Question

The intrinsic carrier density at room temperature in $\text{Ge}$ is $2.37\times {10}^{19}{\text{m}}^{-3}$. If the mobility of electron and hole are $0.38{\text{m}}^2{\text{V}}^{-1}{\text{s}}^{-1}$ and $0.18{\text{m}}^2{\text{V}}^{-1}{\text{s}}^{-1}$, calculate the resistivity.

• A. $0.671\Omega \text{-m}$
• B. $0.471\Omega \text{-m}$
• C. $0.271\Omega \text{-m}$
• D. $0.871\Omega \text{-m}$

Answer 1

The correct option is B $0.471\Omega \text{-m}$

We know that, conductivity,

$\sigma =e(n_e{\mu }_e+n_h{\mu }_h)$

$\Rightarrow \sigma =e{n}_i({\mu }_e+{\mu }_h)$

$\Rightarrow \sigma =1.6\times {10}^{-19}\times 2.37\times {10}^{19}\times (0.38+0.18)$

$\Rightarrow \sigma =2.1235{\Omega }^{-1}{\text{m}}^{-1}$

So, resistivity,

$\rho =\frac{1}{\sigma }=\frac{1}{2.1235}=0.471\Omega \text{-m}$

Hence, option $\left(B\right)$ is the correct answer.