Regular two-dimensional arrays of antidots with periodicities in the range of 200–500 nm are prepared in GaAs-${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As heterostructures by means of Ga-focused ion-beam implantation. Transport measurements at low magnetic fields reveal a strong negative magnetoresistance originating from the localization of the electrons in the potential valleys between antidots. The low-temperature mobilities of the carriers deduced from the B=0 resistance are in the range of 1000–30 000 ${\mathrm{cm}}^2$/V s. Under illumination mobility changes by more than a factor of 20 can be achieved. For high magnetic fields well-defined Shubnikov–de Haas oscillations and quantum Hall plateaus are observed. Close to B=0 a very small structure in the magnetoresistance occurs reflecting the commensurability of the cyclotron diameter and the periodicity of the antidot array.

• Received 12 February 1990

DOI:https://doi.org/10.1103/PhysRevB.41.12307