Semiconductor nanostructures are fabricated by local oxidation of Ga[Al]As heterostructures with an atomic force microscope (AFM). The GaAs surface is locally oxidized by applying a bias between the substrate and a conductive AFM tip in a humidity-controlled environment. For high-quality two-dimensional electron gases (2DEGS) located close enough to the sample surface the electrons get depleted below the oxidized regions. This way the plane of a 2DEG can be cut into various conductive areas which are laterally insulated from each other. The realization of several high-quality semiconductor nanostructures is demonstrated. I. Quantum wires are fabricated with smooth and steep potential. II. Quantum dots tuned by in-plane gate electrodes can be operated in the regime, where electrons tunnel sequentially through individual quantum levels. III. Antidot superlattices with high-precision lattice parameters display characteristic features of classical and quantum transport. (C) 2002 Elsevier Science Ltd. All rights reserved.