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VICTORY Process Cell Full Cell Process Simulator User’s Manual SILVACO, Inc. 4701 Patrick Henry Drive, Bldg. 2 Santa Clara, CA 95054 Phone: (408) 567-1000 Web: www.silvaco.com February 22, 2012 Notice The information contained in this document is subject to change without notice. SILVACO, Inc. MAKES NO WARRANTY OF ANY KIND WITH REGARD TO THIS MATERIAL, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTY OF FITNESS FOR A PARTICULAR PURPOSE. SILVACO, Inc. shall not be held liable for errors contained herein or for incidental or consequential damages in connection with the furnishing, performance, or use of this material. This document contains proprietary information, which is protected by copyright laws of the United States. All rights are reserved. No part of this document may be photocopied, reproduced, or translated into another language without the prior written consent of SILVACO, Inc. ACCUCELL, ACCUCORE, ACCUMODEL, ACCUTEST, ATHENA, ATHENA 1D, ATLAS, BLAZE, C-INTERPRETER, CATALYSTAD, CATALYSTDA, CELEBRITY, CELEBRITY C++, CIRCUIT OPTIMIZER, CLARITYRLC, CLEVER, DECKBUILD, DEVEDIT, DEVEDIT3D, DEVICE3D, DISCOVERY, EDA OMNI, EDIF WRITER, ELITE, EXACT, EXPERT, EXPERT200, EXPERTVIEWS, FERRO, GATEWAY, GATEWAY200, GIGA, GIGA3D, GUARDIAN, GUARDIAN DRC, GUARDIAN LVS, GUARDIAN NET, HARMONY, HIPEX, HIPEX-C, HIPEX-NET, HIPEX-RC, HYPERFAULT, LASER, LED, LED3D, LISA, LUMINOUS, LUMINOUS3D, MAGNETIC, MAGNETIC3D, MASKVIEWS, MC DEPO/ETCH, MC DEVICE, MC IMPLANT, MERCURY, MIXEDMODE, MIXEDMODE3D, MOCASIM, MODELLIB, NOISE, NOMAD, OLED, OPTOLITH, ORGANIC DISPLAY, ORGANIC SOLAR, OTFT, PROMOST, QUANTUM, QUANTUM3D, QUEST, REALTIMEDRC, RESILIENCE, S-PISCES, S-SUPREM3, S-SUPREM4, SCOUT, SDDL, SFLM, SIC, SILOS, SIMULATION STANDARD, SMARTLIB, SMARTSPICE, SMARTSPICERF, SMARTSPICE200, SMARTVIEW, SOLVERLIB, SPAYN, SPDB, SPIDER, SPRINT, STELLAR, TCAD DRIVEN CAD, TCAD OMNI, TFT, TFT3D, THERMAL3D, TONYPLOT, TONYPLOT3D, TWISTER, TWISTERFP, UTMOST, UTMOST III, UTMOST IV, UTMOST IV- FIT, UTMOST IV- MEASURE, UTMOST IV- OPTIMIZATION, VCSEL, VERILOG-A, VICTORY, VICTORY CELL, VICTORY DEVICE, VICTORY PROCESS, VICTORY STRESS, VIRTUAL WAFER FAB, VWF, VWF AUTOMATION TOOLS, VWF INTERACTIVE TOOLS, VWF MANUFACTURING TOOLS, and VYPER are trademarks of SILVACO, Inc. All other trademarks mentioned in this manual are the property of their respective owners. Copyright © 1984 - 2012, SILVACO, Inc. 2 Victory Cell User’s Manual How to Read this Manual Style Conventions Font Style/Convention Description Example • This represents a list of items or • Bullet A terms. • Bullet B • Bullet C 1. This represents a set of directions To open a door: 2. to perform an action. 1. Unlock the door by inserting 3. the key into keyhole. 2. Turn key counter-clockwise. 3. Pull out the key from the keyhole. 4. Grab the doorknob and turn clockwise and pull.  This represents a sequence of FileOpen menu options and GUI buttons to perform an action. Courier This represents the commands, HAPPY BIRTHDAY parameters, and variables syntax. Times Roman Bold This represents the menu options File and buttons in the GUI. New Century Schoolbook This represents the variables of x + y = 1 Italics equations. Note: This represents the additional important information. Note: Make sure you save often when working on a manual. TIMES NEW ROMAN IN SMALL This represents the names of the ATHENA and ATLAS. CAPS SILVACO products. 3 Victory Cell User’s Manual Table of Contents Chapter 1  Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.1.1 Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2 Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3 Efficient Data Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.4 Data Interoperability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.5 Process Statements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.6 Effective Process Flow Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Chapter 2  Tutorial. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.1 Using Victory Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2 Flow of Information. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.3 Description of Input Files. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.3.1 Layout File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.3.2 Rule File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.3.3 Command File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.4 Description of Output Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.4.1 Annotated Layout File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.4.2 Structure File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.4.3 Doping File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.5 Starting Victory Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.5.1 DeckBuild . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.5.2 Batch Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.6 Tutorial Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.7 Trench Isolated MOSFET Device. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.7.1 Layout Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.7.2 Executing the Command File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.7.3 Analyzing Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.8 Ion Implantation into Trench . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Chapter 3  Process Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.1 Physical Models and Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.1.1 Discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.1.2 Etching and Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.1.3 Implantation and Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.2 Etching and Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.2.1 Geometrical or Manhattan Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.2.2 Physical Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.3 Oxidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.4 Lithography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.4.1 The Imaging Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4 Victory Cell User’s Manual Table of Contents 3.4.2 Optical System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.4.3 Digitization Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.5 Ion Implantation Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 3.5.1 Analytic Implant Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 3.5.2 Monte Carlo Implantation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.5.3 Stopping Powers in Amorphous Materials and Range Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 3.6 Diffusion Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 3.6.1 Mathematical Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 3.6.2 The Fermi Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 3.6.3 Impurity Segregation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 3.6.4 Electrical Deactivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Chapter 4  Statements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 4.1 Statement Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.1.1 Syntax Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.1.2 Statement List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 4.2 CARTESIAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4.3 CUT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 4.4 DEPOSIT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4.5 DIFFUSE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 4.6 DOPING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 4.7 ELECTRODES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 4.8 ETCH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 4.9 EXPORT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 4.10 FILTER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 4.11 GDSLAYER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 4.12 GO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 4.13 HELP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 4.14 ILLUMINATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 4.15 IMPROVEMESH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 4.16 IMPLANT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 4.17 INIT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 4.18 LINE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 4.19 MACHINE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 4.19.1 Simultaneous Etching of Multiple Materials with Material Dependent Etch Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 4.20 MASK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 4.21 MATERIAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 4.22 MESH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 4.23 OPTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 4.24 OXIDIZE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 4.25 PUPIL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 4.26 QUIT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 4.27 REFINE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 4.28 RESET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 4.29 SAVE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 4.30 SET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 4.31 SOURCE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 5 Victory Cell User’s Manual Table of Contents 4.32 STRIP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 4.33 SURFACE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 4.34 SYSTEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 4.35 TONYPLOT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 Appendix A  Default Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 A.1 Default Oxidation Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 6 Victory Cell User’s Manual Chapter 1 Introduction Overview Introduction 1.1 Overview VICTORY CELL is a fast, layout-driven 3D process simulator specifically designed for large structures. Using information from the mask layout and process technology, VICTORY CELL creates realistic 3D device structure using its built-in 3D etch/deposit processor, user selectable material names and properties, and its advanced implantation, diffusion, and optolithographical process steps. It also provides a realistic 3D graphical representation of the investigated cell. 1.1.1 Features • Fast 3D process modeling of etch, deposition, implantation, and diffusion. • GDSII layout-driven. • Accurate and fully multi-threaded 3D Monte Carlo implantation. • Mesh algorithms optimized for large device structures. • Automated layout-driven mesh generation. • User-controlled mesh placement. • SUPREM-like syntax • Interface to 3D device simulators ATLAS3D and VICTORYDEVICE. Victory Cell’s Modular Design Some of these features can be grouped into modules. These modules are: • Layout Input Interface (see MASKVIEWS Manual) • Volumetric mesh generation from Layout and user paramaters (see Chapter 2 “Tutorial”) • Complete set of 3D process simulation steps (see Chapters 2 “Tutorial” and 3 “Process Steps”) • Device structure optimization and electrode placement (see Chapters 2 “Tutorial” and 4 “Statements”) The seamless data flow between these modules (see Figure 1-1) gives VICTORY CELL greater flexibility and a complete integration into the SILVACO TCAD frameworks. 8 Victory Cell User’s Manual Overview Introduction Figure 1-1 The Process Flow Overview in Victory Cell 9 Victory Cell User’s Manual Accuracy Introduction 1.2 Accuracy VICTORY CELL is a fast an efficient 3D process simulator and device builder. Nevertheless, it does not sacrifice quality for the sake of speed. Its internal adaptive mesh refinement algorithms allow for fast and accurate pattern transfer from layout to silicon. Manhattan type etch/deposition steps can be simulated over large cells with high aspect ratio layers needed in modern semiconductor technology. When necessary, VICTORY CELL will switch automatically to more advanced, physical etch and deposition, thus, correctly simulating spacers, trench refils, conformal deposition, and so on. VICTORY CELL simulates many process steps well and others superbly, for example ion implantation. VICTORY CELL uses advanced Monte Carlo Ion Implantation simulator to correctly predict dopant distribution in silicon. As the main purpose of VICTORY CELL is to build correct and computationally effective structure for ATLAS3D and VICTORYDEVICE, doping and quality meshing are one of its main strengths. 10 Victory Cell User’s Manual Efficient Data Model Introduction 1.3 Efficient Data Model There are two data sets critically needed for effective TCAD process simulation– boundaries and scalar fields. In 3D, scalar fields are big, boundaries are difficult to represent and control. During process steps, boundaries move, while, scalar fields change. Sometimes they do move and do change simultaneously as in oxidation. VICTORY CELL builds on already established geometrical model and data structure of CLEVER. The original CLEVER development had the best approach of keeping 3D solid geometry. This combined with a powerful methods of manipulating 3D geometry makes it a natural choice for geometry data model. Boundaries in VICTORY CELL are well represented in a compact form, which can be saved in SDB format adopted for all TCAD tools. To represent doping VICTORY CELL uses irregular Cartesian grids with embedded/immersed boundaries. Careful analysis and past experience suggest Cartesian meshes are best suitable for representing scalar fields such as doping and damage. On the other hand, they need more advanced software methods and numerical schemes to account for boundaries. Scalar fields on Cartesian meshes could be represented with sparse, dense, or irregular discretization. There are many programatic structures to aide accounting for boundaries (Embedded boundaries libraries, immersed boundary methods, and so on.). Figure 1-2 shows the data model used in VICTORY CELL. What is important to remember is that data structures on the chart represent different objects: Tetrahedral represents and keeps the boundaries, while Volumetric looks after scalar fields, like doping. Another important aspect is that scalar fields also have to account for presence of boundaries. The mechanism called synchronization will be discussed in Section 1.6 “Effective Process Flow Control”. Figure 1-2 VICTORY CELL’s Data Model. Tetrahedral amd Volumetric are the two data structures handled by the data model. Depending on the process module, operations are carried out on one, the other, or, on both structures. 11 Victory Cell User’s Manual Efficient Data Model Introduction Figure 1-3 shows a typical use of both, Tetrahedral and Volumetric data structures in the Monte Carlo 3D Implantation module. Separation of data representation keeps maintaining compact and effective data structures– typical sizes of geometrical structures are about 110Mb and sizes for doping structures are similar 1-15Mb. In contrast, when those two structures are combined and finally exported to a structure for ATLAS3D device simulation, the size of the SDB structure file is between 50 and 300Mb. Figure 1-3 An example of data exchange and manipulation between a process module and VICTORY CELL data model. Here, the MC Implant module requires both, a geometry structure and a scalar field where doping will be stored. Note, the mapping back of data correctly accounts for the embedded boundaries. 12 Victory Cell User’s Manual Data Interoperability Introduction 1.4 Data Interoperability Data interoperability in VICTORY CELL is the backbone for effective process simulation. Without such functionality, a complete 3D process flow simulation would have not been possible. Let D is the geometrical domain of the process simulation. It is defined by the layout window, silicon wafer thickness and future layers on top. Let g represent material region boundaries or simply material regions and let also F is a scalar field, such as doping, damage, and stress. Then, a typical data interoperability in a process flow would be represented like this (Figure 1-4). Figure 1-4 Data interoperability in VICTORY CELL. The rectangle represents simulator’s common interface for persistent data structures and plug-in process modules. A data flow supervisor controls data exchange between process modules. It decides when to synchronize meshes (see Figure 1-2), selects the scalar fields needed for particular implant/ diffusion step. Synchronization time overhead is small– typical times vary between 15s and 2min. Stability of data synchronization is very good– the process simulator successfully simulated large CMOS photo cells with more than 40 implants, 40+ diffusion steps, equal number of etch/deposition steps. Data synchronization works well also for geometrically more complicated cells with spacers, oxidation, and so on – MOSFET, TFTs. To summarize, in VICTORY CELL two distinctive data structures are used to represent results of process simulation. The main goal is effectiveness of model algorithms. This also contributes to the stability as each process step model uses the most suitable for solving the numerical problem data structure. In order to keep data integrity, a synchronization between data structures is needed. This is achieved by means of advanced meshing and tracing algorithms, which so far shows good stability. The chosen organization of process data keeps memory footprint very low. 13 Victory Cell User’s Manual Process Statements Introduction 1.5 Process Statements VICTORY CELL has the following (major) process statements: Init initialization of simulation structure Deposit models the deposition process Strip removes an exposed material completely Machine defines etch/deposition settings with a machine name Etch models the etching process Cartesian specifies volumetric mesh discretization Doping applies uniform impurity concentration to a material region Implant models the implantation process Diffuse models the annealing process Save saves data structures Electrodes attaches electrodes to the structure Mask applies a layout mask to the current structure Export exports to a device structure Option assigns and triggers different global values Statements in blue use the Volumetric data structure, whereas statements in red use the Tetrahedral data structure, Figure 1-2. Cartesian is a special command used to initialize Volumetric stricture and to synchronize it to the material regions from the Tetrahedral structure. Special care have been taken to make initialization of data structures as close as possible to ATHENA, thus the learning curve for users is low. The most important set of process statements is Etch, Deposit, Implant, and Diffuse. Except for missing fully coupled diffusion, these for commands provide complete process functionality needed for a modern device prototyping. The best way to describe these commands is through examples. 