Simulation of surface evolution of quantum dot using meshfree approximation

An ideal way of fabricating quantum dots is by self-assembly that can be simulated using the Stranski-Krastanow growth mode. This paper presents a numerical scheme to simulate the morphology of the quantum dot “island” due to stresses induced by a buried quantum dot. The surface diffusion equation that governs epitaxial growth is solved for the normal surface velocity by using a meshfree interpolation technique-the moving least square method. The normal surface displacement is then deduced and the process is repeated through a difference scheme to obtain the change in surface shape as a function of time. Simulations using the present method have found that the island morphology is affected by various factors including elastic anisotropy, cap layer thickness and crystal orientation.