### ELE533 Bipolar Devices

Mid Term Exam
July 19, 2002

Name_____________________________________

1. Consider a silicon pn junction. The p side is uniformly doped with 1016 acceptors/cm3. The n side is doped with 5x1018 donors/cm3.
The contact on the p-side is 2 microns from the junction. The contact on the n-side is 10 microns from the junction. The junction area is 10 microns by 10 microns.

2. What is the built in potential?
Vbi = Vt ln[NAND/ni2] = 0.86V

3. What is the position of the Fermi level relative to the intrinsic level on the p side of the junction?

Ei - Ef = Vt ln[NA/ni] = 0.347V

4. What is the saturation current, Is, in the equation,
I = Is*eV/Vt

Is = Aqni2 un Vt / NAWp = 3.315x10-16A

5. Draw the equilibrium energy band diagram for this junction, including numerical values for the Fermi level position relative to the intrinsic level on each side. Show the built-in potential on the diagram.

Vn = 0.51V, Vp = 0.347V, Vbi = 0.8556V

6. For an applied forward voltage of 0.6V, find the,

1. Diffusion capacitance.
Cdiff = wp2 I / 2 Dn Vt

where

I = Is eV/Vt = 3.81 uA

Cdiff = 3.81x10-6(2x10-4)2/ (2 *800*0.259) = 0.142 pF

2. Junction capacitance.
CJ = CJ0/[1 - V/Vbi]½

where

CJ0 = A [qeNA / 2Vbi ]½ = 10-6[1.6x10-19 10-12 1016 / (2*0.8586) = 3x10-14 = 30 f F

CJ = CJ0/[1 - V/Vbi]½ = 30 f F/[1-0.6/0.8586]½ = 55.6 f F = 0.0556 pF