Exciton states in narrow quantum wells In$_x$Ga$_{1-x}$As/GaAs

The reflection spectra of a high-quality heterostructure with a narrow quantum well In$_x$Ga$_{1-x}$As/GaAs ($x$ = 0.022) are studied. Microscopic modeling of the exciton spectrum is performed using a numerical solution of the three-dimensional Schrodinger equation. It is shown that two exciton resonances below the free exciton energy in GaAs are formed by a heavy hole exciton localized in a quantum well. The potential profile of a quantum well is determined within the framework of a theoretical model with parameters calculated ab initio. For the studied structure, the ratio of the discontinuities of the valence band $(E_v)$ and the conduction band $(E_c)$ is obtained: $E_c$: $E_v$ = 64:36.