The resistivity of a pure semiconductor is $0.5 \ \Omega m$. If the electron and hole mobility are $0.39 \ m^2 / V-s$ and $0.19 \ m^2 / V-s$ respectively,then calculate the intrinsic carrier concentration.

When arsenic is added as an impurity to silicon,the resulting material 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.

Statement-$I$: By doping silicon semiconductor with pentavalent material,the electron density increases.
Statement-$II$: The $n$-type semiconductor has a net negative charge.
In the light of the above statements,choose the most appropriate answer from the options given below:

$A$ crystal of intrinsic silicon at room temperature has a carrier concentration of $1.6 \times 10^{16} / m^3$. If the donor concentration level is $4.8 \times 10^{20} / m^3$, then the concentration of holes in the semiconductor is

In an intrinsic semiconductor,the density of conduction electrons is $7.07 \times 10^{15} \, m^{-3}$. When it is doped with indium,the density of holes becomes $5 \times 10^{22} \, m^{-3}$. Find the density of conduction electrons in the doped semiconductor.