Sentaurus.SProcess.User Guide
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Sentaurus™ Process User
Guide
Version I-2013.12, December 2013
Copyright and Proprietary Information Notice
Copyright © 2013 Synopsys, Inc. All rights reserved. This software and documentation contain confidential and proprietary
information that is the property of Synopsys, Inc. The software and documentation are furnished under a license agreement and
may be used or copied only in accordance with the terms of the license agreement. No part of the software and documentation may
be reproduced, transmitted, or translated, in any form or by any means, electronic, mechanical, manual, optical, or otherwise, without
prior written permission of Synopsys, Inc., or as expressly provided by the license agreement.
Destination Control Statement
All technical data contained in this publication is subject to the export control laws of the United States of America.
Disclosure to nationals of other countries contrary to United States law is prohibited. It is the reader’s responsibility to
determine the applicable regulations and to comply with them.
Disclaimer
SYNOPSYS, INC., AND ITS LICENSORS MAKE NO WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, WITH
REGARD TO THIS MATERIAL, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
Trademarks
Synopsys and certain Synopsys product names are trademarks of Synopsys, as set forth at
http://www.synopsys.com/Company/Pages/Trademarks.aspx.
All other product or company names may be trademarks of their respective owners.
Synopsys, Inc.
700 E. Middlefield Road
Mountain View, CA 94043
www.synopsys.com
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Contents
About This Guide
xxxi
Audience . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxxii
Related Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxxii
Typographic Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxxii
Customer Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxxiii
Accessing SolvNet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxxiii
Contacting Synopsys Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxxiii
Contacting Your Local TCAD Support Team Directly. . . . . . . . . . . . . . . . . . . . . xxxiv
Acknowledgments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxxiv
Chapter 1 Getting Started
1
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Setting Up the Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Starting Sentaurus Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Starting Different Versions of Sentaurus Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Using a Command File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Example: 1D Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Defining Initial 1D Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Defining Initial Simulation Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Initializing the Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Choosing Process Models and Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Setting Up a Meshing Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Growing Screening Oxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Measuring Oxide Thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Depositing Screening Oxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Tcl Control Statements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Implantation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Saving the As-Implanted Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Thermal Annealing, Drive-in, Activation, and Screening Oxide Strip . . . . . . . . . . . . 11
Example: 2D Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Defining Initial Structure and Mesh Refinement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Implanting Boron. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Growing Gate Oxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Defining Polysilicon Gate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Working with Masks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Polysilicon Reoxidation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Saving Snapshots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
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Contents
Remeshing for LDD and Halo Implants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Implanting LDD and Halo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Forming Nitride Spacers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Remeshing for Source/Drain Implants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Implanting Source/Drain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Transferring to Device Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Remeshing for Device Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Contacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Saving the Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Extracting 1D Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Adaptive Meshing: 2D npn Vertical BJT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Defining Initial Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Adaptive Meshing Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Buried Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Epi Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Sinker Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Base Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Emitter Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Backend . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Full-Text Versions of Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1D NMOS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2D NMOS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2D npn Vertical Bipolar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Chapter 2 The Simulator Sentaurus Process
43
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Interactive Graphics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Command-Line Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Interactive Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Fast Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Terminating Execution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Environment Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
File Types Used in Sentaurus Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
Syntax for Creating Input Command Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Tcl Input. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Material Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
Aliases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
Default Simulator Settings: SPROCESS.models File. . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Compatibility With Previous Releases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Parameter Database. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
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Parameter Inheritance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Materials in Parameter Database . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Like Materials: Material Parameter Inheritance . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Interface Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Regionwise Parameters and Region Name-handling. . . . . . . . . . . . . . . . . . . . . . . . . . 58
Viewing the Defaults: Parameter Database Browser . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Starting the Parameter Database Browser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Browser PDB Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
PDB Preferences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
Viewing Parameters Stored in TDR Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Creating and Loading Structures and Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
Understanding Coordinate Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
Wafer Coordinate System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
Simulation Coordinate System (Unified Coordinate System) . . . . . . . . . . . . . . . . 67
Visualization Coordinate Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Defining the Structure: The line and region Commands . . . . . . . . . . . . . . . . . . . . . . . 70
Creating the Structure and Initializing Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Defining the Crystal Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Automatic Dimension Control. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Saving and Visualizing Structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Saving a Structure for Restarting the Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Saving a Structure for Device Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Saving Doping Information in SiC and GaN for Device Simulations . . . . . . . . . . 79
Saving 1D Profiles for Inspect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
Saving 1D TDR Files from 2D and 3D Simulations . . . . . . . . . . . . . . . . . . . . . . . 79
The select Command (More 1D Saving Options) . . . . . . . . . . . . . . . . . . . . . . . . . 80
Loading 1D Profiles: The profile Command . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Chapter 3 Ion Implantation
81
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Selecting Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Dios or Default Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Taurus Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
TSUPREM-4 Native Implant Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
Multirotation Implantation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
Energy Contamination Implantation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
Adaptive Meshing during Implantation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Coordinate System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Coordinates for Implantation: Tilt and Rotation Angles . . . . . . . . . . . . . . . . . . . . . . . 89
2D Coordinate System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
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Analytic Implantation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Primary Distribution Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
Gaussian Distribution: gaussian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
Pearson Distribution: pearson. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Pearson Distribution with Linear Exponential Tail: pearson.s. . . . . . . . . . . . . . . . 96
Dual Pearson Distribution: dualpearson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Point-Response Distribution: point.response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
Screening (Cap) Layer-dependent Moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
Lateral Straggle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Depth-dependent Lateral Straggle: Sentaurus Process Formulation . . . . . . . . . . 100
Depth-dependent Lateral Straggle: Dios Formulation . . . . . . . . . . . . . . . . . . . . . 100
Depth-dependent Lateral Straggle: Taurus Formulation . . . . . . . . . . . . . . . . . . . 101
Analytic Damage: Hobler Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Tables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
Implantation Table Library. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
File Formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
Multilayer Implantations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Lateral Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
Local Layer Structure in 2D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
Primary Direction and Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
Point-Response Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Analytic Damage and Point-Defect Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
Implantation Damage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
Point-Defect Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
Backscattering Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
Multiple Implantation Steps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
Preamorphization Implantation (PAI) Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
CoImplant Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
Profile Reshaping. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Ge-dependent Analytic Implantation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
Analytic Molecular Implantation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
Molecular Implantation with Supplied Implant Tables . . . . . . . . . . . . . . . . . . . . 130
BF2 Implant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
Damage Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
Performing 1D or 2D Analytic Implantation in 3D Mode. . . . . . . . . . . . . . . . . . . . . 131
Implantation on (110)/(111) Wafers Using (100) Implant Tables. . . . . . . . . . . . . . . 132
Monte Carlo Implantation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
Running Sentaurus MC or Crystal-TRIM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
Structure of Target Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
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Single-Crystalline Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
Amorphous Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
Polycrystalline Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
Molar Fractions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
Sentaurus MC Physical Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
Binary Collision Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
Electronic Stopping Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
Damage Accumulation and Dynamic Annealing . . . . . . . . . . . . . . . . . . . . . . . . . 149
Crystal-TRIM Physical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
Single-Crystalline Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
Amorphous Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
Damage Buildup and Crystalline–Amorphous Transition . . . . . . . . . . . . . . . . . . 158
Internal Storage Grid for Implantation Damage. . . . . . . . . . . . . . . . . . . . . . . . . . 159
Molecular Implantations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
MC Implantation into Polysilicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
MC Implantation into Compound Materials with Molar Fractions. . . . . . . . . . . . . . 163
MC Implantation into Silicon Carbide. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
Recoil Implantation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
Plasma Implantation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
Simple Source. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
Complex Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
Deposition of Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
Knock-on and Knock-off Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
Conformal Doping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
Other Plasma Implantation–related Parameters and Procedures . . . . . . . . . . . . . 170
MC Implantation Damage and Point-Defect Calculation . . . . . . . . . . . . . . . . . . . . . 172
Sentaurus MC Damage Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
Crystal-TRIM: Damage Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
Point Defects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
Statistical Enhancement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
Trajectory Splitting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
Dose Split . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
Trajectory Replication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
Boundary Conditions and Domain Extension. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
Unified Implant Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
Implant Boundary Conditions using PDB Commands . . . . . . . . . . . . . . . . . . . . . . . 181
Monte Carlo Implant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
Analytic Implant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
Smoothing Implantation Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
Automatic Extraction of Implant Moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
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Required Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
Optional Parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
Output Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
Utilities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
Loading External Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
Loading Files Using load.mc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
Automated Monte Carlo Run. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
Multithreaded Parallelization of 3D Analytic Implantation . . . . . . . . . . . . . . . . . . . . . . 191
Multithreaded Parallelization of Sentaurus MC Implantation . . . . . . . . . . . . . . . . . . . . 192
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
Chapter 4 Diffusion
197
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
Basic Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
Obtaining Active and Total Dopant Concentrations . . . . . . . . . . . . . . . . . . . . . . . . . 200
Transport Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
Recombination and Reaction Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
Other Materials and Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
General Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
Transport Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
ChargedReact Diffusion Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
React Diffusion Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
ChargedPair Diffusion Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
Pair Diffusion Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
ChargedFermi Diffusion Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
Fermi Diffusion Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
Constant Diffusion Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
NeutralReact Diffusion Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
Carbon Diffusion Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
Nitrogen Diffusion Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
Mobile Impurities and Ion-Pairing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
Solid Phase Epitaxial Regrowth Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
Level-Set Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
Phase Field Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
Flash or Laser Anneal Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
Dopant Diffusion in Melting Laser Anneal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
Guideline for Parameter Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
Saving a Thermal Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
Structure Extension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
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Intensity Models for Flash Anneal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
Gaussian Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
Table Lookup Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
User-specified Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
Intensity Model for Scanning Laser. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
Control Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
Diffusion in Polysilicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
Isotropic Diffusion Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
Grain Shape and the Grain Growth Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
Diffusion Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
Anisotropic Diffusion Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248
Diffusion in Grain Interiors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248
Grain Boundary Structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
Diffusion along Grain Boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
Segregation Between Grain Interior and Boundaries . . . . . . . . . . . . . . . . . . . . . . 251
Grain Size Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252
Surface Nucleation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
Grain Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254
Interface Oxide Breakup and Epitaxial Regrowth . . . . . . . . . . . . . . . . . . . . . . . . 255
Dependence of Polysilicon Oxidation Rate on Grain Size. . . . . . . . . . . . . . . . . . 257
Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258
Boundary Conditions for Grain Growth Equation . . . . . . . . . . . . . . . . . . . . . . . . 258
Dopant Diffusion Boundary Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258
Dopant Diffusion in SiGe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
Bandgap Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
Potential Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
Effects on Point-Defect Equilibrium Concentrations . . . . . . . . . . . . . . . . . . . . . . . . 262
Effect of Ge on Point-Defect Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
Impact of Ge on Extended-Defect Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
Impact of Dopant Diffusivities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
SiGe Strain and Dopant Activation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
Germanium–Boron Pairing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
Initializing Germanium–Boron Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
Diffusion in III–V Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
Material Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
Physical Parameter Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266
Dopant Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
ChargedReact Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
Fermi Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
Constant Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
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Activation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
Point-Defect Diffusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
Poisson Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
MoleFractionFields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
Pressure-dependent Defect Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
Electron Concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
Poisson Equation for Hetero-junctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
Bandgap Narrowing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
Epitaxy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282
Using LKMC for Deposition Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
Epi Doping. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
Initialization of Dopant Clusters in Epi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
Epi Auto-Doping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
Epi Doping Using Resistivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
Epi Growth Settings: Low-Temperature Epitaxy . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
Simulating Facet Growth during Selective Epitaxy . . . . . . . . . . . . . . . . . . . . . . . . . 287
Controlling Where Facets Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288
Time-stepping. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288
Other Effects on Dopant Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
Pressure-dependent Dopant Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
Diffusion Prefactors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290
High-Concentration Effects on Dopant Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
Hydrogen Effects on Dopant Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
Dopant Activation and Clustering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
Dopant Active Model: None . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
Dopant Active Model: Solid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
Dopant Active Model: Precipitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
Initializing Precipitation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294
Dopant Active Model: Transient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
Initializing Transient Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298
Dopant Active Model: Cluster. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
Initializing Cluster Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
Dopant Active Model: NeutralCluster. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
Initializing NeutralCluster Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303
Carbon Cluster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303
Nitrogen Cluster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304
Dopant Active Model: FVCluster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304
Initializing the FVCluster Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306
Dopant Active Model: Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306
Dopant Active Model: BIC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307
Initializing BIC Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
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Dopant Active Model: ChargedCluster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
Initializing ChargedCluster Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312
Dopant Active Model: ComplexCluster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312
Initializing ComplexCluster Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314
Dopant and Dopant-Defect Cluster Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . 315
Dopant Trapping at EOR Defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316
Initializing Dopant Trapping in EOR Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
Defect Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
Defect Cluster Model: None . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320
Defect Cluster Model: Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320
Defect Cluster Model: 311. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320
Initializing 311 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
Defect Cluster Model: Loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328
Direct Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328
Size-dependent Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
Initializing Loop Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330
Defect Cluster Model: LoopEvolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331
Initializing LoopEvolution Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332
Defect Cluster Model: FRENDTECH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333
Initializing FRENDTECH Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336
Defect Cluster Model: 1Moment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337
Interstitial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337
Vacancy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339
Initializing 1Moment Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341
Defect Cluster Model: 2Moment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341
Interstitial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341
Vacancy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343
Initializing 2Moment Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345
