We have examined the electron mobility \ensuremath{\mu} as a function of the concentration of a two-dimensional electron gas n, in GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As heterostructures. Depending on the method used to vary n, different values of \ensuremath{\mu} can be obtained for the same n and in the same heterostructure. We suggest the origin of this effect lies in the interdonor interactions leading to spatial correlations of remote impurity charges. It results in a significant mobility enhancement at low temperatures. This finding demonstrates the necessity of taking into account many-body effects within the impurity system in different phenomena occurring in highly doped semiconductors.
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