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 $ 0.39\, m^2/Volt $ , and $ 0.11 m^2/Volt \,sec $ 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)

$\rho = 0.50 \,\Omega - m$
$\sigma = e (n_e u_e + n_hu_h)$
$\because \sigma = \frac{1}{\rho}$
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$