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
  $p$-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 having electron concentration $n_e = 2.5 \times 10^{10} \, m^{-3}$
• D
  $n$-type with electron concentration $n_e = 2.5 \times 10^{23} \, m^{-3}$