$A$ pure $Si$ crystal has $5 \times 10^{28}$ atoms $m^{-3}$. It is doped with $1 \, ppm$ concentration of pentavalent $As$. The number of holes is (Take $n_i = 1.5 \times 10^{16} \, m^{-3}$)

In extrinsic $P$ and $N$-type semiconductor materials,the ratio of the impurity atoms to the pure semiconductor atoms is about

In a $P$-type semiconductor, the acceptor level is $57 \text{ meV}$ above the valence band. What is the maximum wavelength of light (in $\mathring{A}$) required to create a hole?

Explain the recombination coefficient of an intrinsic semiconductor and derive the relation $n_i^2 = n_e n_h$.

$A$ $P$-type semiconductor is:

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.