Software Engineering in Mathematics
數學軟體工程
Goal
Write a course report on “A Mathematical Software for Semiconductor
Device Simulation”
Format:
Title, Abstract, 1. Introduction, 2. Mathematical Model, 3. Gummel’s
Iteration, 4. Finite Element Method, 5. Scharfetter-Gummel Method, 6. Monotone Iterative Method, 7. Numerical
Algorithms, 8. Software Description, 9. Numerical Experiments, 10. Conclusions,
Appendix, Acknowledgements, References.
Prerequisite
2. 2008F數值微分方程
How to do
1.
Self-Study
·
(2/24)
First Self-Evaluation (Form)
·
(4/14)
Second Self-Evaluation
·
(6/9)
Final Self-Evaluation
2.
Set
your own agenda and schedule
3.
Review
your progress in this course week-by-week
Assignments
課程大綱
1. Introduction
1.
Classical Computer Device.ppt
3.
台積電28奈米製程
2.
Mathematical
Models
1.
1D Example:
EE656:
Fundamentals of Carrier Transport
2.
1D Algorithm: 陳婉伶
Report.pdf
3.
Convection-Diffusion-Reaction Model
6.
Quantum-Corrected Energy Transport Model (QCET):
2003jcp-semi.pdf,
2005jcp-semi.pdf (Read these two papers very thoroughly.)
3. Numerical Methods for PDEs
1.
Gummel’s Iteration: 2005jcp-semi.pdf
2.
1D Finite Element Method (FEM): Lecture
8.
3.
Scharfetter-Gummel (SG) Method: SGMethod.pdf
4.
Newton’s Method and Monotone Iterative Methods: 2003jcam-semi.pdf
5.
Adaptive FEM: 1998Adaptive.pdf, 1996OOP.pdf
4. Implementations (Computer Programming)
1.
1D C++ Code: program1D.zip, result1D.zip
2.
2D C++ Code: program2D.zip, matlab2D.zip
教學目標
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Learn
Programming in Scientific Computing
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Learn
Software Development for Semiconductor Device Simulation
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Learn
Numerical Methods for Semiconductor Device Simulation
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Learn
Basic Physics of Semiconductor Devices
授課方式
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Regular
Lecturing, Discussions, Presentations, Demos
評分標準
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Assignments
50%
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Final
Report 50%
教科書
None
參考文獻
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Jinn-Liang Liu, Lecture Notes on Numerical Methods for Partial Differential Equations,
2008.
2008F數值微分方程
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Mark Miller, Lectures
on Semiconductor
Materials, 2006.
Lecture01.pdf Lecture02.pdf Lecture03.pdf Lecture04.pdf Lecture05.pdf
Lecture06.pdf
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E. Suli, Finite Element Methods for Partial Differential Equations, 2007.
Suli-FEM-2007.pdf
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An
Introduction to Software Engineering