Semiconductor Device Modeling and Characterization – EE5342 Lecture 8 – Spring 2011

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

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 ronc@uta.edu, with EE5342 in subject line.

3. Second Assignment • Submit a signed copy of the document that is posted at www.uta.edu/ee/COE%20Ethics%20Statement%20Fall%2007.pdf

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.

5. Shockley-Read-Hall Recomb E Indirect, like Si, so intermediate state Ec Ec ET Ef Efi Ev Ev k

6. S-R-H trapcharacteristics1 • 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”

7. S-R-H trapchar. (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

8. 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

9. S-R-Hrecomb. (cont.) • In the special case where tno = tpo = to the net recombination rate, U is

10. S-R-H “U” functioncharacteristics • 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

11. S-R-H “U” functioncharacteristics (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

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

13. S-R-H rec forexcess 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)

14. Minority hole lifetimes. Taken from Shur3, (p.101).

15. Minority electron lifetimes. Taken from Shur3, (p.101).

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 ?

17. 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. 401-403, 1991.

18. 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. 401-403, 1991.

20. S-R-H rec fordeficient 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

21. The ContinuityEquation • The chain rule for the total time derivative dn/dt (the net generation rate of electrons) gives

22. The ContinuityEquation (cont.)

23. The ContinuityEquation (cont.)

24. The ContinuityEquation (cont.)

25. The ContinuityEquation (cont.)

26. The ContinuityEquation (cont.)

27. The ContinuityEquation (cont.)

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.