Screening by fixed charges in compensated semiconductors

Donor and acceptor ions in compensated semiconductors at low temperatures are not completely randomly distributed---positive and negative charges tend to be closer to each other than allowed by chance. This gives rise to a kind of screening effect, which is usually taken into account in calculations by replacing the ion Coulomb potential by a Debye-type screened potential. We show that this replacement is wrong in principle; it leads to a statistical fluctuation of potential which is too small by a factor of 2 and, at least in the case of small screening lengths, to a distribution of the total ion potential whose shape is substantially different from that obtained in a more fundamental calculation.