Critical currents in quantum Hall conductors with antidot arrays

Abstract

We have investigated the abrupt onset of dissipation in the quantum Hall effect (QHE) in antidot arrays patterned on a two- dimensional electron system. Different lateral configurations (periodic or aperiodic antidot arrays, and single lines of antidots, with diameters between 40 and 100 nm and periods or average spacings between 300 and 1500 nm) show remarkable differences in their non-Ohmic transport properties. In periodic arrays with large antidot diameter (lithographic diameter 100 nm), the breakdown current is systematically reduced with increasing antidot density and determined by the peak value of the local current density. From these measurements, we determined the depletion width around the antidots. In aperiodic arrays, the breakdown current is markedly lower than in periodic arrays of the same antidot size and density due to higher local values of the current density at the same total current. This was experimentally confirmed by measurements of the current dependence of the electron temperature in periodic and aperiodic arrays. Single lines of antidots, placed across the direction of current flow, cause only a small reduction of the breakdown current in comparison with unpatterned reference areas. This is in accordance with the picture of avalanche electron heating for the breakdown of the QHE, where the electrons reach a quasistationary, elevated temperature only after travel distances of several 10 im in a supercritical electric Hall field. In antidot lattices with very small antidot diameter (40 nm) and small lattice period (300 nm), the antidots provide additional inelastic scattering, which effectively suppresses the electron heating. This effect overcompensates the geometrical effect of the antidots and was experimentally verified by the observation of higher breakdown currents compared to the reference area. A complete absence of a hot- electron-induced hysteresis in the current- voltage characteristics was observed for this type of array.