Localised electronic states in semiconductor superlattices

The existence and properties of localised electronic states are described in binary (two layers per period) and polytype (multiple layers per period) semiconductor superlattices. Special attention is paid to surface effects, due to the superlattice potential termination by a clad layer, and the resulting Tamm-like surface states localised at the superlattice/clad-layer interface. The effect of the Bragg confinement of electrons in coupled superlattices, particularly the formation of above-barrier bound states at the junction of superlattices or the spacer layer embedded in a superlattice, is also discussed. Based on peculiar properties of localised superlattices states, with respect to extended miniband states, their importance for both the fundamental research and various device applications is stressed out. The most frequently used Kronig–Penney-like approaches within the framework of effective-mass and envelope-function approximation, namely, the direct-matching procedure and the transfer-matrix technique, are described for bulk- and surface-electronic-structure calculations of terminated binary and polytype superlattices, as well as for coupled superlattices. Comparison of the results with experimental data and/or more advanced computations indicates that these simple models are versatile and accurate (within their domain of validity), when applied to AlGaAs-based heterostructures. Two Green-function techniques, one based on the combined factorisation and Wronskian methods, and the other on the interface-response theory, are presented for the purpose of density-of-states analysis. For terminated binary GaAs/AlGaAs superlattices, an appropriate choice of the superlattice and clad-layer parameters, as well as the surface location within the superlattice period, enables a surface state with desired energy position inside the minigap, and required extension into the superlattice bulk, to be achieved. Introduction of additional layers into the superlattice sequence, resulting in a polytype superlattice, offers a further means of influencing the energies and localisation properties of surface states, but, more importantly, creates an opportunity for surface states to occur under classical Shockley conditions, which is not possible in binary superlattices, where only Tamm-like surface states can exist. The possibility of manipulating the local density of states at the superlattice end is also indicated. For polytype superlattices, the formation of well-defined surface resonances, affecting the overall subsurface density-of-states characteristics, is pointed out. The properties of Bragg-confined states and the density of states of coupled AlGaAs-based superlattices are examined, attention being focused on the transition from interface-localised to above-barrier bound states. Finally, other electronic localisation phenomena in superlattices are briefly reviewed.