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We show that by computing the electron-impurity scattering rate at the firstorder via Fermi's golden rule, and assuming that the localized impuritypotential is of Yukawa form, one obtains a wave vector transfer distributionwhich is inconsistent with the finite temperature linearized Thomas-Fermiapproximation for {\it n}-type semiconductors. Our previous findings show thatthis is not the case for the carrier nondegenerate dynamics, because theaverage wave vector transferred being in general negligible in this regime.Moreover, we examine the behavior of the electron-impurity differentialcross-sections in the first Born approximation for relevant values of the wavevector transfer. We find that in the majority of collisions, the scatteringprobabilities differ at the most by $1$ \% from the estimates computed by meansof the impurity potential at random phase approximation level.

Inconsistency between Linearized Thomas-Fermi Approximation and Electron-Ionized Impurity Scattering Rate in the first Born Approximation