Defect Cluster Model: Full . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346
Interstitial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346
Vacancy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349
Initializing Full Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352
Ion Implantation to Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353
Initializing Solution Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357
HomNeumann . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357
Natural . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358
Surface Recombination Model: PDependent . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358
Surface Recombination Model: InitGrowth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360
Surface Recombination Model: Simple . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360
Surface Recombination Model: Normalized . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360
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Modifying Point-Defect Equilibrium Values at Surface . . . . . . . . . . . . . . . . . . . 361
Segregation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361
Surface Recombination Model: Default . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362
Surface Recombination Model: PairSegregation . . . . . . . . . . . . . . . . . . . . . . . . . 362
Dirichlet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364
ThreePhaseSegregation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365
Surface Recombination Model: Default . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366
Surface Recombination Model: PairSegregation . . . . . . . . . . . . . . . . . . . . . . . . . 368
Trap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369
TrapGen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369
Continuous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369
Periodic Boundary Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370
Boundary Conditions at Moving Interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370
Enhanced and Retarded Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370
Conserving Dose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371
Common Dopant and Defect Dataset Names . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377
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Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381
KMC Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382
Operating Modes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382
Atomistic Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383
Restrictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383
Implant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384
Diffuse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385
Nonatomistic Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386
Atomistic/Nonatomistic Translation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387
Sano Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388
Simulation Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389
Recommended Domain Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389
Internal Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390
Randomization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392
Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392
Parallelism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393
How Parallelism Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393
Estimating CPU Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394
Atomistic Diffusion Simulation with Sentaurus Process KMC . . . . . . . . . . . . . . . . . . . 395
Units. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396
Space Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397
Materials and Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398
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Supported Materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399
Material Alloying. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402
Point Defects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403
Ambiguous Alloying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403
Time Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403
Simulation and CPU Times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404
Parallelism and CPU Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406
Snapshots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407
Movie . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407
Time Internal Representation and Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408
Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408
Particle Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408
Particles in Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 410
Alias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411
Colors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411
Particles and Parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411
Undefining Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414
Defect Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414
Point Defects, Impurities, Dopants, and Impurity-paired Point Defects . . . . . . . . . . . . 415
Interstitials and Vacancies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415
Impurities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418
Migration (Diffusion) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418
Breakup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419
Percolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421
Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421
Parameter Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422
Hopping Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423
The short Mode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423
The long Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423
The double Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424
The longdouble Mode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424
Enabling and Disabling Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424
Interaction Rules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426
Defining Nonstandard Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427
Interaction Rules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427
Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428
Stress Effects on Point Defects, Impurities, Dopants, and Impurity-Paired Point Defects
428
Migration Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429
Binding Energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429
Alloys. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430
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Alloy Diffusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431
Alloy Effects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432
Introducing Alloys in the Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432
Damage Accumulation Model: Amorphous Pockets . . . . . . . . . . . . . . . . . . . . . . . . . . . 432
Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434
Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434
Recombination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434
Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435
Emission. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436
Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437
Amorphous Pockets Life Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439
Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440
Interactions of Amorphous Pockets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440
Interaction with Point Defects: I and V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440
Interaction with Impurities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441
Extended Defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442
{311} Defects (ThreeOneOne) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442
Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443
Capture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444
Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444
Recombination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446
Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446
Dislocation Loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447
Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447
Capture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448
Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448
Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450
Voids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451
Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452
Capture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453
Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453
Recombination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454
Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454
Amorphization and Recrystallization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454
Amorphous Defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456
Material. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456
Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456
Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456
Recombination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456
Diffusion in Amorphous Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456
Direct diffusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457
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Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457
Indirect Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457
Impurity Clusters in Amorphous Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459
Recrystallization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460
KMC: Quasiatomistic Solid Phase Epitaxial Regrowth . . . . . . . . . . . . . . . . . . . . 460
LKMC: Fully Atomistic Modeling of Solid Phase Epitaxial Regrowth . . . . . . . 463
Defect Generation during SPER. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467
Redistributing Damage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469
Impurity Sweep/Deposit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470
Impurity Clusters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472
Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473
Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474
Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474
Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475
Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475
Initial Seeds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477
Percolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477
Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478
Emission. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479
Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480
Recombination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481
Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481
Frank–Turnbull Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481
Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482
Complementary Recombination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483
Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484
Complementary Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484
Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485
Charge Dependency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485
Neutral Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485
Nonneutral Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485
Interactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487
Complex Impurity Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487
Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488
Setting Up Impurity Clusters in a Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489
Fermi-Level Effects: Charge Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 490
Sentaurus Process KMC Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491
Assumptions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491
Formation Energies for Charged Species . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492
Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493
Binding Energies for Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493
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Binding Energies for Impurity Clusters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493
Temperature Dependency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494
Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494
Charge Attractions and Repulsions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495
Fermi-Level Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495
Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 496
Updating Charged States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497
Electronic Concentrations and Charge-State Ratios. . . . . . . . . . . . . . . . . . . . . . . 497
Mobile Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498
Pairing and Breakup Reactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498
Electric Drift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 499
Bandgap Narrowing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 500
Narrowing due to Dopant Concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 500
Narrowing due to Strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501
Narrowing due to Presence of an Alloy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504
Bandgap Narrowing Use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504
Charge Model and Boron Diffusion Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505
Charge Model and Arsenic Diffusion Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506
Interfaces and Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507
Different Interface Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508
Interfaces for Self-Silicon Point Defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509
Capture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509
Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509
Stress. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 510
Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511
Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511
Oxidation-enhanced Diffusion (OED) Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 512
Interfaces for Impurities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514
Simple Material Side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514
Full Material Side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516
Oxidation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 518
Epitaxial Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519
Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521
Including New Impurities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522
Impurities Diffusing without Pairing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525
Normal Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525
Diffusion without Pairing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525
Reports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526
Models Used Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526
Particle Distribution Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527
Cluster Distribution Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 528
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Defect Activity Report. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 528
Interactions Report. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 530
PointDefect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 530
AmorphousPocket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531
ThreeOneOne . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531
Loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531
ImpurityCluster. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531
Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532
Event Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532
PointDefect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532
AmorphousPocket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533
ThreeOneOne . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534
Loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534
ImpurityCluster. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534
Amorphous Defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535
Lattice Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535
Simple Materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535
Extracting KMC-related Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536
Transferring Fields from KMC to Continuum Information: deatomize . . . . . . . . . . 536
Smoothing Out Deatomized Concentrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537
Adding and Obtaining Defects in Simulations: add, defects.add, and defects.write . 539
Using the Sentaurus Process Interface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 541
The select, print, WritePlx, and plot Commands . . . . . . . . . . . . . . . . . . . . . . . . . 541
The init Command . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 542
The struct Command . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 542
The load Command . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 542
The deposit Command . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 542
The diffuse Command . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543
Nonatomistic Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543
Atomistic Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543
Calling Directly the Sentaurus Process KMC Kernel . . . . . . . . . . . . . . . . . . . . . . . . 543
Writing and Displaying TDR Files with KMC Information . . . . . . . . . . . . . . . . 544
Inquiring about KMC Profiles, Histograms, and Defects . . . . . . . . . . . . . . . . . . . . . 547
The histogram Option. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 548
The profile Option . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551
The supersaturation Option . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554
The defects Option . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555
The dose Option . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557
The materials Option . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559
The acinterface Option . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 560
Common Dopant and Point-Defect Names . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 560
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Advanced Calibration for Sentaurus Process KMC . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566
Chapter 6 Alagator Scripting Language
571
Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571
Binary and Unary Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571
Simple Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 572
Differential Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573
Special Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573
The diag Operator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573
String Names . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574
Solution Names and Subexpressions: Terms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574
Constants and Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575
Alagator for Diffusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575
Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 576
Setting Boundary Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 578
Dirichlet Boundary Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 578
Segregation Boundary Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 578
Natural Boundary Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579
Interface Traps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579
External Boundary Condition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 580
Using Terms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 580
Callback Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582
Callbacks during Execution of diffuse Command . . . . . . . . . . . . . . . . . . . . . . . . 583
Using Callback Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586
Setup Procedure: InitProc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587
Preprocessing and Postprocessing Data: diffPreProcess, UserDiffPreProcess,
diffPostProcess, UserDiffPostProcess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 591
Complex Initialization Procedures: InitSolve and EquationInitProc . . . . . . . . . . 592
Diffusion Summary: pdb, TclLib, SPROCESS.models . . . . . . . . . . . . . . . . . . . . . . 594
Alagator for Generic Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596
Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596
Epi Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 598
Callback Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 600
Setup Procedure: InitGrowth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602
Equation Procedure: EquationGrowthProc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603
Epitaxy Growth Rate: GrowthRateProc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605
Generic Growth Summary: pdb, TclLib, SPROCESS.models . . . . . . . . . . . . . . . . . 606
Modifying Diffusion Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 608
UserAddEqnTerm and UserSubEqnTerm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 608
UserAddToTerm and UserSubFromTerm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 609
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Chapter 7 Advanced Calibration
611
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 611
Using Advanced Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 611
Additional Calibration by Users . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 612
Chapter 8 Oxidation and Silicidation
615
Oxidation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615
Basic Oxidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 616
Temperature Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 616
Ambients and Gas Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 617
Specifying Gas Flows. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 618
Computing Partial Pressures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 619
In Situ Steam-generated Oxidation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 620
Oxidant Diffusion and Reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 620
Transition to Linear and Parabolic Rate Constants . . . . . . . . . . . . . . . . . . . . . . . 622
Massoud Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623
Orientation-dependent Oxidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624
Stress-dependent Oxidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624
Trap-dependent Oxidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 626
Dopant-dependent Oxidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 627
Diffusion Prefactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 629
Oxidation with Dielectric on Top . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 630
N2O Oxidation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 630
SiC Oxidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 630
In Situ Steam-generated Oxidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 632
Silicide Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634
TiSi2 Growth Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634
TiSi2 Formation Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635
Tungsten-, Cobalt-, and Nickel-Silicide Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 637
Stress-dependent Silicidation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 637
Oxygen-retarded Silicidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 638
Triple-Point Control. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 639
Dopants and Defects in Oxides and Silicides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 640
Numerics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 640
Outer Time Loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 640
Inner Time Loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 641
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 642
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Chapter 9 Computing Mechanical Stress
643
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643
Material Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644
Viscoelastic Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645
Maxwell Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645
Standard Linear Solid Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646
Purely Viscous Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 648
Shear Stress–dependent Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 648
Purely Elastic Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 649
Anisotropic Elastic Materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 650
Cubic Crystal Anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 650
Orthotropic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 651
Plastic Materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653
Incremental Plasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653
Deformation Plasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655
Viscoplastic Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656
Anand Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656
Power Law Creep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 658
Swelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 660
Mole Fraction–dependent Mechanical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 661
Deprecated Syntax for Mole Fraction–dependent Mechanical Properties of Binary
Compounds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 663
Temperature-dependent Mechanical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664
Deprecated Syntax for Temperature-dependent Mechanical Properties . . . . . . . 665
Plane Stress Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665
Equations: Global Equilibrium Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 666
Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 667
Example: Applying Boundary Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 669
Pressure Boundary Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 670
Advanced Dirichlet Boundary Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 670
Periodic Boundary Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 670
Time Step Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 672
Stress-causing Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 672
Stress Induced by Growth of Material. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 672
Densification-induced Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 673
Selectively Switching Off Grid Movement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 673
Stress Caused by Thermal Mismatch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674
Lattice Mismatch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675
Using the Lattice Mismatch Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 677
Total Concentration Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 678
Reference Concentration Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 679
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Strained Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 679
Edge Dislocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 680
Intrinsic Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 682
