EEL4930/5930: Modeling and Simulation of Semiconductor Devices, Spring 2005

    Course announcements

    How to save and plot the electrostatic potential matrix

      (1) To save electrostatic potential 'phi' from your C-file add the following lines at the end of your code:

      FILE *fp = fopen("a.dat","w");
      for(int i=0; i<dim; i++) fprintf(fp,"%e\n", phi[i]);
      fclose(fp);
      (2) To plot the electrostatic potential in Matlab, use the following command:

      mesh(reshape(load('a.dat'),51,51));


      Please note that, at step (1),  we saved the electrostatic potential in file "a.dat". At step (2) we should load the same file in Matlab and plot it. When you do that make sure that the current directory in Matlab is the directory where you saved your "a.dat" file. To do that you can use the following command: "cd c:\YourDirrectory". Also, at step (2), "51,51" denote your (Nx+1) and (Ny+1) values. You might want to change them according to your values.

    Software for linear systems of equations

      The following projects show how 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 *.sin 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: MWF 11:50-12:40 pm, Rm. B115
      Office hours: MW 1:00-2:30 pm, Rm. B371

    Syllabus

    Target Audience

      Graduate students and advanced undergraduates in electrical and computer engineering and physics, who are particularly interested in 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  
1 1/5/05:W Introduction to modeling and simulations of semiconductor devices  
2 1/7/05:F State variables (n, p, phi)  
3 1/10/05:M The Drift-diffusion and the Density-Gradient models (1)  
3 1/12/05:W The Drift-diffusion and the Density-Gradient models (2)  
3 1/14/05:F The Drift-diffusion and the Density-Gradient models (3)  
4 1/17/05:M NO CLASSES: Martin Luther King, Jr., Day  
5 1/19/05:W Equations for thermal equilibrium  
6 1/21/05:F Numerical analysis of 1-D nonlinear algebraic equations  
7 1/24/05:M Numerical analysis of 1-D nonlinear algebraic equations (Newton method)  
8 1/26/05:W Nonlinear systems of equations (Newton method)  
9 1/28/05:F Nonlinear systems of equations (Newton method)  
10 1/31/05:M PDE: discretization (introduction)  
11 2/2/05:W PDE: discretization of the 2-D nonlinear Poisson equation  
12 2/4/05:F  PDE: sparse vs. dense linear system of equations, computation of the solution of the 2-D nonlinear Poisson equation  
13  2/7/05:M  Metal boundary conditions, artificial boundary conditions  
14  2/9/05:W Oxide-semiconductor boundary conditions  
15  2/11/05:F Discretization of the boundary conditions, SuperLU sover  
16  2/14/05:M Computation of the Jacobian  
17  2/16/05:W Numerical implementation: MOSFET devices (I)  
18  2/18/05:F Numerical implementation: MOSFET devices (II)  
19 2/20/05:M Numerical implementation: MOSFET devices (III)  
20 2/22/05:W Electrostatic potential, electron and hole concentrations (MOSFET devices)  
21 2/24/05:F Global convergence vs. local convergence. Fixed-point theorem  
22 2/28/05:M Globally convergent techniques  
23 3/2/05:W Analysis of 3D semiconductor devices  
24 3/4/05:F Review  
25 3/14/05:M Analysis of quantum mechanical effects by using the Density-Gradient method  
26 3/16/05:W Discretization of the Density-Gradient equations  
27 3/18/05:F Semiconductor equations: Poisson, current continuity, DG  
28 3/21/05:M Semiconductor equations: recombination-generation processes  
29 3/23/05:W Numerical discretization of current continuity equations (1)  
30 3/25/05:F Numerical discretization of current continuity equations (2)  
31 3/28/05:M Numerical implementation of the DG model  
32 3/30/05:W Analysis of quantum mechanical effects  
33 4/1/05:F Numerical solution of the Schrödinger equation  
34 4/4/05:M Quantum mechanical effects on MOSC capacitance  
35 4/6/05:W Small-signal analysis  
36 4/8/05:F Random doping induced fluctuations (2)  
37 4/11/05:M Interface roughness induced fluctuations (1)  
38 4/13/05:W Random geometrical dimensions induced fluctuations(2)  
39 4/15/05:F More on quantum mechanical effects (1)  
40 4/18/05:M More on quantum mechanical effects (2)  
40 4/20/05:W Presentations  
40 4/22/05:F Presentations