Semiconductors

Explain how acceptor dopants contribute holes in valence band in p-type extrinsic semiconductor. Also prove that $\sigma = pe\mu_h$ where symbols have their usual meanings.

Calculate the resistance of pure silicon cubic crystal of $1\ \mathrm{cm^3}$ at room temperature. What will be the resistance of the cube when it is doped with $1$ arsenic in $10^9$ silicon atoms and $1$ boron atom per billion silicon atoms? Atomic concentration of silicon is $5\times10^{22}\ \mathrm{cm^{-3}}$, $n_i=1.45\times10^{10}\ \mathrm{cm^{-3}}$.

The density of states related effective masses of electrons and holes in silicon are approximately $1.08\,m_e$ and $0.56\,m_e$ respectively. The electron and hole drift mobilities at room temperature are $1350$ and $450\ \mathrm{cm^2V^{-1}s^{-1}}$ respectively. Calculate intrinsic concentration and intrinsic resistivity of silicon. The energy band gap for silicon is $1.1\ \mathrm{eV}$.