EE 4345 - Semiconductor Electronics Design Project Spring 2002 - Lecture 04

1. EE 4345 - Semiconductor Electronics Design Project Spring 2002 - Lecture 04 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/

2. Practical Junctions • Junctions are formed by diffusion or implantation into a uniform concentration wafer. The profile can be approximated by a step or linear function in the region of the junction. • If a step, then previous models OK. • If not, 1/2 --> M, 1/3 < M < 1/2.

3. Law of the junction(injection of minority carr.)

4. Carrier Injection and diff. ln(carrier conc) ln Na ln Nd ln ni ~Va/Vt ~Va/Vt ln ni2/Nd ln ni2/Na x xnc -xpc -xp xn 0

5. Ideal diodeequation • I = Is [exp(Va/nVt)-1], Is = Isn + Isp

6. Diffnt’l, one-sided diode conductance ID Static (steady-state) diode I-V characteristic IQ Va VQ

7. Diffnt’l, one-sided diode cond. (cont.)

8. Charge distr in a (1-sided) short diode dpn • Assume Nd << Na • The sinh (see L12) excess minority carrier distribution becomes linear for Wn << Lp dpn(xn)=pn0expd(Va/Vt) • Total chg = Q’p = Q’p = qdpn(xn)Wn/2 Wn = xnc- xn dpn(xn) Q’p x xn xnc

9. Charge distr in a 1-sided short diode dpn • Assume Quasi-static charge distributions • Q’p = Q’p = qdpn(xn)Wn/2 • ddpn(xn) = (W/2)* {dpn(xn,Va+dV) - dpn(xn,Va)} dpn(xn,Va+dV) dpn(xn,Va) dQ’p Q’p x xnc xn

10. Cap. of a (1-sided) short diode (cont.)

11. Diode equivalentcircuit (small sig) ID h is the practical “ideality factor” IQ VD VQ

12. Small-signal eqcircuit Cdiff and Cdepl are both charged by Va = VQ Va rdiff Cdepl Cdiff

13. Reverse biasjunction breakdown • Avalanche breakdown • Electric field accelerates electrons to sufficient energy to initiate multiplication of impact ionization of valence bonding electrons • field dependence shown on next slide • Heavily doped narrow junction will allow tunneling - see Neamen*, p. 274 • Zener breakdown

14. Ecrit for reverse breakdown (M&K**) Taken from p. 198, M&K**

15. Reverse biasjunction breakdown • Assume-Va = VR >> Vbi, so Vbi-Va-->VR • Since Emax= 2(Vbi-Va)/W , when Emax = Ecrit BV = e (Ecrit )2/(2qN-)

16. BV for reverse breakdown (M&K**) Taken from Figure 4.13, p. 198, M&K** Breakdown voltage of a one-sided, plan, silicon step junction showing the effect of junction curvature.4,5

17. References * Semiconductor Physics and Devices, 2nd ed., by Neamen, Irwin, Boston, 1997. **Device Electronics for Integrated Circuits, 2nd ed., by Muller and Kamins, John Wiley, New York, 1986.

18. Diode Switching • Consider the charging and discharging of a Pn diode • (Na > Nd) • Wd << Lp • For t < 0, apply the Thevenin pair VF and RF, so that in steady state • IF = (VF - Va)/RF, VF >> Va , so current source • For t > 0, apply VR and RR • IR = (VR + Va)/RR, VR >> Va, so current source

19. Diode switching(cont.) VF,VR >> Va F: t < 0 Sw RF R: t > 0 VF + RR D VR +

20. Diode chargefor t < 0 pn pno x xn xnc

21. Diode charge fort >>> 0 (long times) pn pno x xn xnc

22. Equationsummary

23. Snapshot for tbarely > 0 pn Total charge removed, Qdis=IRt pno x xn xnc

24. I(t) for diodeswitching ID IF ts ts+trr t - 0.1 IR -IR

25. References * Semiconductor Physics and Devices, 2nd ed., by Neamen, Irwin, Boston, 1997. **Device Electronics for Integrated Circuits, 2nd ed., by Muller and Kamins, John Wiley, New York, 1986.