall Reactor

The growth of 3C-SiC on porous 3C-SiC took place in the cold-wall reactor. This was essentially a homo-epitaxial growth process. Therefore, the etching and carbonization steps were not needed. The samples were subjected to a temperature ramp under H2 and C3 H8 flow at a process pressure of 150 Torr. The SiH4 precursor was introduced 20 ◦ C before the growth temperature was reached. Note that the growth temperature for the homo-epitaxial growth was 1550 ◦ C, which is significantly higher compared with that of the hetero-epitaxial growth since no silicon substrate was involved. Six 3C-SiC substrates with porous thickness ranging from 46 to 72 μm were loaded in one growth run. Three of them were processed by RIE prior to growth. Hence, a total of seven samples were grown on simultaneously so that differences in epitaxial film quality vs porous structure could be inferred (a standard 4H-SiC flag sample was included in the growth to serve as a reference sample). The growth proceeded for 4 h, resulting in a film thickness of 5.5 μm, determined by cross-section SEM analysis on a 4H-SiC control

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(b)

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Figure 3.9 Plan-view SEM micrographs of 3C-SiC grown on (a) standard 3C-SiC, (b) 46 μm thick porous 3C-SiC, (c) 52 μm thick porous 3C-SiC and (d) 72 μm thick porous 3C-SiC

sample. Note the 3C-SiC samples were not cleaved to determine their film thicknesses. Since this was a homo-epitaxial growth, the 4H-SiC control sample was used to give an estimation of the 3C-SiC film thickness. After the epitaxial deposition, the morphology of each sample was evaluated using SEM analysis. Figure 3.9(a) shows the surface morphology of the 3C-SiC epilayers grown on the standard 3C-SiC surface. Figure 3.9(b), (c) and (d) show the surface morphologies of the 3C-SiC films grown on 46, 52 and 72 μm thick porous 3C-SiC surfaces, respectively. Growth on the porous substrates resulted in a slightly more mosaic structure than for the growth on nonporous surface. Comparatively speaking, the epitaxial surface for growth conducted on the thickest porous substrate, 72 μm, resulted in the best film morphology than the two thinner substrates, 46 and 52 μm in thickness. The epitaxial film has relatively the same structure for either growth on the porous portion or growth on the nonporous section of the 72 μm thick porous substrate. Strictly speaking, the epitaxial growth morphology on the 72 μm thick porous substrate should be as good, if not better, than the

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quality on standard Si. No further assessment was made in determining the film quality of these samples due to a lack of resources. The surface morphology of the epilayers grown on porous 3C-SiC subjected to RIE processing was also investigated and the plan-view images are shown in Figure 3.10. The surface morphology of the 3C-SiC epilayer grown on standard RIE-processed 3C-SiC is slightly mosaic [Figure 3.10(a)]. The growth on RIE processed 3C-SiC porous substrates resulted in highly mosaic structure of the epilayer with the quality improving with the increasing thickness of the porous film [see Figure 3.10(b), (c) and (d)]. Further investigations were conducted to determine the quality of the standard and RIE etched porous SiC samples using LTPL analysis, again performed by the group of W.J. Choyke at the University of Pittsburgh. The photoluminescence intensity of the 3C-SiC epilayers increased approximately ten and five times that of the standard 3C-SiC for the 52 and 72 μm thick RIE etched porous 3C-SiC substrates, respectively. In addition, the no-phonon nitrogen bound exciton No line (a)

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(b)

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(d)

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Figure 3.10 Plan-view SEM micrographs of 3C-SiC grown on RIE processed surfaces of (a) standard 3C-SiC, (b) 46 μm thick porous 3C-SiC, (c) 52 μm thick porous 3C-SiC and (d) 72 μm thick porous 3C-SiC

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in the epilayer-on-porous layer shifted approximately 1 meV with respect to the same line for standard epitaxial growth. Although we do not know at the moment the reasons for both these effects, we believe they are in indication that the quality of the epitaxial layer grown on RIE etched porous is improved over that of the standard epitaxial growth. However, as was the case for the growth on stabilized Si porous layers, the morphology is of a lower quality in comparison with non-etched porous 3C-SiC which will require further study to understand.

3.5

GROWTH OF 4H-SiC ON POROUS 4H-SiC

For these experiments, basal plane Si-face 4H-SiC with an n-type doping concentration of about ∼7 × 1018 cm−3 was used as the substrate material. The wafers were oriented 8◦ off from the basal plane toward the 1120 direction. Prior to epitaxial deposition, the substrates were photoelectrochemically etched in an aqueous 5 % HF solution to produce 5 μm and 10 μm thick porous SiC films of triangular morphology [20,21]. Figure 3.11 shows an SEM image of a 4H-SiC sample of such morphology. The image was taken in cross-section, for which the sample was first cleaved, to reveal the porous structure. A more detailed description of the triangular porous morphology is provided in Shishkin et al. [20]. A part of each substrate was left unetched to be used for the quality control purposes. This way, one would be able to study and compare results of the epitaxial films grown on porous and standard substrate at the same time. The horizontal hot-wall CVD reactor used in our experiments has been described in detail by Myers et al. [14]. A schematic drawing of the reactor cross-section is shown in Figure 3.2. The growth was conducted

100 nm

Figure 3.11 Cross-section image of the porous 4H-SiC sample used for the epitaxial deposition experiments. The reader is referred to Chapter 1 for details [21]

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at about 1600 ◦ C with the process pressure set to 150 Torr. Hydrogen purified in a palladium cell was used as the carrier gas. The precursors were 100 % silane (SiH4 ) and 100 % propane (C3 H8 ). The precursor flow rate was varied (the Si/C ratio was held constant at 1.0 for all the experiments) to obtain growth rates from 12 to 30 μm h−1 . Epitaxial film growth on porous SiC substrates is very similar to the epitaxial growth on standard SiC substrates. The difference comes from the fact that the temperature ramp, which is executed in the presence of hydrogen – and hydrogen etches SiC, introduces a problem of etching the front surface of the crystal prior to the actual deposition. The etch rate of SiC by hydrogen is somewhat higher for a porous versus a nonsporous surface. In Sagar et al. [22], 8◦ -offcut 4H-SiC porous layers exhibited an etch rate of 1.6 nm s−1 in hydrogen at atmospheric pressure and a temperature of 1600 ◦ C. During 5 min of H2 etching, the pores opened up and the porosity increased from 15–20 % to approximately 30 % [22]. The average porosity of the porous SiC substrates used in the investigations described here is about 12 %. A porosity gradient is seen in the triangular porous morphology obtained in heavily doped n-type SiC [20]. It is then expected that the top porous layer has a slightly higher porosity of 15–20 %. Consequently, by the time silane, which initiates growth of SiC, was introduced into the growth zone, the surface of the SiC substrate could be 30 % porous due to hydrogen etching. The roughness of the surface due to the presence of surface pores may then limit the mobility of adatoms on the surface. Thus, in order to minimize the etching effect and to ensure a smooth SiC deposition and specular film morphology, additional process steps were implemented. The temperature ramp for these investigations was executed at a reduced hydrogen flow (decrease a factor of three compared with the flow during the deposition run) to minimize etching of the porous layer. At about 20 ◦ C below the temperature set-point, which is 1600 ◦ C in our experiments, the hydrogen flow was increased to the normal flow (30 slm in our case) and the carbon precursor propane introduced into the growth zone. At 1600 ◦ C, a small amount of silane was added to the gas mixture to initiate the growth process at a slow speed of ∼10 μm h−1 . After growth of the thin buffer layer (∼200 nm), the growth rate was increased up to the desired value in increments of 1 μm h−1 per 5 s time intervals by slowly increasing the precursor flow. The reduced hydrogen flow during the temperature ramp was observed to reduce hydrogen etching of the porous substrate, and the initial growth at a reduced speed helped suppress the formation of 3C-SiC nucleation. The LTPL confirmation of this effect has been made but is not shown here.

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(a) epilayer

defect

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Figure 3.12 Cross-section SEM image of a 4H-SiC epitaxial film: (a) not grown under optimal conditions; (b) grown under optimal conditions

Figure 3.12 illustrates differences in the epitaxial films grown on porous SiC layers using a conventional 4H-SiC CVD epitaxial growth process and the method optimized for growth on porous films and described below in the text. The original porous 4H-SiC structure used in these experiments had a triangular morphology, in which interconnecting porous channels propagate parallel to the basal plane and have a triangular shape (sizing about 30 nm) in cross-section. The transformation of the structure of the porous layer during the growth process is clearly evident. Under non-optimal growth conditions [see Figure 3.12(a)], there is an approximately 2 μm thick highly porous transition layer, separating the substrate and the epilayer, whose existence is likely due to the effect of hydrogen etching of the original porous structure. As a result of the rough porous/epilayer interface there are occasional defects in the form of open core channels propagating through the epitaxial film. The thickness of the transition layer separating the porous layer and the epitaxial

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Figure 3.13 XRD rocking curves of the (0004) plane of a 12 μm thick epitaxial film grown on 4H-SiC under optimal conditions [similar to the film shown in Figure 3.12(b)]. Part of the substrate was: (a) 5 μm thick porous (triangular morphology); (b) conventional surface for control purposes

film is thin, and the porous/epilayer interface is substantially improved with optimum growth conditions [Figure 3.12(b)]. Although the triangular pore channels also transform (as seen in cross-section SEM), the newly formed spongy type of porous structure, in which the pores are of spherical shape, does not cause the formation of these open core defects. At this point we would like to note that quality of the epitaxial deposition degraded even using optimum growth conditions when porous substrates used were more than 10 μm thick with porosities more than 15 %. Figure 3.13 shows X-ray diffraction (XRD) rocking curves of the (0004) reflection peak taken on a 12 μm thick 4H-SiC film grown by the optimized technique described above at a growth speed of 24 μm h−1 . The measurement shown in Figure 3.13(a) was done on the part of the epitaxial layer grown on a 5 μm thick porous 4H-SiC layer of triangular morphology. The curve shown in Figure 3.13(b) was taken on the part of the film grown on the control (non-sporous) portion of the SiC surface. Comparing the two peaks, one can see that the full-width at half maximum (FWHM) values are nearly identical. For the other epilayer-onporous films, we observe similar results for the FWHM values. However, the epilayers grown on standard SiC surfaces generally exhibit broader shoulders on the (0004) diffraction peak. This confirms that the structural quality of the epilayer-on-porous SiC layers are of quality which is comparable with, if not better than, the epilayers grown on non-sporous conventional surfaces. LTPL was collected on the samples using a frequency-doubled (FreD) argon-ion laser (244 nm wavelength) with a power of 55 mW as the excitation source. The LTPL measurements and the analysis were

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performed by F. Yan and W.J. Choyke (University of Pittsburgh). Analysis of the LTPL spectra reveals that the doping concentration in the films grown on porous substrates is similar to the doping concentration of the films grown on the original surface of the 4H-SiC wafer. Figure 3.14 shows LTPL spectra for the film whose XRD data are shown in Figure 3.13. The intensity ratio of Q0 to I76 is about the same for the films grown on porous and nonporous parts of the substrate. Here Q0 is the no-phonon line due to neutral nitrogen bound exciton and I76 is the Energy (eV) PL relative intensity (kilocounts)

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Figure 3.14 LTPL spectra of a 12 μm thick epitaxial film grown under optimal conditions on: (a) a 5 μm thick porous 4H-SiC layer (triangular morphology); (b) the original surface of the 4H-SiC wafer. Note the different scales. Data used with permission from W. J. Choyke, Univ. of Pittsburgh

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intrinsic phonon replica line with a momentum conserving phonon energy of 76 meV. The effect of aluminum compensation is negligible since the spectrum of the no-phonon lines due to neutral aluminum acceptor four-particle complex (4Al0 ) is barely visible. Therefore, the measured value of the Q0 /I76 intensity ratio implies that the n-type doping of the epitaxial film is about 1.5 × 1015 cm−3 [23]. Throughout our studies, we found that the intensity of the near bandedge emission is usually a factor of two larger in epitaxial films grown on porous 4H-SiC regardless of its thickness (two different thicknesses, 5 μm and 10 μm, of triangular porous morphology have been explored) and the growth rate (growth rates 12, 24 and 30 μm h−1 were explored). Even with the FreD laser, for which the radiation has a smaller penetration depth than that of a 325 nm wavelength He-Cd laser [24], we are still able to see the broad nitrogen impurity related peak from the substrate on the spectrum of the epitaxial layer grown on the nonporous section. The broad peak is not observed in the spectrum of the epitaxial layer grown on the porous substrate. Optical minority carrier lifetime was also measured in the samples grown at 30 μm h−1 . The measurements were performed by F. Yan and W.J. Choyke (University of Pittsburgh). For this, a pulsed NdYAG laser was employed as the excitation source. The values around 1 μs were obtained for both the epilayers on porous and the epilayers on standard surfaces indicating that growing on porous did not change the concentration of nonradiative recombination centers, and the intensity enhancement observed in photoluminescence is due to other reasons. The samples were analyzed by T.S. Kuan (SUNY at Albany) using high resolution transmission electron microscopy (TEM). Dislocation density was found too low (lower than 104 cm−2 , which is the detection limit of the instrument) to have any detected by cross-sectional TEM in both epilayers on porous and on standard substrates. A final characterization effort was an experiment in which synchrotron white beam X-ray topography (SWBXT) was employed. The SWBXT experiment was conducted by M. Dudley and Yi Chen (SUNY at Stony Brook). The purpose of the experiment was to study the effect of a porous layer on extended defect propagation from the substrate into the epitaxial film. Samples similar to the one shown in Figure 3.12(b) were analyzed with the intent of detecting, identifying and counting defects in epitaxial films. Two regimes were used: the transmission mode which is used for imaging bulk crystal defects; and the grazing incidence mode which predominantly provides information on epilayer defects only (small penetration depth).

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Figure 3.15 SWBXT images obtained in: (a) transmission mode; (b) grazing incidence mode. Data used with permission from M. Dudley, SUNY at Stony Brook

Transmission topographic images show similar basal plane dislocation (BPD) density in both standard and porous substrate region [Figure 3.15(a)], an expected result since the transmission mode is used for imaging bulk crystal defects. However, when the grazing incidence mode is used, the topographs show epilayer-on-porous region has lower BPD density compared with epilayer-on-standard region [Figure 3.15(b)]. The question then is posed whether we have conversion of BPDs into threading edge dislocations (TEDs).

3.6

CONCLUSION

The growth of 3C-SiC on porous Si using the cold-wall LPCVD method resulted in a slightly better film quality compared with that on standard Si, as determined by LTPL. Further improvement in film quality was obtained by growing on a stabilized porous Si substrate. The epitaxial films did contain TBs and APBs at the interface, which is common due to the ∼20 % lattice mismatch between Si and SiC. Epitaxial growth on porous 3C-SiC substrates of different thickness were performed to determine which porous network thickness would result in the best film quality. Although the thickest porous substrate available (72 μm) seemed to have the best surface morphology, LPTL results concluded that the 52 μm thick porous structure actually had the highest film quality. The epitaxial layer grown on the RIE etched porous 3C-SiC of 52 μm thickness, produced a photoluminescence intensity 10 times that compared with the growth on standard 3C-SiC porous. This

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indicates that growth on the 52 μm porous structure results in the highest epitaxial film quality, based on LTPL analysis. In regard to the epitaxial deposition of 4H-SiC by an optimized hotwall CVD process on porous 4H-SiC layers, it was found that the optimum porous layer thickness for subsequent growth was ∼4–10 μm. Optimal porosities less than 15 % should be used for epilayer growth. Moreover, the growth speed as well as the thickness of the porous layer had little effect on the structural quality and the doping of the grown films. Despite this, the intensity of the near bandedge LTPL emission was increased by roughly a factor of two for the films grown on porous vs standard 4H-SiC surfaces. Moreover, SWBXT experiments show conversion of BPDs into TEDs in epilayer grown on porous. More experiments are needed to clarify the results of LTPL and SWBXT.

ACKNOWLEDGEMENTS This work was supported by the DURINT program administered by the Office of Naval Research (Dr C. Wood) under Grant N00014-0110715.

REFERENCES [1] S.E. Saddow, M. Mynbaeva, and M. MacMillan, Chapter 8 ‘Porous SiC technology’, in Silicon Carbide: Materials, Devices and Applications, Zhe Chuan Feng and Jian H. Zhao (Eds), Optoelectronic Properties of Semiconductors and Superlattices, Taylor and Francis Engineering, New York, 2003. [2] S.E. Saddow and A. Agarwal, Advances in Silicon Carbide Processing and Applications, Artech House, Inc., Norwood, 2004. [3] M. Mynbaeva, et al., Growth of SiC and GaN on porous buffer layers, Mater. Sci. Forum, 338–342, 225–228 (2000). [4] M. Mynbaeva, S.E. Saddow, G. Melnychuk, I. Nikitina, M. Scheglov, A. Sitnikova, N. Kuznetsov, K. Mynbaev, and V. Dmitriev, Chemical vapor deposition of 4H-SiC epitaxial layers on porous SiC substrates, Appl. Phys. Lett., 78, 117–119 (2001). [5] J.E. Spanier, G.T. Dunne, L.B. Rowland, and I.P. Herman, Vapor-phase epitaxial growth on porous 6H-SiC analyzed by Raman scattering, Appl. Phys. Lett., 76, 3879–3881 (2000). [6] O. Madelung, Semiconductors: Data Handbook, 3rd Edn, Springer-Verlag, Berlin, 2004. [7] T. Frank, G. Pensl, S. Bai, R.P. Devaty, and W.J. Choyke, Correlation between DLTS and photoluminescence in He-implanted 6H-SiC, Mater. Sci. Forum, 338–342, 753–756 (2000). [8] S.E. Saddow, M. Mynbaeva, W.J. Choyke, R.P. Devaty, S. Bai, G. Melnichuk, Y. Koshka, V. Dmitriev, and C.E.C. Wood, SiC defect density reduction by epitaxy on porous surfaces, Mater. Sci. Forum, 353–356, 115–118 (2001).

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[9] F. Yun, M.A. Reshchikov, L. He, H. Morkoc, C.K. Inoki, and T.S. Kuan, Growth of GaN films on porous SiC substrate by molecular-beam epitaxy, Appl. Phys. Lett., 81, 4142–4144 (2002). [10] C.K. Inoki, T.S. Kuan, C.D. Lee, A. Sagar, and R.M. Feenstra, Growth of GaN on porous SiC substrates by plasma-assisted molecular beam epitaxy, Mater. Res. Soc. Symp. Proc. 722, K1.3.1–K1.3.6 (2002). [11] C.K. Inoki, T.S. Kuan, A. Sagar, C.D. Lee, R.M. Feenstra, D.D. Koleske, D.J. Diaz, P.W. Bohn, and L. Adesida, Growth of GaN on porous SiC and GaN substrates, Phys. Status Solide A, 200, 44–47 (2003). [12] R. Myers, CVD Growth of SiC on Novel Si Substrates, MS Thesis, University of South Florida, Tampa, FL, 2003. [13] R.L. Myers-Ward, High Growth Rate SiC CVD via Hot-Wall Epitaxy, PhD Dissertation, University of South Florida, Tampa, FL, 2006. [14] R.L. Myers, Y. Shishkin, O. Kordina, I. Haselbarth, and S.E. Saddow, High epitaxial growth rate of 4H–SiC using horizontal Hot-wall CVD, Mater. Sci. Forum, 527–529, 187–190 (2006). [15] ‘RCA Clean’, http://www.mines.edu/fs home/cwolden/chen435/clean.htm. [16] A. Powell, L.G. Matus, and M.A. Kuczmarski, Growth and characterization of cubic SiC single-crystal films on Si, J. Electrochem. Soc., 134, 1558–1565 (1987). [17] R. Brendel, Crystalline thin-film silicon solar cells from layer-transfer processes: a review, Proc. 10th Workshop on Crystalline Silicon Solar Cell Materials and Processes, 117–125 (2000). [18] P. Maccagnani, et al., Thick porous silicon thermo-insulating membranes, Sens. Mater., 11, 131–147 (1999). [19] H. Nagasawa, et al., Properties of free-standing 3C-SiC monocrystals grown on undulant-Si(001) substrate, Mater. Sci. Forum, 433–436, 3–8 (2003). [20] Y. Shishkin, W.J. Choyke, and R.P. Devaty, Photoelectrochemical etching of n-type 4H silicon carbide, J. Appl. Phys., 96, 2311–2322 (2004). [21] Yue Ke, Y. Shishkin, R.P. Devaty, and W.J. Choyke, ‘Chapter 1 Porous SiC preparation, characterization and morphology’, in Porous Silicon Carbide and Gallium Nitride, R.M. Feenstra and C.E.C Wood (Eds), John Wiley & Sons, Ltd, Chichester, 2008. [22] A. Sagar, C.D. Lee, R.M. Feenstra, C.K. Inoki, and T.S. Kuan, Morphology and effects of hydrogen etching of porous SiC, J. Appl. Phys., 92, 4070–4074 (2002). [23] L.L. Clemen, M. Yoganathan, W.J. Choyke, R.P. Devaty, H.S. Kong, J.A. Edmond, D.J. Larkin, J.A. Powell, and A.A. Burk, Jr, Calibration procedure to determine the nitrogen impurity concentration in 6H SiC at low concentration levels, Inst. Phys. Conf. Ser., 137, 251–254 (1994). [24] S.G. Sridhara, T.J. Eperjesi, R.P. Devaty, and W.J. Choyke, Penetration depths in the ultraviolet for 4H, 6H and 3C silicon carbide at seven common laser pumping wavelengths, Mater. Sci. Eng. B, 61–62, 229–233 (1999).

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4 Preparation and Properties of Porous GaN Fabricated by Metal-Assisted Electroless Etching T.L. Williamson1 , D.J. D´ıaz2 and P. W. Bohn3 1

Chemistry Division, C-ADI, MS J565, Los Alamos National Laboratory, Los Alamos, NM 87545, USA 2 Department of Chemistry, University of Central Florida, 4000 Central Florida Blvd, Orlando, FL 32816, USA 3 Department of Chemical and Biomolecular Engineering and Department of Chemistry, University of Notre Dame, Notre Dame, IN 46556, USA

4.1

INTRODUCTION

GaN is a wide band gap semiconductor (Eg = 3.4 eV) of considerable technological interest. Light-emitting diodes (LEDs) and laser diodes based on GaN and its alloys of either In or Al have been successfully commercialized for some time. GaN remains a topic of intense interest, and current research primarily focuses on creating more efficient green and red LEDs and laser diodes for solid state lighting and other applications. Porous Silicon Carbide and Gallium Nitride: Epitaxy, Catalysis, and Biotechnology Applications Edited by Randall M. Feenstra and Colin E.C. Wood  C 2008 John Wiley & Sons, Ltd

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This chapter documents efforts to create and characterize porous GaN (PGaN) by an electroless etching technique pioneered in this laboratory. By rendering crystalline GaN porous, the hypothesis was that new or improved material properties might be discovered and utilized. By analogy, porous Si shows increased luminescence efficiency and wavelength tunability after being made porous [1,2]. Initial efforts to make PGaN were motivated by the desire to realize similar effects with an ultraviolet (UV) bandgap material. PGaN necessarily has a higher surface area than crystalline GaN, and since GaN has shown some capacity to act as a chemical sensor [3–11], high surface area porous GaN may allow an increase in sensitivity or dynamic range of sensors. Current device research is focused on creating solar-blind UV chemical sensors from GaN. We and others [12,13] have also shown an increase in the photoconductivity of PGaN relative to bulk. Thus, it is possible that PGaN could replace crystalline GaN in solar-blind UV detectors, enhancing their sensitivity. GaN is plagued by high dislocation densities. While this does not pose a problem in fabricating LEDs based on GaN, it has negative consequences for other device applications [14–19]. Porous GaN is a possible substrate for epitaxial growth, the motivation being that the pores would act as sinks for dislocations and strain within the PGaN layer, lattice mismatch would be eliminated, and higher quality (lower dislocation density) epitaxial material would be obtained.

4.2

CREATION OF POROUS GaN BY ELECTROLESS ETCHING

Compared with other compound semiconductors, the creation of PGaN is relatively unexplored. The first report of PGaN was from Mynbaeva and Tsvetkov in 1997 [20]. In this work the porous film was produced by electrochemical etching. Aside from publications from this group [12,20–24], there are remarkably few [25–33] reports on the fabrication of PGaN, apart from our work [34–37]. Other groups have discussed creating PGaN by other means, including ion implantation [38], conversion of porous GaAs [39] and by dry etching through a physical mask [40,41]. Among these approaches the reports describing the creation of PGaN by physically masking a pattern on the surface show successful creation of bulk porosity, albeit by an approach that is much more complicated than wet etching. Based on a reading of the current literature, creating PGaN via an etching process, either electrochemical or electroless, is the most reliable and convenient method available.

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The metal-assisted electroless etching technique developed by our group is motivated by protocols for rapid stain etching of Si in HF/HNO3 solutions in the presence of a thin Al film [34,42]. Simple, all-chemical etching techniques, such as electroless etching, are very attractive, because they allow the large-scale production of etched GaN, or PGaN. Moreover, the ability to generate PGaN simply and effectively opens the door to studying the properties and applications of porous wide band gap optoelectronic materials. However, a great limitation in producing and studying PGaN is the lack of reliable methods for generation of specific porous morphologies. As noted above, few groups have been able to produce PGaN, and the only demonstration of ordered porous arrays in GaN has been generated by dry etching through a porous alumina mask [41]. The etching mechanisms, structural properties, and reactivity of PGaN are still largely unexplored in comparison with other III–V materials. Another constraint on the production of PGaN and the large-scale utilization of GaN in general is the lack of high quality substrates with low dislocation density and homogeneous properties and morphology. We have developed an electroless etching scheme involving deposition of ultrathin (∼10 nm) Pt island films on the surface to be etched, followed by etching in a CH3 OH:HF:H2 O2 solution under UV illumination. Metals other than Pt have also been used effectively, however Pt yields the fastest, most efficient etching [42–44]. The etch strategy is based on the notion that catalytic reduction of H2 O2 at the Pt islands can combine with UV illumination, hν > 3.41 eV, to inject holes into the valence band, a necessary step in both electrochemical and electroless etching of semiconductors. This method has been effective for generation of porous Si [2,42,45], PGaN [34–37] and porous SiC [46]. Preparation of PGaN by electroless etching proceeds as follows: The GaN substrates are cut into the desired size. The samples are pre-cleaned by sonication in acetone for 3 min, followed by sonication in isopropanol for 3 min. After rinsing in deionized water, the samples are immersed in concentrated HNO3 at 65 ◦ C for 15 min, followed by rinsing once in distilled H2 O and three times in CH3 OH, then drying with N2 . The motivation for cleaning in HNO3 is based on reports in the literature that describe improvements in metal contact performance after chemical ˚ thick are sputter coated treatment [47–49]. Platinum island films 100 A on the pre-treated GaN substrates through a steel mask. Typical patterns exhibit 0.5 mm diameter holes, separated by 1 mm. The thickness of the deposited Pt is monitored by quartz crystal microbalance. It is important to note that these Pt films are sufficiently thin that they are not continuous and, thus, should be considered island films.

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PGaN is created via electroless etching by placing the substrate in a solution of CH3 OH, HF (49 %) and H2 O2 (30 %) in a 1:2:2 CH3 OH:HF:H2 O2 volume ratio (3:6:2 mol ratio). The Pt-coated GaN surface is immersed in the etchant as quickly as possible after sputtering. During etching the substrate is illuminated with a Hg arc-lamp. The Hg lamp illumination, when filtered through a short-pass cutoff filter, placed 10 cm from the sample, results in an irradiance of 0.32 W cm−2 , for λ ≤ 360 nm, i.e. photon energies above the band gap. During normal etching the filter is not used, and all of the wavelengths from the Hg lamp impinge on the substrate. However, the addition of the below band gap illumination has a negligible effect on etching. The time of etching varies from 5 min to 2 h depending on the desired porosity. After etching, the samples are rinsed with distilled H2 O three times, then rinsed with CH3 OH three times to remove any leftover etchant solution and dried with N2 .

4.3 4.3.1

MORPHOLOGY CHARACTERIZATION Porous GaN Derived from Unintentionally Doped Films

Figure 4.1 shows plan view images of sample V830 [unintentionally doped (UID), n ∼ 3 × 1016 cm−3 , d = 8.1 μm, grown by hydride vapor phase epitaxy (HVPE) on sapphire] following the electroless etching protocol described above. The evolution of the etched morphology as the etching time is increased is apparent in Figure 4.1. At short etch times (t < 15 min) a rich network of small pores forms [Figure 4.1(a) and (b)]. These pores have dimensions on the order of 10–20 nm. At longer etch times a three-dimensional ridge structure appears with the formation of porous material between the ridges [Figure 4.1(e) and (f)]. The formation of this trench/ridge morphology evolves with etch time; first growing in size and depth and then disappearing at very long etch times. The pores present between the ridge structures have larger dimensions (80–100 nm) than the pores observed at earlier etch times. Although the ridges obscure the porous material directly beneath them, pores are present over the entire GaN surface, including below the ridges. The pores under the ridges are observable by cross-sectional scanning electron microscopy (SEM). SEM images of sample V1473 (UID, n ∼ 5 × 1016 cm−3 , d = 13.3 μm, HVPE on sapphire) which has only a slightly higher carrier density than V830 (5 × 1016 cm−3 vs 3 × 1016 cm−3 ) proceeds in a qualitatively

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Figure 4.1 Plan-view SEM images of unintentionally doped HVPE GaN (V830), n = 3 × 1016 cm−3 , on sapphire etched in 1:2:1 CH3 OH:HF:H2 O2 solution under UV illumination for (a) 5 min, (b) 15 min, (c) 25 min, (d) 30 min, (e) 35 min and (f) 60 min. Reproduced from Diego J. D´ıaz, Todd L. Williamson, Ilesanmi Adesida, Paul W. Bohn, and Richard J. Molnar, Journal of Applied Physics, 94, 7526 (2003). Copyright 2003, with permission from The American Institute of Physics

similar fashion although at a somewhat higher rate. However, no other differences in the morphology are observed. The rate at which the etched morphology evolves depends on the doping/carrier concentration, indicating the important role that carrier drift and diffusion play in electroless etching. Materials with higher carrier densities may also have a higher number of defects, which could function as nucleation sites for pore etching.

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One interesting and potentially useful feature is that this electroless etching occurs across the whole wafer and is not limited to the areas near the Pt film. As a demonstration of this fact, using a sample in which Pt is present only at the corners of the wafer, it is possible to create a porous layer across an entire 50 mm diameter wafer to produce a substrate for growth of GaN on PGaN [50]. The qualitative etching behavior shows only a weak dependence on distance from the Pt, with pronounced differences only observed within a few micrometers of the island or at very low Pt mass loadings. However, a metal is absolutely required; etching does not occur in the absence of Pt films. Figure 4.2(a) and (c) shows cross sectional images of samples V1473 and V1231, respectively, at 15 min etching. At this short etch time very shallow pores form. Figure 4.2(b) and (d) shows the same materials, respectively, but at 45 min etch time. Figure 4.2(e) and (f), obtained from V1231 etched for 60 min, is presented to explain and clarify the porous structure further. Figure 4.2(e) shows the propagation of the pores through the porous layer, extending quite deep. At this longer etch time many of the pores extend all the way to the GaN–sapphire interface. Figure 4.2(e) shows that three layers are present in PGaN; these include the ridges on the top, followed by a highly branched near surface layer (discussed in more detail below), and pores propagating deep into the GaN layer parallel to the c-axis of the crystal. Figure 4.2(f) shows an example of a ridge structure immediately on top of the porous region. This image shows that the regions beneath the ridges are indistinguishable from those that are not. Measuring the thickness of the GaN layer prior to and after etching shows that the GaN layer thins during etching, consistent with the observed evolution of the ridge structures, and suggesting that simultaneous with GaN being etched into a porous layer, bulk dissolution of GaN is occurring as well, although at a slower rate. The ridges consist of material that is etched at a considerably slower rate than the material that produces the pores. It is the dissolution of the ridge material that ultimately leads to bulk GaN dissolution. In addition to the two etch rates noted, one producing the pores and one characterizing the dissolution of the leftover material/ridges, there also appears to be a third etch rate present. Careful inspection of Figure 4.2(d), (e), and (f) reveals what may be described as anisotropic crystallographic etching with the pores oriented approximately along the 1101 axis, as revealed by the highly branched layer near the surface. This crystallographic etching is consistent across a given sample, as well as between samples, making its assignment as crystallographic etching

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(f)

Figure 4.2 SEM cross-sectional analysis of electrolessly etched unintentionally doped GaN samples. (a) V1473 etched 15 min, (b) V1473 etched 45 min, (c) V1231 etched 15 min, (d) V1231 etched 45 min, (e) V1231 etched 60 min, and (f) V1231 etched 60 min at higher magnification

reasonable. The anisotropic crystallographic etching also appears to be more developed at the near surface region of the porous layer, consistent with the notion that it is slower, taking longer to develop, because it does not propagate independent of pores. Also, the crystallographic region tends to be of similar depth, about 0.5 μm, from sample to sample, and tends not to be much larger than that regardless of etch time. This suggests that the ridges and the anisotropic crystallographic etched region are correlated and may be associated with a common underlying mechanism.

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Transmission Electron Microscopy (TEM) Characterization

While SEM characterization provides an excellent picture of the morphology of PGaN, there is still some information to be gained from TEM. Most notably, since the contrast/imaging effect in TEM derives from local differences in electron density, it is possible to gain information about dislocations in GaN from a cross-sectional TEM image. A cross-sectional TEM image of PGaN created from sample V1473 etched for 45 min is shown in Figure 4.3. These images were acquired by our

(a)

(b)

Pore Dislocation

Figure 4.3 TEM cross-sections of V1473 etched for 45 min. (b) is the same area as (a) and is shown at a different contrast to highlight the pores. Dislocations appear dark (regions of high e− density) and the pores appear light in these images

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collaborators Inoki and Kuan from a PGaN film fabricated using the Pt-assisted electroless etching technique. The key findings of this study are that the dislocations do not terminate at the tips/ends of the pores and that the pores and the dislocations are found separated from each other. The TEM data also suggest that the pore walls are negatively terminated. What these results indicate is that, rather than etching away the dislocations when creating PGaN as some researchers have suggested [22], etching occurs between the dislocations. This result is consistent with the observations of Youtsey and co-workers [51], who saw GaN whiskers composed of dislocations after photoelectrochemical etching (PECE). Thus, the PGaN material that has been created by Pt-assisted electroless etching has a high dislocation density relative to bulk GaN, and ‘good’ crystalline material is removed during etching. This may have interesting consequences for devices derived from PGaN created in this way.

4.4

LUMINESCENCE OF POROUS GaN

Apart from our work [30,31,52], there are only limited published reports regarding the luminescence properties of PGaN. In one of the earliest reports describing the luminescence of PGaN, Mynbaeva and co-workers showed a factor of 2 decrease in PL intensity, both at room temperature and 77 K, of a PGaN film prepared by PECE. The film in this study was a UID film (n ∼5 × 1017 cm−3 , d ∼0.6 μm, grown by HVPE on SiC [12]). The authors of this study also noted a blue-shift of ∼11 meV in the band-edge emission and attributed this shift to an increase in strain due to defects and dislocations in the PGaN film. The yellow-band luminescence (YL) peak remained unchanged. In two recent reports, Vajpeyi and co-workers studied the luminescence response of PGaN films prepared by both PECE and Pt-assisted electroless etching [29,52]. The films used in these studies were metalorganic chemical vapor deposition (MOCVD) grown GaN (n ∼ 1 × 1018 cm−3 ) on sapphire with a thickness of 2.5 μm. For the PECE prepared PGaN, the authors noted a PL intensity increase of a factor of 2, both at room temperature and at 77 K. The authors also noted a small red-shift of 4.5 meV in the band-edge emission, and attributed this shift to a decrease in strain in the porous film relative to bulk. The decrease in strain was confirmed by X-ray diffraction (XRD) and Raman measurements. The XRD measurements also revealed a reduction in the dislocation density in the porous film. The authors concluded that the etching proceeds by dissolving defects, and the increase in PL and

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reduction in strain is a result of this mechanism. For the electrolessly prepared GaN, the authors also noted a PL intensity increase of a factor of 2, both at room temperature and 77 K. For PGaN etched for 1 h, the band-edge emission was red-shifted by 6 meV. The authors attributed these effects to a reduction in strain, which was confirmed by Raman spectroscopy.

4.4.1

Cathodoluminescence (CL) of Porous GaN

Figure 4.4 shows normalized CL spectra obtained from bulk and PGaN films created from UID GaN grown by HVPE. Two different films are shown in the figure, V830 (n ∼ 3 × 1016 ) and V1473 (n ∼ 5 × 1016 ). The band gap peak is red-shifted by a small amount (1–2 nm) in the porous films, which may imply a decrease in strain. The inset in Figure 4.4 shows that both the blue luminescence (BL) and YL peaks increase slightly in the UID PGaN films relative to the bulk films.

Figure 4.4 CL spectra of bulk GaN and PGaN films generated from V830 and V1473. The porous films were both etched for 45 min. The inset shows an expanded view of the BL/YL region of the spectrum for these samples. The spectra were obtained at 10 keV excitation voltage

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(a)

(b)

(c)

(d)

Figure 4.5 (a) CL image taken at 365 nm of a PGaN film created from V830 etched for 45 min and (b) a SEM image of the same area used to obtain the CL image in (a). (c) CL image taken at 365 nm of a PGaN film created from V1473 etched for 45 min and (d) a SEM image of the same area used to obtain the CL image in (c). In both sets of images the ridges appear dark and the porous areas luminesce

Figure 4.5(a) and (b) shows a CL image taken at 365 nm and a SEM image of the same area for V830 PGaN. Figure 4.5(c) and (d) shows a CL image taken at 365 nm and a SEM image of the same area for V1473 PGaN. In these two examples, the contrast between the luminescent, porous areas of the PGaN film and the nonluminescent ridges is quite clear, showing that the luminescence originates from the porous areas of the sample, and not the ridge structures. Dislocations are known to be dark in CL images, because they function as nonradiative recombination centers [53,54]. Since the ridge structures do not luminesce, they are assumed to result from dislocations that have not etched, and remain

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behind on the surface as residual structures. Since it is possible to remove the ridge structures by sonication in methanol, CL images were acquired and show a spatially uniform luminescence.

4.4.2

Photoluminescence (PL) of Porous GaN

Unlike CL, quantitative comparisons may be made between different PL spectra. Sample V1231 (UID, n ∼ 1 × 1017 cm−3 , HVPE) PGaN etched for 60 min shows a fivefold decrease in the luminescence efficiency relative to bulk GaN. This sample exhibited the highest luminescence for any of the V1231 PGaN films. There is no appreciable shift in the band gap peak position in the porous V1231 films. Contrary to the effect observed in the CL spectra of HVPE PGaN, there is no increase in the BL band intensity in V1231 PGaN, or for other HVPE PGaN films studied by PL. A series of PL spectra for HVPE samples V830, V1473, and V1231with n ∼ 3 × 1016 , 5 × 1016 , and 1 × 1017 cm−3 , and 8.1 μm, 13.3 μm, and 19.2 μm thicknesses, respectively, were sonicated in methanol for 15 min to remove the ridge structures. Removing the ridges allows the luminescence intensity to recover to the bulk value for V1231 PGaN. For V1473, the luminescence intensity not only recovers, but shows a twofold increase over the bulk luminescence intensity. For the V830 PGaN film, the intensity is three times as intense as the bulk value. There is also a small red-shift for each of the three films of ∼1 nm, which could be interpreted as a decrease in strain [55,56]. The shift noted here is substantially less than that observed by Chen and co-workers [55], who attributed a large PL red-shift to sample heating due to laser radiation, but this may be the source of the (smaller) shift observed here as well. The recovery of the PL intensity is likely related to changing the area of the PGaN film being probed. Both the ridges and a significant portion of the uppermost, highly branched, porous layer are removed during sonication. The ridges are believed to be primarily dislocations, and, as shown in Figure 4.5, are dark. The uppermost porous layer is composed of small GaN features that are likely highly enriched with dislocations, and therefore do not luminesce as efficiently as the rest of the GaN material. By removing these structures, the PL experiment primarily probes the lower porous layer of the material that, while porous, still contains a significant amount of crystalline GaN. The reason that the luminescence intensity is larger for some of the films is likely due to roughening of the surface and the high surface area.

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There is an apparent trend of increased PGaN luminescence proceeding from V1231 to V1473 to V830. The observed trend follows an obvious carrier concentration dependence, with the lower carrier concentration films having higher luminescence intensities. A plausible explanation is that more highly doped films are likely to have a larger concentration of point-defects and dislocations, which may serve as nonradiative recombination centers. As the film is made porous and the crystalline material is reduced in the PGaN film, a larger proportion of photogenerated holes are created in close proximity to nonradiative recombination centers.

4.5

RAMAN SPECTROSCOPY OF POROUS GaN

The literature relating to Raman studies of bulk and epitaxially grown GaN is extensive, but that pertinent to Raman studies of porous GaN is less developed. In one report by Wang and co-workers [41], PGaN was created by plasma etching through a porous alumina mask created by anodic etching. When these PGaN films were studied by Raman spectroscopy, the researchers found a number of spectral effects in the porous film. The intensity of the scattered light was found to be considerably higher in the porous films. Also, the E2 peak at 568 cm−1 was found to red-shift in the porous samples relative to bulk, an effect that was attributed to a relaxation in strain [57]. The researchers also observed geometry-forbidden transverse (TO) scattering and quasi-phonon modes, indicating off-axis phonon propagation. In a separate study from the same group, Vajpeyi and co-workers prepared a PGaN film by photoassisted electroless etching (PECE) [29]. In this study, the PGaN film more closely resembled the morphology of the PGaN that is created in our work by Pt-assisted electroless etching. This study noted nearly all of the effects seen in the material produced from masked etching [41] with a larger relaxation in strain, as calculated by the red-shift in the E2 mode. In this study [29], the researchers did not observe the presence of quasi-phonon modes. Mynbaeva and co-workers have also noted a relaxation in strain in PGaN films created by anodic etching as determined by a red-shift in the E2 mode [24].

4.5.1

Characteristics of Raman scattering in GaN

Most epitaxially grown GaN, and the films considered here, exist in the wurtzite (hexagonal) crystal structure. Group theory predicts four

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Raman active modes for GaN, an A1 , an E1 and two E2 modes. The E2 modes are designated E2 H (568 cm−1 ) and E2 L (144 cm−1 ). Because the A1 and E1 are also infrared active, they are split into a TO and a longitudinal (LO) component by the long-range electrostatic forces parallel to the longitudinal propagation direction [58]. The LO phonon is shifted to higher frequency due to the effect of the electric field on the force constant of the vibration. In the case of GaN, as with most wurtzite crystals, the long-range electrostatic forces are larger than short-range interatomic forces due to crystalline anisotropy [58,59]. Because of this, the LO-TO splitting (∼200 cm−1 ) is larger than the E1 -A1 splitting (8– 30 cm−1 ). This results in the A1 (TO) and E1 (TO) modes being at 532 cm−1 and 559 cm−1 and the A1 (LO) and E1 (LO) modes at 735 cm−1 and 742 cm−1 [59–61]. In uniaxial crystals, like GaN there are short-range interatomic forces, which, although they are not as large as the electrostatic forces, cause the polarization (symmetry) of the phonons propagating within the crystal to follow symmetry-based selection rules. For A1 phonons, they must be polarized parallel to the optical axis, which is the c-axis of the crystal, or the [0001] direction [62]. The E1 phonons must be polarized perpendicular to the c-axis [62]. The propagation directions of the A1 and E1 phonons are strictly defined. Should the propagation direction be neither parallel nor perpendicular to the c-axis, then a mixing of the A1 and E1 modes must occur [58,59]. For the LO phonon, this involves the mixing of an A1 character phonon propagating along the c-axis and an E1 phonon propagating perpendicular to the c-axis [58]. For the TO phonon, this involves the mixing of an A1 character phonon propagating perpendicular to the c-axis and an E1 phonon propagating along the c-axis [58]. Propagation along an intermediate direction is a result caused by off-axis excitation, due to the requirement that momentum be conserved, i.e. the sum of the vectors involved must be zero. These mixed modes are referred to as quasi-modes and have values that are intermediate to the A1 and E1 values. The frequencies of the quasi-modes are: 2 = ω2A1(LO) cos2 θ + ω2E1(LO) sin2 θ ωquasi−LO

(4.1)

for the quasi-LO phonon [58,59], and: 2 2 2 2 2 ωquasi−T O = ω E1(T O) cos θ + ω A1(T O) sin θ

(4.2)

for the quasi-TO phonon [58,59], where θ is the angle between the c-axis and the propagation direction.

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Raman Spectra of Porous GaN Excited Below Band Gap

Figure 4.6 shows Raman spectra for both unetched GaN and porous GaN created from a UID film (n ∼ 1 × 1017 cm−3 ) excited below the 300 K band gap with visible excitation (441.6 nm). A large increase in the scattering efficiency can be seen in the PGaN relative to unetched GaN. Additionally, two TO modes, A1 (TO) at ∼535 cm−1 and E1 (TO) at ∼560 cm−1 , which are symmetry-forbidden in a backscattering configuration [60], can be seen in the PGaN spectrum. The increased scattering intensity is, at least partially, due to physical surface roughening which means that scattered radiation is out-coupled from the crystal more efficiently, while the presence of the geometry forbidden TO modes can be attributed to the increased importance of scattering off of the sidewalls of the porous structure. Since the dimensions of the pores (∼80 nm) are

Raman intensity (a.u)

E2

E1(TO) A1(TO)

‘LO’ (b)

A1(LO)

Eg (sapph.) (a)

X5 500

550

600

650

Raman shift

700

750

800

(cm−1)

Figure 4.6 Raman spectra of (a) unetched (5×) and (b) PGaN excited at 441.6 nm. The PGaN sample generated from n ∼ 1 × 1017 cm−3 was etched for 45 min. Note the PGaN spectrum is ca. five times more intense than the unetched GaN. Reproduced from Todd L. Williamson et al., Journal of Vacuum Science & Technology B, 22, 925. Copyright (2004), with permission from AVS The Science & Technology Society

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smaller than the wavelength of the excitation radiation, both incident and scattered radiation should interact strongly with the pores. The absence of strong scattering from the sapphire substrate (which would be seen at 418 cm−1 and 750 cm−1 ), even though it is easily observed in the unetched sample, indicates that the observed scattering originates entirely from phonons confined to the porous layer. Furthermore, the scattered radiation also interacts with the porous morphology, thereby frustrating the total internal reflection which occurs for smooth planar surfaces, thereby increasing the outcoupled fraction. The presence of symmetry forbidden TO modes in PGaN is interesting, because it is frequently taken as evidence for disruption of the translational symmetry of the lattice on the scale of the phonon wavelength [63,64]. However, the electroless etching process is comparatively gentle compared with dry etching techniques and is not expected to cause disruption of translational symmetry, beyond removing atoms from the lattice. In addition, there is no other evidence to suggest lattice damage occurs upon etching. Scattering from the sidewalls of the pores, which has been observed in strongly scattering porous GaP of similar morphology [65–68], could give rise to the observed TO scattering. Sidewall scattering is significant, because radiation impinging on the pores at the surface is diffracted according to the well understood theory of light passing through a sub-wavelength aperture [69,70]. In this situation the original purely transverse electric field (Ex,y ) develops longitudinal components (Ez ) upon entering the pore. Thus, there is significant amplitude in the incident radiation in which the Poynting vector is no longer strictly parallel to the crystalline c-axis. These off-axis vectors can induce TO-scattering, which explains the presence of the geometry forbidden TO modes in PGaN, but not in unetched crystalline GaN. The E1 (TO), A1 (TO) and E2 modes in the PGaN spectra are fit to Lorentzian functions in Figure 4.7, to determine the peak positions of the Raman modes. It is not possible to reproduce the convoluted experimental lineshape completely without the addition of a new, broad peak at ca. 550 cm−1 , in addition to the three peaks expected in this region of the spectra. This broad peak could be assigned to a quasi-TO mode resulting from off-axis excitation and mixing of the A1 and E1 TO modes. Other researchers studying porous GaN, who have seen geometry forbidden TO scattering, also note that it is necessary to add an intermediate peak between the A1 and E1 TO modes in order to reproduce the observed spectra adequately [29,41]. The angle of phonon propagation of a quasiTO phonon mode may be calculated from Equation (4.2), and is found to be 39.0◦ . It should be noted that this peak is quite broad, at least two

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Raman intensity (a.u)

POROUS GaN

(a)

E1(TO) A1(TO)

E2

Quasi-TO

(b) 480

500

520

540

560

580

600

620

Raman shift (cm−1)

Figure 4.7 (a) Raman spectrum of PGaN generated from V1231 (n ∼ 1 × 1017 cm−3 ) etched for 60 min excited at 441.6 nm (points) in the region of the E2 mode and curve fit (lines) obtained by combining the A1 (TO), E1 (TO), E2 , and quasi-TO modes. (b) Individual component spectra. Reproduced with permission from Todd L. Williamson, Diego J. D´ıaz, Paul W. Bohn, and Richard J. Molnar, Journal of Vacuum Science and Technology B, 22, 925 (2004). Copyright 2004, AVS The Science & Technology Society

to three times broader than the TO modes, meaning that, in this interpretation, it is likely that the broad peak observed is a convolution of a range of propagation angles. The Raman peak close to the original location of the A1 (LO) mode is broadened and shifted to higher energy relative to the A1 (LO) mode of unetched GaN (Figure 4.8). Furthermore, in highly porous (long etch time) samples a shoulder develops on the low energy side of the peak. These two effects have been seen previously in nanostructured columnar ¨ GaN and attributed to plasmon coupling and Frohlich modes, respectively [71]. The spectrum cannot be adequately fit using Lorentzian functions for the A1 (LO) and E1 (LO) modes at literature values, 735 cm−1 and 742 cm−1 [59,60]. The presence of the E1 (LO) peak, although not symmetry allowed under backscattering conditions [59,60], is plausible, because the A1 and E1 TO modes, which have the same selection rules,

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700

720

740

760

780

800

Raman shift (cm−1)

Figure 4.8 (a) Raman spectrum of PGaN generated from V1231 (n ∼ 1 × 1017 cm−3 ) etched for 60 min excited at 441.6 nm (points) in the region of the A1 (LO) phonon and curve fit (lines) obtained by combining the extraordinary LO (EX-LO), A1 (LO), E1 (LO) and quasi-LO phonons. (b) Individual component spectra. The high-energy tail in the spectrum is due to the Eg mode of the sapphire substrate at 750 cm−1 . Reproduced from Todd L. Williamson et al., Journal of Vacuum Science & Technology B, 22, 925. Copyright (2004), with permission from AVS The Science & Technology Society

i.e. forbidden in the backscattering geometry, were observed in the E2 region of the PGaN spectra. Acceptable spectral fits cannot be obtained without inserting a peak between the A1 (LO) (736 cm−1 ) and the E1(LO) (742 cm−1 ) modes. This peak is assigned to a quasi-LO mode, which arises specifically because the etched material is porous. The appearance of a quasi-TO mode, which was noted in the TO region of the spectra of PGaN is often accompanied by the appearance of a quasi-LO mode. It is unlikely that the PGaN spectra would contain one quasi-mode independent of the other. The observance of both quasi-modes supports this interpretation of the spectra of PGaN. The frequency of the quasi-LO mode is found by Equation (4.1) and is 48.8◦ . The apparent disparity between angles for the quasiTO and quasi-LO mode may be a result of phonon–plasmon coupling,

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which shifts the LO modes to slightly higher values for a given carrier concentration (even the low values representative of this UID film). In addition to the A1 (LO), E1 (LO), and quasi-LO modes, an extraordinary LO mode, i.e. parallel to the c-axis but excited by off-axis electric field components coupling to the imaginary part of the dielectric function, is used to account for the low-energy shoulder of the LO peak. The overall result of the peak fitting analysis can be seen in Figure 4.8.

