Post-annealing effects on InAs islands grown on GaAs(0 0 1) surfaces have been investigated by scanning tunneling microscopy (STM) connected to molecular beam epitaxy (MBE). It is found that for islands grown by 1.6 ML InAs deposition at 450 degreesC, post-annealing at 450 degreesC in an As-4 atmosphere causes dissolving of the InAs islands. In contrast, for larger islands obtained by 2.0 ML InAs deposition at 450 degreesC, the post-annealing leads to coarsening of the islands. The result can be explained in terms of a critical nucleus in heterogeneous nucleation. (C) 2002 Elsevier Science B.V. All rights reserved.