We investigated the maximum density of InAs quantum dots grown by molecular beam epitaxy on GaAs(0 0 1) substrates. Different from most current work, we took advantage of the non-uniformity of the molecular beams to produce a sample in which the amount of InAs material was continuously varied across the surface in order to analyze the evolution of the QDs as a function of the film thickness. A density of structures as high as 1800 mum(-2) could be observed by atomic force microscopy and is around twice the maximum value typically reported in the literature. No loss of size uniformity was detected for such a high density. (C) 2002 Elsevier Science B.V. All rights reserved.