Question

The resistivity of a pure semiconductor is $0.5\Omega m$. If the electron and hole mobility be $0.39$ $m^2/V-s$ and $0.19$ $m^2/V-s$ respectively then calculate the intrinsic carrier concentration.

• A. $2.16\times {10}^{19}/m^3$
• B. $4.64\times {10}^{18}/m^3$
• C. ${10}^{20}/m^3$
• D. $noneofthese$

Answer 1

The correct option is B $4.64\times {10}^{18}/m^3$

The resistivity of the semiconductor, $\rho =0.5\Omega m$

The charge of electron, $q_e=1.6\times {10}^{-19}\text{C}$

The electron mobility, ${\mu }_e=0.39{\text{m}}^2{\text{V}}^{\text{- 1}}{\text{s}}^{\text{- 1}}$

The hole mobility, ${\mu }_h=0.19{\text{m}}^2{\text{V}}^{\text{- 1}}{\text{s}}^{\text{- 1}}$

Now,

$\frac{1}{\mu }=q_e\left(n_i{\mu }_e+n_i{\mu }_h\right)$

$n_i=\frac{1}{\mu .q_e\left({\mu }_e+{\mu }_h\right)}$

$n_i=\frac{1}{\left(0.5\Omega m\right).\left(1.6\times {10}^{-19}\text{C}\right)\left(\left(0.39+0.19\right){\text{m}}^2{\text{V}}^{\text{- 1}}{\text{s}}^{\text{- 1}}\right)}$

$n_i=4.64\times {10}^{18}{\text{m}}^{-3}$