EEL4930/5930: Modeling and Simulation of Semiconductor Devices, Spring 2006

    Course announcements

    • C++ code that implements the Newton technique to solve the Poisson equation for a MOSFET device: poisson.cpp. The algorithm should take about 10 iterations to finish. Since we are using a dense matrix solver, each iteration takes a few seconds on a normal PC. If we used a sparse matrix solver, each iteration would have taken much less time (less than 0.5 s)
     

    Software for solving linear systems of equations

    • C++ code that implements the Gauss technique that we discussed in class to solve linear DENSE systems of equations:
        gauss.cpp You should compile this file with a C++ compiler. I have tested it on Microsoft Visual Studio.NET and in linux (g++ compiler)
        gauss.zip The entire project compiled in Microsoft Visual Studio.NET. To open the project, unzip the files and open the EEL.sln file. You should have Microsoft Visual Studio.NET installed on your computer in order to open it.


    • You can also use the following libraries to solve linear systems of equations:

        • SuperLU2.0 library (800K) - sparse linear system of equations (Microsoft Visual Studio.NET),
        SuperLU2.0 library (800K) - sparse linear system of equations (Microsoft Visual C++ 6.0),
        CLapack library (3.6M) - dense system of equations (Microsoft Visual Studio.NET).
      I strongly recommend that you use the first library (SuperLU) since it is much faster for the applications that we need in class. To open a project, unzip the files and open the *.dsw if you are using Microsoft Visual C++ 6.0 or the *.sln file if you are using Microsoft Visual Studio.NET. These libraries can be easily modified if you work in C and not C++. If you are working in Linux or Unix you might want to download the above libraries from http://crd.lbl.gov/~xiaoye/SuperLU/  and http://www.netlib.org/clapack/. If you are not satisfied with these libraries than you can find plenty of other libraries on the web. Please let me know if you need any help.

    Course meeting times

      Classes: TuTh 1:15-2:30 pm, Rm. A235
      Office hours: TuTh 2:30-3:30 pm, Rm. B364

    Syllabus

    Target Audience

      Graduate students and advanced undergraduates in electrical and computer engineering and physics, who are particularly interested in the modeling and simulation of VLSI devices and circuits.

    Course description

      Students will be introduced to modern topics in submicron semiconductor devices and state-of-the art CMOS technology. The course focuses on the modeling and simulation of nanoscale MOS devices. Topics that will be covered include but are not limited to quantum mechanical effects, high speed devices, effects induced by scaling, high doping concentration, interface roughness, and random doping placement.

      C language will be extensively used in the implementation of various numerical algorithms discussed during the course.



   The dates for the lecture notes are tentative. The content may also be slightly adjusted during the semester.

Lecture Date Topic Misc.
1 1/10/2006: Tu Introduction to the Modeling and Simulation of Semiconductor Devices  
2 1/12/2006: Th The Drift-Diffusion model  
3 1/17/2006: Tu The Density-Gradient model  
3 1/19/2006: Th 1-D Nonlinear equations: bisection method, Newton method  
3 1/24/2006: Tu Convergence properties of the bisection and Newton methods. Linear systems of equations: dense systems vs. sparse systems gauss.cpp
4 1/26/2006: Th Nonlinear systems of equations: Newton method  
5 1/31/2006: Tu Discretization of first- and second-order differential equations  
6 2/2/2006: Th Discretization of second-order partial differential equations. Newman, Dirichlet, and mixed-type boundary conditions (1)  
7 2/7/2006: Tu Discretization of second-order partial differential equations. Newman, Dirichlet, and mixed-type boundary conditions (2)  
8 2/9/2006: Th Numerical implementation of the Newton method. Program implementation  
9 2/14/2006: Tu Discretization of the semiconductor equations. Boundary conditions.  
10 2/16/2006: Th Semiconductors at thermal equilibrium. Theoretical description. Basic equations  
11 2/21/2006: Tu Semiconductors at thermal equilibrium. Discretization of the BC  
12 2/23/2006: Th MOSFET: 2-D and 3-D nonlinear Poisson equation (discretization, convergence properties)  
13 2/28/2006: Tu Iterative techniques for linear/nonlinear systems of equations: Jacobi, Gauss-Seidel, SOR. Convergence analysis  
14 3/2/2006: Th Globally convergent iterative techniques for the nonlinear Poisson equation  
15 3/14/2006: Tu Systems of PDEs. Discretization  
16 3/16/2006: Th Discretization semiconductor equations. Gummel iteration technique  
17 3/21/2006:: Tu Density-Gradient model  
18 3/23/2006: Th Generation-recombination processes  
19 3/28/2006: Tu Carrier mobilities in semiconductors  
20 3/30/2006: Th Time dependent problems  
21 4/4/2006: Tu Small-signal analysis  
22 4/6/2006: Th Small-signal analysis  
23 4/11/2006:Tu Small-signal analysis  
24 4/13/2006:Th Random doping induced fluctuations in semiconductor devices  
25 4/18/2006: Tu Random doping induced fluctuations in MOSFETs  
26 4/20/2006: Th Final project is due!