Stress Rebalancing after Etching and Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . 683
Automated Tracing of Stress History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 683
Saving Stress and Strain Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 684
Description of Output Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 684
Tracking Maximum Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 690
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 690
Chapter 10 Mesh Generation
693
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693
Mesh Refinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694
Viewing Mesh Refinement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695
Static Refinement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695
Standard Refinement Boxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695
Interface Refinement Boxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 696
Interface Offsetting Refinement Boxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 696
Refinement Inside a Mask . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 697
Refinement Near Mask Edges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 698
Adaptive Refinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 699
Adaptive Refinement Criteria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 700
Localizing Adaptive Meshing using refinebox Command. . . . . . . . . . . . . . . . . . 706
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 707
Adaptive Meshing during Diffusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 707
Adaptive Meshing during Implantation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 708
Tips for Adaptive Meshing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 709
Default Refinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 710
Refinement Box Manipulations: Using transform.refinement . . . . . . . . . . . . . . . . . 711
Mesh Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 712
Controlling Mesh during Oxidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 714
TS4 Mesh Library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 714
Control Parameters in TS4Mesh. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715
Moving Mesh and Mechanics Displacements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 717
Grid Spacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 717
Grid Cleanup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 717
Maximum-allowed Rate of Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 718
Miscellaneous Tricks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 718
Meshing for 3D Oxidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 719
MovingMesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 719
UseLines: Keeping User-defined Mesh Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 722
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Using line Commands after init Command . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723
Dimension within Current Spatial Dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . 723
Dimension Greater Than Current Spatial Dimension. . . . . . . . . . . . . . . . . . . . . . 723
Creating More Than One Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 724
The UseLines and transform Commands. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725
The reflect Command . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725
The stretch Command. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725
The rotate Command . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725
The translate Command . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725
The cut Command . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725
Testing line Commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725
Showing Clearing Lines for a New Structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . 726
Data Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 727
Troubleshooting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 727
Chapter 11 Structure Generation
731
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 731
Functionality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 731
Etching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 732
Deposition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 732
Masks and Photoresist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 732
Geometry Creation and Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 732
Etching and Deposition Types and Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 733
Etching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 733
Etching Tips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 736
Etching Type: Isotropic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 736
Etching Types: Anisotropic and Directional . . . . . . . . . . . . . . . . . . . . . . . . . . . . 737
Etching Types: Polygonal and CMP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 740
Etching Type: Fourier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 741
Etching Type: Crystallographic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 744
Etching Type: Trapezoidal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 745
Etching Type: Piecewise Linear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 749
Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 751
Mask Naming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 752
Deposition Type: Isotropic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 752
Deposition Types: Fill and Polygonal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 752
Deposition Type: Crystallographic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 753
Deposition Type: Fourier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 754
Deposition Type: Trapezoidal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 755
Selective Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 756
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Fields in Deposited Layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 756
Stress Handling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 757
Shape Library. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 757
PolyHedronSTI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 758
PolyHedronSTIaccc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 760
PolyHedronSTIaccv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 761
PolyHedronCylinder. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 762
PolygonWaferMask . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 762
PolyHedronEpiDiamond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 763
The mask and photo Commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 764
Photoresist Masks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 767
Boolean Masks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 767
Line Edge Roughness Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 769
Mirrored Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 771
Geometry Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 772
Refinement Handling during Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . 773
Contact Handling during Transformation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 773
The transform reflect Command . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 774
Refinement Handling during Reflection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 774
The transform stretch Command . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 774
Refinement Handling during Stretch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 775
The transform cut Command . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 775
Refinement Handling during Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 776
The transform flip Command and Backside Processing . . . . . . . . . . . . . . . . . . . . . . 776
Refinement Handling during Flip. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 777
The transform rotate Command . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 777
Refinement Handling during Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 778
The transform translate Command . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 778
MGOALS Interface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 778
MGOALS Boundary-moving Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 778
MGOALS Boundary-moving Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 780
MGOALS 3D Boundary-moving Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 782
Summary of MGOALS Etching and Deposition Algorithms . . . . . . . . . . . . . . . . . . 783
MGOALS Backward Compatibility. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 784
Boundary Repair Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 785
Inserting Segments in One Dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 785
Inserting Polygons in Two Dimensions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 785
Inserting Polyhedra in Three Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 786
Reading Polyhedra from a TDR Boundary File . . . . . . . . . . . . . . . . . . . . . . . . . . 786
Creating a Rectangular Prism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 787
Extruding a 2D Polygon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 787
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Creating a Polyhedron from Its Constituent Polygonal Faces . . . . . . . . . . . . . . . 788
Sentaurus Structure Editor Interface: External Mode. . . . . . . . . . . . . . . . . . . . . . 788
Inserting Polyhedra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 789
Structure Assembly in MGOALS Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 790
Multithreading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 790
Sentaurus Structure Editor Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 791
Sentaurus Topography Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794
Sentaurus Topography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794
Sentaurus Topography 3D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 796
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 797
Using Polygon and Rectangle Mask in 2D Simulation . . . . . . . . . . . . . . . . . . . . . . . 797
3D Etching after 2D LOCOS Simulation (Sentaurus Structure Editor Interface) . . . 797
Using Layout File for 3D Etching (Sentaurus Structure Editor Interface) . . . . . . . . 799
3D Trench Etching, Sloped Sidewall with Predefined Angle (Sentaurus Structure Editor
Interface). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 803
3D Etching after 2D LOCOS Simulation using MGOALS. . . . . . . . . . . . . . . . . . . . 805
Structure Assembly in MGOALS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 807
Polygon Creation and Insertion in MGOALS2D . . . . . . . . . . . . . . . . . . . . . . . . . . . 809
Polyhedron Creation and Insertion in MGOALS . . . . . . . . . . . . . . . . . . . . . . . . . . . 812
Reading a TDR file. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 812
Extruding a 2D Polygon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 813
Creating a Polyhedron using Polygons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 814
Defining a Brick . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 815
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 816
Chapter 12 ICWBEV Plus Interface for Layout-driven Simulations
817
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 817
ICWBEV Plus Introduction for TCAD Users. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 818
Opening GDSII Layout Files. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 818
Graphical User Interface of ICWBEV Plus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 819
Sentaurus Markups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 820
Stretch Utility. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 822
Renaming Markups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 824
Auxiliary Layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 825
Editing Polygons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 826
Resizing a Rectangle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 826
Converting a Rectangle to a Polygon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 827
Nonaxis-aligned Simulation Domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 827
Files Relevant to ICWBEV Plus–TCAD Sentaurus . . . . . . . . . . . . . . . . . . . . . . . . . . . . 828
Saving the Sentaurus Markup File. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 829
Contents of Sentaurus Markup File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 830
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Reloading the Markup File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 831
Saving the TCAD Layout File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 832
Contents of TCAD Layout File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 833
Reloading the TCAD Layout File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834
ICWBEV Plus Batch Mode and Macros. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834
Starting ICWBEV Plus in Batch Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834
ICWBEV Plus Macros. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834
Tcl-based Macros for Layout Parameterization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 835
TCAD Layout Reader of Sentaurus Process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 835
Loading the TCAD Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 836
Finding Simulation Domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 836
Finding Layer Names and Layer IDs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 836
Selecting the Simulation Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 837
Loading a GDSII Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 837
Finding Domain Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 838
Finding Bounding Box of Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 838
Interface with line Commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 839
Creating Masks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 839
Layout-driven Meshing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 841
Layout-driven Contact Assignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 842
Aligning Wafer and Simulation Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 844
Additional Query Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 846
Chapter 13 Extracting Results
849
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 849
Saving Data Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 849
Selecting Fields for Viewing or Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 850
Obtaining 1D Data Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 851
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 851
Determining the Dose: Layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 853
Extracting Values and Level Crossings: interpolate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 854
Extracting Values during diffuse Step: extract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 854
Optimizing Parameters Automatically. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855
Fitting Routines: FitLine, FitArrhenius, FitPearson, and FitPearsonFloor. . . . . . . . . . . 856
Resistivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 857
Sheet Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 859
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 860
Chapter 14 Numerics
861
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 861
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Setting Parameters of the Iterative Solver ILS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 862
Partitioning and Parallel Matrix Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 864
Matrix Size Manipulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 867
Node and Equation Ordering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 867
Time Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 868
Time-Step Control. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 869
Time-Step Control for PDEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 869
Error Control for PDEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 871
Time-Step Control for Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 871
Convergence Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 872
Time-Step Adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 873
Time-Step Cutback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 874
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 875
Appendix A Commands
877
Syntax Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 877
Example of Command Syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 878
Common Arguments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 879
alias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 880
ambient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 881
ArrBreak . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 883
Arrhenius. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 884
beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 885
bound. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 887
Compatibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 888
contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 889
contour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 894
CutLine2D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 896
define. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 897
defineproc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 898
DeleteRefinementboxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 900
deposit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 901
diffuse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 908
doping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 917
element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 919
Enu2G . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 920
Enu2K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 921
equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 922
etch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 923
exit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 930
extract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 931
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fbreak . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 933
fcontinue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 933
fexec . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 934
fproc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 934
fset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 934
gas_flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 935
graphics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 938
grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 940
help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 950
icwb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 951
icwb.contact.mask . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 954
icwb.create.all.masks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 956
icwb.create.mask . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 957
icwb.refine.mask . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 959
implant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 961
init . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 978
insert . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 982
integrate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 985
interface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 988
interpolate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 991
KG2E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 993
KG2nu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 994
kmc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 995
KMC2PDE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1007
layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1008
line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1010
line_edge_roughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1013
load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1016
LogFile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1019
mask . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1020
mater . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1025
math. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1027
mgoals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1037
optimize. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1042
paste . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1046
pdbDelayDouble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1048
pdbdiff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1049
pdbDopantLike . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1050
pdbExprDouble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1051
pdbGet and Related Commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1052
pdbIsAvailable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1054
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pdbLike . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1055
pdbSet and Related Commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1056
pdbUnSet-related Commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1059
PDE2KMC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1060
photo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1061
plot.1d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1063
plot.2d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1066
plot.tec. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1070
plot.xy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1076
point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1078
point.xy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1080
polygon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1082
polyhedron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1086
PowerDeviceMode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1089
print.1d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1090
print.data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1092
profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1093
RangeRefineboxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1096
reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1099
refinebox . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1101
region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1110
sde . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1114
select . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1117
SetAtomistic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1121
SetDFISEList . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1122
SetDielectricOxidationMode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1124
SetFastMode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1126
setMobilityModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1127
SetPlxList . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1128
SetTDRList . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1129
SetTemp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1130
SetTS4ImplantMode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1131
SetTS4MechanicsMode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1132
SetTS4OxidationMode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1133
SetTS4PolyMode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1134
SheetResistance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1135
simDelayDouble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1136
simGetBoolean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1137
simGetDouble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1138
simSetBoolean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1139
simSetDouble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1140
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slice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1141
smooth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1144
solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1145
sptopo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1148
stdiff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1149
strain_profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1150
stressdata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1151
StressDependentSilicidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1156
strip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1157
struct . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1158
substrate_profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1163
tclsel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1164
temp_ramp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1166
term . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1173
topo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1176
transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1177
transform.refinement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1182
translate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1186
UnsetAtomistic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1187
UnsetDielectricOxidationMode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1189
update_substrate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1190
WritePlx . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1191
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Sentaurus™ Process User Guide
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About This Guide
The Synopsys Sentaurus™ Process tool is an advanced 1D, 2D, and 3D process simulator
suitable for silicon and nonsilicon semiconductor devices. It features modern software
architecture and state-of-the-art models to address current and future process technologies.
Sentaurus Process simulates all standard process simulation steps, diffusion, implantation,
Monte Carlo (MC) implantation (Taurus MC or Crystal-TRIM), oxidation, etching, deposition,
and silicidation. Capabilities in 3D include meshing of 3D boundary files through the
MGOALS library, implantation through the Imp3D module from FhG Erlangen, mechanics
(stress and strain), diffusion, a limited capability for 3D oxidation, and an interface to
Sentaurus Structure Editor, which is the 3D geometry editing tool based on the ACIS solid
modeling library.
Sentaurus Process uses the Alagator scripting language that allows users to solve their own
diffusion equations. Alagator can be used to solve any diffusion equation including dopant,
defect, impurity, and oxidant diffusion equations. Simulation of 3D diffusion is handled exactly
as for 1D and 2D. Therefore, all the advanced models and user programmability available in
1D and 2D can be used in 3D. In addition, a set of built-in calibrated parameters is available
with Advanced Calibration.
The main chapters are:
■
Chapter 1 describes how to run Sentaurus Process.
■
Chapter 2 presents an overview of how Sentaurus Process operates.
■
Chapter 3 presents the ion implantation technique used in Sentaurus Process.
■
Chapter 4 provides information on the dopant and defect diffusion models and parameters.
■
Chapter 5 describes atomistic kinetic Monte Carlo diffusion.
■
Chapter 6 discusses the Alagator scripting language for solving diffusion equations.
■
Chapter 7 provides details about using Advanced Calibration in Sentaurus Process.
■
Chapter 8 describes the oxidation models.
■
Chapter 9 describes the computation of mechanical stress.
