We 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… Click to show full abstract
We 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.
               
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