# Homework Help: How to solve steady state excess hole density

1. Nov 16, 2011

### alex8214997

1. The problem statement, all variables and given/known data

A hole current of 10^(-5) A/cm2 is injected into the side (x=0) of a long N-silicon. Assuming the holes flow only by diffusion and that at very large values of x, the distribution of excess holes decays to zero, Determine

a)The steady-state excess hole density at x=0
b)Hole current density at x=100μm
c)the rate of generation and recombination of electron-hole pair at x=100μm

a)2.794*10^(10)cm-3
b) 1.667*10^(-6) A/cm2

Given:
J=10^(-5) A/cm2
μp=480 cm2/Vs
μn= 1350 cm2/Vs

2. Relevant equations

J= -q*D*(dp/dx) D= k*T*μp/q

continuity equation:
dp/dt = -(p-p0)/τ- div(J)/q

where p: hole density; p0= hole density at equilibrium.
p-po=Δp

3. The attempt at a solution

dp/dx= J/(-q*D)= -5*10^(12)

I think Δp=p-p0=0 when t=τ=2.5μs
and Δp is at max. when t=0, and x=0

I tried to solve the continuity equation, which is 1 ODE

dp/dt = -(p-p0)/τ- div(J)/q
p'=p0/τ-p/τ-div(J)/q

p= p0-τ*div(J)/q+C*exp(-t/τ)

Since i think Δp=p-p0=0 when t=τ

p=p0-τ*div(J)/q+τ*e*div(J)/q*exp(-t/τ)

at t=0;
Δp=p-p0=τ*div(J)/q*(e-1)

but i can't find div(J)

b) i think J is constant, how it can be a function of x.
c) generation rate: p0/τ= (ni/τ)=4*10^(15)
recombination rate: Δp/τ= (p(x=100μm)-p0)/τ
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution