Binding energy of the screened exciton in two-dimensional systems

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Abstract
Recent optical nonlinearities in GaAs/Ga1−xAlxAs quantum well structures have been attributed to the screening of the electron-hole interaction in such structures by the free carriers generated. In this paper, we perform a variational calculation of the binding energy of the exciton confined in a two-dimensional structure, taking into account the screening of the Coulomb interaction between the electron-hole pair due to the free carriers. The screened potential used is that obtained by Stern and Howard for hydrogenic impurities in semiconducting inversion layers. We find that, although the binding energy of the exciton is reduced because of the presence of screening, the exciton remains bound even for fairly strong screening. This is in contrast to the 3-D case which occurs in bulk semiconductors where the presence of screening can prevent the electron-hole pair from forming an exciton. We have found that the optical absorption at the exciton peak also decreases as the screening increases.