Diffusion of two-dimensional hot electrons in semiconductor quantum wells at low temperatures

A theoretical approach is developed to study the diffusivity of two-dimensional degenerate hot electrons in a quantum well by a semianalytic solution of the Boltzmann equation, including the effect of the diffusion current on the distribution function. Calculations are done with GaAs material parameters for a well 60 Å wide and a sheet carrier concentration of 7×10¹¹ cm^-2 at a lattice temperature of 4.2 K and electron temperatures below 40 K, where momentum is predominantly relaxed through background impurity scattering and energy is predominantly relaxed through deformation potential acoustic scattering. The diffusion is found to be strongly anisotropic, the longitudinal-to-transverse diffusivity ratio increasing with the increased heating of the electron gas. Also, the diffusivity of the two-dimensional electron gas is shown to be more field-dependent than that of the bulk material