Question

In a semiconductor, the concentrations of electrons and holes are $8\times {10}^{18}/m^3$ and $5\times {10}^{18}/m^3$ respectively. If the mobilities of electrons and hole are $2.3m^2$/volt-sec and $0.01m^2$/volt-sec respectively, then semiconductor is:

• A. N-type and its resistivity is 0.34 ohm-metre
• B. P-type and its resistivity is 0. 134 ohm-metre
• C. N-type and its resistivity is 0.034 ohm-metre
• D. P-type and its resistivity is 3.40 ohm-metre

Answer 1

The correct option is A N-type and its resistivity is 0.34 ohm-metre

$n_e=8\times {10}^{18}/m^3,n_h=5\times {10}^{18}/m^3$

${\mu }_e=2.3\frac{m^2}{volt-sec},{\mu }_h=0.01\frac{m^2}{volt-sec}$

$\because n_e>n_h$ so semiconductor is $N-$ type

Also conductivity $\sigma =\frac{1}{Resistivity\left(\rho \right)}=e(n_e{\mu }_e+n_h{\mu }_h)$

$\Rightarrow \frac{1}{\rho }=1.6\times {10}^{-19}[8\times {10}^{18}2.3+5\times {10}^{18}\times 0.01]$

$\Rightarrow \rho =0.34\Omega m$