Percolation transition of the quasi-two-dimensional hole system in δ-doped GaAs structures

The transition from thermally activated conduction to metallic conduction in Be δ-doped GaAs structures was investigated. At room temperature, samples with lower Be concentrations exhibited the thermally activated conduction, and other samples with higher Be concentrations showed the metallic conduction. The activation energy for the conduction of the insulating samples changes linearly with the Be concentration, vanishing at a critical Be concentration. The slope of the linear change corresponds to the density of states in the quasi-two-dimensional hole system of GaAs, suggesting the existence of the mobility edge in this system. A model of percolation via quantum point contacts is used for the analysis of the temperature-dependence of the resistivity in the samples with high Be concentrations. The thermally activated conduction in these samples at low temperatures is explained by assuming the existence of more than one percolation thresholds which result from the nature of quantum point contacts. The temperature dependence of the resistivity at high temperatures for all investigated samples collapses onto a single curve in each of the insulating and metallic side with one scaling parameter T_0. The value of T_0 has a power-law relation with the hole concentration in both insulating and metallic sides with critical exponents being 0.94±0.05 and 1.19±0.16, respectively