The effect of surface charge self-organization on gate-induced electron and hole two-dimensional systems

Abstract

A model is proposed for describing the self-organization of localized charges and quantum scattering in undoped GaAs/AlGaAs structures in which a two-dimensional gas of electrons or holes is created by the corresponding gate voltage. We assume that in such a metal-dielectric-undoped semiconductor structure carrier scattering on surface charges localized at the interface between GaAs and the dielectric dominates. Proposed model considers these charges and the corresponding image charges in the metal gate as a closed system in a thermostat. The electrostatic self-organization for this system in thermodynamic equilibrium is studied numerically using the Metropolis algorithm in a wide temperature range. It is shown that, at T > 100 K, a simple formula derived from the theory of two-dimensional one-component plasma gives almost the same behavior of the structural factor at low wave numbers as the Monte Carlo calculation. The scattering times of gate-induced carriers are described by formulas in which the structural factor characterizes the frozen disorder in the given system. In these formulas, the behavior of the structural factor at small wave numbers is decisive. A calculation using these formulas with disorder corresponding to infinite T gives two to three times shorter scattering times than in the corresponding experiments. We found that the theory is consistent with experiment at a freezing point of disorder T ≈ 1000 K for a sample with a two-dimensional electron gas and T ≈ 700 K for a sample with a two-dimensional hole gas. The found values are an upper estimate of the freezing temperature in the studied structures, since the model ignores sources of disorder other than temperature.