Calculation of exchange energy in quantum dots : application to porous silicon

Abstract
We present a variational calculation of the envelope wave function of an exciton inside a cube, in the effective mass approximation, with one parameter which plays the part of a Bohr radius. This geometry allows one to reduce the sixfold integrals to threefold integrals which shortens tremendously computer calculations. This wave function is used to obtain the exchange energy and the oscillator strength. The limiting cases (large or small cubes) are recovered. We show that recent experimental results in porous silicon can be explained without further hypothesis.