# Equilibrium concentration of majority and minority carriers

1. Mar 7, 2013

### shayaan_musta

1. The problem statement, all variables and given/known data
Give the equilibrium concentration of majority and minority carriers and resistivity for Silicon which is doped with 3x10$^{15}$ boron atoms/cm$^{3}$ at 27°C.

2. Relevant equations
n$_{o}$ = $\frac{N_{d}-N_{a}}{2}$+$\sqrt{(\frac{N_{d}-N_{a}}{2})^{2}+(n_{i})^{2}}$
p$_{o}$ = $\frac{N_{a}-N_{d}}{2}$+$\sqrt{(\frac{N_{a}-N_{d}}{2})^{2}+(n_{i})^{2}}$
n$_{o}$p$_{o}$ = n$_{i}$$^{2}$

3. The attempt at a solution

DATA
n$_{o}$ (equilibrium concentration of majority carriers) = ?
p$_{o}$ (equilibrium concentration of minority carriers) = ?
$\rho$ (resistivity for Silicon) = ?
N$_{a}$ = 3x10$^{15}$ atoms/cm$^{3}$
T = 27°C+273 = 273K
n$_{i}$ (for silicon at 300K) = 1.5x10$^{10}$ atoms/cm$^{3}$

SOLUTION
n$_{o}$ = 0 (I calculated this)
p$_{o}$ = infinity

I used the above given 1st equation to calculate n$_{o}$. And used 3rd equation to calculate the p$_{o}$.
Actually, I am confused whether I extracted right data or not. And I don't know how to calculate resistivity?

Please tell me where is mistake in the data and Solution.

Thanks.

2. Mar 8, 2013