14 Victory Cell User’s Manual Process Statements Introduction Figure 1-5 shows a process flow for a BJT device. Process statements in VICTORY CELL follow close to reality process flow operations in a real FAB. Figure 1-5 A medley of different simulation components for a BJT device. On the left is the process flow input deck, on the right - the final device with the used layout on the top. To summarize, VICTORY CELL has enough meshing power to simulate realistic 3D device structures. The Etch/Deposit module for most of the cases is stable and can provide fast prototyping of a complete device cell. 15 Victory Cell User’s Manual Effective Process Flow Control Introduction 1.6 Effective Process Flow Control VICTORY CELL uses multiple grid approach to simulate a process flow. It is designed to support the complete process flow starting from mask layout and proceeding through all structure transformation steps even if some of these steps are simulated using simplified models (e.g., dry or vertical etch). This approach provides users with better practical capabilities to analyze layout, process, and geometrical feature variations. The complete process simulation flow is shown in Figure 1-6. The GDSII layout file is loaded into the process simulator that selects the masks to perform corresponding structure transformation process steps (e.g., etching and deposition). After each structure transformation step, an optimal tetrahedral mesh is re-created for the new structure. Simultaneously, the Cartesian rectilinear mesh is generated out of user and layout specified discretization and immediately starts synchronizing its immersed boundaries with the geometrical (tetrahedral) mesh. The frequency of synchronization depends on how often an implant or an diffusion statement is used, and it is triggered when tetrahedral mesh has changed, which is usually after each etch and deposition or mask photoresist statements. After each synchronization, the rectilinear mesh does appropriate interpolation between the “old” and “new” immersed boundaries, thus, keeping all physical data intact. Figure 1-6 Block diagram of multiple-grid process flow. 16 Victory Cell User’s Manual Summary Introduction 1.7 Summary VICTORY CELL is a practical, memory efficient, and very fast 3D process simulator by using an approach, which utilizes the most efficient gridding system for each of the process and device simulation steps. By using this "multiple gridding" approach, many of the compromises of using only one type of gridding method for the whole simulation are thus eliminated, reducing simulation times for 3D TCAD down to very reasonable and practical levels. 17 Victory Cell User’s Manual Chapter 2 Tutorial Using Victory Cell Tutorial 2.1 Using Victory Cell This chapter is intended to novice users of VICTORY CELL. It explains the inputs required by the program and the output produced. This is followed by detailed walk-through of two examples to illustrate the key points in using the program effectively. Complete description of the models and input language syntax are found in other chapters. However, you should become familiar with the methodology described in this tutorial before reading these chapters. 19 Victory Cell User’s Manual Flow of Information Tutorial 2.2 Flow of Information Before using VICTORY CELL, you should first understand the information flow that occurs when VICTORY CELL is applied to a problem. To aid in this description the information flow is shown graphically in Figure 2-1. There are three main sections to this diagram: input file generation, 3D VICTORY CELL simulation, and output generation. The core of the diagram is the 3D process simulator and ion implantation and diffusion simulators, which requires a number of input files and which generates the 3D device structure. The purpose and description of the various input and output files can be found in the next sections of this chapter. Input Files 3D Simulator Output Files Layout File 3D Structure Rule File Victory Cell Modified Layout Command File Logfile Figure 2-1 Victory Cell Information Flow 20 Victory Cell User’s Manual Description of Input Files Tutorial 2.3 Description of Input Files THE VICTORY CELL simulator requires two principal input files: a layout file and a Command file containing process description and device electrode placement. 2.3.1 Layout File The layout file contains the same mask set used to create the actual cells, individual devices or interconnects, usually in GDSII format. To view or create the layouts, use MASKVIEWS or EXPERT layout editor. Figure 2-2 shows the normal information flow sequence for creating a mask set for use with VICTORY CELL. You are usually given a mask design from the company's design group in GDSII format. This design is then loaded into MASKVIEWS. Specific electrode name lables for major nodes can then be added to the layout, such as Vdd, Vss, in, out, Bit, and Bitbar. If the simulated circuit consists of numerous active devices, all the labels for device contacts, such as source, gate, drain, substrate, contacts could be added to the layout file automatically using the Rule File described in the next section and therefore do not have to be added manually. For information about MASKVIEWS, see the MASKVIEWS USER’S MANUAL. Design Group User-Added Labels GDS II MASKVIEWS Layout File Figure 2-2 Creation of the Layout File 2.3.2 Rule File The Rule file (or Map file) is used by VICTORY CELL to extract the active device geometries from the information contained in the layout. This file contains a set of Boolean definitions, using the mask layers, that define the location of the active areas and allows their position and area to be extracted by VICTORY CELL. This is done for all active device contacts within a cell. For MOS technology, this means the source/drains, gate, and substrate contacts. Different Rule files are required for different technologies or mask sets. Changes in process flow generally do not mean a change in the Rule file. The Rule file adds information regarding the active devices in the layout and consists of five operations: • Rename masks or define regions. • Various regions of the active devices are defined by logical combinations of the original masks or derived masks. • The connectivity of the mask layers is defined. 21 Victory Cell User’s Manual Description of Input Files Tutorial • The active device terminals are defined. • Exporting of any newly created logical mask combinations to the layout for viewing and debugging in MASKVIEWS. The main use of the Rule file by VICTORY CELL is for renaming masks, defining regions and logical operations on regions. Naturally, in the case of using VICTORY CELL on layouts with no active devices the Rule file is not required. Alternatively, you can create electrodes directly in MASKVIEWS, thus skipping the use of a Rule file. 2.3.3 Command File The command file is an ASCII file listing the process steps used to construct the cell as well as creating the final device structure. Most commands can be easily understood by engineers with basic knowledge of semiconductor processing and fabrication. Only few commands specific to the process simulator require learning. See Chapter 4 “Statements” for a full description. The command file refers to both the layout file and rule file. The process simulator executes the steps in the command file to produce the output files (discussed below.) Command files can be written by simply typing the commands and options or by using the command menus in DECKBUILD. An example of such a menu is shown in Figure 2-3. This is the Oxidize menu. Command files can also be created by editing the examples supplied by SILVACO. New VICTORY CELL users are recommended to consult the on-line examples starting with the simple cases. Figure 2-3 DeckBuild Command Popups for Creating Input File Syntax 22 Victory Cell User’s Manual Description of Output Files Tutorial 2.4 Description of Output Files VICTORY CELL outputs three main files: a modified annotated layout file, a structure file, and an impurity doping file. In addition to these files, a logfile may also be created for specific purposes. 2.4.1 Annotated Layout File The modified layout file consists of the original layout files plus the electrodes added for the device calculation. The modified layout shows additional mask layers that have been exported by the Rule file. For MOS technologies the defined active device contacts, *GATE and *CONT, are automatically saved and added to the annotated layout file. 2.4.2 Structure File The structure file allows you to view the structure generated by VICTORY CELL in 3D using TONYPLOT3D. The 3D graphic allows you to see the geometry of the device structure and the effect of each process step that alters the structure shape. It can also be used to check process results, to ensure that the back-end process flow has succeeded and that the cell has not been damaged by any changes in the processing conditions. If a 2D plane (CUT LINE) or 1D point simulation has been run, the structure files should be viewed in TONYPLOT rather than TONYPLOT3D. 2.4.3 Doping File Doping files in VICTORY CELL contain the irregular Cartesian mesh with immersed boundaries described in Chapter 1 “Introduction” and the available impurities at each node. Doping information is visualised by creating device structure files with the EXPORT command. The device structure files combine the geometry information from the structure files with impurity information from the dopping files. Device structure files can be visualized in TONYPLOT3D. 23 Victory Cell User’s Manual Starting Victory Cell Tutorial 2.5 Starting Victory Cell There are two ways to start VICTORY CELL: • Using DECKBUILD • Using VICTORY CELL in Batch Mode The following shows how to use these methods. 2.5.1 DeckBuild To run VICTORY CELL using DECKBUILD. 1. Open the terminal window and type deckbuild & and the DECKBUILD window will appear. 2. Use the left or right mouse button and select FileOpen to select an input deck (e.g., vcex01.in) from the file browser. 3. Press Run in the DECKBUILD window to start the simulation. Figure 2-4 shows an example. Figure 2-4 Deckbuild showing a Victory Cell Simulation 24 Victory Cell User’s Manual Starting Victory Cell Tutorial 2.5.2 Batch Mode Before running VICTORY CELL in this mode, you should already have a input deck defined. To run VICTORY CELL in batch mode, type victorycell and the name of the input deck (e.g., victorycell vcex01.in) in the terminal window. If you need help, first type victorycell in the terminal window. Then, type help. This will display a list of commands needed to create an input deck. To find out how to use a specific command, type help with the name of the command (e.g, help diffuse). The instructions on how to execute the command will then appear. 25 Victory Cell User’s Manual Tutorial Examples Tutorial 2.6 Tutorial Examples The remainder of this chapter is divided into two sections describing VICTORY CELL examples. The first section shows a trench isolated MOSFET demonstrating different etch/deposition commands, use of layout file and device electrode placement The second section elaborates on how to generate the volumetric mesh and use doping commands. The example shows ion implantation in L-shaped trench and demonstrates the origins of the so called well proximity effect (WPE.) 26 Victory Cell User’s Manual Trench Isolated MOSFET Device Tutorial 2.7 Trench Isolated MOSFET Device Standard examples for VICTORY CELL are available in DECKBUILD. In DECKBUILD, use the right mouse button to click on Main Control, then select Examples and a new Deckbuild: Examples window will open. Scroll down to VICTORYCELL : A Cell Level Process Simulation, and double left-click on the heading to show the list of VICTORY CELL examples. Double-click on vcex01.in: Trench Isolated MOSFET and a description of the example will be shown. This example calculates a trench isolated MOSFET device. It starts with the shallow trench isolation, then proceeds with poly-gate and metalization, and finally assignes the electrodes. Press the Load example button in the upper right corner of the Deckbuild: Examples window to load all files for this example into the current directory. 2.7.1 Layout Definition From DECKBUILD, select ToolsMaskViewsStart MaskViews. A file manager menu will pop-up (see Figure 2-5) that lists the layout files in the directory. Select the desired layout file, in this case vcex01.lay, and click on the Start MaskViews button. MASKVIEWS application will open up displaying selected layout file. Alternatively instead of using DECKBUILD’s Tools menu, simply type maskviews & in a command (UNIX shell) window in the same directory as DECKBUILD was started, to start MASKVIEWS. To load the layout file, right-click on Files and select Layout, and the same file manager menu will pop-up as described above. Figure 2-5 MaskViews Load File menu MASKVIEWS then references a simulator listed in the buttom information bar. If it lists a simulator other than VICTORY CELL (for example, ATHENA), press Edit, then Preferences, and a settings menu will pop-up. From this menu select Document and Defaults, then leftclick on the button next to Simulator and select VICTORY CELL, then click on the Apply button in the bottom right corner. This and other settings can be saved as defaults by selecting Save these settings on exit. 27 Victory Cell User’s Manual Trench Isolated MOSFET Device Tutorial Figure 2-6 MaskViews with vcex01.lay layout The layout is simple– one L-shaped line. By clicking on tren (or NEW) on the right side of MASKVIEWS displays the layer atop the other. Clicking on the color box next to the layer name toggles the layer display. (For a full description of MASKVIEWS, please see the MASKVIEWS USER’S MANUAL.) Labels are often attached to non-connecting lines of the same mask layer. MASKVIEWS layout format allows electrodes to be defined in a given layout. Labels provide this additional information for VICTORY CELL to identify input, output. The labels in Figure 2-6 were made in the following manner: 1. Select the appropriate layer (here, “cont”). 2. From the Edit pull-down menu, select Label. Alternatively, right-click in the layout window, all options from the Edit menu will show, then select Label. 3. On the layout, click on the polygon where the label is to be attached. The MaskViews: Label pup-up menu opens as shown in Figure 2-7. Figure 2-7 MaskViews Label menu 28 Victory Cell User’s Manual Trench Isolated MOSFET Device Tutorial 4. Define the name of the electrode (or node) and select the electrode box, then press OK. In this example, the electrodes have been labeled. (See the MASKVIEWS USER’S MANUAL for more details.) 2.7.2 Executing the Command File Return to the DECKBUILD GUI started earlier. The Command file is an ASCII file describing the process steps. It references the layout file, and uses mask information for structure definition. Other commands save output files, including 3D structure files. The INIT command refers to the layout. For this simple example no Rule file is used. The body of the Command file consists of process commands, including deposit, etch, strip, mask, and electrodes. Mask and Electrodes statements both refer to the mask names in the layout. These process commands are described fully in Chapter 4 “Statements”. Press Run in the middle bar of DECKBUILD to begin the simulation. 2.7.3 Analyzing Results In this example, only one type of output file is generated: a 3D structure file. We will analyze step by step the execution of the process flow commands. The Command file starts with the statement: go VictoryCell This command tells DECKBUILD to execute VICTORY CELL regardless of what the default simulator for DECKBUILD is. It is always a good idea to use this statement in the beginning of every Command file. By default DECKBUILD loads the simulator, which is specified in the Main Control menu under the Main Control sub-menu. The actual simulation starts with the INIT command Init Layout="vcex01.lay" Depth = 1.5 which, sets up the simulation domain in the following manner (see Figure 2-8). The exposed wafer surface is at “0” level on the Z-axis, “Depth=1.5” defines the wafer thickness, while the layout dimensions define the bounding box in the XY-plane. This plane will be the exposed surface for all subsequent process steps. The region above the surface in VICTORY CELL is defined as “Gas”. By default, the thickness of this “Gas” region is 20um. VICTORY CELL needs this region to build atop the neccessary layers (i.e., the gas region could be considered as a working space for the simulation). You need to make sure that the thickness of this region is larger than the total thicknesses of all layers to be built. By default, the initial substrate material is silicon. Its depth has to be sufficient for all etch steps being performed. You should be aware that visualization tools do not display the gas region. 29 Victory Cell User’s Manual Trench Isolated MOSFET Device Tutorial Figure 2-8 Coordinate system orientation of the simulation domain The final outcome of the above INIT command will be a rectilinear domain with two regions, one defined as a silicon with thickness along the z-direction 1.5um, and a second (working area for VICTORY CELL) gas-region with a default thickness of 20um. After this initialization, VICTORY CELL can perform any etch, deposition, or doping command. For complete set of parameters and their use, see Section 4.17 “INIT”. The next command Deposit Resist Thickness= 0.1 Max performs a simple deposition process step In this case, deposits resist with thickness of 0.1um. The last parameter Max, tells VICTORY CELL how deposition is to be performed. 30 Victory Cell User’s Manual Trench Isolated MOSFET Device Tutorial Figure 2-9 Effects on deposition using Min/Max parameters The MAX parameter instructs VICTORY CELL to deposit 0.1um thick resist above the highest point on the current exposed surface of the structure. There is also a MIN parameter instructing a 0.1um only thick photoresist to be deposited from the lowest point on the exposed surface. As a side effect, the Deposit command can work with negative Thickness=-0.1 when the Max parameter is specified, meaning the material will only be deposited to a level 0.1um below the highest point on the exposed surface. Naturally, if large negative thickness with the Max parameter is specified, nothing will be deposited. See Figure 2-9 for possible uses of the Min/Max parameters. The next command simply transfers the pattern from layout layer “tren” onto the photoresist. Mask "tren" A basic rule is what is colored in MASKVIEWS is what remains as a photoresist pattern in the structure. To further analyze process flow commands, we are going to use DECKBUILD’s step by step execution capabilities. To do that, we need to switch on in DECKBUILD the automatic saving of the structure each time it has been processed or altered. Go to Main Control pull down menu, and click on Main Control listed option. In the popped-up window, select the Control Pad tab and then click on the History Props button. Another window called History will pop-up inside the window. Select Enable and then click on Save as defaults. Close the History and Deckbuild: Main Control windows by double clicking on the upper left corner. 