Electronic states in a quantum lens

Abstract

We present a model to find analytically the electronic states in self-assembled quantum dots with a truncated spherical cap (`lens') geometry. A conformal analytical image is designed to map the quantum dot boundary into a dot with semi-spherical 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-Schrödinger perturbation theory is presented to obtain analytical expressions for the energy levels and wavefunctions as a function of the spherical cap height $b$ and radius $a$ of the circular cross section. Calculations for a hard wall confinement potential are presented, and the effect of decreasing symmetry on the energy values and eigenfunctions of the lens-shape quantum dot is studied. As the degeneracies of a semi-circular geometry are broken for $b\ne a$, our perturbation approach allows tracking of the split states. Energy states and electronic wavefunctions with $m=0$ present the most pronounced influence on the reduction of the lens height. The analytical expressions presented here can be used to better parameterize the states in realistic self-assembled quantum dots.

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References in corpus (1)

• Spectroscopy of nanoscopic semiconductor rings

Cited by in corpus (6)

• Observation of shell effects in superconducting nanoparticles of Sn
• Dependence of the electronic structure of self-assembled InGaAs/GaAs quantum dots on height and composition
• Optical transition in self-assembled InAs/GaAs quantum lens under high hydrostatic pressure
• Quasi-conical quantum dot: electron states and quantum transitions
• AC-Stark effect in a semi-spherical quantum dot
• The Role of Geometry in Tailoring the Linear and Nonlinear Optical Properties of Semiconductor Quantum Dots