ece 874: physical electronics
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ECE 874: Physical Electronics. Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University [email protected]. Lecture 08, 25 Sep 12. - PowerPoint PPT PresentationTRANSCRIPT
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
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VM Ayres, ECE874, F12
= hbark
Dispersion diagram: E-k:
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This electron:
Satisfies conservation of energy:
For physical situation U(x,y,z) = 0.
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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
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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
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2. Electron in an infinite potential well
U(x,y,z) => U(x)
a
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2. Electron in an infinite potential well
U(x,y,z) => U(x)
a
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a
Expectations:
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a
Expectations:
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Use conservation of energy to find 2 things:1. (x): correct wave description of electron2. total energy E
For:
U(x)eV
a nm0
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Worked through pp. 37-38 on board:
VM Ayres, ECE874, F12
Worked through pp. 37-38 on board:
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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).
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M. Arai, et al19th IPRM Conference, Matsue, Japan
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Also have discreet energies AND momentum value on the dispersion diagram:
1.43 eV
Conduction band
Valence band