31 Victory Cell User’s Manual Trench Isolated MOSFET Device Tutorial DECKBUILD will now start saving structures named “.historyXX.str”, where “XX” are sequentially increasing numbers. Lets execute vcex01 example step by step. This will allow to gradually analyze process flow commands and results. Click on the kill button in the middle bar of DECKBUILD to exit from the VICTORY CELL simulator. Scroll to the top of vcex01.in file and click anywhere on the first line and then click on the line button of the middle bar. The Line: value to the far right will show “1”. Then you are ready to start executing step by step vcex01 process commands. By clicking next on the middle bar, the first line will be executed telling DECKBUILD to start the VICTORY CELL simulator. Continuing pressing next one by one process step commands will execute. The command line/output window of DECKBUILD shows the execution progress while the cursor in the edit/input window gradually moves down. At any moment, you can go to the output command line/window and type a command that will be immediately executed by VICTORY CELL. Likewise, you can insert a command in the edit/input window, which will be executed when the cursor goes through it. The upper window is under control of DECKBUILD, while the lower window is under control of VICTORY CELL. This stop and continue functionality in DECKBUILD is handy for initial device prototyping, where in order to create the process flow you need a fast, debug style, edit, and run. Returning back to the vcex01 example. After ‘Mask "tren"’ command is executed, DECKBUILD will automatically save the latest structure. What in essence happens is DECKBUILD automatically inserts a SAVE command after each process step resulted in modifying the device structure. You can select the filename of saved structure and visualize it. To do this, highlight the filename (by pressing the left mouse button and dragging the mouse cursor, or by clicking fast three times in a row the left mouse button) after the Save.. information line in the output window of DECKBUILD. Save.. .historyXX.str VictoryCell> Then, go to Tools menu and select PlotPlot structure. A visualization program (TONYPLOT3D) will automatically start displaying the device structure. By default, VICTORY CELL uses a basic etch and deposition models whereby a uniformly thick layer is deposited and etched. This results in the classical "manhattan" geometry where the rectangular shaped structures have the appearance of a Manhattan skyline. A more advanced etching model is used for the shallow trench isolation. In this model etching is performed along a material boundary at a specified Rate and Time. An Isotropic component is also specified so that etching is performed laterally as well as vertically. This results in the "non-manhattan" geometry where the sidewalls are no longer vertical but may have a "slope" or curvature. Etch Silicon Rate=0.1 Time=6 Isotropic=0.1 The thickness of etched or deposited material could be easily estimeted from Rate and Time. For a flat moving front that would be Rate multiplied by Time. The units of Rate and Time should be such chosen so that the product of two gives units in microns. 32 Victory Cell User’s Manual Trench Isolated MOSFET Device Tutorial Trench isolation process continues with thin layer oxidation Deposit Oxide Rate=1 Time=0.03 Isotropic=1 where a Deposit statement is ised with conformal depostion of oxide layer with approximate thickness of 0.03um. The above process step could be written in an equivalent way. Deposit Oxide Thickness=0.03 Conformal Both statements perform the same process step using the advanced deposition model in VICTORY CELL. Finally, the trench is filled in with glass and planarized (see Figure 2-10). Figure 2-10 Trench isolation of MOSFET The remaining commands in the input deck are simple, manhattan like, etch and deposition process steps. The final structure is shown in Figure 2-11. Figure 2-11 final MOSFET structure with placed source, drain, substrate electrodes and polysilicon gate 33 Victory Cell User’s Manual Trench Isolated MOSFET Device Tutorial A final note regarding this device structure is placement of electrodes. Electrodes in VICTORY CELL structure are two dimensional (i.e., they are interface elements between two material regions or exposed surface elements on metal contacts or polysilicon). There is no need the whole area of the contact to be labeled as an electrode (see the MASKVIEWS USER’S MANUAL for how to place labels in a layout layer). It is sufficient to identify only part of it. VICTORY CELL will later on propagate the electrode properties to the whole region when exporting structure for device simulation. The following command will place electrodes on the metal contacts. The Electrodes statement must be used when a particular metal region to be assigned as electrodes is still exposed. VICTORY CELL cannot assign electrode names to a region already burried underneath, like isolation material. The statement Electrodes "cont" Aluminum takes all labels from “cont” layer in the layout vcex01.lay (see Figure 2-12) and assigns them as an electrode names to all exposed aluminum contacts. Electrode assignment is mainly done by polygon position containing the label. If there is any misalignment of transferred pattern and original layout polygon (due to rounding errors or non-manhattan etch/deposition steps), electrode assignement could have unpredictable side effects. To avoid this, you should always point to the material name electrodes that need to be assigned in the case of vcex01 example Aluminum. Figure 2-12 Assigned lables to the “cont” layer in vcex01.lay In the above example, labels are attached to a whole polygon of the layout layer. As VICTORY CELL needs only one point to assign to an exposed face electrode property with a particular label, sometimes a separate layer in the layout is used just for that purpose. Figure 2-13 shows the modified layout demonstrating the alternative approach. 34 Victory Cell User’s Manual Trench Isolated MOSFET Device Tutorial Figure 2-13 Using separate layer with labels for assigning electrodes This approach is safer as sometimes due to alignment errors or use of advanced etch and deposition. The original layout polygon not always matches the transferred pattern and could occasionally cause either unexpected and undesired electrode assignment or bad quality meshing. The second approach is also good because it gives flexibility needed to correctly generate the final electrodes when exporting a structure to the device simulator. 35 Victory Cell User’s Manual Ion Implantation into Trench Tutorial 2.8 Ion Implantation into Trench This example demonstrates all important 3D effects in ion implantation. The final results will show inhomegenous dopant distribution (i.e., extra non-uniform doping at the surface of the trench area caused by ions scattered within photoresist and emerged from the mask edge at different angles). This example will also exercise all important aspects of creating volumetric mesh for doping. As it has been described in Chapter 1 “Introduction”, VICTORY CELL uses a novel concept of a multiple mesh approach to keeping and evolving material interfaces as well as keeping and annealing dopants within materials’ volume. This is a powerful approach allowing each group models to use the most suitable mesh and related algorithms to finish the job. To use a volumetric mesh in the simulation, you need to define its Cartesian discretization. For volumetric data, VICTORY CELL uses irregular Cartesian meshes with embedded boundaries (see Figure 2-14). Figure 2-14 Irregular Cartesian grid with embedded boundaries Cartesian mesh needs to be specified near the top of the simulation deck before any Doping, Diffusion, or Implant statement is used. VICTORY CELL provides convenient commands to easily specify, manipulate and optimize creation of volumetric mesh. Once such mesh is created, VICTORY CELL automatically updates embedded boundaries when new material interfaces are created due to etch or deposition. All available doping data on the Cartesian mesh is synchronized accordingly with the newly added or removed embedded nodes. 36 Victory Cell User’s Manual Ion Implantation into Trench Tutorial To start the example, go to DECKBUILD’s Main Control and select Examples. If during the previous use of Examples the VICTORY CELL section has already been loaded, simply go to the Sub-section pull down menu and select vcex02.in Ion Implantation into L-shaped Trench. The input deck file vcex02.in will be loaded in DECKBUILD. Press the Run button located on the middle bar of DECKBUILD, to execute the process and to see the results. Because now simulation involves Monte Carlo implantation it might take some time to finish. At the end of the simulation the visualization program (in this case, TONYPLOT3D) will be started and the final structure with doping will be displayed. Follow the TONYPLOT3D USER’S MANUAL for how to analyze and display different properties and values in the structure. Examples of doping visualization are shown in Figure 2-15. TONYPLOT3D can display impurities in all or selected materials. You can do any 2D cross-section of the structure and export it to a 2D structure file or to the 2D visualization program TONYPLOT. Figure 2-15 Dopant distribution in L-shaped boron implanted trench 37 Victory Cell User’s Manual Ion Implantation into Trench Tutorial Volumetric discretization in VICTORY CELL is defined by the Cartesian or the short version Cart command (see its full description in the Chapter 4 “Statements”). In the present version of VICTORY CELL, the volumetric discretization should be defined after that place in the input deck where a 3D geometrical structure has been already created. Because in the beginning the initial substrate is a plane, VICTORY CELL starts as an 1D process simulator and depending on layout and process steps it sequentially transforms itself to 2D and 3D dimensional structure as needed. At present, VICTORY CELL is incapable of automatically upgrading to higher dimensionality its volumetric mesh. Therefore, volumetric discretization should be defined when the structure is already three dimensional. You can place CARTESIAN statements right after the INIT command if padding= has been used in the INIT statement. The padding parameter forces VICTORY CELL to immediately upgrade the structure to three dimensional. The following fragments of input deck demonstrate simple use of the Cartesian command to create volumetric discretization. Init silicon Layout="vcex02.lay" Depth=1 padding=0.5 gasheight=1 Cartesian line xdir location=0.25 spacing=0.025 Cartesian line ydir location=0.75 spacing=0.05 Cartesian line ydir location=1.00 spacing=0.01 Cartesian line zdir location=0.00 spacing=0.001 Mesh prism file="output.str" Tonyplot output.str quit Generated volumetric discretization is shown in Figure 2-16. Y Y X Z Figure 2-16 Irregular Cartesian mesh is the basis of keeping volumetric data in VICTORY CELL The initial Cartesian discretization consists of only “regular” nodes (see Figure 2-14). Later on during the course of building the device structure, VICTORY CELL gradually adds and updates the “irregular nodes” that are the basis for embedded boundaries for ion implantation and are used in the immersed boundary method for dopant diffusion. 38 Victory Cell User’s Manual Ion Implantation into Trench Back to the vcex02 example. Figure 2-17 shows volumetric mesh discretization. Tutorial Figure 2-17 Volumetric mesh discretisation in vcex02 Volumetric mesh should be well refined in the trench area as well as near the walls of photoresist– this will show exactly how scattering from walls and shadowing affects overall dopant distribution in silicon. Note: For a proper calculation of ion implantation, volumetric mesh does not need to be refined in all places, you should only refine these regions in the structure where better visualization of dopants is needed or where better grid is required when exporting to device structure. For example, not refining the volumetric mesh in photoreist will not affect ion implantation simulation and final dopant distribution in silicon. 39 Victory Cell User’s Manual Ion Implantation into Trench Tutorial The next three statements introduce dopant impurities into the structure. DOPING defines uniform concentration of specified impurity in silicon, while the IMPLANT statements introduce non-uniformly distributed dopant impurities. Figure 2-18 shows a cross-section from the 3D structure with an interesting effect regarding dopant distribution– “focusing” caused by scattering of implanted ions from photoresist’s walls. IONS “FOCUSING” FROM REFLECTION DIRECTLY IMPLANTED Figure 2-18 2D cross-section from the L-shaped trench structure near the internal corner showing boron dopant distribution and 1D boron and phosphorus profiles 0.006um bellow silicon’s surface. Doping silicon boron=1e15 Implant boron energy=5 dose=1e14 bca n.ion=500000 tilt=45 rotation=0 Implant phosphorus energy=20 dose=1e14 bca n.ion=500000 tilt=45 rotation=0 Along with epitaxial deposition (see Section 4.4 “DEPOSIT”), these are all the commands, which introduce impurities in silicon. Dopant impurities are stored onto the volumetric mesh specified with the Cartesian command. Finally, the statement Export atlas3d file="vcex02.str" perform export to a structure suitable for different device simulators (e.g., ATLAS3D and VICTORYDEVICE). 40 Victory Cell User’s Manual Chapter 3 Process Steps Physical Models and Mesh Process Steps 3.1 Physical Models and Mesh 3.1.1 Discretization Ongoing transition from 2D to 3D process simulation requires careful consideration of numerical methods and corresponding spatial discretization techniques most suitable for efficient computation of each technological step and a complete process flow. VICTORY CELL adopts a flexible approach in which different types of grids are used for different simulation steps inside the 3D process simulation framework. The implemented data model is based on the fact that tetrahedral meshes can effectively and exactly represent material regions and interfaces, whereas irregular Cartesian (rectilinear) grids are mostly suitable for volumetric physical data representation. A Delaunay tetrahedral mesh serves as a geometrical skeleton optimally coarsened to reduce computer memory requirements. The main advantages of this approach are speed and the ability to handle structures featuring large aspect ratios. The tetrahedra based geometrical grid also has following purposes: • It serves as an initial and final state for etching and deposition. • It defines the geometrical topology needed in ion implantation. • It acts as a geometrical server (i.e., keeping and issuing all kind of information related to regions, materials and interfaces). Physical data, such as doping concentrations and damage, are all kept on the irregular Cartesian grid. Two types of nodes are used to store the data: the “regular” nodes, according to rectilinear grid and the “boundary” nodes representing values at the intersection of the Cartesian grid and the material interfaces. Three dimensional interpolation techniques are used during synchronization of the two grids to correctly represent physical values after change of geometry (i.e., move of boundaries). The created immersed boundaries rectilinear grid is further used for simulation of implantation, annealing steps, and serves as a basis for optimal device mesh generation. Figure 3-1 A 50nm MOSFET cell showing trench isolation, spacer, polisilicon gate, and four electrodes 42 Victory Cell User’s Manual Physical Models and Mesh Process Steps 3.1.2 Etching and Deposition Any semiconductor device manufacturing flow includes many process steps, which change geometry of the device structure. Material etching and deposition are main technological methods used to build desirable device structures. Efficient and robust modeling of multiple deposition and etching steps is an important part of the VICTORY CELL 3D process simulation system. The key numerical and gridding problem for etch and deposition simulation is accurate tracking of the moving boundary front. The methods for solving moving boundary problems could be roughly divided into four distinct groups: string-based, cell-based, levelset and volume-of-fluid methods. Each of these methods have their advantages and serious difficulties depending mainly on the size and discretization of simulation domain and complexity of physical models for etching and deposition. To perform etching and deposition steps of a typical process flow, VICTORY CELL uses a 3D extension of a string algorithm based on the adaptive refinement of a tetrahedral grid. In most cases, it is sufficient enough to consider conformal or "step coverage" deposition and arbitrary combination of directional and isotropic etching. The moving boundary algorithm in VICTORY CELL tracks the boundary front after each time step in case of "physical" etching and deposition or captures the final boundary position in case of "geometrical" (or userdefined) removal or addition of a material layer. The moving front calculated from etching or deposition rates or specified geometrically by user is implicitly represented in a tetrahedral mesh. Adaptive mesh refinement with a userdefined resolutions is applied to only those tetrahedra, which are intersected by the front. After that the new front is extracted by splitting and classifying new tetrahedra. This approach is as efficient as the string algorithm in 2D and as robust as the Level-set method in solving difficult problems of de-looping and void formation. Figures 3-1 and 3-2 represent an illustration of the tetrahedral grid generated for a complex 3D process with several etching and deposition steps. Figure 3-2 Final trench refil demonstrating void creation 43 Victory Cell User’s Manual Physical Models and Mesh Process Steps 3.1.3 Implantation and Diffusion VICTORY CELL uses a general purpose Monte Carlo (MC) ion implantation simulator. Its main purpose is the simulation of ion implantation for CMOS devices using physically-based models for stopping and ranges. It is capable of simulating implants into arbitrary surface topography and implant window sizes. The MC implantation simulator uses numerous algorithms to enhance the computational efficiency of ion implant simulation. Thus, being able to perform simulations into large structures in a reasonable amount of time, eliminating, or reducing the need for approximate 3D analytical models. VICTORY CELL also has the standard approach to the 3D ion implantation simulation by making use of analytical 1D profiles tabulated over wide energy range and ion doses. These are then given a lateral Gaussian tail to simulate the 3D dopant density distribution. The parameters for the 1D profiles are obtained either by simulation or experiment. The analytical model is well suited for deep well implants. To calculate dopant redistribution and activation during the anneal process step, the diffusion uses finite difference method for numerical solution of the systems of partial differential equations. The representation of the simulation domain is based on an immersed boundary grid model in which the interfaces of a complex region are cut across an irregular rectilinear Cartesian grid (see Figure 3-3). As a result, it is possible to use easy accessible data storage for structured nodes and an additional set of data for interface nodes along each grid line. This allows you to employ the highly efficient and well understood methods in the regions away from the boundary and confines the use of specific integration approach near the interfaces. Figure 3-3 Irregular Cartesian interval grid with immersed boundaries used in diffusion. 