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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 09, 27 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 09, 27 Sep 12 VM Ayres, ECE874, F12

  3. Example problem: a single quantum well (SQW) that can be approximated as infinite is built with GaAs as the active layer. The SQW is 10 nm wide. The device will operate at room temperature. A) What is the emission wavelength of laser light from this well from the first conduction band energy level to the first valence band energy level? For GaAs m*e = 0.067 m0 m*h = 0.074 m0 (Chp. 03: “light” hole) B) For comparison, what is the emission wavelength from the lowest conduction band energy level to the highest valence band energy level for bulk GaAs? VM Ayres, ECE874, F12

  4. VM Ayres, ECE874, F12

  5. Useful consequence: clean laser light emission from a quantum well. Example: GaAs: Real: small spread around l Ideal: single l 1.43 eV 700 800 900 Wavelength (nm) VM Ayres, ECE874, F12

  6. VM Ayres, ECE874, F12

  7. Example problem: a single quantum well (SQW) that can be approximated as infinite is built with GaAs as the active layer. The SQW is 10 nm wide. The device will operate at room temperature. For GaAs m*e = 0.067 m0 m*h = 0.074 m0 (Chp. 03: “light” hole) A) What is the energy in eV of the first conduction band energy level? B) What is the corresponding momentum p? C) Is the conduction band electron allowed to “have” (occupy an energy level) of: 10 x p2hbar2/2m*ea2 ? VM Ayres, ECE874, F12

  8. A) If you set 0 eV as the top valence band energy level, it’s the same number as in the last problem: 1.43 eV 0 eV VM Ayres, ECE874, F12

  9. A) If you set 0 eV as the lowest conduction band energy level in bulk GaAs it is just the part. 0 eV 1.43 eV Using this definition for 0 eV, next slide VM Ayres, ECE874, F12

  10. B) For energy and corresponding momentum, easiest to use the infinite SQW dispersion diagram: VM Ayres, ECE874, F12

  11. VM Ayres, ECE874, F12

  12. C) Is energy 10 x p2hbar2/2m*ea2 OK? VM Ayres, ECE874, F12

  13. C) NO, 10 x p2hbar2/2m*ea2 is not an allowed infinite SQW energy level. 32 22 12 VM Ayres, ECE874, F12

  14. Comment on 1-D problems: In this multiple quantum well (MQW) physical situation U(x,y,z) => U(x). The important action really does happen in just one direction that you can pick to be x. 3 of these: U(x) eV I (Amps) M. Arai, et al 19th IPRM Conference, Matsue, Japan -∞ 0 a +∞ nm VM Ayres, ECE874, F12

  15. box = well VM Ayres, ECE874, F12

  16. From Lecture 07: VM Ayres, ECE874, F12

  17. VM Ayres, ECE874, F12

  18. Also in Lecture 07: VM Ayres, ECE874, F12

  19. Working tools: VM Ayres, ECE874, F12

  20. Answers I can find: VM Ayres, ECE874, F12

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