Coulomb attraction in the optical spectra of quantum disks

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Abstract
In this paper we present a theory that describes the influence of the Coulomb interaction between electrons and holes on the optical spectra of flat quantum dots within the envelope-function formalism. Starting from a nonlocal Elliott-like formula, absorption and luminescence characteristics are traced back to properties of two-particle wave functions and energies, which are solutions of the corresponding Schrödinger equation for an electron-hole pair under the influence of the Coulomb attraction and confinement potentials, determined by the spatial variation of the band edges of the considered microstructure. We present a complete numerical solution of the two-particle problem for flat quantum dots, i.e., disks for which the size quantization in the growth direction is much stronger than that in the perpendicular plane. The resulting theoretical line shapes are compared with luminescence spectra obtained recently for quantum dots fabricated by laser-induced thermal cation interdiffusion in quantum-well structures.