Excitons in parabolic quantum wells

Abstract

We study theoretically excitons in semiconductor quantum wells in which the confining potential has a parabolic shape. In particular, we compare results of the variational calculations of the exciton binding energy using two different types of trial wavefunctions, namely we assume the trial function either has a simple form with the variables describing the motion within the quantum well plane separated from those describing the motion along the growth axis or, alternatively, has the form where these variables are not separable. It is shown that with a good accuracy one can use the separable trial wavefunction in a variational calculation for the exciton even in the range of the well widths where such choice leads to sizable errors in the case of rectangular quantum wells. By introducing a new characteristic length scale we also applied the fractional dimension approach to the exciton problem in parabolic quantum well structures and compared this result with the variational approaches.