Question

Pure $Si$ at $500K$ 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 $n_e{n}_h=n_i^2$
$n_e=\frac{n_i^2}{n_h}=\frac{{\left(1.5\times 10^{16}{m}^{-3}\right)}^2}{4.5\times 10^{22}{m}^{-3}}$
$=5\times 10^9{m}^{-3}$