1. EE 5340 Semiconductor Device Theory Lecture 14 - Fall 2003
Professor Ronald L. Carter
L 14 Oct 9

2. Project Comments- Forward derivative
A plot of r  dV/d[ln(C)] vs. V has slope = -1/M, and intercept = VJ/M
Forward der. of data gives ri’ = dV/d(ln(C))=[Vi+1-Vi]/[ln(Ci+1)-ln(Ci)], at Vi’ = [Vi+1+Vi]/2
L 14 Oct 9

3. Project Comments- Central derivative
A plot of r  dV/d[ln(C)] vs. V has slope = -1/M, and intercept = VJ/M
Central der. of data gives ri’ = dV/d(ln(C))=[Vi+1-Vi-1]/[ln(Ci+1)-ln(Ci-1)], at Vi’ = [Vi+1-Vi-1]/2 (= Vi only if all DV are equal.
L 14 Oct 9

4. Project Comments- Backward derivative
A plot of r  dV/d[ln(C)] vs. V has slope = -1/M, and intercept = VJ/M
Backward der. of data gives ri’ = dV/d(ln(C))=[Vi-Vi-1]/[ln(Ci)-ln(Ci-1)], at Vi’ = [Vi+Vi-1]/2
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5. Choosing the data range for r vs. V
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6. Choosing the data range for r vs. V
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7. Minority hole lifetimes, taken from Shur** p. 101.
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8. Minority electron lifetimes, taken from Shur** p. 101.
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9. Lifetimes from data vs. that used in simulators
Minority electron lifetimes, taken from Shur** p. 101.
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10. The Continuity Equation (cont.)
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11. Review of depletion approximation
pp << ppo, -xp < x < 0
nn << nno, 0 < x < xn
0 > Ex > -2Vbi/W, in DR (-xp < x < xn)
pp=ppo=Na & np=npo= ni2/Na, -xpc< x < -xp
nn=nno=Nd & pn=pno= ni2/Nd, xn < x < xnc
qVbi Ec
EFp
EFn
EFi Ev x
-xpc
-xp xn
xnc
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12. Review of D. A. (cont.) Ex
-xpc
-xp xn
xnc x
-Emax
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13. 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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14. Law of the junction: “Remember to follow the minority carriers”
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15. Law of the junction (cont.)
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16. Law of the junction (cont.)
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17. Injection Conditions
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18. 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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19. Apply the Continuity Eqn in CNR
Ideal Junction Theory (cont.)
Apply the Continuity Eqn in CNR
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20. Ideal Junction Theory (cont.)
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21. Ideal Junction Theory (cont.)
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22. Diffusion length model
L = (Dt)1/2 Diffusion Coeff. is Pierret* model
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23. Excess minority carrier distr fctn
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24. Forward Bias Energy BandsEv Ec
EFi xn
xnc
-xpc
-xp
q(Vbi-Va)
EFP
EFN
qVa x
Imref, EFn
Imref, EFp
L 14 Oct 9

25. 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
L 14 Oct 9

26. References
* Semiconductor Device Fundamentals, by Pierret, Addison-Wesley, 1996
** Physics of Semiconductor Devices, M. Shur, Wiley.
L 14 Oct 9