1. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/
Semiconductor Device Modeling and Characterization – EE5342 Lecture 8 – Spring 2011
Professor Ronald L. Carter

2. First Assignment e-mail to listserv@listserv.uta.edu
In the body of the message include subscribe EE5342
This will subscribe you to the EE5342 list. Will receive all EE5342 messages
If you have any questions, send to with EE5342 in subject line.
©rlc L08-11Feb2011

3. Second Assignment
Submit a signed copy of the document that is posted at
©rlc L08-11Feb2011

4. Additional University Closure Means More Schedule Changes
Plan to meet until noon some days in the next few weeks. This way we will make up for the lost time. The first extended class will be Monday, 2/14.
The MT changed to Friday 2/18
The P1 test changed to Friday 3/11.
The P2 test is still Wednesday 4/13
The Final is still Wednesday 5/11.
©rlc L08-11Feb2011

5. Shockley-Read- Hall Recomb
Indirect, like Si, so intermediate state Ec Ec ET Ef
Efi Ev Ev k
©rlc L08-11Feb2011

6. S-R-H trap characteristics1
The Shockley-Read-Hall Theory requires an intermediate “trap” site in order to conserve both E and p
If trap neutral when orbited (filled) by an excess electron - “donor-like”
Gives up electron with energy Ec - ET
“Donor-like” trap which has given up the extra electron is +q and “empty”
©rlc L08-11Feb2011

7. S-R-H trap char. (cont.)
If trap neutral when orbited (filled) by an excess hole - “acceptor-like”
Gives up hole with energy ET - Ev
“Acceptor-like” trap which has given up the extra hole is -q and “empty”
Balance of 4 processes of electron capture/emission and hole capture/ emission gives the recomb rates
©rlc L08-11Feb2011

8. tpo = (Ntvthsn)-1, where sn~p(rBohr)2
S-R-H recombination
Recombination rate determined by:
Nt (trap conc.),
vth (thermal vel of the carriers),
sn (capture cross sect for electrons),
sp (capture cross sect for holes), with
tno = (Ntvthsn)-1, and
tpo = (Ntvthsn)-1, where sn~p(rBohr)2
©rlc L08-11Feb2011

9. S-R-H recomb. (cont.)
In the special case where tno = tpo = to the net recombination rate, U is
©rlc L08-11Feb2011

10. S-R-H “U” function characteristics
The numerator, (np-ni2) simplifies in the case of extrinsic material at low level injection (for equil., nopo = ni2)
For n-type (no > dn = dp > po = ni2/no):
(np-ni2) = (no+dn)(po+dp)-ni2 = nopo - ni2 + nodp + dnpo + dndp ~ nodp (largest term)
Similarly, for p-type, (np-ni2) ~ podn
©rlc L08-11Feb2011

11. S-R-H “U” function characteristics (cont)
For n-type, as above, the denominator = to{no+dn+po+dp+2nicosh[(Et-Ei)kT]}, simplifies to the smallest value for Et~Ei, where the denom is tono, giving U = dp/to as the largest (fastest)
For p-type, the same argument gives U = dn/to
Rec rate, U, fixed by minority carrier
©rlc L08-11Feb2011

12. S-R-H net recom- bination rate, U
In the special case where tno = tpo = to = (Ntvthso)-1 the net rec. rate, U is
©rlc L08-11Feb2011

13. S-R-H rec for excess min carr
For n-type low-level injection and net excess minority carriers, (i.e., no > dn = dp > po = ni2/no),
U = dp/to, (prop to exc min carr)
For p-type low-level injection and net excess minority carriers, (i.e., po > dn = dp > no = ni2/po),
U = dn/to, (prop to exc min carr)
©rlc L08-11Feb2011

14. Minority hole lifetimes. Taken from Shur3, (p.101).
©rlc L08-11Feb2011

15. Minority electron lifetimes. Taken from Shur3, (p.101).
©rlc L08-11Feb2011

16. Parameter example tmin = (45 msec) 1+(7.7E-18cm3)Ni+(4.5E-36cm6)Ni2
For Nd = 1E17cm3, tp = 25 msec
Why Nd and tp ?
©rlc L08-11Feb2011

17. M. E. Law, E. Solley, M. Liang, and D. E
M. E. Law, E. Solley, M. Liang, and D. E. Burk, “Self-Consistent Model of Minority-Carrier Lifetime, Diffusion Length, and Mobility,” IEEE Electron Device Lett., vol. 12, pp , 1991.
©rlc L08-11Feb2011

18. M. E. Law, E. Solley, M. Liang, and D. E
M. E. Law, E. Solley, M. Liang, and D. E. Burk, “Self-Consistent Model of Minority-Carrier Lifetime, Diffusion Length, and Mobility,” IEEE Electron Device Lett., vol. 12, pp , 1991.
©rlc L08-11Feb2011

19. ©rlc L08-11Feb2011

20. S-R-H rec for deficient min carr
If n < ni and p < pi, then the S-R-H net recomb rate becomes (p < po, n < no):
U = R - G = - ni/(2t0cosh[(ET-Efi)/kT])
And with the substitution that the gen lifetime, tg = 2t0cosh[(ET-Efi)/kT], and net gen rate U = R - G = - ni/tg
The intrinsic concentration drives the return to equilibrium
©rlc L08-11Feb2011

21. The Continuity Equation
The chain rule for the total time derivative dn/dt (the net generation rate of electrons) gives
©rlc L08-11Feb2011

22. The Continuity Equation (cont.)
©rlc L08-11Feb2011

23. The Continuity Equation (cont.)
©rlc L08-11Feb2011

24. The Continuity Equation (cont.)
©rlc L08-11Feb2011

25. The Continuity Equation (cont.)
©rlc L08-11Feb2011

26. The Continuity Equation (cont.)
©rlc L08-11Feb2011

27. The Continuity Equation (cont.)
©rlc L08-11Feb2011

28. References
*Fundamentals of Semiconductor Theory and Device Physics, by Shyh Wang, Prentice Hall, 1989.
**Semiconductor Physics & Devices, by Donald A. Neamen, 2nd ed., Irwin, Chicago.
M&K = Device Electronics for Integrated Circuits, 3rd ed., by Richard S. Muller, Theodore I. Kamins, and Mansun Chan, John Wiley and Sons, New York, 2003.
1Device Electronics for Integrated Circuits, 2 ed., by Muller and Kamins, Wiley, New York, 1986.
2Physics of Semiconductor Devices, by S. M. Sze, Wiley, New York, 1981.
3 Physics of Semiconductor Devices, Shur, Prentice-Hall, 1990.
©rlc L08-11Feb2011