Optical transitions in geometrical quantum islands

We have calculated the electronic structure and optical transitions in quantum islands of special geometrical shapes, using the finite element method. In this approach, the wavefunction of a carrier is constructed as a linear combination of a basis set formed by localized functions, built up as a product of three Cartesian cubic β-splines. The variational method is used to determine the best set of coefficients for each state. Three different geometries were used to describe quantum islands in the form of lenses and a pyramid. The first case is a simple cut on a spherical island. The second situation describes a deviation from sphericity, which involves cuts in the spheroidal oblate or prolate shapes. In third situation the carrier is confined inside a pyramidal quantum dot. Single-particle transitions for GaAs/Ga1−xAlxAs and InAs/InP heterostructures, as well as for GaAs and CdTe dots surrounded by a vacuum or embedded in glass matrices, were calculated using the simple four-band model to describe the electron and hole energy levels in a zinc-blende semiconductor structure near theΓ-point.