The energetics of an array of three-dimensional coherent strained islands on a lattice-mismatched substrate is studied. The contribution of the edges of islands to the elastic relaxation energy always has a minimum as a function of the size of an island $L$, and the total energy $E\left(L\right)$ may have a minimum at an optimum size $L_{\mathrm{opt}}$. Among different arrays of islands on the (001) surface of a cubic crystal, the total energy is minimum for the 2D periodic square lattice with primitive lattice vectors along “soft” directions [100] and [010]. This is a stable array of islands which do not undergo ripening.

• Received 15 March 1995

DOI:https://doi.org/10.1103/PhysRevLett.75.2968