Computational study of confined states in quantum dots by an efficient finite difference method.

Abstract

Semiconductor quantum dot systems have gained more attention in quantum computation and optoelectronic applications due to the ease of bandstructure tailoring and three-dimensional quantum confinement. Thus, an accurate solution of energy bandstructure within the quantum dot is important for device design and performance evaluation. In this paper, the solutions of bandstructures of quantum dot systems are presented by implementing finite difference technique. To illustrate our analysis procedure, various configurations of quantum dot systems were taken into account. In order to improve the calculation efficiency of the finite difference solution in terms of time and memory consumption, uneven divisions for the quantum dot confinement region were used. In addition, we identified the optimum combination of divisions for each geometrical configuration. Eventually, the eigenstate wavefunctions and eigenvalues were obtained by directly solving the eigen-value problems. Overall, the generated results agreed consistently with the published results obtained by other solution techniques.