Simple Estimation of X- Trion Binding Energy in Semiconductor Quantum Wells

TL;DR

This paper introduces a simple variational method to estimate the binding energy of negatively charged excitons in semiconductor quantum wells, showing good agreement with experimental data and revealing universal behavior.

Contribution

A straightforward variational approach with three parameters is proposed to calculate X- binding energies, highlighting their universal dependence on quantum well width.

Findings

Calculated binding energies agree with experimental data for GaAs, CdTe, ZnSe.

Normalized X- binding energy is nearly independent of electron-to-hole mass ratio.

Binding energy dependence on well width follows a universal curve described by a simple equation.

Abstract

A simple illustrative wave function with only three variational parameters is suggested to calculate the binding energy of negatively charged excitons (X-) as a function of quantum well width. The results of calculations are in agreement with experimental data for GaAs, CdTe and ZnSe quantum wells, which differ considerably in exciton and trion binding energy. The normalized X- binding energy is found to be nearly independent of electron-to-hole mass ratio for any quantum well heterostructure with conventional parameters. Its dependence on quantum well width follows an universal curve. The curve is described by a simple phenomenological equation.