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

2. Lecture 23, 15 Nov 12
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3. With these expressions for n and p, can get several familiar results:
VM Ayres, ECE874, F12

4. Familiar results: for EF =Ei:
pi =
VM Ayres, ECE874, F12

5. Familiar results: doped n and p in terms of intrinsic ni and Ei:
VM Ayres, ECE874, F12

6. New result: Exact position of Ei:
Step 1.
Step 2.
VM Ayres, ECE874, F12

7. New result: Exact position of Ei:
VM Ayres, ECE874, F12

8. New result: effect of degenerate doping (Pr. 4.12):
VM Ayres, ECE874, F12

9. New result: effect of degenerate doping (Pr. 4.12):
“At the degenerate limit”:
EC – EF = 3kT
(EF – EC = -3kT)
EF – EV = 3 kT
(EV – EF = -3kT)
VM Ayres, ECE874, F12

10. VM Ayres, ECE874, F12

11. Return to simple energy band diagrams:
VM Ayres, ECE874, F12

12. Also: KE goes up as PE goes down, and vice versa
PE: same shape as Ec.
Also: KE goes up as PE goes down, and vice versa
V: upside down from PE/Ec
Plot of (-) slope of V
n or p: check EF – Ei or Ei - EF
VM Ayres, ECE874, F12

13. VM Ayres, ECE874, F12

14. Exponential donor doping L to R leading to uniform built-in electric field
Schottky barrier between a p-type semiconductor and a metal having a smaller work function
p-n-p transitor
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15. (b) E : Plot of (-) slope of V
PE: Same shape as Ec
(a) V: Upside down from PE/Ec
(b) E : Plot of (-) slope of V x E
VM Ayres, ECE874, F12

16. (d) KE: PE goes down, KE goes up
(c) PE: Same shape as Ec
(d) KE: PE goes down, KE goes up
(e) n or p: check EF – Ei or Ei - EF
0 n n n
(log)
Concentration
(cm-3) x
VM Ayres, ECE874, F12

17. (d) KE: PE goes down, KE goes up
(c) PE: Same shape as Ec
(d) KE: PE goes down, KE goes up
(e) n or p: check EF – Ei or Ei - EF
0 n n n
(log)
Concentration
(cm-3) p x
VM Ayres, ECE874, F12

18. (b) E : Plot of (-) slope of V
PE: Same shape as Ec
(a) V: Upside down from PE/Ec
(b) E : Plot of (-) slope of V E x
VM Ayres, ECE874, F12

19. (d) KE: PE goes down, KE goes up
PE: Same shape as Ec
(d) KE: PE goes down, KE goes up
(e) n or p: check EF – Ei or Ei - EF n n p
pmax
(log)
Concentration
(cm-3) x
VM Ayres, ECE874, F12

20. (d) KE: PE goes down, KE goes up
PE: Same shape as Ec
(d) KE: PE goes down, KE goes up
(e) n or p: check EF – Ei or Ei - EF n n p
pmax
(log)
Concentration
(cm-3) x
VM Ayres, ECE874, F12

21. Chp. 05: Recombination-Generation Processes
Skipping: space charge neutrality dopant ionization as a function of temperature
Chp. 05: Recombination-Generation Processes
VM Ayres, ECE874, F12