Software Engineering in Mathematics

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Spring 2009


Jinn-Liang Liu

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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

1.     2008S C++ Programming

2.     2008F¼Æ­È·L¤À¤èµ{

 

How to do

1.     Self-Study

¡P        (2/24) First Self-Evaluation (Form)

¡P        (4/14) Second Self-Evaluation

¡P        (6/9) Final Self-Evaluation

2.     Set your own agenda and schedule

3.     Review your progress in this course week-by-week 

 

Assignments

  1. Send biweekly (on Mondays starting 2/23) email to jinnliu@nuk.edu.tw in the following format:
    ¼ÐÃD:©m¦WE#-Topic Title
    Dear Professor Liu,
      
    ¡K (Except
    ©m¦W above in Chinese, write emails strictly in English) ¡K

    Best regards,
    Your name
  2. Send biweekly (on Mondays starting 3/3) your report to jinnliu@nuk.edu.tw in the following format:
    ¼ÐÃD:©m¦WR#-Report Title
     

    Briefly say some thing about the report.
    Write your report in Tex by using
    Scientific WorkPlace 4.0.rar
    Attach your report in pdf format.

     
     
  3. Send 3 C++ programming projects (on 3/10, 4/7, 5/5) to jinnliu@nuk.edu.tw in the following format:
    ¼ÐÃD:©m¦WP#-Project Title

    Define your own projects and describe the project at the beginning of the main program.
    Attach your C++ codes and I/O files.
    Briefly say something about your project in the email.


  4. Two 15-minitute presentations about the report on 4/14 and 6/9 in PowerPoint format written in English. The order of presentations will be drown randomly.
     

 

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1. Introduction  

1.   Classical Computer Device.ppt

2.   ¥x¿n¹q45©`¦Ì»sµ{ ¥þ²y«e¤T±j.pdf

3.   ¥x¿n¹q28©`¦Ì»sµ{

 

2. Mathematical Models

1.     1D Example: EE656: Fundamentals of Carrier Transport

2.     1D Algorithm:  ³¯°û§D Report.pdf

3.      Convection-Diffusion-Reaction Model   

4.      3D Poisson¡¦s Equation.pdf 

5.      Semiconductor Models.pdf

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

 

±Ð¾Ç¥Ø¼Ð 

l           Learn Programming in Scientific Computing

l           Learn Software Development for Semiconductor Device Simulation

l           Learn Numerical Methods for Semiconductor Device Simulation

l           Learn Basic Physics of Semiconductor Devices

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l           Regular Lecturing, Discussions, Presentations, Demos

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l           Assignments 50%  

l           Final Report 50%   

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None

°Ñ¦Ò¤åÄm

l         Jinn-Liang Liu, Lecture Notes on Numerical Methods for Partial Differential Equations, 2008. 
2008F¼Æ­È·L¤À¤èµ{  

l          Mark Miller, Lectures on Semiconductor Materials, 2006. 
Lecture01.pdf  Lecture02.pdf  Lecture03.pdf  Lecture04.pdf  Lecture05.pdf Lecture06.pdf

l         E. Suli, Finite Element Methods for Partial Differential Equations, 2007.
Suli-FEM-2007.pdf

l         An Introduction to Software Engineering

 

 

 

 

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