Confined electron states in corrugated GaAs/AlAs superlattices

The electronic and optical properties of GaAsIAlAs superlattices grown in the [311] direction are investigated in the framework of an empirical tight-binding model which includes second-neighbor interactions. The [3 111 superlattices are of great interest because of their non-flat interfaces and because the periodic corrugation which appears gives rise to a lateral confinement. This results in the formation of quantum wires which present a pronounced degree of optical anisotropy. The characteristics and the energy gap value of these wires are studied as functions of the layer thickness and the differences with [001]-grown superlattices are discussed. The calculated cross-over of Tand X-like levels is in good agreement with the experimental observations. The nature of the lowest conduction states is explained in terms of the symmetry of the superlattice. The GaAsIAlAs system is now often used in the fabrication of artificially layered semiconductor crystals and the improvement of the epitaxial growth techniques allows the achievement of high-quality superlattices with very short periods. These superlattices have been studied extensively mainly for [loo] growth orientation. More recently, synthesis of superlattices grown by molecular beam epitaxy on unusual orientations like [311] have been achieved. Such superlattices are of great interest because, for high enough substrate temperature, the flat (31 1) surfaces break up into (311) facets with lower surface energy and give rise to lateral confinement leading to the formation of quantum wires for thin semiconductor layers[l1. The existence of double periodicity in the superlattice growth direction [311] as well in the lateral direction [Oll] leads complex mixing of all the bulk electronic states which are mapped onto the same point of the superlattice Brillouin zone. Further, this configuration must be studied carefully because in GaAlIAlAs superlattices the confinement effect can lower the states originating from the X valleys in AlAs under the r states in GaAs when the layer thicknesses become sufficiently small. In this paper, we determine the electronic structure of corrugated GaAlIAlAs superlattices. We estimate the effects of the lateral confinement on the electronic states and we clarify the origin of the observed optical transitions. For our calculation, we employ a tight-binding approach. The interest of this method lies in the microscopic description of the materials from the atomic interactions between anions Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jp4:1993557 JOURNAL DE PHYSIQUE IV and cations. It retains the full symmetry of the crystal and avoids preliminary hypothesis on the origin of the superlattice electronic states. The schematic structure of a corrugated superlattice is shown in figure 1. Figure 1: Structure of [3 111-grown corrugated superlattice. We use a sp3 basis including spin-orbit interaction~[~]. As we are mainly interested in the lowest conduction states of the corrugated superlattice, it is important to fit the lowest conduction states of the bulk materials at high symmetry points in the Brillouin zone, e.g. r , X and L conduction edges and their associated effective masses. For this, we have included second-neighbor interactions because neglecting them yields an infinite transverse effective mass in X. The valence-band offset has been taken equal to 35% of the direct band gap difference between AlAs and GaAs. The tight-binding parameters are affected near the interfaces and various geometrical situations occur in corrugated superlattices. These different configurations have been taken into account by the utilisation of mean values of the two bulk parameters. As the very short-period superlattices are not concerned by this work, the electronic band structure is not sensitive to this hypothesis. The slight mismatch (0,16 %) between the lattice constant of AlAs and GaAs is neglected. The unit cell of corrugated superlattices is two-dimensional and the tight-binding basis is very large containing 320N local orbitals for a superlattice of N layers along the growth direction [311]. The electronic energies are computed by direct diagonalization or by alternative methods as the orthogonalized-moment method[3] which are more adapted to handle large dimensional matrices . Figure 2 shows the two lowest conduction states at the center of the Brillouin zone of the superlattice r as a function of the number N of layers of each semiconductor in (G~AS)N/(A~AS)N corrugated superlattices. The solid line denotes the state having mainly a r-like character and the dashed line the state having a X-like character. The identification of these states results from the examination of their wavefunctions. The r state is mainly formed by the contribution of the s atomic orbitals of the cation in GaAs layers and is identified as coming from the r GaAs bulk eigenstate. On the other part, the major contribution to X state is due to the p orbitals of cations in the AlAs layers. The weight of px and py orbitals is insignificant and this state corresponds to the X, valley of AlAs. This analysis is confiied by the behaviour of these states as a function of the layer number.