1. EE 5340 Semiconductor Device Theory Lecture 15 – Spring 2011
Professor Ronald L. Carter

2. Forward Bias Energy BandsEv Ec
EFi xn
xnc
-xpc
-xp
q(Vbi-Va)
EFP
EFN
qVa x
Imref, EFn
Imref, EFp
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3. Law of the junction: “Remember to follow the minority carriers”
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4. Law of the junction (cont.)
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5. Law of the junction (cont.)
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6. Injection Conditions
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7. Ideal Junction Theory 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
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8. Ideal Junction Theory (cont.)
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9. Ideal Junction Theory (cont.)
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10. Ideal Junction Theory (cont.)
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11. Diffusion Length model
L = (Dt)1/2 Diffusion Coeff. is Pierret* model
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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.
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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.
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14. Excess minority carrier distr fctn
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15. Forward Bias Energy BandsEv Ec
EFi xn
xnc
-xpc
-xp
q(Vbi-Va)
EFP
EFN
qVa x
Imref, EFn
Imref, EFp
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16. Carrier Injection ln(carrier conc) ln Na ln Nd ln ni ~Va/Vt ~Va/Vt
ln ni2/Nd
ln ni2/Na x
-xpc
-xp
xnc xn
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17. Minority carrier currents
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18. Evaluating the diode current
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19. Special cases for the diode current
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20. 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]
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21. 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
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22. Diffnt’l, one-sided diode conductance
Static (steady-state) diode I-V characteristic IQ Va VQ
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23. Diffnt’l, one-sided diode cond. (cont.)
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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
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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 xn
xnc
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26. Cap. of a (1-sided) short diode (cont.)
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27. Evaluating the diode current density
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28. General time- constant
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29. General time- constant (cont.)
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30. General time- constant (cont.)
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31. References
1 and M&KDevice Electronics for Integrated Circuits, 2 ed., by Muller and Kamins, Wiley, New York, 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.
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