Stress-Driven Nucleation of Three-Dimensional Crystal Islands: From Quantum Dots to Nanoneedles

Abstract

We study theoretically new effects during the stress-driven nucleation of three-dimensional (3D) crystal islands in lattice mismatched material systems. It is shown that the formation enthalpy of a coherent strained 3D island is a function of two independent variables: the base dimension and the aspect ratio. The minimum nucleation barrier relates to a saddle point of formation enthalpy. If the 3D barrier is smaller than the two-dimensional (2D) one, the islands tend to adopt a 3D form with the energetically preferred aspect ratio, which is a function of the lattice mismatch e0, material constants, and supersaturation. With different approximations for the elastic energy relaxation, we map out the growth diagrams separating the domains of 2D, 3D, and the Stranski−Krastanow (SK) growth. The preferred aspect ratio increases with the lattice mismatch from modest values typical for quantum dots (QDs) at e0 ∼ 4−12% to very large values of the order of ten at e0 = 46%, corresponding to the case of GaAs nanoneed...