Numerical modeling of the InAs quantum dot with application of coordinate transformation and the finite difference method

In order to resolve the three dimensional Schrödinger equation, we report in this paper a method providing sufficient accuracy, stability and flexibility with respect to the size and shape of the quantum dot. This numerical method, already used in the two-dimensional case, is based on a suitable combination of coordinate transformation and the finite difference method. It provides an efficient and simple approach for the energy and wavefunction calculations of quantum nanostructures. The proposed method is used to investigate the electron and hole energy levels as well as their wave functions in InAs/GaAs strained and unstrained quantum dots with the aim to attain the 1.55 μm wavelength with realistic dot size. The optical transition energies and the oscillator strengths are also studied. The obtained results are in agreement with several previous works.