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

2. VM Ayres, ECE874, F12 Lecture 09, 27 Sep 12

3. VM Ayres, ECE874, F12 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 m 0 m* h = 0.074 m 0 (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?

4. VM Ayres, ECE874, F12

5. Useful consequence: clean laser light emission from a quantum well. Example: GaAs: 1.43 eV Wavelength (nm) 700800900 Ideal: single Real: small spread around

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 m 0 m* h = 0.074 m 0 (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  2 h bar 2 /2m* e a 2 ?

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

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

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

11. VM Ayres, ECE874, F12

12. C) Is energy 10 x  2 h bar 2 /2m* e a 2 OK?

13. VM Ayres, ECE874, F12 C) NO, 10 x  2 h bar 2 /2m* e a 2 is not an allowed infinite SQW energy level. 1212 3232 2

14. VM Ayres, ECE874, F12 -∞a0+∞ U(x) eV nm I (Amps) M. Arai, et al 19 th IPRM Conference, Matsue, Japan 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:

15. VM Ayres, ECE874, F12 box = well

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

17. VM Ayres, ECE874, F12

18. Also in Lecture 07:

19. VM Ayres, ECE874, F12 Working tools:

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