44 Victory Cell User’s Manual Etching and Deposition Process Steps 3.2 Etching and Deposition Deposition and Etch processes involve the laying down and removing of material in a controlled manner. These processes are two of the most important steps in the fabrication of modern interconnects. They allow the manufacture of multi-level interconnects required by the everincreasing density of active devices in circuits. Modeling deposition and etch are treated as the same mathematical process of moving the current surface of the simulation structure. With deposition, the surface is moved upwards and outwards as material is added. With etch, the surface is moved inwards and downwards as material is removed. Many of the descriptions in this section can be applied to both deposition and etch processes. VICTORY CELL provides you with two distinct modes, where you can simulate the deposition and etching steps. The first mode is the Geometric Mode, which allows you to quickly build up the Manhattan type structures. These are structures where all regions have either vertical or horizontal faces. The name comes from the look of the resulting structure somewhat resembling the skyline of Manhattan. The second mode is the more accurate Physical Mode (see Section 3.2.2 “Physical Mode”), which is based on parameters such as etch (deposition) rate, etch (deposition) time, and other parameters, provides a generic way of simulating the physics behind process steps, such as Chemical Vapor Deposition (CVD), Chemical Mechanical Polishing (CMP), or Reactive Ion Etching (RIE). The following sections describe the Geometrical and Physical modes, the terminology, and the models used for the simulation of deposition and etching processing steps. 45 Victory Cell User’s Manual Etching and Deposition Process Steps 3.2.1 Geometrical or Manhattan Mode The Geometrical Mode (Manhattan Mode) for deposition and etching in VICTORY CELL is intended to provide you with a fast and memory efficient way of creating complex structures. Apply this mode in situations where a precise physical simulation of the process step isn’t necessary. The examples in the following sections highlight this. Deposition The two main parameters that should be specified when invoking the geometrical deposition mode are the material that will be deposited and the final thickness of the material that is achieved with this processing step. A series of additional parameters will then specify how the thickness parameter is related to the current structure. MAX or PLANAR The MAX parameter (or its equivalent, the PLANAR parameter) applies the given deposition material thickness with respect to the highest point in the current structure. This means that the current structure is filled up to the highest point with the given material and an additional layer of this material is then deposited using the given THICKNESS. Figure 3-4a shows two polysilicon lines that run along the surface of a structure. The next processing step could now be to planarize the structure by depositing a layer of oxide by using the spin-on-glass technique. To simulate this in geometrical mode, use the Planar statement. Figure 3-4b illustrates the structure resulting from this step. Figure 3-4a: Two polysilicon lines running along the surface of a test structure Figure 3-4b: After a planarization step using DEPOSIT MAX 46 Victory Cell User’s Manual Etching and Deposition Process Steps MIN The MIN parameter works in a similar way. The reference point this time is the lowest point in the current structure. VICTORY CELL fills up the structure to the given THICKNESS with respect to the lowest point. Figure 3-5a shows a trench structure, where the next process step refills with TEOS. The normal process sequence would be to fill the trench and then to perform an etch-back step. In geometrical mode, you can combine this into one step by using the MIN parameter. The results of this operation are shown in Figure 3-5b. Figure 3-5a: Trench structure before TEOS refill. Figure 3-5b: Same structure as in 4-3, refilled with TEOS using DEPOSIT MIN. 47 Victory Cell User’s Manual Etching and Deposition Process Steps CONFORMAL Another option for the DEPOSIT statement is the CONFORMAL model. This adds a uniform layer of the given THICKNESS to the current structure. This mode can only be used in conjunction with Manhattan type structures. If it’s used on a structure containing faces other than vertical or horizontal faces, VICTORY CELL will automatically switch to the Physical Deposition Mode. Figure 3-6a shows a Manhattan-type, trench-like structure. Perform a deposition step using the CONFORMAL parameter, and the structure will be covered with a uniform layer of the new material. This is shown in Figure 3-6b. Figure 3-6a: Manhattan type trench-like structure Figure 3-6b: After a UNIFORM deposition step is carried out using geometric mode In conjunction with the CONFORMAL parameter, the STEPCOVERAGE parameter can be used. This parameter ranges from 0 to 1 and denotes the ratio between the layer thickness on vertical faces to the one on horizontal faces. See the “ISOTROPIC” on page 52 for more information. For a full list of options, see Section 4.4 “DEPOSIT”. 48 Victory Cell User’s Manual Etching and Deposition Process Steps Etching The two main parameters that should be specified when using the geometrical etching mode are the material that will be etched away and the final etch thickness that is achieved with this processing step. A series of additional parameters will then specify how the thickness parameter is related to the current structure. MAX The MAX parameter applies the defined THICKNESS with respect to the highest point in the current structure. VICTORY CELL, therefore, cuts away all of the specified material that lies above the point: z0 = HighestPoint – THICKNESS. This parameter is used, for example, when simulating a Chemical Mechanical Polishing process step in geometrical mode. Figure 3-7a shows two polysilicon lines covered by a uniform layer of silicon-dioxide. After applying the Etch statement, everything above a certain point is removed, reducing the original step height. The results are shown in Figure 3-7b. Figure 3-7a: Two polysilicon lines covered by a uniform layer of oxide Figure 3-7b: After performing a planarization step using ETCH MAX 49 Victory Cell User’s Manual Etching and Deposition Process Steps MIN or PLANAR The PLANAR parameter (or its equivalent, the MIN parameter) works in a similar way. This time, the THICKNESS parameter is applied with respect to the lowest point on the structure. Figure 3-8a shows the contact holes of some device that have been filled with aluminum. The next processing step could now be to planarize the structure completely for further deposition steps. The results of applying the PLANAR parameter are seen in Figure 3-8b. Figure 3-8a: Contact holes of a device that were filled Figure 3-8b: After an ETCH PLANAR command with aluminum 50 Victory Cell User’s Manual Etching and Deposition Process Steps UNIFORM The UNIFORM parameter is used to simulate undercut beneath the mask edge in geometrical mode. It can be used in conjunction with the ISOTROPIC parameter. Figure 3-9 illustrates where UNIFORM was used, together with ISOTROPIC = 0.2. Note that the length of the undercut is 20% of the total depth of the resulting trench. See also the discussion in the “ISOTROPIC” on page 52. For a full list of options, see Section 4.8 “ETCH”. Figure 3-9 Simulation of anisotropic etching, resulting in an undercut, in geometrical etch mode 3.2.2 Physical Mode The physical mode in VICTORY CELL provides a generic way of simulating both the deposition and etching processing steps. The main parameter of the simulation is TIME, where the process is to be applied to the current structure. VICTORY CELL divides this time into a number of small time steps and evaluates the evolution of the material front during these time steps. This approach allows an accurate simulation of the underlying physical process. The drawback, however, is the high demand on CPU time and memory. Therefore, you need to find a balance between using the physical mode when necessary for the accuracy of the simulation, and applying the geometric mode when the detailed result of the processing step is of little or no importance to the outcome of the final interconnect simulation. The other main parameter of this mode is the RATE which specifies the velocity, where the material front evolves. The rate can be constant over the whole front or can depend on the location on the material front and other parameters. Note: VICTORY CELL assumes that the TIME parameter is given in minutes, and the unit for RATE is given in microns/minute. In addition to these parameters, you can specify the ISOTROPIC and SIGMA parameters. Both parameters can be applied to the Deposit and Etch statements. 51 Victory Cell User’s Manual Etching and Deposition Process Steps ISOTROPIC The ISOTROPIC parameter ranges from 0 to 1. A value of one indicates a completely isotropic etching or deposition process. This is used to simulate a wet etching process, where the wafer is immersed in a solvent. The chemical reaction taking place is isotropic. Figure 3-10 shows an example of a wet etching process. Note that the undercut underneath the oxide mask is as long as the silicon hole is deep. Figure 3-10 Test structure illustrating the isotropic etch in the physical etch mode At the other extreme, ISOTROPIC=0 indicates a completely directional etching or deposition process. VICTORY CELL at the current time assumes that in this case, the direction where the material front evolves is along the z direction. A value of zero for the ISOTROPIC parameter could be used to simulate a highly tuned plasma etching process that shows little or no undercut underneath the mask. Figure 3-11 is an illustration of such a well-tuned plasma etch process. Figure 3-11 Test structure illustrating anisotropic etch in the physical etch mode The effect of the directional rate on the material front can be looked at as simply displacing all points of the material front by a distance of l=rate*dt along the z direction. This occurs in the negative z direction for deposition processes and in a positive z direction for etch processes. This point displacement (Equation 3-1) has the effect, where the front evolves along its normal at a rate of [1]. 52 Victory Cell User’s Manual Etching and Deposition Process Steps r = rdir  cos 3-1 The evolution along the normal to the front follows the cosine law usually assumes for etching and deposition. Figure 3-12 illustrates this for the case of etching. This figure shows the initial material front (initial line of action) and the final position of the front (advance due to rdir). Figure 3-12 Point Advance due to Directional Influence An intermediate value of the ISOTROPIC parameter represents a mixture between the two extreme cases mentioned above. The rate at which the material front evolves is composed of two vectorial components. One component represents the isotropic part and the other the directional part. The resulting rate vector will then be the sum of these two components, which is shown in Figure 3-13. Note that the shaded region in this figure represents a shadowed region where the front can’t be reached by the incoming particles from the plasma (i.e., no directional etching can take place). The etch rate components in this figure are given by: riso = ISOTROPIC  RATE 3-2 rdir = 1 – ISOTROPIC  RATE 3-3 where ISOTROPIC and RATE are the parameters to be specified with the ETCH statement. 53 Victory Cell User’s Manual Etching and Deposition Process Steps α α Figure 3-13 Regions of Significance of rdir and riso Figure 3-14 illustrates the effects of the directional and isotropic rate component for the case of a deposition process. This figure shows a barrel shaped hole, which is lined with a layer of TEOS using a value of 0.2 for the ISOTROPIC parameter. The deposition rate was 80% directional and 20% isotropic. You can clearly see this at the oxide mask where the final thickness of TEOS is about only 20% on the vertical faces with respect to the horizontal top faces. Note that the thin lining inside the barrel and the thick bulge of TEOS at its center. This is due to the shadowing of incoming particles by the oxide mask. The jump in thickness of the TEOS layer exactly corresponds to the projection line of the oxide mask. The slight slope of this jump results from the slight inwards movement of the projection line due to the deposition of TEOS on the vertical faces of the oxide mask. 54 Victory Cell User’s Manual Etching and Deposition Process Steps Figure 3-14 Hole structure illustrating shadowed deposition capabilities in physical mode. SIGMA When choosing a value of zero for the ISOTROPIC parameter, VICTORY CELL assumes that all incident particles travel along the z direction. Moreover, this assumption isn’t always valid. In plasma etching processes, the particles leaving the plasma will have a certain spread in direction around the average, preferred direction. In the case of deep trench or via etching, this leads to what is often referred to as a barrel shape like structures. This effect is highly undesirable, since it can result in the formation of voids during the refill of the trench or via. In the same way for deposition processes, the distribution of the particle direction may not be constant. VICTORY CELL allows you to take this effect into account by specifying the SIGMA parameter. The distribution function of the particle movement is assumed to be Gaussian and isotropic. The functional relationship of the distribution function is given by:  = 0  exp    –2----------S----I--G-2----M-----A----2-- 3-4 where  is the incident angle of the particles with respect to the z-axis, and 0 is chosen so that the integral over  from 0 to  /2 is normalized. The SIGMA parameter determines the spread of the distribution function and can take on any value greater than zero. For a value of zero, this reduces to the purely directional case simulated by specifying ISOTROPIC=0. Given the distribution function of the incoming particles, VICTORY CELL calculates the particle flux in each point of the surface by integrating over the distribution function. To do so, VICTORY CELL needs to determine the “visibility window” of each point. The visibility window is that area on top of the simulation box that can be seen from a given point on the surface of the simulation structure. Generally, the visibility window consists of one or more complex polygons. Once the particle flux is determined for every point on the surface, the flux is multiplied by the deposition or etching RATE and the points on the surface are moved accordingly. 55 Victory Cell User’s Manual Etching and Deposition Process Steps Figure 3-15 shows a cut through a structure featuring an L-shaped trench. In this structure, a layer of silicon dioxide is deposited using a value of ISOTROPIC=0.2 and SIGMA=0.5. The effect that the particular value of ISOTROPIC has on the deposition process can be seen clearly at the sides of the trench, where the layer thickness of the oxide is only about 20% of that on top of the structure. Figure 3-15 Cut through an L-shaped trench structure illustrating the effects that SIGMA has on the deposition result The effect that SIGMA has on this step in the process is somewhat more subtle. At the bottom of the trench, you can see a variation in oxide thickness decreasing slightly from the center of the trench towards its side walls. This variation is due to the decreasing size of the visibility window and the particular form of the distribution function. At the center of the trench, is the normalized particle flux, despite the limited visibility, nearly equal to 1.0 due to the localized peak in the distribution function. Next to a side wall of the trench, the particle flux is only about 0.5 since one half of the hemisphere is blocked by the trench wall at this location. This means that in Figure 3-16, only one half of the distribution function contributes to the integral, leading to a particle flux of about 0.5. Figure 3-16 Test structure illustrating etch loading effects controlled by SIGMA 56 Victory Cell User’s Manual Etching and Deposition Process Steps Figure 3-16 shows two interesting effects that the particle distribution function has on the etching process. This figure shows three trenches with different widths, all etched at the same time into the silicon dioxide layer. First, note the bowing (or barrel shape) underneath the mask is the result of particles not only reaching the surface parallel to the z-axis (in this case no undercut would be created) but also of particles moving in directions which are slightly off the average direction. Second, observe the different depths that are reached in this etching step. As the width of the trench increases, the depth which is reached also increases. This effect, often referred to as micro loading, is due to the combined effect that the size of the visibility window and the shape of the distribution function has on the final surface profile. As the width of the trench increases, so does the size of the visibility window leading to an increased particle flux reaching the bottom of the trench. 