Engineering Electromagnetics I
Course No. 0909-301-01/02
Fall 2004, 1st Quarter
Lab Project 2: Numerical Modeling of Electrostatic Phenomena
Report due Wednesday,
October
13, 2004
Objective
This project is designed to provide you with techniques to solve
electrostatic boundary value problems using numerical techniques. You
will use Matlab's
Partial Differential Equation Toolbox for computing solutions to
Laplace's and Poisson's equations inside arbitrarily shaped 2-D
geometries.
This project has three parts. In part 1, you will use the PDE Toolbox
to solve a simple boundary value problem for a rectangular geometry. In
part 2, you will apply these solution techniques for calculating the
fringe fields in a parallel-plate capacitor. In part 3, you will
develop electrostatic models of a n-channel enhancement-mode
MOSFET under various operating conditions.
Part 1
- Compute the potential and field distribution for the geometry
shown in Figure 1. You can download the PDE Toolbox tutorial here .
Figure 1: Electrostatic boundary value problem for Part 1.
Part 2: Parallel-plate Capacitor
- Scale the model that you have developed in part 1 for a
plate-plate separation of 0.2 cm and a plate length of 1cm. Augment the
model by surrounding the capacitor in air (relative dielectric
permitivity = 1.0). Vary the permitivity of the dielectric inside the
capacitor; compute and plot the electric flux density for each case.
Observe and demonstrate the fringing fields around the electrodes.
Record and report your obervations and conclusions.
Part 3: Fields inside a MOSFET
- Background: Refer to Dr. Linda Head's presentation on
the
theory of operation of MOSFETs. You can download the presentation here .
- You are required to model, compute and display the electrostatic
field distribution inside the MOSFET for the various operating
conditions: Depletion, Inversion, Linear and Pinch-off. Also, calculate
the drain-source capacitance accross the device for the various
operating conditions. The four operating regions have been reproduced
here - however, refer to the slides handed out to you for clarity. For
each case, record and report your obervations and conclusions.
The lab project report must be in the usual
format .
