Question

Pure $S i$ at $500 K$ has equal number of electron $\left(n_{e}\right)$ and hole $\left(n_{h}\right)$ 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. p-type having electron concentration $n_e=5\times 10^9\, m^{-3}$
• B. n-type with electron concentration $n_e=5\times 10^{22} \,m^{-3}$
• C. p-type with electron concentration $n_e=2.5\times 10^{10}\, m^{-3}$
• D. n-type with electron concentration $n_e=2.5\times 10^{23}\, m^{-3}$

Answer 1

Answer: (A)

$p$-type semiconductor is obtained when Si or Ge is doped with a trivalent impurity like aluminium $( Al )$, boron $( B )$, indium $( ln )$ etc,
Here, $n_{i}=1.5 \times 10^{16} \,m ^{-3}$
$n_{h}=4.5 \times 10^{22} \,m ^{-3}$
As $n_{e} \,n_{h}=n_{i}^{2}$
$n_{e}=\frac{n_{i}^{2}}{n_{h}}=\frac{\left(1.5 \times 10^{16} m ^{-3}\right)^{2}}{4.5 \times 10^{22} m ^{-3}}$
$=5 \times 10^{9} \,m ^{-3}$