1. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/
Lecture 07 Semiconductor Device Modeling and Characterization EE Spring 2001
Professor Ronald L. Carter
L07 Feb 06

2. Charge neutrality => Qp’ + Qn’ = 0, => Naxp = Ndxn
Junction C (cont.) r
+Qn’=qNdxn
+qNd
dQn’=qNddxn
-xp x
-xpc xn
xnc
dQp’=-qNadxp
-qNa
Charge neutrality => Qp’ + Qn’ = 0, => Naxp = Ndxn
Qp’=-qNaxp
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3. Junction C (cont.)
The C-V relationship simplifies to
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4. Junction C (cont.)
If one plots [C’j]-2 vs. Va Slope = -[(C’j0)2Vbi]-1 vertical axis intercept = [C’j0]-2 horizontal axis intercept = Vbi
C’j-2
C’j0-2 Va
Vbi
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5. Arbitrary doping profile
If the net donor conc, N = N(x), then at xn, the extra charge put into the DR when Va->Va+dVa is dQ’=-qN(xn)dxn
The increase in field, dEx =-(qN/e)dxn, by Gauss’ Law (at xn, but also const).
So dVa=-(xn+xp)dEx= (W/e) dQ’
Further, since N(xn)dxn = N(xp)dxp gives, the dC/dxn as ...
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6. Arbitrary doping profile (cont.)
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7. Arbitrary doping profile (cont.)
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8. Arbitrary doping profile (cont.)
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9. Example
An assymetrical p+ n junction has a lightly doped concentration of 1E16 and with p+ = 1E18. What is W(V=0)?
Vbi=0.816 V, Neff=9.9E15, W=0.33mm
What is C’j? = 31.9 nFd/cm2
What is LD? = 0.04 mm
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10. Law of the junction (follow the min. carr.)
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11. Law of the junction (cont.)
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12. Law of the junction (cont.)
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13. Injection Conditions
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14. 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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15. Apply the Continuity Eqn in CNR
Ideal Junction Theory (cont.)
Apply the Continuity Eqn in CNR
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16. Ideal Junction Theory (cont.)
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17. Ideal Junction Theory (cont.)
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18. Excess minority carrier distr fctn
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19. Forward Bias Energy Bands
q(Vbi-Va)
Imref, EFn Ec EF
qVa EF
EFi
Imref, EFp Ev x
-xpc
-xp xn
xnc
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20. 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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21. Minority carrier currents
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22. Evaluating the diode current
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23. Special cases for the diode current
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24. 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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25. 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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26. Diffnt’l, one-sided diode conductance
Static (steady-state) diode I-V characteristic IQ Va VQ
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27. Diffnt’l, one-sided diode cond. (cont.)
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28. 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
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29. 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
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30. References
* Semiconductor Physics and Devices, 2nd ed., by Neamen, Irwin, Boston, 1997.
**Device Electronics for Integrated Circuits, 2nd ed., by Muller and Kamins, John Wiley, New York, 1986.
***Physics of Semiconductor Devices, Shur, Prentice-Hall, 1990.
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