Current through p-type silicon

1. Apr 12, 2013

hogrampage

1. The problem statement, all variables and given/known data
A 1-cm cube of p-type silicon (ρ = 0.1Ω-cm) acquires a linear electron distribution in the x-direction, such that n = 1014/cm3 at one side and n = 105/cm3 at the opposite side.

Wires are attached to the sides of the cube via ohmic contacts, and a 0.1mV voltage source is applied. Find the values of the electron, hole, and total currents that flow in the external circuit.

2. Relevant equations

ρ = R$\frac{A}{L}$ = $\frac{E}{J}$
E = $\frac{V}{L}$
Je = qnμeE + qDe$\frac{dn}{dx}$

Jh = qpμhE + qDh$\frac{dp}{dx}$
i = $\frac{V}{R}$
n0p0 = n2i

3. The attempt at a solution
I started by finding R:

R = ρ$\frac{L}{A}$ = (0.1Ω-cm)$\frac{(1cm)}{(1cm^{2})}$ = 0.1Ω

Then, the total current is:

I = $\frac{V}{R}$ = $\frac{(0.1mV)}{(0.1Ω)}$ = 1mA

p0 = $\frac{n^{2}_{i}}{n_{0}}$ = $\frac{(1.5x10^{10})^{2}}{10^{14}}$ = 225x104/cm3

p1 = $\frac{n^{2}_{i}}{n_{1}}$ = $\frac{(1.5x10^{10})^{2}}{10^{5}}$ = 225x1013/cm3

Now, $\frac{dp}{dx}$ = 225x1013/cm4 and $\frac{dn}{dx}$ = -1x1014/cm4, since dx = 1cm.

Which values would I use for n and p in the following equations, assuming the above steps are correct?

Je = qnμeE + qDe$\frac{dn}{dx}$

Jh = qpμhE + qDh$\frac{dp}{dx}$

Last edited: Apr 12, 2013