57 Victory Cell User’s Manual Oxidation Process Steps 3.3 Oxidation The Oxidation Model can be used to simulate the oxidation process for a limited set of structures. The implementation of this module is based on the work of Guillemot, Pananakakis, and Chenevier [2] who present in their article a model to describe the formation of semi-recessed LOCOS structures often referred to as the “bird’s beak”. The use of the OXIDIZE command is limited to Manhattan type structures, which are structures where the individual layers only have vertical or horizontal faces. Furthermore, the silicon substrate is assumed to be planar and covered by a uniform initial layer of silicon dioxide. This is referred to as the pad oxide. The nitride is masked but, where present, it must have the same thickness throughout the structure. The materials involved in the LOCOS formation are limited to silicon (Si), silicon-dioxide (SiO2) and silicon nitride (Si3N4). The module simulates the “bird's beak” oxide shape for different thicknesses of the nitride mask. It features three modes of operation: ERFC, ERFC0, and ERFC1. The ERFC0 model describes the oxide growth underneath a thin nitride layer, where the stress from the nitride mask layer is negligible. The ERFC1 model describes the oxide growth when nitride layer thicknesses are large enough to cause stress in the oxide, which can result in the oxide layer being pinched. When the default ERFC mode is used, the program automatically chooses one of the models depending on the structure under consideration. Both models are based on the error-function shape of the oxide/silicon and oxide/ambient or oxide/nitride interfaces: Z = AerfcBy + C + D 3-5 Here, the A, B, C, and D parameters are complex functions of several geometric parameters: initial thickness of the oxide lox and nitride ln, current thickness Eox of the oxide given by the Deal-Grove model [3], the length of the lateral oxidation underneath the nitride layer Lbb, and the lifting, H, of the nitride mask during oxidation. All default coefficients were taken from [2] and are given in Appendix A:Appendix A “Default Parameters”. The OXIDIZE command can be applied to structures of all three dimensions. Since the underlying analytic model is inherently two dimensional, in 3D the program propagates a two-dimensional cut along the edges of the nitride mask resulting in a three dimensional LOCOS profile. This method doesn’t take into account the increased lifting of the nitride mask in corner areas which is due to an enhanced flow of oxygen towards the silicon/oxide interface. This approach is valid for structures, where the lateral extent of the “bird’s beak” Lbb [2] is small compared to the length of the mask edges. 58 Victory Cell User’s Manual Oxidation Process Steps Figure 3-17 shows a typical “bird’s beak” structure, which results after oxidizing the initial structure for 70 minutes at a temperature of 950°C. Figure 3-17 Typical LOCOS structure showing the “Bird’s Beak” formation underneath the nitride mask 59 Victory Cell User’s Manual Lithography Process Steps 3.4 Lithography 3.4.1 The Imaging Module VICTORY CELL includes an imaging module that uses the Fourier series approach. The theoretical resolution (RES) and Depth Of Focus (DOF) of a microlithographic exposure system are approximated by: RES = k1  N-----A-- 3-6 and DOF= k2  --------------NA2 3-7 where  is the wavelength of the exposing radiation, NA is the Numerical Aperture of the imaging system, and k1 and k2 are process dependent constants. Typical values for k1 are 0.5 for a research environment and 0.8 for a production process; the value usually assigned to k2 is 0.5. We’ll discuss the basic assumptions upon of the model. Then, we’ll derive the principal equations used for calculation of the image irradiance distribution for objects illuminated by partially coherent light. The treatment presented here assumes the radiation incident on the object to be quasimonochromatic, which means that the spectral bandwidth is sufficiently narrow so that wavelength-dependent effects in the optics or in diffraction angles are negligible. The source is of a finite spatial extent so that the advantages of spatial incoherence are realized in imaging. The mask is completely general in that phase and transmission are variable, but it must be composed of rectangular features. The calculation of the diffraction phenomena is based upon the scalar Kirchhoff diffraction theory. Since the dimensions of the mask are almost the same as the illumination wavelength, we can ignore any polarization taking place as the radiation propagates through the mask. We assume scalar diffraction, which means neglecting the vector nature of the radiation. This is acceptable if all convergence angles are small. According to Watrasiewicz [4], who experimentally investigated the limiting numerical aperture, the breakdown of the scalar theory occurs at angles of convergence greater than 30 degrees, which corresponds to a numerical aperture of 0.5. Similar results were published by Richards and Wolf [5], who used theoretical calculations to investigate the electromagnetic field near the focus produced by an aplanatic system working at a high convergence angle. They also found appreciable departures from scalar theory for convergence angles larger than 30°. Since the convergence angles are calculated in air, we can assume that the accuracy of this model is even better inside the photoresist, where angles are reduced in accordance with Snell’s law. Consequently, it can be stated that the scalar diffraction theory gives a reliable limit for imaging system numerical apertures of 0.5. 60 Victory Cell User’s Manual Lithography Process Steps The approach used for calculation of the image irradiance distribution is based on the work of Hopkins [6, 7], who showed that the partially coherent illumination of the object structure may be simulated in practice by the incoherently illuminated exit pupil of the condenser. The exit pupil serves as an effective source that produces the same degree of coherence in the illuminated object plane as the actual condenser system. The degree of coherence in the object plane is thus determined by the shape and angular size of the effective source. The condenser system is assumed to be diffraction limited, that is, free of aberrations. Residual aberrations of the illuminator do have an appreciable influence on the final image for Koehler type illumination systems, as shown by Tsujichi [8]. Figure 3-18 shows a schematic diagram of a generalized optical system. The actual source and the condenser system are replaced by the equivalent effective source having an irradiance distribution of x0 z0 . The effective source for the object plane U is taken to lie in the exit pupil reference sphere of the condenser lens. This means that directing from arbitrary points x0, z0 on the effective source, plane waves propagate towards the object plane U having irradiance values of x0 z0 . source (condensor) reticle plane Imaging system X X P P′ Image plane U′ h0 α0 P0 h α E X U h′ α′ E′ Figure 3-18 Schematic Diagram of a Generalized System The reduced coordinates [6] on the object plane are defined as: u = -2----  n  sin    3-8 v = 2-----  n  sin    3-9 where  and  are the Cartesian coordinates of the object plane, 2 is the absolute value of the wave vector, and n  sin is equal to the numerical aperture NA in the imaging system. Primed quantities indicate the corresponding coordinates and angles in the image space of the projection system. The fractional coordinates on the object pupil spheres are defined as: 61 Victory Cell User’s Manual Lithography Process Steps x = -- 3-10 h z = -h-- 3-11 where h is the radius of the pupil and the fractional coordinates of the exit pupil of the condenser are given by: x0 = -x- 3-12 z0 = -z- 3-13 In this equation:  = n----0n--------ss---ii--nn--------0-- 3-14 where 0 and  are angular semi-apertures of the condenser and the objective respectively. n0 and n are the refractive indices in the image space of the illuminator and the object space of the imaging system, which is usually both are set to one. The ratio  is the radius of the effective source referred to the aperture of the objective and governs the degree of spatial coherence in the object plane. The limits   0 and    correspond, respectively, to coherent and incoherent illumination. The object is taken to be infinitely thin, so it can be described by a complex amplitude transmission function, which gives the change in magnitude and phase produced on the radiation passing through it. The object has the complex transmission A(u,v). Its real part is given by: Au v=    1 in transparent areas 0 in opaque areas 3-15 The complex amplitude of the Fraunhofer diffraction pattern on the entrance pupil reference sphere at E of the imaging system is given, apart from a constant factor, by: ax z= 2--1----Au v  exp–iux + vz dudv 3-16 which is the inverse Fourier transform of the complex amplitude transmission of the object. If not stated otherwise, integration ranges from –  to +  . If the object is illuminated by an element dx0 dz0 of the effective source at x0 z0 with its amplitude proportional to x0 z0 , then the object spectrum a(x,z) is shifted by a corresponding amount. In this instance, the complex amplitude distribution on the entrance pupil sphere of the objective is: x0 z0  ax – x0 z – z0 3-17 62 Victory Cell User’s Manual Lithography Process Steps The complex amplitude on the exit pupil reference sphere at E’ will be given by: ax z= x0 z0  ax – x0 z – z0fx z 3-18 In this equation, f(x,z) denotes the pupil function of the optical system. If the system has an annular aperture, where the central circular obstruction has the fractional radius  , the pupil function has the form: fx z =        0  0 x z  expi  k  Wx z x2 + z2  2 x2 + z2  1 x2 + z2  1 3-19 (x,y) is the pupil transmission which is usually set to one and W(x,z) denotes the wave-front aberration. For an entirely circular aperture,  becomes zero. Note that the approach taken here is somewhat similar to the one used in the investigations on phase contrast microscopy [12]. The function, W(x,z), gives the optical path difference between the real wave-front and the exit pupil reference sphere. Commonly the wave-front aberration is expanded into a power series [6], giving:  Wx z = Wl m n2 + 2l + X + Zmx2 + z2n 3-20 l m n for a particular position (x,z) in the exit pupil.  and  denote the fractional coordinates of the image field. The values of l, m, and n describe the order of aberrations, while the coefficients, W(l,m,n) determine the magnitude of the aberrations. For third order aberrations l, m, and n take on the following values: l=0 , m=0 , n=2 : spherical aberration l=0 , m=1 , n=1 : coma l=0 , m=2 , n=0 : astigmatism l=1 , m=0 , n=1 : field curvature l=1 , m=1 , n=0 : distortion l=0 , m=0 , n=1 : defocus where isoplanatism is assumed for the particular section of the image field for which the irradiance distribution is calculated. The coefficient, W001, can be determined from: W001 =   ---n----------s--i--n-------------2-2 3-21 where  refers to the distance of the defocused image plane to Gaussian image plane. 63 Victory Cell User’s Manual Lithography Process Steps The resulting amplitude in the image plane due to a wave coming from the point x0,z0 of the effective source is: Ax0 z0;u v= --1---2  x0 z0  ax – x0 z – z0  expiux + v z  dxdz 3-22 where (u’,v’) refers to a point in the image plane. The irradiance distribution associated with the illuminating wave of the effective source will then be represented by: dIx0 z0;u v= Ax0 z0;u v 2dx0dz0 3-23 Since, by definition, the effective source is equivalent to a self-luminous source, the total irradiance at (u’, v’) can be obtained by integrating over the entire source  . Iu v =   Ax0 z0;u v dx0dz0 3-24  where  indicates the area of the effective source for which x0 z0 has non-zero values. For this purpose, Equation 3-24 is put into the form:   Iu v = x0 z0  x0 z0; u v 2dx0dz0 3-25  where: x0 y0; u v = --1---2  ax – x0 y – y0   fx y  exp iu x + vy  dxdy 3-26 x0 z0 ;u v is proportional to the intensity at the point u v due to a wave of unit irradiance passing through x0 z0 of the effective source. In the case of an annular shaped source x0 z0 has the form:    0 for x20 + z20  20  x0 z0 =    1 for x 2 0 + z20  1 3-27    0 for x 2 0 + z20  1  where 0 is the fractional radius of the centered circular obstruction in the exit pupil of the condenser lens. For a circular exit pupil, 0 becomes zero. 64 Victory Cell User’s Manual Lithography Process Steps Equation 3-25 is the principle relation of a generalized Abbe Theory, where the image formation under partially coherent illumination of the object is accounted for by a combination of coherent imaging processes for perpendicular and obliquely incident illuminating plane waves on the object. Since only the image irradiance itself is of interest, it can be determined without using the coherence theory [7] explicitly. For the computation, the whole source is divided into a number of luminous point sources considering the imaging due to each source as an independent coherent image formation process. The contributions from each point source don’t interfere, so the net image irradiance is the sum of the irradiance from each source point. The normalization used in the image calculations is that the mask is illuminated with unit irradiance, so that the ideal image has unit irradiance, where unit magnification is assumed. Therefore, the brightness of the source decreases as its size increases. The object spectrum (see Equation 3-16) is calculated analytically and the coherent image (see Equation 3-23) is calculated using a Fourier Series approach. The shape of a single mask feature must be rectangular. This is due to the fact that the Fourier transform for a rectangular feature is calculated based on an analytical formula. Since the Fourier transform is linear, arbitrary shaped mask features can be composed from the rectangular components. The object spectra of the single mask features (components) are simply added up. The treatment can thus be considered as being exact and no numerical discretization errors in the size and placement of the mask features can occur. 3.4.2 Optical System The optical system used by VICTORY CELL is shown in Figure 3-19. The meshes in the Fourier and Image planes are totally independent. There is no mesh in the object or reticle plane. α’ α source condensor reticle projection lens aperture projection image plane stop lens Figure 3-19 The Generalized Optical System 65 Victory Cell User’s Manual Lithography Process Steps 3.4.3 Digitization Errors The size of the window in the reticle plane (Equation 3-28) is determined by the number of mesh points in the projector pupil, the numerical aperture, and by the chosen wavelength: CW = NP  lambda  NA 3-28 where: • CW is a computational or sampling window (mask or image cell) in the object or reticle plane. • NP is the number of mesh points in the projector pupil. • NA is the numerical aperture of the stepper. • Lambda is the chosen wavelength. For an i-line stepper with NA = 0.54, the size of the sampling window is the square whose side length is equal to 6.8m10  0.365  0.54 . No mask feature should exceed this dimension. You can increase the size of the sampling window for this particular stepper to any size simply by increasing the number of mesh points in the projector pupil. This will be done automatically to accommodate the mask and image windows that have been specified. Mask features can’t be placed outside of the sampling window. As mentioned earlier, the image mesh is totally independent of the mesh in the Fourier plane. This allows you to arbitrarily specify the number and distance of image points. 66 Victory Cell User’s Manual Ion Implantation Models Process Steps 3.5 Ion Implantation Models VICTORY CELL uses analytical and statistical techniques to model ion implantation. By default, the analytic models are used. Analytical models are based on the reconstruction of implant profiles from the calculated or measured distribution moments. The statistical technique uses the physically based Monte Carlo calculation of ion trajectories to calculate the final distribution of stopped particles. 3.5.1 Analytic Implant Models VICTORY CELL uses spatial moments to calculate ion implantation distributions. This calculation method is based on range concepts from “Range Concepts and Heavy Ion Ranges” [9] in which an ion-implantation profile is constructed from a previously prepared (calculated or measured) set of moments. A 3D-distribution could be essentially considered a convolution of a longitudinal (along the implant direction) 1D-distribution and two transverse (perpendicular to implant direction) 1D-distributions, which are orthogonal to each other. In the rest of this section, we will first describe three 1D implant models and the method used to calculate 1D profiles in multi-layered structures. Then, the model of transverse (lateral) distribution and a method of construction of 3D implant profiles will be outlined. Gaussian Implant Model There are several ways to construct 1D profiles. The simplest way is using the Gaussian distribution: Cx = --------------------- exp –------x----–-----R----p-----2- 3-29 2R 2Rp2 where  is the ion dose per square centimeter specified by the DOSE parameter. Rp is the projected range.  Rp is the projected range straggling or standard deviation. Pearson Implant Model Generally, the Gaussian distribution is inadequate because real profiles are asymmetrical in most cases. The simplest and most widely approved method for calculation of asymmetrical ion-implantation profiles is the Pearson distribution, particularly the Pearson IV function. VICTORY CELL uses this function to obtain longitudinal implantation profiles. The Pearson function refers to a family of distribution curves that result as a consequence of solving the following differential equation: d----fd---x-x---- = ---------x-----–----a------f----x---------b0 + b1x + b2x2 3-30 in which f(x) is the frequency function. The constants a, b0, b1, and b2 are related to the moments of f(x) by: a = –-----R---p------A-------+-----3---- 3-31 b0 = –-----R---2-p--------4--A------–----3-------2--- 3-32 67 Victory Cell User’s Manual Ion Implantation Models Process Steps b1 = a 3-33 b2 = –2---------–----A---2----–-----6-- 3-34 where A = 10 - 122 - 18,  and  are the skewness and kurtosis respectively. These Pearson distribution parameters are directly related to the four moments (1 2 3 4 ) of the distribution f(x): Rp = 1 Rp = 2  = ------3-Rp3  = ------4-Rp4 3-35 i is given by:   1 = xfxdx 3-36 –   i = x – Rpifxdx i = 2 3 4 3-37 – The forms of the solution of the Pearson Differential Equation depend upon the nature of the roots in the equation b0+b1x+b2x2=0. There are various shapes of the Pearson curves. You can find the complete classification of various Pearson curves found in “Atomic and Ion Collision in Solids and at Surfaces” [10]. Obviously, only bell-shaped curves are applicable to ion implantation profiles. It is readily shown by Ashworth, Oven, and Mundin [11] that f(x) has a maximum when b0+b1x+b2x2 < 0. You can reformulate this as the following relation between  and  : 9    62 + 5 + 96  16 + 84 + 252 + 1 1  2     -----------------------------------------------------------------------------------------------------------------------------50 – 2 3-38 with the additional constraint that 2 <50. Only Pearson type IV has a single maximum at x = a+Rp and monotonic decay to zero on both sides of the distribution. Therefore, Pearson type IV is usually used for ion implantation profiles. It is the solution of Equation 3-29 when the following conditions are satisfied:  = -3---9------2----+-----4----8----+-----6---------2----+-----4------3------2- and 0  2  32 3-39 32 – 2 68 Victory Cell User’s Manual Ion Implantation Models Process Steps This gives the following formula for Pearson IV distribution: fx = Kb0 + b1x – Rp + b2x – Rp22----1b----2 exp – --------bb--------12-----+-----2----a--------- atan   -2---b---2------x----–-----R---p-------+-----b---2- 4b1b2 – b21  4b1b2 – b21  3-40 where K is defined by the constraint:   fxdx = 1 . 