Question

The intrinsic conductivity of germanium at $27^{\circ} C$ is $2.13 \,mho$ $m ^{-1}$ and mobilities of electrons and holes are $0.38$ and $0.18$ $m ^2 \,V ^{-1}\, s ^{-1}$ 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

Answer: (A)

Conductivity, $\sigma=\frac{1}{\rho}= e \left( n _{ e } \mu_{ e }+ n _{ h } \mu_{ h }\right)$
i.e., $2.13=1.6 \times 10^{-19}(0.38+0.18) n _{ i }$
(Since in intrinsic semi-conductor, $n _{ e }= n _{ h }= n _{ i }$ )
$\therefore $ density of charge carriers, $n _{ i }$
$=\frac{2.13}{1.6 \times 10^{-19} \times 0.56}=2.37 \times 10^{19} m ^{-3}$