1. EE 5340 Semiconductor Device Theory Lecture 15 – Spring 2011 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc

2. ©rlc L15-10Mar20112 Forward Bias Energy Bands EvEv EcEc E Fi xnxn x nc -x pc -x p 0 q(V bi -V a ) E FP E FN qV a x Imref, E Fn Imref, E Fp

3. ©rlc L15-10Mar20113 Law of the junction: “Remember to follow the minority carriers”

4. ©rlc L15-10Mar20114 Law of the junction (cont.)

5. ©rlc L15-10Mar20115 Law of the junction (cont.)

6. ©rlc L15-10Mar2011 Injection Conditions 6

7. ©rlc L15-10Mar2011 Ideal Junction Theory Assumptions E x = 0 in the chg neutral reg. (CNR) MB statistics are applicable Neglect gen/rec in depl reg (DR) Low level injection applies so that  n p < p po for -x pc < x < -x p, and  p n < n no for x n < x < x nc Steady State conditions 7

8. ©rlc L15-10Mar2011 Ideal Junction Theory (cont.) 8

9. ©rlc L15-10Mar2011 Ideal Junction Theory (cont.) 9

10. ©rlc L15-10Mar2011 Ideal Junction Theory (cont.) 10

11. ©rlc L15-10Mar2011 Diffusion Length model L = (D  ) 1/2 Diffusion Coeff. is Pierret* model 11

12. Minority hole lifetimes Mark E. Law, E. Solley, M. Liang, and Dorothea E. Burk, “Self- Consistent Model of Minority-Carrier Lifetime, Diffusion Length, and Mobility, IEEE ELECTRON DEVICE LETTERS, VOL. 12, NO. 8, AUGUST 1991 The parameters used in the fit are τ o = 10 μs, N ref = 1×10 17 /cm 2, and C A = 1.8×10 -31 cm 6 /s. ©rlc L15-10Mar201112

13. Minority electron lifetimes Mark E. Law, E. Solley, M. Liang, and Dorothea E. Burk, “Self- Consistent Model of Minority-Carrier Lifetime, Diffusion Length, and Mobility, IEEE ELECTRON DEVICE LETTERS, VOL. 12, NO. 8, AUGUST 1991 The parameters used in the fit are τ o = 30 μs, N ref = 1×10 17 /cm 2, and C A = 8.3×10 -32 cm 6 /s. ©rlc L15-10Mar201113

14. ©rlc L15-10Mar2011 Excess minority carrier distr fctn 14

15. ©rlc L15-10Mar2011 Forward Bias Energy Bands EvEv EcEc E Fi xnxn x nc -x pc -x p 0 q(V bi -V a ) E FP E FN qV a x Imref, E Fn Imref, E Fp 15

16. ©rlc L15-10Mar2011 Carrier Injection xnxn -x pc 0 ln(carrier conc) ln N a ln N d ln n i ln n i 2 /N d ln n i 2 /N a x nc -x p x ~V a /V t 16

17. ©rlc L15-10Mar2011 Minority carrier currents 17

18. ©rlc L15-10Mar2011 Evaluating the diode current 18

19. ©rlc L15-10Mar2011 Special cases for the diode current 19

20. ©rlc L15-10Mar2011 Ideal diode equation Assumptions: –low-level injection –Maxwell Boltzman statistics –Depletion approximation –Neglect gen/rec effects in DR –Steady-state solution only Current dens, J x = J s expd(V a /V t ) –where expd(x) = [exp(x) -1] 20

21. ©rlc L15-10Mar2011 Ideal diode equation (cont.) J s = J s,p + J s,n = hole curr + ele curr J s,p = qn i 2 D p coth(W n /L p )/(N d L p ) = qn i 2 D p /(N d W n ), W n > L p, “long” J s,n = qn i 2 D n coth(W p /L n )/(N a L n ) = qn i 2 D n /(N a W p ), W p > L n, “long” J s,n > N d 21

22. ©rlc L15-10Mar2011 Diffnt’l, one-sided diode conductance VaVa IDID Static (steady- state) diode I-V characteristic VQVQ IQIQ 22

23. ©rlc L15-10Mar2011 Diffnt’l, one-sided diode cond. (cont.) 23

24. ©rlc L15-10Mar2011 Charge distr in a (1- sided) short diode Assume N d << N a The sinh (see L10) excess minority carrier distribution becomes linear for W n << L p  p n (x n )=p n0 expd( V a /V t ) Total chg = Q’ p = Q’ p = q  p n (x n )W n /2 xnxn x x nc  p n (x n ) W n = x nc - x n Q’ p pnpn 24

25. ©rlc L15-10Mar2011 Charge distr in a 1- sided short diode Assume Quasi-static charge distributions Q’ p = +q  p n (x n,V a )W n /2  Q’ p =q(W/2) x {  p n (x n,V a +  V) -  p n (x n,V a )} W n = x nc - x n (V a ) xnxn x x nc  p n (x n,V a ) Q’ p pnpn  p n (x n,V a +  V)  Q’ p 25

26. ©rlc L15-10Mar201126 Cap. of a (1-sided) short diode (cont.)

27. ©rlc L15-10Mar201127 Evaluating the diode current density

28. ©rlc L15-10Mar201128 General time- constant

29. ©rlc L15-10Mar201129 General time- constant (cont.)

30. ©rlc L15-10Mar201130 General time- constant (cont.)

31. ©rlc L15-10Mar201131 References 1 and M&K Device Electronics for Integrated Circuits, 2 ed., by Muller and Kamins, Wiley, New York, 1986. See Semiconductor Device Fundamentals, by Pierret, Addison-Wesley, 1996, for another treatment of the  model. 2 Physics of Semiconductor Devices, by S. M. Sze, Wiley, New York, 1981. 3 and ** Semiconductor Physics & Devices, 2nd ed., by Neamen, Irwin, Chicago, 1997. Fundamentals of Semiconductor Theory and Device Physics, by Shyh Wang, Prentice Hall, 1989.