Trion ground state energy: simple results

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

arXiv comment9 pages, 1 figure

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Cited by in corpus (1)

• Optical properties of charged excitons in two-dimensional semiconductors