  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 $E_b(r)=0.71347-0.11527
\,r -0.18580\, \sqrt{1-r}\,$, in atomic units, is in full agreement, within our
precision, with our numerical results over the complete range of mass ratio.

Mesoscale and Nanoscale Physics;Other Condensed Matter