Influence of the depletion length on the commensurability effects in tunable antidots

Commensurability effects between the period of an artificial array of scatterers (antidots) in a two-dimensional electron gas and the classical cyclotron radius are found to depend strongly on the size of the antidots in comparison with the period. Magnetotransport experiments on tunable antidot arrays are reported and analyzed. In the region of large depletion zones we find strong deviations of the Hall effect from the Drude slope in magnetic fields up to several teslas. From this, we deduce undepleted regions of less than 60 nm in typical 500-nm period structures. The suppression of the commensurability motion around several antidots observed in the longitudinal magnetoresistance in the case of strong depletion has the same origin and allows us to determine independently and consistently the depletion radius of the antidots.