3-41 – In the narrow area of  – 2 plane where Pearson IV type criterion (Equation 3-39) is not satisfied while bell-shaped profile criterion (Equation 3-38) holds VICTORY CELL, by default, uses other than type IV Pearson functions. These functions are bell-shaped but they are not specified over the whole (–  ) interval. Usually, this doesn’t affect the quality of calculated profiles because the limits of these functions are situated far from their maximums. In all cases when  and  do not satisfy one of the mentioned criteria, VICTORY CELL will automatically increase  up to the value that satisfies the criterion used. In the standard Pearson model, the longitudinal dopant concentration is proportional to the ion dose  : Cx = fx 3-42 This single Pearson approach (method) has been proved to give an adequate solution for many ion/substrate/energy/dose combinations. But, there are many cases when the channeling effects make the Single Pearson Method inadequate. Dual Pearson Model To extend applicability of the analytical approach toward profiles heavily affected by channeling, Al Tasch [12] suggests the dual (or Double) Pearson Method. With this method, the implant concentration is calculated as a linear combination of two Pearson functions: Cx = 1f1x + 2f2x 3-43 where the dose is represented by each Pearson function f1,2(x), f1(x), and f2(x) are both normalized, each with its own set of moments. The first Pearson function represents the random scattering part (around the peak of the profile) and the second function represents the channeling tail region. Equation 3-42 can be restated as: Cx = f1x + 1 – f2x 3-44 where  = 1 + 2 is the total implantation dose and  = 1   . To use dual Pearson distribution, supply nine parameters— four moments for each Pearson function with the dose ratio  . The dual Pearson model will be used only when all nine parameters are present in internal tables. Otherwise, the single Pearson formula will be used. 69 Victory Cell User’s Manual Ion Implantation Models Process Steps SIMS-Verified Dual Pearson (SVDP) Model By default, VICTORY CELL uses SIMS-Verified Dual Pearson (SVDP) implant models. These are based on the tables from the University of Texas at Austin. These tables contain dual Pearson moments for B, BF2, P, and As extracted from high quality implantation experiments are also conducted by the University of Texas at Austin. Table 3-1 show these implantation tables contain dose, energy, tilt, rotation angle, and screen oxide thickness dependence. Table 3-1 Range of Validity of the SVDP Model in Victory Cell Ions Energy (keV) Dose (cm-2) Tilt Angle(°) Rotation Angle(°) Screen Oxide (Å) B 1 100a BF2 1 80c P 12 200d As 1 200e 1013  81015 0  10 1013  81015 0  10 1013  81015 0 10 1013  81015 0  10 0  360 0  360 0  360 0  360 native oxide  500b native oxide native oxide native oxide a Experimentally verified for 5-80keV. For energy range, 1-5keV, an interpolation between 5keV and 0.5keV calculated with UT-MARLOWE, is used; an extrapolation is used for energy range 80± 100keV. b Only for 15-80keV. c Experimentally verified for 5-65keV. For energy ranges, 1-5keV and 65-80keV, the same procedures is used for boron. d Experimentally verified for 15-80keV. Numerical extrapolation is outside this energy range. e Experimentally verified for 5-180keV. Interpolation between 5keV and UT-MARLOWE, [16], calculated profile at 0.5keV. If you choose a simulation outside the parameter ranges, described in Table 3-1, VICTORY CELL will not use the Dual Pearson Implant SVDP Models but will use the standard tables instead. When using the Dual Pearson model, remember the following: • For implant energies below 15keV, for boron, BF2 and arsenic, the simulation predicts the dopant profiles for implants into a bare silicon surface (i.e., silicon wafer subjected to an HF etch less than two hours before implantation). Low energy implant profiles at such low implant energies are found to be extremely sensitive to the presence of a thin (0.51.5nm) native oxide layer or disordered silicon layer on the wafer surface [13]. Remember this fact when using the model for the simulation of low energy ion implantation and when performing implantations. • For implant energies between 10keV and 15keV, the simulations are performed for boron, BF2, and arsenic by using an interpolation between the Dual Pearson Model parameters at 15keV, and the Dual Pearson Model parameters at 10keV. The parameters at 15keV correspond to implantation through a native oxide layer (0.5-1.5nm), while the parameters at 10keV correspond to implantation into a bare silicon surface (i.e., silicon wafer subjected to an HF etch less than two hours before implantation). • For implant energies below 5keV, the models for boron, BF2, and arsenic have not been verified experimentally. The simulations in this range of implant energy are performed using an interpolation between experimentally verified Dual Pearson parameters at 5keV and parameters based on UT-MARLOWE estimates at 0.5keV. 70 Victory Cell User’s Manual Ion Implantation Models Process Steps • The SIMS measurements upon which these profiles are based have a concentration sensitivity limit in the order of 5  1015 to 2  1016cm–2 , increasing with dose from the implant. The profiles have been extended below these limits, following the trends that occur within the sensitivity limits of the SIMS. • The screen oxide thickness range has been verified from 1.5 to 40nm (only for boron and 15-80keV energy range). But the oxide range has been extended to 50nm. Creating Three-Dimensional Implant Distributions VICTORY CELL calculates 3D implant distributions inside the whole simulation domain using integration of “point-source” 3D functions build by convolution of 1D longitudal (vertical) profiles described in the previous section with 2 orthogonal Gaussian functions in transversal (lateral) directions. This “point-source” function represents the 3D distribution generated by ions implanted through the single point (xi, yi) at the top surface of simulation box: fix, y, z = fLz, xi, yiGx, xiGy, yi 3-45 where fL(z, xi, yi) is 1D profile (Gauss, Pearson, or Dual Pearson distribution) calculated at the point (xi, yi) and Gaussians are: Gx, xi = --------1---------2Y exp –------x-2---–-----Yx---i----2- 3-46 Gy, yi = --------1---------2Y exp –------y-2---–-----Yy---i----2- 3-47 where (Y is the transversal (lateral) standard deviation. The single point-source function in Equation 3-45 is analytically integrated over rectangular element (dxi, dyi) with centre at the point (xi, yi) : Cix, y, z = fLz, xi, yi  erfcx-----–----x---i---–-----0---.--5----d---x---i – erfc x-----–----x---i---–-----0---.--5----d---x---i 2Y 2Y  erfc y-----–----y---i---–-----0---.-5----d---y---i – erfcy-----–----y---i---–-----0---.--5----d---y---i 2Y 2Y 3-48 After that the normalized doping concentration in each point (xj, yj, zj) of Cartesian grid is calculated by summation of contribution from all rectangular elements:  Cxj, yj, zj = Cixj, yj, zj 3-49 i To speed up calculations, only elements within 6Y distance from (xj, yj, zj) are taken into account. 71 Victory Cell User’s Manual Ion Implantation Models Process Steps 3.5.2 Monte Carlo Implantation Model The analytical models described in the previous section give very good results when applied to ion implantation into simple planar structures (bare silicon or silicon covered with thin layer of other material). But for structures containing many non-planar layers (material regions) and for the cases, which have not been studied yet experimentally requires more sophisticated simulation models. The most flexible and universal approach to simulate ion implantation in non-standard conditions is the Monte Carlo technique. This approach allows calculation of implantation profiles in an arbitrary structure with accuracy comparable to the accuracy of analytical models for a single layer structure. VICTORY CELL’s physically based Monte Carlo ion implantation simulator uses numerous algorithms to enhance the computational efficiency of ion implant simulation. Thus, being able to perform simulations into large structures in a reasonable amount of time, eliminating, or reducing the need for approximate 3D analytical models. The MC implantation simulator could be divided into three logically separate units– physical model, topography and target description, and optimization/acceleration algorithms. Advanced physical model is critical for a predictive ion implantation and our implementation in the MC simulator is described elsewhere [14, 15]. To keep the efficiency of the algorithm, the damage model implemented is that of Kinchin-Pease, [16, 17]. The interstitial and vacancy concentrations are derived from the Frenkel pairs (FP) distribution, differing only by the impurity concentration (the so called "+1" model). It is possible to modify this behavior to "+n", which is more suitable for heavy ions. The simulator maintains its own adaptive grid, which fits to the desired topology, thus, treating effectively shadowing, reflection and reimplantation effects. One of the critical and time consuming tasks of MC ion implantation in crystalline materials is finding the neighboring atoms for interaction. Because of crystal symmetry, a special search algorithm needs to be implemented. The present algorithm implements special look-ahead techniques, which, compared to previous 2D MC simulator, accelerate three to four times the finding of a collision partner. In addition, a rare-event and a stratified-sampling algorithms are implemented in order to improve statistics along depth or about fine special details in the topology. Furthermore, in case of simple topologies, the program can use trajectory replication for flat (i.e., 1D in character) regions. Nature of the Physical Problem A beam of fast ions (energy range, approximately 50 eV/amu to 100 keV/amu) entering crystalline or amorphous solid is slowed down and scattered due to nuclear collisions and electronic interaction. Along its path, an individual projectile may create fast recoil atoms that can initiate collision cascades of moving target atoms. These can either leave the surface (be sputtered) or deposited on a site different from their original one. Together with the projectiles being deposited in the substrate, this results in local compositional changes, damage creation and finally amorphization of the target. Depending on the crystal orientation or the direction of the beam or both, the implanted projectiles and the damage created by them has different spatial distribution. With even more higher fluency, these phenomena will cause collisional mixing in a layered substances, changes of the surface composition due to preferential sputtering, and the establishment of a stationary range profile of the implanted ions. 72 Victory Cell User’s Manual Ion Implantation Models Process Steps Method of Solution The paths of the individual moving particles and their collisions are modeled by means of the binary collision approximation for a crystalline, polycrystalline and amorphous substance, using a screened Coulomb potential for the nuclear collisions and a combination of local and non-local free-electron-gas approximation for the electronic energy loss. For each nuclear collision, the impact parameter and the Azimuthal Deflection Angle are determined according to the crystal structure using its translational symmetry. For amorphous materials, the impact parameter and the azimuthal deflection angle are determined from random numbers. A proper scaling is chosen so that each incident projectile (pseudo-projectile) represents an interval of implantation dose. Subsequent to the termination of each pseudo-projectile and its associated collision cascades, the local concentrations of the implanted species, created vacancies and interstitials are calculated according to the density of the matrix. Nuclear Stopping As mentioned before, during their passage through matter ions interact not only with the atoms from the lattice but also with the electrons. Figure 3-20 shows the scattering geometry of two particles in the Laboratory Coordinate System. In the computational model, it is assumed that ions from one deflection point to the next move along straight-line segments, these being the asymptotes of their paths. At each collision, ion loses energy through quasielastic scattering by a lattice atom and by an essentially separate electron energy loss part. Figure 3-20: The trajectories of the ion (projectile) and the lattice atom (recoil) The scattering angles of the projectile and the recoil are as follows: tan 1 = Af sin   1 + Af cos 3-50 tan2 = f sin  1 + f cos  3-51 73 Victory Cell User’s Manual Ion Implantation Models Process Steps where: f = 1 – Q  Er 3-52 Q is the energy lost by electron excitation. A = M2  M1 is the ratio of the mass of the target (scattering) atom to that of the projectile (implanted ion).  is the barycentric scattering angle calculated as follows:   =  – 2p -------1-------- dr R r2gr 3-53 where: gr = 1 – p----2r2 – V---E----rr--- where: • p is the impact parameter, • Er = AE0  1 + A is the relative kinetic energy, • E0 is the incident energy of the projectile, • r is interatomic separation, • Vr is the interatomic potential, • R is defined from equation gR = 0 . In VICTORY CELL, the intersections of the incoming and outgoing asymptotes are evaluated with the hard core approximation of the time integral: x1 = p tan  2 3-54 x2 = 0 3-55 74 Victory Cell User’s Manual Ion Implantation Models Process Steps Interatomic Potential VICTORY CELL uses two-body screened Coulomb potentials with a screening function, which is a numerical fit to the solution given by Firsov [18]. It also preserves the same analytic form as for the isolated atom: Vr = Z----1---Z--r--2---e---2-    -a-r--0- 3-56 where Z1 and Z2 are the atomic numbers of the two atoms and a0 is the screening length defined by a0 = 0.8853aBZ–1  3 3-57 where Z is an ‘average’ atomic number of the two atoms calculated as Z–1  3 = Z10.23 + Z20.23–1M . 3-58 The main drawback of these two-body potentials is their relatively slow decay as r   . The screening parameter, a0 , is often regarded as an adjustable parameter for each two-body combination, which can be matched either to self-consistent field calculations or to experimental data. VICTORY CELL uses the screening function in the form 4   = ai exp–bix 3-59 i=1 where ai and bi are taken from [19]. 75 Victory Cell User’s Manual Ion Implantation Models Process Steps Electronic Stopping Electronic stopping used in the simulation consists of two essentially separate mechanisms for inelastic energy losses: local and non-local. These two types of electronic stopping are quite different in nature and behavior– they have different energy and spatial dependencies [20]. The local inelastic energy losses are based on the model proposed by Firsov [21]. In this model, the estimation of the electronic energy loss per collision is based on an assumption of a quasi-classical picture of the electrons (i.e., the average energy of excitation of electron shells, and electron distribution and motion according to the Thomas-Fermi model of the atom). In this quasi-classical picture, the transfer of energy, E , from the ion, to the atom, is due to the passage of electrons from one particle to the other. Thus, resulting in a change of the momentum of the ion (proportional to its velocity , , and a rising of a retarding force acting on the ion). When ions move away from the atom (despite being trapped by ions) electrons will return to the atom. There is no transfer of momentum calculated back, because the electrons fail in higher energy levels. The energy loss in the Firsov's Model is calculated as follows: –E = -0---.--0---5---9----7---3------------Z---1-----+-----Z---2-----5------3--------E-------M-----1--eV 1 + 0.31Z1 + Z21  3R05 3-60 where: • R0 is their distance of closest approach in A , which is approximately equal to the impact parameter in case of small-angle collisions. • E is the energy of the moving atom (the ion) in eV. • M1 is its mass in a.m.u. In a binary collision, the scattering angles are affected by the inelastic energy loss E (see Equation 3-60) through the parameter f . The non-local electronic energy losses are based on the model proposed by Brandt and Kitagawa [22]. Their stopping power, S = –d-d---Ex-- , of the medium for an ion is in the first approximation proportional to a mean-square effective ion charge. They derive the effective stopping power charge of a projectile, Z1 from a given ionization state, q. If a fractional effective charge of an ion with the given ionization state, q is defined as   Z--Z--1--1-- = S----q-S---=q----1- 1  2 3-61 where Sq = 1 is the stopping power for bare nucleus. Brandt and Kitagawa theories produces the following simple expression for the fractional effective charge of an ion:   q + CkF1 – q ln 1 + 2vFa0v02 3-62 76 Victory Cell User’s Manual Ion Implantation Models Process Steps where: • q = Z1 – N  Z1 is the fractional ionization, • N is the number of electrons still bond to the projectile nucleus, • a0 and r0 are Bohr's radius and velocity, • kF and vF are Fermi wave vector and velocity. For the screening radius  , Brandt and Kitagawa assume exponential electron distribution, which becomes:  = -Z---1------10----.–-4----8N---N----2---7---3-N----1------ 3-63 The only undefined quantity, C, is of about 0.5 and somewhat depends on the target. The degree of ionization, q, can be expressed as q = 1 – exp    -–v---00--Z-.