4.6

SUMMARY AND CONCLUSIONS

The preparation of porous GaN by the metal-assisted electroless etching protocol developed in this laboratory offers a useful alternative to the more standard electrochemical oxidation route in that it is a contact-free means of etching. The porous material generated displays substantially different generic behavior than the porous variants of Si. In particular, the optical properties of the material remain largely unchanged. Thus, the two principal applications – use of PGaN as a substrate to grow lowstrain epitaxial layers and the use of PGaN for chemical and biochemical sensing – both exploit the geometric/physical properties. In particular the use of PGaN in chemical sensing applications is likely to exploit the robust nature of the crystal and the ultrahigh surface-to-volume ratios characteristic of the porous material. The robustness makes PGaN a natural for application in chemically or physically hostile environments, while the surface-to-volume ratio means that sensing modalities which depend on surface interactions can be maximally sensitive.

ACKNOWLEDGEMENTS Work described here from the authors’ laboratories was supported by the Air Force Office of Scientific Research under grant F49620-02-1-0381.

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[22]

[23]

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[25]

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[30] [31]

[32]

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[34]

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[37] T. L. Williamson, D. J. Diaz, P. W. Bohn, and R. J. Molnar, Structure–property relationships in porous GaN generated by Pt-assisted electroless etching studied by Raman spectroscopy, J. Vac. Sci. Technol. B 22, 925–931 (2004). [38] S. O. Kucheyev, J. S. Williams, C. Jagadish, J. Zou, V. S. J. Craig, and G. Li, Ionbeam-induced porosity of GaN, Appl. Phys. Lett. 77, 1455–1457 (2000). [39] B. K. Ghosh, T. Tanikawa, A. Hashimoto, A. Yamamoto, and Y. Ito, Reduced-stress GaN epitaxial layers grown on Si(111) by using a porous GaN interlayer converted from GaAs, J. Cryst. Growth 249, 422–428 (2003). [40] Y. D. Wang, S. J. Chua, M. S. Sander, P. Chen, S. Tripathy, and C. G. Fonstad, Fabrication and properties of nanoporous GaN films, Appl. Phys. Lett. 85, 816–818 (2004). [41] Y. D. Wang, S. J. Chua, S. Tripathy, M. S. Sander, P. Chen, and C. G. Fonstad, High optical quality GaN nanopillar arrays, Appl. Phys. Lett. 86, 1917 (2005). [42] X. Li and P. W. Bohn, Metal-assisted chemical etching in HF/H2 O2 produces porous silicon, Appl. Phys. Lett. 77, 2572–2574 (2000). [43] B. S. Shelton, T. G. Zhu, M. M. Wong, H. K. Kwon, C. J. Eiting, D. J. H. Lambert, S. P. Turini, and R. D. Dupuis, Ultrasmooth GaN etched surfaces using photoelectrochemical wet etching and uitrasonic treatment, Electrochem. Solid State Lett. 3, 87–89 (2000). [44] C. Youtsey, I. Adesida, L. T. Romano, and G. Bulman, Smooth n-type GaN surfaces by photoenhanced wet etching, Appl. Phys. Lett. 72, 560–562 (1998). [45] S. Chattopadhyay and P. W. Bohn, Direct-write patterning of microstructured porous silicon arrays by focused-ion-beam Pt deposition and metal-assisted electroless etching, J. Appl. Phys. 96, 6888–6894 (2004). [46] T. L. Rittenhouse, P. W. Bohn, and I. Adesida, Structural and spectroscopic characterization of porous silicon carbide formed by Pt-assisted electroless chemical etching, Solid State Commun. 126, 245–250 (2003). [47] B. J. Kim, J. W. Lee, H. S. Park, Y. Park, and T. I. Kim, J. Electron. Mater. 27, L32 (1998). [48] S. Tripathy, S. J. Chua, and A. Ramam, Electronic and vibronic properties of n-type GaN: the influence of etching and annealing, J. Phys. Cond. Matter 14, 4461–4476 (2002). [49] K. N. Lee, S. M. Donovan, B. Gila, M. Overberg, J. D. MacKenzie, C. R. Abernathy, and R. G. Wilson, Surface chemical treatment for the clearing of ALN and GaN Surfaces, J. Electrochem. Soc. 147, 3087 (2000). [50] C. K. Inoki, T. S. Kuan, A. Sagar, C. D. Lee, R. M. Feenstra, D. D. Koleske, D. J. Diaz, P. W. Bohn, and I. Adesida, Growth of GaN on porous SiC and GaN substrates, Phys. Status Solidi A 200, 44–47 (2003). [51] C. Youtsey, L. T. Romano, and I. Adesida, Gallium nitride whiskers formed by selective photoenhanced wet etching of dislocations, Appl. Phys. Lett. 73, 797–799 (1998). [52] A. P. Vajpeyi, S. Tripathy, S. J. Chua, and E. A. Fitzgerald, Investigation of optical properties of nanoporous GaN films, Phys. E 28, 141–149 (2005). [53] T. Sugahara, H. Sato, M. S. Hao, Y. Naoi, S. Kurai, S. Tottori, K. Yamashita, K. Nishino, L. T. Romano, and S. Sakai, Direct evidence that dislocations are nonradiative recombination centers in GaN, Jpn J. Appl. Phys. 37, L398–L400 (1998). [54] S. J. Rosner, E. C. Carr, M. J. Ludowise, G. Girolami, and H. I. Erikson, Correlation of cathodoluminescence inhomogeneity with microstructural defects in epitaxial GaN

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5 Growth of GaN on Porous SiC by Molecular Beam Epitaxy Ashutosh Sagar1,3 , R.M. Feenstra1 and J.A. Freitas, Jr2 1

Department of Physics, Carnegie Mellon University, Pittsburgh, PA, USA Naval Research Laboratory, Electronics Materials Branch, Washington, DC, USA 3 Current address: Intel Corp., Hillsboro, OR, USA 2

5.1

INTRODUCTION

One of the major hurdles in the epitaxial growth of high quality GaN thin films is the unavailability of suitable substrates. The lack of suitable substrates leads to poor quality epitaxial films with dislocation densities in the range of 1010 –1012 cm−2 for GaN grown on sapphire [1,2] and SiC [3]. Such high defect densities are detrimental to the device performance; conventional III–V (like GaAs) devices have defect densities about four orders of magnitude lower than presently achievable in GaN. Two important crystal properties that should ideally be closely matched between the GaN and the substrate are the lattice parameter and the coefficient of thermal expansion. Any mismatch between these properties can result in defects in the film (misfit and threading dislocations due to lattice mismatch and cracking or bowing due to the thermal Porous Silicon Carbide and Gallium Nitride: Epitaxy, Catalysis, and Biotechnology Applications Edited by Randall M. Feenstra and Colin E.C. Wood  C 2008 John Wiley & Sons, Ltd

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mismatch). An ideal substrate for GaN epitaxy will be a high quality GaN wafer itself, however, this approach is severely limited due to the absence of high quality, large area GaN substrates. Therefore one has to resort to the heteroepitaxial growth of GaN. Heteroepitaxial growth of GaN is usually performed on sapphire or SiC (13 % and 3.4 % lattice mismatch, respectively, with GaN). Such a lattice mismatch between GaN and these substrates results in a high dislocation density in the epitaxial films. A variety of techniques have been employed in the past to reduce this high dislocation density and one of the common methods has been to engineer the substrate surface to control, and thus inhibit, the formation of threading dislocations. An early paper on substrate engineering to control the dislocations in a strained film was published by Luryi and Suhir [4]. Using Six Ge1−x film growth on Si substrates as a model, they showed that the critical height of the epitaxial film (maximum thickness of the GaN film before dislocations form to relieve strain) can effectively be infinite by using patterned substrates in which epitaxial growth starts only on ‘seed pads’ smaller than a given size. They demonstrated that in this case, the strain energy per unit area of the film will never exceed the threshold energy needed for creating dislocations, and they showed that such a substrate can be prepared by patterning it prior to the growth so that the epitaxial growth starts on the ‘seed pads’ only. In addition, they suggested that porous Si is a good candidate for this substrate. These ideas on using patterned substrates led to several subsequent works exploring the use of nano-sized islands as growth nucleation sites. Such patterned substrates were also shown to be compliant under stress due to lattice mismatch [5]. In this approach, the substrate was patterned (by photolithography for example) into tiny pillars. Another promising technique recently developed for reducing dislocation density in GaN epitaxial films is lateral epitaxial overgrowth (LEO) [6]. In brief, the LEO technique relies on two specific growth properties: selective area epitaxy and growth anisotropy. Selective area epitaxy corresponds to spatially controlled growth of an epitaxial layer through openings in a masking material which is typically a dielectric film like silicon dioxide or silicon nitride. Growth anisotropy occurs because the diffusing molecular species on the surface are preferentially incorporated at different crystallographic sites so that growth proceeds faster along some crystal directions than others. In the LEO technique, a few micrometers of GaN is grown on either sapphire or 6H-SiC, followed by deposition of a masking layer, typically SiO2 or Si3 N4 deposited using chemical vapor deposition (CVD). Then a set of parallel stripes separated

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GaN film mask GaN template substrate

Figure 5.1 Schematic of the LEO technique for growing defect-free GaN. The black lines extending from the substrate to the top of the film represent dislocations

by window areas is opened in the mask by using standard photolithography techniques. Subsequent deposition, under appropriate conditions [7–10], leads to selective area epitaxy in which the growth is initiated on the GaN layer exposed by the window without any nucleation on the mask layer. Under proper conditions, once the GaN growing film reaches the top of the mask, epitaxial lateral growth over the masks starts and finally leads to full coalescence of the film. This technique leads to the filtering of the dislocations by the masks and the lateral overgrown GaN film will be relatively defect free. A schematic of this technique is shown in Figure 5.1. Despite the success of the LEO technique in reducing dislocation density [6], the use of photolithography steps involved in the standard LEO technique makes it a complicated process. A process which can simplify the steps used for preparing a patterned substrate will be of great value and the use of porous SiC substrates offers such a possibility. By using porous SiC substrates for GaN epitaxy, selective area epitaxy and lateral overgrowth can potentially be realized on these substrates without the need for any photolithography steps. Figure 5.2 shows a

(a)

(b)

Figure 5.2 Schematic illustration of two defect reduction mechanisms for a strained film (dark gray) grown on a porous substrate (light gray). (a) Dislocations bending toward the open surface at the tube walls. (b) Formation of relatively dislocation-free regions in the GaN film where the film has laterally grown over the pores. Reproduced from C. K. Inoki et al., Phys. Stat. Soli. (a) 200, 44. Copyright (2003), with permission from John Wiley & Sons, Ltd

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schematic view of two possible mechanisms by which growth on a porous substrate can lead to defect reduction. For growth by molecular beam epitaxy (MBE), as discussed in this chapter, pores in the substrate often tend to propagate straight up into the film as open tubes, as shown in Figure 5.2(a). These open tubes in the GaN film provide additional free surface where the dislocations can terminate. In addition, if epitaxial growth begins at the areas between the pores, then lateral growth over the pores can result in areas which are dislocation free, as shown in Figure 5.2(b). This chapter is devoted to the discussion of MBE growth of GaN on porous SiC substrates. MBE, compared with CVD, has the advantage of straightforward and well understood nucleation of the GaN on the SiC substrates [3,11,12]. However, the growth temperatures for GaN in MBE (≈750 ◦ C), are significantly less than those in CVD (≈1020–1050 ◦ C), and the resulting lateral growth rates turn out to be much less for MBE (probably because this lateral growth involves significant lateral mass transport over the surface). For this reason, dislocation reduction mechanisms involving lateral overgrowth are expected to be less effective using MBE than CVD. In the present work we do indeed find limited lateral overgrowth in our MBE films; although we observe instances of lateral growth over the pores and concomitant reduced dislocation density in those regions, we do not find any overall dislocation reduction when averaging over the entire area of the films. In this chapter we first briefly discuss the techniques of porous SiC substrate preparation and some of the relevant properties of the substrates. Following that, we describe the results from our GaN films on the porous SiC substrates, including details of both dislocation mechanisms and strain evolution in the films.

5.2 5.2.1

MORPHOLOGY AND PREPARATION OF POROUS SiC SUBSTRATES Porous Substrates

Porous SiC samples used in this study were purchased from TDI, Inc. They were anodized at a current density of 7 mA cm−2 for 3 min, with a 250 W Hg lamp illuminating 2 in. diameter wafers. We used three different types of Si-face (0001) oriented SiC wafers: 6H with no intentional miscut (i.e. on axis), 6H with 3.5◦ miscut and 4H with 8◦ miscut. In the ¯ direction. latter two cases the miscut was in the [1120]

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Figure 5.3 Cross-sectional SEM image of the porous 6H-SiC. The sample was tilted to allow simultaneous viewing of the porous network in cross-section along with the pores on the top surface. Pore formation starts at the surface and then it develops into an inverted V-shaped branched structure in the bulk. Reproduced from A. Sagar et al., J. Appl. Phys. 92, 4070. Copyright (2002), with permission from the American Institute of Physics

Figure 5.3 shows a scanning electron microscopy (SEM) image of a fractured porous 6H-SiC layer, revealing surface pores and the underlying porous network. It is seen in this image that the porosity of the bulk porous network is much less than that of the surface. Transmission electron microscopy (TEM) bright field images of a similar porous layer are shown in the Figure 5.4. From these images, we find the pore size (i.e. minimum distance across a pore) of about 20 nm and a bulk porosity of typically 20–30 % for the layers studied here. From Figure 5.4(a) and (b), it is also seen that the pores extend downwards in a highly branched structure. In the cross-sectional images, the pores appear like partially open cones. The angle between the upper cone sidewall and a line normal to the (0001) surface is about 75◦ near the surface, decreasing to 55◦ at a depth of about 1.5 μm. Close to the surface the porous layer is not very dense, leading to the existence of a nonporous skin layer. The general morphology of the porous network is quite similar to that described by Zangooie et al. [13].

5.2.2

Hydrogen Etching

As-received porous SiC samples are not ideal as substrates for MBE growth because of polishing damage on the surface. Hydrogen etching is often used to remove such polishing damage [14–18]. This method

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Figure 5.4 Cross-sectional TEM images of two porous layers. There are relatively few pores on the surface compared with the bulk, with the top skin layer being most clearly visible in (a). The V-shaped branched structure of the porous network is clearly seen in (b). Reproduced from A. Sagar et al., J. Appl. Phys. 92, 4070. Copyright (2002), with permission from American Institute of Physics

involves heating the SiC surface to 1600–1700 ◦ C in hydrogen. In addition, hydrogen etching removes the nonporous skin layer from the top of the porous samples and enlarges the pore sizes. This effect provides us with an effective means of preparing atomically flat samples with controlled surface porosity. Figure 5.5 shows a plan-view SEM image of 4H-SiC sample after hydrogen etching for 60 s at 1680 ◦ C. The pores have clearly opened up after the hydrogen etching process; identical results were obtained on 6H-SiC samples. The average size of the pores in Figure 5.5 is about 100 nm, corresponding to a surface porosity of about 3.5 %. Additional hydrogen etching causes the surface porosity to increase further and it also modifies the bulk porous structure. Figure 5.6(a) is a cross-sectional image of the same sample hydrogen etched for 60 s. It is clear that the bulk pores have opened up after the hydrogen etching process and the network morphology is changed from an unetched sample. The bulk porosity after 60 s of hydrogen etching was about 18 % and the average pore size was about 100 nm. The bulk porosity increased to about 24 % after 120 s of hydrogen etching and after 300 s of etching the bulk porosity was 31 %. The latter case is shown in Figure 5.6(b). These observations indicate that the

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Figure 5.5 Plan-view SEM image of the hydrogen etched surface of porous 4H-SiC. Pores have opened up after 60 s of hydrogen etching at 1680 ◦ C. The average pore size is about 100 nm and the surface porosity is about 3.5 %. Reproduced from A. Sagar et al., J. Appl. Phys. 92, 4070. Copyright (2002), with permission from the American Institute of Physics

Figure 5.6 Cross-sectional SEM images of porous 4H-SiC, hydrogen etched at 1680 ◦ C for (a) 60 s and (b) 300 s. The bulk porosity is about (a) 18 % and (b) 31 %. The pores have enlarged due to the hydrogen etching. Reproduced from A. Sagar et al., J. Appl. Phys. 92, 4070. Copyright (2002), with permission from American Institute of Physics

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hydrogen etching increasingly opens up the pores with longer etch time. The resulting increase in porosity also has an effect on the hydrogen etch rate; greater porosity providing less surface area for etching in a given horizontal plane and thereby increasing the etch rate of a porous surface [18].

5.3

MBE GROWTH OF GaN ON POROUS SiC SUBSTRATES

In this section we will discuss the use of porous SiC substrates for MBE growth of GaN and study its effects on dislocations in the film. We have grown GaN on both porous and nonporous SiC under nominally identical conditions and we provide results on the effect of substrate porosity on the film quality in terms of defect structure and dislocation density. TEM images show that the GaN film grown on porous substrates contains open tubes and a relatively low dislocation density in regions between tubes due to the lateral epitaxial overgrowth. We will discuss various growth mechanisms that can lead to these defect features in the GaN film. We also show the existence of half-loop dislocations at the walls of the open tubes in the GaN films. It is found from the Raman scattering that the GaN films grown on porous SiC were not more strain relaxed compared with those grown on nonporous substrate, despite earlier reports in the literature of the existence of such strain relaxation.

5.3.1

Experimental Details

The porous SiC samples used in this study are the same as described in Section 5.2.1. All our samples used for the GaN growth were 6H polytype with a 3.5◦ miscut angle. The MBE growth of GaN was performed on the (0001) face of the porous SiC samples under Ga-rich conditions [19]. Figure 5.7(a) shows a plan-view SEM image of a typical porous SiC surface. The surface pores are 20–50 nm wide. The morphology of the bulk porous layer is as described in Section 5.2.1, where we also discussed the presence of the thin nonporous skin layer, typically ∼50 nm thick. One means of removing this skin layer is reactive ion etching (RIE) in SF6 gas, which thus increases the surface porosity without affecting the bulk porous structure [18]. We have used this RIE process to increase the surface porosity of our samples so that, combined with the

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Figure 5.7 Plan-view SEM images of porous SiC surfaces: (a) as-received porous surface without any surface etching treatment; (b) the surface after hydrogen etching for 1 min at 1700 ◦ C; (c) the surface after RIE in SF6 for 6 min followed by hydrogen etching for 1 min at 1700 ◦ C. Images (a)–(c) refer to the same wafer, after various processing steps. Image (d) is from a different wafer, prepared by hydrogen etching at 1700 ◦ C for 1 min. Reproduced from A. Sagar et al., J. Vac. Sci. Technol. B 21, 1812. Copyright (2003), with permission from the American Institute of Physics

non-RIE samples, we have a wide range of samples with different surface porosities. Brief (1 min) hydrogen etching was used following the RIE etching to remove surface damage from the wafers although as discussed in Section 5.2.1 the hydrogen etching also affects the pore size (making the pores larger) [18]. For example, Figure 5.7(a) shows nano-size (20–50 nm) pores in a plan-view SEM image of an as-received porous SiC sample. Figure 5.7(b) is an image of the same sample after it has been hydrogen etched for 1 min. Figure 5.7(c) shows another image of a sample from the same wafer, which was reactive ion etched in SF6 plasma for 6 min and then hydrogen etched for 1 min. Figure 5.7(d) shows an SEM image of a different sample which was not reactive ion etched but was only hydrogen etched for 1 min. The surface porosity of our samples was measured simply by counting the number of surface pores after the hydrogen etching. The surface pore density of the samples in Figure 5.7(b), (c) and (d) was 3.5, 13 and 11.5 μm−2 , respectively. It is important to note that although Figure 5.7(b) and (c) show comparable pore density, the porous surface in Figure 5.7(c) is much less flat than in Figure 5.7(d) because the RIE step exposed the subsurface porous network. Using this

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combination of RIE and hydrogen etching, we prepared a range of samples with different surface porosities needed for the present study. After the hydrogen etching, samples were loaded into the MBE chamber, GaN growth was performed in Ga-rich conditions at the substrate temperature of 750 ◦ C. A nitrogen plasma cell was used for the nitrogen source and the growth proceeded for 8 h. After the growth, samples were characterized using X-ray diffraction by measuring the full width at ¯ half-maximum (FWHM) of the symmetric (0002) and asymmetric (1012) rocking curves to estimate screw and threading dislocation density in the films. TEM images were taken in cross-section to study the dislocations in the GaN films. Also, Raman scattering (RS) data were acquired to verify if any changes in film strain had occurred. RS is a convenient nondestructive technique to investigate vibrational phenomena in solids. Inelastic light scattering in crystal is susceptible to selection rules resulting from momentum conservation, which limited the study of optical phonons near the center of the Brillouin zone. This limitation can be removed by the introduction of impurities, defects, or by fabricating crystals with larger lattice constant along the growth direction than that of the corresponding single crystals, e.g. a superlattice. The use of an optical confocal microscope to reduce the laser spot size and increase light collection makes RS spectroscopy (micro-RS) extremely convenient to probe small crystals and thin films.

5.3.2

Film Structure

Figure 5.8(a) shows a cross-sectional TEM image, viewing along the ¯ [1100] direction, of a GaN film grown on nonporous SiC. A high density of threading dislocations was observed to emerge from the GaN/SiC interface and propagate upward during the growth. Figure 5.8(b) shows ¯ direction, grown on a porous SiC the GaN film, viewing along the [1120] surface, whose plan-view image is shown in Figure 5.7(c). As mentioned earlier, the porous SiC substrate shown in Figure 5.8(b) was reactive ion etched in SF6 for 6 min, before being hydrogen etched for 1 min. The surface pore density for the substrate shown in Figure 5.8(b) is 13 μm−2 . The substrate pores in Figure 5.8(b) were generally found to be filled with Ga droplets after the GaN growth. GaN nucleates on the pore walls close to the substrate surface and then grows laterally. Such local GaN LEO process caps some of the pore openings. These regions, where the significant lateral growth over the substrate pores has taken place are marked by ‘D’ in Figure 5.8, and these regions contain relatively fewer

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111 (c)

(a)

GaN

T T

T

T

a

0.5 µm

np SiC

g

0.5 µm

ps SiC (b)

T

(d)

T

D

D

D

T D

ps SiC

0.5 µm

ps SiC g

0.5 µm

Figure 5.8 Cross-sectional TEM images of GaN films on (a) nonporous SiC substrate, and (b)–(d) on porous SiC substrates. The label ‘ps’ denotes a porous substrate and ‘np’ denotes a nonporous substrate. The surface pore density of the substrate in (b) is 13 μm−2 , and in (c) and (d) is 11.5 μm−2 . The open tubes in the GaN films on porous substrates are marked by ‘T’ (the tubes appear white in contrast near the top of the film where they are empty, and black near the interface where they are filled by Ga). The regions labeled ‘D’ contain a relatively low number of threading dislocations originating at the interface (due to the lateral epitaxial growth over the substrate pores), and they contain dislocation half-loops gliding in from tubes. One half-loop is faintly seen to the right of ‘a’ in (c). Reproduced from A. Sagar et al., J. Vac. Sci. Technol. B 21, 1812. Copyright (2003), with permission from the American Institute of Physics

threading dislocations. However, at the openings that are only partially closed by LEO, open tubes can extend vertically all the way to the top surface. These open tubes are marked by ‘T’ in these images. Most of these tubes are partially filled with Ga due to the Ga-rich growth conditions. The regions around these tubes have a relatively low density of threading dislocations originating from the film/substrate interface. In the regions around these tubes, dislocation half loops, marked by ‘a’, are seen to punch in horizontally from the tube walls [Figure 5.8(c)]. These half loops are also shown in the Figure 5.9(a) and (b). This result is in contrast to Figure 5.8(a), i.e. for a film grown on a nonporous substrate where the dislocations are mostly created and propagated from the film/substrate interface.

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Figure 5.9 Magnified images of GaN on porous 6H-SiC. The half-loops are clearly seen in (a), with some of them indicated by arrows. The region marked by ‘D’ in (b) shows nearly defect-free GaN due to the lateral epitaxial growth over the pores. The open tubes are marked by ‘T’

Figure 5.8(b) is taken under a many-beam condition to reveal all defect features, whereas in Figure 5.8(c) and (d) the sample is tilted to reveal strong contrast from the tubes and dislocation loops, respectively, in the same sample area. The GaN film in Figure 5.8(c) and (d) was grown on a porous substrate, which was only hydrogen etched for 1 min, resulting in a surface pore density of 11.5 μm−2 , comparable with the substrate in the sample shown in Figure 5.8(b). Figure 5.8(c) was imaged with the sample tilted close to a two-beam condition with Burgers vector g = ¯ ¯ direction. We observed in Figure 5.8(c) [1103], viewing along the [1120] open tubes originated from essentially all pores at the substrate surface and extended up through the film, suggesting that lateral overgrowth of GaN has not occurred on such a flat porous surface. The dislocation loops are barely visible under the imaging condition in Figure 5.8(c). Dislocation half loops are observed, however, in strong contrast in Figure 5.8(d) where the same sample is tilted about the c-axis ∼30◦ away from ¯ Figure 5.8(c) (now viewing along the [1100] direction) and is imaged ¯ ¯ under a two-beam condition with g = [1120]. This suggests that the half¯ as is expected for loops that loop dislocations must have g = 1/31120 glide horizontally from the tubes. A loop marked by ‘a’ in Figure 5.8(c) is clearly seen to glide out from a tube. We note that the image taken with a horizontal g [Figure 5.8(d)] shows no contrast from the tubes.

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800 (a) 600

FWHM (arc s)

400 200 0 (b) 700 600 500 400 0

5

10

15

Surface pore density (µm−2)

¯ X-ray Figure 5.10 Triple axis (a) symmetric (0002) and (b) asymmetric (1012) rocking curve FWHM of the GaN films grown on porous SiC. The horizontal axis shows the density of surface pores on various substrates. The dashed lines are drawn as guides to the eye. Reproduced from A. Sagar et al., J. Vac. Sci. Technol. B 21, 1812. Copyright (2003), with permission from the American Institute of Physics

Remarkably, we find maximum contrast from the tubes only when using an inclined g vector (i.e. not completely horizontal or vertical). Strain variations around the open tubes should play some role in determining the contrast. Figure 5.10 shows a plot of symmetric and asymmetric rocking curve FWHM of GaN film as a function of substrate pore density. On average, there does not seem to be any significant improvement in the X-ray FWHM for the films grown on the various porous substrates. In particular, for the symmetric rocking curves, the values for films on porous substrates are significantly greater than for growth on nonporous substrates (i.e. at zero pore density); the latter are exceptionally low since our GaN films on SiC have a very low density of dislocations with [0002] component in their Burgers vector [3]. Aside from this difference, the X-ray rocking curve results do not show a significant variation with surface pore density of the substrate. Since the X-ray FWHM is a measure of the mosaic structure and strain variation in a large area of the film (due to the beam size ∼1 mm2 ) and also through the entire thickness of the

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GaN film, this value is not a true indication of the defect structure and growth mechanisms working at the nano-scale. Even though X-ray results are not significantly improved for growth on the porous substrates, TEM images discussed earlier show that the porous substrate is able to produce local areas in the GaN film having relatively low defect density.

5.3.3

Film Strain

In addition to defect density, another important characteristic of heteroepitaxial growth of the mismatched materials is the degree of strain relaxation in the film compared with the substrate. It was found in previous work that use of porous substrates can lead to significant strain relaxation in the film, at least in certain cases [20,21]. The hexagonal crystalline phase of GaN, or wurtzite structure, belongs to the space group C4 6v , and has two molecules per Brillouin unit cell. Group theory predicts eight zone center optical phonon modes, represented by 1A1 (TO), 1A1 (LO), 2Bi , 1E1 (TO), 1E1 (LO), and 2E2 . The two B1 are silent modes, or Raman inactive, but all the six allowed first order phonons have been observed in thin films [22]. These phonons have also been observed in thick and high quality free-standing hydride vapor phase epitaxy (HVPE) GaN substrates and their energy has been used to estimate the biaxial stress in our samples [23]. To verify the strain relaxation of our GaN films we have carried out micro-RS, which is performed in a backscattering geometry, with the results shown in Figure 5.11. Spectrum (a) shows the result for a GaN film grown on nonporous SiC, and spectra (b)–(d) show results for films on porous SiC. The observed location of the GaN E2 line near 567 cm−1 is nearly the same in all cases; from Gaussian fitting we find locations of 566.7, 566.7, 566.5, and 566.8 cm−1 for spectra (a)–(d), respectively, with an error of ±0.1 cm−1 for each measurement. The Raman line positions are thus essentially the same for all samples, demonstrating no additional strain relaxation for the films grown on the porous substrates. Generally, MBE-grown GaN films on SiC tend to have a small amount of compressive strain arising from the lattice mismatch between GaN and SiC (the thermal mismatch leads to tensile strain, but this effect is smaller) [24]. Indeed, from wafer curvature measurements we observe some residual compressive strain for our films grown on the porous substrates (for the films grown on nonporous substrates the curvature measurements were hindered by the presence of a molybdenum film on the backside of the wafers, leading to artifacts in the results) [25]. Strain measurements by electron diffraction during TEM have also been done on such

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Figure 5.11 Raman spectroscopy of GaN films grown on (a) nonporous and (b)–(d) porous SiC substrates. Raman shifted lines due to the SiC substrate and due to the GaN film are resolved. The zero intensity level in consecutive spectra are shifted for ease of viewing

films [19]; some differences in strain were observed in that case between films grown on nonporous and porous substrates, although differences in growth temperature for those samples could affect those results [24]. We conclude that the porosity of the SiC substrate has only a small, or zero, effect on the strain in the GaN films. This conclusion is, perhaps, not surprising when we carefully consider the geometry of the situation. The prior work which did observe a strain reduction was for GaN growth on porous GaN, employing a GaN buffer layer that was then etched to make it porous [20,21]. It was found that the pores extended vertically down into the layer, i.e. following the columnar nature of the film [20]. By removing material from around the columns, the material inside the columns can elastically relax (so long as the depth of the etched material is comparable with the width of the column). Subsequent overgrowth then led to a reduced strain level in the film. In contrast, for the present experiments it is the SiC substrate that is porous, with the GaN grown epitaxially on that. The GaN will be strained by its mismatch to SiC, and there is no real mechanism associated with the porosity for this strain to be relaxed. It is important to realize in this regard that the porous SiC itself is very rigid (removing some material to make it porous will lead to only a small decrease in its elastic constants), and hence in no way can it act as a type of ‘compliant’ substrate. Hence, no significant strain relaxation in the GaN film is found.

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Figure 5.12 Finite element analysis of shear stress distribution around a circular pore under biaxial stress. (a) The finite element analysis model, showing a single circular pore in a solid brick. (b) Plot of shear stress along a diagonal line in the model as a function of distance from pore wall. The units are arbitrary and the length scale of the stress field is determined by the pore diameter in the model (10 distance units)

Another manifestation of the strain in the films is the presence of the half-loop dislocations extending out from the open tubes in the GaN films grown on the porous substrates, as discussed in the previous section. Regarding the origin of these half-loops, it is easy to see that open tubes (or voids) in a strained film will act as stress concentrators: since the normal component of the stress is necessarily zero at the tube wall, the material near the wall will be displaced relative to its position in the absence of the void, and the tangential in-plane component of the stress is thereby increased. In other words, during growth, the shear stress field of the GaN film will be locally concentrated around these open tubes in the film. The open tubes provide a free surface where these half-loops can nucleate due to the increased stress. We have performed finite element analysis on a simple model to demonstrate the concentration of shear stress around the pore wall. Figure 5.12(a) shows the model used and Figure 5.12(b) is a plot of shear stress as a function of distance from the pore wall. It is evident that there is considerable stress concentration in the film around the substrate pores, which can lead to the formation of the half-loop dislocations.

5.4

SUMMARY

In this chapter, we have discussed the MBE growth of GaN on porous SiC. We discussed the morphology of porous SiC and the effect of hydrogen

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etching on substrate porosity. It was seen that the MBE grown GaN film on porous SiC has open tubes extending over the substrate pores, and we observed the instances of LEO GaN films over the porous substrates. We have shown, with cross-sectional TEM images that in the regions of LEO, the GaN films on porous SiC substrates have low dislocation density. However, we did not find any overall improvement in the FWHM of the symmetric and asymmetric X-ray rocking curves on these GaN films grown on substrates with different porosities. In addition, it was found from Raman spectra that the films on porous SiC were not significantly strain relaxed compared with the films on nonporous substrates.

ACKNOWLEDGEMENTS This work was supported by the DURINT program administered by the Office of Naval Research (Dr C. Wood) under Grant N00014-0110715. We are grateful to Dr T. S. Kuan for collaboration and numerous stimulating discussions.

REFERENCES [1] D. Kapolnek, X. H. Wu, B. Heying, S. Keller, B. P. Keller, U. K. Mishra and S. P. Denbaars, ‘Structural evolution in epitaxial metalorganic chemical vapor deposition grown GaN films on sapphire’, Appl. Phys. Lett., 67, 1541 (1995). [2] S. Keller, B. P. Keller, Y.-F. Wu, B. Heying, D. Kapolnek, X. H. Wu, J. S. Speck, U. K. Mishra and S. P. Denbaars, ‘Influence of sapphire nitridation on properties of gallium nitride grown by metalorganic chemical vapor deposition’, Appl. Phys. Lett., 68, 1525 (1996). [3] C. D. Lee, V. Ramachandran, A. Sagar, R. M. Feenstra, D. W. Greve, W. L. Sarney, L. Salamanca-Riba, D. C. Look, Song Bai, W. J. Choyke and R. P. Devaty, ‘Properties of GaN epitaxial layers grown on 6H-SiC(0001) by plasma-assisted molecular beam epitaxy’, J. Electron. Mater., 30, 162 (2001). [4] S. Luryi and E. Suhir, ‘New approach to the high quality epitaxial growth of latticemismatched materials’, Appl. Phys. Lett., 49, 140 (1986). [5] D. Zubia and S. D. Hersee, ‘Nanoheteroepitaxy: the application of nanostructuring and substrate compliance to the heteroepitaxy of mismatched semiconductor materials’, J. Appl Phys., 85, 6492 (1999). [6] E. Frayssinet, B. Beaumont, J. P. Faurie, P. Gibart, Z. Makkai, B. Pecz, P. Lefebvre and P. Valvin, ‘Micro epitaxial lateral overgrowth of GaN/sapphire by metal organic vapour phase epitaxy’, MRS Internet J. Nitride Semicon. Res., 7, 8 (2002). [7] T. S. Zheleva, O.-H, Nam, M. D. Bremser and R. F. Davis, ‘Dislocation density reduction via lateral epitaxy in selectively grown GaN structures’, Appl. Phys. Lett., 71, 2472 (1997).

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[8] A. Sakai, H. Sunakawa and A. Usui, ‘Defect structure in selectively grown GaN films with low threading dislocation density’, Appl. Phys. Lett., 71, 2259 (1997). [9] S. Kuarai, K. Nishino and S. Sakai, ‘Nucleation control in the growth of bulk GaN by sublimation method’, Jpn J. Appl. Phys., 36, L184 (1997). [10] J. Wang, S. Tottori, H. Sato, M.-S. Hao, Y. Ishikawa, T. Sugahara, K. Yamashita and S. Sakai, ‘Lateral overgrowth of thick GaN on patterned GaN substrate by sublimation technique’, Jpn J. Appl. Phys., 37, 4475 (1998). [11] M. Ebihara, S. Tanaka and I. Suemune, ‘Nucleation and growth mode of GaN on vicinal SiC surfaces’, Jpn J. Appl. Phys., 46, L348 (2007). [12] P. Waltereit, S.-H. Lim, M. McLaurin and J.S. Speck, ‘Heteroepitaxial growth of GaN on 6H-SiC(0001) by plasma-assisted molecular beam epitaxy’, Phys. Status Solidi (A), 194, 524 (2002). [13] S. Zangooie, J. A. Woolam and H. Arwin, ‘Self-organization in porous 6H-SiC’, J. Mater. Res., 15, 1860 (2000). [14] C. Hallin, A. S. Baskin, F. Owman, P. Martensson, O. Kordina and E. Jangen, ‘Study of the hydrogen etching of silicon carbide substrates’, Silicon Carbide and Related Materials 1995, Kyoto, Japan, Inst. Phys. Conf. Ser. No. 142 (IOP, Bristol, 1996), Ch. 3. [15] T. L. Chu and R. B. Campbell, ‘Chemical etching of silicon carbide with hydrogen’, J. Electrochem. Soc., 112, 955 (1965). [16] V. Ramachandran, M. F. Brady, A. R. Smith and R. M. Feenstra, ‘Preparation of atomically flat surfaces on silicon carbide using hydrogen etching’, J. Electron. Mater., 27, 308 (1998). [17] C. D. Lee, R. M. Feenstra, O. Shigiltchoff, R. P. Devaty and W. J. Choyke, ‘Structural properties of GaN films grown by molecular beam epitaxy on singular and vicinal 6H-SiC(0001)’, MRS Internet J. Nitride. Semicond. Res., 7, 2 (2002). [18] A. Sagar, C. D. Lee, R. M. Feenstra, C. K. Inoki and T. S. Kuan, ‘Morphology and effects of hydrogen etching of porous SiC’, J. Appl. Phys., 92, 4070 (2002). [19] C. K. Inoki, T. S. Kuan, C. D. Lee, A. Sagar, R. M. Feenstra, D. D. Koleske, D. J. Diaz, P. W. Bohn and I. Adesida, ‘Growth of GaN on porous SiC and GaN substrates’, J. Electron. Mater., 32, 855 (2003). [20] M. Mynbaeva, A. Titkov, A. Kryganovskii, V. Ratnikov, K. Mynbaev, H. Huhtinen, R. Laiho and V. Dmitriev, ‘Structural characterization and strain relaxation in porous GaN layers’, Appl. Phys. Lett., 76, 1113 (2000). [21] B. K. Ghosh, T. Tanikawa, A. Hashimoto, A. Yamamoto and Y. Ito, ‘ Reduced-stress GaN epitaxial layers grown on Si(111) by using a porous GaN interlayer converted from GaAs’, J. Cryst. Growth, 249, 422 (2003). [22] J. A. Freitas Jr and M. A. Khan, ‘Raman and photoluminescence studies of undoped and magnesium-doped GaN films on sapphire’, Mater. Res. Soc. Symp. Proc., 339, 547 (1994). [23] J. A. Freitas Jr, ‘Optical studies of bulk and homoepitaxial films of III–V nitride semiconductors’, J. Cryst. Growth, 281, 168 (2005). [24] B. J. Skromme, H. Zao, D. Wang, H. S. Kong, M. T. Leonard, G. E. Bulman and R. J. Molnar, ‘Strain determination in heteroepitaxial GaN’, Appl. Phys. Lett., 71, 829 (1997).

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[25] A. Sagar, C. D. Lee, R. M. Feenstra, C. K. Inoki and T. S. Kuan, ‘Plasma-assisted molecular beam epitaxy of GaN on porous SiC substrates with varying porosity’, J. Vac. Sci Technol. B, 21, 1812 (2003). Regarding the wafer curvature results reported in this work, the results for nonporous substrates are in error since those substrates had a coating of molybdenum on their backside that itself induced significant curvature in the substrate. This coating was absent for the films grown on the porous substrates.

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6 GaN Lateral Epitaxy Growth Using Porous SiNx, TiNx and SiC ¨ Ozg ¨ ur ¨ and H. Morkoc¸ J. Xie, Y. Fu, U. Department of Electrical and Computer Engineering, Virginia Commonwealth University, Richmond, VA 23284-3068, USA

6.1

INTRODUCTION

Currently, the available single crystal GaN substrates are limited by the size and point defects that make them unsuitable for mass production [1]. An alternative to native GAN substrates is to use free-standing GaN templates prepared by hydride vapor phase epitaxy (HVPE), which has a typical thread dislocation (TD) density of 105 –106 cm−2 , however, the high price limits their availability [2]. Currently and for the foreseeable future, most GaN-based devices still have to be grown on foreign substrates including sapphire (α-Al2 O3 ), silicon carbide (SiC) and (111) silicon [2]. The large lattice mismatch and different thermal expansion coefficients between GaN and those substrates generate a high density of defects. Among them, misfit dislocations (MDs) and basal plane stacking faults (BSFs) are located near the GaN/substrates interface and have somewhat filtered effect on the Porous Silicon Carbide and Gallium Nitride: Epitaxy, Catalysis, and Biotechnology Applications Edited by Randall M. Feenstra and Colin E.C. Wood  C 2008 John Wiley & Sons, Ltd

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window

overgrown GaN

SiO2 GaN

GaN

sapphire

sapphire

(a)

(b)

Figure 6.1 Conventional epitaxy lateral overgrowth. (a) GaN templates patterned with SiO2 strips along[1120]. (b) GaN growth vertically through windows and laterally over SiO2 mask. During this process, extend defects can be efficiently blocked by SiO2 mask

properties of the top GaN layer. However, extended defects, including TDs, nanopines (the term is used very liberally here), inverted domains (IDs) and prismatic stacking faults (PSFs), compromise the device performance. Especially, theoretical and experimental results showed that leakage path can be formed through TDs. Furthermore, TDs, together with other point defects, can act as scattering center for two-dimensional electron gas (2DEG) and nonradiative center, which degrade the device performance and reliability [2]. Typically, GaN thin films grown on sapphire or SiC substrates have a TD density ∼109 cm−2 . With the epitaxy lateral overgrowth (ELO) method (Figure 6.1), the density of TD is effectively reduced to ∼106 cm−2 in the wing region, however the windows region remains the same, and the size of the wing area is limited [3]. ELO requires extra procedures, including photolithography, which increase the cost and result in possible undesired contamination. Therefore, it is preferable to have new growth techniques which can utilize the concept of ELO but with less or even without any ex situ steps. In this chapter, we will discuss the epitaxy growth of GaN using in situ formed porous SiNx and TiNx (as ELO mask in nanometer scale), as well as porous SiC prepared by electrical chemical etching.

6.2

EPITAXY OF GaN ON POROUS SiNx NETWORK

Unlike conventional ELO method, nanometer-thick SiNx layers with a porous morphology can be prepared in situ by simply flowing appropriately diluted silane for a short period on the substrate under the similar growth condition (chamber pressure and temperature, etc.) used for

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123 Seed at 200 Torr/1000°°C

(1101) facets

GaN

GaN

Growth at 200 Torr/1050°C

GaN

Figure 6.2

GaN

Three-step growth method for GaN using in situ SiNx nanonetwork

typical GaN growth [4]. The premise of this method is to form GaN seeds on the template via the spontaneously formed open pores in the porous SiNx layer followed by the growth emanating from the initial GaN seeds on the SiNx nanomask. Thus, in order to maximize the dislocation reduction, the precise control of SiNx coverage and the initial GaN seed layer is imperative. The caveat, as in the case of standard ELO, is that the SiNx layer is expected to affect the electrical properties of the overgrown GaN epilayers by Si diffusion. In this section, we will discuss the parameters affecting the morphology of the initial GaN seed layers on in situ SiNx nano-network and the resultant structural, optical and electrical properties of the overgrown GaN epilayers.

6.2.1

Three-step Growth Method

A typical growth process using SiNx nanonetwork by metalorganic chemical vapor deposition (MOCVD) requires three major steps (Figure 6.2). The first step is the proper control of SiNx coverage by adjusting the deposition time and or the silane flux. The second step is to promote seeds with proper density and shape. The last step involves the use of growth condition that enhances the lateral growth rate to achieve a coalesced surface.

6.2.1.1

SiNx Coverage

SiNx coverage is very sensitive to silane flux and deposition time. Figure 6.3 displays a series of scanning electron microscopy (SEM)

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Figure 6.3 Effect of silane density and deposition time on the SEM surface morphology of overgrown 2 μm GaN on the porous SiNx thin films as viewed by SEM. (a) 2 % silane for 10 min, (b) 250 ppm silane for 10 min, (c) 100 ppm silane for 5 min, and (d) 100 ppm silane for 2 min with a flow rate of 50 sccm. Reproduced from Moon YT et al., Journal Of Crystal Growth, 291(1): 301–308. Copyright (2006), with permission from Elsevier

images to illustrate the effect of SiNx deposition conditions on the surface morphology of the overgrown 2 μm GaN. Figure 6.3(a) shows randomly distributed, low density, large domain size polycrystalline GaN when 2 % silane was used to deposit SiNx for 10 min. This result demonstrates that there is no coherence between the overgrown GaN and the template due to the lack of open pores in the thick SiNx . Figure 6.3(b) shows well-aligned hexagonal GaN islands in the growth direction of the c-axis when 250 ppm silane was introduced for 10 min. This result is indicative of the presence of open pores in the thinner SiNx so that the pores could act as nucleation centers for GaN overgrowth. When silane was further diluted to 100 ppm and flowed for 5 min, partial coalescence of the overgrown GaN islands was observed as shown in Figure 6.3(c). Figure 6.3(d) shows the coalesced and flat surface morphology of a 2 μm GaN grown on the SiNx deposited using 100 ppm silane for 2 min. It is reasonable to assume that as the exposed area of

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the underlying template increases by decreasing the SiNx film thickness, the spatial separation between the GaN nuclei during the initial stage of regrowth will be relatively small, which would result in a rapid coalescence of overgrown GaN. In terms of the dislocation reduction efficacy, however, the rapid coalescence of regrown GaN is not desirable because a high density of initial GaN nuclei will: (i) increase the probability of threading dislocation penetration from the template into the overgrown GaN through the open pores; (ii) decrease the length of effective lateral overgrowth between initial GaN nuclei; and (iii) increase the number of grain boundaries in the overgrown GaN layer. Thus, in order to efficiently reduce the threading dislocation density in the overgrown GaN within a reasonable film thickness for practical device applications, we need to precisely control the properties of the initial GaN seed layers on the SiNx nanonetwork. In our investigations, a silane concentration of 100 ppm was used to deposit SiNx layers unless specified. Formation of nanopores are directly observed by scanning Auger microscopy (SAM) data for that surface region [5]. From SEM and SAM images taken from same area, after SiNx nanonetwork deposition, nanometer scale pores without Si were observed, and the area between GaN islands was indeed covered by SiNx . Meanwhile, the density of nanopores was probably much larger than nucleation density.

6.2.1.2

Seed Layer

In this section, we will discuss the seed layer growth condition which will affect the overall quality dramatically. Figure 6.4 shows the effect of the reactor pressure on the surface morphology for nominally 0.5 μm thick GaN seed layers grown on the same SiNx nanonetwork with a fixed V/III ratio of 2000 at 970 ◦ C using 2 μm GaN templates. When the growth pressure of the initial GaN seed layer was 30 Torr, the surface almost coalesced with hexagonal pinholes formed during coalescence of the initial GaN islands [Figure 6.4(a)]. When the growth pressure increased to 200 Torr, randomly distributed initial GaN seeds partially coalesced and had arbitrary shapes [Figure 6.4(b)]. The initial GaN seeds became discontinuous and assumed a hexagonal shape when the growth pressure increased to 300 Torr [Figure 6.4(c)]. Hexagonal facets of the initial GaN seeds at 300 Torr became obvious when the seed layer thickness increased to 1 μm [Figure 6.4(d)]. The dramatic change in the seed layer morphology at different growth pressures is due to different nucleation energy and lateral growth rate.

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Figure 6.4 Effects of growth pressure and layer thickness of initial GaN seed layers on the SEM surface morphology. (a) 30 Torr, 0.5 μm thick, (b) 200 Torr, 0.5 μm thick, (c) 300 Torr, 0.5 μm thick, and (d) 300 Torr, 1 μm thick. The seed layers were grown at 970 ◦ C with a V/III ratio of 2000. Reproduced from Moon YT et al., Journal Of Crystal Growth, 291(1): 301–308. Copyright (2006), with permission from Elsevier

At lower pressures, gallium adatoms have a smaller diffusion barrier and larger migration length, therefore, nucleation density would be much higher than at higher pressure in relative terms. Furthermore, higher lateral growth rate at low pressures would result in a continuous film within a shorter growth time compared with the higher pressure case. We observed that as we increased the reactor pressure from 30 to 200, and then to 300 Torr, the density of GaN seeds continually decreased, meanwhile, the vertical to lateral ratio increased. In addition, the increase of the reactor pressure will enhance the development of thermodynamically stable crystallographic facets of wurtzite GaN seeds due to enhanced chemical etching by the hydrogen and ammonia gas mixture during growth. The crystallographic facets of hexagonal GaN seeds grown at 200 and 300 Torr became obvious when the growth temperature increased from 970 to 1020 ◦ C, as shown in Figure 6.5(a) and (b), respectively. An increase of growth temperature enhances the development of thermodynamically preferred crystallographic facets due to the enhancement of adatom surface diffusivity. An increase of growth temperature also

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Figure 6.5 Effects of growth pressure and V/III ratio of initial GaN seed layers on the surface morphologies. (a) 200 Torr, V/III ratio 2000, (b) 300 Torr, V/III ratio 2000, and (c) 200 Torr, V/III ratio 4000. The 0.5 μm thick seed layers were grown at 1020 ◦ C. The thick scale bar is 10 μm. Reproduced from Moon YT et al., Journal of Crystal Growth, 291(1): 301–308. Copyright (2006), with permission from Elsevier

decreases the density of GaN seeds, the explanation of which is given below. Thermodynamically, it is expected that the atoms in relatively small GaN seeds will be more thermally unstable than those in large GaN seeds since small seeds have a relatively large surface energy contribution to the total Gibbs free energy. Thus, when the growth temperature increases, the adatoms on relatively small GaN seeds will become more unstable than those on larger seeds. In addition, the diffusivity of mobile Ga atoms on the SiNx surface will increase as the growth temperature increases. This will in turn cause mobile Ga atoms to thermodynamically prefer depositing on relatively large and stable GaN seeds formed on larger open pores in SiNx . Consequently, an increase of growth temperature will retard the development of relatively small GaN seeds on smaller open pores, resulting in a decrease of the density of GaN islands. The density of GaN seeds grown at 200 Torr and 1020 ◦ C further decreased when the V/III ratio increased from 2000 [Figure 6.5(a)] to 4000 [Figure 6.5(c)]. The hexagonal micro-facetted GaN pyramids which are uniformly distributed and well aligned on the SiNx nanomask are beneficial for the reduction of threading dislocations when used as seeds for GaN regrowth. However, large-sized micro-facetted GaN seeds with a low density require a longer time to obtain coalescence and smooth GaN surfaces with no appreciable surface undulations. Thus, an optimum thickness of the initial GaN seed layer needs to be determined, and another set of growth conditions which can enhance lateral overgrowth on the seed layer needs to be applied to attain a flat GaN surface with a reasonable film thickness. The desirable lateral epitaxial overgrowth conditions on the GaN seeds formed on a SiNx layer will call for the enhancement of facet-controlled lateral overgrowth from the micro-facetted GaN seeds. Simultaneously, the formation of the small undesirable GaN clusters among the large hexagonal GaN islands

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during GaN overgrowth must be minimized in order to efficiently reduce the threading dislocation density in the overgrown GaN layer.

