ECE 606 Solid State Devices L18.3: Semiconductor Equations - Numerical Solutions

Table of Contents:
00:00 S18.3 Numerical Solutions
00:13 Section 18 Semiconductor Equations
00:25 Preface
01:50 Equations to be solved
02:09 1) The Semiconductor Equations
06:07 1) The Mathematical Problem
07:40 Section 18 Semiconductor Equations
07:44 Section 18 Semiconductor Equations
07:49 2) The Grid
09:23 Finite Difference Expression for Derivative
10:28 The Second Derivative …
11:44 Section 18 Semiconductor Equations
11:55 Section 18 Semiconductor Equations
12:07 2) Control Volume
12:39 Discretizing Poisson's Equation
16:17 Discretizing Continuity Equations
18:21 Three Discretized Equations
18:43 Numerical Solution – Poisson Equation Only
20:09 Boundary conditions
21:32 Section 18 Semiconductor Equations
21:46 Section 18 Semiconductor Equations
21:49 Numerical Solution…
25:11 3) Uncoupled Numerical Solution
27:00 Summary
27:49 Section 18 Semiconductor Equations

This course provides the graduate-level introduction to understand, analyze, characterize and design the operation of semiconductor devices such as transistors, diodes, solar cells, light-emitting devices, and more.

The material will primarily appeal to electrical engineering students whose interests are in applications of semiconductor devices in circuits and systems. The treatment is physics-based, provides derivations of the mathematical descriptions, and enables students to quantitatively analyze device internal processes, analyze device performance, and begin the design of devices given specific performance criteria.

Technology users will gain an understanding of the semiconductor physics that is the basis for devices. Semiconductor technology developers may find it a useful starting point for diving deeper into condensed matter physics, statistical mechanics, thermodynamics, and materials science. The course presents an electrical engineering perspective on semiconductors, but those in other fields may find it a useful introduction to the approach that has guided the development of semiconductor technology for the past 50+ years.