Theories of electron scattering by ionized impurities in semiconductors are reviewed. The early foundations based on the Born approximation and their subsequent refinements are discussed thoroughly. The phase-shift method which is not restricted to the Born approximation is also presented. The situation in heavily doped semiconductors is described. The theories are then compared critically with experiments. Finally, conclusions are drawn and some plausible lines of future work are outlined.

DOI:https://doi.org/10.1103/RevModPhys.53.745