1. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/
EE Semiconductor Electronics Design Project Spring Lecture 03
Professor Ronald L. Carter
L03 01/22/02

2. Induced E-field in the D.R.Ex
p-contact
N-contact O - O +
p-type CNR
n-type chg neutral reg O - O + O - O +
Exposed Acceptor Ions
Depletion region (DR)
Exposed Donor ions W x
-xpc
-xp xn
xnc
L03 01/22/02

3. Depletion approx. charge distribution
+Qn’=qNdxn
+qNd
[Coul/cm2]
-xp x
-xpc xn
xnc
-qNa
Charge neutrality => Qp’ + Qn’ = 0, => Naxp = Ndxn
Qp’=-qNaxp
[Coul/cm2]
L03 01/22/02

4. Soln to Poisson’s Eq in the D.R.Ex
-xp xn x
-xpc
xnc
-Emax
L03 01/22/02

5. Comments on the Ex and Vbi
Vbi is not measurable externally since Ex is zero at both contacts
The effect of Ex does not extend beyond the depletion region
The lever rule [Naxp=Ndxn] was obtained assuming charge neutrality. It could also be obtained by requiring Ex(x=0-dx) = Ex(x=0+dx) = Emax
L03 01/22/02

6. Effect of V > 0
Define an external voltage source, Va, with the +term at the p-type contact and the -term at the n-type contact
For Va > 0, the Va induced field tends to oppose Ex due to DR
For Va < 0, the Va induced field tends to add to Ex due to DR
Will consider Va < 0 now
L03 01/22/02

7. Effect of V > 0
L03 01/22/02

8. One-sided p+n or n+p jctns
If p+n, then Na >> Nd, and NaNd/(Na + Nd) = Neff --> Nd, and W --> xn, DR is all on lightly d. side
If n+p, then Nd >> Na, and NaNd/(Na + Nd) = Neff --> Na, and W --> xp, DR is all on lightly d. side
The net effect is that Neff --> N-, (- = lightly doped side) and W --> x-
L03 01/22/02

9. Junction Capacitance
The junction has +Q’n=qNdxn (exposed donors), and (exposed acceptors) Q’p=-qNaxp = -Q’n, forming a parallel sheet charge capacitor.
L03 01/22/02

10. Junction C (cont.)
This Q ~ (Vbi-Va)1/2 is clearly non-linear, and Q is not zero at Va = 0.
Redefining the capacitance,
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11. Charge neutrality => Q’p + Q’n = 0, => Naxp = Ndxn
Junction C (cont.)
dQj = dQ’nA r
+Q’n=qNdxn
+qNd
dQ’n=qNddxn
-xp x
-xpc xn
xnc
-qNa
Charge neutrality => Q’p + Q’n = 0, => Naxp = Ndxn
dQ’p=-qNadxp
Q’p=-qNaxp
L03 01/22/02

12. Depletion Capacitance

13. Junction C (cont.)
The C-V relationship simplifies to
L03 01/22/02

14. Junction C (cont.)
If one plots [Cj]-2 vs. Va Slope = -[(Cj0)2Vbi]-1 vertical axis intercept = [Cj0]-2 horizontal axis intercept = Vbi
Cj-2
Cj0-2 Va
Vbi
L03 01/22/02

15. Practical Junctions
Junctions are formed by diffusion or implantation into a uniform concentration wafer. The profile can be approximated by a step or linear function in the region of the junction.
If a step, then previous models OK.
If not, 1/2 --> M, 1/3 < M < 1/2.
L03 01/22/02

16. Law of the junction (injection of minority carr.)

17. Carrier Injection and diff.
ln(carrier conc)
ln Na
ln Nd
ln ni
~Va/Vt
~Va/Vt
ln ni2/Nd
ln ni2/Na x
-xpc
-xp
xnc xn
L03 01/22/02

18. Ideal diode equation I = Is [exp(Va/nVt)-1], Is = Isn + Isp

19. Diffnt’l, one-sided diode conductance
Static (steady-state) diode I-V characteristic IQ Va VQ
L03 01/22/02

20. 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.
L03 01/22/02