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ECE 874: Physical Electronics

ECE 874: Physical Electronics. Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University ayresv@msu.edu. Lecture 08, 25 Sep 12.

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ECE 874: Physical Electronics

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  1. ECE 874:Physical Electronics Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University ayresv@msu.edu

  2. Lecture 08, 25 Sep 12 VM Ayres, ECE874, F12

  3. 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

  4. VM Ayres, ECE874, F12

  5. VM Ayres, ECE874, F12

  6. No use made of GaAs: purely wave-like. VM Ayres, ECE874, F12

  7. No use made of GaAs: purely wave-like. VM Ayres, ECE874, F12

  8. Travelling wave moving R l VM Ayres, ECE874, F12

  9. VM Ayres, ECE874, F12

  10. 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

  11. VM Ayres, ECE874, F12

  12. Dispersion diagram: E-k: = hbark VM Ayres, ECE874, F12

  13. This electron: Satisfies conservation of energy: For physical situation U(x,y,z) = 0. VM Ayres, ECE874, F12

  14. 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 (hard in 3D due to plenty of scattering) • 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

  15. 2. Electron in an infinite potential well Describing its wave properties: y(x,y,x,t) Several choices: physical situation in conservation of energy selects the right one VM Ayres, ECE874, F12

  16. 2. Electron in an infinite potential well U(x,y,z) => U(x) a VM Ayres, ECE874, F12

  17. 2. Electron in an infinite potential well U(x,y,z) => U(x) a VM Ayres, ECE874, F12

  18. Expectations: VM Ayres, ECE874, F12

  19. Expectations: VM Ayres, ECE874, F12

  20. Use conservation of energy to find 2 things:1. y(x): correct wave description of electron2. total energy E For: U(x) eV VM Ayres, ECE874, F12 0 a nm

  21. Worked through pp. 37-38 on board: VM Ayres, ECE874, F12

  22. Worked through pp. 37-38 on board: VM Ayres, ECE874, F12

  23. Useful consequence: clean laser light emission from a quantum well. Example: GaAs: 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 DE (next page). 1.43 eV VM Ayres, ECE874, F12

  24. M. Arai, et al 19th IPRM Conference, Matsue, Japan VM Ayres, ECE874, F12

  25. Also have discreet energies AND momentum value on the dispersion diagram: Conduction band 1.43 eV Valence band VM Ayres, ECE874, F12

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