Ab-initio modeling of asymmetrical finite-barrier quantum wire structures

A rigorous semi-numerical method for analyzing quantum wire and quantum dot structures has been developed. The method consists of developing a hierarchy of auxiliary problems which mimic a given (original) problem with increasing similarity and resolution. In each generation of the auxiliary problems the differential operators involved are Hermitian, thus ensuring positivity of the eigenvalues (eigenenergies of the system) and orthogonality of the corresponding eigenfunctions. Details of the method, its robustness and versatility are demonstrated by analyzing a quantum wire structure characterized in terms of a fairly complex potential function. Application of the proposed method to several structures involving periodically arranged finite-aperture quantum wires, sandwiched between symmetric or asymmetric finite barriers, will conclude the paper.