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)

$2.5 \times 10^{19}/m^3$

Answer 2

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