Application of coordinate transformation and finite differences method in numerical modeling of quantum dash band structure
The authors propose an efficient method for the band structure calculation of semiconductor quantum dashes. The method combines a coordinate transformation (mapping) based on an analytical function and the finite differences method (FDM) for solving the single-band Schrödinger equation. They explore suitable coordinate transformations and propose those, which might simultaneously provide a satisfactory fit of the quantum dash hetero-interface and creation of an appropriate computational domain which encloses the quantum dash structure. After a mapping of the quantum dash and the rest of computational domain, the Schrödinger equation is solved by the FDM in the mapped space. For the proposed coordinate transformations, they investigate and analyze applicability, robustness and convergence of the method by varying the FDM grid density and size of the computational domain.
scientific article; zbMATH DE number 5901265