Spatially dependent screening calculation of binding energies of hydrogenic impurity states in GaAs-Ga1−xAlxAs quantum wells

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Abstract
The effect of spatially dependent screening is taken into account with an r-dependent dielectric response to evaluate the binding energies of shallow hydrogenic impurity states in GaAs-Ga1-xAlxAs quantum wells. A variational calculation, in the effective-mass approximation, was performed as a function of the position of the impurity in a quantum well of finite depth and for various well thicknesses. It is shown that spatially dependent screening effects can be quite important for acceptors in a GaAs-Ga1-xAlxAs quantum well due to the relatively small effective Bohr radius (22 A) of the hole. The binding energies of on-edge impurities are shown to increase, for sufficiently large well thicknesses, when the barrier potential (or the Al concentration) decreases, a behavior which contrasts with results previously reported in the literature. © 1988 The American Physical Society