Semiconductor Device Theory - Ideal Junction Theory and Carrier Injection

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

2. q(Vbi-Va) Imref, EFn Ec EFN qVa EFP EFi Imref, EFp Ev x -xpc -xp xn xnc 0 Forward Bias Energy Bands

3. Law of the junction: “Rememberto follow the minority carriers”

4. Law of the junction (cont.)

5. Law of the junction (cont.)

6. InjectionConditions

7. Ideal JunctionTheory Assumptions • Ex = 0 in the chg neutral reg. (CNR) • MB statistics are applicable • Neglect gen/rec in depl reg (DR) • Low level injection applies so that dnp < ppo for -xpc < x < -xp, and dpn < nno for xn < x < xnc • Steady State conditions

8. Ideal Junction Theory (cont.)

9. Ideal JunctionTheory (cont.)

10. Ideal JunctionTheory (cont.)

11. Diffusion Length model L = (Dt)1/2 Diffusion Coeff. is Pierret* model

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 τo = 10 μs, Nref= 1×1017/cm2, and CA = 1.8×10-31cm6/s.

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 τo = 30 μs, Nref= 1×1017/cm2, and CA = 8.3×10-32 cm6/s.

14. Excess minoritycarrier distr fctn

15. q(Vbi-Va) Imref, EFn Ec EFN qVa EFP EFi Imref, EFp Ev x -xpc -xp xn xnc 0 Forward Bias Energy Bands

16. CarrierInjection 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

17. Minority carriercurrents

18. Evaluating thediode current

19. Special cases forthe diode current

20. Ideal diodeequation • Assumptions: • low-level injection • Maxwell Boltzman statistics • Depletion approximation • Neglect gen/rec effects in DR • Steady-state solution only • Current dens, Jx = Js expd(Va/Vt) • where expd(x) = [exp(x) -1]

21. Ideal diodeequation (cont.) • Js = Js,p + Js,n = hole curr + ele curr Js,p = qni2Dp coth(Wn/Lp)/(NdLp) = qni2Dp/(NdWn), Wn << Lp, “short” = qni2Dp/(NdLp), Wn >> Lp, “long” Js,n = qni2Dn coth(Wp/Ln)/(NaLn) = qni2Dn/(NaWp), Wp << Ln, “short” = qni2Dn/(NaLn), Wp >> Ln, “long” Js,n << Js,p when Na >> Nd

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

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

24. Charge distr in a (1-sided) short diode dpn • Assume Nd << Na • The sinh (see L10) 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

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

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

27. Evaluating the diode current density

28. General time-constant

29. General time-constant (cont.)

30. General time-constant (cont.)

31. References 1 and M&KDevice 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 m model. 2Physics 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.