Q. Pure $Si$ at $500\ K$ has equal number of electron $(n_{e})$ and hole $(n_{h})$ concentrations of $1.5 \times 10^{16}m^{- 3}$. Doping by indium increases $n_{h}$ to $4.5 \times 10^{22}m^{- 3}$. The doped semiconductor is of

A) $n -$type with electron concentration $n_{e} = 2.5 \times 10^{23}m^{- 3}$
B) $p -$type having electron concentration $n_{e} = 5 \times 10^{9}m^{- 3}$
C) $n -$type with electron concentration $n_{e} = 5 \times 10^{22}m^{- 3}$
D) $p -$type with electron concentration $n_{e} = 2.5 \times 10^{10}m^{- 3}$
Explanation

(b) $n_{i}^{2} = n_{e}n_{h}$
$\left( 1.5 \times 10^{16} \right)^{2} = n_{e}(4.5 \times 10^{22})$
$n_{e} = 0.5 \times 10^{10} = 5 \times 10^{9}$
$n_{h} = 4.5 \times 10^{22}$
$n_{h} \gg n_{e}$
Semiconductor is $p$-type and $n_{e} = 5 \times 10^{9}m^{- 3}$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.