Hydrogenic-impurity ground state inGaAs−Ga1−xAlxAsmultiple—quantum-well structures

We report the results of a variational calculation for the hydrogenic-impurity ground state in a multiple—quantum-well structure consisting of alternating slabs of GaAs and ${\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x\mathrm{As}$. Calculations have been carried out with the assumption that the impurity envelope wave function spreading beyond the next-nearest-neighbor GaAs wells is negligible. Impurity envelope wave functions have been plotted for some typical GaAs well and ${\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x\mathrm{As}$ barrier thicknesses to find the extent of wave-function spreading. The binding energy is found to vary substantially as a function of the barrier thickness. Calculations are performed for the variations of the binding energy as a function of the well thickness and also as a function of the barrier thickness. The main peak in the impurity binding energy in superlattices with equal well and barrier thickness is shifted towards a thickness larger than that in single-well systems. A secondary peak appears at a very small thickness, which arises because the model includes only three wells. The results of the present calculation in various limiting cases agree with previous results.