ECE 606 Lecture 3: Emergence of Bandstructure

By Gerhard Klimeck

Electrical and Computer Engineering, Purdue University, West Lafayette, IN

Published on

Abstract

Table of Contents:

00:00 ECE606: Solid State Devices Lecture 3
00:24 Motivation
01:17 Time-independent Schrodinger Equation
02:22 Time-independent Schrodinger Equation
04:23 A Simple Differential Equation
05:29 Presentation Outline
05:46 Full Problem Difficult: Toy Problems First
06:07 Case 1: Solution for Particles with E>>U
06:57 Free Particle …
07:57 Full Problem Difficult: Toy Problems First
08:02 Case 2: Bound State Problems
10:53 1-D Particle in a Box – A Solution Guess
11:57 1-D Particle in a Box – Visualization
13:01 1-D Particle in a Box – Normalization to ONE particle
15:02 1-D Particle in a Box – The Solution
16:06 1-D Particle in a Box – Quantum vs. Macroscopic
17:17 Presentation Outline
17:26 Full Problem Difficult: Toy Problems First
17:33 Five Steps for Closed System Analytical Solution
19:03 Case 2: Bound-levels in Finite Well (steps 1,2)
20:36 Case 2: Bound-levels in Finite Well (steps3)
23:39 Case 2: Bound-levels in Finite Well (step 4)
25:08 Case 2: Bound-levels in Finite Well (steps 4 graphical)
26:18 Case 2: Bound-levels in Finite Well (steps 4 graphical)
26:49 Case 2: Bound-levels in Finite Well (steps 5 wavefunction)
27:12 Step 5: Wave-functions
27:42 Key Summary of a Finite Quantum Well
29:16 Presentation Outline
29:24 Transmission through a single barrier Scattering Matrix approach
30:17 Tunneling through a single barrier
30:48 Single barrier case
32:38 Generalization to Transfer Matrix Method
33:31 Single barrier case
36:38 Single barrier : Concepts
39:25 Effect of barrier thickness below the barrier
40:29 Single Barrier – Key Summary
41:00 Presentation Outline
41:05 Double Barrier Transmission: Scattering Matrix approach
41:17 Reminder: Single barrier
41:52 Double barrier: Concepts
42:37 Double barrier: Quasi-bound states
43:23 Effect of barrier height
44:59 Effect of barrier thickness
45:00 Double barrier energy levels Vs Closed system
45:31 Particle in a box
45:44 Double barrier & particle in a box
46:33 Open systems Vs closed systems
47:36 Reason for deviation?
48:30 Double Barrier Structures - Key Summary
49:07 Presentation Outline
49:14 1 Well => 1 Transmission Peak
49:37 2 Wells => 2 Transmission Peaks
50:09 3 Wells => 3 Transmission Peaks
50:19 4 Wells => 4 Transmission Peaks
50:20 5 Wells => 5 Transmission Peaks
50:21 6 Wells => 6 Transmission Peaks
50:24 7 Wells => 7 Transmission Peaks
50:25 8 Wells => 8 Transmission Peaks
50:39 9 Wells => 9 Transmission Peaks
50:40 19 Wells => 19 Transmission Peaks
50:42 29 Wells => 29 Transmission Peaks
50:44 39 Wells => 39 Transmission Peaks
50:45 49 Wells => 49 Transmission Peaks
51:20 N Wells => N Transmission Peaks
52:30 1 Well => 1 Transmission Peak => 1 State
52:37 2 Wells => 2 Transmission Peaks => 2 States
52:39 3 Wells => 3 Transmission Peaks => 3 States
52:39 4 Wells => 4 Transmission Peaks => 4 States
52:40 5 Wells => 5 Transmission Peaks => 5 States
52:40 6 Wells => 6 Transmission Peaks => 6 States
53:05 7 Wells => 7 Transmission Peaks => 7 States
53:05 8 Wells => 8 Transmission Peaks => 8 States
53:06 9 Wells => 9 Transmission Peaks => 9 States
53:06 19 Wells => 19 Transmission Peaks => 19 States
53:09 29 Wells => 29 Transmission Peaks => 29 States
53:09 39 Wells => 39 Transmission Peaks => 39 States
53:11 49 Wells => 49 Transmission Peaks => 49 States
54:05 N Wells => N Transmission Peaks => N States
54:53 N Wells => N States => 1 Band
55:07 N Wells => 2N States => 2 Bands
55:48 N Wells => 2N States => 2 Bands
55:59 X States/Well => X Bands
57:10 X States/Well => X Bands
57:37 Formation of energy bands
57:59 Presentation Outline
58:41 Five Steps for Closed System Analytical Solution
59:10 Open System: Generalization to Transfer Matrix Method
59:36 Presentation Outline
59:39 Numerical solution of Schrodinger Equation
60:09 (1) Define a grid …
60:33 Second Derivative on a Finite Mesh
62:06 (2) Express equation in Finite Difference Form
62:56 (3) Define the matrix …
63:44 (4) Solve the Eigen-value Problem

Cite this work

Researchers should cite this work as follows:

  • Gerhard Klimeck (2012), "ECE 606 Lecture 3: Emergence of Bandstructure," http://nanohub.org/resources/15124.

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Location

CIVL 2104, Purdue University, West Lafayette, IN

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