6.2.1.3

Lateral Growth

The last step involves the enhancement of lateral growth rate by adopting a high-temperature and low-pressure [6], and Ga-rich growth condition [7]. However, as we discussed in the previous section, low pressure growth probably will have more undesirable nucleation through nanopores during the growth, since the actual density of pores is much higher than the island density. Meanwhile, during the growth, especially at high temperatures, new pores could be formed due to decomposition and hydrogen etching. As a result, optimized growth condition requires: (i) a relatively high pressure (200 Torr in this investigation); (ii) a proper temperature (∼1050 ◦ C); and (iii) a low V/III ratio.

6.2.2

Structural and Optical Characterization

In order to observe the effect of SiNx coverage, one set of samples (Figure 6.6) was prepared using in situ SiNx nanonetworks with varying deposition time (from 0 to 6 min, the longest deposition time corresponding to ∼2 nm SiNx ).

Figure 6.6 Investigated GaN sample structures with single or double SiNx nanonetworks. The topmost 500 nm GaN:Si layers (n ∼ 0.5–1 × 1017 cm−3 ) were deposited later for the deep level transition spectrum (DLTS) measurements. Reproduced from Xie JQ et al., Applied Physics Letters 90(26): Art. No. 262112. Copyright (2007), with permission from the American Institute of Physics

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Based on the discussion in previous sections, a silane concentration of 100 ppm was used to deposit SiNx nanonetworks and nominally ∼300 nm thick seed layers were in turn grown at 200 Torr/1000 ◦ C. The SiNx nanonetworks were deposited on ∼2 μm thick GaN/Al2 O3 templates (2 in. diameter wafers) first, and followed by overgrowth of GaN at 200 Torr without any interruption. The overgrown GaN was 4 μm thick for SiNx deposition time up to 5 min, and 6 μm for 6 min SiNx . As shown in Figure 6.6, one sample with double SiNx was also prepared to study the effect of multi-SiNx nanonetwork. With increasing SiNx coverage, the sample surface morphology was characterized by parallel and straight atomic steps as shown in Figure 6.7.

6.2.2.1

Structural Properties

The effect of SiNx deposition conditions on the epitaxial structural quality was characterized first by the full width at half-maximum (FWHM) values of X-ray diffraction (XRD) (0002) and (1012)rocking curves. As shown in Figure 6.8, the FWHM value of (0002) and (1012) diffractions for ∼6 μm thick GaN without SiNx nanonetwork are 252 and 405 arc s which were comparable with other reports [8]. When the SiNx nanonetwork was used, the FWHM value decreased dramatically especially for the asymmetric (1012) diffraction. When the SiNx deposition

8 nm

4 nm

0 nm

Figure 6.7 Surface morphology of coalesced GaN (undoped) surface with 6 min SiNx nanonetwork. Reproduced from Xie JQ et al., Applied Physics Letters 90(26): Art. No. 262112. Copyright (2007), with permission from the American Institute of Physics

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Figure 6.8 FWHM values of symmetric (0002) and asymmetric (1012) rocking curve scan for different SiNx nanonetwork deposition time (0, 3, 4, 4.5, 5 and 6 min, the longest deposition time corresponding to ∼2 nm SiNx ). Scan conditions: step size, 0.002◦ ; time/step, 0.4 s; 4×Ge monochromator aperture, 1 × 1 mm; detector, no slit; power, 40 kV, 40 mA. Reproduced from Xie JQ et al., Applied Physics Letters 89(15): Art. No. 152108. Copyright (2006), with permission from the American Institute of Physics

time was increased from 3 to 6 min, (0002) and (1012) FWHM values decreased from 246 and 345 arc s to 210 and 190 arc s, respectively. Compared with the reference sample, the FWHM value of the (1012) diffraction was reduced nearly by half, indicating a significant improvement of the film quality. Since the FWHM values of (0002) and (1012) are correlated to screw type and edge type dislocations, respectively, our XRD data suggest that the SiNx nanonetwork can reduce the edge type dislocation density effectively. The mechanism of dislocation reduction by the SiNx nanonetwork is to reduce the nucleation sites, in other words, grains will be larger. This is confirmed by SEM study. After in situ hydrogen etching at 1000 ◦ C in the metal-organic chemical vapor deposition (MOCVD) chamber, the typical grain size increased from below 0.5 μm (without SiNx ) to over 3 μm (with 5 min SiNx ). The cross-sectional TEM image of the sample with a 5 min SiNx is shown in Figure 6.9. Most TDs are blocked by the SiNx network, and those emanating from the pores are mostly bent into horizontal configurations. GaN islands (seeds) formed at high pressure (200 or 300 Torr) typically have (1101)facets (images obtained by SEM are not shown), and

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Figure 6.9 Cross-sectional TEM micrograph of a GaN thin film grown with (a) 4.5 and (b) 5 min in situ SiNx network by MOCVD on sapphire. Reproduced from Xie JQ, et al., Applied Physics Letters 90(4): Art. No. 041107. Copyright (2007), with permission from the American Institute of Physics

they will grow vertically and laterally until a fully coalesced surface is achieved. During this evolution, dislocations are easily bent toward the facet surface. During the lateral growth that follows, some dislocations may propagate laterally until they run into other dislocations at the coalescing boundaries. This mechanism has already been dubbed as the ‘two-step growth’ [9] or the ‘facet-controlled ELO’ (FACELO) [6] for (1100) patterned ELO to reduce TDs in both window and wing areas. In our case, we believe that naturally formed (1101) facets play a key role in TD reduction when using the in situ SiNx network, since the total reduction in TD density is achieved not only by the blocking efficiency of the SiNx network but also by the degree of dislocation bending. The dislocation bending strongly depends on the GaN seed growth conditions in the second step. If the seed layers were grown at low pressures (e.g. 30 Torr), the island density would be high and uniform, and all islands would have a small height to base ratio. However, at a higher pressure (e.g. 200 Torr used in this study), the seed density is relatively low, and the GaN islands have a larger height to base ratio, and (1101) side facets. Between these two types of seeds, the ones grown at high pressure would bend dislocations more effectively. For the same reason, a high growth pressure is also desirable in the last step for dislocation bending, but at the expense of a thicker layer being needed to achieve complete coalescence. Plan-view TEM images of samples with 4.5 and 5 min SiNx shown in Figure 6.10 reveal a significant reduction in dislocation. Direct counting from the images indicated that the total dislocation densities are reduced to 2 × 108 cm−2 and 6 × 107 cm−2 for the 4.5 min and 5 min SiNx samples, respectively. A small change in SiNx deposition time (0.5 min)

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Figure 6.10 Plan-view TEM micrographs of GaN thin films grown with (a) 4.5 min and (b) 5 min in situ SiNx network by MOCVD on sapphire substrates. Reproduced from Xie JQ, et al., Applied Physics Letters 90(4): Art. No. 041107. Copyright (2007), with permission from the American Institute of Physics

resulted in a factor of three difference in the total TD density, indicating that TD reduction is extremely sensitive to the SiNx coverage, and therefore the seed density. From the discussion above, we can conclude that further increases in the SiNx deposition time will result in more effective dislocation reduction up to a point. However, much thicker GaN overlayers or modified growth conditions are needed for coalescence as the SiNx deposition time is increased. When SiNx was deposited more than 6.5 min, we could not get a coalesced surface even at 10 μm regrowth under the current growth conditions employed. The possible reasons might be the unoptimized lateral overgrowth rate when islands with (1101) prismatic planes were formed as well as the larger separation between nucleation sites.

6.2.2.2

Optical Properties

Low temperature photoluminescence (PL) spectra of all samples with SiNx nanonetwork exhibited similar features around the band edge which are dominated by exciton peaks, but with steady improvement with increasing SiNx coverage. Figure 6.11 shows the excitonic region of PL signal measured at 15 K for sample with 5 and 6 min SiNx compared with control sample. The spectra contain peaks at 3.485, 3.494 and 3.505 eV which correspond to FXA , FXB , and FXA excited state transitions, respectively [10]. The main donor-bound exciton D0 X A emission is seen at 3.479 eV. The FWHM values of the FXA , FXB and D0 XA peaks

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Figure 6.11 Typical near band edge PL spectra at 15 K for samples grown with 5 and 6 min SiNx single interlayers and a control sample without SiNx . The spectra were displaced vertically for clarity. Reproduced from Xie JQ et al., Applied Physics Letters 90(26): Art. No. 262112. Copyright (2007), with permission from the American Institute of Physics

are also given in Table 6.1, where the line width of DXA and FXA are seen to decrease with increasing SiNx deposition time from 3.0 to 6 min. Further, FXB appears as a shoulder in the reference sample but is clearly visible in samples with SiNx nanonetworks. For further evaluation of the material quality, dovetailed with the effect of SiNx network on the point defect reduction, time-resolved Table 6.1 Summary of XRD, TEM, 15 K PL and room temperature TRPL results for GaN thin films with different SiNx deposition times

SiNx (min)

15 K PL line Time-resolved PL XRD FWHM TEM TDs width (meV) at 200 μJ cm−2 (arc min) (×107 cm−2 ) (0002), (1012) edge, screw D0 X A FX A FX B τ 1, τ 2 (ns) A2 /A1

0 3 4 4.5 5 6

4.20, 6.75 4.10, 5.76 3.94, 5.09 3.77, 4.32 3.62, 3.52 3.50, 3.17

TiNx 15 min Freestanding GaN

6.43, 6.11

9.6, 10 1.7, 4.4

3.2 3.6 3.1 2.5 2.3 2.5

4.8 4.0 3.7 3.1 3.2 3.3

4.3 3.4 3.3 3.6

0.18, 0.40 0.20, 0.52 0.24, 0.81 0.35, 1.21 0.45, 2.22 0.53, 2.67

0.74 0.66 0.90 0.71 0.75 0.88

0.47, 1.86

0.59

0.34, 1.73

0.33

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photoluminescence (TRPL) measurements were performed using 325 nm (3.81 eV) excitation from a Ti:sapphire oscillator/regenerative amplifier pumped optical parametric amplifier. Figure 6.12 shows the 200 μJ cm−2 excitation TRPL data normalized to 1 for samples with different SiNx deposition times and also for the 15 min annealed TiNx sample (discussed in Section 6.3) for comparison. The decays for all samples were fitted by a biexponential decay function, A1 exp(−t/τ1 ) + A2 exp(−t/τ2 ), and the decay constants and the amplitude ratios (A2 /A1 ) obtained from the fits are summarized in Table 6.1. The measured decay times, τ 1 and τ 2 for the fast (A1 ) and slow (A2 ) decaying components, respectively, are both limited by nonradiative recombination, therefore longer decay times and larger A2 /A1 ratios indicate reduced nonradiative relaxation pathways. Consistent with the observations from XRD and transmission electron microscopy (TEM) analysis, both decay times increased with increasing SiNx deposition time. The fully coalesced 5 min SiNx sample exhibited a slower decay and larger A2 /A1 ratio (τ 1 = 0.45 ns, τ 2 = 2.22 ns, and A2 /A1 = 0.75) compared with the best TiNx network sample (τ 1 = 0.47 ns, τ 2 = 1.86 ns, A2 /A1 = 0.59, discussed in the next section). For a longer SiNx deposition time (6 min), decay times were even longer (0.532 ns, 2.674 ns). As mentioned previously, the improvement in decay times with increasing SiNx coverage is due to the reduction of TD

Figure 6.12 Normalized TRPL spectra for GaN thin films grown with different in situ SiNx deposition times, control sample, and a 15 min annealed TiNx sample. The solid lines are biexponential fits to the data. Reproduced from Xie JQ et al., Applied Physics Letters 90(4): Art. No. 041107. Copyright (2007), with permission from the American Institute of Physics

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which paves the way to nonradiative recombination channels. It is well known that many point defects also have an adverse effect on the optical emission efficiency and carrier lifetime in GaN. Our study catalogs the correlation between the TD density and those point defects that act as nonradiative recombination centers via the carrier lifetime.

6.2.3

Schottky Diodes (SDs) on Undoped GaN Templates

SDs were fabricated on both undoped and doped GaN templates with varying SiNx deposition time to study the effect of SiNx coverage. The Si doped GaN layers were deposited to achieve reasonable capacitance for the DLTS measurement. Planar SDs were fabricated using standard photolithography on 0, 3, 4 and 5 min SiNx samples (undoped). Before metallization, all samples were cleaned in acetone, methanol, and deionized (DI) water in an ultrasonic bath, followed by boiling aqua regia cleaning for 20 min and 5 min DI water rinse. Ti/Al/Ti/Au (30/100/30/100 nm) ohmic contacts were deposited by e-beam and thermal evaporation, followed by a 60 s rapid thermal annealing (RTA) at 900 ◦ C in nitrogen ambient. Finally, 200 μm diameter Ni/Au (30/120 nm) SDs were deposited by e-beam evaporation. The distance between SDs and ohmic contacts was 50 μm. Typical room temperature current–voltage (I–V) characteristics of Ni/Au SDs are plotted in Figure 6.13. As we can see, the saturation current decreases monotonously with increasing SiNx deposition time from 0 (the control sample) to 5 min which means that the effective Schottky barrier height increased owing to shallow defect reduction. Meanwhile, the series resistance and ideality factor also decreased when longer SiNx deposition times were used. Based on the thermionic emission model, the forward current density at V > 3kT/q has the form [11]: J = J S [exp(qV/nkT) − 1]

(6.1)

where the saturation current Js is expressed as: J S = A∗∗ T 2 exp(−qφ B /kT)

(6.2)

where A∗∗ is the effective Richardson constant with a theoretical value of 26.4 A cm−2 K−2 , φ B is the barrier height, and n is the ideality factor. Using Equations (6.1) and (6.2), we calculated the barrier height and ideality factor which are listed in Table 6.2. For the sample without the

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Figure 6.13 Room temperature forward and reverse I–V characteristics of Ni/Au SDs with different SiNx deposition time. Reproduced from Xie JQ et al., Applied Physics Letters 89(15): Art. No. 152108. Copyright (2006), with permission from the American Institute of Physics

SiNx nanonetwork, the barrier height is 0.76 eV. When the SiNx deposition time is increased, the barrier height increases from 0.84 (3 min SiNx ) to 1.13 eV (5 min SiNx ). At the same time, the ideality factor reduces from 1.3 (no SiNx ) to 1.06 (5 min SiNx ) which indicates that the SDs are nearly ideal in samples grown with the SiNx nanonetwork. Incidentally, this improved value is consistent with the work function of Ni (5.2 eV) and the electron affinity of GaN (4.1 eV). In the literature, a value of 1.099 eV (Ni) barrier height was achieved only after the GaN surface was treated with (NH4 )2 Sx [12], which is known to passivate the surface defects albeit temporarily. Our results indicate that the Ni Schottky barrier height is very sensitive to the crystalline quality and the excess current

Table 6.2 Properties of Ni/Au SDs on GaN with different SiNx nanonetwork deposition time SiNx (min) 0 3 4 5

n

 B(I−V) (eV)

 B(I VT) (eV)

1.3 1.13 1.08 1.06

0.76 0.84 0.98 1.13

— 0.77 0.91 1.05

A∗∗ (A cm−2 K−2 ) — 0.0003 2.07 2.66

Breakdown (V) 76 250 >210 >210

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is most likely related to the point defects already present in the film as opposed to being induced during processing as has been suggested [13]. Temperature dependent I–V measurements in the temperature range 300–500 K, which allowed determination of the activation energy, were also performed, and the results are listed in Table 6.2. The barrier heights calculated from the Richardson plot using Equation (6.2) are consistent with the room temperature values for each sample. However, the calculated effective Richardson constant is much smaller than the theoretically expected value which is commonly reported in the literature for GaN [2]. As we can see in Table 6.2, the effective Richardson constant is also related to the crystal quality, and obviously further work is required to shed light on the discrepancy between the measured and theoretical values endemic to GaN. To further evaluate the quality of SDs, the reverse breakdown voltages were measured and are shown in Figure 6.14. For voltages less than 210 V, we used a Keithly 4200 parameter analyzer. For voltages larger than 210 V, we used a high voltage power supply and continuously increased the bias manually until breakdown. A remarkable improvement of the breakdown was achieved with SiNx nanonetwork. As can be seen in Figure 6.14, the breakdown voltage is −76 V for the reference sample. When 3 min SiNx nanonetwork was used, it increased to −250 V.

Figure 6.14 Reverse breakdown for samples without and with SiNx nanonetwork. Inset shows semi-log plot of sample with 3 min SiNx nanonetwork. Reproduced from Xie JQ et al., Applied Physics Letters 89(15): Art. No. 152108. Copyright (2006), with permission from the American Institute of Physics

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This value is comparable with Schottky rectifiers fabricated on bulk [14] and thick HVPE [15] GaN in planar structures without a guard ring or surface passivation. In all the samples with different SiNx deposition times, the breakdown was observed for voltages larger than 210 V, with the 3 min one showing the best uniformity and lowest leakage current at −210 V. This is consistent with the reverse bias I–V characteristics shown in Figure 6.13. Considering the similar background doping, the leakage current at high reverse bias seems related to the thickness after coalescence. Since a shorter SiNx deposition allows coalescence with ease, the top layer after coalescence is much thicker for the 3 min SiNx deposition than for the 5 min one. However, the real mechanism of leakage current at high reverse bias still needs further investigation.

6.2.4

Deep Level Transition Spectrum

SDs were fabricated on Si doped GaN (∼500 nm, 5 × 1016 –2 × 1017 cm−3 ) using various GaN templates discussed in the previous section (see Figure 6.6) as well as one reference sample and one ELO sample. The comparison of DLTS spectra with rate window of 120 s−1 for all measured samples is shown in Figure 6.15. Since the trap concentration determined by DLTS is proportional to N D and Cmax , where N D is the

Figure 6.15 DLTS spectra measured for all samples under study. The pulse width is 10 ms and the rate window is 120 s−1 . Reproduced from Xie JQ et al., Applied Physics Letters 90(26): Art. No. 262112. Copyright (2007), with permission from the American Institute of Physics

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donor concentration and can be determined from a capacitance–voltage (C-V) profile and Cmax is the peak amplitude of the DLTS spectra corresponding to a particular trap, a stronger peak is indicative of a larger concentration of the particular trap for the same carrier concentration [16]. A significant reduction of deep levels was achieved by using SiNx nanonework compared with reference sample. Furthermore, for both traps A and B, the sample with 6 min SiNx has the lowest trap densities, even better than standard ELO samples. The concentrations of both traps A and B were the highest for the reference sample and the lowest for the sample with 6 min SiNx nanonetwork. Together with the XRD and TEM results in the previous section, the reduction of electron trap concentration for samples with SiNx network compared with the reference sample is indicative of the link between extended defects and DLTS active traps. Since SiNx nanonetwork reduced the nucleation sites and enlarged the grain size, the dislocation density related to the grain boundaries, and consequently electron traps and other recombination centers affected by dislocations, would be effectively reduced. Typically, there are two mechanisms by which TDs can affect the electron traps. First, TDs themselves can act as electron traps. It has been theoretically shown that the edge TDs in n-GaN can exist with a variety of core structures (full-core, opencore, Ga-vacancy, and N-vacancy) and induce several states in the band gap acting as electron traps [17,18]. The activation energies determined from Arrhenius plots for the deep levels in our samples suggest that trap A could be caused by full-core and N-vacancy edge dislocations and trap B by Ga- and N-vacancy edge dislocations. In addition, experimental results suggested that screw and mixed-type dislocations were also responsible for trap B [19]. Secondly, due to the strong stress field in the vicinity of dislocations, point defects could be captured by TDs to form deep levels [20]. Our studies [21], which demonstrated selective filling of trap A with the logarithmic capture mechanism for up to ∼20 ms filling pulse widths, supported this premise. The long filling pulse at which the saturation occurs indicates presence of a repulsive potential most probably due to close proximity of defects responsible for trap A along the dislocations. Regardless of the actual mechanism, the concentration of the electron traps affected by TDs would be reduced if the dislocations were significantly reduced. The dependence of trap B on the sample structure is similar to that of trap A. Our results therefore suggest that, for electron trap reduction, increasing the SiNx coverage (e.g. from 5 to 6 min deposition) in a single layer is a more effective approach than adding a second nanonetwork layer with the same SiNx coverage (double 5 min SiNx nanonetworks).

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6.3

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EPITAXIAL LATERAL OVERGROWTH OF GaN ON POROUS TiN

Similar to the GaN growth on the SiNx network discussed in the previous section, the GaN growth on the porous TiN can effectively reduce the defect density in GaN with a simple growth procedure. This porous TiN/GaN template is in situ generated in the MOCVD reactor by annealing the Ti/GaN structure in H2 and NH3 at a temperature of ∼1050 ◦ C. During the annealing, the Ti film on the GaN seed layer is transformed to TiN by the N radicals dissociated from NH3 . The surface porosity of TiN/GaN results from partial decomposition of the TiN and the underlying GaN seed layer. This annealing step is followed directly by GaN growth on the porous TiN where the surface pores act as growth windows for GaN nucleation. The GaN nucleate on the porous TiN as isolated islands which expand laterally and vertically during growth and finally lead to a coalescent GaN layer. During this growth process, the density of TDs is reduced by an order of magnitude compared with the reference GaN grown without the porous TiN. This defect reduction results from both the TD blockage by the TiN and the GaN ELO on the TiN. The improved quality of GaN on the porous TiN is also confirmed by its superior optical property. The porous TiN has also been employed in the growth of GaN by HVPE. Researchers in Hitachi Cable Ltd use the porous TiN interlayer to facilitate the separation of free-standing GaN template from sapphire substrate [22]. This easy separation benefits from the existence of dense voids at the GaN/porous TiN interface. Recently, this company announced that it has prototyped a 3 in. GaN substrate based on this technology.

6.3.1

Formation of Porous TiN

The porous TiN is formed by in situ annealing Ti/GaN structure in the MOCVD reactor. The GaN seed layer underneath the Ti film is grown on sapphire or SiC substrate by MOVPE using the low-temperature-grown nucleation layers. A thin Ti film (5–10 nm thick) is deposited on this seed layer by electron-beam evaporation. After the Ti deposition, the Ti/GaN structure is re-loaded into the MOCVD reactor and is thermally annealed in mixed hydrogen and ammonia at ∼1050 ◦ C. This annealing step transforms Ti/GaN into porous TiN/GaN, and is followed directly by GaN growth on the porous TiN. Although the GaN growth process

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Figure 6.16 SEM images of porous TiN/GaN templates (a) with low porosity and (b) with high porosity. Reproduced from Fu Y. et al., Journal of Applied Physics 99(3): Art. No. 033518. Copyright (2006), with permission from the American Institute of Physics

on the porous TiN requires one ex situ step (Ti deposition), it is still much simpler than the conventional ELO process which requires photolithographic and etching steps. The porosity of porous TiN can be controlled by adjusting the annealing temperature, the hydrogen content in the annealing ambient, and the annealing time. Increasing these values not only increases the density but also the size of surface pores. In addition, a thinner Ti film on the GaN seed layer always results in a high porosity of porous TiN if other parameters are kept constant. Figure 6.16(a) and (b) shows the SEM images of porous TiN surfaces with low porosity (T63) and high porosity (T68), respectively. Information on the GaN seed layer and annealing parameters are listed in Table 6.3. In Figure 6.16(a), the surface of T63 features small and isolated surface pores. These pores are Table 6.3 List of GaN templates and annealing time. For all Ti-covered GaN, annealing temperature is 1050 ◦ C, annealing gas ratio (NH3 :H2 ) is 1:1 for T63 and 1:3 for other samples

Sample

GaN template

Control-I

1 μm GaN/AlN buffer/SiC

Ti Annealing GaN grown XRD FWHM thickness time on TiN (0002),(10 1 2) (nm) (min) (μm) (arc min) —

—

3.5

4.0, 8.2

CVD481 CVD489

10 10

10 20

3 3

4.4, 5.7 5.5, 5.7

Control-II 0.7 μm GaN/GaN buffer/sapphire T63 T68

—

—

5

3.9, 7.6

20 20

30 60

13 7.5

4.4, 4.6 3.8, 5.4

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actually surface pinholes consisting of GaN(1101)facets. These surface pores have sizes ranging from tens of nanometers to 1–2 μm, and the density of pores is in the order of 106 cm−2 . The highly porous T68, as shown in Figure 6.16(b), has surface pores with larger sizes and higher density. Because many of these pores connect to each other, T68 features trenches and isolated GaN mesas. GaN inside these trenches almost decomposes completely during the enhanced annealing, exposing sapphire substrate at the bottom of these trenches. The porosity of porous TiN determines the GaN growth time required for surface coalescence and the efficacy of defect reduction in GaN, which will be discussed in detail later. For the porous TiN formed on GaN seed layer grown on SiC substrate, a similar relationship between surface porosity and annealing parameters is observed. This in situ formed TiN layer on GaN is of the form of textured polycrystals with their (111) planes parallel to the GaN (0001) plane [23]. The crystalline nature of the porous TiN is also confirmed by the selective area diffraction (SAD) pattern in our TEM analysis. The detailed mechanism for the formation of porosity on TiN/GaN is unclear. It is plausible that the pores are formed preferentially at the defective surface regions of the GaN seed layer, because these defective regions should be liable to thermally decompose due to perturbed Ga–N bonds. Such defective regions mainly include the intersection points of TDs with GaN surface. An inspection of the cross-sectional TEM images indicates that these surface pores do not necessarily correspond to TDs. Eaglesham et al. [24] reported that tiny holes form on the grain boundaries of TiN layer after thermal decomposition. In the TiN/GaN heterostructure, we expect a high density of grain boundaries in the TiN film due to the lattice mismatch between TiN and GaN. It is possible that such holes initiating on TiN grain boundaries finally develop into larger surface pores. The formation of pores on porous TiN/GaN may also associate with the surface modulation of GaN seed layer. For example, the surface pinholes on the seed layer (resulting from incomplete GaN coalescence) may be the origins of pores on porous TiN/GaN because thinner Ti is deposited on the inclined facets.

6.3.2

Growth of GaN on Porous TiN

High temperature nucleation of GaN on TiN is effectively suppressed because the Ga has a much higher sticking coefficient (near unity) [25]

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Figure 6.17 (a) Patterned Ti stripes on GaN template and (b) selective GaN growth on the patterned TiN/GaN template

on the GaN surface than on the TiN surface. Hence, it is unlikely for Ga adatoms to bond to the TiN surface in sufficient numbers and for a sufficiently long time to nucleate before they desorb into the vapor. Figure 6.17(a) shows a patterned Ti/GaN template fabricated by the photolithographic process. The width of GaN window stripe is ∼8 μm and the width of Ti mask stripe is ∼4 μm. This GaN surface features lots of pinholes due to incomplete surface coalescence. The patterned Ti/GaN is then loaded into the MOCVD reactor and annealed in H2 and NH3 at 1030 ◦ C for 10 min followed by GaN growth at 1030 ◦ C for 15 min. This mild annealing condition converts Ti stripes into TiN but does not generate additional porosity on the TiN/GaN. After 15 min GaN growth, the SEM image [Figure 6.17(b)] shows that no GaN nucleation happens on the TiN stripes. The observation strongly confirms the high selectivity of GaN nucleation on TiN and GaN. The morphology evolution of GaN grown on porous TiN T63 and T68 (Figure 6.16) is studied by SEM. The GaN growth is carried out at 1030 ◦ C and 200 Torr. As shown in Figure 6.18(a), isolated GaN islands are observed on the T63. These GaN nucleation islands have the shape of hexagonal islands with six (1101) facets and a flat (0001) top. It should be noted that the density of GaN nucleation islands is about an order of magnitude lower than that of the surface pores, suggesting only the large pores act as effective growth windows for GaN on the porous TiN under certain growth condition. This selective nucleation of GaN from large pores can be changed by lowering the GaN growth pressure, which results in a uniform GaN nucleation from most surface pores regardless of their sizes. The issue will be discussed later. With higher surface porosity, T68 has denser GaN nucleation islands which begin to coalesce after 1 h growth [Figure 6.18(b)]. The morphology of GaN layers grown for

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Figure 6.18 Morphology evolution of GaN grown on T63 (a) after 1 h growth, (c) after 3 h growth, (e) after 5 h growth; and on T68 (b) after 1 h growth, (d) after 3 h growth, (f) after 5 h growth

3 h on T63 and T68 are shown in Figure 6.18(c) and (d), respectively. At this stage, GaN grown on T63 coalesces only partially and has lots of large surface pinholes. In contrast, the GaN on T68 is fully coalescent with a flat surface. After GaN growth for 5 h [Figure 6.18(e) and (f)], both samples show a mirror-like surface but a few surface pinholes on T63 are still visible by SEM. From the discussion above, we note that the coalescence of GaN surface on porous TiN can be difficult because the (1101) facets of GaN

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nucleation islands have small lateral growth rate. Increasing the density of GaN nucleation islands can speed the coalescence of overgrown GaN. One approach to increase the density of GaN nucleation islands is using the highly porous TiN template. However, it results in a low efficacy of defect reduction. Another method to achieve high GaN nucleation density and enhance GaN surface coalescence, but without degrading the efficacy of defect reduction, is to nucleate GaN on porous TiN at reduced pressure. Figure 6.19(a) and (b) shows the porous TiN on GaN seed layer grown on 6H-SiC substrates. The structures and annealing parameters of these two samples are listed in Table 6.3. CVD489 has a porous TiN layer with higher porosity compared with CVD481, due to its longer annealing time. Although the TiN porosities of CVD489 and CVD481 are lower than that of T63, fully coalescent GaN overlayers with a thickness of only 3 μm are obtained on these two samples [as shown in Figure 6.19(c) and (d)]. The fast coalescence of GaN on CVD481 and CVD489 mainly results from the low pressure (76 Torr) used for GaN nucleation.

Figure 6.19 Surface of porous-TiN layers on (a) CVD481 and (b) CVD489; the surface of 3 μm thick GaN layers on the porous TiN of (c) CVD481 and (d) CVD489. Reproduced from Fu Y. et al., Journal of Applied Physics 99(3): Art. No. 033518. Copyright (2006), with permission from the American Institute of Physics

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The density of effective GaN nucleation islands increases with decreasing growth pressure. As will be shown later, although a lower GaN nucleation pressure generates dense GaN nucleation islands, the efficacy of TD reduction by porous TiN is not degraded.

6.3.3

Characterization by XRD

The FWHM of the XRD peak on GaN (1012)plane is an indicator of the total density of TDs. The XRD(1012) data of all samples are listed in Table 6.3. The (1012) FWHMs of GaN layers grown on porous TiN are smaller than those of their reference samples, indicating the effectiveness of porous TiN on defect reduction.

6.3.4

Characterization by TEM

In this section, we employ TEM to study the detailed mechanisms of defect reduction in GaN by porous TiN. The cross-sectional TEM images of GaN layers grown on T63, T68 and the reference sample are shown in Figure 6.20(a), (b) and (c), respectively. The TEM images are taken with a diffraction vector g = (1120) to visualize all types of TDs. The first thing to note is the abrupt decrease of TD density in GaN above the porous TiN layer, while no noticeable difference of TD density at the same thickness can be observed in the reference sample. This result confirms the effectiveness of TiN on the defect reduction in GaN, consistent with the XRD data. In the GaN grown on porous TiN, most TDs from the seed GaN layer are blocked by TiN penetrating into the upper layer. Based on TEM, the blockage of TDs by TiN is the main mechanism contributing to defect reduction in T63 and T68. A small portion of the TDs in the seed layer penetrate into the upper layer from the surface pores. During GaN lateral overgrowth on the TiN, some of the TDs penetrate into the upper layer bend and extend laterally. Such laterally extending TDs may encounter each other and get eliminated if the two reacting TDs have equal but opposite Burgers vectors. In T63, both the pores and the TiN between those pores have an average size of ∼1 μm, so that the TiN layer has a surface coverage of ∼50 %. Most TDs from the GaN seed layer are blocked by the TiN layer, while those penetrating through the pores tend to bend and/or cluster into dislocation arrays in the upper layer. The size of pores in T68 increases to 3–4 μm with a reduced TiN coverage,

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Figure 6.20 Cross-sectional TEM images of (a) T63, (b) T68 and (c) reference sample. Reproduced from Fu Y. et al., Applied Physics Letters 86(4): Art. No. 043108. Copyright (2005), with permission from the American Institute of Physics

because longer annealing time leads to increased TiN decomposition. In T68, higher density of TDs penetrates through TiN than in T63. An assessment of the amount of dislocation reduction can be made by directly counting the number of dislocations in plan-view TEM micrographs. The different efficacies of defect reduction in T63 and T68 are clearly revealed by Figure 6.21(a) and (b). The plan-view image in Figure 6.21(c) of the GaN reference sample shows a high density of edge/mixed dislocation arrays (∼1.5 × 109 cm−2 ) as marked by ‘e’, and

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Figure 6.21 Plan-view TEM images of (a) T63, (b) T68 and (c) reference sample. Reproduced from Fu Y. et al., Applied Physics Letters 86(4): Art. No. 043108. Copyright (2005), with permission from the American Institute of Physics

a much lower density of isolated screw dislocations (∼1.3 × 108 cm−2 ) as marked by ‘s’. The end-on screw dislocations show strong, characteristic contrast aligned with the imaging reflection vector, and the contrast from edge/mixed dislocation is much weaker due to smaller Burgers vectors and strain-relieving array configurations. The plan-view image of sample T63 shows a significantly (∼10×) lower density of edge/mixed dislocations (∼1.6 × 108 cm−2 ) and ∼2× reduction in screw dislocations (∼0.7 × 108 cm−2 ). In sample T68, we find even fewer edge dislocations (∼0.9 × 108 cm−2 ) and more screw dislocations (∼ 1.4 × 108 cm−2 ) than in sample T63. These plan-view observations suggest that the thin porous TiN can be effective in reducting the density of edge/mixed

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dislocations by an order of magnitude. However, the reduction efficacy of screw dislocation by porous TiN is small. Romanov et al. [26] suggested the low reduction efficacy of screw type dislocations in GaN lateral overgrowth is due to the fact that the bending of screw dislocations is not energetically favorable. Such an argument is experimentally supported by TEM analysis of lateral grown GaN [27]. For GaN grown on porous TiN with high porosity, an additional mechanism can result in the defect reduction. On highly porous porous TiN/GaN, GaN overgrowth can initiate from the sidewalls of large trenches and then proceed laterally, which induces the bending or inclination of TDs towards the center of trenches. Due to the rapid lateral growth rate of GaN, the trenches can be buried by GaN before refilling. This results in sub-surface voids. A typical sub-surface void is shown in Figure 6.22, with a round shape and a size of ∼0.3 μm. Some adjacent TDs were attracted to the sub-surface void and consolidated into a single TD which extended vertically. Let us look at the efficacy of TD reduction by porous TiN when using a lower GaN nucleation pressure (76 Torr). Plan-view images of CVD481 and the reference sample are shown in Figure 6.23. The reference GaN layer shows a high density of edge dislocation (∼3 × 109 cm−2 ) and a lower density of mixed and screw type dislocations (∼8 × 108 cm−2 ). The plan-view image of CVD481 shows a significantly lowered (∼15×) density of edge dislocations (∼2 × 108 cm−2 ). This comparison again

Figure 6.22 Consolidation of dislocations at sub-surface voids below porous TiN. Reproduced from Fu Y. et al., Journal of Applied Physics 99(3): Art. No. 033518. Copyright (2006), with permission from the American Institute of Physics

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Figure 6.23 Plan-view TEM images of (a) CVD481 and (b) reference sample. Reproduced from Fu Y. et al., Journal of Applied Physics 99(3): Art. No. 033518. Copyright (2006), with permission from the American Institute of Physics

indicates the effectiveness of porous TiN in reducing the edge dislocation density. The density of mixed and screw TDs are two times lower (∼3 × 108 cm−2 ) than that of the control sample. These results are similar to what was observed in sample T63. It should be noted that the using of low GaN nucleation pressure realizes not only a defect reduction efficacy of ∼15 but also a very fast surface coalescence rate. The GaN nucleation and the TD behavior on porous TiN are different at 200 Torr and 76 Torr. This comparison is demonstrated in Figure 6.24. The GaN nucleation on CVD481 is carried out at 76 Torr. The sample T70, which has similar TiN porosity as CVD481, is grown at 200 Torr for the whole process. These TEM images are taken under the diffraction vector g = (1101) to visualize all types of TDs. On sample T70, long voids present at the GaN/porous TiN interface resulting from the GaN lateral overgrowth on porous TiN. Most TDs in the GaN seed layer are terminated by these interfacial voids. The size of the effective growth windows is around 1–2 μm and the distance between the neighboring windows is ∼3 μm. This confirms that only the large pores can act as effective growth windows at the pressure of 200 Torr. It is worth noting that the locations of surface pores are not necessarily at the dislocated region on the surface of the GaN seed layer. For GaN nucleation on CVD481 at 76 Torr, most surface pores act as effective GaN growth windows. Small and short voids are observed at the interface corresponding to discontinuous TiN layer. Most TDs in the seed layer penetrate through the dense growth windows and extend into the upper

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Figure 6.24 Cross-sectional TEM image of (a) CVD481 and (b) T70. Reproduced from Fu Y. et al., Journal of Applied Physics 99(3): Art. No. 033518. Copyright (2006), with permission from the American Institute of Physics

layer. This behavior of TDs is significantly different from that in T70. The TDs penetrate through the porous TiN but cannot reach the top GaN surface because they react with each other strongly within a ∼0.5 μm thick region above the GaN/porous TiN interface. These TD reactions result from submicrometer-scale GaN ELO on porous TiN, and lead to the formation of dense TD half-loops. By comparison, the TDs reduction in T70 is mainly through the TD blockage by porous TiN. In Figure 6.24(a), lots of tiny and undeveloped GaN crystallites are observed in the long interfacial voids. These tiny GaN crystallites are grown from the surface pores with sub-micrometer size. The growth of these GaN crystallites is suppressed so they are not incorporated into the overgrown GaN. In Figure 6.24(b), a high density of nucleation islands, with micrometer-scale or submicrometer-scale sizes, effectively grow up and are incorporated into the upper GaN layer. This results in reduced dimensions of lateral growth and fast coalescence of overgrown GaN.

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The different nucleation behaviors at 200 and 76 Torr originate from the different partial pressures of hydrogen in the growth ambient. It is well known that small GaN crystallites are more liable to decompose than the large islands since the equilibrium vapor pressure around the former is higher than that around the latter. At temperature higher than 900 ◦ C, this GaN decomposition can be further enhanced by increasing the H2 pressures in the growth or annealing ambient [28]. In the case of GaN nucleation on porous TiN with a high H2 partial pressure, the preferential decomposition of small crystallites is enhanced which retards their growth. However, the decomposition of GaN (both the large islands and small crystallites) is suppressed by the low H2 partial pressure. In this case, most GaN islands and crystallites can grow up effectively and incorporate into the upper layer.

6.3.5

Characterization by PL

The low temperature PL spectra of GaN layers grown on T63, T68 and the reference GaN layer are shown in Figure 6.25. For all three samples, the dominant emission peaks are related to donor-bound exciton recombination (D0 X). The FWHMs of D0 X for sample T63, T68 and reference GaN are 2.4, 3.8, and 3.0 meV, respectively, again consistent

108

PL intensity

107

T63 106

Control 105

T68

104 3.45

3.50

3.55

Photon energy (eV)

Figure 6.25 Low temperature PL spectra of T63, T68 and reference sample. Reproduced from Y. Fu et al., J. Appl. Phys., 99(3), Art. no. 033518. Copyright (2006), with permission from the American Institute of Physics

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153

with the trend observed from X-ray and TEM analyses. Furthermore, the intensity of D0 X in T63 is about 30 times higher than that of the control sample. The narrower excitonic peak width, as well as the much stronger emission intensity, correlates with the reduced density of defects in GaN growth on porous TiN. Excess carrier dynamics in GaN grown on porous TiN has been characterized by TRPL at 300 K [10, 29]. The decay of PL intensity is fitted by two exponentials to yield a fast and a slow component of carrier lifetime. In GaN, complex mechanisms for trapping and detrapping play a significant role in the photogenerated carrier dynamics. Short carrier lifetimes indicate that high density of defects trap the carriers and prevent them from radiative recombination. In contrast, long carrier lifetimes indicate a low density of defects in GaN. Figure 6.26 shows the TRPL spectra of a GaN layer grown on porous TiN, a 200 μm thick free-standing HVPEgrown template, and a reference GaN sample grown by MOCVD. This porous TiN was generated by annealing for 15 min. The thickness of GaN grown on this porous TiN is approximately 6.5 μm. These decay times measured for GaN on porous TiN are even longer than those for the free-standing HVPE-grown template, indicating the superior optical quality of the GaN grown on porous TiN in this respect. This result agrees well with the TEM results.

PL intensity (arb. units)

15 min TiN free-standing

control

system response 0

1 2 Time delay (ns)

3

4

Figure 6.26 TRPL of GaN grown on porous TiN, reference sample and a freestanding GaN grown by HVPE. Reproduced from Fu Y. et al., Journal of Applied Physics 99(3): Art. No. 033518. Copyright (2006), with permission from the American Institute of Physics

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GROWTH OF GaN ON POROUS SiC

The reduction of defects in GaN grown on SiNx network and porous TiN benefits from the selective growth of GaN as well as the micrometer-scale GaN ELO on porous templates. The advantage of SiNx and porous TiN porous templates lies mostly on the fact that they can be formed conveniently in the MOCVD reactor, leading to a simplified growth procedure compared with conventional GaN ELO procedure. Recently, nanoscale porous substrates for GaN epitaxy have attracted much attention due to their potential as compliant substrates and as nano-patterned substrates for GaN heteroepitaxy and nano-ELO. The reported porous templates for GaN growth include: (i) porous GaN templates or porous SiC substrates fabricated by electrochemical etching in HF/H2 O under ultraviolet light excitation [30]; (ii) short columnar GaN or Si structures fabricated by utilizing a highly ordered anodic aluminum oxide (AAO) porous template [31]; and (iii) SiO2 or Si3 N4 masked substrates which are patterned with nano-scale openings by interferometric lithography [32]. Porous substrates have proved effective to reduce the TD density in SiGe and GaAs epilayers [33,34]. In these cases, the defect reduction benefits from the ‘compliance’ of porous substrates, which partially accommodates the mismatch between epilayer and substrates without generating misfit defects. The essence of compliant porous substrate for heteroepitaxy was introduced by Lo [35] in 1991, relying on an ultra-thin porous layer on top of a universal substrate. In a conventional heteroepitaxial bi-layer system, most of the misfit strain is taken by the epilayer because the substrate (several hundred micrometers) is much thicker than the epilayer (several micrometers). For the heteroepitaxy on the ‘compliable’ porous substrate, however, a large part of misfit strain can be partitioned to the porous layer due to its ultra-thin thickness as well as its small shear modulus. The small shear modulus of porous layer results from its porosity [36,37], and makes the porous layer ‘softer’ (less energy is required to generate defects in the porous layer). Due to the strain partition, fewer defects are generated in the epilayer. If a porous layer is thin and soft enough to partition most misfit strain, the epilayer can be free of misfit strain (or under very small strain) and no defect is generated in the epilayer. From the discussion above, there are two critical requirements for the porous substrate to work effectively as a compliant substrate. First, the porous layer must be very thin (comparable with the critical thickness of epilayer on a given substrate) to partition a significant part of misfit strain. Secondly, the porous layer must weakly attach to the universal substrate to perform free deformation. Proper porous

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substrates satisfying these two requirements are difficult to fabricate. Up to now, there has been no successful demonstration of defect reduction in GaN grown on compliant porous templates. Another proposed mechanism of TD reduction on the nanoporous substrates is nanoheteroepitaxy (NHE). The mechanism of TD reduction by NHE lies mostly on the rapid decay of misfit strain during the nanoscale growth of GaN on the porous substrates. It was predicted by Luryi and Suhir [38] that the TD reduction in epilayers grown on lattice-mismatched substrates can be achieved if the size of growth pads on the patterned substrates are reduced to 10–100 nm. In this case, the mismatch stress is decayed exponentially along the growth direction, resulting in a small misfit strain which can be relaxed by low density of misfit defects. The theory of NHE predicts that the mismatch defects can be eliminated if the lattice mismatch between the epilayer and substrate is 4.2 % (or less) and if the size of growth pattern is less than 40 nm. The effectiveness of NHE was demonstrated by the epitaxial growth of thick Ge on oxidized Si substrates [39]. It is possible that the porous substrates could reduce the defect density in GaN by acting as compliant substrates or facilitating the GaN NHE process. However, the only mechanism which has been observed to improve the GaN quality on porous substrate is the GaN nano-ELO process [31,40]. The main advantages of GaN nano-ELO on porous substrates include: (i) fast surface coalescence of overgrown GaN due to the nano-scale lateral growth length; (ii) most TDs can be confined inside a small thickness above the porous substrate; and (iii) foreign masks are not necessary and introduction of impurities into GaN can be reduced. Here we discuss our current work on GaN growth on nanoporous SiC substrate by MOVPE. SiC wafers are chosen to fabricate the porous substrate because (i) SiC has small lattice mismatch with GaN (∼3.4 %) and (ii) porosity on SiC can be realized by electrochemical etching steps. The structure of nanoporous SiC substrates is schematically shown in Figure 6.27. The average diameter of pores is around 15 nm and the average interpore distance is approximately 60 nm. The pore diameters can be enlarged by hydrogen polishing with polishing temperature and time being critical parameters determining the final size of the pores. The purpose of hydrogen etching is to remove the surface damage on the porous SiC introduced during mechanical polishing. However, special mechanical chemical polish procedures are available which produce seemingly scratch free surfaces. In that case, hydrogen polishing may not be imperative and the pore size can be dialed in during the photo-assisted electrochemical etching. These pores run through the entire thickness of

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Columnar region

Pore

~15 nm

~60 nm

220 µm

Planar region (a)

(b)

Figure 6.27 Schematic diagrams illustrating (a) the plan-view and (b) the crosssectional structure of porous SiC substrate

SiC substrate, completely eliminating the possibility of GaN growth inside the pores. It should be noted that every piece of porous SiC substrate has two regions, a porous area located in the center and a surrounding planar part on the edge which is not in contact with the etch due to the design of the etch vessel. This allows a comparative analysis of growth on the porous part and the standard part of SiC.

6.4.1

Fabrication of Porous SiC

The porous SiC is fabricated from commercial SiC substrate (4H or 6H) by electrochemical etching. An electrolyte is placed in contact with the SiC substrate. A bias is introduced across the electrolyte and the semiconductor materials causing a current to flow between the electrolyte and the semiconductor material. The SiC partially decomposes in this electrolyte and forms high density of pores with nano-scale diameter. This decomposition initiates from the carbon-face of SiC substrate because the carbon-face is less chemically inert compared with the silicon-face. These as-etched pores have a depth of approximately 200 μm but do not reach the silicon-face of SiC. To fabricate porous silicon-face SiC (silicon-face is used as the growth plane for GaN), SiC with thickness of tens of micrometers is polished away from the silicon-face to expose the surface pores. Two surface preparation procedures, hydrogen polishing and chemical mechanical polishing, have been applied to the as-polished silicon-face porous SiC to improve its surface perfection.