■
■
■
■
Chapter 10 describes the mesh algorithms and meshing parameters available in Sentaurus
Process.
Chapter 11 discusses etching and deposition, and other geometry manipulations available
in Sentaurus Process.
Chapter 12 presents strategies for using the IC WorkBench EV Plus–TCAD Sentaurus
interface.
Chapter 13 presents strategies for analysing simulation results.
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About This Guide
Audience
Chapter 14 discusses numerics-related issues, time integration methods, and the linear
solvers used in Sentaurus Process.
■
Appendix A lists the available commands, including descriptions, options, and examples.
■
Audience
This user guide is intended for users of the Sentaurus Process software package.
Related Publications
For additional information about Sentaurus Process, see:
The TCAD Sentaurus release notes, available on SolvNet® (see Accessing SolvNet on
page xxxiii).
■
Documentation available through SolvNet at https://solvnet.synopsys.com/DocsOnWeb.
■
Typographic Conventions
xxxii
Convention
Explanation
<>
Angle brackets
{}
Braces
[]
Brackets
()
Parentheses
Blue text
Identifies a cross-reference (only on the screen).
Bold text
Identifies a selectable icon, button, menu, or tab. It also indicates the name of a field or an
option.
Courier font
Identifies text that is displayed on the screen or that the user must type. It identifies the names
of files, directories, paths, parameters, keywords, and variables.
Italicized text
Used for emphasis, the titles of books and journals, and non-English words. It also identifies
components of an equation or a formula, a placeholder, or an identifier.
Menu > Command
Indicates a menu command, for example, File > New (from the File menu, select New).
NOTE:
Identifies important information.
Sentaurus™ Process User Guide
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About This Guide
Customer Support
Customer Support
Customer support is available through SolvNet online customer support and through
contacting the Synopsys support center.
Accessing SolvNet
SolvNet includes an electronic knowledge base of technical articles and answers to frequently
asked questions about Synopsys tools. SolvNet also gives you access to a wide range of
Synopsys online services, which include downloading software, viewing documentation, and
entering a call to the Synopsys support center.
To access SolvNet:
1. Go to the SolvNet Web page at https://solvnet.synopsys.com.
2. If prompted, enter your user name and password. (If you do not have a Synopsys user name
and password, follow the instructions to register with SolvNet.)
If you need help using SolvNet, click Help on the SolvNet menu bar.
Contacting Synopsys Support
If you have problems, questions, or suggestions, you can contact Synopsys support in the
following ways:
■
■
Go to the Synopsys Global Support Centers site on www.synopsys.com. There you can find
e-mail addresses and telephone numbers for Synopsys support centers throughout the
world.
Go to either the Synopsys SolvNet site or the Synopsys Global Support Centers site and
open a case online (Synopsys user name and password required).
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About This Guide
Acknowledgments
Contacting Your Local TCAD Support Team Directly
Send an e-mail message to:
■
support-tcad-us@synopsys.com from within North America and South America.
■
support-tcad-eu@synopsys.com from within Europe.
■
support-tcad-ap@synopsys.com from within Asia Pacific (China, Taiwan, Singapore,
Malaysia, India, Australia).
■
support-tcad-kr@synopsys.com from Korea.
■
support-tcad-jp@synopsys.com from Japan.
Acknowledgments
Sentaurus Process is based on the 2000 and 2002 releases of FLOOPS written by
Professor Mark Law and coworkers at the University of Florida. Synopsys acknowledges the
contribution of Professor Law and his advice in the development of Sentaurus Process. For
more information about TCAD at the University of Florida, visit
http://www.swamp.tec.ufl.edu.
Sentaurus Process Kinetic Monte Carlo is based on DADOS written by Professor Martin Jaraiz
and coworkers at the University of Valladolid, Spain. Synopsys acknowledges Professor Jaraiz’
contribution and advice. For more information, visit http://www.ele.uva.es/~simulacion/
KMC.htm.
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CHAPTER 1
Getting Started
This chapter describes how to run Sentaurus Process and guides you
through a series of examples.
This chapter is not a comprehensive reference but is intended to introduce some of the more
widely used features of Sentaurus Process in a realistic context. For new users, the sections
Interactive Mode on page 46, Syntax for Creating Input Command Files on page 50, and
Creating the Structure and Initializing Data on page 71 would be useful to refer to while
reading this chapter. For more advanced users who need to adjust model parameters, Like
Materials: Material Parameter Inheritance on page 57 would be useful. For the TCAD
Sentaurus Tutorial and examples, go to:
$STROOT/tcad/$STRELEASE/Sentaurus_Training/index.html
where STROOT is an environment variable that indicates where the Synopsys TCAD
distribution has been installed, and STRELEASE indicates the Synopsys TCAD release number.
Overview
Sentaurus Process is a complete and highly flexible, multidimensional, process modeling
environment. With its modern software architecture and extensive breadth of capabilities,
Sentaurus Process is a state-of-the-art process simulation tool. Calibrated to a wide range of
the latest experimental data using proven calibration methodology, Sentaurus Process offers
unique predictive capabilities for modern silicon and nonsilicon technologies.
Sentaurus Process accepts as input a sequence of commands that is either entered from
standard input (that is, at the command prompt) or composed in a command file. A process
flow is simulated by issuing a sequence of commands that corresponds to the individual
process steps. In addition, several commands allow you to select physical models and
parameters, grid strategies, and graphical output preferences, if required. You should place
parameter settings in a separate file, which is sourced at the beginning of input files using the
source command.
In addition, a special language (Alagator) allows you to describe and implement your own
models and diffusion equations.
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Setting Up the Environment
Setting Up the Environment
The STROOT environment variable is the TCAD Sentaurus root directory, and you must set this
variable to the installation directory of TCAD Sentaurus. The STRELEASE environment
variable can be used to specify the release of the software to run, for example, H-2013.03. If
STRELEASE is not set, the default version is used which is usually the last version installed.
To set the environment variables:
1. Set the TCAD Sentaurus root directory environment variable STROOT to the TCAD
Sentaurus installation directory, for example:
* Add to .cshrc
setenv STROOT
* Add to .profile, .kshrc, or .bashrc
STROOT=; export STROOT
2. Add the /bin directory to the user path.
For example:
* Add to .cshrc:
set path=(/bin $path)
* Add to .profile, .kshrc, or .bashrc:
PATH=/bin:$PATH
export PATH
Starting Sentaurus Process
You can run Sentaurus Process in either the interactive mode or batch mode. In the interactive
mode, a whole process flow can be simulated by entering commands line-by-line as standard
input. To start Sentaurus Process in the interactive mode, enter the following on the command
line:
> sprocess
Sentaurus Process displays version and host information, followed by the Sentaurus Process
command prompt. You now can enter Sentaurus Process commands at the prompt:
sprocess>
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Using a Command File
This is a flexible way of working with Sentaurus Process to test individual process steps or
short sequences, but it is inconvenient for long process flows. It is more useful to compile the
command sequence in a command file, which can be run in batch mode or inside Sentaurus
Workbench.
To run Sentaurus Process in batch mode, load a command file when starting Sentaurus Process,
for example:
> sprocess input.cmd
Starting Different Versions of Sentaurus Process
You can select a specific release and version number of Sentaurus Process using the -rel and
-ver options:
> sprocess -rel -ver
For example:
> sprocess -rel H-2013.03
The command:
> sprocess -rel H-2013.03 -ver 1.2 nmos_fps.cmd
starts the simulation of nmos_fps.cmd using the 1.2 version of Release H-2013.03 as long as
this version is installed.
Using a Command File
As an alternative to entering Sentaurus Process commands line-by-line, the required sequence
of commands can be saved to a command file, which can be written entirely by users or
generated using Ligament. To save time and reduce syntax errors, you can copy and edit
examples of command files in this user guide or use Ligament to create a template.
If a command file has been prepared, run Sentaurus Process by typing the command:
sprocess
Alternatively, you can automatically start Sentaurus Process through the Scheduler in
Sentaurus Workbench. By convention, the command file name has the extension .cmd. (This is
the convention adopted in Sentaurus Workbench.)
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Example: 1D Simulation
The command file is checked for correct syntax and then the commands are executed in
sequence until the simulation is stopped by the command exit or the end of the file is reached.
Since Sentaurus Process is written as an extension of the tool command language (Tcl), all Tcl
commands and functionalities (such as loops, control structures, creating and evaluating
variables) are available in the command files. This results in some limitations in syntax control
if the command file contains complicated Tcl commands. Syntax-checking can be switched off
with the command-line option -n, for example:
sprocess -n inputfile
Sentaurus Process ignores character strings starting with # (although Sentaurus Workbench
interprets # as a special character for conditional statements). Therefore, this special character
can be used to insert comments in the simulation command file.
A file with the extension .log is created automatically whenever Sentaurus Process is run from
a command line, that is, outside the Sentaurus Workbench environment. This file contains the
run-time output, which is generated by Sentaurus Process and is sent to standard output. When
Sentaurus Process is run by using a command file _fps.cmd, the output
file is named _fps.log.
When Sentaurus Process is run in Sentaurus Workbench, no log file is created. Instead, the file
_fps.out is generated as a copy of the standard output. For a complete
list of all commands, see Appendix A on page 877.
Example: 1D Simulation
Many widely used process and control commands are introduced in the context of a nominal
0.18 µm n-channel MOSFET process flow. The MOSFET structure is simulated in 1D and
2D, and the processing of the isolation is excluded.
In this section, a simple 1D process simulation is performed.
Defining Initial 1D Grid
The initial 1D grid is defined with the line command:
line
line
line
line
line
line
4
x
x
x
x
x
x
location=0.0 spacing= 1 tag=SiTop
location= 10 spacing= 2
location= 50 spacing= 10
location=300 spacing= 20
location=0.5 spacing= 50
location=2.0 spacing=0.2 tag=SiBottom
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Example: 1D Simulation
The first argument of the line specifies the direction of the grid. For 1D, this is always x.
The grid spacing is defined by pairs of the location and spacing keywords. The keyword
spacing defines the spacing between two grid lines at the specified location. Sentaurus
Process expands or compresses the grid spacing linearly in between two locations defined in
the line command.
NOTE
Units in Sentaurus Process can be specified explicitly by giving the units
in angle brackets. For most cases, the default unit of length is
micrometer. Therefore, the statements location=2.0 and
location=2.0 are equivalent. In this section, units are given
explicitly.
You can label a line with the tag keyword for later use in the region command.
Defining Initial Simulation Domain
The initial simulation domain is defined with the region command:
region Silicon xlo=SiTop xhi=SiBottom
The keyword Silicon specifies the material of the region. The keywords xlo and xhi take
tags as arguments, which are defined in the line command.
NOTE
For 2D and 3D, the additional keywords ylo, yhi, zlo, and zhi are
used to define rectangular or cuboidal regions. In general, the initial
simulation domain can consist of several regions.
Initializing the Simulation
The simulation is initialized with the init command:
init concentration=1.0e15 field=Boron
Here, the initial boron concentration in the silicon wafer (as defined in the previous region
15
–3
command) is set to 10 cm .
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Example: 1D Simulation
Choosing Process Models and Parameters
The set of physical models and parameters to be used is declared with the
AdvancedCalibration command:
AdvancedCalibration I-2013.12
This command loads the Advanced Calibration set of models and parameters. This is
recommended for accurate process simulation of all silicon and germanium technologies. For
more information about the Advanced Calibration models and parameters, refer to the
Advanced Calibration for Process Simulation User Guide.
Setting Up a Meshing Strategy
The initial grid is valid until the first command that changes the geometry, such as oxidation,
deposition, and etching. For these steps, a remeshing strategy must be defined.
The Sentaurus Mesh meshing engine tries to preserve the initial mesh as much as possible and
only modifies the mesh in the new layers and in the vicinity of the new interfaces.
To define a remeshing strategy, use:
pdbSet Grid SnMesh min.normal.size 0.003
pdbSet Grid SnMesh normal.growth.ratio.2d 1.4
;# this is for 1D and 2D
where:
■
■
■
■
The command pdbSet is used to set the parameter value in parameter database (PDB).
The parameter min.normal.size determines the grid spacing of the first layer starting
from the interface in micrometers.
The parameter normal.growth.ratio.2d determines how fast the grid spacing can
increase from one layer to another. This parameter is unitless.
The semicolon hash mark (; #) indicates the end of the command line and starts the inline
comments.
