Electronic states in a quantum lens - art. no. 125319

We present a model to find analytically the electronic states in self-assem bled quantum dots with a truncated spherical cap ("lens'') geometry. A conf ormal analytical image is designed to map the quantum dot boundary into a d ot with semispherical shape. The Hamiltonian for a carrier confined in the quantum lens is correspondingly mapped into an equivalent operator and its eigenvalues and eigenfunctions for the corresponding Dirichlet problem are analyzed. A modified Rayleigh-Schrodinger perturbation theory is presented to obtain analytical expressions for the energy levels and wave functions a s a function of the spherical cap height b and radius a of the circular cro ss section. Calculations for a hard wall confinement potential are presente d, and the effect of decreasing symmetry on the energy values and eigenfunc tions of the lens-shape quantum dot is studied. As the degeneracies of a se micircular geometry are broken for b not equal a, our perturbation approach allows tracking of the split states. Energy states and electronic wave fun ctions with m = 0 present the most pronounced influence on the reduction of the lens height. The method and expressions presented here can be straight forwardly extended to deal with more general Hamiltonians, including strain s and valence-band coupling effects in Group III-V and Group II-VI self-ass embled quantum dots.