Carrier concentration — UPSC Physics Optional CSE 2019 Paper II

A silicon semiconductor sample is doped with 6\times10^{16}\,\mathrm{cm^{-3}} of aluminium and 7\times10^{15}\,\mathrm{cm^{-3}} of phosphorus atoms. Given at T=300\,\mathrm{K}, the intrinsic carrier concentration, n_i=1.5\times10^{10}\,\mathrm{cm^{-3}}; the band gap, E_g=1.1\,\mathrm{eV}; the electron mobility, \mu_n=1250\,\mathrm{cm^2\,V^{-1}\,s^{-1}} and the hole mobility, \mu_p=480\,\mathrm{cm^2\,V^{-1}\,s^{-1}}. Determine in the sample of the following:

(i) The type of the semiconductor, n or p

(ii) The hole carrier concentration

(iii) The electron carrier concentration

(iv) The position of the Fermi level in the sample with respect to the bottom of the conduction band

(v) The conductivity of the sample