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Dissertation
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Acknowledgment
Contents
1. Introduction
1.1 Purpose of TCAD Tools
1.2 TCAD Frameworks
1.3 Optimization Tasks
1.4 Outline
2. Solving Optimization Tasks in Microelectronics Applications
2.1 TCAD Optimization Tasks
2.1.1 Process Tuning
2.1.2 Tool Calibration
2.1.3 Technology Development
2.1.4 Inverse Modeling
2.1.5 Demand for a General Optimization Framework
2.2 The VISTA Project
2.2.1 The Input Deck Library
2.2.2 The Model Library
2.3 The VISTA Framework
2.4 The SIESTA Framework
2.4.1 Model Module
2.4.2 Queue Manager
2.4.3 SIESTA Graphical User Interface
3. Statistical Analysis
3.1 Design of Experiments
3.1.1 Types of Experimental Designs
3.1.2 Nominal Design
3.1.3 Screening Analysis
3.1.4 Full Factorial Design
3.1.5 Central Composite Designs
3.1.6 Random Design
3.1.7 Gauß Random Design
3.1.8 Diagonal Design
3.1.9 Full Grid Design
3.1.10 Two Dimensional Grid Design
3.1.11 Latin Hypercube Design
3.1.12 Fractional Factorial Design
3.1.13 Plackett-Burman Design
3.1.14 Orthogonal Main Effect Design
3.1.15 Supplemantary Design
3.1.16 Three Level Factorial Design
3.1.17 Transformations
3.1.18 Comparison
3.2 Response Surface Methodology
3.2.1 Mathematical Background
3.2.2 Solving the Least-Squares Problem
3.2.3 Numerical Aspects
3.2.4 Transformation
3.2.5 Use of Higher Order Polynomials
3.2.6 Analysis of Variance Table
3.3 Framework Integration
3.4 Practical Use
3.4.1 Analysis Using Response Surface Methodology
3.4.2 Comparison
4. Optimizer
4.1 Optimization Methods
4.1.1 Gradient Based Optimization Methods
4.1.2 Step direction
4.1.3 Steepest-descent
4.1.4 Newton Direction
4.1.5 Finite-Difference Approximations of First Derivatives
4.1.6 Approximation of the Second Derivatives
4.1.7 Step Length Method
4.1.8 Trust Region Method
4.1.9 Comparison of Step Length and Trust Region Methods
4.2 Genetic Algorithms
4.3 Least-Squares Problems
4.3.1 Mathematical Background
4.3.2 Levenberg-Marquardt Algorithm
4.3.3 Implementation
4.3.4 Constraints
4.3.5 SIESTA Interface
4.3.6 Model Library
4.4 General Nonlinear Optimization Problems
4.5 Integration into a TCAD Framework
4.5.1 Parallel Execution
4.5.2 Fault Recovery
4.5.3 SIESTA Optimizer Module
4.5.4 Example of a Calibration Task
4.5.5 Example of a Nonlinear Optimization Task
4.5.6 Parameters in the Experiment File
4.5.7 Graphical User Interface
4.6 Optimizer Module Interactions
4.7 Optimizer Protocol
5. Application
5.1 Optimization with a Complete Process Simulation
5.1.1 Structure of a VDMOS Transistor
5.1.2 Goal of the Optimization Task
5.1.3 Simulation Flow of the Device Structure
5.1.4 Solving the Optimization Problem
5.1.5 Results
5.2 Optimization of Analytical Doping Profiles
5.2.1 Analyzed Transistor
5.2.2 Optimization
5.2.3 Results
5.3 Inverse Modeling of Analytical Doping Profiles
5.4 Task Description
5.4.1 Process Modeling
5.4.2 Actual Device
5.4.3 Profile Extraction
5.4.4 Optimization of the Doping Profiles
5.4.5 Optimization Using Electrical Parameters
5.4.6 Results
6. Discussion
6.1 Optimization in a TCAD Environment
6.2 Setting Up an Analysis Task
6.3 Stability
6.4 Implementation
6.5 Result Database
A. Overview of the Input Deck Programming Language
B. Optimization
B1. Jacobian Matrix
B2. Hessian Matrix
B3. Two Norm
B4. Some Derivatives of Scalar Value Functions With Respect to a Vector
B5. Gauß Function
B6. Pearson Function
B7. Error Function
B8. F-Distribution
B9. F-Test
C. Guides for Finding a Suitable Optimizer
D. Design of Experiments Program vdoe
D1. Synopsis
D2. Input Deck
D3. Transformations
D4. Designs
D5. Example
E. Response Surface Methodology Program vrsm
E1. Synopsis
E2. Input Deck
E3. Transformations
E4. Example
F. Levenberg-Marquardt Optimizer lmmin
F1. Synopsis
F2. Input Deck
F3. Statistical Output
G. Levenberg-Marquardt Optimizer with Model Library Interface
G1. Synopsis
G2. Input Deck
G3. Model Library File
H. General Nonlinear Constrained Optimizer donopt
H1. Synopsis
H2. Input Deck
Bibliography
List of Publications
List of Figures
List of Tables
R. Plasun
