Quantum Monte Carlo studies of binding energy and radiative lifetime of bound excitons in direct-gap semiconductors

We calculate the binding energy and the oscillator strength for radiative recombination of the bound exciton in direct-gap semiconductors in the spherical effective-mass approximation. The variational Monte Carlo method is used to evaluate the ground-state energy with a variational wave function that includes all pair correlations between particles. An importance-function Monte Carlo method is used to evaluate the corresponding optical-matrix element. We obtain variational energies for the donor bound exciton at all electron-hole mass ratios and recover about 60% of the experimental binding energy for various direct-gap semiconductors. The matrix element squared for the donor bound exciton in this model is twice as large as previous estimates, confirming the large disrepancy between the experimental and theoretical estimates of its radiative lifetime.