ELECTRONIC STATES IN GRADED-COMPOSITION HETEROSTRUCTURES

The purpose of this work is to develop and demonstrate the practical u se of very efficient algorithms which can be readily used to study sys tems with significant inhomogeneities. We have developed two algorithm s which can be used to study inhomogeneous discrete systems. The first one is an extension of known algorithms for homogeneous media and res ts on the notion of transfer matrices, which are then used to evaluate the desired elements of the Green-function matrices to be employed in surface Green-function matching calculations. The second one is total ly different and yields the Green-function matrices directly. Both wor k quite efficiently. When tested in practice for a graded-composition quantum well they give the same results for the local density of state s at the interfaces. We apply the algorithms to the study of quantum w ells consisting of AlAs in the barriers and N(w) layers Alx(n)Ga1-x(n) As in the well region, with x varying linearly from x =0.3 to x = 0. T he sp3s empirical tight-binding model and the virtual-crystal approxi mation are used. We studied three wells of different thicknesses (N(w) = 21,35,51). The ground-state and some excited-state energies of the conduction and valence bands are studied in detail: Spatial dependence and orbital composition of the corresponding spectral strengths show all the expected features.