Trion ground-state energy: Simple results

International audienceWe investigate the trion binding energy in a three-dimensional semiconductor, with bare Coulomb interaction between charges, and effective mass approximation for the electron and hole dispersion relations. This is done by making use of a previously proposed exact method for the three-body problem. The calculations cover the complete range of electron-to-hole mass ratio. We find a perfect agreement with existing variational calculations. Investigating the small and large mass ratio regimes, we build a three parameters interpolating formula for the trion binding energy E b (r) in terms of the exciton binding energy, where r is the electron to exciton mass ratio. This formula E b (r) = 0.71347 − 0.11527 r − 0.18580 √ 1 − r , in atomic units, is in full agreement, within our precision, with our numerical results over the complete range of mass ratio