Size dependence of the polarizability and Haynes rule for an exciton bound to an ionized donor in a single spherical quantum dot

International audienceWe study the effect of an external electric field on an exciton bound to an ionized donor (D+, X) confined in a spherical quantum dot using a perturbative-variational method where the wave function and energy are developed in series of powers of the electric field strength. After testing this new approach in the determination of the band gap for some semiconductor materials, we generalize it to the case of (D+, X) in the presence of the electric field and for several materials ZnO, PbSe, and InAs, with significant values of the mass ratio. Three interesting results can be deduced: First, we show that the present method allows to determine the ground state energy in the presence of a weak electric field in a simple way (E = E-0 - alpha f(2)) using the energy without electric field E-0 and the polarizability a. The second point is that our theoretical predictions show that the polarizability of (D+, X) varies proportionally to R-3.5 and follows an ordering alpha(D0) < alpha(X) < alpha((D+, X)). The last point to highlight is that the Haynes rule remains valid even in the presence of a weak electric field