Question

The intrinsic conductivity of germanium at $27$${}^{\circ }C$ is $2.13$ $mho/m$ and mobilities of electrons and holes are $0.38$ and $0.18$ $m$${}^2/Vs$ respectively. The density of charge carriers is

• A. $2.37$ $\times$ $10$${}^{19}$$/m$${}^3$
• B. $3.28$ $\times$ $10$${}^{19}$$/m$${}^3$
• C. $7.83$ $\times$ $10$${}^{19}$$/m$${}^3$
• D. $8.47$ $\times$ $10$${}^{19}$$/m$${}^3$

Answer 1

The correct option is A $2.37$ $\times$ $10$${}^{19}$$/m$${}^3$

Conductivity, $\sigma =\frac{1}{\rho }=e(n_e{\mu }_e+n_h{\mu }_h)$
i.e., $2.13=1.6\times {10}^{-19}(0.38+0.18)n_i$

(Since, in intrinsie semi-conductor, $n_e=n_h=n_i$)
$\therefore$ density of charge carries, $n_i$$=\frac{2.13}{1.6\times {10}^{-19}\times 0.56}=2.37\times {10}^{19}/m^3$