Effect of shape of quantum dots on strains: a finite element study

It is fairly well established that self-aligned quantum dots can form in strained epitaxial systems. One system that has been studied extensively is the InAs/GaAs system wherein the difference in lattice parameter is about 7.0%. Strains within the dot and the surroundings are known to influence the optical properties of the system. However, very little information is available on the strains in these quantum dots. In particular, the effect of shape of the initial shape of quantum dots and boundary conditions are not very well known. Strains in InAs quantum dots embedded in GaAs have been examined using the finite element method within a thermo-mechanical framework. The initial shape of the dot is assumed to be conical in 3D with different width/height ratio typical of quantum dots. Modeling is accomplished using a 2-D axi-symmetric finite element model. Results of the simulation show that initially conical shaped dots become more rounded in shape and become lens-shaped. It has been shown that the width/height ratio is critical in determining the strains within the quantum dots. Results of the calculation are compared with the results of other calculations and experimental measurements of strains using the STM.