Electrooptical constants in spherical quantum dots

The electrooptical properties of a spherical quantum dot (QD) are theoretically investigated when the QD radius R is smaller than the bulk exciton Bohr radius. The electronic energy levels are obtained as a function of one universal parameter t = 2 /q/ m*FR(3)/h(2), where m* and q are the quasiparticle mass and charge, respectively, and F is the applied electric field. The carrier polarization and the interband electron-hole oscillator strength are investigated as functions of both t and the electron-hole mass ratio. Using the Kramers-Kronig relations the change of the complex dielectric constant due to the electric field is derived. A definition of the complex electrooptical function, which describes the main features of the spherical QD optical constants in presence of an electric field, is given. In the strong electric field regime, where perturbation theory cannot be applied to the Schrodinger equation, a quasi-linear dependence on F is predicted for the electroabsorption variation spectrum. The obtained results are used to explain recent experimental data for the decay of electron-hole pairs.