ECE 874: Physical Electronics Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University ayresv@msu.edu
Lecture 07, 20 Sep 12 VM Ayres, ECE874, F12
Chp. 02: 3 important examples of electron showing wavelike properties Free electron An electron between scattering events during transport in a semiconductor is often nearly free Motivation: low heat transistors Electron in an infinite potential well Electron in a finite potential well Pr. 2.7: Electrons in a triangular well = realistic Motivation: these are all about Quantum well lasers: Arai article: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4265925 Transitions between quantized energy levels DE = hc/l : what you see is light of precise wavelength l VM Ayres, ECE874, F12
Approach: conservation of energy applied to wavelike electrons VM Ayres, ECE874, F12
Approach: conservation of energy applied to wavelike electrons/particles: VM Ayres, ECE874, F12
Approach: conservation of energy applied to wavelike electrons VM Ayres, ECE874, F12
Approach: conservation of energy applied to wavelike electrons VM Ayres, ECE874, F12
Approach: conservation of energy applied to wavelike electrons VM Ayres, ECE874, F12
Example problem: what is the KE of a nearly free electron in GaAs, described by the traveling wave: VM Ayres, ECE874, F12
Example problem: what is the KE of a nearly free electron in GaAs, described by the traveling wave: Travelling wave moving R * VM Ayres, ECE874, F12
VM Ayres, ECE874, F12
VM Ayres, ECE874, F12
Example problem: what is the total energy E of a nearly free electron in GaAs, described by the traveling wave: VM Ayres, ECE874, F12
VM Ayres, ECE874, F12
This is a particular example of a problem that has a time independent formulation, p 31-32. VM Ayres, ECE874, F12
I’d ask: what do I need to get to this since I know it equals 1. VM Ayres, ECE874, F12
VM Ayres, ECE874, F12
1. Free or nearly free electron/particle: Find y(x,t) VM Ayres, ECE874, F12
VM Ayres, ECE874, F12
VM Ayres, ECE874, F12
Already did these as example problems: For a free particle, the energy is all kinetic. The pot’l energy U(x,y,z) associated with its physical situation is 0. VM Ayres, ECE874, F12
Dispersion diagram: E-k: = hbark VM Ayres, ECE874, F12