Growing Screening Oxide
The 1D process simulation is started by thermally growing a thin layer of sacrificial screening
oxide:
gas_flow name=O2_1_N2_1 pressure=1 flowO2=1.2 flowN2=1.0
diffuse temperature=900 time=40 gas_flow=O2_1_N2_1
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Example: 1D Simulation
The gas_flow statement is used to specify the gas mixture. The name keyword defines a
gas_flow record for later use in a diffuse command. The pressure of the ambient gas is set
to 1 atm, and the flows of oxygen and nitrogen are set to 1.2 l/minute and 1.0 l/minute,
respectively.
NOTE
Other gas flow parameters, such as ambient gases and partial pressures,
can be defined as well (see gas_flow on page 935 for details).
The thermal oxidation step is started with the diffuse command. Here, the wafer is exposed
to the oxidizing gases, defined in the gas_flow statement, for 20 minutes at an ambient
temperature of 900°C .
NOTE
More options, such as temperature ramps and numeric parameters, are
available (see Oxidation on page 615 for details).
Sentaurus Process prints information about the progress of the oxidation step:
Anneal step:
Time=40min, Ramp rate=0C/s, Temperature=900.0C
Temperature > minT. Diffusion: On
Reaction: On
Assembly: Serial
SProcess parallel assembly thread count = 1
Reaction :
0s
to
0.0001s
step
:
0.0001s
temp: 900.0C
SProcess Pardiso thread count = 1
Mechanics:
0s
to
0.0001s
step
:
0.0001s
temp: 900.0C
--- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- -Initializing:
--- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- -Initialization is done.
--- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- --- -Diffusion:
0s
to
0.0001s
step (d):
0.0001s
temp: 900.0C
Reaction :
0.0001s
to 0.0001712s
step
: 7.125e-05s
temp: 900.0C
Mechanics:
0.0001s
to 0.0001712s
step
: 7.125e-05s
temp: 900.0C
Diffusion:
0.0001s
to 0.0001712s
step (d): 7.125e-05s
temp: 900.0C
Reaction : 0.0001712s
to 0.0002387s
step
: 6.741e-05s
temp: 900.0C
Mechanics: 0.0001712s
to 0.0002387s
step
: 6.741e-05s
temp: 900.0C
Diffusion: 0.0001712s
to 0.0002387s
step (d): 6.741e-05s
temp: 900.0C
...
Reaction :
37.29min to
40min step
:
2.714min temp: 900.0C
Mechanics:
37.29min to
40min step
:
2.714min temp: 900.0C
Diffusion:
37.29min to
40min step (d):
2.714min temp: 900.0C
Elapsed time for diffuse 41.34s
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1: Getting Started
Example: 1D Simulation
Measuring Oxide Thickness
To measure the thickness of the thermally grown oxide, use:
select z=1
layers
The select command chooses a quantity for postprocessing. Selecting 1 is a way to obtain
the material thicknesses.
The layers command prints a list of regions with their respective top and bottom coordinates.
This command also gives the integral over the selected quantity in each region. Having selected
1, the integral equals the thickness (in units of cm):
{
{
{
Top
-6.178796082035e-03
3.676329713272e-03
Bottom
3.676329713272e-03
2.000000000000e+00
Integral
Material }
9.855125795306e-07 Oxide }
1.996323670287e-04 Silicon }
Here, 3.67 nm of silicon was consumed in the thermal oxidation process, and the final oxide
thickness is 9.85 nm.
NOTE
Internally, Sentaurus Process uses centimeters (cm) as the unit for
length.
Selecting boron, the output of layers command would look like:
{
{
{
Top
-6.178796082035e-03
3.676329713272e-03
Bottom
3.676329713272e-03
2.000000000000e+00
Integral
Material }
3.012697967871e+09 Oxide }
1.969873116640e+11 Silicon }
The integral boron concentration in the silicon layer is:
11
1.97 ×10 cm
–2
15
–3
–4
–7
= 1 ×10 cm ( 2 ×10 cm – 3.67 ×10 cm )
(1)
which is consistent with the specified wafer doping.
Depositing Screening Oxide
A faster alternative to the simulation of the oxide growth is to deposit an oxide layer and to
simulate afterwards a thermal cycle to account for the thermal budget during the oxidation.
This is an efficient way to emulate the creation of the screen oxide if oxidation-enhanced
diffusion (OED) and the silicon consumption during the oxidation are not important.
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Example: 1D Simulation
To deposit a 10 nm layer of screening oxide and perform a thermal cycle in an inert
environment, use:
deposit Oxide type=isotropic thickness=10.0
diffuse temperature=900 time=40
The diffuse command assumes an inert environment if no gas flow is specified.
When you want to omit the oxide growth but OED is not negligible, specification of a reacting
ambient together with the following flag:
pdbSetBoolean Grid Reaction.Modify.Mesh 0
switches on OED without applying velocities to the mesh nodes. This is often used in three
dimensions.
Tcl Control Statements
Tcl constructs can be freely used in the command file of Sentaurus Process. (For an
introduction to Tcl, refer to the Tool Command Language module in the TCAD Sentaurus
Tutorial.)
The following code segment simulates oxidation or performs a deposition depending on the
value of the Tcl variable SCREEN:
set SCREEN Grow
if { $SCREEN == "Grow" } {
#--- Growing screening oxide ----------------------------------------gas_flow name=O2_1_N2_1 pressure=1 flowO2=1.2 flowN2=1.0
diffuse temperature=900 time=40 gas_flow=O2_1_N2_1
} else {
#--- Depositing screening oxide -------------------------------------deposit Oxide type=isotropic thickness=10.0
diffuse temperature=900 time=40
}
Implantation
To implant arsenic with an energy of 50 keV, a dose of 10
a wafer rotation 0° , use:
14
cm
–2
, an implant tilt of 7° , and
implant Arsenic energy=50 dose=1e14 tilt=7 \
rotation=0
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Example: 1D Simulation
where “\” immediately followed by a new line (without any space in between) is used to
continue a command line. Sentaurus Process reports:
Species
=
Dataset
=
Energy
=
Dose (WaferDose) =
BeamDose
=
Tilt
=
Rotation
=
Temperature
=
Total implant time:
- - - - - - - - - Dose in:
Boron
Arsenic
Int
Vac
ICluster
O2
B4
- - - - -
Arsenic
Arsenic
30keV
1e+14/cm2
1.0075e+14/cm2
7deg
0deg
300.00K
0.61sec
- - - - - - - - - - - - - - - - - - - - - - - - - - - -
Silicon_1
Oxide_1
Total
Silicon
Oxide
1.9699e+11 3.0127e+09 2.0000e+11
9.9703e+13 2.7722e+12 1.0247e+14
9.4629e+07 7.8031e+02 1.1463e+08
8.9179e+09 1.3391e+06 8.9393e+09
2.2353e+07 9.8551e+00 4.2353e+07
1.9963e-04 2.6215e+10 3.6215e+10
3.0629e-10 0.0000e+00 3.0629e-10
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
The report shows that due to the nonzero tilt angle, Sentaurus Process adapted the beam dose
so that the total dose deposited on the wafer is as specified. The slice angle denotes the angle
between the simulation plane and the normal to the wafer flat. By default, the simulation
domain is parallel to the wafer flat.
The report shows the integrated doping concentrations for each species and region.
Saving the As-Implanted Profile
To save the as-implanted profile, use:
SetPlxList { BTotal Arsenic_Implant }
WritePlx 1DasImpl.plx
The SetPlxList command defines which solution variables are to be saved in the .plx file.
Here, only the total (chemical) boron and the as-implanted arsenic concentrations are saved. If
the SetPlxList command is omitted, all available solutions are saved in the .plx file by
default.
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Example: 1D Simulation
Besides the file name, here 1DasImpl.plx, the WritePlx command also accepts a material
specifier, which restricts the plot to the given material. For 2D and 3D structures, the x-, y-, or
z-coordinates of the 1D cutline must be given.
Figure 1
As-implanted arsenic profiles and background boron concentration
Figure 1 shows the as-implanted arsenic profiles and the background boron concentration. The
black vertical line marks the oxide–silicon interface. Note the boron depletion at the interface,
which is caused by boron segregation during the oxide growth.
Figure 1 is generated by loading the .plx file into Inspect with:
> inspect 1DasImpl.plx
Thermal Annealing, Drive-in, Activation, and Screening
Oxide Strip
To anneal the damage during implantation, or to drive the dopants deeper into the substrate, or
to activate the implanted dopants in an inert environment, use:
diffuse temperature=1000 time=30
strip Oxide
SetPlxList { BTotal BActive AsTotal AsActive }
WritePlx 1Danneal.plx
Here, the structure is annealed at a constant temperature of 1000°C for 30 minutes. The
annealing is performed in an inert gas because no particular environment is specified.
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Example: 2D Simulation
The annealed profiles are written to the file 1Danneal.plx. The total (chemical)
concentration of boron and arsenic, as well as the respective electrically active (substitutional)
concentrations are saved.
Figure 2
Comparison of as-implanted and annealed arsenic profiles
Figure 2 compares the as-implanted and the annealed arsenic profiles. It is generated by
loading both .plx files into Inspect with:
> inspect 1DasImpl.plx 1Danneal.plx
Example: 2D Simulation
Many widely used process and control commands are introduced in the context of a nominal
0.18 µm n-channel MOSFET process flow. The MOSFET structure is simulated in 2D, and
the processing of the isolation is excluded. A simplified treatment is presented using only
default parameters and models.
Defining Initial Structure and Mesh Refinement
The command math coord.ucs is used to switch on the unified coordinate system (UCS).
Using the UCS is recommended because the default behavior is to rotate the structure when
saving and loading to the DF–ISE coordinate system. With the UCS, the structure is not
rotated. Therefore, the axes in Tecplot SV match the axes in the Sentaurus Process command
file. It is recommended to insert this as the first command in the command file.
The line command is used to:
■
12
Define the initial size of the structure.
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Example: 2D Simulation
■
Subdivide the structure.
Mesh refinement starts from the user-defined subdivisions; therefore, the specification of lines
helps to compartmentalize mesh refinement. In turn, compartmentalization of the mesh
prevents moving boundaries, and therefore, moving mesh refinement from affecting
geometrically static areas. Whenever mesh lines move, interpolation must be used to obtain
new field values, such as dopant concentrations, and this introduces errors in the simulation.
During the polysilicon reoxidation step, the oxide–silicon and oxide–polysilicon boundaries
move, and this interface movement may cause mesh lines to move. This could be prevented by
inserting lines as follows:
line
line
line
line
line
line
x
x
x
y
y
y
location=
location=
location=
location=
location=
location=
0.0
3.0
10.0
0.0
85.0
0.4
;# just deeper than reox in silicon
;# just deeper than reox in poly
To minimize this effect, the silicon and polysilicon regions are isolated from the moving
interfaces by introducing lines immediately inside the final oxide depth in both regions as
shown in Figure 3.
User-defined mesh lines
X
-0.1
0
0.1
0
0.1
0.2
0.3
Y
Figure 3
Final structure showing placement of user-defined lines: these lines are used to
isolate silicon and polysilicon regions from boundary movement at the oxide
interfaces
Sentaurus Process uses coordinate systems such that 1D, 2D, and 3D simulations are
consistent. Independent of the current simulation dimension, the positive x is into the wafer; y
is positive to the right, and z is positive out of the page.
NOTE
By default, the simulation dimension is promoted only when necessary.
Therefore, until a mask is introduced, the simulation remains in 1D.
Similarly, when going from 2D to 3D, until a 3D mask is introduced
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Example: 2D Simulation
(one that varies in the z-direction in the defined simulation domain), the
simulation remains in 2D.
The initial simulation domain is defined with the region command. Many, if not most,
simulations start with a block of silicon. The shorthand for this situation is to define a region
of silicon that spans all defined lines:
region Silicon
The region command also can be used to define a new region between specified lines. To limit
the size of the region to be less than all defined lines, the lines must be given a tag with the tag
parameter. These tags are used in the region command with the xlo, xhi, ylo, yhi, zlo,
and zhi parameters.
Finally, the initial mesh and background doping is specified using the init command as
follows:
init concentration=1.0e+15 field=Phosphorus wafer.orient=100
Here, an n-doped substrate with a phosphorus concentration of 10
orientation is set to 100, which is the default.
15
cm
–3
is used. The wafer
The Advanced Calibration set of physical models and parameters is loaded (this is the
recommended choice for accurate process simulation):
AdvancedCalibration I-2013.12
Usually, localized refinement is defined by introducing refinement boxes. This strategy
prevents excessive mesh that can result if mesh refinement is based solely on the line
command (with the spacing parameter). Lines specified with the line command run the
entire length (or breadth or depth) of the structure.
