Quantum well, wire, and dot nanostructures have a wide variety of technological applications, including semiconductor diode lasers and advanced semiconductor devices.
Numerical quantum mechanical methods are being developed for calculating the electronic states and transport properties of such systems. Initial calculations have been started on T-shaped semiconductor quantum wires at intersections of quantum wells formed by cleaved edge overgrowth. These structures exhibit lasing from bound exciton states localized in the T intersection region.
The exciton wave function is calculated by solving the Schroedinger equation using a discrete variable representation, localized to a grid of points that cover the cross section of the wires, to define basis functions for the problem. The solution requires finding the lowest few eigenvalues and eigenvectors of a large dimension sparse matrix, for which we are developing a parallel eigenvalue solver.
The figure illustrates the confinement potential and ground state wavefunction for a nanostructure with 8 nm wide GaAs channels surrounded by AlGaAs barriers. Calculated energy levels agree well with the measured ones.
The figure illustrates the confinement potential and ground state wavefunction for a nanostructure with 8 nm wide GaAs channels surrounded by AlGaAs barriers. Calculated energy levels agree well with the measured ones.