Question

What is the conductivity of a semiconductor (in ${\Omega }^{-1}{\text{m}}^{-1}$) if electron density $5\times {10}^{12}{\text{cm}}^{-3}$ and hole density $8\times {10}^{13}{\text{cm}}^{-3}$
$[{\mu }_e=2.3{\text{m}}^2{\text{V}}^{-1}{\text{s}}^{-1}\text{and}{\mu }_h=0.01{\text{m}}^2{\text{V}}^{-1}{\text{s}}^{-1}]$

• A. $5.6$
• B. $2.0$
• C. $3.4$
• D. $8.0$

Answer 1

The correct option is B $2.0$

Given,

$n_e=5\times {10}^{12}{\text{cm}}^{-3};n_h=8\times {10}^{13}{\text{cm}}^{-3}{\mu }_e=2.3{\text{m}}^2{\text{V}}^{-1}{\text{s}}^{-1};{\mu }_h=0.01{\text{m}}^2{\text{V}}^{-1}{\text{s}}^{-1}]$

The electrical conductivity of a semiconductor is,

$\sigma ={\sigma }_e+{\sigma }_h=e{n}_e{\mu }_e+e{n}_h{\mu }_h=e[n_e{\mu }_e+n_h{\mu }_h]$

$\sigma =1.6{\times }^{-19}[5\times {10}^{12}\times 2.3+8\times {10}^{19}\times 0.01]$

$\sigma \approx 2{\Omega }^{-1}{\text{m}}^{-1}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ is the correct answer.