The refinement boxes can be inserted at any time during the simulation. The simplest form of
the refinement box, used in this example, consists of minimum and maximum coordinates
where the refinement box is valid and local maximum mesh spacing in the x-, y- and
z-directions. A refinement box specified for a 2D simulation will be applied to 1D if it is valid
for y = 0.0. Similarly a 3D refinement box will be applied if it covers z = 0.0.
The following refinement boxes specify refinement only in the x-direction for the 1D part of
the simulation:
#--- Refinement
refinebox clear
refinebox min =
refinebox min =
refinebox min =
14
in vertical direction --------------------------------;# remove all default refinement
0
max = 50.0 xrefine = {2.0 10.0}
50.0 max = 2.0 xrefine = {10.0 0.1 0.2}
2.0 max = 10.0 xrefine = {0.2 2.0}
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Example: 2D Simulation
The other type of refinement box used in this example is the interface refinement type. Interface
refinement is a graded refinement that is refined near an interface in the perpendicular direction
and relaxed away from the interface. Using the refinebox command, you can specify
interface refinement using the interface.materials or interface.mat.pairs
parameter:
■
■
Use interface.materials to indicate refinement will occur at all interfaces to the
specified materials.
Use interface.mat.pairs to choose interface refinement only at specific material
interfaces.
#--- Interface refinement --------------------------------------------refinebox interface.materials = { PolySilicon Silicon }
For more details on mesh refinement, see Mesh Refinement on page 694.
Implanting Boron
First, three sets of boron implants are performed:
implant Boron dose=2.0e13 energy=200 tilt=0 rotation=0
implant Boron dose=1.0e13 energy= 80 tilt=0 rotation=0
implant Boron dose=2.0e12 energy= 25 tilt=0 rotation=0
The first high-energy implant creates the p-well, the second medium-energy implant defines a
retrograde boron profile to prevent punch-through, and the third low-energy implant is for a Vt
adjustment.
Growing Gate Oxide
The gate oxide is grown at a temperature of 850°C for 10 minutes in pure oxygen using:
diffuse temperature=850 time=10.0 O2
select z=Boron
layers
The layers command shows that the thickness of the grown oxide is 3.2 nm:
{
{
{
Top
-2.500551327519e-03
7.862861879285e-04
Bottom
7.862861879285e-04
1.000000000000e+01
Integral
Material }
1.247399405710e+10 Oxide }
3.197435354292e+13 Silicon }
For details, see Measuring Oxide Thickness on page 8.
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Example: 2D Simulation
Defining Polysilicon Gate
The polysilicon gate is created using:
deposit PolySilicon type=isotropic thickness=0.18
mask name=gate_mask left=-1 right=90
etch PolySilicon type=anisotropic thickness=0.2 mask=gate_mask
etch Oxide type=anisotropic thickness=0.1
First, 0.18 µm of polysilicon is deposited over the entire structure. The keyword
type=isotropic means that the layer is grown equally in all directions, but since the
simulation is in 1D, it would be the same as type=anisotropic.
A mask is defined to protect the gate area with the mask command. In this project, only half of
the transistor is simulated. Therefore, the left edge of the gate mask is unimportant. In general,
you should run the mask over the sides of the simulation to prevent round-off errors that could
prevent complete mask coverage. The name gate_mask is associated with this mask for later
reference.
The first etch command refers to the previously defined mask and, therefore, only the exposed
part of the polysilicon is etched. The requested etching depth ( 0.2 µm ) is larger than the
deposited layer. This overetching ensures that no residual islands remain. The etching is
specified to be anisotropic, that is, the applied mask is transferred straight down, without any
undercut.
The second etch statement does not refer to any masks. However, the polysilicon naturally
acts as a mask for this selective etching process. Again, a considerable overetching is specified.
Working with Masks
Masks must be defined before they are used. For example, ex_mask blocks processing from
–1 to 2 µm and from 4 to 20 µm :
mask clear
mask name=ex_mask segments = { -1.0 2.0 4.0 20.0 }
segments specifies a list of coordinates of mask segments. Several mask segments can be
specified at the same time. The first coordinate defines the beginning of a segment; the second
defines the end of the segment; the third defines the beginning of the segment; and so forth. In
3D simulations, mask segments are extended across the entire structure in the z-direction.
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Example: 2D Simulation
Masks can be inverted using the negative option. For example, etch_mask prevents
processing from 2 to 4 µm :
mask clear
mask name=etch_mask segments = { -1.0 2.0 4.0 20.0 } negative
Commands that use masking include etch, photo, and deposit.
Polysilicon Reoxidation
To release stresses, a thin oxide layer is grown on the polysilicon before the spacer formation:
diffuse temperature=900 time=10.0 O2
In all diffusion steps, Sentaurus Process automatically deposits a thin native oxide layer before
starting oxidation. This layer is always present on silicon exposed to air and quickly forms on
newly created interfaces.
-0.15
-0.1
-0.05
0
0
Figure 4
0.05
0.1
0.15
Polysilicon reoxidation
During oxidation, mesh movement is controlled by the TSUPREM-4 mesh library in 2D. In 1D
and 3D, it is controlled by an internal moving-boundary mesh algorithm. Both of these movingboundary algorithms perform local atomic mesh operations (element removal, edge splitting,
edge flipping, and so on) which leave the rest of the mesh untouched. Mesh points are moved
with the material to maintain dopant dose conservation and the dopant segregation condition at
oxide–silicon and oxide–polysilicon interfaces. Figure 5 shows a close-up of the mesh after the
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Example: 2D Simulation
polysilicon reoxidation step has been performed. Note that the mesh in the brown oxide layer
follows the growth contours.
-0.01
-0.005
0
0.005
0.08
Figure 5
0.085
0.09
0.095
Mesh in thin oxide layer and in adjacent polysilicon and silicon
Saving Snapshots
To save a snapshot of the current structure, the struct command is used. For example:
struct tdr= NMOS4
The keyword tdr specifies that the snapshot is saved in the TDR file format. The argument
specifies the stem used for the file name. Here, the file NMOS4_fps.tdr is created. The figures
in this section were generated from such snapshots.
For more information about the TDR format, refer to the Sentaurus™ Data Explorer User
Guide.
Remeshing for LDD and Halo Implants
Next, the LDD and halo implants are performed. Before that, however, the mesh must be
refined to properly capture the implant. The previously defined refinement boxes specified
vertical refinement with the xrefine parameter.
Now, lateral refinement is required to resolve the source and drain extensions (also known as
low-doped drain (LDD)) as well as the halo implants. This is accomplished by introducing a
new refinebox command that specifies:
18
■
Lateral refinement using the yrefine parameter.
■
Additional vertical refinement using the xrefine parameter.
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Example: 2D Simulation
NOTE
When specifying multiple overlapping refinement, the most refined
specification (smallest edge length) wins.
refinebox silicon min= {0.0 0.045} max= {0.1 0.125} \
xrefine= 0.01 yrefine= 0.01
grid remesh
The min and max keywords take x-, y-, and z-coordinates. Not all coordinates must be
specified. For example, if only one number is given for minimum, it means that refinement
applies to all y- and z-coordinates less than the max coordinate.
NOTE
The refinebox command only specifies a refinement criterion, but the
mesh is not changed. The grid remesh command forces a remesh.
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.05
Figure 6
0.1
0.15
A combination of overlapping refinement boxes is used to define a finer mesh for
LDD and halo; if multiple criteria overlap, the finest mesh specification wins
Implanting LDD and Halo
The LDD and halo implants are performed using:
#--- LDD implantation ------------------------------------------------implant Arsenic dose=4e14 energy=10 tilt=0 rotation=0
#--- Halo implantation: Quad HALO implants ---------------------------implant Boron dose=1.0e13 energy=20 tilt=30 \
rotation=0 mult.rot=4
diffuse temperature=1050 time=5.0
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Example: 2D Simulation
14
–2
The LDD implant uses a high dose of 4 × 10 cm and a relatively low energy of 10 keV.
The halo is created by a quad implant using the mult.rot parameter, that is, the implant is
performed in four steps. Each step is separated in rotation by 360/4 = 90° starting with the
specified rotation of 0. This is performed to ensure that the boron penetrates well into the
channel at the tips of the source–drain extensions. Again, a relatively high total dose of
14
–2
1 × 10 cm is used.
The implants are activated with a short thermal cycle or rapid thermal anneal (RTA).
Forming Nitride Spacers
The nitride spacers are formed using:
#--- Nitride spacer --------------------------------------------------deposit Nitride type=isotropic
thickness=60
etch
Nitride type=anisotropic thickness=84 isotropic.overetch=0.01
etch
Oxide
type=anisotropic thickness=10
First, a uniform, 60-nm thick layer of nitride is deposited over the entire structure. The keyword
type=isotropic ensures that the growth rate of the layer is the same in all directions. Then,
the nitride is etched again; however, now an anisotropic etching is used. This means that the
nitride deposited on the vertical sides of the gate is not fully removed and can serve as masks
for the source/drain implants. For this step, an isotropic overetch is specified. Specifying a
fraction of the etch thickness, 0.01 implies a 1% isotropic component. This is needed because
the oxide formed during poly oxidation has a nonvertical sidewall. Without the small
isotropic.overetch, a small nitride residual would remain. Finally, the thin oxide layer
grown during the poly reoxidation step is removed.
Remeshing for Source/Drain Implants
Next the source/drain implants are performed. However, before that, the mesh is refined again.
refinebox Silicon min= {0.04 0.11} max= {0.18 0.4} \
xrefine= 0.01 yrefine= {0.02 0.05}
grid remesh
This refinement box ensures that the grid is fine enough in the vertical direction to resolve the
junction depth.
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Example: 2D Simulation
Implanting Source/Drain
The source and drain regions are created using:
implant Arsenic dose=5e15 energy=40 tilt=7 \
rotation=-90
diffuse temperature=1050 time=10.0
To ensure a low resistivity of the source and drain regions, this implant step uses a very high
15
–2
dose of 5 × 10 cm . A tilt of 7° is used to reduce channeling and a rotation of – 90 °
ensures that the plane of incident is parallel to the gate stack, such that the 7° tilt angle does
not lead to asymmetry between the source and drain.
Transferring to Device Simulation
To transfer from process simulation to device simulation, the normal steps are:
■
The structure bottom is cropped.
■
The full transistor is created by reflecting about the symmetry plane.
■
A new mesh strategy is specified appropriate for device simulation.
■
Contacts are specified.
■
The struct command is called which remeshes and saves the structure.
Remeshing for Device Simulation
The following example shows the standard technique used to produce a structure and mesh
appropriate for device simulation. First, the structure bottom is truncated; then a new mesh
strategy is introduced:
#--Remove bottom of structure-----------------------------------------transform cut location= 1.00 down
#--Change refinement strategy and remesh------------------------------refinebox clear
line clear
pdbSet
pdbSet
pdbSet
pdbSet
pdbSet
Grid
Grid
Grid
Grid
Grid
Adaptive 1
AdaptiveField Refine.Abs.Error 1e37
AdaptiveField Refine.Rel.Error 1e10
AdaptiveField Refine.Target.Length 100.0
SnMesh DelaunayType boxmethod
refinebox name= Global refine.min.edge= {0.01 0.01} \
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Example: 2D Simulation
refine.max.edge= {0.1 0.1} refine.fields= { NetActive } \
def.max.asinhdiff= 0.5 adaptive
refinebox name= SiGOX min.normal.size= 0.2 normal.growth.ratio= 1.4 \
max.lateral.size= 5.0 min= {-0.01 -0.1} max= {0.01 0.1} \
interface.materials= {Silicon}
refinebox name= GDpn1 min= {0.0 0.04} max= {0.06 0.1} xrefine= 0.005 \
yrefine= 0.005 silicon
refinebox name= TopActive min= {0.0 0.0} max= {0.3 0.4} \
refine.min.edge= {0.02 0.02} refine.max.edge= {0.05 0.05} \
refine.fields= { NetActive } def.max.asinhdiff= 0.5 \
adaptive silicon
grid remesh
#--Reflect --------------------------------------------------------transform reflect left
The new mesh strategy uses a combination of interface refinement, fixed boxwise refinement,
and adaptive refinement on dopants.
Contacts
Next, contacts are added to the structure using the contact command. These contacts are
added to structure files upon writing. They are not present in the internal Sentaurus Process
structure, but are added only as required when writing the structure. There are two types of
contact specification:
■
■
Box: For these contacts, you specify a box and a material, and all interfaces of that material
that are inside the box become the contact.
Point: For this contact, you specify a point inside a chosen region. The chosen region is
removed, and all interfaces between the chosen region and bulk materials become part of
the contact.
