We report on the use of shadow masks for the growth of GaAs quantum wells with spatially varying thicknesses. Using cathodoluminescence we observe a clear shift of the luminescence energy as a function of the lateral position. Combining masked and directional epitaxy, the quantum wells can be both laterally and vertically patterned. This way, stacked, two‐dimensional electron gases are realized which can be selectively contacted without the use of complicated in‐situ or post‐growth patterning techniques. The quality of the epitaxial material grown through the openings of the masks is investigated by optical and electrical characterization. ©1995 American Institute of Physics.