Modeling quantum structures with the boundary element method

A detailed analysis of the boundary element formulation of the electronic s tates of quantum structures is presented. Techniques for minimizing computa tion time by reducing the number of boundary integrals, utilizing the repet itive nature of embedded multiple quantum structures, and eliminating bound ary elements for modeling the effects of quantum wells that contain quantum structures are discussed. Boundary element solutions for isolated and coup led quantum wires and pyramidal quantum dots are presented. The results for the coupling of such quantum structures clearly show the splitting of grou nd and excited states into "bonding" and "antibonding" states for both wire s and dots. The numerical algorithm is shown to accurately capture these sy mmetry proper-ties of a system of quantum structures if the boundary elemen t and quadrature points are properly organized. For an asymmetric system of coupled dots, depending on the energy level, the center of charge is shown to be either above or below that for a pair of uncoupled dots with the sam e dot separation and orientation. Results are also presented showing the in crease in energy levels resulting from the additional confinement arising f rom placing quantum dots into a quantum well. (C) 2001 Academic Press.