1. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/
Semiconductor Device Modeling and Characterization – EE5342 Lecture 11 – Spring 2011
Professor Ronald L. Carter

2. Minority carrier currents
©rlc L11-23Feb2011

3. Evaluating the diode current
©rlc L11-23Feb2011

4. Special cases for the diode current
©rlc L11-23Feb2011

5. Ideal diode equation Assumptions: Current dens, Jx = Js expd(Va/Vt)
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]
©rlc L11-23Feb2011

6. Ideal diode equation (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
©rlc L11-23Feb2011

7. Diffnt’l, one-sided diode conductance
Static (steady-state) diode I-V characteristic IQ Va VQ
©rlc L11-23Feb2011

8. Diffnt’l, one-sided diode cond. (cont.)
©rlc L11-23Feb2011

9. 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
©rlc L11-23Feb2011

10. 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 xn
xnc
©rlc L11-23Feb2011

11. Cap. of a (1-sided) short diode (cont.)
©rlc L11-23Feb2011

12. General time- constant
©rlc L11-23Feb2011

13. General time- constant (cont.)
©rlc L11-23Feb2011

14. General time- constant (cont.)
©rlc L11-23Feb2011

15. Effect of carrier recombination in DR
The S-R-H rate (tno = tpo = to) is
©rlc L11-23Feb2011

16. Effect of carrier rec. in DR (cont.)
For low Va ~ 10 Vt
In DR, n and p are still > ni
The net recombination rate, U, is still finite so there is net carrier recomb.
reduces the carriers available for the ideal diode current
adds an additional current component
©rlc L11-23Feb2011

17. Effect of carrier rec. in DR (cont.)
©rlc L11-23Feb2011

18. Effect of non- zero E in the CNR
This is usually not a factor in a short diode, but when E is finite -> resistor
In a long diode, there is an additional ohmic resistance (usually called the parasitic diode series resistance, Rs)
Rs = L/(nqmnA) for a p+n long diode.
L=Wn-Lp (so the current is diode-like for Lp and the resistive otherwise).
©rlc L11-23Feb2011

19. High level injection effects
Law of the junction remains in the same form, [pnnn]xn=ni2exp(Va/Vt), etc.
However, now dpn = dnn become >> nno = Nd, etc.
Consequently, the l.o.t.j. reaches the limiting form dpndnn = ni2exp(Va/Vt)
Giving, dpn(xn) = niexp(Va/(2Vt)), or dnp(-xp) = niexp(Va/(2Vt)),
©rlc L11-23Feb2011

20. High level inj effects (cont.)
©rlc L11-23Feb2011

21. Summary of Va > 0 current density eqns.
Ideal diode, Jsexpd(Va/(hVt))
ideality factor, h
Recombination, Js,recexp(Va/(2hVt))
appears in parallel with ideal term
High-level injection, (Js*JKF)1/2exp(Va/(2hVt))
SPICE model by modulating ideal Js term
Va = Vext - J*A*Rs = Vext - Idiode*Rs
©rlc L11-23Feb2011

22. Diode Diffusion and Recombination Currents
©rlc L11-23Feb2011

23. Diode Diffusion and Recombination Currents – One Sided Diode
©rlc L11-23Feb2011

24. Plot of typical Va > 0 current density equations
ln(J)
data
Effect of Rs
Vext
VKF
©rlc L11-23Feb2011

25. References
*Semiconductor Device Modeling with SPICE, 2nd ed., by Massobrio and Antognetti, McGraw Hill, NY, 1993.
**MicroSim OnLine Manual, MicroSim Corporation, 1996.
©rlc L11-23Feb2011