Consider silicon at $T=300K$ that is doped with donor impurity atoms to a concentration of $N_d=1{10}^{17}c{m}^{-3},$ the intrinsic carrier concentration is $n_i=1{10}^{10}c{m}^{-3},$ the excess carrier lifetime is $1{10}^{-6}s.$

If we add excess electrons and holes so that $n=p={10}^{12}c{m}^{-3},$ is the semiconductor in low$-$level injection? Explain why or why not. $(10$pt$)$

Where are the quasi$-$Fermi levels, Fn and Fp located with respect to the intrinsic, Ei$?$ Provide the numerical value and show the Fn and Fp on the energy band diagram below. $(10$pt$)$

Determine the thermal equilibrium recombination rate of holes. $(10$pt$)$

Excess carriers are generated such that $n=p={10}^{12}c{m}^{-3}.$ What is the recombination rate of holes for this condition? $(10$pt$)$