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157

GaN Growth on Hydrogen Polished Porous SiC

All the porous SiC substrates in this study received mechanical polishing to flatten the porous SiC surface. This mechanical polishing was carried out using diamond based slurries, where the abrasive size was successively reduced, eventually ending with a submicrometer slurry. The mechanically polished porous SiC features a dense network of scratch lines on its surface, which is visible to the naked eye. An atomic force microscopy (AFM) image of the mechanically polished porous SiC is shown in Figure 6.28(a). Most of the surface scratches have depths of 1–2 nm and widths ranging from 50 to 100 nm, with a few scratches much deeper (3–7 nm) and wider (100–300 nm). No pore is visible on this mechanically polished porous SiC probably because the sensitivity of the AFM tip to the nanopores is compromised by the rough surface of porous SiC. Lots of studies on GaN growth on planar SiC substrates have indicated that the SiC surface imperfection has a deleterious effect on the GaN quality [41–434]. In our laboratory, a thermal polishing performed in flowing hydrogen at temperatures above 1500 ◦ C has proved effective to remove the residual surface damage and produce an atomically flat surface on commercial planar SiC substrates. During the hydrogen polishing, the top defective SiC layer is removed by forming volatile hydrocarbon and silane with hydrogen radicals. Before the preliminary GaN growth on porous SiC, we used a moderate hydrogen polishing temperature (1200 ◦ C for 10 min) to prevent the possible destruction of pores. This

(a)

(b)

1 µm

1 µm

Figure 6.28 AFM images of porous SiC receiving (a) mechanical polishing and (b) mechanical polishing and low-temperature hydrogen polishing

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hydrogen polishing effectively reduces the density of scratches on porous SiC [Figure 6.28(b)]. However, there is still no pore visible by AFM. The growth of GaN (CVD1163) was performed in a vertical MOCVD reactor at 30 Torr. Trimethylgallium (TMG) and NH3 were used as Ga and N sources, respectively. The flow rates of TMG (118 μmol min−1 ) and NH3 (0.31 mol min−1 ) were kept constant during growth. An intermediate temperature (850 ◦ C) was used to promote GaN nucleation on porous SiC, because Ga atoms have low sticking coefficient on SiC. As shown in Figure 6.29(a), the GaN initiation layer has a nominal thickness of 100 nm, and consists of GaN nano-nuclei with a diameter around 45 nm. After deposition of the GaN initiation layer, the growth temperature was ramped to 1030 ◦ C and held at this temperature for 3 min to anneal the GaN initiation layer in H2 and NH3 . The purpose of annealing is to improve the crystalline coherence of the GaN initiation layer by preferentially decomposing defective GaN initiation islands. On the annealed surface of the initiation layer [Figure 6.29(b)], nano-scale GaN islands were transferred into a flat GaN layer indicating the occurrence

Figure 6.29 (a) As deposited GaN nucleation layer, (b) thermally annealed GaN nucleation layer and (c) a 3 μm thick GaN epilayer on porous SiC for CVD1163

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Table 6.4 Growth parameters and XRD data for CVD1163 and CVD1296 Sample

Hydrogen polishing

CVD1163

1200 ◦ C for 10 min

CVD1296

1500 ◦ C for 10 min

GaN nucleation layer

GaN epilayer

XRD FWHM (10 1 2) (arc min)

Temperature 850 ◦ C Pressure 30 Torr Thickness 100 nm Temperature 900 ◦ C Pressure 30 Torr Thickness 100 nm

1030 ◦ C 30 Torr 3 μm 1030 ◦ C 30 Torr 3 μm

On porous SiC 18 On planar SiC 17 On porous SiC 8.8 On planar SiC 9

of GaN evaporation and re-deposition. This annealing also generates scratches and high density of pits on the GaN initiation layer, which originate from the porous SiC surface damage. Finally, a 3 μm thick GaN epilayer was grown on the GaN initiation layer at 1030 ◦ C with a mirror-like surface [Figure 6.29(c)]. XRD is employed to characterize the crystalline quality of this GaN layer. As shown in Table 6.4, the the FWHMs of the XRD(1012) diffraction peak on GaN grown on planar and porous SiC regions is 17 and 18 arc min, respectively. These XRD data suggest that the GaN layers grown on porous SiC and planar SiC have similar quality and a high density of TDs present in both layers [45]. The AFM images (Figure 6.30) of these GaN layers reveal dense termination pits for atomic steps resulting from high density of screw type and mixed type TDs, consistent with the XRD result. However, the study of TD behavior in CVD1163 by TEM indicates that the utilizing of porous SiC substrate could be a promising approach

Figure 6.30 AFM images of CVD1163 (a) GaN grown on the porous SiC region and (b) GaN grown on the planar SiC region

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for GaN TD reduction. A cross-sectional TEM image is presented in Figure 6.31(a). The round and black dots in these images were introduced during TEM sample preparation. We note that the TDs in this sample are in the form of clusters, with the regions between the TD clusters nearly TD-free. In addition, a high density of interfacial voids present at the GaN/porous SiC interface. In Figure 6.31(b) a high resolution TEM image of the GaN/porous SiC interface is shown. The most remarkable outcome of TEM observation is the presence of nano-scale TD half-loops near the GaN/porous SiC interface, as marked by ‘o’ in Figure 6.31(b). The lateral dimension of these loops is around ∼50 nm, matching well with the distance of neighboring pads beside each pore. This indicates that the nano-ELO is performed by the neighboring GaN

Figure 6.31 CVD1163

(a) Large and (b) high resolution cross-sectional TEM images of

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nuclei extending over the pores between them. These TD loops not only annihilate TDs but also confine them inside a ∼50 nm thick region above the interface, suggesting the GaN growth on porous SiC is promising to achieve thin GaN layer with high quality. However, residual TDs of ∼ 5 × 108 cm−2 still exist in this GaN layer. A detailed inspection of Figure 6.31(b) reveals that most of the residual TDs are related to the surface imperfections of porous SiC. These surface imperfections include voids and impurities, as marked by ‘v’ and ‘c’. The density of surface impurities is much lower than that of the interfacial voids. These surface impurities might possibly be due to incomplete removal of foreign particles trapped inside the pores. TEM also reveals that the porous SiC surface is not flat but has damaged regions. Most interfacial voids at GaN/porous SiC are located on the damaged regions on the SiC surface. These surface imperfections not only interfere with GaN nucleation but also disturb the coherence of GaN nuclei nearby. As a result, TDs are generated to accommodate the enhanced twist or tilt between the affected GaN nuclei. The deleterious effect of scratches on the porous SiC surface is clarified by checking the surface of a partially coalescent GaN grown on porous SiC. As shown in Figure 6.32, this 1.8 μm thick GaN layer has wide surface voids and many hexagonal pinholes which locate exactly where the surface scratches are. A higher density of smaller scratches is found buried by flat GaN and not associated with surface pinholes. However, they still act as origins of TDs in GaN. Based on these results, the moderate hydrogen polishing was not

Figure 6.32

GaN growth is prevented by the scratches on porous SiC

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well suited to achieve a low-defect porous SiC surface. A more thorough removal of surface scratches on porous SiC is required. The hydrogen polishing of porous SiC performed at higher temperatures is tested to remove the surface damage on porous SiC more thoroughly. For this set of experiments, two pieces of porous SiC were polished in H2 at 1400 ◦ C and 1500 ◦ C, respectively, for 10 min. Before hydrogen polishing, the surfaces of these two porous SiC substrates featured dense scratches similar to that shown in Figure 6.28(a). On the porous SiC polished at 1400 ◦ C [Figure 6.33(a) and (b)], blurred but continuous terrace steps emerge which indicates an effective removal of ˚ corresponddefective SiC layer. The height of each terrace step is ∼15 A ing to the height of a 6H-SiC unit cell. However, the price paid for the high temperature polishing is increased pore diameter (∼30 nm) which

Figure 6.33 AFM images of porous SiC polished in hydrogen at (a), (b) 1400 ◦ C and (c), (d) 1500 ◦ C (scale bar in μm unit)

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is almost double the original diameter (∼15 nm). A few discontinuous, deep scratches with depths as much as 15 nm present on the porous SiC after the hydrogen polishing. Such deep scratches were not observed on the mechanically polished porous SiC or the porous SiC polished in hydrogen at lower temperatures, indicating that the deep scratches are sub-surface defects and can only be exposed by high temperature polishing. Figure 6.33(c) and (d) shows the surface of porous SiC polished at 1500 ◦ C for 10 min. More straight and regular terrace steps have been produced with pore diameter still around 30 nm. On the porous SiC polished in hydrogen at 1500 ◦ C for 10 min, a 3 μm GaN epilayer (CVD1190) is grown after the deposition of a 100 nm thick GaN nucleation layer. Figure 6.34 shows the surface evolution of GaN on this porous SiC. In Figure 6.34(a) and (b), the GaN nuclei aligned preferentially along the terrace edge of porous SiC because more dangling bonds are available at the step edges. Such GaN nucleation behavior is similar to that on planar SiC, suggesting the pores do not change the diffusion length of Ga adatoms on porous SiC (the Ga adatoms diffuse on

Figure 6.34 Surface evolution of GaN (CVD1190) grown on the porous SiC polished in hydrogen at 1500 ◦ C (a) after 1 min deposition of GaN nucleation layer, (b) after 4 min deposition of GaN nucleation layer, (c) with a 400 nm thick epilayer on the nucleation layer, (d) fully coalescent GaN epilayer

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the growth surface mainly in vapor). A coalescent GaN layer is achieved after 3 μm growth of epilayer. This GaN has a reduced FWHM of XRD diffraction peak on the (1012) plane, as listed in Table 6.4. However, AFM and TEM analyses indicate the density of TDs is still around 5 × 108 cm−2 .

6.4.3

GaN Growth on Chemical Mechanical Polished Porous SiC

Although the hydrogen polishing performed at 1500 ◦ C can effectively remove damage on the surface of porous SiC, this high temperature polishing results in severe surface decomposition of porous SiC, destroys pore structure, enlarges the pore size and may diminish the usefulness of porous SiC substrate. In this vein, the chemical mechanical polishing (CMP) procedure is employed to achieve surface perfection of porous SiC. This CMP of porous SiC is performed by NovaSic, utilizing the combination of chemical oxidation followed by mechanical abrasion. The continuous and simultaneous friction and chemical attack leads to material removal resulting in extremely planar surfaces with zero or near zero sub-surface damage to the extent that can be determined by surface topology. As shown in Figure 6.35, the CMP treated porous SiC surface shows clear semi-ordered surface pores without any observable surface damage. The pore diameter is approximately 15 nm with an interpore distance of 60 nm.

Figure 6.35

AFM images of porous SiC receiving CMP

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Table 6.5 Growth parameters and XRD results of CVD1456 and CVD1489 grown on CMP porous SiC Sample

Hydrogen polishing

GaN nucleation layer

GaN epilayer

XRD FWHM (10 1 2) (arc min)

CVD1456

—

Temperature 930 ◦ C Pressure 30 Torr Thickness 100 nm

1030 ◦ C 76 Torr 3 μm

On porous SiC 6 On planar SiC 8.4

CVD1489

—

Temperature 960 ◦ C Pressure 200 Torr Thickness 600 nm

1030 ◦ C 76 Torr 3 μm

On porous SiC 4.2 On planar SiC 3.6

Two GaN layers are grown on the CMP porous SiC substrates with different nucleation parameters, as listed in Table 6.5. Before growth, the CMP porous SiC substrates are cleaned with standard RCA procedure followed by HF-dip to remove the surface oxide. For CVD1456, a 100 nm thick GaN nucleation layer is deposited at 930 ◦ C and 30 Torr, followed by a 3 μm thick GaN epilayer grown at 76 Torr and 1030 ◦ C. For CVD1489, a 600 nm thick GaN nucleation layer is deposited at 960 ◦ C and 200 Torr, followed by a 3 μm thick GaN epilayer grown with the same parameters as those of CVD1456. For CVD1456, the XRD (1012) diffraction peak of the GaN grown on the porous SiC region has a FWHM of 6 arc min, while the GaN grown on planar SiC has a FWHM of 8.4 arc min. The XRD data clearly indicate an improved GaN quality is achieved on the porous SiC. This quality improvement is further confirmed by AFM measurement, as shown in Figure 6.36. The pit density of step termination in GaN grown on porous SiC is approximately 15 times lower than that on planar SiC. The change of nucleation condition from growth of CVD1456 to CVD1489 is based on the GaN growth optimization on the standard planar SiC substrates. This optimization indicates a higher nucleation pressure and nucleation temperature lead to improved GaN quality. For CVD1489, the XRD (1012)diffraction peak of the GaN grown on the porous SiC region and planar SiC region has a FWHM of 4.2 and 3.6 arc min, respectively. These XRD FWHM values are smaller than those of CVD1456, indicating the change of GaN nucleation parameters improves the quality of GaN grown on porous SiC. For CVD1489, however, the XRD data suggest the GaN grown on the porous region does not show an advantage over the GaN grown on the planar region. The TD densities counted on the plan-view TEM images (Figure 6.37) support the XRD result. The TD density of GaN grown on the planar

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Figure 6.36 AFM images of CVD1456 on (a) the porous SiC region and (b) the planar SiC region

SiC region is 9.5 × 107 cm−2 , and the TD density in GaN grown on the porous SiC region is 1.5 × 108 cm−2 . At the time of writing, the cross-sectional TEM characterization of GaN grown on CMP porous SiC is still in progress. Currently we have no solid evidence why for CVD1489, the GaN grown on the porous SiC region does not show an advantage over the GaN grown on the planar SiC region. However, it is possible that the GaN nucleation scheme used for CVD1489 uses only a very small portion of surface pores due to the low density of GaN islands nucleating on SiC at high temperature and high pressure. A consensus on improving the quality of GaN epilayer lies at decreasing the GaN nucleation density (increasing the grain size)

Figure 6.37 Plan-view TEM images of CVD1489 on (a) the porous SiC region and (b) the planar SiC region

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to reduce the defective grain boundaries regions. However, it seems that the full advantage of porous SiC substrate can be taken only with high density and small size of nucleation islands (which makes the nano-ELO process possible). This nucleation scheme can be realized by lowering the nucleation temperature, as we did for CVD1189. However, the lower nucleation temperature results in inferior quality of GaN nucleation islands. To resolve this dilemma, one possible solution is to employ growth technology similar to atomic layer epitaxy, which could obtain decent crystal quality of GaN at low growth temperature. In our MOCVD, the precise control of precursor pulse for one or two monolayers at each circle is possible. Furthermore, lowering the GaN nucleation rate at low nucleation temperature may also be helpful to achieve high density and high quality of GaN nucleation islands on porous SiC at the same time.

ACKNOWLEDGEMENTS This work was supported by the DURINT program administered by the Office of Naval Research (Dr C. Wood) under Grant N00014-0110715.

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7 HVPE Growth of GaN on Porous SiC Substrates M. Mynbaeva, D. Tsvetkov and K. Mynbaev Ioffe Physico-Technical Institute, St Petersburg 194021, Russia

7.1

INTRODUCTION

In recent years, new methods of substrate engineering have been developed to lower defect density in heteroepitaxial layers. The concept of these methods is based on mismatch strain management in the epitaxial film/substrate system, in an attempt to reduce introduction of defects, which result from mismatch strain relaxation. For example, compliant substrates are viewed as an approach for controlling mismatch strain by sharing it between the substrate and the epitaxial film. The role of the compliant substrate is to reduce the strain in the epitaxial layer via partitioning the strain in the layer with a very thin substrate [1]. Another approach is nanoheteroepitaxy that exploits three-dimensional stress relief mechanisms, which are available to nanoscale patterned substrates, to reduce the strain energy in lattice-mismatched epitaxial layers. In addition, the local availability of a free surface at the edges of the nano-size islands modifies the defect formation and propagation kinetics and can, in some cases, confine the defects to a local region at the initial interface in the epitaxial layer [2,3]. Both approaches of stress controlling Porous Silicon Carbide and Gallium Nitride: Epitaxy, Catalysis, and Biotechnology Applications Edited by Randall M. Feenstra and Colin E.C. Wood  C 2008 John Wiley & Sons, Ltd

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in heteroepitaxial layer/substrate system were utilized in the growth on porous substrates. For example, the compliant substrate approach was implemented for growing high-quality Ge0.2 Si0.8 heteroepitaxial layers on porous silicon (PS) [4], while the nanoheteroepitaxy-like approach was employed when porous GaN substrates with high surface porosity were used for improved AlGaN growth [5]. In this chapter, various aspects of the growth of GaN films on porous SiC (PSC) by hydride vapor phase epitaxy (HVPE) are discussed (here, we understand that a porous SiC substrate is a SiC wafer with a several micrometer-thick porous layer in it). First, the preparation of PSC substrates under various conditions, and the properties of the PSC fabricated are described. Next, mechanisms of formation of different types of PSC structure and the stability of porous substrates under thermal and plasma treatment are considered. The final part of the chapter treats GaN epitaxial growth, film properties, and explanations for improved epitaxy provided by porous substrates.

7.2

PSC SUBSTRATE FABRICATION AND PROPERTIES

PSC layers were fabricated by surface anodization of commercially available 2 in. diameter n-type conductivity 6H-SiC wafers. The starting wafers had resistivities in the range 0.05–0.1  cm. PSC was fabricated in an electrochemical cell, which allowed anodization of up to 30 cm−2 SiC wafers. Anodization did not require metallization (normally employed as back contacts or surface mask) to avoid contamination effects on epitaxial growth. The surface and the bulk PSC crystal quality was studied by reflection high-energy electron diffraction (RHEED) and X-ray diffraction (XRD). Surface chemical compositions were determined with Auger electron spectroscopy (AES) and secondary-ion mass spectrometry (SIMS). Atomic force microscopy (AFM), transmission and scanning electron microscopy (TEM and SEM) were used to monitor PSC morphology and structure. PSC samples were prepared in galvanostatic regime at current density (j) = 4–120 mA cm−2 in dilute hydrofluoric acid without illumination. PSC samples prepared at j ∼ 4–80 mA cm−2 remained stoichiometric (Si/C ratio = 1), so below we refer to this as SPSC.

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Figure 7.1 shows cleaved edge micrographs of the three types of SPSC morphology, for different j regimes:1

r Figure 7.1(a) shows typical uniform ‘nanoporous’ structure with r r

pore diameters d p ∼30–40 nm for anodization currents in the range 4–10 mA cm−2 . Figure 7.1(e) shows uniform ‘microporous’ structure with pore diameters d p ∼100–150 nm obtained at j = 80 mA cm−2 . Figure 7.1(c) shows mixed porous structure, formed under intermediate anodization currents (16–30 mA cm−2 ).

XRD and RHEED showed all three SPSC types to be single crystalline SiC [see insets in Figure 7.1(b) and (d), respectively]. The broadening of RHEED Kikuchi lines showed some degradation of surfaces prepared with j > 80 mA cm−2 . SEM and AFM revealed uniformly distributed shallow flat-bottom pits in nanoporous PSC [Figure 7.1(b)]. Such pits are ascribed to pore nucleation sites or ‘nucleation pits’. In addition, surfaces with micro-porous and mixed-type structures had nonuniformly distributed openings, somewhat larger than nucleation pits [Figure 7.1(d) and (f)]. Possible genesis of these openings is discussed below.

7.2.1

Formation of Various Types of SPSC Structure

From the three types of SPSC discussed above, the first one forms by directed growth of nanopores from the surface into the sample bulk. As to micropores, they nucleate at the interface between the already formed nanoporous layer and nonporous SiC, and grow into the bulk of the nanoporous layer towards the surface of the wafer. This is illustrated in Figure 7.2, which shows the development of microporosity in nanoporous PSC layers. The process starts from the micropore nuclei, appearing at the nanoporous SiC/SiC interface [Figure 7.2(a)], and its progress results in the formation of a mixed-type [Figure 7.2(b) and (c)] or uniform microporous structure [Figure 7.2(d)]. When a micropore approaches the surface, an opening is formed [Figure 7.2(e)], which 1 Note

that when designating the fabricated porous structures in this way, we do not follow classification recommended for structural characterization of porous inorganic materials by the International Union of Pure and Applied Chemistry (IUPAC) [6], but simply proceed from the actual size of the pores. Classification of porous structures fabricated in SiC cannot yet be considered as established [7,8].

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Figure 7.1 TEM (a), SEM (b–e) and AFM (f) images of PSC samples: cross-sectional images of the samples prepared at j = 8 mA cm−2 (a), j = 30 mA cm−2 (c), and (e) j = 80 mA cm−2 , present nanoporous, mixed- and microporous PSC structures, respectively; (b, d) are plan-view images of nanoporous and microporous SiC. The insets in (b) and (d) are the RHEED patterns obtained from the corresponding samples, which illustrate changes in surface perfection; (f) is an AFM image of the surface opening marked by an arrow in (d). (a) Reproduced from M.G. Mynbaeva et al., Phys. Sol. State, 47, 1630–1636. Copyright (2005), with permission from Elsevier

explains the peculiarity of the surface morphology of the PSC samples with mixed-type and microporous structure, discussed above. Therefore, there are good reasons to believe that the nanoporous SiC structure is a ‘primary’ one, i.e. formed directly by local anodic currents, while the microporous structure is a ‘secondary’ one, in that it results

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Figure 7.2 SEM cross-sectional images of PSC fabricated at: 10 mA cm−2 (a), 16 mA cm−2 (b), 30 mA cm−2 (c), and 80 mA cm−2 (d–f)

from evolution of nanoporous structure. If the forming nanoporous SiC/SiC structure is considered as a two-phase system of a matrix of crystalline SiC and surrounding pores, the transformation of nanoporous into microporous material can be described by coarsening (Ostwald ripening) [9,10]. In general, the coarsening phenomenon defines the structural evolution at meso- and nano scales, when larger objects grow at the expense of smaller ones to reduce the interfacial area, thence the total free energy of the two-phase system. The interphase boundaries and related surface tensions/interfacial energy play an important role in the initiation and the coarsening process. Thus micropores can be formed from void

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Figure 7.3

SEM images of macropores formed in SiC

coarsening, starting at nanoporous SiC/SiC interfaces, reducing the high net interface free energy of nanoporous SiC. Figure 7.2(a–e) demonstrates that micropore formation increases with j. Also the shape and propagation direction of micropores near the free surface differ from those deeper into the PSC layer [Figure 7.2(d) and (e)]. This further supports that porous structure evolution is governed by the drive to reduce aggregated interphase surface tension. The SiC resistivity also strongly affects pore evolution, and the resulting porous structure. Figures 7.2(f) and 7.3(a) and (b) show the evolution of microporous into macroporous SiC (‘macroporous’ notation is in accordance with that accepted for PS). The experimental conditions in this case were the same as for the sample whose image is presented in Figure 7.2(d), but the starting material in the case had a higher resistivity. Similar to the already discussed case of microporous structure formation, one can see pores with lower dimension at the upper part of the cleaved edge presented in Figures 7.2(f) and 7.3(a), and pores with bigger size can be seen along the PSC/SiC interface. It appeared that the cross-section of macropores had a hexagonal form, which is especially clearly seen in Figure 7.3(b), where a (0001) plane, which is normal to the cleaved edge, is seen. The faceting phenomenon supports the idea that the PSC structure evolution does originate in the coarsening process. In particular, it is known that a microstructure resulting from the coarsening of a two-phase system should be determined by the elastic property of the host matrix, as the size of incorporated objects of the second phase increases [11,12]. Yet another mechanism, which should be taken into consideration, is that if the pores (voids) grow sufficiently large (along with decreasing of the interpore distance) the fracturing of the surface of the voids may be ¨ a¨ et al. [13] and references therein). driven by their interaction (see Seppal

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Figure 7.4 HRTEM cross-sectional image taken near the surface of SiC sample prepared at j = 8 mA cm−2 . Sub-surface region of the porous structure contains only remaining spherical pores. The cross-sectional image in the inset shows the nucleation pit situated in the dense layer. Reproduced from M.G. Mynbaeva et al., Phys. Sol. State, 47, 1630–1636. Copyright (2005), with permission from Elsevier

7.2.2

Dense Layer

The specific feature of the fabricated SPSC layers was the presence of a dense surface layer, which contained no pore channels. The existence of the dense layer means that the porous structure is buried in the subsurface layer at a depth of a few tens of nanometers, so we actually deal with a closed porosity. Figure 7.4 presents a high-resolution TEM (HRTEM) cross-sectional image taken near the surface of a nanoporous SiC sample. The monatomic layers distinguishable in this image indicate high structural perfection of the dense layer. There are strong grounds for believing that the dense layer formation occurs at the stage of the development of the primary nanoporous structure, and can be explained with the classical coarsening theory as well. The driving force of this trend is described by the Gibbs–Thomson effect, which alters the vacancy concentration at pore–matrix interfaces depending on the curvature of the interface. This dependence results in the gradient of chemical potential. As a result, vacancies diffuse from regions of higher curvature to regions of lower curvature and large pores grow at the expense of smaller ones, so the latter eventually disappear [10]. Thus, if we consider the free surface of the porous structure as the ‘largest pore’ with an infinite radius, formation of the dense layer proceeds through ‘shrinking’ of pore channels within subsurface region via vacancy diffusion mechanism. As a result, very few

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nanoscaled pores with spherical shape and nucleation pits are left within the region as shown in the inset in Figure 7.4.

7.2.3

Monitoring of Anodization Process

Computer control over the parameters of the electrochemical cell allows one to predict the type of the forming porous structure during anodization. Figure 7.5 presents output voltage (U) vs anodization duration (t) curves. 7.2.3.1

Stoichiometric PSC Formation Regimes

Confronting the recorded U(t) curves and SEM images of the porous structure formed, the following can be concluded: formation of uniform nanoporous structure corresponds to a steep increase of U(t) during

Figure 7.5 U(t) dependence obtained during anodization runs performed at j = 8 mA cm−2 (a), j = 30 mA cm−2 (b), j = 80 mA cm−2 (c), and j = 120 mA cm−2 (d)

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anodization. This part of the curve follows the initial peak, which is associated with the process of polarization of the semiconductor electrode [14]. In Figure 7.5(a) this is illustrated by the U(t) dependence for anodization current density 8 mA cm−2 . Formation of the mixed-type and uniform microporous structure corresponds to the flat part of the U(t) curve. In Figure 7.5(b) and (c) this is illustrated by the U(t) curve for anodization current density 30 and 80 mA cm−2 , respectively. Interestingly, the shape of the U(t) curves presented in Figure 7.5(a–c) appeared to be similar to that of the chronopotentiometry and chronoamperometry curves recorded for the Si/HF system, as presented in Dubin [15] and Smith and Collins [16]. This confirms the earlier suggestion that electrolytic behavior of silicon carbide should be quite similar to that of silicon [17,18].

7.2.3.2

Nonstoichiometric PSC Formation Regimes

Under anodization current density higher than 80 mA cm−2 , the character of U(t) evolution in general looks similar to that observed for microporous structure formation regimes. The U value shows rapid decay after the polarization stage, and after that is stabilized within a certain range. The main difference is that within this range the pronounced voltage oscillations are observed. This is illustrated in Figure 7.5(d), which presents the U(t) curve recorded when SiC was anodized at 120 mA cm−2 . Under these regimes nonstoichiometric PSC is formed. The oscillatory anodization voltage (current) behavior during electrochemical treatment of a semiconductor is a well-known phenomenon. For Si, the oscillations are observed under electropolishing regimes, which require high currents (voltages), as well as under moderate regimes, when electropolishing and formation of PS proceed simultaneously. In the latter case, the resulting structure is generally porous in nature but pore diameters rapidly increase as the electropolishing regime is approached [16]. Similar features of porous structure obtained under regimes with current oscillations are observed in SiC. The SEM images of the surface and cross-section of the PSC sample prepared at j = 120 mA cm−2 are shown in Figure 7.6(a) and (b). It can be seen that the anodized surface had a developed morphology in the form of individual crystalline fibers [Figure 7.6(a)]. [It is worthy of being noted that the PSC morphology presented in Figure 7.6(a) is very similar to that reported for anodized SiC by Konstantinov et al. [18] and later by Lagemaat et al. [19]]. The bulk structure of the PSC layer [Figure 7.6(b)] was characterized by a

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Figure 7.6 SEM images of the PSC sample prepared at j = 120 mA cm−2 : (a) is a plan-view image showing fiber-like morphology of the anodized surface; the inset is a RHEED pattern obtained from the corresponding sample surface; (b) is crosssectional image taken within the PSC bulk; (c) and (d) are HRTEM images obtained in the vicinity of the pore wall of the samples anodized at j = 120 mA cm−2 and at j = 8 mA cm−2 , respectively. (a) and (b) Reproduced from M.G. Mynbaeva et al., Phys. Sol. State, 47, 1630–1636. Copyright (2005), with permission from Elsevier

considerable decrease in lateral dimension of SiC crystallites with intercrystallite spacing increasing as compared with that of both nanoand microporous SiC structures [Figure 7.1(a) and (e)], obtained under lower anodization currents. Thus, taking into account that SiC anodization conditions considered in this section lie in between electropolishing regimes with HF-based electrolyte as established by Brander and Boughey [17] and those for SPSC formation, it can be suggested that the applied conditions corresponded to a certain transition region, where formation of porous structure and orthodox SiC etching coexisted. Yet another characteristic feature of the PSC fabricated at high anodization currents was the existence of a disordered phase at the

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surface and within the bulk of porous structures. According to AES and RHEED data, the material obtained under these conditions loses crystalline perfection and stoichiometry of the SiC compound. For example, anodization at 120 mA cm−2 led to the formation of PSC layers with high carbon content (C=74%, Si=26%). This finding was confirmed by RHEED studies: the insert in Figure 7.6(a) shows an electronogram of the surface of the fabricated PSC sample. In contrast to the SPSC, the RHEED pattern, along with the point reflexes from the crystalline SiC planes, contained a number of half-circles, which corresponded to the reflexes from polycrystalline carbon, existing in the graphite form. In addition, HRTEM study clearly showed the presence of the disordered phase at the pore walls [Figure 7.6(c)] within the bulk of the PSC sample. In contrast, HRTEM examination of the pore walls of the SPSC revealed that the structure remained monocrystalline [Figure 7.6(d)]. In the latter case, the presence of monatomic layers in the image indicates a high perfection of crystalline material in the vicinity of the pore wall. Note that the existence of the disordered phase, which was identified as carbon-rich, was reported also for the samples anodized under much lower currents, when ethanol-containing HF-based electrolytes were used [20–23]. To provide an explanation for the loss of stoichiometry in PSC prepared under high anodization currents, we can turn to the chemical aspect of anodization of silicon. In particular, under the electropolishing regime silicon can be oxidized directly to Si(IV), forming a silicone dioxide, which is chemically dissolved in fluoride-containing electrolyte. The transition from polishing to moderate current regimes is accompanied by the change of the valence of the electrochemical reactions and dissolution of Si occurs through consecutive reactions with formation of intermediate reaction products [16,24–26]. Following the fundamentals of Si electrochemical behavior, it can be assumed that deviation from stoichiometry, observed in forming PSC, originates from the contribution of the simultaneous dissolution process, which resulted in formation of carbonaceous intermediates. Considering the influence of applied conditions on stoichiometry deviation in SiC under electrochemical treatment, let us also present some data related to silicon carbide anodization in the potentiostatic regime. The treatment was performed using HF-based electrolyte under conditions where anodic current density values are 4–10 mA cm−2 . In spite of the value of the current being comparable with that used for the formation of nanoporous PSC structures, SiC anodization under potentiostatic conditions results in built-in adherent film (“anodic film” in the

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Figure 7.7 SEM images showing the honeycomb structure of the anodic film obtained as a result of SiC anodization in potentiostatic regime (a). (b) shows inhomogeneity of the structure of anodic film, related to a structural defect in the SiC specimen

following). The anodic film growth proceeds much more slowly than PSC formation, as the film reached the thickness of 0.3–0.5 μm in 60–90 min. SEM studies show that the morphology of the anodic film is essentially different from that of all types of PSC structures considered above. Figure 7.7 shows the images of the anodic film formed as a result of SiC treatment in the potentiostatic regime. The films have a honeycomb structure with pronounced inhomogeneity caused by the existence of structural defects in the SiC specimen, as illustrated in Figure 7.7(b). Such ‘defect decoration’ was never observed, if any type of PSC structure was formed. An elemental analysis of the anodic films performed both with AES and SEM energy-dispersive X-ray spectrometry (EDXS) showed that the films had 11 at.% average deviation from the starting material stoichiometry towards carbon enrichment, and contained 6 at.% of oxygen and 9 at.% of fluorine. Also, current–voltage (I–V) measurements of the specimen/electrolyte junction (performed under illumination) before and after the treatment revealed enhancement of photoresponse from the SiC surface covered with the anodic film as compared with the starting material. By analogy with photosensitive anodic films appearing over the surface of silicon during its treatment in fluorine-containing electrolytes, it can be suggested that the built-in film represents a mixed phase of electrochemical reaction products or results from the anodized surface amorphization [27,28]. In its turn, this indicates that under potentiostatic conditions the chemical processes at the SiC/HF junction are predominant. The results obtained emphasize that not every porous-like phase formed as a result of SiC anodization can be considered as PSC.

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7.2.4

183

Vacancy Model of Primary Pore Formation

On the basis of experimental observations of the formation of the three types of structure of SPSC, it has been suggested that the evolution of pores within SiC bulk proceeds through three stages: (i) formation of pore nucleation centers on the anodized surface (nucleation pits); (ii) formation of primary pores (nanopores); and (iii) development of largesize pores (micropores) within the bulk of the already existing porous structure. This is consistent with classical concepts of the development of diffusion porosity in solids in the way that the latter involves a similar three stages: pore nucleation; pore growth; and porous structure coarsening, resulting in enlargement of pores. These stages of porous structure development are associated with directed vacancy fluxes in local regions of the material [29]. This correlation allows for suggesting that primary porosity in SiC has a vacancy genesis, i.e. occurs through a vacancy diffusion mechanism. According to the majority of models of the formation of porous structure in semiconductors, this process is determined by electrochemical processes, which occur when the electrical current flow is localized, and the electric field is enhanced, at the bottom of the pores formed [30–32]. The analysis of the contributions from the physical processes to the formation of a porous structure in semiconductors is reduced primarily to the consideration of the excitation of a charge subsystem (hole generation) in the material [30,33,34]. However, it can be expected that similar local disturbances will also excite a subsystem of intrinsic defects, because these conditions necessarily give rise to temperature gradients and, consequently, thermoelastic stresses in the crystal. In turn, this should lead to a redistribution of the already existing vacancies and to the generation of nonequilibrium vacancies. Therefore, the possibility of the aforementioned physical processes occurring in regions adjacent to the channels of growing pores in the crystal matrix calls for separate investigation. Let us consider the growth of an individual pore and the contribution only from the vacancy diffusion mechanism. We will restrict our consideration to analyzing the redistribution of already existing vacancies without indicating the sublattice in which this redistribution occurs, because it is known that, in binary compounds, the deviation of the vacancy distribution from equilibrium in one sublattice necessarily brings about vacancy redistribution in the other [35]. It is assumed that, at the initial instant of time, the pore channel has a radius R0 = 0.1 nm, and, then, it grows in the radial and longitudinal directions at an identical rate. The localization of the current flow on the pore walls will give rise to a

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temperature gradient T(r) and, consequently, to a stress σ (r) (r is the distance to the pore center). Since the electrical resistivity has a maximum value in the region of the pore bottom [31], the heat release in this region is also maximum. This circumstance allows for introducing a point heat source into the model. The heat transfer is described by the thermal conduction equation. This equation in polar coordinates, which are convenient for analyzing the radial growth of an individual pore, has the following form: ρC p ∂ T(r, t) = T − r T −2 [T(r ) − T0 ] χ ∂t

(7.1)

Here ρ is the density, χ is the thermal conductivity coefficient, C p is the specific heat capacity, and rT is the characteristic range of variation in the temperature. The boundary conditions are specified at infinity and for the boundary of the pore of radius R in the form: T|r =∞ = T0

 dT  W =−χ 2π Rh dr r =R

(7.2)

where W is the direct-current power (in the experiments under consideration, U = 100 V and I = 10−11 A is the electric current in one channel at a current density j = 10−2 A cm−2 and at a pore density of 109 cm−2 ) and h is the thickness of the region in which the electrical resistivity is maximum. At the initial instant of time, we have T = T0 . In the boundary conditions in Equation (7.2), the first equality is introduced for an individual pore for which the temperature at a large distance remains unchanged and equal to the initial temperature T0 . The second equality relates the heat flux through the pore boundary to the source power. The radially symmetric solution to Equation (7.1) has the form: T(r ) = T0 +

C0 K0 (r/r T ) RK1 (R/r T )

(7.3)

where C0 = Wr T /χ 2π h and K0 (x) and K1 (x) are the zero-order and firstorder modified Bessel functions (Macdonald functions), respectively. In what follows, we will be interested only in the temperature at the boundary of the growing pore, i.e. when r = R(t): T[R(t)] = T0 +

C0 K0 (R/r T ) RK1 (R/r T )

(7.4)

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Equation (7.4) describes the dependence of the temperature at the pore boundary on the pore radius. As follows from Equation (7.4), an increase in the pore radius results in a decrease in the temperature at the pore walls. As was noted above, local nonuniform heating of the crystal in the pore region should give rise to stresses around the pore. In the framework of the theory of thermoelasticity, an expression relating the stresses to the temperature distribution can be obtained. For this purpose, using the methods described in Gatewood [36] a relationship can be derived for the radial component of the elastic stress tensor at the pore boundary: R+   rT  αE αE R2 r T(r )dr − r T(r )dr 1 − σr (R) = 2 (R + )2 (R + )2 r T − R2 R

R

(7.5)

where α is the thermal expansion coefficient and E is the Young modulus. The quantity  determines the position of the maximum in the thermoelastic stress distribution with respect to the pore boundary and depends on the radii R and rT . However, the inclusion of this dependence in our theoretical treatment significantly complicates subsequent calculations. In order to simplify further analysis, numerical estimates of the quantity  as a function of the pore radius at rT = 200 nm [37] were made, and, according to these estimates, it was assumed that  = 10R0 . After substituting the temperature distribution in the explicit form [Equation (7.3)] into Equation (7.5), the final relationship for the radial stress component at the pore boundary is obtained: ⎡ 2 2 α EC0 ⎣ (R + ) − R σr (R) = RK1 (R/r T )(R + )2 r T2 − R2 R+ 

⎤

rT r K0 (r/r T )dr R

r K0 (r/r T )dr ⎦

− R

α EC0r T = RK1 (R/r T ) − (R + )K1 (R + /r T ) RK1 (R/r T )(R + )2  (R + )2 − R2 − [RK (R/r ) − r K (1)] (7.6) 1 T T 1 r T2 − R2 The calculated dependence σ r (R) is plotted in Figure 7.8. In this case, the value of h is taken equal to 1 nm. The parameters α, E, and χ are

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Figure 7.8 Calculated dependence of the radial component of the elastic stress tensor at the pore boundary on the pore radius. Reproduced from M.G. Mynbaeva et al., Phys. Sol. State, 47, 1630–1636. Copyright (2005), with permission from Elsevier

taken equal to 4.3 × 10−6 K−1 , 22 × 1010 N m−2 , and 3.7 W K−1 cm, respectively [38]. In Kukushkin [39] it was demonstrated that stresses in the crystal generate a vacancy flux, which, in the case under consideration, is proportional to the radial component of the elastic stress tensor. This vacancy flux can be represented by the following expression: jel =

νυ 1/3 exp(−ε D/kT)σr kT

(7.7)

where ν is the frequency of atomic vibrations, v is the volume of one vacancy, ε D is the activation barrier to vacancy diffusion, and k is the Boltzman constant. The vacancy mobility μ in the stress field σ can be determined from the formula μ = D/kT ∼ υ 2/3 νexp(−ε D/kT)/kT, where D is the vacancy diffusion coefficient. The second component of the vacancy flux is related to the temperature gradient. In Stark [40] it was shown that, in the presence of a temperature gradient in the crystal, there arise an atom flux and a counter vacancy flux, which can be written in the form: jT =

DT nv ε D ∇T kT 2

(7.8)

where DT is the thermal diffusion coefficient of vacancies and nv is the initial vacancy concentration in the crystal. By assuming that DT ∼ D

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and using the explicit form of the dependence T(R), the above vacancy flux jT can be rewritten in the form: jT =

nv νυ 2/3 ε DC0 1 exp(−ε D/kT) kr T RT 2

(7.9)

The total vacancy flux in the crystal under the given conditions can be written as: jv = jel + jT + jc

(7.10)

where jc = −DVnv is the diffusion flux proportional to the vacancy concentration gradient. The equation for the pore growth due to the motion and clustering of vacancies has the form dR = υv jv dt

(7.11)

For simplicity of calculations, let us ignore the concentration flux in Equation (7.10) under the assumption that the concentration gradients are relatively small. Then, the equation for the pore growth takes the form:     εD Sr (R) 1 dR = C1 + C2 exp − (7.12) dt T(R) RT 2 (R) kT(R) Here, the quantity Sr (R) = σ r (R)/(αEC0 ) was introduced for convenience. The constants C1 and C2 at nv = 1018 cm−3 [41] and ε D = 3 eV [42] take on the following values: C1 =

1 4/3 υ να EC0 ∼ = 1.9 × 1016 nm2 Ks k

C2 =

nv νυ 5/3 ε DC0 ∼ = 9.7 × 107 nm2 K2 s kr T

In Equation (7.12), the first term in the pre-exponential factor determines the contribution of the elastic stresses to the radial growth of the pore and the second term accounts for the effect of the temperature gradient on this growth. As follows from the ratio between the constants C1 and C2 , the temperature contribution is negligible as compared with the contribution of the stress σ r . It should be noted that, apart from the stresses caused by the temperature gradients, there arise stresses due to the formation of the

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pore as a local disturbance of the lattice. However, these stresses rapidly decrease to zero with distance from the pore [39] and, hence, can be ignored when considering the formation of an individual pore channel. In order to obtain the analytical solution of Equation (7.12), let us introduce the following three approximations. In the pre-exponential factor on the right-hand side of Equation (7.12), we will discard the second (temperature) term. Then, we will use the approximate relationship for the dependence T(R) with the asymptotic expression for the Macdonald function K0 (x) = ln(2/γ x). Finally, we will disregard the dependence of the factor Sr (R)/T(R) on R, because this factor varies slowly as compared with the exponential factor at ε D > kT. Under these assumptions, the analytical solution of Equation (7.12) can be derived in the following form:   2π hχ T0 ln(t1 /t) 2r T exp − R(t) = γ W ln(t/t0 )

(7.13)

where γ is the Euler constant and t1 is the characteristic time given by the formula: t1 = t0 exp(ε D/kT0 )

(7.14)

It follows from Equation (7.13) that the lateral growth of an individual pore through the vacancy mechanism ceases when the pore radius reaches a specific steady-state value in a time t1 . Figure 7.9 depicts the

Figure 7.9 Calculated dependence of the pore radius on the anodization time. Reproduced from M.G. Mynbaeva et al., Phys. Sol. State, 47, 1630–1636. Copyright (2005), with permission from Elsevier

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dependence R/rT (t) calculated from Equation (7.13) for the growth of an individual pore under the given conditions. According to numerical estimates, the steady-state radius of the pore is equal to 200 nm. Thus, it turned out that the calculated diameter of the individual pore exceeds the experimentally observed diameters (30–40 nm). However, it should be remembered that the above estimates were obtained without regard for a number of factors, for example, the formation of side pore branches, which requires an additional expenditure of energy. In a real system, proper allowance must also be made for the interaction of growing pores with each other as according to experimental data, the mean distance between pores is of the order of or less than the value of rT and the averaged diffusion field of vacancies should be determined by the entire ensemble of pores. Thus, the results of our calculations predict the formation of PSC with a steady-state pore radius of several tens of nanometers, and count in favor of the inference that nanopores in SiC can be formed as a result of physical processes, namely, diffusion and clustering of vacancies. Note that here the formation of nanoporous structure in crystalline matrix of the anodized semiconductor is considered as a primary event, which results from the specific physical processes caused by current flow localization. However, the contribution of chemical processes cannot be excluded either. In particular, coexistence of two competing mechanisms (porous structure formation and SiC dissolution) resulting in formation of non-SPSC, was proposed above. Validity of the above deductions on the genesis of primary pores and on the origin of the existence of a variety of porous structures in stoichiometric SiC, as a result of the subsequent evolution of the pores, is supported by the experimental observations related to the development of porous structure in bulk GaN crystals. Figure 7.10 demonstrates that the development of porosity in bulk GaN is similar to that in silicon carbide. Figure 7.10(a–d) shows that evolution of GaN porosity with anodization current density increasing proceeds through the three-stage mechanism proposed for PSC. Here similar stages are observed: from nanoscale pores, to the enlargement of pores resulting in formation of mixed and uniform porous structure containing re-sized pores. In Figure 7.10(d) it is clearly seen that, similar to the case of SiC anodization, the process of pore enlargement starts from the nuclei appearing at the nanoporous GaN/GaN interface and develops towards the surface of the sample. This emphasizes that the idea of the existence of ‘primary porosity’ with a vacancy genesis, which is considered to precede the formation of other types of porous structure morphologies, is not exotic and valid only for SiC, but could apply to other semiconductors as well.

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Figure 7.10 SEM cross-sectional images of porous bulk GaN illustrating the development of the porous structure under anodization (a–d). In (d) marked is a micropore nucleus appearing at the nanoporous GaN/GaN interface. In the inset the primary nanoscale porous structure under higher magnification is depicted

7.2.5

Stability of SPSC Under Post-Anodization Treatment

The behavior of PSC under thermal treatment is of real importance, since during the growth the substrate is exposed to high temperatures. To study this behavior, the annealing experiments at 900–1700 ◦ C were conducted in both Ar atmosphere and in a vacuum in a resistive furnace. SEM study revealed the changes in porous structure as a result of annealing. An illustration of this phenomenon is given in Figure 7.11(a–d), which presents SEM cross-sectional images of microporous SiC annealed in a vacuum at 1200–1700 ◦ C. It is also seen there that annealing at 1700 ◦ C led to complete destruction of the porous structure near the surface down to several micrometers in depth, as shown in Figure 7.11(d). AES showed that thermal treatment of porous material could result in the change of C/Si ratio as compared with initial stoichiometry. Namely, carbon concentration gradient with the carbon content continuously increasing towards the surface was detected in PSC structures annealed under certain conditions.

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Figure 7.11 SEM cross-sectional images of microporous SiC annealed in vacuum at 1200 (a), 1500 (b), and 1700 ◦ C (c,d). (d) Reproduced from M. Mynbaeva et al., Mater. Sci. Forum, 483–485, 269–272. Copyright (2005), with permission from Trans Tech Publications

Experimental data on the thermal stability of SPSC can be summarized as follows: (i) no essential changes in porous material composition (within AES accuracy), when nanoporous SiC was annealed at temperatures up to 1700 ◦ C in Ar ambient and 1500 ◦ C in a vacuum were found; (ii) the composition of microporous SiC annealed in Ar ambient did not change after the treatment at temperatures up to 1500 ◦ C; (iii) microporous SiC structures were thermally stable in vacuum within the 900–1200 ◦ C temperature range; (iv) PSC surface graphitization occurred in both types of PSC structure after annealing in a vacuum at 1700 ◦ C. On this basis, the following conclusions were derived: 1. The magnitude of applied temperature determined the degree of PSC structure evolution under annealing. 2. Both the annealing temperature and the type of ambient determined the degree of PSC compositional changes. 3. PSC is less thermally stable in a vacuum than in a gas ambient. Nanoporous structure is stable in a wider temperature range than a microporous one.

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The explanation of the observed PSC structure evolution under thermal treatment may be given on the basis of general mechanisms of the behavior of porous solids under annealing as covered by the classical theory of sintering (for the sintering theory see Skorohod [43] and references therein). Concerning porous solids, the term ‘sintering’ refers to the changes in pore shape and dimension during the heating. From the theory of sintering it is known that, in the absence of externally applied stress, the changes are motivated by surface tension, since the external surface energy decreases as pores are coalescing and take a more compact shape. From the annealing experiments it follows that the same mechanism is responsible for the PSC structure evolution. Figure 7.12 is given as an illustration of the pore coalescence phenomenon: here one can trace this effect from the stage of pore channels welding together [Figure 7.12(a)–(c)] to the formation of big spheroid voids [Figure 7.12(d)] at high temperature. Comparison of SEM and AES results clearly shows the existence of a correlation between the extent of the structure evolution and the degree of compositional changes in the annealed PSC. This can be related to

Figure 7.12 Various stages of the evolution of the porous structure in SiC under thermal treatment. Reproduced from M. Mynbaeva et al., Mater. Sci. Forum, 483– 485, 269–272. Copyright (2005), with permission from Trans Tech Publications

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Figure 7.13 SEM images of the surface of PSC annealed at 1500 ◦ C in a vacuum chamber (a), and at 1700 ◦ C in the sandwich cell (b)

the known effect of mass transport during the sintering process [44,45], which may result in segregation effect, that takes place if the host matrix consists of two or more types of atoms with different diffusion mobility. In such cases segregation effect manifests itself in an increase in the concentration of more rapidly diffusing atoms at the vicinity of vacancy sources, which are pore walls, and outer interfaces [46]. Thus, following fundamentals of solid-state sintering, a conclusion can be drawn that the extent of porous structure evolution is one of the factors, which determine the degree of compositional changes within annealed PSC. Another factor, which influenced the degree of compositional changes in annealed PSC specimens, is surface evaporation. This is illustrated in Figure 7.13(a), where a SEM image of PSC annealed at 1700 ◦ C in a vacuum shows terraces at the surface of the sample, which appeared as a result of the treatment. Indeed, as at high temperature the equilibrium vapor pressure of Si atoms is much higher than that of carbon-containing molecules, such as Si2 C or SiC2 , it can be expected that silicon preferably evaporates from SiC leaving carbon behind, which in extreme cases may lead to graphitization. This statement was proven by preliminary studies performed by E.N. Mokhov (Ioffe Institute). The studies showed that annealing of PSC in a closed isothermal cell (sandwich cell), which allows the vapor pressure over the surface of a sample to be controlled, permitted the stoichiometry to be kept close to that of the starting PSC material up to 2200 ◦ C [47]. Figure 7.13(b) illustrates that adjusting the annealing conditions suppresses the effect of PSC surface evaporation. Another kind of treatment, to which substrates are often subjected prior to the growth, is the plasma cleaning procedure. It appears, however, that this treatment is not always suitable for PSC substrates, since it causes both surface morphology degradation and coarsening of the

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Figure 7.14 Plain-view (a,b) and cross-sectional (c,d) SEM images of plasma-treated microporous SiC

porous structure, as illustrated in Figure 7.14(a) and (b) and Figure 7.14(c) and (d), respectively. In this instance, microporous SiC was subjected to Ar plasma exposure at room temperature. As a result of the processing, the surface morphology of PSC was determined by blistering-like effect, which resulted in tearing off of the dense layer, and, through this, in open pores appearing at the irradiated surface. Bulk porous morphology modification, in its turn, is defined by radiation-stimulated coalescence of pores. In general, radiation-induced coalescence looks similar to the process of thermal pore coalescence, which is caused by the fact that small pores eject vacancies more intensively than bigger ones. Both processes lead to the growth of big pores as a result of dissolution of smaller ones, however, physical reasons behind thermally and radiation-induced coalescence are altogether different. In contrast to thermally induced coalescence, radiation-induced coalescence is not related to the ejection of vacancies but results from pore preference δ p being inversely related to the pore radius (δ p = α iv /R, where α iv is the difference between the interaction constant of a pore with a vacancy and with an interstitial generated by irradiation). As a result of this relation, small pores adsorb

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the excess of interstitials and dissolve, while big ones grow. The rate of radiation-induced coalescence exceeds that of thermally induced by two to four orders of magnitude [29]. Summarizing this section, the formation of PSC and its stability under post-anodization treatment were considered. It appears that by adjusting the conditions of PSC preparation it is possible to produce porous material, which demonstrates both no changes in stoichiometry as related to the SiC compound, and low surface porosity due to the existence of the dense layer. These important properties of the SPSC fabricated can be considered as an advantage, as they make this material an ‘epi-ready’ substrate. This can be stated on the basis of the existing experience on epitaxial growth over porous substrates. In particular, according to the modern concept of epitaxial growth over large-area PS substrates, low surface porosity of the substrates is required to achieve low defect density in epitaxial films [48,49]. This can be attained by adjusting anodization conditions on the stage of PS preparation [50], or by applying special pore sealing procedures prior to the growth. Also, it is obvious that the compositional inhomogeneity of the porous substrate should be regarded as a disadvantage. In this connection our results indicate that the conditions of PSC substrate treatment prior to the growth, especially those which require heating, must be adjusted to avoid PSC surface decomposition and graphitization. Depending on the growth temperature and ambient for a particular growth method, the PSC structure type must be chosen correctly in terms of its stability.

7.3 7.3.1

EPITAXIAL GROWTH OF GaN FILMS ON PSC SUBSTRATES The Growth and Its Effect on the Structure of the PSC Substrate

GaN films 1 μm thick were grown by HVPE [51]. To compare the properties of GaN films grown on porous substrates with those of films grown on non porous SiC, SPSC layers were fabricated only on half of each wafer. HRTEM post-epitaxial study revealed that the growth conditions used did not affect the crystalline quality of the PSC and that the structure of the dense layer retained its high crystalline perfection. Along with that, the study showed that both the nucleation pits and the surface

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Figure 7.15 Cross-sectional HRTEM image taken near the GaN/PSC interface, which shows the bridging over a surface opening in the porous substrate (a). It is seen that the growth did not affect the properties of the dense layer, and its structure retained high perfection. (b) shows filling of a micropore-related opening with GaN. Reproduced from M. Mynbaeva et al., J. Cryst. Growth, 303, 472–479. Copyright (2007), with permission from Elsevier

openings at PSC surface were healed during epitaxy and did not cause defect formation in the GaN films. Figure 7.15(a) represents an HRTEM image taken near the GaN/PSC interface, which shows the bridging of the epitaxial film over a pit situated on the substrate surface, and a defectfree portion of the GaN material located above. The micropore-related openings were filled with GaN material during the growth process, as illustrated by Figure 7.15(b). After the growth, remarkable changes in the bulk of PSC layers were observed, namely, the specific evolution of pore shape, which was very different from that as induced by thermal treatment. The evolution of the porous structure occurred within a 0.7–1 μm thick region adjacent to the GaN/PSC boundary. The degree of the changes was found to be dependent on the thickness of the porous layer used. In particular, if the thickness of the PSC layer did not exceed 1 μm, initial channel-like pores [Figure 7.1(a)] evolved into microcrack-shaped features extended parallel to the GaN/PSC boundary for 0.2–0.5 μm, as illustrated in [Figure 7.16(a) and (b)]. The evolution of pore shape was accompanied by the expansion of the dense layer, whose thickness increased from an initial 50–70 nm before the growth up to about 100–150 nm. In thicker PSC layers, the changes in the porous structure were much weaker, as shown in Figure 7.16(c). The crack-shaped features [indicated by arrows in Figure 7.16(d)] initiated at the pore walls (which kept their shape), and expanded into the PSC matrix for a few nanometers. No increase in the thickness of the dense layer was observed in thick PSC layers after the growth.

