Superlattice with multiple layers per period.

With recent advances in epitaxial crystal-growth techniques, it has become possible to grow the semiconductor superlattice systems composed of alternate layers of two different semiconductor materials. This leads the band edges to exhibit a periodic variation with the position along the direction of crystal growth, The most extensively studied superlattice is the one consisting of alternate layers of GaAs and Gal „Al„As.' The GaAs layers form quantum ~elis and the Gal „Al„As layers form potential barriers. The energy spectrum of the superlattice can be controlled by the choice of Al concentration in Gal „Al As, and the thicknesses of the alternate layers. For Al concentration less than about 40% (x (0.4), Ga~ „Al„As has a direct band gap at the I point. The conduction and the valenceband discontinuity at the interface have been suggested to be about 859o and 15'/0, respectively, of the direct band-gap difference between the two semiconductors. "" Esaki, Chang, and Mendez recently proposed the idea of polytype (ABC) superlattices and applied it to the case of InAs-GaSb-AlSb multiheterojunctions. Bastard also discussed the dispersion relation of polytype superlattices by using the envelope-function approximation. Compared with binary (AB) superlattices, a polytype superlattice provides additional degrees of freedom. On the other hand, it has more complex properties which introduce additional difficulties in fabrication and in physical treatments. In this paper, we have investigated the band structure of a binary GaAsGal Al„As superlattice consisting of double layers of GaAs and Gal „Al„As materials per period. The band structure in terms of the potential-barrier height (or equivalently, the x value) and the sizes of the quantum wells and barriers in each period have been calculated. Experimentally, no additional difficulties will be encountered in growing the superlattice of this type compared with those in the growth of the usual lattices (one well and one barrier in each period). The unusual band structure arising from this periodic structure will be useful in technological applications. For the usual superlattices, only three variab1es (thicknesses of the well and barrier layers in each period, and the height of the potential barrier} are used. If additional layers are introduced in each period, more parameters will be available for getting the desired electronic, optical, and other physical properties. The compositional semiconductor superlattice, as shown in Fig. l, is a periodic sequence of ultrathin layers of two different semiconductors. In Fig. I, b~ (b2) denotes the thickness of the first (second) layer of the well material in each period and L the periodic length. The periodic potential barriers are assumed in the analysis to be infinitely repeated. The calculation of the miniband structure was based on the assumptions that the mean free path of the electron (hole) is much larger than the superlattice period, so the collision effects may be neglected; and that the interfaces between the layers are sharply defined so as to be devoid of any surface effect, so the superlattice potential distribution may simply be considered as an one-dimensional array of rectangular wells. In addition, different values for the effective mass in both the barrier and the well materials have been used. Using the matrix method' and the continuity conditions of the wave function P(x) and (I/m')8$/BX across the interface, we obtain the dispersion relation