Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/ EE 4345 - Semiconductor Electronics Design Project Spring 2002 - Lecture 03 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/ L03 01/22/02

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

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

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

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

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

Effect of V > 0 L03 01/22/02

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

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

Junction C (cont.) This Q ~ (Vbi-Va)1/2 is clearly non-linear, and Q is not zero at Va = 0. Redefining the capacitance, L03 01/22/02

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

Depletion Capacitance

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

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

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

Law of the junction (injection of minority carr.)

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

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

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

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