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The theory of hot electrons is developed for high-mobility GaAs heterolayers at low temperature, where the electron system is two-dimensionally itinerant with a highly degenerate distribution, and the scattering is predominantly elastic. The inelastic scattering which controls the electron heating is by acoustic-mode phonons, with both deformation and piezoelectric coupling to the electrons. Both ‘‘equipartition’’ and ‘‘Bloch’’ temperature ranges are considered. The assumption of an electron temperature, for the hot distribution, is critically investigated.

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