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Two-dimensional electron gas separated from Coulomb centers by a spacer is considered. Electrons are treated semi classically in limit of weak fluctuation and T = 0. Two screening models, Thomas-Fermi and RPA, are independently used. The second moment of the potential energy distribution is calculated analytically as a function of the spacer width. The qualitative arguments for the Gaussian character of the distribution are given and the density of states for such a distribution is calculated.

Potential Energy Fluctuation in Quasi Two-Dimensional Electron Gas Due to External Ionized Impurities