Atomic force microscopy (AFM, Nanoscope IIIA) is used to study InAs quantum-dot structures grown by molecular-beam epitaxy (MBE) on a shallow spherically shaped crater (also called a dimple) with the continuous polar misorientation and azimuthal orientation prepared on GaAs (001) substrate by a Model 656 Dimple Grinder. It is shown that the step bunches become larger after the growth, suggesting that the Schwoebel barrier, which causes the step bunching, may be decreased by the change of surface reconstruction after the introduction of small amount of In atoms to GaAs surfaces in the initial stage of growth. The number n of the InAs quantum dots per 3 x 3 mum(2) area decreases with increase in polar misorientation angles a but does not depend on the azimuthal orientation angle. These results are plotted for the polar misorientation angles along the [(1) over bar 10], [110] and [100] directions. The reduction in quantum dots with an increase in polar misorientation angle is due to the suppression of lattice-mismatched strain. It is observed that the quantum dots tend to form on the humps and valleys. (C) 2003 Elsevier B.V. All rights reserved.