1. ECE 875: Electronic Devices
Prof. Virginia Ayres
Electrical & Computer Engineering
Michigan State University

2. Net transition rate U for: Chp. 01: find a time t: a lifetime
Lecture 13, 07 Feb 14
Chp. 01 – Chp. 02
Net transition rate U for:
Chp. 01: find a time t: a lifetime
Chp. 02: find an extra current due to generation or recombination
VM Ayres, ECE875, S14

3. Definition and uses of U:
U = net transition rate = # of band-to-band transitions / Vol s.
The corresponding current is: IR-G = q U length Area
Definition of band-to band transitions: from EV to EC and from EC back to EV
Electrons in EC and holes in EV  to usable current I (Amps)
Band-to band transitions can happen via direct band-to-band generation and recombination OR
Band-to band transitions can happen via intermediate trap-based generation and recombination
“Injection” refers to operation of a pn junction

4. Low level injection in a trap-dominated material: U  Eq (92) (indirect bandgap material like Si):
Eq’s 95 assume: Et = Ei in Eq (92):

5. Review: Low level injection: normal forward bias operation of a pn junction:
pp0 ≈ NA-
nn0 ≈ ND+
Minority carrier pn0 < Dp < majority carrier nn0
Minority carrier np0 < Dn < majority carrier pp0
pn0 ≈ ni2/n=ND+ Lp
np0 ≈ ni2/p=NA- Ln
excess holes: Dp
electrons: Dn
VM Ayres, ECE875, S14

6. Example: What are n and p under conditions of low level injection:
(a) on the n-side?
(b) on the p-side?

7. Answer:
(a)
(b)

8. Example: What is (np – ni2) under conditions of low level injection:
(a) on the n-side?
(b) on the p-side?

9. Answer:
(a)

10. (a)
Example: moderately doped 300K

11. Also: for fully ionized: exact

12. Either way: Answer:
(a)

13. Answer:
(b)

14. Low level injection in a trap-dominated material: U  Eq (92) (indirect bandgap material like Si):
Pr. 1.25: Et = Ei in Eq (95): what happens when it is not?
Pr. 1.25: sp = sn = s0
tp = tn = tr0

15. VM Ayres, ECE875, S14

16. Find U in usual way
Note that s0 can be written in terms of tr0
Set U that you found = U as given to solve for tr
Set tr = 2t0
Solve for Et - Ei
Importance of Pr. 1.25: that you can deal with Et a little above or a little below Ei since this is what you will really be working with.

17. Net transition rate U for: Chp. 01: find a time t: a lifetime
Lecture 13, 07 Feb 14
Chp. 01 – Chp. 02
Net transition rate U for:
Chp. 01: find a time t: a lifetime
Chp. 02: find an extra current due to generation or recombination
VM Ayres, ECE875, S14

19. Igen = ? OR
Irec = ?
Which: are you in forward or reverse bias?
What happens to the depletion region WD?

27. Igen = ? OR
Irec = ?
Which: are you in forward or reverse bias?
What happens to the depletion region WD?

29. = everything that’s left in U
In Pr. 2.07: tg is given.

31. Igen = ? OR
Irec = ?
Which: are you in forward or reverse bias?
What happens to the depletion region WD?