# Resistivity and Mobility

1. Feb 7, 2010

### roeb

1. The problem statement, all variables and given/known data
Assume the mobility ratio u_n/u_p = b in Si is a constant independent of impurity concentration. Find the maximum resistivity $$\rho_m$$ in terms of the intrinsic resistivity $$\rho_i$$. If b = 3 and the hole mobility of intrinsic Si is 450 cm^2/Vs calculate $$\rho_i$$ and $$\rho_m$$

2. Relevant equations

3. The attempt at a solution

Well I know that conductivity is $$\sigma$$ = q(u_n * n + u_p * p)
For the intrinsic conductivity $$\sigma_i$$ = q(u_p *b * n_i + u_p * n_i) = q u_p n_i (b + 1).

Now I'm having a bit of trouble expressing $$\sigma_m$$ where this is a minimum conductivity (or maximum resistivity)...
$$\sigma_m$$ = q ( b * u_p * n + u_p * p)
To get a minimum conductivity I would think that n should be extremely low but I fail to see how I can express this in terms of the intrinsic conductivity. I know that n_i at 300 K is 10^10/cm^3. Does anyone have any hints?