Doped semiconductor-to find the resistance?

[humanist rho]

Homework Statement

An extrinsic semiconductor sample of cross section A and length L is doped in such a way that the doping concentration varies as N_d=N₀ Exp(-x/L)
Assume that mobility μ of the majority carriers remain constant.What is the resistance of the sample?

Homework Equations

σ=neμ
ρ=1/σ
R=Lρ/A=L/(Aμen)

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/(AμeN_oExp(-x/L))
But this is not the right answer.

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

Thanks.

 

[SammyS]

Homework Statement

An extrinsic semiconductor sample of cross section A and length L is doped in such a way that the doping concentration varies as N_d=N₀ Exp(-x/L)
Assume that mobility μ of the majority carriers remain constant.What is the resistance of the sample?

Homework Equations

σ=neμ
ρ=1/σ
R=Lρ/A=L/(Aμen)

The Attempt at a Solution

In the eqn n is the free electron concentration.
I thought this will be equal to doping concentration.
then,R = L/(AμeN_oExp(-x/L))
But this is not the right answer.

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

Thanks.

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 .

 

[humanist rho]

That was really helpful.Thank you.