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9.4.3 Examples
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Dissertation Clemens Heitzinger
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10. Introduction
III
. Applications
As far as the laws of mathematics refer to reality,
they are not certain;
and as far as they are certain,
they do not refer to reality. If you are out to describe the truth,
leave elegance to the tailor. A
LBERT
E
INSTEIN
Subsections
10
. Introduction
10
.
1
Manufacturing Steps
10
.
1
.
1
Wafers and Crystal Preparation
10
.
1
.
2
Masks
10
.
1
.
3
Photolithographic Process
10
.
1
.
4
Deposition
10
.
1
.
5
Etching
10
.
1
.
6
Doping
10
.
1
.
7
Conductors and Resistors
10
.
1
.
8
Oxides
10
.
1
.
9
Epitaxy
10
.
2
Topography Simulation and Motivation
10
.
3
Outline of the Second Part
11
. Smoothing Monte Carlo Simulation Results
11
.
1
Introduction
11
.
2
The Algorithm
11
.
3
A Three-Dimensional Example
11
.
4
Summary
12
. Simulation of Surface Evolution
12
.
1
Introduction
12
.
2
Overview of Topography Simulation
12
.
3
The Transport of Particles above the Wafer
12
.
4
A Radiosity Formulation for Luminescent Reflection
12
.
5
The Mechanism of Deposition of Silicon Dioxide from TEOS
12
.
5
.
1
The Heterogeneous Deposition Model
12
.
5
.
2
The Homogeneous Intermediate-Mediated Deposition Model
12
.
5
.
3
The Heterogeneous Deposition with Byproduct Inhibition Model
12
.
5
.
4
Deposition Rate
12
.
6
The Mechanism of Deposition of Silicon Nitride
12
.
7
Simulation of Silicon Dioxide from TEOS for Power MOSFETs
12
.
8
Simulation of Void Formation during Backend Processes
12
.
9
Simulation of Deposition after Transport in the Diffusion Regime
12
.
10
Summary
13
. The Level Set Method
13
.
1
Methods for Describing Moving Boundaries
13
.
1
.
1
String Based Methods
13
.
1
.
2
The Cellular Approach
13
.
1
.
3
The Level Set Method
13
.
2
The Basics of the Level Set Method
13
.
3
Variations of the Level Set Method and Advanced Algorithms
13
.
3
.
1
The Boundary Value and the Initial Value Formulation
13
.
3
.
2
Methods for Speeding Up the Solution of the Level Set Equation
13
.
3
.
3
Extending the Speed Function
13
.
4
Surface Extraction and Void Detection
13
.
5
Finite Difference Schemes
13
.
5
.
1
First Order Space Convex
13
.
5
.
2
Second Order Space Convex
13
.
5
.
3
Stability
13
.
6
A Fast and Precise Level Set Algorithm
13
.
7
Coalescing Surface Elements
13
.
8
The ELSA Simulator
13
.
9
Summary
14
. Inverse Modeling of Silicon Self-Interstitial Cluster Formation
14
.
1
Introduction
14
.
2
Modeling Silicon Self-Interstitial Cluster Formation and Dissolution
14
.
3
Inverse Modeling and Results
14
.
4
Summary
15
. Inverse Modeling of Arsenic Diffusion after Pre-deposition
15
.
1
Introduction and Measurements
15
.
2
Inverse Modeling and Results
The First Step: Six Measurements
The Second Step: All 19 Measurements
15
.
3
Summary
16
. Conclusion and Outlook
Conclusion
Outlook
A. Mathematical Preliminaries
A.
1
Norms
A.
2
Means
A.
3
Inequalities
A.
4
Analysis
B. Multivariate Bernstein Polynomials
Previous:
9.4.3 Examples
Up:
Dissertation Clemens Heitzinger
Next:
10. Introduction
Clemens Heitzinger 2003-05-08