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

2. Lecture 21, 12 Nov 12
VM Ayres, ECE874, F12

3. f(E) = probability = Fermi distribution function
Streetman and Banerjee, Solid State Electronic Devices
(Pierret Section 4.2 and Pr. 4.8)
VM Ayres, ECE874, F12

4. The Fermi (energy) level EF:
50%
VM Ayres, ECE874, F12

5. At T = 0K:
VM Ayres, ECE874, F12

6. f(E) at T above 0K:
VM Ayres, ECE874, F12

7. f(E) at T above 0K:
VM Ayres, ECE874, F12

8. DOS available states Versus f(E) and EF
VM Ayres, ECE874, F12

9. VM Ayres, ECE874, F12

10. VM Ayres, ECE874, F12

11. Approximation/limits on f(E):
Recall:
Two conditions:
Temperature T
E – EF > 0
E – EF < 0
VM Ayres, ECE874, F12

12. Restricting E to values for which there are available states this is:
Two conditions:
Temperature T
E – EF > 0, where E > EC
E – EF < 0, where E < EV E EC Ei EV
VM Ayres, ECE874, F12

13. Two conditions => Four conditions:
Temperature T
Degeneracy
E – EF > 0 => EF < EC < E versus EC < E < EF
1. Non-degenerate n-type doping
2. Degenerate n-type doping EF E EC EC EF Ei Ei EV EV
VM Ayres, ECE874, F12

14. Four conditions: E Temperature T Degeneracy
EF – E > 0 => E < EC < EV versus E < EV < EF
3. Non-degenerate p-type doping
4. Degenerate p-type doping EC EC Ei Ei EF EV EV E EF
VM Ayres, ECE874, F12

15. Approximation/limits on f(E):
VM Ayres, ECE874, F12

16. Approximation/limits on f(E):
VM Ayres, ECE874, F12

17. Approximation/limits on f(E):
Use the “hot” limit in ECE 874.
VM Ayres, ECE874, F12

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