Forward Biased PN Junction Help: Silicon Band Diagram & Capacitance Calculation

[CptMad]

Homework Statement

Assume silicon, at room temperature (300k) and complete ionization.
An abrupt n+-p junction with Nd=10^20 cm^-3 and Na=10^17 cm^-3 is forward biased at 0.5V

Homework Equations

a)Draw the band diagram, label n and p regions, show direction of the current flow. Also what is the current type (electrons or holes, drift or diffusion) in the p-type region just outside the depletion region?
b)Calculate the depletion charge capacitance per unit area.

The Attempt at a Solution

I have managed to draw the band diagram but I'd appreciate it if there was a way I could check my answers. Also I get confused with the wording for the 2nd portion of part A. I understand that the current in a forward biased pn junction is due to diffusion would this be considered the same for p-type region?

For part B would it be correct if I use the equation

C'=[(eεsNaNd)/(2(Vbi-Vr)(Na+Nd))]^1/2

But I get stuck since C=AC' but I can't seem to figure out the value for A, would I be able to use A=10^-4cm^2?

 

[KataKoniK]

For part A, you can check your answers by comparing them to a known band diagram for a similar junction, or by using a simulation tool like Matlab or SPICE.

For the second portion of part A, the wording is asking about the current type in the p-type region just outside the depletion region. This means the region where there is still majority carrier concentration, but it is lower than the concentration in the bulk p-type region. In this region, the current is due to both diffusion and drift of carriers.

For part B, yes you can use the equation you provided to calculate the depletion charge capacitance per unit area. The value for A can be estimated using the dimensions of the junction (e.g. width and length) if they are given in the problem, or you can use a typical value for the area of a pn junction (e.g. 1 mm^2).