In the following example, only box-type contacts are used:
#--- Contacts --------------------------------------------------------contact name= "substrate" bottom Silicon
contact name= "source" box Silicon adjacent.material= Gas \
xlo= 0.0 xhi= 0.005 ylo= -0.4 yhi= -0.2
contact name= "drain" box Silicon adjacent.material= Gas \
xlo= 0.0 xhi= 0.005 ylo= 0.2 yhi= 0.4
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Example: 2D Simulation
contact name= "gate" box PolySilicon xlo= -0.181 xhi= -0.05 \
ylo= -0.088 yhi= 0.088
Saving the Structure
To save the structure, use:
struct tdr=NMOS !Gas
The file NMOS_fps.tdr is created with contacts and can be loaded into Sentaurus Device to
obtain device electrical characteristics.
-0.2
-0.1
0
0.1
0.2
-0.4
Figure 7
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
Final structure showing contacts and refinement appropriate for device simulation
Extracting 1D Profiles
You can save 1D profiles at any point in the process flow using:
SetPlxList {BTotal NetActive}
WritePlx NMOS_channel.plx y=0.0 silicon
as well as:
struct tdr=NMOS_channel.tdr y=0.0
For details, see Saving the As-Implanted Profile on page 10.
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Adaptive Meshing: 2D npn Vertical BJT
Adaptive Meshing: 2D npn Vertical BJT
A simple 2D npn vertical bipolar transistor example is introduced to show how the adaptivemeshing capabilities in Sentaurus Process can be used to ease mesh setup and allow for mesh
evolution during dopant diffusion. For examples, see 2D npn Vertical Bipolar on page 38.
For all the applications involving long thermal diffusion steps or simulations of relatively large
structures (in which doping profiles may evolve greatly), using static mesh criteria is
impracticable because it requires using a fine mesh in many parts of the simulation domain.
Moreover, the placement of the refinement boxes is not straightforward because often the
location of gradients and junctions at the end of the thermal steps is not precisely known. For
such purposes, adaptive meshing could be used. Using this feature, you only have to define
some refinement criteria, more or less stringent depending on the level of accuracy required.
The meshing engine checks the mesh and decides automatically where, when, and if the mesh
needs to be refined.
Overview
Adaptive meshing can be switched on globally with:
pdbSet Grid Adaptive 1
which creates a default adaptive box covering the entire structure.
Adaptive refinement parameters can be set in the following ways:
■
Fieldwise in the PDB with the pdbSet command
■
Boxwise as parameters of the refinebox command
■
Materialwise, specifying a material in a box definition
■
Regionwise, specifying a region in a box definition
To prevent the number of mesh points from growing too large, switch off the keep.lines
option (which is switched on by default in silicon) when using adaptive meshing:
refinebox !keep.lines
Many different refinement criteria have been implemented in Sentaurus Process for flexibility
in handling different types of field and structure. For a complete list and detailed descriptions
of the refinement criteria, see Adaptive Refinement Criteria on page 700.
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Adaptive Meshing: 2D npn Vertical BJT
The criteria in the following example are the most commonly used and are referred to as
relative difference and local dose error. Each computes the so-called desired edge length
(DEL), which is defined formally as:
DEL = min (l12 * MaxError/Error)
where l12 is the length of the edge between two mesh points 1 and 2. Error (computed
internally) is the error between points 1 and 2, and MaxError (set by users) is the maximum
allowable error. The right-hand side of the expression is computed over all the fields that can
be refined (by default, all the solution variables): the minimum value is the DEL for the
corresponding criterion. The expression for Error and the name and the meaning of
MaxError vary from criterion to criterion. For the relative difference criterion, these quantities
have the form:
Error = 2*|C1 - C2|/(C1 + C2 + alpha)
MaxError = Rf
where C 1 and C 2 are the concentration of the field in points 1 and 2, respectively, R f is the
relative error that sets the maximum-allowed change of the field across an edge, and alpha is
the absolute error, a type of cutoff threshold below which refinement is smoothed out. They can
be set in the PDB as follows:
pdbSet Grid Boron Refine.Abs.Error 1e15
pdbSet Grid Boron Refine.Rel.Error 0.5
or in the refinebox commands as:
refinebox name=Active refine.fields= {Boron Arsenic} \
rel.error= {Boron=0.5 Arsenic=0.5} abs.error= {Boron=2e15 Arsenic=1e16} \
Adaptive min= {-1.0 -0.1} max= {2.0 16.0}
For the definition of Error and MaxError for the local dose error criterion, see Local Dose
Error Criteria on page 703.
All the edges are compared to DEL to check the percentage of long edges by using the
following additional parameter:
pdbSetDoubleArray Grid Refine.Factor {X 2.0 Y 2.0}
These coefficients can be set directionwise and act in the following way: An edge is defined as
long when it is larger than Refine.Factor*DEL for at least one of the selected refinement
criteria. When the percentage of long edges is larger than certain values, adaptive refinement
is actually triggered. This value can be set as:
pdbSet Grid Refine.Percent 0.01
When adaptive meshing is switched on, it automatically affects refinement whenever a mesh is
generated (such as after geometry-changing operations). During the diffuse command, the
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Adaptive Meshing: 2D npn Vertical BJT
mesh is checked after a certain number of steps that can be separately set depending on the
nature of the diffusion step:
pdbSet Diffuse Compute.Regrid.Steps 10 ;# during inert annealings
pdbSet Diffuse Growth.Regrid.Steps -1 ;# during oxidation and silicidation
pdbSet Diffuse Epi.Regrid.Steps -1
;# during epitaxy
When the number of long edges is larger than Refine.Percent, remeshing is performed. The
mesh quality check can be omitted by setting:
pdbSet Grid Refinement.Check 0
which can save some CPU time when performing simulations on large meshes, where the mesh
checking is time consuming.
NOTE
Formally, the adaptive-meshing feature consists of field-based and
implant-based adaptation. There is a small difference in the way
refinement criteria are applied. For details, see Adaptive Meshing
during Implantation on page 708 and Interval Refinement on page 704.
However, as the two modules use the same parameters, you do not need
to define them twice.
NOTE
Adaptive-meshing syntax to set up parameters is the same in any
dimension.
The relative error criterion is effective in refining doping profiles in steep gradient regions. In
the vicinity of maxima and minima, the profiles are almost flat and some loss of accuracy may
occur there. Further reduction of Rel.Error would increase significantly the number of
points in the steep slope with negligible improvements at the peaks. In that case, the max dose
loss criterion can be used more effectively. This explains why the combination of these two
criteria provides an optimum adaptive-remeshing strategy.
Defining Initial Structure
The command math coord.ucs is used to switch on the unified coordinate system (UCS).
Using the UCS is recommended because the default behavior is to rotate the structure when
saving and loading to the DF–ISE coordinate system. With the UCS, the structure is not
rotated. Therefore, the axes in Tecplot SV match the axes in the Sentaurus Process command
file. It is recommended to insert this as the first command in the command file.
The line commands are used to compartmentalize the structure according to the meshing
strategy described in the previous example:
line x loc= 2.0
line x loc= 4.0
26
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Adaptive Meshing: 2D npn Vertical BJT
line
line
line
line
line
line
line
line
line
line
x
x
y
y
y
y
y
y
y
y
loc= 6.0
loc= 10.0
loc= 0.0
loc=1.5
loc=2.5
loc=8
loc=13
loc=22
loc=24
loc=30.0
tag=SubBottom
tag=SubLeft
tag=SubRight
Along the x-axis, few lines are specified: the two tagged ones are needed to define the initial
silicon substrate. The other two lines are defined to have uniform spacing within the box
defined to refine the buried layer. Along the y-axis, more lines are defined because a coarse
initial mesh would degrade the quality of the mesh resulting from adaptation during
implantation. These lines are set corresponding to the mask edges: This information is usually
known to users, especially if the simulation starts from a layout, and the process flow is set up
in Ligament.
Adaptive Meshing Settings
As previously mentioned, adaptive parameters can be set in different ways, which lead to
different refinement strategies:
pdbSet Grid Adaptive 1
pdbSet Grid AdaptiveField Refine.Abs.Error 1e25
pdbSet Grid AdaptiveField Refine.Rel.Error 2.0
pdbSet Grid Damage Refine.Min.Value 1e25
pdbSet Grid Damage Refine.Max.Value 1e25
pdbSet Grid Damage Refine.Target.Length 1
Here the following strategy is used:
■
■
■
The default relative difference–type refinement is switched off by setting high values for
absolute and relative errors and for the interval damage refinement.
When parameters are set for AdaptiveField, they are applied to all the existing fields
that can be refined.
Actual refinement will be then controlled in specific regions by using refineboxes.
Three refinement boxes are defined as the structure and the process flow clearly identifies three
main significant areas: buried layer, collector region, and base-emitter region:
refinebox name=BL refine.fields= {Antimony Phosphorus} \
rel.error= {Antimony=0.6 Phosphorus=0.6} \
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Adaptive Meshing: 2D npn Vertical BJT
abs.error= {Antimony=1e16 Phosphorus=1e16} Adaptive min= {2.0 -0.1} \
max= {10.1 30.1} refine.min.edge= {0.2 0.4} max.dose.error= {Antimony=1e8} \
The min and max parameters set an xy pair of coordinates to define the extent of the box. The
keyword all means that refinement must be applied to all materials. When using a material
name, refinement is applied to the specified material only.
NOTE
More than one adaptive type can be specified in the same box. In the BL
box, the relative difference and local dose loss criteria are selected by
specifying the parameters rel.error or abs.error and
max.dose.error, respectively.
refinebox name=Sinker refine.fields= {Phosphorus Arsenic} \
rel.error= {Phosphorus=0.5 Arsenic=0.5} \
abs.error= {Phosphorus=5e15 Arsenic=1e16} Adaptive min= {-1.0 16} \
max= {2.0 30.1} refine.min.edge= {0.1 0.2}
refinebox name=Active refine.fields= {Boron Arsenic} \
rel.error= {Boron=0.5 Arsenic=0.5} abs.error= {Boron=2e15 Arsenic=1e16} \
Adaptive min= {-1.0 -0.1} max= {2.0 16.0} refine.min.edge= {0.025 0.05} \
The BL box is defined to refine the buried layer: a high level of accuracy is not required here
and the values are more relaxed than in the other boxes. The refine.min.edge parameter
adds the additional directionwise constraint not to refine edges below the specified values
(units in micrometers).
The Sinker box is defined to refine the n-doped collector region, which contacts the buried
layer. More restrictive values are used in it.
The Active box is used to refine the base–emitter region. Higher accuracy is required here to
properly catch the base length, which all the main electrical parameters of the device are a
function of:
pdbSet Diffuse Compute.Regrid.Steps 10
pdbSet Grid Refine.Percent 0.01
According to these last two commands, the mesh is checked every 10 diffusion steps in inert
annealings, and remeshing is performed if there are more than 0.01% of long edges.
Buried Layer
The buried layer is obtained with high-energy and high-dose antimony implantation:
deposit material= {Oxide} type=isotropic time=1 rate= {0.025}
implant Antimony dose=1.5e15 energy=100
etch material= {Oxide} type=anisotropic time=1 rate= {0.03}
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Adaptive Meshing: 2D npn Vertical BJT
Before the implantation, 25 nm of a screening oxide is deposited. Here an alternate syntax is
used to specify the deposit material. The deposited oxide thickness is determined by the
product of rate and time. The implantation is performed with default angles (tilt of 7° and
rotation of 90° ). After the implantation, the oxide is etched to clean the surface and to prepare
it for the subsequent epi step.
Epi Layer
For speed and simplicity, an epitaxial regrowth step is not performed here. Instead, a simpler
–3
15
deposition of a silicon layer with 1 ×10 cm
arsenic concentration is followed by a
diffusion step:
deposit material= {Silicon} type=isotropic time=1 rate= {4.0} Arsenic \
concentration=1e15
diffuse temp=1100 time=60 maxstep=4
The maximum diffusion step is limited to 4 minutes to avoid having too much diffusion
between two subsequent adaptive remeshing steps. An alternative would be to reduce
Compute.Regrid.Steps, but this would lead to numerous remeshings at the beginning of
the annealing when the time step is small.
The following sections describe the process steps to create sinker, base, and emitter regions. At
the end of each group of steps, results are saved in TDR files.
Sinker Region
This is the beginning of the 2D simulation. A 50-nm screening oxide is deposited before the
phosphorus implantation to contact the buried layer. The Sinker mask protects the silicon area
where the base will be created. The Photo command is used to deposit the photoresist (mask
definition not shown here). The subsequent annealing is long (5 hours). For this reason, the
maximum time step is allowed to increase up to 8 minutes.
