Exchange Interaction and Oscillator Strength in Neutral Bound Exciton

Abstract

In an exciton bound to a neutral donor the electron-hole exchange interaction mixes states of opposite symmetry with respect to the interchange of two electrons [1]. We take a perturbation parameter proportional to the electron-hole exchange integral and use a variational-perturbation method to compute wave function in the first order and the ground state energy in the second order. The basis functions of Page and Fraser with nonlinear parameters of Stebe and Munschy [2] and reoptimized scale parameter for each electron-to-hole mass ratio, practically reproduce the best ground state energy, and are used to compute the linear combinations for the envelope function corrections symmetric and anti-symmetric with respect to interchange of two electrons. The electric dipole moment of the exciton radiative recombination is proportional to overlap integral of the envelope and the donor ground state wave function. Squared overlap integral gives the ratio of the bound exciton to the conduction-band-to-valence-band transition. The Page-Fraser 70-term envelope function and the correction due to electron-hole exchange interaction with the exchange integral taken from the free exciton singlet-triplet splitting [3], lead to agreement of the calculated oscillator strength for bound exciton recombination with the measured radiative lifetime of bound excitons in wurtzite type semiconductors CdS [4] and CdSe.