# Doped semiconductor-to find the resistance?

1. Jan 18, 2012

### humanist rho

1. The problem statement, all variables and given/known data
An extrinsic semiconductor sample of cross section A and length L is doped in such a way that the doping concentration varies as Nd=N0 Exp(-x/L)
Assume that mobility μ of the majority carriers remain constant.What is the resistance of the sample?

2. Relevant equations
σ=neμ
ρ=1/σ
R=Lρ/A=L/(Aμen)

3. The attempt at a solution
In the eqn n is the free electron concentration.
I thought this will be eqal to doping concentration.
then,R = L/(AμeNoExp(-x/L))
But this is not the right answer.

Can this resistance be varrying with x since doping concentration depend on x?

Thanks.

2. Jan 18, 2012

### SammyS

Staff Emeritus
The resistance, dR, for a very short length, dx, of semi-conductor is $\displaystyle dR=\frac{dx}{A\mu N_0 e^{-x/L}}$

Integrate that .

3. Jan 25, 2012

### humanist rho

That was really helpful.Thank you.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook