Two-dimensional exciton

In the ideal screened-Coulomb model confined to a plane, the relative-motion energies are $-R^{\ast }/(\nu -1/2{)}^2$ for $\nu =1,2,\dots$, where $R^{\ast }=(\mu /m_e)13.6\mathrm{eV}/{\epsilon }_r^2$. The ground-state binding is $4R^{\ast }$ rather than the three-dimensional value $R^{\ast }$. Finite-width wells need not be exactly planar.

The first two optically active hydrogenic levels have separation $32R^{\ast }/9$ in the planar model, versus $3R^{\ast }/4$ in the bulk model. The separation cancels an uncertain common continuum threshold, making it useful when rounded band parameters do not reproduce every absolute peak energy.