ece 874: physical electronics prof. virginia ayres electrical & computer engineering michigan...
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VM Ayres, ECE874, F12 Example problem: what is the average value of the x-component of linear momentum p for a nearly free electron in GaAs, described by the traveling wave: Travelling wave moving RTRANSCRIPT
ECE 874:Physical Electronics
Prof. Virginia AyresElectrical & Computer EngineeringMichigan State [email protected]
VM Ayres, ECE874, F12
Lecture 08, 25 Sep 12
VM Ayres, ECE874, F12
Example problem: what is the average value of the x-component of linear momentum p for 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
No use made of GaAs: purely wave-like.
VM Ayres, ECE874, F12
No use made of GaAs: purely wave-like.
VM Ayres, ECE874, F12
Travelling wave moving R
VM Ayres, ECE874, F12
VM Ayres, ECE874, F12
Example problem: for this nearly free electron in GaAs, write a simple statement of conservation of energy (no calculation required):
Travelling wave moving R
VM Ayres, ECE874, F12
VM Ayres, ECE874, F12
= hbark
Dispersion diagram: E-k:
VM Ayres, ECE874, F12
This electron:
Satisfies conservation of energy:
For physical situation U(x,y,z) = 0.
VM Ayres, ECE874, F12
Chp. 02: 3 important examples of electron showing wavelike properties
1. Free electronAn electron between scattering events during transport in a semiconductor is often nearly freeMotivation: low heat transistors (hard in 3D due to plenty of scattering)
2. Electron in an infinite potential well3. Electron in a finite potential well4. 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 E = hc/what you see is light of precise wavelength
VM Ayres, ECE874, F12
2. Electron in an infinite potential well
Describing its wave properties: (x,y,x,t)
Several choices: physical situation in conservation of energy selects the right one
VM Ayres, ECE874, F12
2. Electron in an infinite potential well
U(x,y,z) => U(x)
a
VM Ayres, ECE874, F12
2. Electron in an infinite potential well
U(x,y,z) => U(x)
a
VM Ayres, ECE874, F12
a
Expectations:
VM Ayres, ECE874, F12
a
Expectations:
VM Ayres, ECE874, F12
Use conservation of energy to find 2 things:1. (x): correct wave description of electron2. total energy E
For:
U(x)eV
a nm0
VM Ayres, ECE874, F12
Worked through pp. 37-38 on board:
VM Ayres, ECE874, F12
Worked through pp. 37-38 on board:
VM Ayres, ECE874, F12
Useful consequence: clean laser light emission from a quantum well. Example: GaAs:
1.43 eV
In a transition from the first conduction band energy level to the first valence (bonding) band energy level, en electron will loose this amount of energy E(next page).
VM Ayres, ECE874, F12
M. Arai, et al19th IPRM Conference, Matsue, Japan
VM Ayres, ECE874, F12
Also have discreet energies AND momentum value on the dispersion diagram:
1.43 eV
Conduction band
Valence band