The Bohr radius of the fifth electron of phosphorus (atomic number $Z = 15$) acting as a dopant in silicon (relative dielectric constant $\varepsilon_r = 12$) is ....... $\mathring{A}$.

The temperature $(T)$ dependence of resistivity $(\rho)$ of a semiconductor is represented by

In an extrinsic semiconductor,the number densities of holes and electrons are ${N_p}$ and ${N_e}$ respectively. Then:

$A$ silicon specimen is made into a $p$-type semiconductor by doping,on an average,one indium atom per $5 \times 10^7$ silicon atoms. If the number density of atoms in the silicon specimen is $5 \times 10^{28} \text{ atoms } m^{-3}$,then the number of acceptor atoms in silicon per cubic centimeter will be:

If $n_e$ and $n_h$ are electron and hole concentrations in an extrinsic semiconductor and $n_i$ is the intrinsic carrier concentration, then:

When $Ge$ crystals are doped with phosphorus atoms,then it becomes