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Figure 7.16 Cross-sectional images of the structures with different PSC layer thickness, taken after the growth: (a) TEM image taken near GaN/PSC interface with PSC thickness 0.7 μm; (b) SEM image showing the porous structure morphology in the bulk of the 0.7 μm thick porous layer; (c) TEM image taken near GaN/PSC interface with porous layer thickness 3.6 μm; (d) TEM image showing the porous structure morphology in the bulk of the 3.6 μm thick porous layer. The arrows indicate microcrack-shaped features discussed in the text. Reproduced from M. Mynbaeva et al., J. Cryst. Growth, 303, 472–479. Copyright (2007), with permission from Elsevier

An explanation for the evolution of pores into crack-shaped features, accompanied with the expansion of the dense layer, can be given on the basis of the known phenomena, which is conversion of pores into quasi two-dimensional objects and pore healing that occur in loaded crystalline solids [52,53]. Thus, the observed changes in the PSC structure after the growth may be considered as evidence of growth stress partitioning between the GaN film and the PSC layer. It means that the stress determined by the mismatches in material properties [54], acts as external pressure and causes evolution of PSC structure within the region close to the heterointerface. Assuming that the porous structure can absorb the mismatch strain via evolution of the pore shape, the strain energy per unit volume of porous layer must decrease as the PSC layer thickness increases. This should result in different degree of the structural changes within thin and thick PSC layers, which is exactly what was observed in the experiment.

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To investigate the effect of the porous layer on the state of strain in the epitaxial film, the radius of curvature Rc of the GaN/SiC and GaN/PSC samples using XRD was measured [55,56]. The measurements showed that GaN films grown on nonporous SiC experienced biaxial tensile stress, which resulted from film/substrate mismatches. In contrast, the films grown on PSC were compressed. The Rc measurements also revealed that with increase of the thickness of the PSC layer the value of the compressive stress increased.

7.3.2

Properties of the GaN Films Grown

Crystalline quality of the films was assessed through measurements of XRD rocking curves (RCs). XRD study was performed in both 2θ -ωand ω-scan modes at (0002) reflection. The full-width at half-maximum (FWHM) values of RCs for 2θ -ω-scan were around 20 arc s for the films grown on SiC and 20–30 arc s for the films grown on PSC. The ω-scan diffraction peaks showed RC FWHM values of 155–280 and 180–490 arc s for GaN grown on SiC and PSC, respectively. These results indicated good crystalline quality of the material grown on both types of substrates. Along with that, a relation between the broadening of the GaN XRD RC and the thickness of the PSC layer in the substrate was observed. An example of the dependence of the FWHM (ω) on PSC layer thickness is presented in Figure 7.17.

Figure 7.17 FWHM of the ω (0002) XRD RC of GaN films. Filled symbols correspond to GaN grown on PSC with the different thickness of the porous layer. Open symbols correspond to the films grown on nonporous substrates in the same growth runs, and are given for reference purposes only. Reproduced from M. Mynbaeva et al., J. Cryst. Growth, 303, 472–479. Copyright (2007), with permission from Elsevier

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Defect density in the epitaxial films was determined both on crosssectional and plan-view bright field TEM images. Two-beam conditions were recorded in order to image dislocations with various Burgers vectors. In GaN films grown on nonporous SiC the density of threading dislocations (TDs) was estimated to be as high as 5 × 109 –1010 cm−2 . At the same time, in GaN films grown on PSC, an exponential reduction in TD density with porous layer thickness increasing from 0.7 to 6 μm was observed. The minimal value of the threading defect density, as low as 108 cm−2 , was obtained for the films grown on 4–6 μm thick PSC layers. With further increase of the thickness of the porous layer from 6 to 8 μm, the TD density in the films grew to 4 × 108 –2.1 × 109 cm−2 . The density of the threading defects vs PSC layer thickness is plotted in Figure 7.18. As follows from comparison of Figures 7.17 and 7.18, XRD revealed almost linear increase of the GaN RC FWHM with PSC layer thickness increasing, within the very range of the thickness values, where exponential decay of TD density was observed by TEM. Thus, the XRD and TEM data seemed to be in contradiction, yet a possible explanation for this phenomenon will be given below, when the defect structure of the GaN films will be discussed in more detail. Figure 7.19 represents cross-sectional TEM images of the films grown on SiC and PSC with various thicknesses of the porous layers. It appeared

Figure 7.18 Dependence of TD density in GaN films on the thickness of the PSC layer. Open and filled symbols correspond to the total threading defect value calculated from TEM cross-sectional and plan-view images, respectively. The dashed curve is the exponential fit of the defect density decay. Reproduced from M. Mynbaeva et al., J. Cryst. Growth, 303, 472–479. Copyright (2007), with permission from Elsevier

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Figure 7.19 Bright-field cross-sectional TEM images of GaN/SiC (a,b), GaN/PSC (2.2 μm thick) (c) and GaN/PSC (4.1 μm thick) (d) structures. Reproduced from M. Mynbaeva et al., J. Cryst. Growth, 303, 472–479. Copyright (2007), with permission from Elsevier

that in GaN films grown on PSC, in addition to TDs there were planar defects (PDs), expanded parallel to the layer/substrate boundary and concentrated near the heterointerface. In what follows such defects will be referred to as (0001) PDs. Important is that the (0001) PDs appeared as features, which formed only in the films grown on PSC; they were not observed in the films grown on nonporous SiC. This is illustrated by a TEM cross-sectional image from a GaN/SiC specimen presented in Figure 7.19(b). The image is obtained from the thinner region of the TEM specimen. This allowed for better resolution of the defect structure near the heterointerface, as in this case it was less hidden by the TDs, imaged with a higher density in the thicker region of the sample under study [Figure 7.19(a)]. Only TDs originating at the GaN/SiC interface are seen in Figure 7.19(b). Figure 7.19(c) presents a cross-sectional image of a GaN film, grown on relatively thin (2.2 μm) PSC layer. It can be seen that the film contains both (0001) PDs and TDs with somewhat reduced density. TDs penetrate into the film in the areas between the PDs.

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Figure 7.19(d) shows the cross-sectional SEM image of the GaN film grown on thicker PSC layer (4.1 μm). The defect structure of the film could be divided into three regions: 1. There is a 200 nm thick area above the GaN/PSC interface, where the main type of defects are (0001) PDs, which form a continuous band along the interface. 2. The 0.5 μm thick area above the GaN/PSC boundary contains mainly threading defects, which most likely are stacking mismatch boundaries (SMBs). Such defects are known to originate from threedimensional growth mode of GaN on a foreign substrate and terminate within GaN rather than extend to the free surface [57,58]. 3. Above the 0.5 μm thick area near the film/PSC interface the imaged part of the GaN film is almost free of the threading defects. Figure 7.20 presents the results of the TEM study of the GaN/PSC interfacial region of this sample performed with higher magnification. Parallel lines in Figure 7.20(a) represent the (0001) PDs formed within 200 nm thick GaN film region adjacent to the heterointerface. The (0001) PDs were found to be organized in batches with length of 50–400 nm. At the borders, where separate PD batches adjoined each other, the PDs, which corresponded to neighboring batches, demonstrated relative displacement [indicated by an arrow in Figure 7.20(a)]. Figure 7.20(b) shows a selected microdiffraction pattern of the interfacial region containing (0001) PDs. There are extra spots between the rows of the fundamental

Figure 7.20 High-magnification TEM image of the GaN/PSC (5 μm–thick) interface (a), and selected microdiffraction pattern of the interfacial region (b). Arrows in the inset show extra spots arising from the presence of a superlattice-like structure. Reproduced from M. Mynbaeva et al., J. Cryst. Growth, 303, 472–479. Copyright (2007), with permission from Elsevier

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spots parallel to the [0001] direction (as indicated in the inset). The presence of extra spots suggested the existence of a superlattice-like structure within the region. The existence of planar defects in GaN films grown on a foreign substrate may mean the occurrence of a disorder in the stacking sequence driven by mismatch stress [59,60]. In particular, the disorder within the host phase can result from diffusionless solid phase transformation, which causes deformation faulting. The characteristic feature of the diffusionless transformation is its reversibility, i.e. the newly formed disordered phase, being metastable, can be transformed back into the equilibrium phase as a result of annealing [61]. In order to determine the nature of the defect structure near the GaN/PSC interface, the structures formed on the basis of porous substrates were subjected to the annealing at 700 ◦ C with subsequent study by X-ray topography using CuKα1 radiation under conditions involving Bragg reflection geometry. Figure 7.21 shows the topograms of the as-grown [Figure 7.21(a)] and annealed [Figure 7.21(b)] GaN/PSC structures. In the image of the asgrown GaN/PSC structure observed were stacking faults organized in the form of a cross-hatch pattern [Figure 7.21(a)], which originated from the borders that separated neighboring (0001) PD batches. In Figure 7.21(b) one can see that the defect network disappeared. This points to the fact that the annealing caused transformation of the interfacial defective area into the unfaulted phase, i.e. a recovery of stacking sequence in the GaN region adjacent to the heterointerface. Hence, it can be concluded that

Figure 7.21 X-ray topography images taken from the same areas of a GaN/PSC sample before (a) and after (b) annealing. Reproduced from M. Mynbaeva et al., J. Cryst. Growth, 303, 472–479. Copyright (2007), with permission from Elsevier

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(0001) PDs formation observed in as-grown GaN/PSC samples is related to deformation faulting within GaN films. Important is that deformationrelated faulting in solids is known to contribute significantly to the XRD RC broadening [62–64]. This easily explains the above-mentioned illusory contradiction between the XRD and TEM data. The photoluminescence (PL) spectra of GaN films, recorded for a series of 1 μm thick films grown over half-porous SiC wafers with SPSC layer thickness 4–6 μm, exhibited: (i) an exciton edge emission band (peak at 3.44 eV), (ii) a donor–acceptor emission band (3.24 eV) with the corresponding phonon replicas; and (iii) the characteristic ‘blue’ and ‘yellow’ emission bands, all according to Reshchikov and Morkoc¸ [65]. A distinctive feature of the PL spectra of GaN films grown on PSC was a significant increase in the intensity of all emission bands as compared with that of the similar bands observed for the films grown on nonporous parts of the substrates. Figure 7.22 shows the typical PL spectra of GaN films grown on the PSC and SiC parts of the substrate. For better illustration, the spectra are plotted against a semilogarithmic ordinate scale. As can be seen in Figure 7.22, the intensity of emission from a film grown on PSC is significantly greater than that from a similar film grown on SiC. This indicated that a mechanism of the increase was reduction in the density of nonradiative centers. Taking into account the TEM data obtained, and proceeding from the modern notions on the negative influence of dislocations on the

Figure 7.22 PL spectra of GaN films grown on a nonporous SiC substrate (A) and a PSC substrate (B). The spectra were measured at 80 K with excitation at 337 nm. Reproduced from K.D. Mynbaev et al., Tech. Phys. Lett., 33, 83-–85. Copyright (2007), with permission from Springer

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process of radiative recombination in GaN [66,67], it can be concluded that the centers of nonradiative recombination in the samples studied were related to dislocations. This conclusion was also confirmed by electroluminescence measurements performed with GaN/AlGaN structures grown on porous and nonporous SiC substrate [68]. Thus, on the basis of experimental observations related to GaN epitaxial growth over PSC substrate, the following results can be emphasized: 1. Advanced PSC substrates with low surface porosity allow for growing GaN epitaxial films with reduced dislocation density as compared with those grown on conventional SiC substrate. 2. TD density in the epitaxial films was found to depend on the thickness of PSC layers formed within the substrate. 3. As a result of the growth, modification of the porous structure within the substrate was observed. This could be considered as direct evidence of growth stress partitioning between the PSC substrate and the GaN epitaxial film. 4. The formation of (0001) PDs, which were organized in superlatticelike stricture, was observed only in the GaN films grown on PSC substrates. The PD formation seems to be a major factor in TD density reduction in the films. 5. Residual strain inversion from tensile to compressive was observed in the GaN films grown on PSC. The explanation for GaN improved growth over PSC may be done on the basis of the existing concept of porous substrate compliance. Namely, it can be suggested that in a GaN/PSC system the mismatch stress, which accumulates in the heterostructure as the thickness of the growing film increases, is effectively lowered through the expenditure of the system’s free energy on the modification of porous structure within the substrate. From the experimental data presented it is clear that the thickness of the PSC layer is an important factor, which determines the ‘degree’ of porous substrate compliance, and through it, the density of threading defects in the epitaxial films. In particular, PSC layers thinner than 0.7– 1 μm appeared to be too thin for substantial TD density reduction due to a ‘hardening’ of the porous structure within the substrate, which, as a sequence, loses its compliance. The hardening is manifested in the increase of the thickness of the dense layer and/or drastic evolution of porous structure, caused by the growth stress imposed on the thin porous layers, as shown in Figure 7.16. At the same time, there is an optimal range (4–6 μm) of the thickness of the PSC layers, where no drastic

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changes of the PSC structure was observed, which allowed for obtaining the lowest TD density. As suggested earlier, the compliance of porous substrate results in the implementation of the mechanism of mismatch strain relaxation, which is different from that typical for the growth on conventional substrate [4]. The specific character of mismatch strain relaxation mechanism in GaN films grown on PSC manifested itself in the formation of (0001) PDs. As substantial reduction of TD density in the films containing PDs was observed, it can be suggested that their formation takes place at the early stages of epitaxial growth, when mismatch strain in GaN/PSC heterostructure relaxes elastically. There is also good reason to believe that the internal interfaces of the (0001) PD superlattice serve as energy barriers, which hinder the dislocations from penetration into the growing film at later stages of plastic relaxation of the growth strain. This conclusion is in agreement with the existing experimental data, which show that occurrence of stacking disorder within nucleation layers may cause the TD density reduction in GaN films grown by various methods [3,69–71]. The increase in the TD density in the films grown on relatively thick (6–8 μm) PSC is most probably caused by a specific plastic relaxation process, occurring as a reaction to a particular state of strain that appears in these epitaxial films. This can be stated on the basis of strain inversion in the films grown on PSC, as well as on the increase in compressive stress with the thickness of the PSC layer increasing. These effects show that apart from the stress caused by the GaN/SiC lattice mismatches, an additional built-in stress arises in the films. Obviously, the additional stress is caused by the presence of (0001) PDs, because one can expect that a part of GaN film within the faulted region may have altered its mechanical properties as compared with unfaulted material [72]. Then the increase in dislocation density in GaN grown on relatively thick PSC can be explained by a plastic relaxation process, which relieves the builtin stress and occurs because this internal stress/(0001) PD density reaches a certain critical value. At the same time, the compressive stress developed in GaN films grown on PSC substrates is not a great disadvantage. This stress helps to compensate the tensile mismatch stress, which is normally observed for the GaN/SiC system, and thus reduces the probability of cracking. For instance, no cracking was observed, when 1 μm thick epitaxial films were grown over the substrates containing 4–8 μm thick PSC layers. In contrast, GaN-on-SiC ‘reference’ samples with similar thickness of the epitaxial films were heavily cracked.

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Summarizing this section, a SiC substrate containing a porous layer may indeed serve as a compliant one, allowing for reduction in the density of threading defects in the heteroepitaxial films via absorbing strain caused by the lattice mismatch. Important is that the substantial dislocation density reduction in GaN films can be achieved within the limited range of PSC layer thickness. The thickness of the SiC porous layers (4– 6 μm), which was found to be optimal for the anodization and growth regimes used in this work, provided conditions, when formation of TDs was effectively prevented through the generation of PDs in the epitaxial films near the GaN/PSC interface. In particular, in 1 μm thick HVPEgrown GaN films it allowed us to achieve a threading defect density value as low as 108 cm−2 . This value is two orders of magnitude lower than that typical for thin GaN films grown by HVPE on nonporous SiC substrates, and is comparable with that achievable in thick (>50 μm) HVPE- grown heteroepitaxial GaN layers [73–75]. This indicates that, from the practical point of view, the use of the porous substrate is more efficient than commonly explored thick GaN growth on standard substrates, where TD density reduction is attained through the dislocation reaction mechanism [75]. Nevertheless, it is important to remember that the use of PSC substrate does not change the GaN growth mode, and it remains the same as for conventional heteroepitaxy. Thus, it could be suggested that further improvement in GaN film quality may be achieved with homoepitaxy using porous substrates made from GaN/SiC templates or GaN bulk material, with development of porous substrate on the basis of bulk material holding greater promise [76,77].

7.4

SUMMARY

A key challenge to advancing the performance of III nitrides-based optoelectronics and high power devices is reducing the high density of threading defects, which originate from mismatches in parameters of epitaxial films and foreign substrates. In this regard, the development of PSC substrate technology is a good leverage for epitaxial growth of GaN films with reduced defect density. In this chapter, a method for fabricating conductive PSC substrates achieving practical size of 2 in. in diameter was presented. The properties of porous substrate material have been optimized for HVPE growth process, and through this a substantial reduction of TD density in GaN epitaxial films has been achieved. The coupling of large area PSC substrate with HVPE growth has great potential for producing low dislocation

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density templates for subsequent homoepitaxial growth with advanced cost/performance ratio.

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8 Dislocation Mechanisms in GaN Films Grown on Porous Substrates or Interlayers T. S. Kuan and C. K. Inoki Department of Physics, University at Albany, State University of New York, Albany, NY 12222, USA

8.1

INTRODUCTION

GaN thin layers grown epitaxially on either sapphire or SiC substrates contain various defects induced during the growth process. These include dislocations, cracks, open tubes, Ga inclusions, stacking faults, point defects, etc. In this chapter we will discuss growing the GaN layer on a porous substrate or through a thin porous interlayer in an attempt to reduce the density of dislocations. We will not give a survey of the field, but rather focus on what we have learned from our growth experiments carried out under the ONR MURI and DURINT programs [1]. We will describe the dislocation mechanisms in a normal growth, followed by the observed dislocation behavior in a lateral growth, and the effects of porous substrates and interlayers.

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EXTENDED DEFECTS IN EPITAXIALLY GROWN GaN THIN LAYERS

The threading dislocations in GaN layers, i.e. those that propagate along the c growth axis, can be of the edge, screw, or mixed types. The direction and magnitude of the Burgers vectors associated with these types are listed in Table 8.1. An edge-type threading dislocation can turn into a screw type by bending into certain horizontal configurations. Likewise, screw dislocations subjected to stress can also bend and turn into edge types. The total numbers of threading dislocations produced at the initial growth stage are quite high (>1012 cm−2 ), with the edge types outnumbering the others. As the layer grows thicker, the populations of dislocations (particularly edge types) drop rapidly by orders of magnitude through mutual recombination. It has been shown that no matter what type – edge, screw, or mixed – they all act as nonradiative centers in GaN [2,3]. When we grow GaN on SiC, the lattice mismatch involved is small (∼3.5 %), and the initial growth mechanism is very simple. By polishing and ion milling away most of the SiC substrate and GaN growth layer until a thin (<50 nm thick) bi-layer remains, we can observe directly by transmission electron microscopy (TEM) the size and orientation of both lattices, and the configuration of misfit dislocations at the GaN/SiC interface. A diffraction pattern in Figure 8.1 indicates that there is no lattice rotation between the overgrown GaN layer and the SiC substrate. A plan-view micrograph in Figure 8.2 reveals a rather irregular hexagonal misfit dislocation network present at the GaN/SiC interface, with an average dislocation spacing of ∼70 nm. Since there is no lattice rotation involved, the network thus consists mostly of edge-type misfit dislocations. A regular network of edge-type dislocations on an atomic flat interface, as depicted in Figure 8.3, can in principle relax all the misfit strain, allowing the GaN overgrown layer to be totally free of threading dislocations. In real growths, however, the interface is rarely flat, and the dislocation Table 8.1 Dislocations observed in epitaxially grown GaN Type

Burgers vector

Edge Screw Mixed

1/31120

0001

1/31123

Magnitude

Energy

0.319 nm 0.518 nm 0.608 nm

∝ a2 ∝ c2 ∝ a 2 + c2

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Figure 8.1 Diffraction pattern obtained from a GaN/SiC plan-view sample showing no lattice rotation between the GaN epitaxial layer and the SiC substrate. Reflections from GaN and SiC are marked by horizontal arrows and vertical arrows, respectively. All other reflections arise from double diffraction. The (0110) reflection is forbidden in 6H-SiC. The GaN layer was grown by H. Morkoc¸ and his group at the Virginia Commonwealth University by MOCVD on (0001) SiC at 900◦ C. Most of the GaN grown layer and SiC substrate were polished and ion milled away until a thin (<50 nm thick) bi-layer remains for the transmission electron microscope observations

network is never regular. As the neighboring islands coalesce, unresolved dislocations are bent upward into the boundaries and turn into threading dislocations. As the growth proceeds, pairs of nearby threading dislocations with opposite Burgers vectors can combine and annihilate each other, forming dislocation half-loops, as observed in Figure 8.4. Such a

Figure 8.2 Plan-view transmission electron micrograph of misfit dislocation network formed at the GaN/SiC interface. The network consists mostly of edge dislocations. A step on the SiC surface can interact with the network to form mixed-type dislocations. Some mixed-type threading dislocations, emerging from the interface, are visible through their characteristic image contrast, as indicated by arrows

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Figure 8.3 Schematic of a regular misfit dislocation network at the GaN/SiC interface. The sense and Burgers vectors of the edge type misfit dislocations are marked by arrows. Missing segments such as AB and CD would lead to threading dislocations emerging from the interface upward into the GaN growth layer. Edge dislocations initiating at A and B can combine and annihilate each other. Other pairs such as (B, C) or (A, D) can also interact and eliminate each other. Surface steps create screwor mixed-type threading dislocations, which are harder to pair up for recombination

recombination process rapidly reduces the density of threading dislocations to the order of 109 –1010 cm−2 , and at that point the remaining dislocations become too far apart to interact. Mixed-type threading dislocations are also generated when there are surface steps present at the SiC growth surface. A step at the interface is essentially an edge dislocation with a Burgers vector c, which can interact with the network and

Figure 8.4 Cross-sectional transmission electron micrograph showing dramatic reduction in dislocation density through recombination at the initial stage of GaN growth

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produce mixed-type dislocations. Mixed-type dislocations are much less likely to get annihilated in subsequent growth. The growth of GaN on sapphire is much more complicated because it involves a 30◦ lattice rotation and a large lattice mismatch (∼14 %). Here the initial GaN growth islands are tilted as well as twisted slightly, relative to each other and the substrate; consequently, more dislocations are generated at island coalescence [4,5]. Similar to the growth on SiC, the dislocation density decreases to ∼1010 cm−2 after certain growth thickness through recombination. To further reduce the number of dislocations in GaN grown on either SiC or sapphire below ∼1010 cm−2 , we can: (a) lower the number of mixed-type dislocations emerging from the growth surface by growing on a flat substrate surface; or (b) mask or etch away part of the substrate surface, so that fewer threading dislocations are produced; or (c) rely on lateral growth to facilitate more recombination. We are utilizing approaches (b) and (c) by growing GaN on either a porous substrate or on a porous interlayer, as will be discussed in the following sections.

8.3

DISLOCATION MECHANISMS IN CONVENTIONAL LATERAL EPITAXY OVERGROWTH OF GaN

In a conventional lateral growth scheme, the substrate surface is patterned by a thin insulator layer, allowing GaN to grow only on an array of narrow windows. The GaN islands nucleated at the long and parallel windows are then coalesced through lateral growth. In principle, the threading dislocations would be reduced by the same fraction as the masked areas. However, the regularity of the growth geometry often produces an undesirable tilting of the c-axis and additional dislocations. It is commonly observed that most vertical threading dislocations bend toward the lateral grown direction, in response to the image force associated with the tilted growth surfaces [6–9]. This bending turns the original edge dislocations into screw types propagating horizontally on the (0001) planes. However, it is the subsequent actions of these horizontal arrays of screw dislocations that bring about the observed c-axis tilt [10]. A planar array of parallel screw dislocations carries a strong strain field which does not decrease with the distance from the array. Therefore the elastic strain energy builds up rapidly with volume. (It takes two arrays of screw dislocations normal to each other to form a twist boundary to

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Figure 8.5 Schematic cross-sectional view (a) and plan view (b) of dislocation mechanisms leading to c-axis tilt in lateral epitaxial overgrowth of GaN. At region A, vertical edge-type threading dislocations bend into horizontal screw-type dislocation arrays. At region B, The screw-type dislocation arrays bend again into edge-type dislocation arrays running parallel to the lateral growth surface. At region C, the geometrically necessary edge-type dislocation arrays are generated above the original arrays at region B. The extra atomic planes associated with the edge dislocations are indicated in (a)

cancel out the constant long-range strain field.) As the lateral growth proceeds, this array of screw dislocations has to bend 90◦ again, becoming arrays of edge dislocations, in order to prevent a further increase in strain energy (Figures 8.5–8.7). The bending direction (+90◦ or −90◦ ) depends on the Burgers vectors and sense of the dislocations and is the direction that would shorten the surface steps (Figure 8.5). The accumulated shear stress σθr from the screw dislocations is evidently strong enough to counter the surface image force, allowing the new edge dislocations to be buried under the progressing growth surface (Figure 8.5). A plan-view electron micrograph in Figure 8.7 shows clearly this collective bending of the screw arrays from originally normal to the growth surface into edge arrays now parallel to the growth surface. This second bending is inevitable, since it is the only way to terminate further strain energy build-up in the lateral growth regions. This new edge array

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Figure 8.6 Cross-sectional transmission electron micrograph, viewing along the [1100] direction, showing (A) the first bending of vertical edge dislocations into horizontal screw-type dislocations, (B) the second bending of screw-type arrays into edge-type arrays, viewed end-on in the image, and (C) layers of edge-type arrays generated to accommodate the curved lattice produced at (B). Lateral growth of GaN imaged here was carried out by HVPE at 1100 ◦ C by T. F. Kuech and his group at the University of Wisconsin [10]

Figure 8.7 Plan-view transmission electron micrograph of the same lateral growth as in Figure 8.6, with the [0001] direction normal to the image plane, showing the bending of screw-type dislocations into edge-type dislocation arrays at (B) during the lateral growth [10]

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constitutes a tilt boundary and produces no long range strain field. It is this edge array that is responsible for the c-axis tilt often associated with the lateral growth [10]. However, once the lattice is bent, the top overgrown layers will continue to need the geometrically necessary arrays to accommodate the bending. These additional arrays of edge dislocations are observed by cross-sectional TEM in Figure 8.6 [10]. Methods have been designed to minimize the c-axis tilt, e.g. by adjusting the mask width, mask pattern and materials, etc. [11,12]

8.4

GROWTH OF GaN ON POROUS SiC SUBSTRATES

The idea behind growing GaN on a porous substrate is to reduce the GaN/substrate interface area without using a mask, and also to take advantage of the dislocation bendings during lateral growth to facilitate interaction and recombination of threading dislocations. If the lateral growth takes place at the curved periphery of the pore, the c-axis tilting resulting from a straight lateral growth front described in the previous section should not happen. In the early part of the DURINT program, we have grown GaN on porous SiC, with pore size 20–100 nm, using plasma-assisted molecular beam epitaxy (MBE) [13,14]. Since the MBE technique does not provide a sufficient lateral growth rate, incomplete coalescing results in open tubes formed on top of each surface pore. These open tubes are effective sinks for dislocations, capable of lowering the dislocation density in regions between tubes. However, they can serve as dislocation sources as well. Upon cooling from the growth temperature to room temperature, numerous dislocation half-loops are observed to emerge from the open tubes to relax the thermal strain. Overall, the porous growth by MBE does yield a more strain-relaxed film, but fails to produce the desired defect reduction [14]. The surface pores as well as the open tubes often trap gallium droplets during growth – a feature not desirable for applications. We can use metal-organic chemical vapor deposition (MOCVD) to enhance the GaN lateral growth rate and eliminate open tubes on surface pores. W. J. Choyke and his group at the University of Pittsburgh have developed techniques to produce columnar pore structures in SiC with uniform and small pore sizes (Figure 8.8). Earlier GaN growth using MOCVD on C-face columnar porous SiC by H. Morkoc¸ and his group at the Virginia Commonwealth University produced only marginal defect reduction because of poor GaN nucleation. Growth on Si-face provides

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Figure 8.8 Plan-view transmission electron micrograph of columnar porous SiC with vertical pores of diameter ∼20 nm. Most of the SiC, except the top porous layer, was removed by polishing for this transmission image

much better wetting, however the defect density remains high. Growing GaN on a columnar porous SiC is still a promising field. The high number of defects we encountered so far in the GaN growth on columnar SiC is mostly related to the cleanliness and flatness of the porous substrate. An effective process to remove the surface oxide or contaminants on the porous substrate surface still remains to be developed. The commonly used H2 etching at a high temperature alters pore morphology and generates surface rounding in between pores. As shown in Figure 8.9, surface contaminants can lead to nucleation voids, and a non-flat

Figure 8.9 Cross-sectional transmission electron micrograph of GaN grown on a columnar SiC substrate. The SiC surface was annealed in hydrogen at 1200 ◦ C for 10 min. A thin GaN buffer layer was grown first at 850 ◦ C, followed by a thick GaN overlayer at 1030 ◦ C. Surface contaminants not removed by hydrogen etching were found to produce small voids (v) in the buffer layer

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surface produces a higher density of dislocations and stacking faults. During the low temperature (850 ◦ C) buffer growth, a large fraction of edge dislocations recombine and form half loops. The remaining dislocations emerging from this layer (mostly screw or mixed type) are still in the 108 cm−2 range. A smooth porous SiC growth surface, possibly achieved by chemical-mechanical polishing, should improve the nucleation and further reduce the defect density.

8.5

GROWTH OF GaN ON POROUS SiN AND TiN INTERLAYERS

Interlayers have been used to separate the grown GaN layer from the substrate [15]. As a medium to reduce the growth surface, an interlayer is a reversal of a porous surface. A porous surface removes isolated circular growth areas, while an interlayer exposes isolated growth windows. An interlayer can block a large fraction of threading dislocations present in the template, and those dislocations propagating through the porous layer will bend sideways as the GaN islands nucleated at the growth windows grow laterally (Figure 8.10). The interlayer can have certain advantages over a porous substrate: (a) no new dislocations are generated at the growth windows or during coalescence, since the GaN islands are grown homoepitaxially on a single GaN template; (b) the growth surfaces exposed at the windows are automatically flat and free of oxides; (c) inserting an interlayer in a growth sequence is easier to implement than preparing a porous growth surface. Better results have so far been obtained by growing on interlayers than on porous substrates.

Figure 8.10 Schematic of an interlayer blocking threading dislocations from the template. Dislocations propagating through a window bend sideways as the GaN island grows laterally

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8.5.1

223

GaN Growth on a TiN Interlayer

A thin TiN interlayer is implemented by depositing a 20 nm thick Ti film on a GaN template, followed by an annealing above 1000 ◦ C in a mixture of NH3 and H2 gases, to form a TiN network [16,17]. The GaN template contains a high density of dislocations, since it is grown on a sapphire or SiC substrate. Typical morphology of a TiN network consists of isolated, irregular chains of openings about 0.5 μm wide and several micrometers long (Figure 8.11). The feature size of openings increases with longer annealing time and higher H2 flow rate [16]. Voids always form in GaN accompanying the nitridation of Ti during the high-temperature anneal in NH3 /H2 and during subsequent growth of the GaN overlayer. As observed in Figure 8.12, these voids with Ga droplets, resulting from Ti-induced decomposition of GaN, can occur above the TiN interlayer or deep inside the GaN template. The sub-surface voids can attract and consolidate dislocations in the template [18]. However, these voids also produce additional normal and shear stresses during the post-growth cooling and induce [0001] stacking faults in the GaN layers. Such voids and stacking faults are not observed in GaN growths on a SiN interlayer. We expect a large fraction of threading dislocations in the GaN template to be blocked by the TiN interlayer. However, eliminating these blocked dislocations requires that, in the neighborhood linked by the interlayer, their Burgers vectors can cancel out in pairs or in groups. Statistically, this would become harder to achieve as the dislocation density drops below a certain level. Among those dislocations penetrating

Figure 8.11 Scanning electron micrograph showing the morphology of TiN network formed on a GaN template. Reproduced from [16] with permission from the American Institute of Physics

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Figure 8.12 Cross-sectional transmission electron micrograph of GaN grown on a TiN interlayer. Voids (V) and Ga droplets are observed above as well as beneath the TiN interlayer. Most dislocations in the template are either consolidated at the voids or blocked by the interlayer. Stacking faults (SF) observed in the GaN overgrown layer are likely induced by void-related thermal stress, since no stacking faults or voids are observed in GaN growths on a SiN interlayer

through the interlayer, the edge types are more prone to bending and recombination by the lateral growth at the openings, as we have discussed in Section 8.3. Plan-view TEM of the top layer of the overgrown GaN is most accurate in quantifying the efficacy of the TiN interlayer. The image contrast can distinguish the screw/mixed dislocations from the edge dislocations (Figure 8.13). Our TEM analysis of growth experiments carried out on a sapphire substrate by the H. Morkoc¸ group verified that the TiN interlayer is most effective in eliminating edge-type dislocations from a high density (>109 cm−2 ) down to a certain low level (∼1 × 108 cm−2 ). In a GaN control layer grown without the interlayer, there are ten times more edge dislocations than screw/mixed dislocations. With the TiN interlayer, the density of edge dislocations is reduced by an order of magnitude (from ∼1.5 × 109 to ∼0.9 × 108 cm−2 ), while that of screw/mixed dislocations remains more or less the same (∼1.4 × 108 cm−2 ) [16].

8.5.2

GaN Growth on a SiN Interlayer

The SiN interlayer is deposited in situ on a GaN template at 1030 ◦ C by flowing 100 ppm silane into the growth chamber, while maintaining the ammonia flow (TMG off). The thickness and porosity of the SiN interlayer is controlled by the deposition time [19–22]. GaN growth

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Figure 8.13 Plan-view transmission electron micrograph of GaN grown on a TiN interlayer [16]. Screw- or mixed-type threading dislocations (s) exhibit a characteristic black/white image contrast aligned with the scattering vector (g). Contrast from edge dislocations (e) is much weaker. Reproduced from [16] with permission from the American Institute of Physics

experiments indicate that a 5 min deposition time produces optimum results [21], while longer than 5 min leads to a polycrystalline GaN overlayer [20]. The density and distribution of the pores can be determined by SEM of GaN islands emerging at the pores. At 5 min deposition time, the average distance between pores is about 5 μm [20]. The pores are sparse compared with the fine chain-like openings in a TiN interlayer. One can expect blocking and bending of threading dislocations by the SiN interlayer, similar to TiN, except that we do not have the voids and associated stress issues to complicate the defect mechanisms. In a growth experiment carried out on a SiC substrate, a SiN interlayer inserted in the growth resulted in reducing the edge dislocations from ∼1.2 × 109 cm−2 in a GaN control layer down to ∼4 × 108 cm−2 , while the original low density of screw/mixed dislocations (∼4 × 107 cm−2 ) remained unchanged [21]. When a second SiN interlayer was inserted in the growth sequence, no further reduction in either edge- or screw-type dislocations was found [21]. It was thus concluded that ∼3 × 108 cm−2 is the low boundary for the SiN interlayer to act on dislocations. In a more recent growth experiment on a sapphire substrate (Figure 8.14), the overgrowth

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Figure 8.14 Transmission electron micrograph of GaN grown on a SiN interlayer. Some dislocations were blocked by the interlayer, and those dislocations propagating through the openings in the interlayer were observed to bend sideways

on a SiN interlayer was performed at high pressure (200 Torr) to promote GaN islands with (1101) facets. Such facets were found to bend dislocations more effectively [9], and as a result the low boundary for the SiN interlayer was lowered further down to ∼2 × 107 cm−2 for the edge dislocations and ∼4 × 107 cm−2 for the screw/mixed dislocations [22]. The low boundary of defect reduction for the SiN interlayer is correlated to the average spacing between pores in the interlayer. We would need at least two screw/mixed dislocations with opposite Burgers vectors, or three edge dislocations with a zero Burgers vector sum, present in an area between pores in order for them to annihilate each other. For this to happen, the √ average spacing between the screw dislocations needs to between pores. The minimum spacing of be at least 1/ 2 of the spacing√ edge dislocations is likewise 1/ 3 of the pore spacing. An average interlayer pore spacing of ∼5 μm would correspond to a dislocation spacing of ∼3 μm, or a low density boundary of ∼1 × 107 cm−2 , close to what we have observed experimentally.

8.6

SUMMARY

Lateral epitaxial overgrowth is widely used in manufacturing to lower the dislocation density in thick GaN layers. In this chapter we explored

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new growth approaches which seek defect reduction by growing GaN on a porous substrate or on a porous interlayer. A porous substrate with a reduced growth surface should produce fewer misfit dislocations. An interlayer can block, but not necessarily eliminate, a large portion of threading dislocations. Both techniques rely on local lateral growth to achieve coalesced and continuous films. A columnar SiC substrate offers a high degree of control in pore size distribution and can potentially lower the thermal stress. However, processes to clean and to planarize the porous surface are critical. The SiN interlayer seems easier to implement than the TiN interlayer, since the former can be deposited in situ, and the latter produces voids and stacking faults. There is a low boundary in dislocation density for the interlayers. Further lowering of the currently achieved low boundary of ∼1 × 107 cm−2 remains a key challenge of the field.

ACKNOWLEDGEMENT This work was supported by an ONR MURI program (Grant N0001496-1-1179) and a DoD/DURINT program (Grant N00014-01-1-0715). Both programs were monitored by Dr Colin Wood. We would like to thank Drs R. M. Feenstra, H. Morkoc¸, W. J. Choyke, and T. F. Kuech and their group members for collaborations and stimulating discussions.

REFERENCES [1] ONR MURI Grant N00014-96-1-1179, Large Area Heteroepitaxial Growth Using Compliant Substrates, 7/96–6/01; DoD/DURINT Grant N00014-01-1-0715, Nanoporous Templates for Large Defect Reduction in SiC and GaN, Nanocatalysis, Magnetic Clusters, and Biotechnology, 5/01–4/06. [2] T. Sugahara, H. Sato, M. Hao, Y. Naoi, S. Kurai, S. Tottori, K. Yamashita, K. Nishino, L. T. Romano, and S. Sakai, Direct evidence that dislocations are non-radiative recombination centers in GaN, Jpn J. Appl. Phys. 37, L398–L400 (1998). [3] T. Miyajima, T. Hino, S. Tomiya, K. Yanashima, H. Nakajima, T. Araki, Y. Nanishi, A. Satake, Y. Masumoto, K. Akimoto, T. Kobayashi, and M. Ikeda, Threading dislocations and optical properties of GaN and GaInN, Phys. Status Solidi B 228, 395–402 (2001). [4] F. A. Ponce, Defects and interfaces in GaN epitaxy, MRS Bull. 22, No. 2, 51–57 (1997). [5] S. D. Hersee, J. C. Ramer, and K. J. Malloy, The microstructure of metalorganic chemical-vapor-deposition GaN on sapphire, MRS Bull., 22, No. 7, 45–51 (1997).

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[6] T. S. Kuan, C. K. Inoki, Y. Hsu, D. L. Harris, R. Zhang, S. Gu, and T. F. Kuech, Dislocation mechanisms in the GaN lateral overgrowth by hydride vapor phase epitaxy, Mater. Res. Soc. Symp. 595, W2.6.1–W2.6.6 (2000). [7] A. Sakai, H. Sunakawa, A. Kimur, and A. Usui, Dislocation propagation in GaN films formed by epitaxial lateral overgrowth, J. Electron Microsc. 49, 323–330 (2000). [8] N. Kuwano, K. Tsukamoto, W. Taki, K. Horibuchi, K. Oki, Y. Kawaguchi, T. Shibata, N. Sawaki, and K. Hiramatsu, Gradual tilting of crystallographic orientation and configuration of dislocations in GaN selectively grown by vapour phase epitaxy methods, J. Electron Microsc. 49, 331–338 (2000). [9] T. S. Zheleva, O. H. Nam, W. M. Ashmawi, J. D. Griffin, and R. F. Davis, Lateral epitaxy and dislocation density reduction in selectively grown GaN structures, J. Crystal Growth 222, 706–718 (2001). [10] T. S. Kuan, C. K. Inoki, R. Zhang, S. Gu, and T. F. Kuech, Origin of the c-axis tilt occurring during the lateral epitaxial overgrowth of GaN, presented at the 2001 APS March Meeting, unpublished results. [11] G. Feng, X. M. Shen, J. J. Zhu, B. S. Zhang, H. Yang, and J. W. Liang, Reduction in crystallographic tilt of lateral epitaxial overgrown GaN by using new patterned shape mask, Phys. Status Solidi C 0, 2167–2170 (2003). [12] N. Gmeinwieser, K. Engl, U. T. Schwarz, J. Zweck, W. Wegscheider, S. Miller, A. ¨ Leber, A. Weimar, A. Lell, and V. Harle, Strain, wing tilt and photoluminescence in epitaxial lateral overgrown GaN on SiC substrates, Phys. Status Solidi A 201, 2760–2763 (2004). [13] C. K. Inoki, T. S. Kuan, C. D. Lee, Ashutosh Sagar, R. M. Feenstra, D. D. Koleske, D. J. Diaz, P. W. Bohn, and I. Adesida, Growth of GaN on porous SiC and GaN substrates, J. Electron. Mater. 32, 855–860 (2003). [14] A. Sagar, C. D. Lee, R. M. Feenstra, C. K. Inoki, and T. S. Kuan, Plasma-assisted molecular beam epitaxy of GaN on porous SiC substrates with varying porosity, J. Vac. Sci. Technol. B 21, 1812–1817 (2003). [15] Y. Oshima, T. Eri, M. Shibata, H. Sunakawa, K. Kobayashi, T. Ichihashi, and A. Usui, Preparation of freestanding GaN wafers by hydride vapor phase epitaxy with void-assisted separation, Jpn J. Appl. Phys. 42, L1–L3 (2003). ¨ Ozg ¨ ur, ¨ J. Q. Xie, S. Dogan, ˘ [16] F. Yun, Y. T. Moon, Y. Fu, U. H. Morkoc¸, C. K. Inoki, T. S. Kuan, L. Zhou, and D. J. Smith, Effectiveness of TiN porous templates on the reduction of threading dislocations in GaN overgrowth by organometallic vaporphase epitaxy, Appl. Phys. Lett. 86, 043108 (2005). [17] Y. Fu, F. Yun, Y.-T. Moon, U. Ozgur, J. Q. Xie, X. F. Ni, N. Biyikli, H. Morkoc¸, Lin Zhou, D. J. Smith, C. K. Inoki, and T. S. Kuan, Dislocation reduction in GaN grown on porous TiN networks by metal-organic vapor-phase epitaxy, J. Appl. Phys. 99, 033518 (2006). ¨ Ozg ¨ ur, ¨ J. Q. Xie, S. Dogan, ˘ [18] F. Yun, Y. T. Moon, Y. Fu, U. H. Morkoc¸, C. K. Inoki, T. S. Kuan, L. Zhou, and D. J. Smith, Effectiveness of TiN porous templates on the reduction of threading dislocations in GaN overgrowth by organometallic vaporphase epitaxy, Appl. Phys. Lett. 86, 043108 (2005), Figure 8. [19] S. Haffouz, B. Beaumont, P. Venn´egu`es, and P. Gilbart, Phys. Status Solidi A 176, 677 (1999). [20] A. Sagar, R. M. Feenstra, C. K. Inoki, T. S. Kuan, Y. Fu, Y. T. Moon, F. Yun, and H. Morkoc¸, Dislocation density reduction in GaN using porous SiN interlayers, Phys. Status Solidi A 202, 722–726 (2005).

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[21] F. Yun, Y.-T. Moon, Y. Fu, K. Zhu, U. Ozgur, H. Morkoc¸, C. K. Inoki, T. S. Kuan, A. Sagar, and R. M. Feenstra, Efficacy of single and double SiNx interlayers on defect reduction in GaN overlayers grown by organometallic vapor-phase epitaxy, J. Appl. Phys. 98, 123502 (2005). ¨ Ozg ¨ ur, ¨ Y. Fu, X. Ni, H. Morkoc¸, C. K. Inoki, T. S. Kuan, J. V. Foreman, [22] J. Xie, U. and H. O. Everitt, Low dislocation densities and long carrier lifetimes in GaN thin films grown on a SiNx nanonetwork, Appl. Phys. Lett. 90, 041107 (2007).

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9 Electrical Properties of Porous SiC D.C. Look and Z.-Q. Fang Semiconductor Research Center, Wright State University, Dayton, OH 45435, USA and Materials and Manufacturing Directorate, Air Force Research Laboratory, Wright-Patterson Air Force Base, OH 45433, USA

9.1

INTRODUCTION

Porous semiconductor material has unique properties that permit certain functionalities not available from single crystals. The high interest in this particular class of structures is evidenced by the fact that in the last 30 years over 5000 papers have been published on just one member of this class, namely, porous Si [1]. However, another member of great recent interest is porous SiC [2–5], and that will be the main emphasis of this chapter and indeed of this whole book. Since semiconductor materials are, by and large, useful because of their current-carrying properties, it is certainly of interest to ask how those properties are affected by porosity. Clearly, pores, or ‘voids’, would be expected to reduce the ability of a material to conduct current, and thus cause an increase in resistance. This is a correct assumption, but the relevant mechanism involves not only a loss of material, but also carrier trapping, a more subtle and interesting phenomenon. We will investigate both of these factors in detail, especially

Porous Silicon Carbide and Gallium Nitride: Epitaxy, Catalysis, and Biotechnology Applications Edited by Randall M. Feenstra and Colin E.C. Wood  C 2008 John Wiley & Sons, Ltd

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the latter, and show how they can lead to a semi-insulating form of material that can be very useful for electronic devices.

9.2

RESISTIVITY AND HALL EFFECT

Consider a rectangular parallelepiped of length l, width w, and height h, and suppose we place metal contacts on each end (area wh). If we now pass a constant current I from end to end, the voltage between ends will be given by V = I(l/wh)ρ, where ρ is called the resistivity, usually measured in units of  cm. The resistivity is a fundamental property of the material, independent of the geometrical factors. More information may be obtained by applying a magnetic field B, say parallel to the height h. Then, a voltage V H (the ‘Hall voltage’) will appear parallel to w, and the carrier concentration n in the sample can be calculated from the simple relationship n = IB/V H h. Finally, the mobility μ follows from μ = 1/(eρn), where e is the electronic charge. Actually, the relationships for n and μ in this formulation are exactly valid only for degenerate electrons, but they typically are in error by less than 20 % for nondegenerate electrons, also. To illustrate the effects of pores on the electrical properties, it is instructive to consider removal of a rectangular parallelepiped of dimensions αw, βh, and γ l, from the center of our sample. The current, flowing in the l direction, will encounter the pore and will, over a length γ l, be forced through a region of smaller area, wh(1 − αβ). As a first approximation, we can postulate that the pores do not accumulate any charges on their surfaces. Then, viewing the sample as three series resistances, of lengths l(1 − γ )/2, γ l, and l(1 − γ )/2, respectively, and assuming uniform current flow, it can be shown that the resistance will increase by the factor [1 + αβγ /(1 − αβ)]. If ‘porosity’ P is defined as the fraction of the sample occupied by pores, then P = αβγ in this case, and the fractional resistance increase is [1 + P/(1 − αβ)]. Extending this picture to N noninteracting pores, P = Nαβγ . The above model qualitatively illustrates one of the reasons for an increase in resistance, namely, that pores reduce the volume in which the current can flow. Quantitatively, however, the situation is more complex, because the pores will attain a charge in order to direct the current flow around them. The charge distribution will, in general, depend upon a pore’s shape and whether or not it is isolated from other pores (i.e. has neutral material in between). Juretschke et al. [6] have shown that, for cylindrical pores that are parallel to the magnetic field (h direction) and

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perpendicular to the electric field (l direction), the apparent resistivity will be given by ρ app = ρ(1 + P)/(1 − P). For this particular geometry, the measured carrier concentration is unaffected, i.e. napp = n. However, if the cylinders are perpendicular to the electric field and to the magnetic field, then napp = n(1 – P), while the formula for ρ app is the same as that above. Interestingly, a decrease in n by a factor (1 – P) is what would naively be expected as a first guess, because the Hall-effect experiment in homogeneous material measures the total carrier concentration, and this quantity is indeed reduced by a factor (1 – P) due to the material loss. Following the preceding arguments, we can easily understand the increase in apparent resistivity and decrease in apparent carrier concentration resulting from the fact that pores remove material. However, this mechanism cannot explain the common observation that even moderately porous material can be semi-insulating. To understand this phenomenon, we must recognize that pores are basically surfaces, and surfaces often contain electronic gap states, either donor-like or acceptorlike. For example, in GaAs it is known that surface states pin the surface Fermi level at EC – 0.7 eV, in n-type material, and EV + 0.5 eV, in ptype material. Such surface states, in various materials, can be produced by atomic reconstructions or by incorporation of impurities or point defects. Crystalline, n-type SiC is known to have deep, acceptor-like surface states of sheet concentration 1012 cm−2 or greater [7]. Thus, it is not surprising that the surfaces of pores in SiC would also have acceptor-like states, which could deplete electrons from the surrounding regions. In the porous SiC sample discussed below, the pores are basically spherical with average diameter about 40 nm. Since their density is about 5 × 1015 cm−3 , the fraction of porous material P is about 0.2. However, it turns out that approximately 34 nm of material is depleted of free electrons around each pore, so the total fraction of material depleted is closer to 0.8. Thus, about 20 % of the electron loss is due to missing material, and about 60 %, trapping on pore surfaces. Clearly, both mechanisms are important for this sample, but it must be pointed out that the relative importance of each mechanism for other samples will depend on pore size, shape, and surface-state density. Note also that the trapping phenomenon makes it easily possible to create semi-insulating SiC, of great interest to the electronics industry. In our sample, only a slightly higher pore density would have produced semi-insulating material. Our discussion above has mainly been concerned with steady-state current transport, which is of obvious importance for electronic devices. However, transient effects are also of interest, because the current in such devices is usually modulated, often at very high speeds. The pores in SiC,

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at least in our example, act as ‘giant traps’, because each 40 nm pore will hold about 125 electrons. Thus, it is important to understand the capture and emission properties of these pores, and that is a subject that can be addressed by deep level transient spectroscopy (DLTS), discussed below.