-9--21-2---3-v--r- 3-64 where vr   v1 – ve  is the relative velocity between the projectile and the target electrons, which are calculated as follows: vr = -3--4-v---F- 1 +    3-2---vv---22F1--- – 1--1--5-   v-v--F-1 for v1 < vF 3-65 vr = v11 + 5--v--v-F2--12---- for v1  vF 3-66 77 Victory Cell User’s Manual Ion Implantation Models Process Steps Damage Accumulation Model The present model includes dynamic processes of the transformation from crystalline to amorphous state as ion implantation proceeds. Each pseudo-projectile in the simulation represents a portion of the real dose  , where N is the number of projectiles.  = -N-- 3-67 The deposited energy is accounted for each grid point of the target and accumulated with the number of projectiles. As the implantation proceeds, deposited energy increases and the crystalline structure gradually turns into an amorphous structure. This is quantified by the Amorphization Probability Function as follows: fr = 1 – exp -----EE----c--r--- 3-68 Here, Er is the energy deposited per unit volume at the grid point r, and Ec is the critical energy density, which represents the deposition energy per unit volume needed to amorphize the structure in the relevant volume. It is defined as: EcT = Ec0    1 – exp E----20----k--T-B---T-–---T-T-------- –2   3-69 where E is activation energy, kB is Boltzmann's constant, and T is the temperature at and above which the infinite dose is required for crystalline to amorphous transition. Some experimental values for EcEc0 are given by F. L Vook [23]. In the BCA module, the value f(r)=0.6 corresponds to a fully amorphized state and any additional energy deposited at point r does not contribute to the amorphization process. 78 Victory Cell User’s Manual Ion Implantation Models Process Steps Implantation Geometry Figure 3-21 shows the orientation of the ion beam, relative to the crystallographic orientation of the substrate. There two major planes regarding ion implantation in crystalline materials, mainly: • the implantation plane  • the surface plane  The implantation plane is where the initial beam of incoming ions lays in. It equivocally defines the direction of the incoming beam: tilt and rotation. If the orientation of the surface plane is [100], which is the only substrate orientation available currently in the Binary Collision approximation implantation module (BCA or CRYSTAL parameters), the offset of the rotation angle is the direction <101> on this plane. This means that the tilt angle, , specified by the TILT parameter in the IMPLANT statement will be the polar angle in laying this plane, while the rotation angle, , specified by the rotation parameter will be the difference of azimuths of the line where the implantation plane, , crosses the surface plane, , and the direction <101>. See Figure 3-21. Note: Presently, the surface orientation of the substrate is always {100}. Figure 3-21: Implantation geometry 79 Victory Cell User’s Manual Ion Implantation Models Process Steps Amorphous Material Monte Carlo In the doping of semiconductors, the rest distribution of the implantations is of principal importance. The penetration of ions into amorphous targets is most simply described by using a Statistical Transport Model, which is the solution of Transport Equations or Monte Carlo Simulation. Among the two approaches, Monte Carlo is more convenient for multiple components and two or three dimensional targets, which is partly possible because the Monte Carlo method treats an explicit sequence of collisions, so the target composition can change on arbitrary boundaries in space and time. The rest of the distribution is built up from a vast number of ion trajectories and the statistical precision of which depends directly on this number:  N . As the ion penetrates a solid, it undergoes a sequence of collisions with the target atoms until it comes to rest. A simplified model of this interactions is a sequence of instantaneous binary nuclear collisions separated by straight line segments (free flight path lengths) over which the ion experiences continuous (non-local) electronic energy loss. The collisions are separated (i.e., the state of an ion after a collision depends solely on the state of the ion before the collision). The model assumes that the arrangement of the target atoms is totally randomized after each collision (i.e., the target has no structure and no memory). As a result, a sequence of collisions is described by randomly selecting the location of the next collision partner relative to the pre-flight location and velocity direction of the ion. This means that this model cannot simulate the anomalous tail penetration observed for implanted ions into aligned single crystal targets. The model adequately describes the ion penetration into multilayer non-planar structures. Crystalline Material Monte Carlo The crystalline model used in VICTORY CELL is based on the program CRYSTAL described elsewhere [14]. To calculate the rest distribution of the projectiles, VICTORY CELL simulates atomic collisions in crystalline targets using the Binary Collision Approximation (BCA). The algorithm follows out the sequence of an energetic atomic projectiles (ions) launched from an external beam into a target. The targets may have many material regions, each with its own crystal structure, (crystalline or amorphous) with many kinds of atoms. The slowing-down of the projectiles is followed until they either leave the target or their energy falls below some predefined cut-off energy. The crystal model is invoked with the MONTE parameter in the IMPLANT statement. VICTORY CELL will then choose which model to use depending on the predefined crystal structure of the material. 80 Victory Cell User’s Manual Ion Implantation Models Process Steps 3.5.3 Stopping Powers in Amorphous Materials and Range Validation Stopping powers in amorphous materials have been validated against available experiments. Figure 3-22 shows a validation of boron and phosphorus ranges in amorphous silicon where compiled experimental data are taken from [20]. Figure 3-22: Comparison of Monte Carlo simulated project ranges (lines) and measured ranges (dots) for Boron and Phosphorus in Silicon. Experiments are from [20]. The solid lines were calculated with VICTORY CELL’s Monte Carlo module. The spread of the experimental points in Figure 3-22 is typical and cannot be avoided. For example, systematic errors due to the depth calibrations and memory effects in SIMS measurements if accounted improperly would yield less accurate (usually longer) ranges. Therefore, the Monte Carlo module in VICTORY CELL is calibrated to give overall agreement with the available experimental data. The figure also demonstrates that there can be a possible disagreement with individual set of measurements. Similar stopping powers validations were performed for other important materials. The accuracy of the calculated ranges in VICTORY CELL is within 10% for majority of ion/material combinations, which is close to the best possible achievements of today’s theory of stopping and ranges. 81 Victory Cell User’s Manual Diffusion Models Process Steps 3.6 Diffusion Models The diffusion models in VICTORY CELL describe how implanted profiles of dopants/defects (see the Note below) redistribute themselves during thermal treatment, due to concentration gradients and internal electric fields. When modeling the actual diffusion process, there are additional effects to consider such as impurity clustering, activation, and how interfaces are treated. Fundamentals of the models described in this section could be found in [24], [25], and [26]. Note: In the following sections, the terms impurity and dopant shall be used interchangeably, although an impurity doesn’t necessarily have to be a dopant. Also the term, defect, shall mean the same as point defect, unless otherwise indicated in the context. The diffusion model in VICTORY CELL uses the concept of Chemical and Active Concentration Values. The chemical concentration is the actual implanted value of the dopant but when dopants are present at high concentrations, clustering or electrical deactivation can occur so that the electrically active concentration may be less than the corresponding chemical concentration. This is described in Section 3.6.4 “Electrical Deactivation”. VICTORY CELL creates structures that can have multiple materials and interfaces such as the polysilicon-oxide-silicon interface in MOSFETs. Each interface within VICTORY CELL has boundary or interface conditions that model impurity segregation. The model details are described later in this chapter. You should, however, be aware that the gas/solid interface (the surface of the silicon if exposed) and solid/solid interfaces have been strictly modelled within VICTORY CELL. Effects such as dopant loss from exposed silicon and dopant pile-up at interfaces are simulated. 3.6.1 Mathematical Description The mathematical definition of a diffusion model includes the following specifications for every diffusing species present: • a Continuity Equation (often called a Diffusion Equation). • one or more flux terms. • a set of boundary and interregional interface conditions. In the case of impurity diffusion in semiconductors, we need a set of equations for each dopant present and for each type of point defect if point defects are explicitly represented in the model. Since dopants can only diffuse as participants in dopant-defect pairs, the dopant continuity equation is actually a continuity equation for defect-dopant pairs. In the sections that follow, we apply standard notation used in the literature for dopants, point defects (interstitials and vacancies), and the different charge states as shown in Table 3-2. In Table 3-2, the x designates the neutral charge state, - is a single negatively charged state, and = is a double negatively charged state. 82 Victory Cell User’s Manual Diffusion Models Process Steps Physical Entity Dopant Point Defect Charge State Table 3-2 Notational standards in diffusion literature Generic Symbol Replacement Values A B, P, As, Sb,... X I, V c x, -, =, +, ++ Many physical entities or parameters are temperature-dependent. In VICTORY CELL, this dependence upon temperature is modelled by the Arrhenius expression (unless otherwise indicated): QT = Q.0 exp  – Q--k---.T--E--   3-70 where: • Q.0 is the pre-exponential factor. • Q.E is the activation energy. • k is the Boltzmann constant. • T is the absolute temperature. Generic Diffusion Equation All diffusion models follow the same generic mathematical form of a continuity equation. A continuity equation merely expresses particle conservation, that is, the rate of change with time of the number of particles in a unit volume must equal the number of particles that leave that volume through diffusion, plus the number of particles that are either created or annihilated in the volume due to various source and sink terms. This basic continuity equation for the diffusion of some particle species (C) in a piece of semiconductor material is a simple Second Order Fick’s Equation [27]: ----C----Ct----h = –JA + S 3-71 where CCh is the total particle (chemical) concentration, JA is the flux of mobile particles,  is the gradient operator, and S accounts for all source and sink terms. The difference between the total (chemical) concentration and the actual mobile concentration is described in a later section entitled Section 3.6.4 “Electrical Deactivation”. In semiconductor diffusion problems, there are generally two contributors to the particle flux. The first contributor is an Entropy Driven Term, which is proportional to the concentration gradient of mobile particles. The coefficient of proportionality, DA, is called the diffusivity. The second contributor is a Drift Term, which is proportional to the local electric field. Notice that if there are several types of electrically charged species present, this term establishes a coupling between them, since all charged particles both contribute to and are influenced by the local electric field. 83 Victory Cell User’s Manual Diffusion Models Process Steps The Flux Term, JA, can be written as: JA = –DACCA + CAE 3-72 where CA designates the mobile impurity concentration,  is the mobility, and E is the electric field. It should also be observed that Equation 3-72 is non-linear, since both the diffusivity DA and the electric field E in general depend on the concentration of all present species. In thermodynamical equilibrium, the Einstein relation relates mobility and diffusivity through the expression D = k--q--T-  . Substituting for  in Equation 3-72 is writing the particle charge as a signed integer, ZA, times the elementary charge, q, giving us this Flux Expression. JA = –DA C    CA – ZA CA q-k---ET-- 3-73 In insulator and conductor materials, the electric field is zero. In semiconductor materials, the electric field is given by: E = –= –kq----Tn- n 3-74 where is the electrostatic potential and n is the electron concentration. If charge neutrality is assumed, then the electron concentration may be rewritten as: n = N-----D-----–----N----A-- + 2   N-----D----2-–----N----A-- 2 + n2i 3-75 where ND and NA are the electrically active donor and acceptor impurity concentrations, and ni is the intrinsic carrier concentration calculated as: ni = NI.0  exp   –N---k--I-T-.--E-- TNI.POW 3-76 where you can specify the NI.0, NI.E, and NI.POW parameters in the MATERIAL statement. The electrically active and mobile impurity concentrations are equivalent. Boundary Conditions Boundary conditions within VICTORY CELL are of mixed type and are expressed mathematically as:   CA +   nCA = R 3-77 where ( are real numbers and nCA designates the flux of CA across the boundary. The right hand term, R, accounts for all source terms on the boundary. Boundary conditions are applied at two main regions. The first region is at the top of the simulation region (the surface). The second region is at the inter-regional interfaces for which the species in question only has a meaningful existence in one of the region materials (e.g., an interstitial on a silicon/oxide interface). 84 Victory Cell User’s Manual Diffusion Models Process Steps Interface Conditions Between any two regions there must be some control on how any impurity species can exist in the vicinity of the interface. For every such interface, you must specify a Concentration Jump Condition and a Flux Jump Condition. The Concentration Jump Condition accounts for discontinuities in particle concentrations across interfaces and encompasses particle transport across material interfaces due to different solid solubility ratios of the impurity species in the two materials. The Flux Jump Condition enables the formulation of interface source and sink terms such as surface recombination, particle injection, and particle pile-up at a moving interface. For all species, no flux boundary conditions are employed on the sides and at the bottom of the simulation structure. This is hardwired into the software, which means it is not userdefinable. 3.6.2 The Fermi Model The Fermi Model assumes that point defect populations are in thermodynamical equilibrium and does not need direct representation. All effects of the point defects on dopant diffusion are built into the pair diffusivities. The main advantage for using the Fermi Diffusion model is it will greatly improve the simulation speed, since it does not directly represent point defects and only needs to simulate the diffusion of dopants. In the Fermi Model, each dopant obeys a continuity equation of the form:  ----C----Ct----h =  X = I V  D AX    CA–ZACA q-k---ET-- 3-78 where CCh is the chemical impurity concentration, ZA is the particle charge (+1 for donors and -1 for acceptors), DAV and DAI are the joint contributions to the dopant diffusivity from dopant-vacancy and dopant-interstitial pairs in different charge states [5]. CA is the mobile impurity concentration and E is the electric field. The terms DAV and DAI depend on both the position of the Fermi level as well as temperature and are expressed as: DAX(T,n-n--i) = DAx X + DA–  X n-n--i 1 + DA= X   n-n--i 2 + DA+ X   n-n--i –1 + DA+X+   n-n--i –2 3-79 where the temperature dependency is embedded in the intrinsic pair diffusivities, which are specified by Arrhenius expressions of the type: DAc X = D.0Ac X exp   – D-----.--kE---T-Ac---X---- 3-80 Table 3-3 shows the names of the pre-exponential factors, D.0, and activation energies, D.E, for each of the charge states, c, of the various intrinsic pair diffusivity terms. Pair charge states beyond two are unlikely to occur, which is why they have been omitted. Also, for most dopants it is seldom that more than three of the terms above are non-vanishing. 85 Victory Cell User’s Manual Diffusion Models Process Steps Table 3-3 Table of intrinsic pair diffusivities for different pair types Pair Charge State Pre--exponential factor Activation Energy AV x AV - AV = AV + AV ++ AI x AI - AI = AI + AI ++ DVX.0 DVM.0 DVMM.0 DVP.0 DVPP.0 DIX.0 DIM.0 DIMM.0 DIP.0 DIPP.0 DVX.E DVM.E DVMM.E DVP.E DVPP.E DIX.E DIM.E DIMM.E DIP.E DIPP.E Note: Since the point defect populations are by definition assumed to be in equilibrium in the Fermi model, there are no separate continuity or boundary condition equations for these species. Additionally, neither the vacancy concentration, CI, nor the interstitial concentration, CV, appear explicitly in Equations 3-78, 3-79, or 3-80. 86 Victory Cell User’s Manual Diffusion Models Process Steps 3.6.3 Impurity Segregation Model In multilayer structures, dopant segregation across material interfaces must be considered. Such interfaces can represent either a solid/solid interface or a gas/solid interface (the surface). Interface segregation is modeled empirically by a first order kinetic model for the interregional flux: Fs = h12    M--C----1-1-2- – C2 3-81 where: • C1 and C2 are the particle concentrations in the immediate vicinity of the interface in the regions 1 and 2. • h12 is the interface transport velocity. • M12 is the segregation coefficient. The transport velocity and segregation coefficients are temperature-dependent parameters defined through the following Arrhenius expressions: h12 = TRN.0  exp –-T---R--k--N-T----.-E--- 3-82 M12 = SEG.0  exp –S----E--k--G-T----.-E-- 3-83 3.6.4 Electrical Deactivation When dopants are present at high concentrations, the electrically active (mobile) concentration, Cact, may be less than the corresponding chemical concentration, Cchem. In order for an impurity to become electrically active in a semiconductor material, it must be incorporated into a substitutional lattice site, which then will contribute with a carrier to either the valence band (an acceptor impurity) or the conduction band (a donor impurity). Above certain dopant concentrations, however, it is impossible to incorporate more dopants into substitutional lattice sites. The excess dopants are said to be non-active. The threshold where the deactivation occurs is often called the solid solubility limit, since impurities can exist in different phases in the crystal. But for this section, we’ll call it deactivation threshold. Therefore, it isn’t well-defined which phase transition the solid solubility limit might refer to. For example, excess dopants could be participating in small clusters or larger precipitates. Deactivation threshold would be a more proper designation for this limit and will be used throughout the rest of this section. The notation, Cathct will be used for the deactivation threshold. Therefore, for all the models described in this section, the following points are assumed for each dopant type: • Dopants in excess of the deactivation threshold are considered electrically inactive (i.e., they do not contribute to the carrier populations). • Additionally, dopants in excess of the deactivation threshold are considered to be immobile (i.e., they cannot diffuse). 87 Victory Cell User’s Manual Chapter 4 Statements Statement Definition Statements 4.1 Statement Definition 4.1.1 Syntax Types VICTORY CELL executes a file that describes the process, layout, and extraction to be used in a simulation. The contents of the file are statements, each of which prompts an action or sets a characteristic of the simulation. This chapter is a reference to the command language used to control VICTORY CELL. This chapter refers to commands, statements, and parameters. A line in an input file is referred to as a statement (or statement line). A VICTORY CELL statement is specified in the general format: = where is the command name, is the parameter name, and is the parameter value. There are five types of parameters are used in VICTORY CELL. These parameters are: Real, Integer, Logical, Character, and String. The space character is used to separate parameters from a command or from other parameters. Parameter Character Integer Logical Real String Table 4-1 Types of Parameters Description Value Required An alphanumeric string typically Yes surrounded by quotes Any whole number Yes Value is set to true if the parameter is No present Any real number Yes Replace italic text with a string No Example LAYOUT=”MOS.LAY” DIMENSION=3 CAPACITANCE ADAPT=0.05 MATERIAL(“myTEOS”) For example, in the statement line: DEPOSIT NITRIDE CONFORMAL THICK=0.35, the CONFORMAL parameter has a (logical) value of true and the THICK parameter has a (real) value of 0.35. The NITRIDE parameter is a string variable. In the statement descriptions of this chapter, parameters listed in italics are replaced by certain strings. Here, the general parameter material of the DEPOSIT statement is replaced by the string NITRIDE. Many parameters are provided with default values. If a parameter isn’t specified, its default value will be used. Except where noted, the command language isn’t case sensitive, and can be entered using either upper case or lower case letters. 89 Victory Cell User’s Manual Statement Definition Statements Abbreviations You don’t always input the entire statement or parameter name. The simulator requires only that you input enough letters to distinguish that command or parameter from other commands or parameters. For example, DEPO can be used to indicate the DEPOSIT command. Continuation Lines Since it may be necessary for a statement line to contain more than 80 characters, continuation lines are allowed. If a statement line ends with a backslash (\), the next line will be interpreted as a continuation of the previous line. Comments Comments are indicated by a number sign (#). All characters on a line that follow a comment indicator (#) won’t be processed by VICTORY CELL. 4.1.2 Statement List This chapter contains a complete description (in alphabetical order) of every statement used by VICTORY CELL. The following documentation is provided for each statement: • The statement name. • A list of all of the parameters of the statement and their type. • A description of each parameter or group of similar parameters. • An example of the correct usage of each statement. The VICTORY CELL command language encompassed by this document describes its usage with both VICTORY CELL and EXACT. Certain command options are only available in VICTORY CELL and others are only available in EXACT. Note: An error message will be generated if you try to specify a statement or parameter for a product that hasn’t been licensed. The following list provides a brief description of VICTORY CELL statements and their use. Processing Statements • DEPOSIT – deposition process step • DIFFUSE – diffusion process step • DOPING – doping process step • ETCH – etch process step • FILTER – defines optical filter parameters • ILLUMINATION – defines lithography process • IMPLANTATION – defines implantation process • MACHINE – defines process steps as machine definitions • MASK – masking/lithography process • OXIDIZE – oxidation process step • PUPIL – defines the optical pupil for lithography • STRIP – shortcut for removing a layer of material 90 Victory Cell User’s Manual Statement Definition Structure and Layout Initialization Statements • INIT – defines the initial layout and substrate • GDSLAYER – defines a new GDS2 layout layer • SURFACE – imports external textured into the structure • MESH – sets export mesh parameter Structure Editing Statements • CARTESIAN – reduces the structure dimensions • CUT – reduces the structure dimensions • REFINE – refines the structure mesh • IMPROVEMESH – improves the mesh • EXPORT – creates device structure for ATLAS3D and VICTORYDEVICE • LINE – specifies a Cartesian mesh line Parasitic Extraction Statements • ELECTRODES – defines the electrical nodes for parasitic extraction • MATERIAL – defines material properties Simulation Control Statements • GO – starts the simulator • OPTION – assigns different global control parameters • QUIT – exits the simulator • RESET – clears the simulator of all information • SAVE – saves results files to disk • SET – defines variables to be used in substitutions later • SOURCE – runs an external file • SYSTEM – executes UNIX commands within the input file • TONYPLOT – plots the simulation structure in 2D or 3D Miscellaneous Statements • HELP – displays on-line help information about the commands and syntax Statements 91 Victory Cell User’s Manual CARTESIAN Statements 4.2 CARTESIAN CARTESIAN specifies a mesh line during volumetric grid definition. Syntax Cartesian|Cart | Mask=“”> [Spacing=] Spacing.Ratio= Spacing.On|Off Table 4-2 Cartesian Parameters Parameter Description Default “Maskname” X.dir Y.dir Z.dir Location Spacing Line Mask Spacing.Ratio= Spacing.On|Off string logical logical logical real real logical character real logical none none -1 none 1.5 Off Units microns microns Description This statement defines the position and spacing of mesh lines. All CARTESIAN statements should be placed without any other statements in between. The CARTESIAN statements could be placed immediately after the INIT command provided the INIT command uses a PADDING parameter. CARTESIAN set of commends could be placed anywhere in the input deck, but before any DOPING, IMPLANT, DIFFUSE, or DEPOSIT with epitaxy commands are used. The CARTESIAN commands will fail if the generated structure at the place of their execution is not yet three dimensional. VICTORY CELL will start any structure as 1D unless a PADDING parameter in the INIT statement is provided. Then it will gradually promote the structure to two and three dimensional one depending on layout and process steps. At present, VICTORY CELL does not have the ability to automatically update the CARTESIAN mesh discretization with structure dimension. Therefore, you need to make sure the CARTESIAN set of statements are used when structure is already three dimensional. X.DIR, Y.DIR, and Z.DIR (or X|Y|Z) specify whether a mesh line is horizontal(x,y direction) or vertical(z direction). The x coordinate increases from left to right. The y coordinate increases from front to back. The z coordinate increases into the substrate, that is, from top to bottom. This is somewhat confusing, does not comply with the standard analytic geometry rule, but is very convenient for describing the simulation domain in the silicon substrate (i.e., initial surface is at zero level and depth increases positively). 92 Victory Cell User’s Manual CARTESIAN Statements LOCATION specifies the location along the chosen axis (in microns) at which the line should be positioned. SPACING specifies the local grid spacing, in microns. VICTORY CELL adds mesh lines to the ones given according to the following recipe. Each user line has a spacing whether userspecified or inferred from the nearest neighbor. These spacings are then smoothed out so no adjacent intervals have a ratio greater than 1.5. New grid lines are then introduced so that the line spacing varies geometrically from one end of the interval to the other. The example below might alleviate the confusion assotiated with this parameter. MASK points to a mask layer from the layout that is used to specify horizontal mesh lines(x, y direction). All polygon edges from the layer define mesh lines in x or y direction. The MASK parameter can be used along with SPACING. One CARTESIAN command with a MASK parameter is equivalent to several CARTESIAN LINE commands in the x and y directions. SPACING.RATIO defines maximum ratio between neighboring intervals. The default value is 1.5. SPACING.ON|OFF turns on the use of the spacing parameter for Cartesian discretisation. By default, it is off (i.e., spacing between neighboring intervals is automatically defined by the proximity of user-defined grid points). Example Cart Line X.dir Location=0.1 Spacing=0.01 Cart Line X.dir Location=0.5 Spacing=-1 Cart Line X.dir Location=0.9 Spacing=0.01 Cart Line Y.dir Location=0.1 Spacing=0.01 Cart Line Y.dir Location=0.5 Spacing=-1 Cart Line Y.dir Location=0.9 Spacing=0.01 Cart Mask=”CONT” Cart Mask=”METAL” Spacing=0.2 Cart Line Z.dir Location=0 Spacing=0.001 Note: It is difficult to predict how many lines are going to be generated in each interval. The initial mesh specification is quite important to the success of the simulation. 93 Victory Cell User’s Manual CUT Statements 4.3 CUT CUT performs a 1D, 2D, or 3D cut through the existing simulation structure and replaces the current structure with the results of the cut. Syntax Cut Point = (,) Cut Line = (,,,) Cut Box = (,,,,,) Parameter Line Point Box Table 4-3 Cut Parameters Description List of two pairs of real numbers List of two real numbers List of six real numbers Default none none none Units microns microns microns Description This is used to cut the current structure vertically along a given line, point, or cut out a 3D box from the current structure. For cut points or cut lines, the complete extent of the structure in the z-direction is maintained. All coordinates are in microns and interpreted as locations in the layout coordinate system. BOX specifies two sets of X, Y, Z coordinates pairs. The current simulated structure after the CUT BOX statement will be focused inside the box. The simulation is still in 3D. The CUT BOX statement will add vertical electrodes on the cutting edges of conductors. LINE specifies two sets of X,Y coordinate pairs (for a total of four coordinates). The current simulated structure is cut along this plane to form a 2D structure. The coordinates of the plane are relative to the coordinates in the original layout. When capacitance extraction is performed in 2D, the capacitances are in F/µm. Likewise, the unit of 2D resistance is µm. POINT specifies a pair of X,Y coordinates. The current simulated structure will be cut into a 1D section at this point. The X,Y coordinates are relative to the original layout coordinates. Note: Using the CUT command replaces the original simulation structure with the resultant cut structure. The previous structure will be lost if it’s not explicitly saved. Examples Convert a 2D or 3D simulation to 1D at the location (1,1). Cut Point = (1.0, 1.0) Convert a 3D structure to 2D along the plane (1,1) to (3, 1). Cut Line = (1.0, 1.0, 3.0, 1.0) Convert a 3D structure to a 3D structure inside the box bounded by 1 < x, y, z < 3 Cut Box = (1.0, 1.0, 1.0, 3.0, 3.0, 3.0) 94 Victory Cell User’s Manual DEPOSIT Statements 4.4 DEPOSIT DEPOSIT models the deposition process. A specified material is deposited on the preexisting structure. Syntax Deposit )>Thickness=[Max|Min| Conformal [StepCoverage=]] [IMPURITY=] Deposit Time=[Isotropic=][Sigma=] ”)>|Machine= >[ dT=
] [Voidsize=][dL=
] Table 4-4 Deposit Parameters Parameter Type Default Units CONFORMAL CONSTRAINT DL DT logical integer real real false 0 0.2 0.1*time um minutes ISOTROPIC real 1.0 none MACHINE MATERIAL MATERIAL(“val”) MAX MIN RATE SIGMA STEPCOVERAGE character string string logical logical real real real true false 0.0 0.0 1.0 m/minute radians none THICKNESS real microns TIME VOIDSIZE IMPURITY real real real 0.0 infinity minutes microns 1/cm3 Description The Deposit statement is used to model all deposition processing steps. There are two separate deposition modes: Geometric and Physical. The Geometric mode corresponds to a simplified fast mode that approximates geometry where all material interfaces are either vertical or horizontal. The Physical mode allows a realistic description of the deposition processing. 95 Victory Cell User’s Manual DEPOSIT Statements Parameters applicable to both Geometric and Physical Modes COPPER, SILICON, OXIDE, NITRIDE, OXYNITRIDE, POLYSILICON, ALUMINUM, RESIST, BPSG, BSG, PSG, SOG, TUNGSTEN, TEOS, SiGE, SiC, TiSix, TiN, HfO2, Sapphire, ITO, GaN, InGaN, Cobalt, CoSi, Nickel, NiSi, Titanium, WSi, and MATERIAL(“string”) specify the material to be deposited. One of these material parameters is mandatory. The MATERIAL(“val”) parameter should only be used for user-defined materials, where val is the name of the user-defined material. Note: We recommend that you don’t use the name of one of the supported default parameters in the user-defined material string. For example, don’t use Material(“oxide”). Geometric Mode Parameters CONFORMAL or UNIFORM specifies conformal deposition on the whole surface. With this mode, THICKNESS is defined as the layer thickness deposited on every exposed surface in the structure. The thickness deposited on any sidewall equals the thickness deposited on any plane surface multiplied by the factor, STEPCOVERAGE. This type of deposition is the default in process simulators such as SSUPREM4. MAX or PLANAR specifies planarized deposition, where THICKNESS is measured from the highest point of the original surface. In this model, THICKNESS may be zero to planarize the structure to the existing highest point, or even negative to partially refill trenches in the structure. The default setting is TRUE. MIN specifies a planarized deposition, where THICKNESS is measured from the lowest point of the original surface. STEPCOVERAGE specifies a number between 0 and 1 that specifies the ratio between horizontal and vertical deposition. The default value is one, giving 100% conformal deposition. THICKNESS specifies the thickness, in microns, of the deposited layer. This parameter is mandatory in Geometric mode. It is very important to note that the exact definition of the thickness of the film is determined by the settings of the following logical parameters. One of the parameters below is required in Geometric mode. IMPURITY invokes an epitaxial like deposition. The allowed impurities are boron, bf2, arsenic, phosphorus, and antimony. If deposition is performed over the same material, the impurity will be added to the deposited material provided the layer underneath had some minimal bulk concentration of the same impurity. Physical Mode Parameters CONSTRAINT sets a region boundary for two neighbor regions with the same material. The default is NO. DL specifies an alternative spherical construction meshing algorithm for realistic DEPOSIT and ETCH statements. In general, it limits the maximum size of the mesh in modified regions to the specified value. A good value to choose as a starting point would be the depth of the etch or deposit. For example, if etching or depositing poly of 0.2um thickness in physical mode, try DL=0.2 for good results. 96 Victory Cell User’s Manual DEPOSIT Statements DT specifies the initial time step in minutes. Note that the time integration is usually a trade off between simulation time and accuracy. The simulator makes an internal guess as to the best choice for the time steps. In rare cases, you might want to change the behavior with this parameter. ISOTROPIC specifies a number between 0 and 1 that specifies the ratio between horizontal and vertical deposition. The default value is one, giving 100% conformal deposition. MACHINE specifies the name of a deposition machine. The parameters for this machine must be defined earlier in the input file with the MACHINE statement. See Section 4.19 “MACHINE” for more information. RATE specifies the deposition rate in units of um/minute. This rate applies to vertical deposition on flat surfaces. The deposition rate on sidewalls is defined as the product of RATE and ISOTROPIC. SIGMA specifies the spread of the distribution function for the incoming particles. The distribution function is assumed to be Gaussian, so SIGMA defines the width of this function. See “SIGMA” on page 55 for details. TIME specifies the deposition time in minutes. This must be specified for all physical mode deposition steps. VOIDSIZE specifies the minimum size of voids that can be created by a deposition step. The default is infinity, which means no voids will be created. Examples To deposit a planarized layer of metal to a height of 0.5 microns above the current top of the structure, type: Deposit Aluminum Thickness=0.5 MAX To fill all trenches or open vias in the structure with oxide, type: Deposit Oxide Thickness=0.0 MAX Use a negative value such as THICKNESS=-0.1 value would imply the trenches to be refilled to within 0.1 microns of the top. To deposit a 0.8 micron layer of a user-defined dielectric called my_TEOS, type: Deposit Conformal Material("my_TEOS") Thickness=0.8 \ Stepcoverage = 0.75 This layer is to be deposited conformally with 0.75 step coverage. Therefore, the sidewall deposition thickness is 0.8*0.75=0.6 microns. Using a physical model to deposit 1.0 microns of Aluminum with a step coverage of 60% (see example below). Deposit Aluminum Rate=0.5 Time=2.0 Isotropic=0.6 Below, the same example is using a MACHINE definition. Machine Name=”my_cvd” Deposit Aluminum Rate=0.5 Isotropic=0.6 Deposit Time=2.0 Machine="my_cvd" Epitaxial-like deposition Deposit Silicon Conformal Thickness=0.1 Boron=1e17 97 Victory Cell User’s Manual DIFFUSE Statements 4.5 DIFFUSE DIFFUSE runs an annealing step on the wafer and calculates diffusion of impurities. Syntax Diffuse Time=

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