The density of nanoholes created by self-assembled Al droplet etching of AlAs surfaces during molecular beam epitaxy is studied. We find a clear decrease of the hole density with increasing etching temperature T up to a threshold temperature T = 620 degrees C. At T > 620 degrees C, the hole density saturates at a minimum of 2 x 10(8) cm(-2). We attribute this saturation to a change of the AlAs surface reconstruction. On the other hand, at reduced T, hole densities up to 2 x 10(9) cm(-2) have been achieved. However, this hole density increase is accompanied by a reduction of the hole depth. To generate high density holes with larger depth suited for quantum dot fabrication, we have studied the effect of repeated etching steps. (C) 2013 Elsevier B.V. All rights reserved.