Figure 8 on page 30 shows the doping concentration distribution at this point of the simulation:
deposit material= {Oxide} type=isotropic time=1 rate= {0.05}
photo mask=Sinker thickness=1
implant Phosphorus dose=5e15 energy=200
strip Resist
diffuse temp=1100 time=5
maxstep=8
struct tdr=vert_npn2
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Adaptive Meshing: 2D npn Vertical BJT
0
5
10
0
Figure 8
5
10
15
20
25
30
Doping concentration after phosphorus implantation and diffusion to contact
antimony buried layer
Base Region
14
The p-doped base region is created with a 1 ×10
a 35-minute inert annealing:
cm
–2
dose of implanted boron followed by
photo mask=Base thickness=1
implant Boron dose=1e14 energy=50
strip Resist
diffuse temp=1100 time=35 maxstep=4
struct tdr=vert_npn3
Emitter Region
15
–2
The highly n-doped emitter region is created with a 5 ×10 cm dose of implanted arsenic
followed by a 25-minute inert annealing. Emitter mask is designed such that arsenic is
implanted also in the sinker region to increase the doping concentration at the collector contact.
In addition to a TDR file, 1D profiles are extracted. Figure 9 on page 31 shows the final doping
distribution:
photo mask=Emitter thickness=1
implant Arsenic dose=5e15 energy=55 tilt=7 rotation=0
strip Resist
diffuse temp=1100 time=25 maxstep=4
struct tdr=vert_npn4
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SetPlxList {BTotal SbTotal AsTotal PTotal}
WritePlx Final.plx y=5.0
WritePlx Sinker.plx y=23.0
0
5
10
0
5
Figure 9
10
15
20
25
30
Final doping distribution
Backend
The real backend steps are not simulated here. A sequence of masked etching and deposition
steps are used to define emitter, base, and collector contacts:
etch material= {Oxide} type=anisotropic time=1 rate= {0.055} mask=Contact
deposit material= {Aluminum} type=isotropic time=1 rate= {1.0}
etch material= {Aluminum} type=anisotropic time=1 rate= {1.1} mask=Metal
struct tdr=vert_npn5
Figure 10 shows some details of the final mesh.
-1
-2
-0.5
0
0
0.5
2
1
4
1.5
6
2
0
Figure 10
1
2
3
18
20
22
24
26
28
Details of final mesh: (left) the emitter–base region and (right) the buried layer
with collector contact
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Full-Text Versions of Examples
The relative difference criterion refines the doping profiles, not the junctions. Obviously, if the
profiles are reproduced correctly, the junctions also will be in the right place. To obtain a
junction-like refinement with the relative difference criterion, set abs.error close to the
doping level of the less-doped side of the junction. A more effective way is to select
NetDoping as the field to be refined and apply to it the inverse hyperbolic sine (asinh)
difference criterion (for details, see Inverse Hyperbolic Sine (asinh) Difference Criteria on
page 702).
Full-Text Versions of Examples
The following full-text versions of the examples allow convenient electronic copying of text
into Sentaurus Process command files.
1D NMOS
# 1D Grid definition
#------------------line
line
line
line
line
line
x
x
x
x
x
x
location=0.0
location= 10
location= 50
location=300
location=0.5
location=2.0
spacing= 1 tag=SiTop
spacing= 2
spacing= 10
spacing= 20
spacing= 50
spacing=0.2 tag=SiBottom
# Initial simulation domain
#-------------------------region Silicon xlo=SiTop xhi=SiBottom
# Initialize the simulation
#-------------------------init concentration=1.0e15 field=Boron
# Set of physical models and parameters
# ---------------------------------------------AdvancedCalibration 2013.12
# Settings for automatic meshing in newly generated layers
#--------------------------------------------------------pdbSet Grid SnMesh min.normal.size 0.003
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Full-Text Versions of Examples
pdbSet Grid SnMesh normal.growth.ratio.2d 1.4 ;# this is for 1D and 2D
set SCREEN Grow
if { $SCREEN == "Grow" } {
# Growing screening oxide
#-----------------------gas_flow name=O2_1_N2_1 pressure=1 flowO2=1.2 flowN2=1.0
diffuse temperature=900 time=40 gas_flow=O2_1_N2_1
# Measuring the oxide thickness
#-----------------------------select z=1
layers
} else {
# Depositing screening oxide
#--------------------------deposit material= {Oxide} type=isotropic time=1.0 rate= {0.01}
diffuse temperature=900 time=40
}
# Implanting Arsenic
#------------------implant Arsenic energy=30 dose=1e14 tilt=7 \
rotation=0
# Plotting out the "as implanted" profile
#---------------------------------------SetPlxList { BTotal Arsenic_Implant }
WritePlx 1DasImpl.plx
# Thermal annealing
#-----------------diffuse temperature=1000 time=30
strip Oxide
SetPlxList { BTotal BActive AsTotal AsActive }
WritePlx 1Danneal.plx
2D NMOS
#---------------------------------------------------------------------# 2D nMOSFET (0.18um technology)
#---------------------------------------------------------------------math coord.ucs
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Full-Text Versions of Examples
pdbSet Oxide Grid perp.add.dist 1e-7
#--- Specify lines for outer boundary and to separate moving boundaries
#
from the rest of the structure-----------------------------------line
line
line
line
line
line
x
x
x
y
y
y
location=
location=
location=
location=
location=
location=
0.0
3.0 ;# just deeper than reox in silicon
10.0
0.0
85.0 ;# just deeper than reox in poly
0.4
#--- Silicon substrate definition ------------------------------------region silicon
#--- Initialize the simulation ---------------------------------------init concentration=1.0e+15 field=Phosphorus
# Set of physical models and parameters
# -----------------------AdvancedCalibration 2013.12
#--- Refinement
refinebox clear
refinebox min =
refinebox min =
refinebox min =
in vertical direction --------------------------------0 max = 50.0 xrefine = {2.0 10.0}
50.0 max = 2.0 xrefine = {10.0 0.1 0.2}
2.0 max = 10.0 xrefine = {0.2 2.0}
#--- Interface refinement --------------------------------------------refinebox interface.materials = { PolySilicon Silicon }
#--- Sentaurus Mesh settings for automatic meshing in newly generated layers pdbSet Grid SnMesh min.normal.size 1.0e-3 ;# in micrometers
pdbSet Grid SnMesh normal.growth.ratio.2d 1.4 ;# used in 1D and 2D
#--- Create starting mesh from lines and refinement
grid remesh
#--- p-well, anti-punchthrough & Vt adjustment implants --------------implant Boron dose=2.0e13 energy=200 tilt=0 rotation=0
implant Boron dose=1.0e13 energy= 80 tilt=0 rotation=0
implant Boron dose=2.0e12 energy= 25 tilt=0 rotation=0
#--- p-well: RTA of channel implants ---------------------------------diffuse temperature=1050 time=10.0
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Full-Text Versions of Examples
#--- Saving structure ------------------------------------------------struct tdr=NMOS1 FullD; # p-Well
#--- Gate oxidation --------------------------------------------------diffuse temperature=850 time=10.0 O2
select z=Boron
layers
struct tdr=NMOS2 FullD; # GateOx
#--- Poly gate deposition --------------------------------------------deposit poly type=isotropic thickness=0.18
#--- Poly gate pattern/etch ------------------------------------------# MGoals settings for etch/depo
mgoals accuracy=2e-5
mask name=gate_mask segments = { -1 90 }
etch poly type=anisotropic thickness=0.2 mask=gate_mask
etch oxide type=anisotropic thickness=0.1
struct tdr=NMOS3 ; # PolyGate
#--- For graphics, first run "tecplot_sv -s:ipc" and uncomment
#
the next line before running this file
# graphics on
#--- Poly reoxidation ------------------------------------------------diffuse temperature=900 time=10.0 O2
struct tdr=NMOS4 ; # Poly Reox
#--- LDD implantation ------------------------------------------------refinebox silicon min= {0.0 0.045} max= {0.1 0.125} \
xrefine= 0.01 yrefine= 0.01
grid remesh
implant Arsenic dose=4e14 energy=10 tilt=0 rotation=0
SetPlxList { BTotal Arsenic_Implant }
WritePlx 1DasImpl.plx y= 0.25
diffuse temperature=1050 time=0.1 ; # Quick activation
struct tdr=NMOS5 ; # LDD Implant
#--- Halo implantation: Quad HALO implants ---------------------------implant Boron dose=1.0e13 energy=20 \
tilt=30 rotation=0 mult.rot=4
#--- RTA of LDD/HALO implants ----------------------------------------diffuse temperature=1050 time=5.0
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Full-Text Versions of Examples
struct tdr=NMOS6 ; # Halo RTA
#--- Nitride spacer --------------------------------------------------deposit nitride type=isotropic
thickness=60
etch
nitride type=anisotropic thickness=84 isotropic.overetch=0.01
etch
oxide
type=anisotropic thickness=10
struct tdr=NMOS7 ; # Spacer
#--- N+ implantation -------------------------------------------------refinebox silicon min= {0.04 0.11} max= {0.18 0.4} \
xrefine= 0.01 yrefine= {0.02 0.05}
grid remesh
implant Arsenic dose=5e15 energy=40 \
tilt=7 rotation=-90
SetPlxList { BTotal Arsenic_Implant }
WritePlx 1DasImpl2.plx y= 0.25
#---- N+ implantation & final RTA ------------------------------------diffuse temperature=1050 time=10.0
struct tdr=NMOS8 ; # S/D implants
# - 1D cross sections
SetPlxList
{BTotal NetActive}
WritePlx NMOS_channel.plx y=0.0 silicon
SetPlxList
{AsTotal BTotal NetActive}
WritePlx NMOS_ldd.plx y=0.1 silicon
SetPlxList
{AsTotal BTotal NetActive}
WritePlx NMOS_sd.plx y=0.35 silicon
#----------------------------------------------------------------------#
#Transfer to device simulation
#----------------------------------------------------------------------#
#--Remove bottom of structure-----------------------------------------transform cut location= 1.00 down
#--Change refinement strategy and remesh------------------------------refinebox clear
line clear
pdbSet Grid Adaptive 1
pdbSet Grid AdaptiveField Refine.Abs.Error
pdbSet Grid AdaptiveField Refine.Rel.Error
36
1e37
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Full-Text Versions of Examples
pdbSet Grid AdaptiveField Refine.Target.Length 100.0
pdbSet Grid SnMesh DelaunayType boxmethod
refinebox name= Global \
refine.min.edge= {0.01 0.01} refine.max.edge= {0.1 0.1} \
refine.fields= { NetActive } def.max.asinhdiff= 0.5 adaptive
refinebox name= SiGOX \
min.normal.size= 0.2 normal.growth.ratio= 1.4 \
max.lateral.size= 5.0 min= {-0.01 -0.1} max= {0.01 0.1} \
interface.materials= {Silicon}
refinebox name= GDpn1 \
min= {0.0 0.04} max= {0.06 0.1} xrefine= 0.005 yrefine= 0.005 \
silicon
refinebox name= TopActive \
min= {0.0 0.0} max= {0.3 0.4} \
refine.min.edge= {0.02 0.02} refine.max.edge= {0.05 0.05} \
refine.fields= { NetActive } def.max.asinhdiff= 0.5 \
adaptive silicon
grid remesh
#--- Reflect --------------------------------------------------------transform reflect left
#--- Contacts --------------------------------------------------------contact name= "substrate" bottom Silicon
contact name= "source" box Silicon adjacent.material= Gas \
xlo= 0.0 xhi= 0.005 ylo= -0.4 yhi= -0.2
contact name= "drain" box Silicon adjacent.material= Gas \
xlo= 0.0 xhi= 0.005 ylo= 0.2 yhi= 0.4
contact name= "gate" box PolySilicon \
xlo= -0.181 xhi= -0.05 ylo= -0.088 yhi= 0.088
#--- Final --------------------------------------------------------struct tdr=NMOS !Gas
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Full-Text Versions of Examples
2D npn Vertical Bipolar
# 2D NPN Vertical Bipolar Transistor
#----------------------------------math coord.ucs
line
line
line
line
line
line
line
line
line
line
line
line
x
x
x
x
y
y
y
y
y
y
y
y
loc= 2.0
loc= 4.0 tag=SubTop
loc= 6.0
loc= 10.0 tag=SubBottom
loc= 0.0 tag=SubLeft
loc=1.5
loc=2.5
loc=8
loc=13
loc=22
loc=24
loc=30.0