9.3 9.3.1

DEEP LEVEL TRANSIENT SPECTROSCOPY Fundamentals of DLTS

In its simplest and most commonly used form, DLTS is based on the depletion capacitance arising from a metal Schottky barrier on a semiconductor [8,9]. As illustrated in Figure 9.1, the Schottky metal (at depth = 0) draws (‘depletes’) electrons from a thickness w of the semiconductor (assumed n-type) under it, and this thickness w can be varied by applying bias between the metal and the semiconductor. Because charge is being transferred from semiconductor to metal or vice versa, the system acts as a capacitor. In the DLTS experiment, a large reverse (negative) bias is first applied to the metal for a long time, producing a region [from the surface (z = 0) to depth wr ] depleted of free electrons. Furthermore, any electron traps in the somewhat smaller region, 0 to wr − λ, will also lose their electrons. Then, a forward bias pulse is applied to the metal for a time tp , reducing the depletion region to a thickness w f ; during this pulse, the traps in region w f − λ to wr − λ will begin to fill. This is the capture process, and most of the common traps will fill in a time tp = 1 ms, or

e φB

Energy (eV)

1.0

cond. band shallow donors

0.5

free electrons

0 EF –0.5 –1.0

trap w-λ 0

w 200 400 Depth (nm)

600

Figure 9.1 Schematic diagram of the emission of electrons from filled traps after a filling pulse

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less. Finally, the reverse bias is reapplied, and the filled traps (shown with the arrows) will begin to emit their captured electrons. Even though the bias is now the same as before the capture process, the capacitance is not, because of the captured charge on the traps. This charge will eventually bleed off the traps, and the capacitance will return to its quiescent value. It is this capacitance transient arising from the emission process that is the heart of the DLTS experiment. In the ‘boxcar’ method of transient analysis, used in our experiment [8,9], the capacitance transient is evaluated at two points, t1 and t2 , and the signal is then defined as S = C(t1 ) − C (t2 ). The values of t1 and t2 are fixed, defining a ‘rate window’, and temperature is swept, say from 20 to 450 K. At very low temperatures, the emission is very slow, and thus the transient is very flat, giving C(t1 ) ∼ C(t2 ), or S ∼ 0. Similarly, at very high temperatures the transient is very fast, so that it has mostly decayed even before time t1 . In this case, C(t1 ) ∼ C(t2 ) ∼ 0, so S again is ∼ 0. However, between the high and low temperatures, S will go through a maximum, depending on the trap energy, and it is this peak that is analyzed in the DLTS experiment. The analysis of capture and emission is based on the usual master equation: df = −en f + cn (1 − f ) dt

(9.1)

where f is the fractional occupation of the trap states, en is the emission rate from filled traps, and cn is the capture rate to empty traps. For a point-charge trap, e.g. a substitutional impurity, the cn and en terms are relatively simple: cn (n,T) = σ v(T)n, and en (T) = σ emis v(T)NC B (T)exp(−Ess /kT), where v(T) = (8 kT/π m* )1/2 is the thermal velocity, NC B (T) = 2(2π m* kT)3/2 /h3 is the effective conduction band density of states (in the Boltzmann approximation), n is the free electron concentration, σ is the capture cross-section for a single trap, and σ emis = (g0 /g1 )σ exp(α/k), where g0 and g1 are the degeneracies of the unoccupied and occupied trap states, respectively, and α is a linear temperature coefficient: E SS = E SS 0 (1 − αT). The equation for cn is rather intuitive, and the equation for en results from setting df/dt = 0, in equilibrium, and then comparing the resulting equation, f = 1/(1 + en /cn ), with the relevant Fermi function. Equation (9.1) is easily solved and gives an exponential form for f. Typically, during capture, cn  en , giving f = 1 – exp(−cn t p ), while during emission en  cn , giving f = exp(−en t). While this simple picture suffices to explain the vast majority of DLTS results, it does not in general hold for pore-related traps. The reason

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is that a pore can hold more than one electron, and as it begins to fill with electrons, it will present a potential energy barrier to other electrons approaching it. This barrier will depend on the filling fraction f and the distance from the surface of the pore. At the surface, defined by radius r p ,

will have its maximum value, (r p , f), and only a fraction exp(− /kT) of the n electrons in the vicinity of the surface will have enough energy to overcome the barrier and be captured. Thus, we must modify our equations for cn and en to read:  

sph (r p , f ) cn (n, T, f ) = σ v(T)n exp − kT  

sph (r p , f ) ≡ cn0 (n, T) exp − kT   ESS + sph (r p , f ) en (T, f ) = σemis v(T)NC B (T) exp − kT  

sph (r p , f ) ≡ en0 (T) exp − kT

(9.2)

(9.3)

where a spherical pore ( sph ) has been assumed as an example. In this case, Equations (9.1)–(9.3) cannot be solved in closed form, except for special cases of . However, it is possible to write a general, transcendental, integral equation for f(t), describing both capture and emission [10]: 

fβ fα

9.3.2



sph (r p , f ) exp kT  d f = cn0 (n, T)(tβ − tα )  en0 (T) 1− f 1+ cn0 (n, T)

(9.4)

Method of Solving the General Equation

As described above, the DLTS experiment consists basically of applying a forward bias to a normally reverse-biased Schottky barrier or p-n junction [8,9]. In reverse bias, more of the traps are in a region depleted of free electrons, and thus experience a very low free-electron concentration, n = nr  nb, where nb is the bulk (neutral) value, ∼1018 cm−3 in our case. Thus, cn0 (nr ,T) is very small, so that emission dominates and the traps are almost empty. Then, in forward bias, the traps are suddenly exposed to the bulk free-electron concentration n = nb for a time t p , the filling

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pulse length, and at the end of this pulse the filled fraction is defined as f p . Thus, the trap filling process is described by solving Equation (9.4) for f p under the conditions fα = 0, fβ = f p , n = nb, tα = 0, and tβ = t p . (One convenient means of solving this equation is by use of the ‘root’ function in Mathcad [11].) When the filling pulse has ended at time t p , i.e. upon reapplication of the reverse bias, the traps are once again suddenly exposed to a very small value of n, i.e. n = nr . [Note that the solution of Equation (9.4) is very insensitive to the exact value of nr , as long as nr  nb.] The traps now emit their carriers, so that the original fractional occupation f p is now reduced to fe , in total time t p + te . Thus, in emission, Equation (9.4) is solved for fe under the conditions fα = f p , fβ = fe , n = nr , tα = t p , and tβ = t p + te . As mentioned above, the ‘boxcar’ method of DLTS analysis defines the signal as S ≡ f(t1 ) – f(t2 ). Such a signal is simulated simply by solving Equation (9.4) at two times, t p + t1 , and t p + t2 . Before applying Equation (9.4) to the problem at hand, it is instructive to solve it in two special cases, which apply to the majority of present-day DLTS analyses. In the first case, the most common of all, we set (r p ,f) = 0 (or a constant). Then, Equation (9.4) immediately yields closed-form exponential capture and emission equations, as shown earlier. The other special case of interest is realized under two conditions: (1) small f , such that the denominator of the integrand in Equation (9.4) can be approximated by unity; and (2) (r p ,f) ∝ f. Then, Equation (9.4) yields a logarithmic solution for f [cf. Equation (3) of Hierro et al. [12]], which has been seen experimentally for trapping along dislocation lines [12,13].

9.4

SAMPLE CONSIDERATIONS

We now return to the problem at hand, namely, pores in SiC, which have a much more complicated potential energy surface (r p ,f). Our particular porous SiC sample, designated P-SiC, was prepared by photoassisted electrochemical etching [3] of n-type 6H-SiC. The electrolyte was a mixture of HF acid and ethanol. The resistivity of the nonporous starting material, designated NP-SiC, was about 0.2  cm, and the carrier concentration ∼1018 cm−3 . The capacitance–voltage (C–V) and DLTS data were obtained by means of a BioRad DL4600 DLTS apparatus, which operated over the temperature range 80–450 K. From the C–V data (Figure 9.2), the carrier concentration in the NP-SiC was uniform at mid1018 cm−3 , whereas that in the P-SiC dropped to about 1017 cm−3 at a depth of about 80 nm. Cross-sectional transmission electron microscopy

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Carrier concentration (cm–3)

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10

19

T = 300 K nonporous

10

18

10

17

10

porous

20

30

40 50 Depth (nm)

60

70

Figure 9.2 Concentration vs depth (from C–V measurements) for the nonporous and porous SiC samples used in this study

(TEM), using a 200 kV Phillips CM-200 instrument, was used to study the pore size and density. At depths of 50–100 nm below the surface, the pore radii ranged in size from 10 to 25 nm, with an average size of about 20 nm and a density of about 5 × 1015 cm−3 , increasing with depth. The sizes and densities of these pores are very typical of those found at the same depth (just below the so-called ‘skin layer’) in other P-SiC samples [2–4]. It should be noted that not all pores observed in P-SiC are spherical, and in fact, several different shapes have been seen [5]. However, we will consider only spherical and cylindrical pores, because they are among the most common reported, and also because they have electrostatic potentials that are relatively easy to calculate.

9.5

POTENTIAL ENERGY NEAR A PORE

It will turn out that the value of N SS (sheet acceptor-state density) necessary to fit our DLTS data is about 2.5 × 1012 cm−2 , within range of surface-state densities reported for crystalline SiC [7]. The total number of traps per pore is then 4πr p2 NSS , giving, in this case, about 125 total electrons for an average pore of radius r p = 20 nm. As more and more electrons are trapped in the filling process, a negative (repulsive) potential φ sph builds up, and the trapping rate diminishes. As mentioned above, a spherical region depleted of free electrons, described by a local band bending of energy sph = −eφ sph (r p ), forms at the surface (r = r p ) of the pore. The value of can be calculated from Poisson’s equation, which, for spherical pores, is most conveniently expressed in spherical

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coordinates. The symmetry precludes the need for angular terms, so that Poisson’s equation becomes: ρ eND 1 d 2 dφsph r =− =− 2 r dr dr ε ε

(9.5)

where ρ is the charge density, ε is the dielectric constant, and N D is the net donor density (actually, N D – N A, where N A is the acceptor concentration). We solve this equation in the depletion approximation, in which both φ and dφ/dr are required to vanish at w, defined as the radius of the total depleted region, including the pore radius. [In setting φ(w) = 0, we have arbitrarily set the zero of potential at the conductionband edge in the neutral region. Thus, φ represents the ‘band bending’.] Charge conservation requires that (4/3)π (w3 – r p 3 )N D = 4π r p 2 N SS , so that the final expression for energy, = −eφ, can be shown to be:      r 2 − r 2p NDr p r p e2 NSS r p f ND

sph (r, f ) = + 1+ −1 ε r p NSS f 6 3NSS f r

  r p ND 3NSS f 2/3 1− 1+ (9.6) +1 + 2NSS f r p ND where f is the fractional occupation of the trap states on the pore, i.e. f = N SS − /N SS . Equation (9.6) holds for r p ≤ r ≤ w, and is cast in a form which is convenient in that the first two terms drop out for r = r p . (For r ≥ w, = 0.) In our case, N D ≈ 1018 cm−3 , so that (r p ) ≈ 0.2 eV, for f = 1. For completeness, we also consider cylindrical pores, which are appropriate for defects such as threading dislocations or nanopipes. Here the charge-conservation condition is π (w2 – r p 2 )LN D = 2π r p LN SS , where L is the pore length. By solving Poisson’s equation in the cylindrical coordinate system [let r2 → r, in Equation (9.5)], we get, again for r p ≤ r ≤ w:      r p ND e2 NSS r p f 2NSS f r

cyl (r, f ) = 1+ ln 1 + − 2 ln 2ε 2NSS f r p ND rp    2 r − r 2p ND −1 (9.7) + 2r p NSS f In this case, (r p ) ≈ 0.3 eV, for f = 1.

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ΔC/C (10–3)

0.6 0.4

T4

0.2 1.0 5.0 20

T3

0.2

t p (ms)

t p (ms)

T1

ΔC/C (10–3)

T2

T0

0.2 1.0 5.0 20

20

20 T1 5.0

10

T2

1.0

T3

0 100

200 300 T (K)

(a)

0

400

100

0.2

200 300 T (K)

(b)

400

Figure 9.3 DLTS signal amplitude vs filling pulse width t p for the nonporous (a) and porous (b) samples used in this study. Note that the pore-related trap T0 has much different filling characteristics

9.6

DLTS DATA AND ANALYSIS

6

10

5

2

10

4

10

3

10

2

10

1

T /en (K s)

10

2

The DLTS signals as a function of forward-bias pulse length t p are shown in Figure 9.3. For the NP-SiC [Figure 9.3(a)] all the traps saturate (reach their maximum amplitudes) within a few milliseconds. However, a new trap, T0 , appears in the P-SiC [Figure 9.3(b)] and this trap is not nearly saturated even for t p = 20 ms. The energies of these traps are given by a standard Arrhenius analysis, shown in Figure 9.4. Note that trap T0 is very deep, with an energy of 0.8 eV with respect to the conduction band edge.

T0 T2 (0.80 eV) (0.52 eV)

tp = 1 ms

T3 (0.42 eV) T4 (0.23 eV)

2

3

4

5

6

103/T

(K–1)

7

8

9

Figure 9.4 Arrhenius plots of traps in the nonporous (open symbols) and porous SiC (solid symbols) samples used in this study

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1.0 exp. approx.

Fraction filled

0.8 0.6 exact

0.4 0.2 0

log. approx.

0.001

tp

0.01

t1

t2

0.1

t (s)

Figure 9.5 Fractional occupation, during capture and emission at 350 K, of a pore in porous SiC. An exact calculation is compared with exponential and logarithmic approximations. The filling pulse length is t p , and the ‘boxcar’ sampling points on the emission transient are t1 and t2 , respectively. Reproduced from [10], with permission from the American Physical Society

We believe that the T0 traps represent surface states on the pores, and we analyze these curves by solving Equation (9.4) with the spherical potential energy given in Equation (9.6). In Figure 9.5, we compare the capture and emission solutions for three different cases: (1) exact analysis [Equation (9.4)]; (2) exponential analysis [setting sph = 0, in Equation (9.4)]; and (3) logarithmic analysis [for f  1, and sph = Ke2 N SS r p f/ε in Equation (9.4)]. To generate the curves, we have used some SiC parameters from the literature: m* /m0 = 0.4, and ε/ε0 = 10; some parameters measured by TEM or C–V: r p = 2 × 10−6 cm; N D ≈ nb ≈ 1018 cm−3 ; and ne ≈ 109 cm−3 (fit not sensitive to ne ); and some fitted parameters [i.e. those needed to fit the DLTS data of trap T0 in Figure 9.3(b)]: N SS = 2.5 × 1012 cm−3 ; E SS 0 = 0.8 eV; σ = 1 × 10−22 cm2 ; and σ emis = 3 × 10−13 cm2 . A filling pulse length t p = 20 ms was assumed for the curves in Figure 9.5. The exponential approximation is the one assumed in the vast majority of DLTS experiments, and indeed, it works well for simple, isolated traps such as T2 [cf. Figure 9.3(a)]. However, it rises much too fast to explain the capture process of the pore-related traps [T0 , in Figure 9.3(b)]. The logarithmic approximation, however, works fairly well for filling fractions up to about 0.5, but fails beyond that point. From the exact solution, it is seen that even at t p = 20 ms, complete saturation has not taken place. In emission, the exact solution is also much slower than the exponential solution, because at higher values of f the emitting electrons experience a strong coulomb barrier and are slowed down. In Figure 9.5, we have also simulated a boxcar analysis on

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T0

experimental theoretical

−ΔC/C

0.008 0.006

20 ms 5

0.004 0.002

T1 T2

1 0.2

0 220 240 260 280 300 320 340 360 380 T (K)

Figure 9.6 Experimental (dashed lines) and theoretical (solid lines) DLTS curves for different filling-pulse lengths, 0.2, 2, 5, and 20 ms, in porous SiC. Trap T2 is a ‘normal’ trap (impurity or point defect), which obeys exponential kinetics, and trap T0 is related to the pores. Reproduced from [10], with permission from the American Physical Society

the BioRad DL4600 instrument by indicating a common set of sampling points, t1 = 61.0 ms and t2 = 152.6 ms, referenced with respect to t p . This choice leads to an emission rate of ln(t2 /t1 )/(t2 – t1 ) = 10 s−1 at the signal maximum of a trap such as T2 [Figure 9.3(a)]), which has an exponential emission [8,9]. However, the emission for trap T0 is far from exponential, so that the ‘standard’ analysis will be highly inaccurate in this case. The experimental DLTS data, for filling pulse lengths of 0.2, 1.0, 5.0, and 20 ms, are repeated as dashed lines in Figure 9.6. Here we have plotted C/C, where C = C(t1 ) – C(t2 ), and C is the equilibrium capacitance under the reverse-bias condition, Vr = −5 V. It can be shown that − C/C ∼ = Fλ NT /2N D, where NT is the trap concentration, and Fλ is a factor which is close to unity for small trap concentrations (NT  N D) and energies that are not too deep, but <1 otherwise [9]. For our case, NT = 4π r p 2 N SS N p , where N p is the volume density of pores. From the TEM measurements, the sheet density of pores is about 3 × 1010 cm−2 , and the volume density N p is then, very approximately, (3 × 1010 )3/2 ≈ 5 × 1015 cm−3 . Thus, NT ≈ 6 × 1017 cm−3 , and from this value and also ET = E SS = 0.8 eV, we can calculate Fλ = 0.25 [9]. The actual DLTS signal is ∝ NT [f(t1 ) – f(t2 )], and f(t1 ) – f(t2 ) is calculated to be 0.646 at the peak of the 20 ms theoretical curve, in Figure 9.6. Thus, from the TEM data, we would predict that Fλ NT [f(t1 ) – f(t2 )]/N D ≈ 0.10, whereas we actually need a value of about 0.03 to fit the data at the peak, as shown. In other words, we need an NT value of about 2 × 1017 cm−3 (or an N p value of about 2 × 1015 cm−3 ) to fit the data, and this value of N p is not outside the error of that determined by TEM (5 × 1015 cm−3 ), considering that the latter is a rather crude estimate.

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The normalization factor for the 20 ms curve is now applied to the other three theoretical curves, and they reproduce their respective experimental peak magnitudes quite well. Furthermore, the temperature shifts are also well reproduced, giving strong validity to our model. Finally, both the experimental and theoretical curves become narrower at larger values of t p . The experimental curves are of course broader than their theoretical counterparts, because we have not considered the known variations in r p , and the possible variations in E SS . The variation in r p is not likely the cause of the broadening, because neither a doubling nor a halving of the pore size moves the curves by more than a few kelvin. However, an increase of E SS from 0.80 to 0.85 eV moves the curves up by almost 20 K, which is sufficient to explain the line broadening. Indeed, a ±0.05 eV variation in E SS seems quite reasonable, since some of the pores will undoubtedly be close enough to influence each other. Moreover, it should be noted that adding more traps at different values of E SS would also bring the total, fitted NT closer to the TEM estimate. In summary, we first of all have used TEM results to determine that r p ∼ 20 nm and N p ∼ 5 × 1015 cm−3 , and thus have been able to calculate the sample porosity P = (4/3)π r p 3 N p ≈ 0.2. That is, about 20 % of the free-carrier loss in our sample is due to the removal of material. Then, an analysis of DLTS results has shown that acceptorlike surface states on the pores produce a depleted volume of radius w ∼ 34 nm around each pore. Therefore, the total fractional volume depleted of free electrons is (4/3)π w3 N p ≈ 0.8. This means that about 60 % of the carrier depletion is due to traps on the pore surfaces, not the pores themselves. The calculated carrier depletion (80%) is quite consistent with C–V measurements (Figure 9.2), which indicate that n (averaged over the depleted regions [3]) has fallen from mid-1018 to about 1017 cm−3 in the region sampled by the DLTS experiment.

ACKNOWLEDGEMENT This work was supported by the DURINT program administered by the Office of Naval Research (Dr C. Wood) under Grant N00014-0110715.

REFERENCES [1] A.G. Cullis, L.T. Canham, and P.D.J. Calcott, ‘The structural and luminescence properties of porous silicon’, J. Appl. Phys., 82, 909 (1997). [2] A. Sagar, C.D. Lee, R.M. Feenstra, C.K. Inoki, and T.S. Kuan, ‘Morphology and effects of hydrogen etching of porous SiC’, J. Appl. Phys., 92, 4070 (2002).

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[3] S. Soloviev, T. Das, and T.S. Sudarshan, ‘Structural and electrical characterization of porous silicon carbide formed in n-6H-SiC substrates’, Electrochem. Solid State Lett. 6, G22 (2003). [4] P. A. Ivanov, M. Mynbaeva, and S. E. Saddow, ‘Effective carrier density in porous silicon carbide’, Semicond. Sci. Technol, 19, 319 (2003). [5] Y. Shishkin, W.J. Choyke, and R.P. Devaty, ‘Triangular pore formation in highly doped n-type 4H SiC’, Mater Sci. Forum, 457–460, 1457 (2004). [6] H.J. Juretschke, R. Landauer, and J.A. Swanson, ‘Hall effect and conductivity in porous media’, J. Appl. Phys., 27, 838 (1956). [7] P.A. Ivanov, M.E. Levinshtein, J.W. Palmour, and S.L. Rumyantsev, ‘Noise spectroscopy of local surface levels in semiconductors’, Semicond. Sci. Technol., 15, 164 (2000). [8] D.V. Lang, ‘Deep level transient spectroscopy—new method to characterize traps in semiconductors’, J. Appl. Phys., 45, 3023, (1974). [9] D.C. Look and J.R. Sizelove, ‘Depletion width and capacitance transient formulas for deep traps of high-concentration’, J. Appl. Phys., 78, 2848 (1995). [10] D.C. Look, Z.-Q. Fang, S. Soloviev, T.S. Sudarshan, and J.J. Beockl, ‘Anamolous capture and emission from internal surfaces of semiconductor voids: Nanopores in SiC’, Phys. Rev. B, 69, 195205 (2004). [11] Mathsoft, Cambridge, MA, USA. [12] A. Hierro, A.R. Arehart, B. Heying, M. Hansen, J.S. Speck, U.K. Mishra, S.P. DenBaars, and S.A. Ringel, ‘Capture kinetics of electron traps in MBE-grown nGaN’, Phys. Status Solidi B 228, 309 (2001). [13] T. Wosinski, ‘Evidence for the electron traps at dislocations in GaAs crystals’, J. Appl, Phys., 65, 1566 (1989).

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10 Magnetism of Transition Metal Doped GaN Nanostructures Q. Wang and P. Jena Physics Department, Virginia Commonwealth University, Richmond, VA 23284, USA

10.1

INTRODUCTION

The current information revolution puts increasing demand for faster, smaller, low power and high storage capacity devices for processing of information. Spin-based electronics, commonly referred to as spintronics, is an emergent technology that innovatively manipulates the spin and charge states of electrons to carry and store information. Since the spintronic devices are smaller, more versatile and robust than the traditional electronic devices, they have the potential to fundamentally alter the electronics industry. In order to make a spintronics device, the primary requirement is to have a system that can generate a current of spin polarized electrons, and a system that is sensitive to the spin polarization of the electrons. The simplest method of generating a spin polarized current is to inject the current through a giant magnetoresistance (GMR) device. A typical GMR Porous Silicon Carbide and Gallium Nitride: Epitaxy, Catalysis, and Biotechnology Applications Edited by Randall M. Feenstra and Colin E.C. Wood  C 2008 John Wiley & Sons, Ltd

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device consists of at least two layers of FM materials separated by a spacer layer. When the two magnetization vectors of the FM layers are aligned, an electrical current will flow freely, whereas if the magnetization vectors are antiparrallel then the resistance of the system is higher. So, spintronic materials have the basic requirements – high spin polarization and long spin relaxation time. Realization of functional spintronic devices requires the materials to be FM at operational temperature. Dilute magnetic semiconductors (DMSs) are good candidates for spintronic devices. DMS materials are based on nonmagnetic wide band gap semiconductors such as GaN and ZnO where several atomic % of Ga or Zn atoms are substituted by transition metal atoms, such as Mn, Cr, and Fe. At low dopant concentration, crystal structure of the host semiconductor material is unchanged and the DMS materials possess the properties of not only a FM material, but also that of the semiconductor host. Among the various DMSs, transition metal doped GaN materials are particularly interesting and are regarded as prime candidates for spintronics applications since GaN is a direct wide band gap semiconductor with high thermal, chemical, and mechanical stability. Moreover, Mn and Cr atoms have high magnetic moments. Since the discovery of ferromagnetism in (Ga,Mn)As [1] and the subsequent theoretical prediction [2] that Mn-doped GaN can be FM at or above room temperature, numerous experimental attempts have been made to synthesize this promising DMS material [3–19]. However, the results have been rather confusing. Not only the reported Curie temperatures [3–14] vary over a wide range (10–945 K), but also it is uncertain whether the ground state of (Ga, Mn)N is FM or antiferromagnetic (AFM) [15–21]. The nature and origin of the magnetic coupling in this material continue to be a hotly debated issue. The mechanism for the observed magnetic behavior is complex and appears to depend on a number of factors, including the sample preparation conditions, presence of defects, Mn–Mn separation, and carrier density and type. An understanding of the controversy between FM and AFM is both important and challenging [20, 21]. However, several groups have recently reported above room temperature ferromagnetism for (Ga, Cr)N [22–25] in both bulk and thin film forms. A fundamental understanding of the magnetic coupling between Mn atoms and Cr atoms in GaN is crucial for the development of spintronics devices from these DMSs. To understand the origin of magnetism in Mn- and Cr-doped GaN, we have performed extensive theoretical calculations on (Ga,Mn)N and (Ga,Cr)N systems from zero-dimensional clusters to one-dimensional nanowires, nanotubes, and nanoholes; two-dimensional surfaces and

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thin films; and three-dimensional crystals. These extensive studies enable us to unravel how the inter-atomic distance, local coordination, and dimensionality of a material control not only the magnetic moments of atoms but also the coupling between them. This understanding is also helpful in designing new DMSs such as Mn-doped nanoporous GaN. Note that a nanopore is characterized by large surface area whose orientation can differ from those of bulk surfaces. In the following we discuss these results by concentrating on GaN host.

10.2

Mn-DOPED GaN CRYSTAL

We begin with the study of the electronic structure, energetics and magnetism of Mn-doped GaN crystal. Pure GaN normally crystallizes into the hexagonal wurtzite structure, which consists of Ga and N planes stacked alternatively along the c-axis with the Ga and N ions tetrahe˚ and c = drally coordinated. The lattice constants are a = b = 3.189 A, ˚ with a space group P63 mc (no. 186). We first generated a (2 × 5.185 A, 2 × 2) supercell to explore the electronic structure and magnetic properties of bulk Ga1−x Mnx N, which consists of 16 formula units of GaN. To study the magnetic coupling between the Mn atoms, it is necessary to replace at least two Ga atoms with Mn in the supercell. The Mn–Mn distance and Mn-N-Mn bond angles were varied by replacing the Ga atoms at different sites, until the total energy reached a minimum. To study the influence of the surpercell size and the Mn doping concentration on the magnetic coupling, the calculations were repeated by constructing a (3 × 3 × 2) supercell. Theoretical calculations were carried out by using the density functional formalism [26]. Exchange and correlation effects were incorporated using the PW91 functional [27] for the generalized gradient approximation (GGA). The electronic structure, total energies and magnetic properties were calculated using a plane-wave basis set with the projector augmented wave (PAW) method [28] as implemented in the Vienna Ab initio Simulation Package (VASP) [29]. The cutoff energy was set at 330 eV for the plane-wave basis (the default of maximum cut-off energy is 269.89 eV). In all calculations, self-consistency was achieved with a tolerance in the total energy of at least 1 meV. Hellman–Feynman ˚ −1 . force components on each ion in the supercells converged to 1 meV A We first discuss the results based on a GaN (2 × 2 × 2) supercell having wurtzite structure. Two Ga atoms in this supercell were replaced with Mn atoms, corresponding to a Ga14 Mn2 N16 supercell and a 12.5 % Mn doping concentration. Note that in recent experiments Mn concentration

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from 3 to 15% have been investigated. Since it is a priori not clear which of the two Ga sites Mn atoms would prefer to substitute, we carried out an extensive search for all possible geometrical configurations. In each case, the geometry (ionic coordinates and c/a ratio) was fully optimized without any symmetry constraint. The total energies, electronic structure and magnetic moments located at each Mn atom were calculated selfconsistently for different spin alignments (FM and AFM) for each of these configurations. The k-point convergence was achieved with (6 × 6 × 6) Monkhorst–Pack grid [30]. We found that without structure optimization the coupling between these two Mn atoms is FM as predicted by previous studies [31–35]. The FM state lies 0.053 eV in energy lower than the AFM state. When the geometry is fully optimized (including ionic coordinates and c/a ratio), the FM state is still lower in energy than the AFM state by 0.077 eV. ˚ which is in good The relaxed Mn–N bond length is found to be 1.99 A, ˚ [36]. Thus the agreement with the experimental value of 2.01 ± 0.03 A geometry optimization in the bulk does not alter the preferred magnetic coupling. The calculations were repeated using a (3 × 3 × 2) supercell that corresponds to 72 atoms (Ga36 N36 ). With two Ga atoms in this supercell replaced with Mn at different sites, the resulting Mn doping concentration corresponds to 5.6 %. The (5 × 5 × 5) Monkhorst–Pack k-point mesh was used. The calculated results were found to be nearly the same as that given for the smaller supercell, namely, the ground state in Mndoped GaN bulk is FM and lies 0.10 eV lower in energy than the AFM ˚ Thus, it is clear that the FM state. The Mn–N bond length is 1.98 A. coupling between Mn atoms in bulk GaN is independent of the Mn concentration or supercell size.

10.3

Mn-DOPED GaN THIN FILMS

The above discussion does not explain why in certain experiments the coupling between Mn atoms exhibits antiferromagnetism or spin glass behavior. We note that most of these experiments involve thin films. It is, therefore, important to understand if the magnetic behavior of Mn on surfaces and in thin films is fundamentally different from that in the bulk. For example, do Mn atoms prefer to reside on the surface, do they prefer to cluster, and does the Mn–Mn distance depend upon the crystallographic orientation of the surface? In the following we discuss these aspects.

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10.3.1

249

Mn-doped GaN (1120) Surface

We have modeled a thin film having the (1120) surface orientation by a nine-layer slab with the supercell [37] containing 72 atoms (Ga36 N36 ) as shown in Figure 10.1. To preserve symmetry, the top and bottom layers of the slab were taken to be identical, and each slab was separated from ˚ The central three layers were held the other by a vacuum region of 10 A. fixed at their bulk configuration while the three surface layers on either side of the slab were allowed to relax without any symmetry constraint. K-point convergence was achieved with (6 × 4 × 1) grid, and tests with up to (8 × 6 × 2) mesh were made. To study the site preference of a Mn atom, we have first replaced one Ga atom with Mn on the surface layer, the second layer and the third layer on either side of the slab. It was found that Mn atom prefers to reside on the surface site which lies 1.37 and 1.54 eV lower than that of the second and third layer, respectively. This is consistent with the

Figure 10.1 Schematic representation of a nine-layer slab model for wurtzite GaN (1120) surface. The numbered spheres are Ga. Reproduced from Q. Wang, Phys. Rev. B 72, 045435-2. Copyright (2005), with permission from the American Physical Society.

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POROUS SILICON CARBIDE AND GALLIUM NITRIDE Table 10.1 Relative energies (EFM and EAFM ) with respect to the ground state for the Ga32 Mn4 N36 supercell. E is the energy difference between AFM and FM states (E = EAFM − EFM ) Configuration

EEF (eV)

EAFM (eV)

E (eV)

I (1,3/35,33) II (2,3/36,33) III (3,4/33,34) IV (3,6/33,29) V (5,6/30,29)

0.403 1.722 1.773 2.550 3.438

0.000 1.694 1.708 2.465 3.226

−0.403 −0.028 −0.065 −0.085 −0.212

experimental finding where Mn atoms doped in GaN were found to migrate to the surface site upon annealing. The magnetic coupling between Mn atoms was studied by replacing two Ga atoms with Mn on either side of the slab. This amounts to a supercell consisting of Ga32 Mn4 N36 . There are many ways to reach this replacement. We have considered five different configurations, which have been specified in Table 10.1. Geometry optimization and total energy calculation were carried out. We found that configuration I with AFM coupling between Mn atoms is the lowest energy configuration and the FM state is 0.40 eV higher in energy than the AFM state. Other configurations are also AFM and are much higher in energy relative to the ground state. This indicates that Mn atoms couple antiferromagnetically in GaN (1120) thin film. The total densities of states (DOS) and partial DOS of Mn atom for Ga32 Mn4 N36 slab with and without geometry optimization are shown in Figure 10.2. For the unrelaxed surface, the coupling is FM, the DOS exhibits half-metallic behavior similar to that in (Ga, Mn)N crystal. When the surface is fully optimized, the coupling becomes AFM and the spin-up and spin-down DOS are identical as the total moment of the system is zero. The magnetic moment at each of the Mn site is found to be 3.0 μB with opposite spin orientation. The main contribution to this moment comes from the Mn 3d electrons as can be seen from the partial DOS for the Mn atom in Figure 10.2(c). The hybridization between N 2p and Mn 3d reduces the magnetic moment as compared with that of a free Mn atom. As discussed above, the magnetic coupling between Mn atoms in the crystal is not affected by the relaxation of the structure. However, the situation is different in the surface case. If the surface is not relaxed, the coupling is FM, which becomes AFM upon relaxation. To understand the physics involved, we checked the changes in bond lengths. Due to relaxation, the bond lengths near the film surface

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30

Total DOS of (Ga,Mn)N

Spin-up

(a)

20 10 0 −10 −20 Ef

−30 30

Spin-down Spin-up

(b)

20 10 0 −10 −20 Ef

−30 1.5 Partical DOS of Mn

251

(c)

Spin-down

Spin-up

1.0 0.5 0.0 −0.5

4s 3p 3d

−1.0 −1.5

−8

Ef

Spin-down

−6 −4 −2 0 2 4 Energy relative to Fermi energy (eV)

6

Figure 10.2 Total DOS for (a) an unrelaxed (FM) and (b) a relaxed Ga1−x Mnx N (AFM). The corresponding partial DOS of Mn atom are shown in (c). Reproduced from Q. Wang, Phys. Rev. Lett. 93, 155501-3. Copyright (2004), with permission from the American Physical Society

layers are contracted. For example, in the ground state the bond lengths ˚ and Mn–Mn (2.978 A) ˚ in the first surface layer of Mn–N (1.822 A) are significantly shorter than the corresponding bulk values (1.990 and ˚ respectively). In the second layer the bond lengths of Mn–N and 3.233 A, ˚ respectively. In the third layer, they are Mn–Mn are 1.920 and 3.093 A, ˚ 1.951 and 3.111 A, respectively. We see that the bond length contraction mainly occurs in the first two layers, and the magnetic couplings become AFM. Therefore, we can expect an evolution from AFM to FM coupling when Mn atoms diffuse from the surface to the film interior, as the bond length contraction vanishes gradually. However, energetically this is not

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preferred and it has been observed experimentally that Mn atoms diffuse from the film interior to its surface. We note that in the above (1 × 2) (1120) surface slab model, the Mn atoms on the surface form a continuous zigzag chain along the [0001] direction. One may wonder if the magnetic coupling results from the formation of these Mn–Mn chains on the surface and if there is an interaction between the impurity atom and its image in the nearest supercell. To clarify this point, we generated a (2 × 2) seven-layer GaN (1120) slab containing 56 Ga atoms and 56 N atoms, in which the minimum distance between the impurity atom and its image in the nearest su˚ along the [0001] direction. When two Mn percell is larger than 10 A atoms are substitutionally doped at Ga sites on either side of the slab, a Ga52 Mn4 N56 supercell with a 7.14 % Mn concentration is formed. Following the same procedure as described above for the (1 × 2) nine-layer slab, the geometry of the supercell was optimized fully by using (5 × 5 × 1) Monkhorst–Pack k-point mesh. Again, the AFM state is found to be more stable than the FM state with an energy difference of 0.06 eV per ˚ and Mn atom. The Mn–N bond length on the surface layer is 1.82 A, ˚ the Mn–Mn distance is 2.91 A. Thus it is clear that the AFM coupling in the thin film is due to bond length contraction, which is insensitive to Mn concentration or the construction of the GaN supercell.

10.3.2

Mn-doped GaN (1010) Surface

In order to study if the magnetic coupling between Mn atoms depends upon the orientation of the thin film surface, we have considered (Ga, Mn)N thin film having wurtzite structure and [1010] orientation [38]. Note that the Mn–Mn distances may depend upon the surface orientation and hence may affect the magnetic ordering between them. The GaN (1010) surface was modeled by a (2 × 2) 10-layer slab that contains 40 Ga atoms and 40 N atoms in the supercell (Figure 10.3). ˚ Each slab was separated from the other by a vacuum region of 10 A in the [1010] direction. The central four layers of the slab were held at their ideal bulk position while the three layers on either side of the slab were allowed to relax without any symmetry constraint. To study the magnetic coupling between the Mn atoms in the GaN (1010) thin film, we again substituted two Ga atoms with two Mn on both top and bottom sides of the Ga40 N40 slab. Consequently, a total replacement of four Ga atoms with Mn results in a 10.00 % Mn doping concentration and a Ga36 Mn4 N40 supercell. We have considered six different configurations to simulate the different Mn–Mn distance and Mn-N-Mn bond

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Figure 10.3 Supercell of a 10-layer slab for GaN (1010) surface. The larger and lighter spheres are Ga. Reproduced from Q. Wang, Phys. Rev. B 75, 035322-2. Copyright (2007), with permission from the American Physical Society

angle. We have specified the six configurations in the first column of Table 10.2 by giving the sites where the Ga atoms are replaced by Mn (Figure 10.3). The calculations of total energies and forces, and optimizations of geometry have been carried out the same way as described above for the (1120) surface. The main results are summarized in Table 10.2. It is found that configuration I is the ground state with the AFM coupling lying 0.541 eV lower in energy than the FM one, where the two Mn atoms reside on the surface layer sites, and cluster around N atoms. The optimized ˚ corresponding Mn–N bond length along the [0001] direction is 1.798 A, to a contraction of −2.6 % as compared with that for the undoped GaN ˚ however, is unchanged from surface. The Mn–Mn distance of 3.189 A, the corresponding Ga–Ga distance in the undoped case. Comparing the relative energies, we note that the total energy increases as the Mn atoms move from surface layer to the interior sites of the film. Configurations

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Table 10.2 The Relative energy (ε) calculated with respect to the ground state (configuration I), the energy difference (E) between the AFM and FM states (E = EAFM − EFM ), the optimized bond length between Mn and its nearest neighboring N (dMn-N ) along the [0001] direction, and the optimized distance between the two Mn atoms (dMn-Mn ) for Ga36 Mn4 N40 Configuration I (2,4/38,40) II (1,4/37,40) III (1,2/37,38) IV (4,8/40,35) V (6,8/33,35) VI (9,10/32,30)

ε (eV)

E (eV)

Coupling

0 1.084 1.178 1.795 2.307 3.228

−0.541 0.096 0.002 −0.047 0.113 0.084

AFM FM FM AFM FM FM

˚ dMn−N (A)

˚ dMn−Mn (A)

1.798(−9.65%) 1.813(−8.89%) 1.816(−8.74%) 1.835(−7.79%) 1.973(−0.85%) 1.975(−0.75%)

3.189 5.185 6.087 2.969 3.189 3.189

V and VI, where the two Mn atoms occupy, respectively, the subsurface and the third layer sites, are found to be 2.307 eV and 3.228 eV higher in energy than the ground state, respectively. This shows again that Mn atoms prefer the surface sites and this site preference is not affected by the Mn concentration. Meanwhile, it is interesting to note that although the Mn–Mn distances in configurations I, V and VI have the same value ˚ their corresponding Mn–N bond lengths are quite (dMn-Mn = 3.189 A), ˚ respectively, and the magdifferent, namely 1.798, 1.973, and 1.975 A netic couplings between the Mn atoms in these configurations are also different, i.e. the Mn atoms couple ferromagnetically in configurations V and VI. The coupling in configuration I, however, is AFM. This demonstrates that at certain Mn–Mn distance, the contraction of Mn–N bond length plays a critical role in driving the AFM coupling between the Mn atoms. This is in agreement with the results obtained in the calculations on the (1120) slab. The total DOS for the ground state configuration I, and the corresponding partial DOS of Mn atom and the partial DOS for Mn 3d and N 2p are plotted in Figure 10.4. We note that the total DOS for spin-up and spin-down are identical leading to zero magnetic moment. The magnetic moment on each Mn atom is 3.05μB and mainly comes from the Mn 3d orbital (2.95μB ). Small contributions to the moment also arises from the Mn 3p (0.03μB ) and Mn 4s (0.1μB ) orbitals due to the sp and d hybridization, as shown in Figure 10.4(a2 ). The neighboring N atom of Mn is polarized antiferromagnetically with a magnetic moment of 0.06μB which mainly comes from N 2p orbitals (0.05μB ) [Figure 10.4(a3 )]. To study the effect of the Mn concentration on the magnetic coupling between the Mn atoms, we performed extensive calculations on the GaN slabs with different thickness along the [1010] direction, as well as the

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Total Dos of Ga36Mn4N40

MAGNETISM OF DOPED GaN NANOSTRUCTURES

Spin-up

(a)

Ga36Mn4N40

Ef

Spin-up

(a)

Spin-up

(b)

Ga36Mn4N40C4

Ef

Spin-down

(b)

Spin-up

Mn 4s C 2p

Mn 3p Ef

Mn 3d

Partial Dos of Mn and N

Spin-down

255

Spin-down Spin-up

(a)

Spin-up

N 2s Ef

Mn 3d −6

Spin-down

(b)

N 2p

−8

Ef

Mn 3d

−4

−2

Spin-down 0

2

4

Energy relative to Fermi energy (eV)

Ef

N 2p −8

−6

−4

−2

Spin-down 0

2

4

Total DOS of Ga40 Mn4 N36 C4

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Figure 10.4 (a1 ) Total DOS, (a2 ) partial DOS of Mn, and (a3 ) partial DOS of Mn 3d and neighboring N 2p for Ga36 Mn4 N40 supercell. (b1 ) Total DOS, (b2 ) partial DOS of Mn 3d and neighboring C 2p, and (b3 ) partial DOS of N for C codoped Ga36 Mn4 N36 C4 supercell. Reproduced from Q. Wang, Phys. Rev. B 75, 035322-3. Copyright (2007), with permission from the American Physical Society

[0110] direction. At first, we increased the thickness of the slab to twelve layers based on the above (2 × 2) 10-layer slab along [1010] direction to reach a lower Mn doping concentration. We have also replaced two of the Ga atoms with Mn on either side of the slab, corresponding to a 8.30 % Mn doping concentration. It was found that the configuration where the Mn atoms occupy the nearest neighbor Ga sites on the surface layer is again the ground state with the AFM state being 0.535 eV lower in energy than the FM state. We then performed the calculations for the Mn-doped (2 × 2) eight-layer slab (Ga28 Mn4 N32 ) to reach a larger Mn concentration. The ground state is once again found to be AFM with both the Mn atoms residing on the nearest neighbor Ga sites of the surface. The AFM state is 0.549 eV lower in energy than the FM state.

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We also performed calculations by changing the Mn concentration by increasing the slab thickness along the [0110] direction. We used a (5 × 2) six-layer slab containing 60 Ga atoms and 60 N atoms, in which the minimum distance between the Mn atom and its image in the ˚ along the [0110] direction. In this way, no nearest supercell is 10.07 A Mn–Mn chain can be formed along the [0110] direction, and no interaction between the Mn atom and its image can occur. When two Mn atoms are substitutionally doped at Ga sites on either side of the slab, a Ga56 Mn4 N60 supercell with a 6.70 % Mn concentration is formed. We have carried out extensive search for the most favorable geometric and magnetic configuration. Once again, we found that the Mn atoms prefer to reside on the nearest surface Ga sites and couple antiferromagnetically. To further examine the magnetic coupling between Mn atoms in the dilute condition, we have also generated eight-layer, 10-layer and 12-layer (4 × 2) GaN (1010) slabs. The Mn doping concentrations of 6.25, 5.00 and 4.20% have been achieved by substituting two Ga atoms with Mn on either side of these slabs, respectively. The results are found to be almost the same as those given in the smaller slabs; namely, the ground state is AFM and lies about 0.1 eV per Mn atom lower in energy than the FM state, where the Mn atoms occupy the nearest surface sites of the ˚ The Ga atoms and form clusters. The Mn–N bond length is about 1.8 A. magnetic moment on each Mn atom is about 3μB . The main results for the ground state configurations corresponding to various slabs are summarized in Table 10.3. Thus, it is clear that in Mn-doped GaN thin films, the AFM ordering at 0 K is energetically favorable, relative to the FM Table 10.3 Composition of Mn-doped GaN slab, Mn concentration, the energy difference (E) between the AFM and FM states, the magnetic moment on each Mn atom, the optimized nearest Mn–N bond length (dMn-N ) along the [0001] direction, and the optimized Mn–Mn distance (dMn-Mn ) for the supercells that are listed in the first column

System Ga28 Mn4 N32 Ga36 Mn4 N40 Ga44 Mn4 N48 Ga56 Mn4 N60 Ga60 Mn4 N64 Ga76 Mn4 N80 Ga92 Mn4 N96 L, layer.

Slab layers

Mn concentration (%)

E (eV)

Magnetic moment (μB )

dMn-N ˚ (A)

dMn-Mn ˚ (A)

(2 × 2)-8L (2 × 2)-10L (2 × 2)-12L (5 × 2)-6L (4 × 2)-8L (4 × 2)-10L (4 × 2)-12L

12.50 10.00 8.30 6.70 6.25 5.00 4.20

−0.549 −0.541 −0.535 −0.401 −0.422 −0.432 −0.399

3.01 3.05 3.05 3.10 3.09 3.09 3.10

1.799 1.798 1.798 1.794 1.795 1.795 1.794

3.189 3.189 3.189 3.102 3.095 3.098 3.098

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state, due to the Mn–N bond length contraction. The magnetic coupling between Mn atoms is insensitive to the concentration of Mn over a wide range of concentration from 4.2 to 12.5 %.

10.3.3

Mn and C Codoped in GaN (1010) Surface

We have explored the possibility that the Ga1−x Mnx N system when codoped with C could turn into a ferromagnet since replacing N with C would introduce hole carriers, which in turn could mediate the FM coupling between the Mn atoms. To this end, we have chosen the 10-layer (2 × 2) GaN slab codoped with Mn at Ga sites and C at N sites. We calculated the magnetic coupling between Mn atoms following the same procedure as performed for the Ga1−x Mnx N systems. We replaced respectively one, two and three N with C atoms on either side of the slab, generating corresponding supercells of Ga36 Mn4 N38 C2 , Ga36 Mn4 N36 C4 , and Ga36 Mn4 N34 C6 . For each of these C doping concentrations, we calculated the total energies of various configurations resulting from the replacement of the Ga and N at different sites with Mn and C, respectively. We studied both FM and AFM spin alignments and the effect of full geometry optimization. When one N atom was replaced with C atom, we found that the ground state configuration is still AFM, in which both the Mn atoms form the nearest neighbor on the surface sites (2, 4) with the C at site 45 binding to both the Mn atoms (Figure 10.3). However, the energy difference between AFM and FM states is considerably reduced (from −0.135 to −0.045 eV per Mn atom). This indicates that a small concentration of C cannot lead to a transition from AFM to FM states. We, therefore, increased the hole concentration by replacing more N atoms with C on either sides of the slab. For the supercell Ga36 Mn4 N36 C4 , it is interesting to note that for each of the six initial Mn configurations when two N atoms are replaced by C, the ground state is found to be FM, and their corresponding energy differences E between AFM and FM range from 0.03 to 0.08 eV per Mn atom. In Figure 10.5, we plot the energy difference E and the average magnetic moment on Mn atom for the ground states corresponding to the six initial configurations with the C codoping. For comparison, we also plotted the results for the six configurations before C codoping. The effect of C concentration on the magnetic coupling between Mn atoms was further examined by replacing three N atoms with C at different sites on the either side of the slab. It was found that, in the ground

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Energy difference ΔE (eV)

1.5

3.5 3.0

1.0

Ga36Mn4N40 Ga36Mn4N36C4

2.5

0.5

2.0

0.0

1.5 1.0

−0.5 −1.0

0.5

Ga36Mn4N40 Ga36Mn4N36C4

I

II III IV V Configuration number

Magnetic moment (μB)

258

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0.0 VI

Figure 10.5 Energy difference E between AFM and FM states and the average magnetic moment on Mn atom for the six configurations with and without C codoping. The six configurations are defined in Table 10.3. Reproduced from Q. Wang, Phys. Rev. B 75, 035322-5. Copyright (2007), with permission from the American Physical Society

state configuration where the two Mn atoms reside at sites (2, 4) and C are at sites (41, 42, 45), the FM state is lower in energy by 0.237 eV than the AFM state. Once again, we show that the magnetic coupling between Mn atoms changed from AFM to FM when C is codoped in the Ga1−x Mnx N system. More importantly, the FM coupling is enhanced by increasing the C concentration, as the energy difference E is increased. To explore the origin of the FM coupling in C codoped (Ga, Mn)N, we examined the electronic structure corresponding to the ground state configuration of Ga36 Mn4 N36 C4 supercell and compared it with that for Ga36 Mn4 N40 . The calculated total spin DOS, the partial spin DOS for Mn 3d and C 2p and the partial spin DOS for N atoms in Ga36 Mn4 N36 C4 are plotted in Figure 10.4(b1 ), 4(b2 ) and 4(b3 ), respectively. Comparing the total DOS in Figure 10.4(a1 ) and (b1 ), we see that the C codoping has introduced new states near the Fermi level resulting in a half-metallic character of this codoped system. Replacing the group V anion, N, sites with C introduce holes, and electrons are transferred to Mn, which is observed by a strong increase in the Mn2+ spin densities at the Fermi level in Figure 10.4(b1 ). These induced hole carriers mediate the interaction of the magnetic ions, Mn, resulting in the FM state. As shown in Figure 10.4(a2 ), without C codoping, neither Mn nor N introduce DOS at the Fermi energy although there is hybridization between the Mn 3d and N 2p states. However, there is a distinct overlap between Mn 3d and C 2p in the spin-up bands in Figure 10.4(b2 ), which leads to new states at the Fermi energy and hence results in a change of the magnetic coupling. Thus, it is clear that the interaction between the localized spins on the

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Mn ions and delocalized carriers (holes originating from the C valence band) is responsible for the magnetic transition.

10.4

Mn- AND Cr-DOPED GaN ONE-DIMENSIONAL STRUCTURES

Recently one-dimensional nanostructures consisting of nanowires (NWs), nanotubes (NTs) and nanoholes (NHs) of GaN have been successfully synthesized [39–53]. Because of their unique physical properties and high chemical reactivity and their potential for applications in lasers, transistors, and spintronics devices, these materials have attracted considerable attention. Moreover, their properties can be easily influenced by coating and doping. In particular Mn-doped GaN NWs have been found to be FM up to 300 K [54–57]. Thus, these materials represent an important class of nanoscale building blocks for miniaturized electronic and optical devices. A fundamental understanding of the electronic and magnetic properties of these low dimensional FM semiconductor nanostructures is crucial for the development of spintronics devices. Therefore, we performed a comprehensive theoretical study on the GaN low dimensional nanostructures from first principles to provide an understanding of the experiment and to predict new materials. We used spin polarized density functional theory and different levels of correlation corrections (GGA, LSDA+U and GGA+U) implemented in the VASP code.

