Electroabsorption by confined excitons with Gaussian interaction potential

Abstract: We consider the effects of electron-hole interaction, 2D confinement and applied electric field on direct allowed transitions in III-V semiconductors, with InGaAs as a study case. Instead of Coulomb interaction, we use Gaussian potential. It is finite at the origin and has a finite effective range, which allows for a more efficient numerical solution of Schr\"{o}dinger equation. Yet, we can expect electroabsorption phenomena to remain qualitatively similar to the ones observed for Coulomb excitons. Moreover, we use variation of parameters to fit both position and magnitude of the first absorption peak to the Coulomb case. We combine and compare several numerical and approximate methods, including spectral expansion, finite differences, separation of variables and variational approximation. We find that separation of variables approach works only for quantum well widths smaller than the exciton radius. After separation of variables, finite difference solution of the resulting interaction equation gives a much better agreement with the full spectral solution than naive variational approximation. We observe that electric field has a critical effect on the magnitudes of exciton absorption peaks, suppressing previously allowed transitions and enhancing forbidden ones. Moreover, for excited states, initially suppressed transitions are enhanced again at higher field strengths.