The valence of an impurity added to germanium crystal in order to convert it into a $P-$type semiconductor is

Why is it required to add impurity to a pure semiconductor? Mention its condition and explain what impure semiconductors are.

Indium impurity in germanium makes

For a pure $Si$ crystal at $300 \ K$,the electron $(n_e)$ and hole $(n_h)$ concentrations are equal,being $1.5 \times 10^{16} \ m^{-3}$. On doping with Indium,the hole concentration increases to $4.5 \times 10^{22} \ m^{-3}$. Calculate the new electron concentration $(n_e)$ in the doped $Si$.

$A$ semiconductor has equal electron and hole concentration of $6 \times 10^8 \, m^{-3}$. On doping with a certain impurity,the electron concentration increases to $9 \times 10^{12} \, m^{-3}$. The new hole concentration is:

The $n-$type semiconductors are obtained when germanium is doped with