1. 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 injections apply so that dnp < ppo for -xpc < x < -xp, and dpn < nno for xn < x < xnc
Steady State conditions
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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 (follow the min. carr.)
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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. Apply the Continuity Eqn in CNR
Ideal Junction Theory (cont.)
Apply the Continuity Eqn in CNR
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8. Ideal Junction Theory (cont.)
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9. Ideal Junction Theory (cont.)
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10. Excess minority carrier distr fctn
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11. Carrier Injection ln(carrier conc) ln Na ln Nd ln ni ~Va/Vt ln ni2/Naxn
-xpc
ln(carrier conc)
ln Na
ln Nd
ln ni
ln ni2/Nd
ln ni2/Na
xnc x
~Va/Vt
-xp
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12. Minority carrier currents
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13. Evaluating the diode current
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14. Special cases for the diode current
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15. 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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16. 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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17. Diffnt’l, one-sided diode conductance
Static (steady-state) diode I-V characteristic IQ Va VQ
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18. Diffnt’l, one-sided diode cond. (cont.)
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19. Charge distr in a (1- sided) short diode
dpn
Assume Nd << Na
The sinh 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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20. 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

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

22. General time- constant
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23. General time- constant (cont.)
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24. General time- constant (cont.)
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25. References
*Fundamentals of Semiconductor Theory and Device Physics, by Shyh Wang, Prentice Hall, 1989.
**Semiconductor Physics & Devices, by Donald A. Neamen, 2nd ed., Irwin, Chicago.
M&K = Device Electronics for Integrated Circuits, 3rd ed., by Richard S. Muller, Theodore I. Kamins, and Mansun Chan, John Wiley and Sons, New York, 2003.
1Device Electronics for Integrated Circuits, 2 ed., by Muller and Kamins, Wiley, New York, 1986.
2Physics of Semiconductor Devices, by S. M. Sze, Wiley, New York, 1981.
3 Physics of Semiconductor Devices, Shur, Prentice-Hall, 1990.
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