The valence of the impurity atom that is to be added to a germanium crystal to make it an $N$-type semiconductor is:

$A$ pure semiconductor has equal electron and hole concentration of $10^{16} \ m^{-3}$. Doping by gallium increases $n_{h}$ to $5 \times 10^{22} \ m^{-3}$. Then,the value of $n_{e}$ in the doped semiconductor is

In pure silicon,the electron-hole concentration at $T = 300 \ K$ is $7 \times 10^{15} \ m^{-3}$. Antimony is added as an impurity to silicon at a rate of $1$ atom per $10^7 \ Si$ atoms. Assume that half of the impurity atoms contribute their electrons to the conduction band. Calculate the factor by which the number of charge carriers increases. Given: the number density of silicon atoms is $5 \times 10^{28} \ m^{-3}$.

$A$ pure semiconductor crystal has $5 \times 10^{22}$ atoms per $cm^3$. It is doped by $1$ ppm concentration of pentavalent element. The number of holes in the doped semiconductor is (given that $n_i = 1.5 \times 10^{10} cm^{-3}$):

In an intrinsic semiconductor,the energy gap $E_{g}$ is $1.2 \; eV$. Its hole mobility is much smaller than electron mobility and independent of temperature. What is the ratio between conductivity at $600 \; K$ and that at $300 \; K$? Assume that the temperature dependence of intrinsic carrier concentration $n_{i}$ is given by $n_{i} = n_{0} \exp \left(-\frac{E_{g}}{2 k_{B} T}\right)$,where $n_{0}$ is a constant.

$A$ semiconductor doped with a donor impurity is