The formation of dislocation-free three-dimensional islands by heteroe
pitaxial growth of lattice mismatched materials is utilized to produce
partially ordered arrays of quantum dots. The equilibrium shape of th
ese islands results from the competition between surface and elastic e
nergies. We have studied the system InAs/GaAs(001) in detail. InAs sur
face energies have been computed ab initio for several orientations, a
nd the elastic energy of the islands has been calculated within a cont
inuum theory. The resulting equilibrium islands are hills bounded by {
110}, {111}, and {(111) over bar} facets and a (001) surface on top. W
e compare to experiment and discuss the influence of growth kinetics o
n the shape.