Statistical model of electronic structure in InAs, InP, GaSb, and Si quantum dots with surface roughness

Simulations based on the sp 3 d 5 s * empirical tight-binding method were performed to provide a statistical understanding of the electronic structures and bandgap distributions of III-V (InAs, InP, GaSb) and IV (Si) semiconductor quantum dots (QDs) with surface roughness. The electronic states and wavefunctions of QDs with surface roughness of different sizes, shapes, and materials were computed. The effects of surface roughness on the electronic structures and the bandgap distributions of QDs were investigated. The results show that the bandgaps of QDs of considered materials/sizes/shapes increase on average when introducing surface roughness. It is shown that the simulated bandgap distributions of QDs with surface roughness can be reproduced by a simple model formula, which can be applied to different materials, sizes, and shapes. The model formula was derived by assuming that removing and adding of one atom procedures are independent random processes.