10.4.1

Mn-doped GaN Nanowires

We first present our results on the Mn-doped GaN NWs. The GaN NW has been generated from a bulk GaN (7 × 7 × 2) supercell having the wurtzite structure by removing the outside part of the circled area in Figure 10.6(a) along the [0001] direction [58]. The supercell consists ˚ vacuum space along the of 96 atoms (Ga48 N48 ) and has about 12 A [1010] and [0110] directions to prevent the NW from interacting with its image. The NW has 1.0 nm diameter and infinite length along the [0001] direction, as shown in Figure 10.6(b). In Figure 10.7 we show the various sites where Ga atoms were replaced by Mn to study not only their site preference but also how their magnetic coupling depends on the Mn–Mn distance and coordination. For each of these configurations we computed the total energies corresponding to both FM and AFM

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[0001] (a)

(b)

[1010]

Figure 10.6 (a) Top view of a 7 × 7 × 2 GaN supercell having wurtzite structure. (b) Ga48 N48 supercell which yields a NW of infinite length along the [0001] direction. Reproduced from Q. Wang et al., Phys. Rev. Lett. 95, 167202-1. Copyright (2005), with permission from the American Physical Society

[1010] [0001] o

I

II

III

IV

V

VI

[0110]

Figure 10.7 Six configurations of Ga46 Mn2 N48 supercell identifying various Ga sites that have been replaced by Mn. The lighter spheres are N, the grey spheres are Ga, and the black spheres are Mn. Reproduced from Q. Wang et al., Phys. Rev. Lett. 95, 167202-2. Copyright (2005), with permission from the American Physical Society

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Table 10.4 Energy difference (E) between AFM and FM states, the relative energy (ε) calculated with respect to the ground state (configuration V), the optimized Mn-N (dMn−N ) and Mn-Mn (dMn−Mn ) distances, and the magnetic moments at Mn (μMn ) and its nearest neighbor N (μN ) atoms for the configurations given in Figure 10.7 Configuration

E (eV)

ε (eV)

˚ dMn-N (A)

˚ dMn-Mn (A)

μMn (μB )

μN (μB )

I II III IV V VI

0.162 −0.363 −0.14 0.067 0.075 0.02

1.458 0.617 0.66 0.191 0 0.283

1.913 1.774 1.818 1.834 1.839 1.837

3.075 2.755 2.677 3.293 2.965 5.19

3.388 2.165 2.706 3.194 3.488 3.269

−0.0121 −0.05 −0.025 −0.09 −0.114 −0.02

alignments of the Mn spins. The atomic coordinates of all the atoms in the supercell were optimized without any symmetry constraint. Results of our calculation are summarized in Table 10.4. We see that the FM state of configuration V has the lowest energy with its AFM state lying 0.075 eV above the FM state. In this configuration the two Mn atoms reside in the outermost surface sites and form the zigzag chain along the [0001] direction. The next two higher energy configurations (IV and VI) which lie 0.191 and 0.283 eV above the ground state are also FM. For these two configurations the Mn–N distances are ˚ nearly the same as that in the ground state configuration, namely 1.84 A, ˚ but the Mn–Mn distances are very different, namely 3.293 and 5.190 A. This could imply that the Mn–N distance may play a more crucial role than the Mn–Mn distance in dictating the magnetic coupling between the two Mn atoms. To study the effect of the wire diameter on the magnetic properties of Mn-doped GaN NW, we performed the calculations for the thinnest GaN NW which has been created from a GaN (5 × 5 × 4) supercell by cutting the part outside of the innermost hexagonal unit along [0001] direction. The corresponding supercell consists of 48 atoms (Ga24 N24 ) with a diameter of 0.45 nm. We have also replaced two of the Ga atoms with Mn at different sites to check the magnetic coupling between Mn atoms. It was found that the configuration where the two Ga atoms at the nearest neighbor sites were replaced by Mn is the ground state with the FM state being lower in energy by 0.08 eV than the AFM state, similar to what we found in the previous thicker wire. Therefore, we confirmed that Mn atoms couple ferromangetically, even in such small size GaN NW.

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Due to the smaller size of the NW and the large bond length contraction, magnetic moments on Mn sites are small, namely the two Mn atoms only carry magnetic moment of 0.604 and 0.555μB . These Mn moments are smaller than any existing values in bulk or thin films. Therefore, in one-dimensional systems the wire thickness can be used to control the magnitude of the magnetic moment.

10.4.2

Cr-doped GaN Nanotubes

The GaN NT has been generated from a (7 × 7 × 3) GaN bulk supercell having wurtzite crystal structure (Figure 10.8) [59]. We removed the atoms from the outside and inside areas of the two circles and replaced them with vacuum space. The NT supercell thus created extends to infinity along the [0001] direction through the repetition of the supercell. This GaN NT has a polygon periphery. The geometry optimization was carried out and it was found that the initial polygon structure transformed ˚ – GaN single into a perfect cylindrical tube with a diameter of 9.84 A wall nanotube (SWNT), as shown in Figure 10.9. It is interesting to note that this optimized SWNT has the same structural feature as the carbon (9, 0) SWNT. To check the structural stability of the GaN SWNT, we performed finite-temperature ab initio molecular dynamics calculations. It was found that the tubular structure at T = 0 K remains stable at 300 K after 2000 time steps with a time step of 1.0 fs. No significant distortions have been found.

[0001] [0110] [1010] (a)

(b)

Figure 10.8 (a) Top view of a 7 × 7 × 3 GaN supercell having wurtzite structure. (b) GaN-NT supercell (Ga54 N54 ) which extends to infinite length along the [0001] direction. Reproduced from Q. Wang, Phys. Rev. B 73, 115411-1. Copyright (2006), with permission from the American Physical Society

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(b)

Figure 10.9 Schematic representation of the initial (a) and optimized (b) GaN NT supercell, viewed along the [0001] direction. The lighter spheres are Ga and the darker spheres are N. Reproduced from Q. Wang, Phys. Rev. B 73, 115411-2. Copyright (2006), with permission from the American Physical Society

The preferred site and magnetic coupling between Cr atoms in the GaN NT was studied by carrying out total energy calculations for both FM and AFM configurations and for six different placements of the Cr atoms. We started the calculations with the initial polygonal geometry, since it is not clear if the NT’s geometry would change into the SWNT, once Cr is doped. It was found that the initial geometries of all the configurations change substantially following the relaxation. The optimized geometries of all the configurations are tubular with almost the same radius as that of the pure GaN SWNT and similar to that for the carbon (9, 0) SWNT. The configuration with two Ga atoms at nearest neighbor sites on the same (0001) plane was found to be the ground state. The FM state is 0.245 eV lower in energy than the AFM state. The surface relaxation has ˚ resulted in a large change of the Cr–Cr distance, from 3.189 to 3.408 A. To study the effects of the thickness of the NT wall and the Cr concentration on the magnetic coupling between Cr atoms, we performed additional calculations for a GaN multi-wall nanotube (MWNT). This was generated from a (9 × 9 × 2) GaN supercell following the same procedure as discussed for the GaN SWNT. The MWNT supercell contains ˚ for the innermost wall a total of 192 atoms with a diameter of 7.808 A ˚ and a diameter of 16.259 A for the outermost wall. We have replaced a pair of the nearest neighbor Ga atoms with two Cr atoms to study their magnetic coupling. These replacements resulted in four configurations (Figure 10.10), and correspond to a 2.1 % Cr doping concentration (Ga94 Cr2 N96 ). It was found that configuration I is the ground state with FM state lying lower in energy by 0.074 eV than that in AFM state. The

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Figure 10.10 Schematic representation of the four configurations of Cr-doped GaN MWNT supercells

other three configurations are respectively 0.214, 0.882 and 1.132 eV higher in energy than the ground state configuration I. Therefore, it is apparent that the FM coupling between the Cr atoms is not affected by the thickness of GaN NT. To further confirm that the calculated ferromagnetism in Cr-doped GaN NTs is not a consequence of the approximation to exchange and correlation potential, we have employed the LSDA+U method [60, 61]. This replaces the Coulomb interaction among the localized electrons (e.g. transition metal d) by statically screened parameters U and J. We considered the Coulomb correction for Cr 3d electrons in the calculations for the ground state configurations of both the SWNT and the MWNT. We chose the same value for the exchange interaction parameter J, namely, 0.87 eV, which was used in some previous calculations [62, 63] and varied the Coulomb correction U from 2 to 6 eV treating it as a screened parameter. It was found that the FM states are always lower in energy than the AFM states, the introduction of U over a quite large range does not change the magnetic coupling between Cr atoms. This shows the high stability of the FM coupling between Cr atoms in GaN NTs.

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Figure 10.11 Schematic representation of a GaN NH (Ga88 N88 ) supercell (a) and GaN NH arrays (b). Reproduced from Q. Wang, Phys. Rev. B 75, 075312-2. Copyright (2007), with permission from the American Physical Society

10.4.3

Cr-doped GaN Nanohole Arrays

The GaN NH supercell has been generated from a (5 × 5 × 2) GaN bulk supercell by removing the atoms in a central hexagonal unit along the [0001] direction and replaced with a vacuum space [64]. A supercell containing 88 Ga atoms and 88 N atoms, as shown in Figure 10.11(a), models the NH arrays that extend to infinity through the supercell repetition along the three directions [see Figure 10.11(b)]. To study the magnetic coupling between Cr atoms in the NH, we have again replaced a pair of Ga atoms with Cr at the nearest neighbor sites and at the next nearest sites on the NH surface along different directions to see if clustering of Cr atoms seen in GaN bulk, thin film and NWs still persists in the NH array. To study the effect of curvature of the NH on the site preference of Cr atoms, we created the configurations where one Ga atom at the surface site and another one at the nearest bulk site or two Ga atoms at bulk sites forming the nearest neighbor were replaced with Cr atoms. Total energy calculations with full geometry optimizations were performed for both FM and AFM spin alignments for all the configurations. The configuration with the Cr atoms replacing two Ga at the nearest surface sites in the same (0001) plane was found to be the ground state with the FM state lying 0.128 eV lower in energy than the AFM state. The configurations with the two Cr atoms at the bulk sites and one at bulk site and another at surface are found to be higher in energy by 0.958 and 0.910 eV than the ground state, respectively, which indicates that Mn atoms couple ferromagnetically in the NH, the Cr atoms like to be close to each other and reside on the surface sites of the NH.

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Ef

Ga88N88

Spin-up

Spin-down

Density of states (arb. unit)

(b)

Ga86Cr2N88 Ga86Cr2N88(U)

Spin-up

Spin-down (c)

Cr-4s Cr-3p Cr-3d Cr-3d (U)

(d)

Cr-3d N-2p

Spin-up

Spin-down Spin-up

Ef

−8

−6

−4

−2

Spin-down 0

2

4

Energy relative to Ferimi energy (eV)

Figure 10.12 (a) Total DOS corresponding to pure Ga88 N88 NH, (b) total DOS of Cr-doped GaN NH, (c) partial spin DOS of Cr atom, and (d) partial spin DOS of Cr 3d and N 2p in Ga86 Cr2 N88 supercell. Reproduced from Q. Wang, Phys. Rev. B 75, 075312-3. Copyright (2007), with permission from the American Physical Society

We plot the total DOS and the partial DOS for the NH with and without Cr doping using GGA and GGA+U in Figure 10.12. The total DOS show the semiconductor feature for the pure NH and half-metallic feature for Cr-doped NH. The Cr 3d majority states dominate the total DOS in the band gap region. There is a visible overlap between Cr 3d and N 2p states [Figure 10.12(d)]. The Coulomb correlation effect is obvious: it enhances the gap in the spin-down DOS and the exchange splitting of Cr 3d at the Fermi level. As shown in Figure 10.12(c), there is a downward shift of the Cr 3d spin-up valence states (i.e. the high peak DOS near ∼ −1.2 eV shifts down to ∼ −1.6 eV from the Fermi energy

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Figure 10.13 Four configurations of Ga85 Cr3 N88 supercell. The yellow spheres are Ga, the blue spheres are N, and the red spheres are Cr. Reproduced from Q. Wang, Phys. Rev. B 75, 075312-5. Copyright (2007), with permission from the American Physical Society

EF ), and an upward shift of the Cr 3d spin-down conduction states (from ∼1.6 to ∼2.6 eV away from the EF ). To further explore the magnetic interaction between the Cr atoms and the effect of Cr concentration on the magnetic coupling between Cr atoms in the GaN NH system, we have performed additional calculations for the configurations where three and four Ga atoms were replaced by Cr in the supercell, corresponding to a slightly higher Cr concentration of 3.4 and 4.5 %, respectively. We have carried out an extensive search for their most favorable geometric and magnetic configurations. Four typical configurations, as shown in Figure 10.13, have specifically been discussed for the case where three Cr atoms were substituted. For each configuration, calculations were carried out for different spin alignments, namely FM (↑↑↑), and ferrimagnetic (↑↓↑), (↑↑↓), (↓↑↓), (↑↓↓). It was found that the configuration I is the energetically most stable state lying lower in energy by 0.182, 0.344 and 0.680 eV than the other three configurations, respectively. For the ground state configuration, it was found that the (↑↑↓) spin alignment is lower by 0.051, 0.230, 0.192, and 0.221 eV in energy than that for (↑↑↑), (↑↓↑), (↓↑↓), and (↑↓↓), respectively. The total moment for this ground state was found to be 2.775μB with each Cr atom carrying a local moment of (2.274, 2.990, −2.695)μB . For the case where four Cr atoms were substituted,

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the total energy calculations also clearly show that Cr atoms prefer to cluster. The most stable configuration is the one where the four Cr atoms occupy the nearest neighbor sites at the NH surface. For this ground state configuration, calculations were also carried out for different spin alignments, namely (↑↑↑↑), (↑↓↑↓), (↑↓↓↑), (↑↑↓↓), (↓↑↑↑), (↑↓↑↑), (↑↑↓↑) and (↑↑↑↓). It was found that the energetically most favorable spin state again is ferrimagnetic (↓↑↑↑) with a total magnetic moment of 6.863 μB . The results indicates that the Cr atoms indeed prefer to cluster in the GaN NH, the preferred magnetic coupling is ferrimagnetic for the Cr cluster larger than two atoms, and the magnetic interaction in the Cr-doped NH is shorted ranged, as found in Cr-doped GaN bulk system [65, 66].

10.5

N-DOPED Mn AND Cr CLUSTERS

From the above study, we note that the clustering of Mn or Cr around N is responsible for the ferromagnetism of Mn- or Cr-doped bulk GaN as well as the large variation in the Curie temperature of different samples. Although Mn and Cr are both AFM in bulk phase, these impurity atoms, when doped into GaN, go to Ga substitutional sites as Cr3+ and Mn3+ valence states in d3 and d4 configurations, respectively, and result in ferromagnetism in Mn- or Cr-doped GaN bulk systems. Note that Mn4 N is known to be FM with a Curie temperature 745 K [67]. This raises the question whether, under suitable growth conditions, Mn-doped in GaN can form Mn4 N clusters. It is, therefore, interesting to examine how Mnx N clusters form in the gas phase and how their structure evolve with the addition of Mn atoms one at a time.

10.5.1

Giant Magnetic Moments of MnxN Clusters

Calculations of the equilibrium geometries, total energies, electronic structure, and magnetic properties have been carried out for Mnx N clusters for x = 1–5 [68]. The geometries are given in Figure 10.14. We found that the binding energy of Mn clusters can be substantially enhanced by N atoms by having their hybridized s-d electrons bond with the p electrons of N. This stabilization is accompanied by FM coupling between the Mn atoms which, in turn, are antiferromagnetically coupled to N atoms. This N mediated FM coupling also gives rise to giant magnetic moments of Mnx N clusters with total magnetic moments of 4 μB , 9 μB , 12 μB , 17 μB , and 22 μB for x = 1–5, respectively. On the contrary, Mnx

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Figure 10.14 Geometries of Mnx N clusters in their ground states. The bond lengths are given in angstroms. The spin density surfaces corresponding to 0.005 a.u. for these clusters are plotted on the right. The green surfaces represent negative spin densities around the N site while the blue represents positive spin density around Mn sites. Reproduced from B. K. Rao et al., Phys. Rev. Lett. 89, 185504-2. Copyright (2002), with permission from the American Physical Society

clusters are weakly bound and Mn7 is known to exhibit FM behavior. Thus, study of Mnx N clusters in the gas phase sheds light on the magnetic properties of Mn-doped GaN.

10.5.2

N-induced Magnetic Transition in Small CrxN Clusters

Although Cr and Mn are neighbors in the periodic table, they exhibit very contrasting behavior while sharing some common features. Cr atoms

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bind strongly with another Cr atom and the resulting sextuple bonding in ˚ and a large binding energy a Cr2 dimer yields a very short bond (1.68 A) (1.44 eV). However, Mn2 is very weakly bonded and has the largest bond length of any dimer in the 3d series. However, both Mn and Cr are AFM in their bulk phase. It is interesting to see if Cr clusters couple ferromagnetically when doped with a N atom, just as Mnx N clusters have been seen to do [68]. Calculations show that Crx clusters are antiferromagnetically coupled with total magnetic moments of 0 μB , 6 μB , 0 μB , and 2 μB for x = 2–5, respectively, while the doping of N drastically modifies their magnetic properties. Crx N clusters are ferromagnetically coupled with Cr atoms coupled antiferromagnetically to the nearest-neighbor N atom. The magnetic moments of Cr2 N and Cr3 N are, respectively, 9μB and 13μB . The binding of N and Cr is substantially larger than that between the Cr atoms. Thus, clustering of Cr atoms around N is energetically favorable in the gas phase. These observations in N-doped Mn and Cr clusters have relevance to the studies of the observed ferromagnetism in Mn- and Cr-doped GaN, as in these systems, it is possible that Mn and Cr atoms could cluster around N. Therefore, Curie temperatures could be enhanced since it is proportional to the square of the moment. Thus, one can expect that as an impurity (Mn or Cr) in GaN, the giant ‘cluster magnets’ may play a significant role in the observed ferromagnetism in (Ga,Mn)N or (Ga,Cr)N semiconductors.

10.6

SUMMARY

A comprehensive study of the electronic structure and magnetic properties of the Mn- and Cr-doped GaN has been carried out to study how the dimensionality, local coordination, and symmetry play a role not only on the magnetic moments of transition metal atoms but also on their magnetic coupling. The system we have studied include crystalline bulk, (1120) and (1010) thin films, NTs, NWs, NH arrays, and clusters. Our work has led to the following conclusions: (1) We have shown that the magnetic coupling between transition metal atoms in Mn- and Cr-doped GaN can be altered by selecting the dimensionality of the system. In onedimensional Mn-doped GaN nanostructures, the special topology of the surface and the confinement of electrons in the radial direction drive the coupling to be FM while in thin films the Mn atoms couple antiferromagnetically. In addition, the magnitude of the magnetic moments can be tuned by changing the size of the nanostructures. The flexibility of both

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controlling the magnetic coupling and magnetic moment by choosing the dimensionality and the size of the nanostructures may be useful in practical applications. (2) The magnetic coupling between transition metal (TM) atoms is mediated by the N atom in GaN and is very sensitive to the inter-atomic distance between them as well as between the TM atoms and the nearest N atom. (3) The TM atoms prefer to cluster around the N atoms and in general reside on the surface. (4) The surface relaxations in thin films, NTs, NH arrays, and NWs are large and lead to magnetic coupling that may differ strongly from than in the bulk crystals. (5) Our results on (Ga,Mn)N system codoped with C further suggest that it is possible for the Mn atoms to couple ferromagnetically when the concentration of C is increased beyond a critical limit. This FM coupling is due to the hole carriers introduced by C. The density of states in C codoped (Ga, Mn)N shows half metallic behavior where C introduces states at the Fermi level in the spin-up band. The overlap between Mn 3d and C 2p leads to the change in the magnetic coupling. Our theoretical results explain the origin of the vast disagreement between many experiments as due to sample preparation conditions and demonstrate the key parameters that need to be controlled in order for the transition metal doped GaN to be FM. Porous GaN with tailored pore size has the potential for a spintronics material as it contains large surface area with varying curvature and coordination.

ACKNOWLEDGEMENT This work was supported by the DURINT program administered by the Office of Naval Research (Dr C. Wood) under Grant N00014-0110715.

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[7] G. T. Thaler, M. E. Overberg, B. Gila, R. Frazier, C. R. Abernathy, S. J. Pearton, J. S. Lee, S. Y. Lee, Y. D. Park, Z. G. Khim, J. Kim, and F. Ren, Appl. Phys. Lett. 80, 3964 (2002). [8] J. M. Lee, K. I. Lee, J. Y. Chang, M. H. Ham, K. S. Huh, J. M. Myoung, W. J. Hwang, M. W. Shin, S. H. Han, H. J. Kim, and W. Y. Lee, Microelectron. Eng. 69, 283 (2003). [9] P. P. Chen, H. Makino, J. J. Kim and T. Yao, J. Cryst. Growth. 251, 331 (2003). [10] S. S. A. Seo, M. W. Kim, Y. S. Lee, T. W. Noh, Y. D. Park, G. T. Thaler, M. E. Overberg, C. R. Abernathy, and S. J. Pearton, Appl. Phys. Lett. 82, 4749 (2003). [11] Y. Shon, Y. H. Kwon, Sh. U. Yuldashev, Y. S. Park, D.J. Fu, D. Y. Kim, H. S. Kim, and T. W. Kang, J. Appl. Phys. 93, 1546 (2003). [12] T. Kondo, S. Kuwabara, H. Owa, and H. Munekata, J. Cryst. Growth 237, 1353 (2002). [13] M. E. Overberg, C. R. Abernathy, S. J. Pearton, N. A. Theodoropoulou, K. T. McCarthy, and A. F. Hebard, Appl. Phys. Lett., 79, 1312 (2001). [14] K. Sardar, A. R. Raju, B. Bansal, V. Venkataraman and C. N. R. Rao, Solid State Commun., 125, 55 (2003). ¨ [15] S. Dhar, O. Brandt, A. Trampert, L. Daweritz, K. J. Friedland, K. H. Ploog, J. Keller, ¨ B. Beschoten, and G. Guntherodt, App. Phys. Lett. 82, 2077 (2003). [16] S. Dhar, O. Brandt, A. Trampert, K. J. Friedland, Y. J. Sun, and K. H. Ploog, Phys. Rev. B 67, 165205 (2003). [17] K. H. Ploog, S. Dhar, and A. Trampert, J. Vac. Sci. Technol. B 21, 1756 (2003). [18] M. Zajac, J. Gosk, M. Kamiska, A. Twardowski, T. Szyszko, and S. Podsiado, Appl. Phys. Lett.79, 2432 (2001). [19] K. Ando, Appl. Phys. Lett. 82, 100 (2003). [20] T. Graf, M. Gjukic, M. S. Brandt, M. Stutzmann, and O. Ambacher, Appl. Phys. Lett. 81, 5159 (2002). [21] S. J. Pearton, C. R. Abernathy, G. T. Thaler, R. M. Frazier, D. P. Norton, F. Ren, Y. D. Park, J. M. Zavada, I. A. Buyanova, W. M. Chen and A. F. Hebard, J. Phys.: Condens. Matter 16, R209 (2004). [22] S. E. Park, H.-J. Lee, Y. C. Cho, S.-Y. Jeong, C. R. Cho, and S. Cho, Appl. Phys. Lett. 80, 4187 (2002). [23] M. Hashimoto, Y.-K. Zhou, M. Kanamura, and H. Asahi, Solid State Commun. 122, 37 (2002). [24] J. S. Lee, J. D. Lim, Z. G. Khim, Y. D. Park, S. J. Pearton, and S. N. G. Chu, J. Appl. Phys. 93, 4512 (2003). [25] H. X. Liu, S, Y. Wu, R. K. Singh, L. Gu, D. J. Smith, N. Newman, N. R. Dilley, L. Montes, and M. B. Simmonds, App. Phys. Lett. 85, 4076 (2004). [26] W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965). [27] Y. Wang and J. P. Perdew, Phys. Rev. B 44, 13298 (1991). [28] G. Kresse and J. Joubert, Phys. Rev. B 59, 1758 (1999). ¨ [29] G. Kresse and J. Furthmuller, Phys. Rev. B 54, 11169 (1996). [30] H. J. Monkhorst and J. D. Pack, Phys. Rev. B 13, 5188 (1976). [31] M. van Schilfgaarde and O. N. Mryasov, Phys. Rev. B 63, 233205 (2003). [32] K. Sato and H.K. Yoshida, Jpn J. Appl. Phys. 40, L485 (2001); Semiconductor Sci. Technol. 17, 367 (2002). [33] L. Kronik, M. Jain, and J. R. Chelikowsky. Phys. Rev. B, 66, 041203 (2002).

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11 SiC Catalysis Technology A.H. Kababji and J.T. Wolan Department of Chemical Engineering, University of South Florida, Tampa, FL 33620, USA

11.1

INTRODUCTION

A catalyst, in simple terms, is a material that enhances the rate and selectivity of a chemical reaction and is cyclically regenerated in the process. Heterogeneous catalysis typically involves the use of a porous catalyst in a different phase from the reactants. Typical examples involve a solid catalyst with the reactants as either liquids or gases. In this process, reactants adsorb onto an active site on the surface of the solid porous catalyst, are activated by chemical interaction with the catalyst surface, then rapidly and selectively transformed into adsorbed products. These products then desorb from the surface regenerating an active site thus repeating the catalytic cycle. In general, commercial catalysts are biphasic being composed of a support material and one or more active phase components (metal or oxide). Support materials provide a porous framework permitting access to the active phase for the reactants and free exit for the products from the catalyst particles. The support must be able to disperse the active phase in order to increase the active surface in contact with the reactant. It must also have high mechanical and thermal stability in order to avoid surface area collapse during reaction or oxidative regeneration which can induce the formation of hot spots. All of Porous Silicon Carbide and Gallium Nitride: Epitaxy, Catalysis, and Biotechnology Applications Edited by Randall M. Feenstra and Colin E.C. Wood  C 2008 John Wiley & Sons, Ltd

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this must be achieved with the support being chemically resistant, cheap, abundant and not strategically limited. Easy preparation of large, well characterized samples of the support material is also necessary. Usually, industrial supports are based on high surface area γ -Al2 O3 or SiO2 , pure or doped with different elements in order to improve the mechanical and thermal stability of the support [1]. Under normal reaction conditions, γ -Al2 O3 and silica are stable, but at temperatures between 700 ◦ C and 1000 ◦ C and in the presence of steam, a phase transformation occurs for γ -Al2 O3 , first to metastable δ- and θ -Al2 O3 leading to the formation of α-Al2 O3 with a low surface area [2]. In addition, the chemical interaction between alumina and silica supports with the active phase can lead to the formation of new compounds such as silicates, resulting in loss of the active phase and as a consequence, the catalytic activity [3]. Finally, during an oxidative regeneration, in order to burn off the carbonaceous residues deposited on the catalyst during the catalytic operation, hot spots, or temperature runaway can occur resulting in the support sintering due to the low thermal conductivity of alumina and silica. For these reasons, it is of interest to find new supports resistant to the sintering phenomenon. In addition, the metals used as active phases are generally precious metals or environmentally dangerous metals and should be recovered. Porous silicon carbide shows several advantages when compared with these oxide supports.

11.2

SILICON CARBIDE SUPPORT

Silicon carbide (SiC) has been developed for use in a broad range of applications, including biomedical materials, high temperature semiconducting devices, synchrotron optical elements, and lightweight/high strength structures [4]. SiC exhibits a high thermal conductivity, high resistance towards oxidation (due to the formation of SiO2 layers), high mechanical strength and chemical inertness, properties required for heterogeneous catalyst support materials. This latter property is particularly useful during oxidative regeneration (frequently used in the heterogeneous catalysis field in order to burn off the carbonaceous deposit on the catalyst surface during the reaction) and, in general, high thermal conductivity allows new options in designing processes which are highly exothermic or endothermic. Additionally, the chemical inertness of the support allows easy recovery of the active phase without severe processes such as those generally employed for alumina- and silica-based spent catalysts.

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All of these advantages lead to the conclusion that silicon carbide is a promising candidate for a heterogeneous catalyst support. However, for SiC to be useful as a catalyst support it must be prepared in a high surface area form (20–30 m2 g−1 ) and an inability to do so has been the limiting factor in its application in catalysis. The discovery in recent years of facile routes for obtaining high surface area metal carbides has led to a rapid advance in the application of these materials to problems in heterogeneous catalysis [5]. Recent catalytic results with transition metal carbide materials indicate that a new class of highly active and selective catalysts is on the horizon for application in the petroleum, chemical and automotive industries. Briefly, three points of porous SiC-based catalytic support properties can be emphasized: (i) SiC shows very good mechanical properties which gives resistance to erosion and attrition, in addition to a high thermal stability; (ii) SiC has a higher thermal conductivity compared with the more conventional supports which could prevent the metal sintering; (iii) SiC is particularly inactive with respect to chemical reagents such as acids or bases. Therefore, the active phase can be easily reprocessed after simple acidic or basic treatments. Among refractory materials, the thermal conductivity of silicon carbide, SiC (500 W m−1 K−1 for crystalline state, at room temperature) is close to that of metals such as Ag or Cu (400–500 W m−1 K−1 ).

11.3

HEAT EFFECTS DURING REACTION

When a reaction is so fast that the heat released or absorbed by the support cannot transport rapidly enough to keep the support close to the temperature of the bulk fluid, nonisothermal effects may be encountered. These include temperature variation within the support pellet or a temperature gradient between the pellet and the surrounding fluid. The latter is generally due to a stagnant layer or film between the surrounding flowing fluid and the support pellet. For exothermic reactions, heat is released and the support pellets are hotter than the surrounding fluid. However, for endothermic reactions the pellet is cooler than the surrounding fluid. Thus, harmful effects of thermal shock, sintering of the catalyst surface, or drop in selectivity can result. For film T resistance one can equate the rate of heat removal through the film with the rate of heat generated or absorbed by the reaction within the porous support. Thus for the general heterogeneous catalytic

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reaction, A → B:  ) (−Hr ) Qgenerated = (Vpellet )(−r A,obs

(11.1)

Qremoved = hSpellet (Tg − Ts )

(11.2)

and on combining we find: Tfilm = (Tg − Ts ) =

 )(−Hr ) L(−r A,obs

h

(11.3)

where L is the characteristic size of the pellet, Q is the heat duty, Tg and Ts  are bulk and surface temperatures, respectively, −r A,obs is the observed reaction rate based on volume of catalyst pellets, −Hr is the change in enthalpy of the reaction and h is the heat transfer coefficient. One can also show that Tpellet ∝ 1/keff , where keff is the effective thermal conductivity of the pellet. Utilizing SiC as a catalytic support material greatly increases both h and keff . This translates to reduced temperature effects and increased catalyst lifetime, selectivity, and reduced thermal run-away and reaction temperatures.

11.4

REACTIONS ON SiC AS CATALYTIC SUPPORTS

Reactions in both oxidative and reductive environments have been investigated on SiC. One of the first reactions to be tried successfully on SiC in an oxidative environment was the oxidation of propylene to acrylaldehyde on CuO/SiC [4]. Three-way automotive catalysts (TWCs) used to remove hydrocarbons, CO and NO from auto exhaust gases have been extensively investigated using porous SiC supported metal catalysts. The commercial Pt-Rh catalyst is supported on Al2 O3 , which covers a cordierite, (Mg, Fe)2 Al4 Si5 O18 , monolith and usually contains several other proprietary elements (Ce, La, Ba) in combination for better performance [6]. TWCs experience severe and variable exposure to high temperature excursions and humidity. This causes sintering and loss of active phase with time, and a corresponding decrease in performance. The mechanical properties, thermal stability and chemical inertness of SiC make it an ideal candidate to replace Al2 O3 and its cordierite support in this application.

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Several reactions on porous SiC supported catalysts in reductive atmosphere have also been reported. For example, hydrogenation of carbon dioxide to hydrocarbon products on Pt/SiC and Ni/SiC at 200–5000 ◦ C has been described [7]. In this initial report it was observed that the SiC supported metal catalyst had activities comparable with those of Al2 O3 and SiO2 , but the selectivity was different, especially for the Ni/SiC, which exhibited complete selectivity to CH4 and excellent activity with respect to conventionally supported Ni catalysts. The increasingly strict environmental regulations with respect to the aromatic content of liquid transportation fuels have driven the improvement of isomerization catalysis. As will be shown, porous SiC supported metal catalysis converts low octane value linear hydrocarbons into high octane value branched hydrocarbons for automotive fuel, or high cloud point temperature linear hydrocarbons into low cloud point temperature branched molecules for diesel fuels. Also, improved lubricating oils can be produced by isomerizing linear alkanes.

11.5 11.5.1

EXAMPLES OF SiC CATALYST APPLICATIONS Pt/β-SiC Catalyst for Catalytic Combustion of Carbon Particles in Diesel Engines

Diesel engines compared with gasoline engines have been subjected to a great expansion for personal transport especially in the industrially developed countries. They are more efficient than gasoline engines and emit less CO2 , a greenhouse effect gas. This green image has, however, a darker face related to emission of large amounts of carbon particles which constitute potential health risks for humans. Carbon particulates with diameter smaller than 10 μm can be easily inhaled and remain accumulated in the lungs. In order to meet the legislative requirements, an alternative solution has been developed, i.e. diesel particles filter (DPF) based on the direct trapping of these particles accompanied by a periodical burn-off by post-combustion [8]. The commercial DPFs are based on the use of a low surface area α-SiC material disposed as straight channel filtering with porous walls and trapping the particles [9]. The good thermal conductivity of SiC coupled with its relatively high resistance to oxidation makes it a suitable carrier compared with other existing ceramics, i.e. cordierite or alumina. SiC synthesized by the gas–solid reaction combines high thermal conductivity, high oxidative resistance, chemical

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(a)

6H-PSC/PD 10μm

Figure 11.1 SEM images of Pd/6H-αSiC (a) and Pd atom identified by energy dispersion analysis by X-ray spectroscopy (b)

inertness and lightness, which render it an interesting support for automotive exhaust reactions.

11.5.2

Complete Oxidation of Methane

Various Pd based catalysts have been prepared by impregnation of β-SiC (high surface area) or α-SiC (low surface area) support with Pd (II) (Figure 11.1). The samples have been prepared by impregnation of SiC with an adequate amount of the Pd complex; the catalytic properties of the Pd/SiC samples were monitored during the total oxidation of methane. Methane conversion was measured as a function of the reaction temperature. The Pd content has been chosen to be near 1 wt% in order to obtain high dispersion with low loadings on supports having a relatively low specific area (α-SiC case). These solids are active and selective for the complete oxidation of methane but their thermal stability, after ageing at 800 ◦ C under the reaction mixture, depends on their activation treatment. The Pd/β-SiC catalyst is very active, but it completely deactivates after ageing under the reaction mixture at 800 ◦ C. This is due to the encapsulation of Pd particles in the SiOx layer formed on the support [10].

11.5.3

SiC-Supported MoO3 -Carbon-Modified Catalyst for the n-Heptane Isomerization

Isomerization of linear saturated hydrocarbons into their branched isomers presents an alternative for refiners to increase the octane number

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of unleaded gasoline. However, due to the presence of acid sites on the surface and due to the reaction mechanism, commercial catalysts (Pt supported on acidic alumina or zeolite) do not allow a high yield of isomers at high conversion for hydrocarbons heavier than C6 to be obtained due to the predominant acid cracking reactions [11–14]. It has also been reported by Ledoux and coworkers [15,16] that MoO3 -carbon-modified phase (oxycarbide phase) is an efficient isomerization catalyst for C6+ alkanes, with excellent selectivity even at high conversion. It has been reported by Ledoux et al. [17] that SiC can be used as an efficient catalytic support material in isomerization reactions. The SiC-supported catalyst shows a higher activity compared with that obtained on alumina, due to the weak interaction between the oxide precursor and the support. The formation of the molybdenum oxycarbide, the active and selective phase for isomerization, was easily achieved. It was also reported that the activity developed was strongly linked to the activation conditions such as H2 /hydrocarbon ratio and the total activation pressure.

11.5.4

Selective Oxidation of H2 S Over SiC-Supported Iron Catalysts into Elemental Sulfur

The H2 S-containing acid gases (generated by oil refineries or natural gas plants) have become more and more important due to the ever increasing standards of efficiency required by environmental protection pressures. The general trend is to selectively transform the H2 S into elemental sulfur, which is a valuable product. It has been reported that the nickel sulfide or iron based catalysts supported on high surface area SiC were active and very selective catalysts for the oxidation of H2 S into elemental sulfur at temperatures between 40 ◦ C and 120 ◦ C. The active phase is probably an iron oxysulfide or a nonstoichiometric sulfate phase. It is stable for several weeks in an industrial micro pilot plant, and no deactivation is observed even in the presence of a large amount of steam. These performances are due to the intrinsic physical properties of the SiC carrier but also because of the optimal dispersion of the active phase [18]. The catalytic results have shown that the starting iron phase (oxide or sulfate) was subsequently modified under the reactant mixture. The SiC-supported iron-based catalyst also exhibited a high stability as a function of timeon-stream, and no deactivation was ever observed even in the presence of a large amount of steam. The overall sulfur removal efficiency obtained through this process is around 99.5 % [19].

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11.5.5

Partial Oxidation of n-Butane to Maleic Anhydride Using SiC-Mixed and Pd-Modified Vanadyl Pyrophosphate (VPO) Catalysts (Case study)

One of the major difficulties for the production of maleic anhydride (MA) by the partial oxidation of n-butane is the highly exothermic behavior of the reaction [20]. This is compounded by the probability of full oxidation as well as the exothermic reoxidation of the solid catalyst at increased temperatures. Furthermore, nonisothermal operating conditions can lead to decreased productivity through severe hot spotting in the catalyst bed [20,21]. In this study, a 2 μm α-SiC crystalline commercial powder was used to modify an in-house prepared VPO catalyst as a means to extract the heat generated from this reaction. SiC is an excellent thermal conductor with a thermal conductivity at room temperature exceeding that of any metal [21]. In addition, the α-SiC utilized has a relatively high surface area (10.2 m2 g−1 ), excellent robustness and resistance to attrition, and possible synergy with the catalyst material itself. In this study, the evaluation of the prepared catalysts was performed using a fixed-bed microreactor shown schematically in Figure 11.2. Commercially, the predominant butane partial oxidation process employs a fixed-bed reactor as well, where a low concentration of n-butane is passed over the catalyst [22]. Fourier transform infrared (FTIR) spectrometry

BioRad FTIR FTS 3000 equipped witha 2.4 m gas cell

Tube mixer

Electric furnace Fixed-bed catalytic reactor

Catalyst bed

Oxygen Nitrogen n-butane

MA collector

500 nm filter Vacuum pump

MFC

Exhaust gas to fume hood

Pressure gauge On/Off plug valves

Figure 11.2 Schematic of the fixed-bed catalytic microreactor. The gaseous effluent is continuously analyzed using an FTIR spectrometer equipped with a gas cell

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was used as the principle reaction assessment tool since (FTIR) spectroscopy is one of the few techniques capable of detecting surface compounds in heterogeneous reaction systems under the reaction conditions [23]. As stated, SiC is expected to act as an efficient heat transfer medium to distribute heat and assist with hot-spot reduction associated with the very high exothermicity of this reaction. The use of SiC as a catalyst support was expected to result in an increase in catalyst lifetime and the prevention of VPO over oxidization [24,25]. To be effective, the thermally conductive material should have a thermal conductivity of at least 1 W m−1 K−1 [20], making α-SiC a good candidate material, having a thermal conductivity ranging from 3.7 to 4.9 W m−1 K−1 . In this work, varying weight percents of the α-SiC were used as a modifier for the as-prepared VPO catalyst. In addition, the small reactor inner diameter (4 mm) ensures that isothermal conditions are favored. Surface area studies done using the Brunauer–Emmet–Teller (BET) method showed an average surface area in the range of 10–15 m2 g−1 for VPO catalyst prepared via an aqueous medium process and in the range of 10–50 m2 g−1 for VPO catalysts prepared using an organic medium [26]. Using an organic solvent, BET analysis showed that the surface area for the in-house prepared VPO pyrophosphate phase used in this study was 12 m2 g−1 . Figure 11.3 shows the conversion of n-butane as a function of reaction temperature for a range of α-SiC/VPO mixtures, with bulk VPO shown for comparison. The α-SiC modified VPO resulted in at least a 70 ◦ C reduction in the light-off temperature (the temperature at which n-butane starts to convert into products) of the reaction, converting n-butane to MA, water, COx gases and other products. At a reaction temperature of approximately 420 ◦ C, samples with 10 wt% and 26 wt% α-SiC/VPO gave 64 % and 45 % n-butane conversion, respectively, compared with 12 % for bulk VPO. However, at 500 ◦ C the conversion was up to almost 90 % and 70 % for the 10 wt% and 26 wt% α-SiC/VPO samples, respectively, in comparison with only 34 % conversion for bulk VPO. In this study, a 10 wt% α-SiC/VPO mixture was found to produce the maximum amount of product (Table 11.1). Figure 11.4 shows higher loadings of α-SiC-modified VPO catalysts. No significant increase in conversion was noted as the α-SiC loading was increased. Sample 50 wt% α-SiC/VPO gave 42 % n-butane conversion at 420 ◦ C in comparison with about 26 % conversion for the 80 wt% α-SiC loaded VPO sample. The pure α-SiC sample tested did not produce any desired products but rather favored the complete oxidation of butane. The lower percentage loadings of SiC in VPO samples (6–26 wt %) had

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bulk VPO 6 wt% SiC/VPO

90

10 wt% SiC/VPO 26 wt% SiC/VPO

Butane conversion (%)

80 70 60 50 40 30 20 10 0 300

350

400

450

500

Temperature (°C)

Figure 11.3 Butane conversion vs temperature in the partial oxidation to MA for lower loadings of α-SiC (2 μm)/VPO mixtures. The bulk VPO curve is shown for comparison

Table 11.1 Actual total product yield and space time yield results for all catalyst systems prepared

Sample VPO only 6 wt% α-SiC (2 μm)/VPO 10 wt% α-SiC (2 μm)/VPO 26 wt% α-SiC (2 μm)/VPO 50 wt% α-SiC (2 μm)/VPO 80 wt% α-SiC (2 μm)/VPO 90 wt% α-SiC (2 μm)/VPO 0.5 wt% Pd/VPO 1.0 wt% Pd/VPO 1.5 wt% Pd/VPO 1.5 wt% Pd/10 wt% α-SiC (2 μm)/VPO a Based

Total Total Space Catalyst product product time yield g total product weight weight actual (g) (g) yield (%)a kg catalyst × hoperation 0.38 0.38 0.38 0.38 0.50 0.50 0.50 0.50 0.50 0.50 0.50

on total product theoretical yield.

0.58 0.40 0.77 0.35 0.25 0.10 0.05 0.63 1.40 1.20 2.02

7.20 5.01 9.67 4.38 3.13 1.25 0.62 7.89 17.54 15.04 25.27

76 53 102 46 25 10 5 63 140 120 202

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70 60 50 40 30 20 10 0 300

350

400

450

500

°

Temperature ( C)

Figure 11.4 Butane conversion vs temperature in the partial oxidation to MA for higher loadings of α-SiC (2 μm)/VPO mixtures. The bulk VPO curve is shown for comparison

higher n-butane conversion and produced more desired products at the same temperatures when compared with higher loadings (50–90 wt %) of SiC in VPO (Table 11.1). Figure 11.5 shows the spectra obtained from FTIR in the attenuated total reflectance (ATR) mode of fresh bulk VPO, activated bulk VPO, and after reaction over-oxidized VPO. Figure 11.6 shows the FTIR-ATR spectra of 10 wt% α-SiC/VPO particles fresh before mixing, activated mixed, and after reaction for the mixed sample. Both figures show that the peaks corresponding to the fresh bulk VPO are similar and are in good agreement with the powder infrared (IR) spectra of VPO catalyst. The presence of a single distinct crystalline phase revealed by X-ray powder diffraction (XRD) in Figure 11.7 is believed to be responsible for the single strong sharp band around 950 cm−1 present in both fresh VPO spectra [27,28]. The activated bulk VPO spectrum in Figure 11.5 shows different IR band positions than the activated mixed spectrum in Figure 11.6. This is due to the mixing with α-SiC particles which are

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(c)

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1000 1500 Wavenumbers (cm−1)

Figure 11.5 FTIR-ATR spectra of bulk VPO powder: (a) fresh bulk; (b) activated bulk; (c) after reaction

indicated by the IR high intensity bands around 800 cm−1 . The after reaction spectrum in Figure 11.5 shows major band frequency and shape changes in comparison with the activated spectrum, which explains the loss of catalyst activity in this sample after reaction. However, the after reaction mixed sample spectrum in Figure 11.6 is similar to the one in

Arbitrary units

(c)

(b)

(a)

500

1000 1500 Wavenumbers (cm−1)

Figure 11.6 FTIR-ATR spectra of 10 wt% α-SiC(2 μm)/VPO powder: (a) fresh before mixing; (b) activated mixed; (c) after reaction

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Arbitrary units

(a)

(b)

(c)

10

20

30

40

50

60

70

80

90

100

2θ

Figure 11.7 Comparison of XRD patterns of (a) activated (30 h), (b) pure α-SiC (2 μm) particles and (c) 10 wt% α-SiC (2 μm)/activated VPO

Figure 11.5 but shows a band around 1075 cm−1 which is a result of the interaction of VPO with the added α-SiC particles to the sample, but may also provide an explanation of why that sample was not totally over-oxidized and still showed catalytic activity. This work has demonstrated that a VPO catalyst modified with α-SiC (2 μm) crystallites for use in the partial oxidation of n-butane to MA showed at least an 18 % increase in yield of MA as compared with bulk VPO Table 11.1. Loadings of approximately 10 wt% α-SiC (2 μm) modified VPO catalysts reduced the light-off temperature of n-butane conversion to MA. This is presumed to be attributed to increased thermal dissipation. Higher loadings showed no increase in yield indicating that α-SiC shows no intrinsic catalytic activity toward MA. Samples containing Pd as a promoter with or without the addition of α-SiC had a higher selectivity and yield to MA. The optimum system investigated in this study consisted of 1.5 wt% Pd-10 wt% α-SiC/VPO. This newly developed catalyst formula lowered the reaction light-off temperature from around 420 to 300 ◦ C as compared with bulk VPO resulting in a 84 % butane conversion to products at reaction temperature (420 ◦ C) and a 25 % total product yield.

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PROSPECTS AND CONCLUSIONS

The recent results reported above make it likely that SiC will become an object of intense research as a potential new catalyst support material. Chemical inertness allows SiC to behave in a different way with transition metals compared with SiO2 - and Al2 O3 -supported catalysts affecting the ease of active phase formation and the degree of dispersion. This may be demonstrated by the fact that a well studied catalytic material such as Ni exhibits a different selectivity on SiC than that normally shown on a conventional support in a CO/H2 reaction. Another example is that a catalytically active phase such as molybdenum oxycarbide is more easily formed on SiC than on conventional materials allowing its catalytic properties to be strongly revealed for the first time. High surface area porous SiC effectively disperses transition metals. Additionally, the chemical inertness appears to allow easier regeneration of the catalyst or complete recovery of the metal by simple acid washing. The high thermal conductivity of SiC may turn out to facilitate new process designs for highly exothermic or endothermic reactions in which heat transfer must be carefully controlled. Furthermore, because the SiC can be formed from carbon in any shape or porosity due to the ‘shape memory effect’, a catalyst with good activity and selectivity in a particular reaction can be formed closer to a commercially acceptable form without an extensive development project. For all these reasons it is expected that research will accelerate rapidly in order to understand, improve and develop this novel material.

REFERENCES [1] M. Zwinkels, S. Jaras, P. Menon and T. Griffin, Catalytic materials for hightemperature combustion, Catal. Rev. - Sci. Eng., 35, 319–358 (1993). [2] J. Schwartz, A. Contescu and C. Contescu, Methods for preparation of catalytic materials, Chem. Rev., 95, 477–510 (1995). [3] H. Yao, H. Stepien and H. Gandhi, Metal-support interaction in automotive exhaust catalysts: Rh-washcoat interaction, J. Catal., 61, 547–550 (1980). [4] H. Sanders, Ultra-fare refractory particle formation in counter-flow diffusion flames, Chem. Eng. News, 62, 26–33 (1984). [5] Y. Ke, F. Yan, R. Devaty and W. Choyke, Columnar pore growth in n-type 6H-SiC, Mater. Sci. Forum, 527–529, 739–742 (2006). [6] B. Harrison, A. Diwell and C. Hallett, Promoting platinum metals by ceria: metalsupport interactions in autocatalysts, Platinum Met. Rev., 32, 73–83 (1988).

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[7] M. Vannice, Y. Chao and R. Friedman, The preparation and use of high surface area silicon carbide catalyst supports, Appl. Catal., A, 20, 91–107 (1986). [8] B. Van Setten, M. Makkee and J. Moulijn, Science and technology of catalytic diesel particulate filters, Catal. Rev. - Sci. Eng., 43, 489–564 (2001). [9] J. Summers, S. Vanhoutte and D. Psaras, Simultaneous control of particulate and NOx emissions from diesel engines, Appl. Catal., B, 10, 139-156 (1996). [10] C. M´ethiver, B. B´eguin, M. Brun, J. Massardier and J. Bertolini, Pd/SiC catalysts characterization and catalytic activity for the methane total oxidation, J. Catal., 173, 374–382 (1998). [11] M. Steijns and G. Froment, Hydroisomerization and hydrocracking; product distributions from n-decane and n-dodecane, Ind. Chem. Prod. Res. Dev., 20, 654–660 (1981). [12] G. Giannetto, G. Perot and M. Guisnet, Hydroisomerization and hydrocracking of n-alkanes; ideal hydroisomerization PtHY catalysts, Ind. Chem. Prod. Res. Dev, 25, 481–490 (1986). [13] J. Campelo, F. Lafont and J. Marinas, Hydroisomerization and hydrocracking of n-heptane on Pt/SAPO-5 and Pt/SAPO-11 catalysts, J. Catal., 156, 11–18 (1995). [14] E. Blekkan, C. Pham-Huu, M. Ledoux and J. Guille, Isomerization of n-heptane on an oxygen-modified molybdenum carbide catalyst, Ind. Chem. Prod. Res. Dev., 33, 1657–1664 (1994). [15] M. Ledoux, P. Del Gallo, C. Pham-Huu and A. York, Molybdenum oxycarbide isomerization catalysts for cleaner fuel production, Catal. Today, 27, 145–150 (1996). [16] M. Ledoux, C. Pham-Huu and R. Chianelli, Catalysis with carbides, Curr. Opin. Solid State Mater. Sci., 1, 96–100 (1996). [17] M. Ledoux, C. Pham-Huu, P. Del Gallo and E. Peschiera, n-Hexane and n-heptane isomerization at atmospheric and medium pressure on MoO3 -carbon-modified supported on SiC and Al2 O3 , Appl. Catal., A, 132, 77–96 (1995). [18] N. Keller, C. Pham-Huu and M. Ledoux, Continuous process for selective oxidation of H2 S over SiC-supported iron catalysts into elemental sulfur above its dewpoint, Appl. Catal., A, 217, 205–217 (2001). [19] S. Savin, J. Nougayr`ede, W. Willing and G. Bandel, New developments in sulfur recovery process technology, Int. J. Hydrocarbon Eng., 3, 54–56 (1998). [20] M. Ledoux, C. Crouzet, C. Pham-Huu, V. Turines, K. Kourtakis, P. Mills and J. Lerou, High-yield butane to maleic anhydride direct oxidation on vanadyl pyrophosphate supported on heat-conductive materials: SiC, Si3 N4 , and BN, J. Catal., 203, 495–508 (2001). [21] P. Masri, Silicon carbide and silicon carbide-based structures: the physics of epitaxy, Surf. Sci. Rep., 48, 1–51 (2002). [22] F. Meunier, P. Delporte, B. Heinrich, C. Bounchy, C. Crouzet, C. Pham-Huu, P. Panissod, J. Lerou, P. Mills and M. Ledoux, Synthesis and characterization of high specific surface area vanadium carbide: application to catalytic oxidation, J. Catal., 169, 33–44 (1997). [23] Z. Xue and G. Schrader, Transient FTIR studies of the reaction pathway for n-butane selective oxidiation over vanadyl pyrophosphate, J. Catal., 184, 87–104 (1999). [24] R. Kerr, US Patent 3 156 705 to Petro Pex Chem. Corp. (1964). [25] R. Schneider, US Patent 3 864 280 to Chevron (1975). [26] M. Ledoux, US Patent 6 660 681 to du Pont Co. (2003).

