Question

An intrinsic semiconductor has a resistivity of $0.50\Omega m$ at room temperature. Find the intrinsic carrier concentration, if the mobilities of electrons and holes are $0.39m^2/Volt$ , and $0.11m^2/Voltsec$ respectively

• A. $1.2\times 10^{18}/m^3$
• B. $2.5\times 10^{19}/m^3$
• C. $1.9\times 10^{20}/m^3$
• D. $3.1\times 10^{21}/m^3$

Answer 1

Answer: (B)

$\rho =0.50\Omega -m$
$\sigma =e(n_e{u}_e+n_h{u}_h)$
$\because \sigma =\frac{1}{\rho }$
In intrinsic semi-conductor
$n_e=n_h=n$
$\frac{1}{\rho }=e\times n({\mu }_e+{\mu }_h)$
$\frac{1}{0.50}=1.6\times 10^{-19}\times n(0.39+0.11)$
$\frac{1\times 10^{19}}{0.5\times 0.5\times 1.6}=n$
$\frac{100\times 10^{19}}{25\times 1.6}=n$
$\frac{40}{16}\times 10^{19}=n$
$n=2.5\times 10^{19}/m^2$