The effect of the dielectric mismatch on excitons and trions in freestanding nanowires

We investigate the energy levels of excitons (X) and trions (X±) in free-standing nanowires with strong lateral carrier confinement. Within the adiabatic approximation the two (resp. three) particle problem reduces to an effective one (resp. two) dimensional Schrödinger equation for the relative motion which is solved numerically. Dielectric mismatch effects are taken into account that result in a distorted Coulomb interaction between the charged particles. We obtain the X and X± binding energies as function of the dielectric mismatch ratio. We also construct tractable analytical expressions for the effective potential which significantly reduce the amount of computational time for future work.