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[27] M. Dente, S. Pierucci, E. Tronconi, M. Cecchini and F. Ghelfi, Selective oxidation of n-butane to maleic anhydride in fluid bed reactors: detailed kinetic investigation and reactor modelling, Chem. Eng. Sci., 58, 643–648 (2003). [28] N. Govender, H. Friedrich, M. Van Vuuren, S. Chengh and A. Ko, Controlling factors in the selective conversion of n-butane over promoted VPO catalysts at low temperature, Catal. Today, 97, 315–324 (2004).

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12 Nanoporous SiC as a Semi-Permeable Biomembrane for Medical Use: Practical and Theoretical Considerations A.J. Rosenbloom1 , R.P. Devaty2 , S. Nie3 , Y. Ke 2 and W.J. Choyke2 1

Institute for Complex Engineered Systems and Molecular Biosensors and Imaging Center, Carnegie Mellon University, Pittsburgh, PA 15213, USA 2 Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260, USA 3 Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213, USA

12.1

THE RATIONALE FOR IMPLANTABLE SEMI-PERMEABLE MATERIALS

The development of microchip-based bioassays and the proliferation of soluble markers of disease processes, such as cancer, suggests that implantable sensors will eventually be used to detect diseases very early in their course. The low concentrations of markers early in disease, and

Porous Silicon Carbide and Gallium Nitride: Epitaxy, Catalysis, and Biotechnology Applications Edited by Randall M. Feenstra and Colin E.C. Wood  C 2008 John Wiley & Sons, Ltd

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their confinement to affected tissues or organs, makes blood tests and radiologic imaging less likely to identify target molecules until disease has progressed. Implantable sensors can potentially sample tissue or blood continuously over long periods of time. Also, with the growing awareness of food, water and environmental contaminants, implantable sensors could give real time warnings, helping to limit exposure. Sensor elements will require protection but also access to soluble molecules. Semi-permeable membranes that allow molecules of interest access to the sensor elements by passive diffusion are a logical solution. Relatively large pore membranes that allow the passage of macromolecules such as proteins will be required for these applications.

12.2

THE BIOLOGY OF SOLUBLE SIGNALING PROTEINS IN TISSUE

The cells of the body are bathed in fluid, known as the interstitial fluid. Thousands of dissolved molecules transit this fluid continuously. Many serve an information carrying function i.e. are ‘signaling molecules’. Some reach local cells by diffusion, others enter blood or lymph and are carried by convection to distant sites. Still others become attached to local tissue frameworks, establishing gradients of immobilized signal that mobile cells can follow to the source. The complexity of the signaling traffic, and its importance, is obvious from the large number of different signal receptor proteins on each cell surface. Each receptor binds to one or more signaling molecules and then evokes a change within the cell. Signals may tell the cell to live or die, move or stay, multiply, attack intruders, ingest debris, secrete more signaling molecules, etc. It can generally be stated that every process requiring the coordination of populations of cells is reliant on signals carried through tissue fluid, blood or other fluid between them. So, growth and development, including abnormal growth (tumors), inflammation, immune response to infection or cancer, development of blood vessels, development of blockage within blood vessels, and wound healing would not be possible without coordinating signals. These signals and their results are necessary for survival but also integral to the most important diseases of our time. Measuring them, interpreting their interplay and eventually manipulating them are work that is only at the very earliest stage. It is clear that the signals are dynamic, numerous and interacting. Getting access to tissue and measuring relevant signal molecules in great numbers, rapidly and repeatedly are some of the challenges in harvesting this information. These challenges

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have been partially solved by a technology known as microdialysis and by advances in the detection and quantitation of biomolecules. In order to demonstrate the utility of implantable sensors, this section will focus on the measurement of small signal proteins known as cytokines by microdialysis, the best current technology for measuring proteins in living tissue. It must be kept in mind that cytokines are but a small subset of signaling molecules. Cytokine is a generic term for small proteins that cause cells (cyto-) to do something (kinetic). These can be divided into interleukins (communication between white blood cells and tissue cells), chemokines (white blood cell attractants, activators of various white cell and tissue cell functions), and a plethora of growth factors. These signal proteins are, with few exceptions, in the size range of about 8000–20 000 Da (1 Da = mass of hydrogen atom) with diameters of roughly 3 nm and diffusion coefficients in the 10−6 cm2 s−1 range. Important roles of cytokine-driven regulation in health and disease are too numerous to list but some notable examples are seen in the function of the immune system, in inflammatory conditions, bone marrow function and cancer. Immune cells known as T-lymphocytes (T-cells) are responsible for regulating the response to viruses, intracellular bacteria, fungi, parasites and for regulating the production of antibodies to toxins and bacteria. Destruction of T-cells produces immunodeficiency typical of Aquired Immunodeficiency Syndrome (AIDS). T-cells use an extensive repertoire of cytokines to guide and control many of their actions. Different T-cells secrete distinct sets of cytokines. This fact has led to the classification of T-cells by their cytokine production. The most important subclasses are the Th1 (T helper 1) and Th2 (T helper 2). These subsets of T-cells are important in understanding the immune response to many illnesses, including asthma, allergic disorders, inflammatory bowel disease, and kidney disease [1–6]. Cytokine production by T-cells is crucial to the control of the immune response. T-cell cytokine biology has been intensely studied in cancer, autoimmune diseases and multiple types of infections. Another important subset of cytokines is growth factors. Growth factors, as their name implies, are required for cell proliferation. Growth factors are of great interest in tumor biology. Not only do some solid tumor cells require them, but also the blood vessel cells that must grow to support the growing tumor. The normal bone marrow cells (blood stem cells) require continuous stimulation to produce new cells as the old ones wear out and die. These growth factors have become important drugs for use in those with low blood counts. Tissue growth factors are

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important for wound healing and tissue regeneration. Thus, in response to injuries, growth factors aid in scar formation. This response is necessary, ubiquitous and ironically problematic for implanting foreign material, including sensors, into living tissues. One of the great obstacles to the development of implantable biosensors and artificial neural interfaces is the cytokine and growth factor response to foreign material. The ensuing scar formation around these devices renders them isolated and ineffective. The development of materials that evoke little or no scar formation is central to the effort of implanting sensors, joint prostheses, and other devices. Finally, chemokines, which attract white blood cells, are important in the control of inflammation. They are highly specific in which type of cells they attract. They are extremely important in multiple aspects of inflammation and in many inflammatory diseases [7]. The Human Immunodeficiency Virus (HIV) virus has evolved to use chemokine receptors to enter T-lymphocytes, providing an important vulnerability for attack on the immune system by the virus. Thus chemokines have generated much interest in HIV research. Also, since chemokines and their receptors target white cells to tissue sites, they have become of interest in the process of cell targeting in general. A specific area of increasing study has been the use of similar targeting mechanisms by cancer cells that migrate to other areas of the body, i.e. metastasize [8,9].

12.3

MEASURING CYTOKINE SECRETION IN LIVING TISSUES AND ORGANS

The most practical and widely used method of continuously sampling interstitial fluid is microdialysis. In microdialysis, a buffer solution is pumped through a small semi-permeable tube that has been placed into living tissue. Molecules in the tissue interstitial fluid diffuse into the buffer and are pumped out and collected for measurement (Figure 12.1). Much of the pioneering work on the development of microdialysis was done in the 1970s [10]. Its basic principles have been reviewed [11]. Early microdialysis focused on measurements of small molecules with molecular weights in the hundreds of daltons. However, in the mid 1990s, larger pore polymer membranes became available, and it was shown that proteins could diffuse through them. Our group [12] and others demonstrated that proteins up to 29 000 Da molecular weight could be recovered with good efficiency through these membranes. This molecular size range is sufficient for obtaining most cytokines from tissues.

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Figure 12.1 Principles of microdialysis. Fluid circulates from inner tube to outer tube. The outer tube is semi-permeable. Molecules small enough to enter the pores are captured in the fluid and flow out of the probe for sampling. Reproduced from A.J. Rosenbloom et al., Mat. Sci. Forum. 457–460, pp. 1463–6. Copyright (2004), with permission from Trans Tech Publications

The ability of microdialysis to recover multiple cytokines from tissue was demonstrated by our group [13] in a study of the immune defenses of the oral cavity in persons with HIV infection and healthy controls. Catheters were placed into the inside of the left cheek, under the mucosa, after local anesthesia was administered. Microdialysis was performed for 6 h. Samples were later analyzed with fluorescent dye labeled antibodies for 16 cytokines. Although studies such as these can help to elucidate transient cytokine responses, only short-term studies are practical with these methods (Figure 12.2). A more global understanding of intracellular signaling will require more prolonged measurements. This is obvious when the timescale of disease – weeks, months or years – is considered. The most likely technology to perform this function is an implanted microchip.

12.4

CREATING A BIOCOMPATIBLE TISSUE – DEVICE INTERFACE: ADVANTAGES OF SiC

A semi-permeable membrane will shield sensor elements from mechanical trauma, and from the harsh environment of the tissue, including attack from cells and their reactive oxygen species, and protein and platelet deposition (biofouling).

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Figure 12.2 Subject ‘wired’ for microdialysis with catheters inserted into the mucosa in the inside of the cheek. Only short-term studies are practical using this method

Many semiconductor materials in various forms have been tested for biocompatibility and also compared with traditionally implanted materials such as titanium. We have reviewed this work previously [14]. Much work has been done with polymers to create biocompatible surfaces that resist protein fouling, i.e., non specific adsorption. A membrane composed of modified polyethersulfone (PES) (Omega Membrane) resisted albumin (ALB) absorption 24 times better than unmodified PES, and three times better than regenerated cellulose, a material known to resist biofouling. We compared porous SiC, both n-type and p-type, to the Omega Membrane [14] and found a very similar resistance to ALB absorption (Figure 12.3).

12.5

THE TESTING OF SiC MEMBRANES FOR PERMEABILITY OF PROTEINS

The development of nanoporous SiC membranes is described in Chapter One. For measuring protein permeability of the membranes, free-standing nanoporous SiC membranes were glued onto circular

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Figure 12.3 Both n-type and p-type SiC bound I 125-labeled albumin to a degree comparable with low-protein absorbing polymer. Reproduced from A.J. Rosenbloom et al., Mat. Sci. Forum. 457–460, pp. 1463–6. Copyright (2004), with permission from Trans Tech Publications

polystyrene plastic supports and placed into a small fluidic chamber. The schematic of the experimental arrangement is shown in Figure 12.4. The plastic supports exposed approximately 3 mm2 of the membrane surface. Protein-containing solution (350 μl) was placed under the membrane in contact with it. This was the source solution. Air was excluded from the membrane’s pores by soaking them in ethanol, and then water (double distilled in glass) prior to use. Bubbles were excluded from the chambers by carefully placing the membrane onto the surface of the liquid in the test chamber. Since the membranes are thin and translucent, the presence of even very tiny bubbles could be observed through the membranes with a dissecting microscope. The mix was stirred continuously with a magnetic stir bar. Buffer (30 μl of phosphate buffered saline,

Figure 12.4 Set-up for testing SiC membranes for protein permeability. Reproduced from A.J. Rosenbloom et al., Biomed. Microdevices. 6(4): 261–7. Copyright (2004), with permission from Kluwer

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pH 7.4, 0.1 % sodium azide as a bacteriostatic agent) was placed on top of the membrane, covering its exposed surface. This was the receiving solution. Molecules within the source solution below the membrane diffused through the membrane into the receiving solution above. Samples of the receiving solution were removed (7 μl) at 0, 2, 4, 6, and 18 h. After each sample was taken, volume was replaced with 7 μl of fresh buffer, with mixing. This method of sampling introduces an error, because a significant amount of protein (23 % of the receiving solution) is removed for sampling at each time point. The data therefore underestimate the actual amount of protein recovery through the membrane. This method was chosen because of simplicity and elimination of the confounding effects of biofouling – all the data points were obtained during the first contact with protein, eliminating the effect of incomplete washing and the risk of damaging the thin membranes during washes. The chamber was sealed with ParafilmTM in order to prevent evaporation. Protein concentrations in the receiving solution were measured by a sodium dodecyl sulfate capillary electrophoresis (PACE/MDQ system, Beckman-Coulter, San Jose, CA, USA). The results are expressed as the percentage of relative recovery. The relative recovery is defined as the ratio of the concentration of a protein in the receiving solution to the concentration in the source solution. A relative recovery of 100 % for a protein would indicate that the protein had achieved the same concentration in the receiving solution as in the source solution. Depletion of protein from the source solution was negligible. The receiving solution was 8.6 % of the volume of the source solution (30 μl/350 μl) and the receiving solution only attained 20 % of the concentration of the source solution with the most permeable protein (myoglobin). Thus the depletion of the source solution was roughly 1.7 % (8.6 %/5) for myoglobin (the most permeable protein). Other proteins were depleted less. For an investigation of the capability of macromolecules to diffuse through the membranes, we used six test proteins ranging in molecular weight from 17 000 to 80 000 Da: myoglobin (MYO, 17 000 Da); soybean trypsin inhibitor (STI, 20 000 Da); carbonic anhydrase (CAR, 29 000 Da); ovalbumin (OVA, 45 000 Da); bovine serum albumin (ALB, 66 000 Da); and human transferrin (TFN, 80 000 Da). Figure 12.5(a) and (b) shows the results of the diffusion of the six proteins through our n-type and p-type porous SiC membranes, respectively. Membranes of both n-type and p-type SiC exclude proteins in the same size range. The n-type material allowed much more protein to diffuse through, by a factor of as much as four times (for myoglobin). We have not yet investigated the effect of membrane thickness. Each membrane

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Figure 12.5 Relative recovery of different proteins expressed as a percentage of the original concentration after passing through (a) the n-type porous 6H SiC membrane and (b) the p-type porous 6H-SiC membrane. Reproduced from A.J. Rosenbloom et al., Mat. Sci. Forum. 457–460, pp. 1463–6. Copyright (2004), with permission from Trans Tech Publications

type passed proteins of up to 29 000 Da molecular weight but excluded larger proteins with a molecular weight of 45 000 Da and higher. These molecular weights correspond to molecular diameters of less than 4.7 nm (permeable) and greater than 5.0 nm (excluded). The discrimination between the 29 kDa and 44 kDa proteins is likely complex, and not simply based on size (4.7 and 5.0 nm, respectively). For example, charge, hydrophilic or hydrophobic interactions, as well as dimerization in solution or differential adsorption to the SiC, to the glue, to the plastic tube or membrane backing, etc., could all play roles. This same behavior was observed when we tested the same six-protein mix with commercial polymer membranes (data not shown), i.e. ovalbumin is excluded to a much greater degree than carbonic anhydrase.

12.6

IMPROVING THE STRUCTURE OF SiC MEMBRANES FOR BIOSENSOR INTERFACES

Early membranes that were tested had nonuniform pores. Having demonstrated good resistance to protein adhesion for SiC, and the ability to make free-standing semi-permeable membranes, it was decided to attempt to improve the membranes by making more uniform and consistent pore structures. The goal was to improve the protein throughput. The ‘second generation’ porous structures consisted of a hybrid morphology with 1 μm diameter cylindrical pores between much smaller

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(a) 1.46µm

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MYO(17KDa) STI(20KDa) CAR(29KDa) OVA(45KDa) ALB(66KDa) TFN(80KDa)

60 50 40 30 20 10 0 0

10

20

30

40

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Time (h)

Figure 12.6 (a) The pores are much larger, more uniform and transition the entire membrane thickness. (b) The protein permeability is shown over 48 h. The smaller molecules are recovered at 60 % of their concentration in the test solution

branching pores that are about 20–40 nm in diameter [Figure 12.6(a)]. Samples were fabricated by photoelectrochemical etching on the Si-face of n-type (n ∼ 5.7 × 1017 cm−3 ) 6H-SiC crystals in aqueous electrolytic solution containing 5% HF and 5% ethanol (mass percentage) with ultraviolet (UV) light (350–450 nm wavelength interval) illumination. The UV power density at the SiC sample surface is about 200 mW cm−2 , as measured by a thermopile power meter. A two-electrode electrochemical cell is used with a SiC sample as the anode and a platinum plate as the cathode with 50 or 60 V overpotential applied. After the etching, the porous structure is separated from the substrate and forms a selfsupporting free-standing membrane [15]. These membranes had areas of large, relatively straight pores with a high density in some areas [Figure 12.6(a)]. The protein permeability of these membranes was very good [Figure 12.6(b)]. Although these membranes are usable for probe interfaces, it is obvious that the pore structures are nonuniform. Most of the diffusion likely occurs in a few areas of high porosity with large areas of nonpermeable membrane in between. The next work aimed at two goals: first, better pore morphology and spacing and, secondly, to demonstrate the ability to integrate the membranes with microchip architecture. The first goal was to make pores that would uniformly cover more area of the chip surface, that would be straight, would penetrate the entire width of the membrane and that would be packed at a higher density. Of course, care must be given not to remove so much material that the membrane would be too fragile. The details of production have been described in Chapter One. This material was not permeable to protein, likely because the pore sizes are too small. It was also not permeable to small molecules, such as fluorescent

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(b)

(a)

100 nm

Figure 12.7 (a) Nanoporous SiC with very regular pore spacing. (b) Porous area (center) surrounded by nonporous margins, as seen with transmitted light

dye (Cy3, 767 Da) for unclear reasons (data not shown). Work is under way to enlarge the pore sizes. Nonetheless, the morphology is extremely promising, with extremely regular pores that penetrate the entire thickness, with a very high pore density [Figure 12.7(a)]. In order to integrate membranes with other microchip components, chip layouts will have to place porous areas adjacent to nonporous architecture. Since pore formation requires light, it is possible, by masking, to precisely position porous areas anywhere on the chip. This was demonstrated by making a central porous area on a square of SiC [Figure 12.7(b)]. In summary, it has been demonstrated that SiC is a biocompatible and versatile material that can be made into nanoporous membranes which are permeable to proteins in the size range of cytokines. Pores can be made with excellent uniformity, high density and complete penetration of substrate at least for 150 μm thicknesses (images not shown). Furthermore, it is possible to precisely position the porous areas on the SiC substrate, leaving untouched areas for bonding or for subsequent etches.

12.7

THEORETICAL CONSIDERATIONS: MODELING DIFFUSION THROUGH A POROUS MEMBRANE

The experiment consists of a reservoir, volume VA , containing the protein solution, and the receiving solution, volume VB , separated by the

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porous membrane. It is convenient to consider a slab geometry defined by the area of the membrane, with effective thicknesses of the reservoir, receiver and membrane LA , LB , and L, respectively. Let D be the diffusion constant associated with the permeable membrane, C0 the initial concentration of a protein in the reservoir, and CB (t) the time dependent concentration of the protein, initially zero, in the receiving solution. The relative recovery of protein is CB (t)/C0 . The concentrations of protein in the reservoir and receiving solution are assumed uniform, which can be achieved by stirring. Barnes [16] presented a rigorous solution of the diffusion equation for this problem as an infinite series. The complexity is introduced by the finite sizes of the reservoirs and by the initial conditions. A simple, approximate solution is obtained by assuming that a steady state has been achieved in the sense that the flux of protein is the same at every point within the membrane. This is clearly not the case initially (t ∼ L2 /D), and in fact is not true throughout the process because the protein concentration in the receiving solution is continuously increasing. The solution is: CB (t) =

12.7.1

   C0 VA D(VA + VB ) t . 1 − exp − VA LLB (VA + VB )

(12.1)

Effective Medium Models for a Porous Membrane

We apply simple effective medium models in an attempt to understand the diffusion process in the complex pore network of a porous SiC sample. There is an analogy between the quantities involved in the electrostatics problem and the steady state diffusion problem for a uniform external diffusion flux impinging on a coated sphere. Kalnin et al. [17] provide the details of such a calculation for the Maxwell Garnett (MG) model [18]. The quantity involved in the averaging is the product of the diffusion constant and the porosity for each component of the composite medium. The effective medium approach does not take into account possible effects due to charges on the molecules and/or pore surfaces, details in the size and shape of the protein molecules, fouling (shown to be negligible in porous SiC), and potentially important features of the microstructure such as bottlenecks. We consider two effective medium models, corresponding to distinct morphologies on the micro- or nanoscale. The resulting quantity (pD)eff replaces D in Equation (12.1). Subscripts 1 and 2 refer to the two

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components, Di (i = 1,2) is the diffusion constant for the molecules within the pores and pi is the porosity for the ith component. p and 1 − p are the fractions of components 1 and 2, respectively, in the material. For a morphology of aligned parallel rods: ( pD)eff = p ( p1 D1 ) + (1 − p) ( p2 D2 )

(12.2)

which is symmetric in the two components. The MG model [18] corresponds to a morphology of coated spheres. If medium 2 is the sphere and medium 1 the coating, the MG expression is: ( pD)eff = ( p1 D1 )

2 p ( p1 D1 ) + (3 − 2 p) ( p2 D2 ) (3 − p) ( p1 D1 ) + p ( p2 D2 )

(12.3)

This expression clearly is not symmetric in the two components. References [17,19–21] contain representative examples of applications of the MG model to diffusion in porous media. For application to porous SiC membranes, let medium 1 be the solution and medium 2 the SiC, so that D1 = D, the diffusion constant of the molecule in the solution, p1 = 1, D2 = 0 and p2 = 0. The expressions for the two effective medium models simplify considerably: Parallel columnar channels: ( pD)eff = pD

MG Model: ( pD)eff =

2 pD 3− p

(12.4)

(12.5)

In these expressions, p is the porosity of the SiC, i.e. the volume fraction of empty space. In the asymmetric MG model, we have chosen the coating to be the solution, since the opposite choice of SiC-encapsulated liquid spheres will not permit diffusion through the medium. With this choice, the SiC does not percolate and hence there is no structural support. The selectivity of the membrane is based in part on the size and shape of the protein molecules. The expressions for (pD)eff in the effective medium models [Equations (12.2) and (12.3)] do not contain a size scale, but it is necessary to introduce a scale in order to account for the size of a protein molecule. For simplicity, we assume that the proteins are spherical with effective (hydration) radius r. The excluded volume within the pores due to nonzero size is taken into account by replacing the porosity p with an effective porosity p* . For the columnar

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morphology, p* = (1 − r/R)2 p, where R is the pore radius. For the MG model, p* = 1 − (1 − p)(1 + r/R)3 , where R is the radius of the SiC sphere. To apply this model, we can set 2R to the measured interpore spacing (SiC wall thickness between adjacent pores). For the MG model, p* is negative when r < [(1 − p)−1/3 − 1]R. For r < 0, we use p* = 0, thereby excluding diffusion of these molecules through the membrane. Diffusion will take place for p > 1 − (1 + r/R)−3 . This effect, which can be attributed in part to the tortuosity of the pore network, can be important for remarkably small values of r/R. The diffusion constant of a protein is calculated using the Stokes– Einstein equation, D = kT/6πηr , where T is the absolute temperature, η = 1.0 × 10−2 g cm−1 s−1 is the viscosity, r is the effective (hydrodynamic) protein radius and k is Boltzmann’s constant. For the protein radius we use the radius of gyration obtained from dynamic light scattering experiments [22]. The values (in nm) are: MYO, 2.12; STI, 2.19; CAR, 2.35; OVA, 2.98; BSA (ALB), 3.56, and TFN, 4.02.

12.7.2

Comparison with Experiment

Figure 12.6(b) shows the measured relative recovery for a hybrid columnar porous SiC membrane. This sample, made at an early stage of our efforts to fabricate columnar porous SiC, contains a relatively low volume fraction of large diameter columnar pores penetrating porous SiC with dendritic porous morphology on a finer scale. The model is based on Equation (12.2). The second component is calculated using the MG model [Equation (12.5)] with the porosity chosen so that the overall porosity agrees with the gravimetrically measured value. The correction for excluded volume due to the size of the protein molecules is applied to both types of pores. Specifically, we used 250 nm for the radius of the columnar pores, 20 nm for the radius in the MG model, 5 % for the porosity of the columnar pores, 35 % for the overall porosity, 50 μm for the layer thickness, 12.6 mm2 for the area of the porous layer, 700 μl for the volume of the protein solution, and 30 μl for the volume of receiving solution. As demonstrated in Figure 12.8, the smaller dendritic pores make a significant contribution to the relative recovery for the three smallest proteins. This model [Figure 12.8(a)] qualitatively accounts for the measurements [Figure 12.6(b)]. In particular, it predicts recovery of all six proteins and accounts for the separation of the six proteins into two groups of three. Rosenbloom et al. [23] provides additional details of this work.

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Figure 12.8 (a) Calculated relative recovery for hybrid columnar porous SiC based on a composite columnar/MG effective medium model [23]. (b) Calculated relative recovery through the columnar pores only. See text for details. Reproduced from A.J. Rosenbloom et al., Mat. Sci. Forum. 457–460, pp. 1463–6. Copyright (2004), with permission from Trans Tech Publications

12.8

FUTURE DEVELOPMENT: MARRIAGE OF MEMBRANE AND MICROCHIP

Microelectromechanical systems (MEMS) combine the electronics of microchips with micromechanical features and microfluidics to create unique devices. The multitude of MEMS applications continues to grow including many types of accelerometers, radio frequency (RF) devices, variable capacitors, strain and pressure sensors, deformable micromirrors for image projection systems, vibrating micro-membranes for acoustic devices, ultrasound probes, micro-optical electromechanical systems (MOEMS) and MEMS gyroscopes, to name a few.

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BioMEMS is the term for biomedical applications of MEMS. Combining microfluidics with electronics has produced protein and DNA microarrays, protein separation (on-chip electrophoresis), interfaces with mass spectroscopy, and DNA sequencing on chips. The pathway to developing a fully implantable microchip capable of prolonged and reliable detection of proteins is long and challenging; however, progress is being made. The major fundamental problems to be solved are development of: (1) a biocompatible, protein-friendly tissue/device interface; (2) a reliable and quantitative protein sensor for continuous use over long periods; (3) a power supply; and (4) a means of wireless data transmission, probably using RF that can tolerate the attenuation of transmitting through salt water. MEMS devices are the most logical platform for high throughput measurements of proteins that could eventually be implanted into living tissues [24]. There are emerging methods for making multiple protein measurements. Perhaps the most well established is the MEMS microcantilever [25–28]. Microcantilevers are structurally analogous to diving boards – long, thin strips of silicon, released from the Si substrate by etching. Their extraordinarily small mass makes them very sensitive to the addition of mass due to adsorbed proteins. Specificity is assured by using specific capture reagents bound to the cantilever. In the case of proteins, antibodies are commonly used as specific capture reagents. When the protein of interest interacts with the antibody, the mass of the system increases. Any specific protein binder can be used; thus any protein – protein interaction pair (not just protein–antibody) will work. The readout method can be by measuring changes in the surface stress (only one side is allowed to bind protein, producing asymmetric loading) or resonance of the cantilever. Surface stress can be quantitated by optical beam deflection or changes in the resistance of a piezoelectric film on the cantilever. This film can also be used to excite bending of the cantilever and to read out changes in resonance frequency. A variation on the cantilever is the flexural plate resonator design [29]. There are many other promising technologies for protein handling and measurement on MEMS devices [26,30–34]. Although most of this work has been done with Si, MEMS capabilities, including the fabrication of cantilevers, has been demonstrated with SiC as well [35–38]. In order to detect proteins, to transduce the information into a quantitative measure, and transmit the information to the outside, a power supply will be needed. There are two basic approaches to powering autonomous implantable MEMS devices: on-chip power supply and

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induced power from an outside source. With the increasing deployment of remote and embedded sensors, there is great motivation to develop sustainable on-chip power supplies for microchips. Designs using RF have been implemented with reasonable efficiency [39]. Any such devices are constrained by limits to the RF power that can be directed at living tissue. However, radio frequency identification (RFID) microchips have been implanted in animals and humans for several years. Energy can also potentially be harvested from mechanical movement by piezoelectric means [40]. Various micro-fuel systems utilizing butane [41], methanol [42], and ethanol [43] have been demonstrated and microbatteries have been described [44]. Finally, in order to obtain the information collected by implanted sensor microchips, the data must be transmitted to the outside. Unfortunately, the salt-water environment of the body is quite attenuating to RF transmissions. However, RF transmission into and out of devices implanted within the body has been developed for RFID tags that are now commercially available. Furthermore, there is ongoing development in the area of RF and RF components on MEMS and microchips in general [45–48].

12.9

CONCLUSIONS

The development of nanoporous semipermeable membranes using semiconductor materials is an enabling technology for the construction of implantable microchip-based sensors. Such sensors may detect the earliest stages of diseases such as cancer, inflammatory and autoimmune illnesses, infection, atherosclerosis and others by sensing the accumulation of protein biomarkers and signalling molecules. They may also sense environmental contaminants. Although the technological barriers to fully independent implanted long-term sensors are formidable, progress is being made toward overcoming these challenges with multiple innovative approaches.

ACKNOWLEDGEMENTS This work was supported by the DURINT program administered by the Office of Naval Research (Dr C. Wood) under N00014-01-1-0715.

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Index References to figures are given in italic type. References to tables are given in bold type. References in the index to silicon carbide and gallium nitride are to the porous forms of the materials unless otherwise specified. aluminum diffusion rate 42–43, 43 into nonporous substrates 46–47, 47 anisotropic crystalline etching, gallium nitride 82–83 annealing gallium nitride, on silicon carbide substrate 158–159 silicon carbide, under thermal treatment 192–193 anodization 2–3 charge, and pore density, columnar silicon carbide 19 and pore formation, silicon carbide 178–183 time and pore growth, silicon carbide 188 and porous layer thickness 40–42 applications, gallium nitride 77–78 Arrhenius plots, silicon carbide, and electron trapping 240 Bell laboratories 1 biosensors on-chip 305–307 overview 291–292

silicon carbide-based, advantages 295–296 boron diffusion rate 42–43, 43 into nonporous substrate 45–46, 46 breakdown voltages, gallium nitride, on silicon nitride nanonetwork 137–138 Burgers vectors, for dislocations in epitaxially grown gallium nitride 214 n-butane, catalysis of oxidation 282–287 cantilevers, microscopic 306 capacitance, and voltage, silicon carbide, nickel contacts 52–53 carbon as gallium nitride codopand with manganese 257–259 particles in diesel exhaust 279 carbonation, of silicon 58–59 catalysis overview 275–276 applications, combustion in diesel engines 279–280 isomerization 280–281

Porous Silicon Carbide and Gallium Nitride: Epitaxy, Catalysis, and Biotechnology Applications Edited by Randall M. Feenstra and Colin E.C. Wood  C 2008 John Wiley & Sons, Ltd

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312 catalysis (Continued) oxidation 280, 281 reactions, on silicon carbide 278–279 cathodoluminescence, gallium nitride 86–88 channel alignment, silicon carbide 7–9 chemical mechanical polishing (CMP) 164–167 chemical sensors 78 chemical vapor deposition (CVD) 56–57 chemokines 294 chromium as dopant gallium nitride clustering 269–270 in nanohole arrays 265–268 nanotubes 262–264 cold-wall reactors, chemical vapor deposition (CVD) 57 columnar pores, silicon carbide 15–26, 239 conductivity silicon carbide and pore density 10–11 and pore formation 176 see also resistivity contacts (electrical) 49–53 contrast cathodoluminescent, from dislocations, gallium nitride 86–88, 87 gallium nitride columnar pores 113 cracks, in gallium nitride, on silicon carbide 196–197 current density and pore density 45 and reaction rate, silicon carbide 22 silicon carbide 10 current-voltage (I-V) characteristics, deposited nickel contacts 51 cytokines overview 293–294 measurement in vivo 294–295 deep level transient spectroscopy (DLTS) 234–237 data analysis 240–243 of gallium nitride, on silicon nitride nanonetworks 138–139 defects and deep level transition spectra 138–139

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INDEX density 3C silicon carbide on silicon carbide substrate 61–62 stabilized 63–64 gallium nitride, on silicon carbide substrate, substrate layer thickness 198–200 and substrate porous layer thickness 65–66 gallium nitride 121–122 reduction gallium nitride by substrate patterning 103–104 on titanium nitride 146–152 and porous substrates 56 silicon carbide, and substrate type 73–74 surface, in silicon carbide, effect on gallium nitride growth 161–162 see also dislocations Defense University Research Initiative on Nanotechnology (DURINT) 55–56 density of states, manganese 250 depletion layer 9 deposition time, silicon nitride nanonetworks, and defect density 129–130 diesel particles filter 279–280 diffusion of dopants 42–47 experimental setup 42 into nonporous substrates 45–46 gallium, on silicon nitride nanonetwork surface 127 of proteins through SiC membranes 301–304 dilute magnetic semiconductors (DMS) 246 dislocations cathodoluminescence 87 density control, silicon nitride deposition on gallium nitride 124–125 gallium nitride 78 and substrate choice 102 edge, and strain reduction, gallium nitride 214–215, 216 gallium nitride lateral epitaxic growth 217–220 on porous silicon carbide substrate 220–222 on sapphire 217

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INDEX on silicon carbide substrate 111–112 mechanisms on patterned planar substrate 217–220 as a result of lattice mismatch 214–217 screw gallium nitride in lateral epitaxic growth 217–218 on titanium nitride 148–149 thread gallium nitride 122 on silicon carbide 159–161 on titanium nitride 146–147, 149–152 on titanium nitride interlayer 223–224 mixed-type 216–217 dissolution rate, modelling 11 dopants aluminum diffusion rate 42–43, 43 nonporous substrates 46–47, 47 boron, diffusion rate, nonporous substrate 45–46, 46 chromium 265–268, 269–270 clustering 268–270, 269 concentration and etching rate, gallium nitride, from unintentionally doped films 81 gallium nitride, and defects 89 and magnetic properties, gallium nitride, nanohole arrays 267 and pore morphology 34–39, 39 diffusion 42 nonporous substrates 45–46 manganese 259–262, 268–270, 269 penetration, and substrate thickness 44 doping 42–47 edge dislocations planar defects as 216–217 and strain reduction, gallium nitride 214–215, 216 electrical properties silicon carbide with deposited nickel contacts 50–53 and pore density 10–11

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313 and pore formation 176 resistivity 232–234 transient 138–139, 234–237 see also magnetic properties electron trapping 233–234 modelling 235–236 epilayers, defect reduction 154 epitaxy cold-wall on porous substrate 58–62 on porous 3C substrate 64–67 stabilised 62–64 gallium nitride on porous silicon nitrite 122–123 on silicon carbide 195–198 on titanium nitride 142–146 hot-wall 67–73 hydride vapor phase (HVPE) 121, 140, 172–207 molecular beam (MBE) 104, 108–116 etching breakdown mechanisms, silicon carbide 32 and crystal orientation, silicon carbide 6–7 non-electrical hydrogen, of silicon carbide, for use as gallium nitride substrate 105–108 and porous gallium nitride 78–80 photoelectrochemical 3 anodization 2–3 current and pore formation 19–26 reactive ion etching 6, 18 silicon carbide, columnar porous 18–26 rate by hydrogen, of silicon carbide 68 and crystal orientation 12–13 silicon carbide columnar porous 16–17, 19–23 constant voltage vs. constant current 23–26 and crystal orientation 19–23 and crystal orientation 16 voltage (of etching anodization), and pore formation 19, 19–26 see also pores, formation evaporation, of silicon from silicon carbide surface under thermal treatment 193

OTE/SPH OTE/SPH JWBK104-IND JWBK104-Feenstra

February 12, 2008

314 fabrication gallium nitride 78–80 porous titanium nitride 140–142 silicon carbide triangular porous 3 for use as gallium nitride substrate 104–105, 172–173 facet-controlled ELO (FACELO) 130–131 ferromagnetism see magnetic properties FWHM, and defect density 113 gallium arsenide 154 gallium nitride overview 77–78 from unintentionally doped films 80–83 luminescence 85–89 pore development 189 Raman scattering characteristics 89–90 on silicon carbide 110–114, 154–167 growth profile 195–196 on silicon nitride nanonetwork 129–132 as substrate 121 on titanium nitride 143–146 giant magnetoresistance (GMR) device 245–246 ground state configurations, manganese-doped gallium nitride 256 growth factors 293–294 growth rates, chemical vapor deposition (CVD), hot-wall vs. cold-wall 57 half-loop dislocations formation 215–216 gallium nitride, on silicon carbide, as result of cooling 220 heat transfer, in pore growth 184–185 n-heptane, catalysis of isomerization 280–281 hot-wall reactor, chemical vapor deposition (CVD) 58 hydride vapor phase epitaxy (HVPE) 121 gallium nitride on silicon carbide 172–207 on titanium nitride 140 I-V (current-voltage) characteristics, nickel contacts 51

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INDEX interlayers overview 222 for gallium nitride silicon nitride 123–125, 129–132 and threading dislocation reduction 224–226 titanium nitride, and threading dislocation reduction 223–224 interstitial fluid 292 isomerization, catalysis 280–281 lateral epitaxial overgrowth (LEO) 102–103 lattice mismatch and dislocation mechanisms 214–217 gallium nitride, and defect density 101–102 reduction of strain using porous substrate 56, 154 sapphire, with gallium nitride 102 silicon carbide, cubic, on silicon substrate 58 strain reduction gallium nitride, on silicon carbide 204–205 via porous intermediate film 154 lattice structure, silicon carbide 13–15, 14 luminescence see cathodoluminescence; photoluminescence magnetic properties gallium nitride manganese- and carbon- doped, thin films 257–259 manganese-doped crystalline 247–248 thin films 249–257 nanoholes 265 nanotubes 262–264 nanowires 259–262 manganese as dopant clustering around nitrogen 268–269, 269 nanowires 259–262 Maxwell Garnett diffusion model, proteins through silicon carbide membranes 302–303 membranes diffusion modelling 301–304 comparison with experiment 304

OTE/SPH OTE/SPH JWBK104-IND JWBK104-Feenstra

February 12, 2008

INDEX silicon carbide biosensor performance improvement 299–301 protein permeability 296–299 MEMS 305–307 metal-organic chemical vapor deposition (MOCVD), and defect reduction in gallium nitride 220–222 methane, catalysis of oxidation 280 microchips, silicon carbide membrane integration 301, 305–307 microdialysis 294–295, 296 microelectromechanical (MEMS) systems 305–307 micropores, in silicon carbide 174–176 mismatch stress see lattice mismatch molecular beam epitaxy (MBE), gallium nitride 104, 108–116 nanoheteroepitaxy (NHE) 155 nanoholes 265–268 nanonetworks, silicon nitride 123–128 nanotubes 262–264, 263 nanowires 259–262 nitrogen, clustering of dopants 268–270 nucleation gallium nitride on silicon carbide 166–167 on titanium nitride 144–145 optical properties see photoluminescence orientation (of crystal) gallium nitride, and magnetic effects 252–257 silicon carbide and columnar pore formation 16–17 and etching rate 19–23 and oxide layer thickness 49 Ostwald ripening, in porous silicon carbide substrates 174–175 oxidation catalysis of hydrogen sulfide 281 of methane 280 and pore formation, silicon carbide 32 of silicon carbide 47–49 and substrate stabilization, silicon carbide 62

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315 phonons, propogation, gallium nitride 90 photoelectrochemical etching, silicon carbide, columnar porous 18–26 photoluminescence 3C silicon carbide, grown on porous silicon carbide substrate 66–67 gallium nitride 88–89 on silicon carbide 203 on silicon nitride nanonetworks 132–135, 133 on titanium nitride 152–153 porous 4H silicon carbide, on porous 4H silicon carbide substrate 70–71 spectra, and defect density 56–57 planar defects considered as edge dislocation 216–217 gallium nitride grown on porous silicon carbide 200–202 and lattice mismatch stress reduction, in gallium nitride, on silicon carbide 205 plasma cleaning, and pore morphology, silicon carbide 193–194 platinum, interlayers, for gallium nitride, defect reduction 79 Poisson equation 9 polishing hydrogen silicon carbide, and gallium nitride nucleation behaviour 162–163 of silicon carbide, for use as gallium nitride substrate 157–164 mechanochemical, silicon carbide 164–167 pores coalescence 194–195 electric potential near 238–239 electrical resisitivity effects 232–233 electron trapping 233–234 formation and crystal orientation, columnar 16–17 mechanisms 32–42 by hydride vapor phase epitaxy (HVPE) 173–176 silicon carbide columnar 15–26 during etching anodization 178–183 modelling 11

OTE/SPH OTE/SPH JWBK104-IND JWBK104-Feenstra

February 12, 2008

316 pores (Continued) parameters affecting 32 triangular 9–12 vacancy model 183–189 growth and anodization time 188 and heat transfer 184–185 stress at boundaries 185–186 through coalescence 194–195 micro-, in silicon carbide 174–176 shape columnar, electrical potential 239 and dopant concentration 34–39 parameters affecting 32 and plasma cleaning 193–194 silicon carbide triangular 12–15 modelling 12–15 and substrate dopant concentration 34–39 size and electrical resistivity 237–238 gallium nitride, from unintentionally doped films 80 in porous silicon carbide substrate, effect on cubic silicon carbide growth 60 and protein permeability 300 silicon carbide, as gallium nitride substrate 155–156 and substrate dopant concentration 39 stress at boundaries 116 and pore growth 185–186 sub-surface voids, gallium nitride, on titanium nitride 149 volume fraction and etching anodization charge 19 current density 41 measurement 5 silicon carbide 5 columnar porous 17–18 and hydrogen etching 106–108, 107 and strain relaxation, gallium nitride 115 titanium nitride 141 variation 5 porosity see pores, volume fraction preparation silicon carbide columnar porous 15–16

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INDEX triangular porous 3 pressure and defects, gallium nitride, on silicon nitride nanonetwork 128 gallium nitride on titanium nitride nucleation 145–146 and thread dislocation density 149–152 proteins detection, using microelectromechanical devices 306–307 signalling 292–294 silicon carbide permeability 296–299 Raman spectroscopy and film strain determination 114–115 gallium nitride 89–90, 91–95 planar vs. porous 91–92 reactive ion etching 6, 18 relative recovery rate 198 resistivity silicon carbide 32, 232–234 see also conductivity ridges, in gallium nitride under electroless etching 82 RIE (reactive ion etching) 6, 18 rocking curves, X-ray diffraction 198 sapphire as gallium nitride substrate, dislocation types 217 lattice mismatch with gallium nitride 102 Schottky contacts 49–53 Schottky diodes on undoped gallium nitride 135–138 deep level transition spectra 138–139 screw dislocations gallium nitride in lateral epitaxic growth 217–218 on titanium nitride 148–149 seed layer, gallium nitride grown with silicon nitride interlayer 125–128 shear stress gallium nitride around pores 116 from screw dislocations, on planar substrate 218–219 signalling proteins 292–294

OTE/SPH OTE/SPH JWBK104-IND JWBK104-Feenstra

February 12, 2008

INDEX silane and porous substrate epitaxy 68 and silicon nitride deposition on gallium nitride 123–124 silicon, carbonation to form porous silicon carbide 58–59 silicon carbide advantages in biosensing applications 295–296 as catalytic support material 276–277 morphology columnar porous 15–27 triangular porous 2–15 resistivity 237–238 and pore formation 32 stability under thermal treatment 190–195 as substrate for gallium nitride 104–117, 154–167, 221–222 fabrication 156 lattice mismatch 102 structural changes induced by growth of gallium nitride film over 195–198 for silicon carbide 58–62 3C 64–67 4H 67–73 stabilisation 62–64 triangular porous 4 silicon germinide 154 sintering 192–193 size discrimination, of proteins by silicon carbide membranes 299 space charge region, and pore formation 9 spintronics 245–246 stabilization of porous silicon carbide 62 stacking faults, gallium nitride, on porous silicon carbide 202 strain relaxation, gallium nitride, on silicon carbide substrate 114–116 stress at pore boundaries, silicon carbide, and pore growth 185–186 determination, using Raman scattering 114–115 shear at pore boundaries, gallium nitride 116

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317 gallium nitride, from screw dislocations, on planar substrate 218–219 see also lattice mismatch sub-surface voids, gallium nitride, on titanium nitride 149 substrates for gallium nitride 101–102 patterning 102 sapphire, dislocation types 217 nonporous, dopant diffusion rate 45–46, 46–47, 46, 47 patterning, and defect reduction 102–103 thickness and dopant penetration 44 and film morphology 65–66 and oxidation time 48 silicon carbide, for gallium nitride, and film quality 198 surface effects, and electrical resisitivity 233 surface layer silicon carbide 177–178, 180–181 porosity 5, 35, 36 synchrotron white beam X-ray topography (SWBXT) 72–73 T-cells 293 temperature and catalytic conversion rate 283, 284 and defects, gallium nitride, on silicon nitride nanonetwork 127 and gallium nitride nucleation on titanium nitride interlayer 143 and Schottky barrier height, gallium nitride with Schottky diodes, on silicon nitride nanonetwork 137 and silicon carbide stability 191 thermal properties silicon carbide 277–278 in catalysis applications 283 thickness of porous layers, measurement 33 of substrate, gallium nitride on silicon carbide, and defect density 198–200 thread dislocations gallium nitride 122, 214–217 on silicon carbide substrate 159–161

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February 12, 2008

318 thread dislocations (Continued) on titanium nitride substrate 146–147, 149–152 mixed-type 216–217 on titanium nitride interlayer 223–224 titanium nitride 140–142 transient electronic effects 138–139, 234–237 transmission electron microscopy (TEM) 84–85 triangular porous silicon carbide 2–15 tunnelling breakdown 32 two-step growth, gallium nitride with silicon nitride interlayer 130–131

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INDEX vanadyl pyrophosphate (VPO), modification with silicon carbide 282–287 voltage and capacitance, silicon carbide, deposited nickel contacts 52–53 and current, deposited nickel contacts 51 of etching anodization oscillations, in silicon carbide 179–180 and pore formation, silicon carbide, columnar porous 24–25 Westinghouse research laboratories 1

ultraviolet illumination and hole formation 32 in silicon carbide etching 3

X-ray diffraction spectra, FWHM, and defect density 113

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8 nm

4 nm

0 nm

Figure 6.7 Surface morphology of coalesced GaN (undoped) surface with 6 min SiNx nanonetwork. Reproduced from J.Q. Xie et al., Appl. Phys. Lett., 90(26), Art. no. 262112. Copyright (2007), with permission from the American Institute of Physics

(a)

(b)

1 µm

1 µm

Figure 6.28 AFM images of porous SiC receiving (a) mechanical polishing and (b) mechanical polishing and low-temperature hydrogen polishing

Figure 6.30 AFM images of CVD1163 (a) GaN grown on the porous SiC region and (b) GaN grown on the planar SiC region

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Figure 6.33 AFM images of porous SiC polished in hydrogen at (a), (b) 1400 ◦ C and (c), (d) 1500 ◦ C

Figure 6.35

AFM images of porous SiC receiving CMP

2

Ef

Spin-up

Ga36Mn4N40C4

Spin-down

Ef

Spin-down

(b)

Spin-up

(a)

Spin-up

Mn 4s C 2p

Mn 3p Ef

Mn 3d

Partial Dos of Mn and N

(b)

Spin-up

Ga36Mn4N40

Char Count= 0

Spin-down Spin-up

(a)

Spin-up

N 2s Ef

Mn 3d −6

Spin-down

(b)

N 2p

−8

Ef

Mn 3d

−4

−2

Spin-down 0

2

Ef

N 2p −8

4

Energy relative to Ferimi energy (eV)

−6

−4

−2

Spin-down 0

2

4

Total DOS of Ga40 Mn4 N36 C4

(a)

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January 31, 2008

Partial Dos of C in Ga40 Mn4 and N36 C4

Partial Dos of Mn

Total Dos of Ga36Mn4N40

OTE/SPH OTE/SPH JWBK104-CP JWBK104-Feenstra

Energy relative to Ferimi energy (eV)

Figure 10.4 (a1 ) Total DOS, (a2 ) partial DOS of Mn, and (a3 ) partial DOS of Mn 3d and neighboring N 2p for Ga36 Mn4 N40 supercell. (b1 ) Total DOS, (b2 ) partial DOS of Mn 3d and neighboring C 2p, and (b3 ) partial DOS of N for C codoped Ga36 Mn4 N36 C4 supercell

3.5

1.0

3.0

Ga36Mn4N40 Ga36Mn4N36C4

2.5

0.5

2.0 1.5

0.0

1.0

−0.5

0.5

Ga36Mn4N40 Ga36Mn4N36C4

−1.0 I

Magnetic moment (μB)

Energy difference ΔE (eV)

1.5

0.0

II III IV V Configuration number

VI

Figure 10.5 Energy difference E between AFM and FM states and the average magnetic moment on Mn atom for the six configurations with and without C codoping. The six configurations are defined in Table 10.3

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II

I

IV

III

Figure 10.10 Schematic representation of the four configurations of Cr-doped GaN MWNT supercells

14

42 15

41

N6 13

16

N5

40

12

N2

11

17

3 N3 5

10 18

N4

6 19

39 1 N1

38 37

36

4

2

35

7

34

8 20

33 9

21

27 23

22

25 24

32

28

31 29

(a)

(b)

Figure 10.11 Schematic representation of a GaN NH (Ga88 N88 ) supercell (a) and GaN NH arrays (b)

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(a)

Ga88N88

(b)

Ga86Cr2N88 Ga86Cr2N88(U)

(c)

Cr-4s Cr-3p Cr-3d Cr-3d (U)

(d)

Cr-3d N-2p

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Ef

Spin-up

Dnesity of states (arb. unit)

Spin-down Spin-up

Spin-down Spin-up

Spin-down Spin-up

Ef

−8

−6

−4

−2

Spin-down 0

2

4

Energy relative to Ferimi energy (eV)

Figure 10.12 (a) Total DOS corresponding to pure Ga88 N88 NH, (b) total DOS of Cr-doped GaN NH, (c) partial spin DOS of Cr atom, and (d) partial spin DOS of Cr 3d and N 2p in Ga86 Cr2 N88 supercell

II(ΔεII = 0.182 eV)

I(ΔεI = 0.000 eV)

III(ΔεIII = 0.344 eV)

IV(ΔεIV = 0.680 eV)

Figure 10.13 Four configurations of Ga85 Cr3 N88 supercell. The yellow spheres are Ga, the blue spheres are N, and the red spheres are Cr

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Figure 10.14 Geometries of Mnx N clusters in their ground states. The bond lengths are given in angstroms. The spin density surfaces corresponding to 0.005 a.u. for these clusters are plotted on the right. The green surfaces represent negative spin densities around the N site while the blue represents positive spin density around Mn sites

6