Transporte eletrônico em semicondutores anisotrópicos via matriz de transferência e função de Green recursiva no equilíbrio

Abstract

Since the 1980s, it has been possible to grow/synthesize structures and devices where the dimensions are actually smaller than the characteristic lengths of interest. The physical phenomena observed in such systems exhibit quantum effects due to the confinement of carriers, unlike those materials in the bulk version, which can be described using semi-classical approaches. In the transport properties context, bulk materials are well described by Boltzmann transport equation or similar kinetic equation approximation, whereas in quantum devices a theoretical treatment requires the combined use of different techniques and approximations, such as: the transmission formalism, like the Landauer formula, Büttiker probes, and scattering or transfer matrix method, as well as as well as the Green function formalism. The first is usually considered in situations where dissipations are ignored and the length of the region being simulated is considerably smaller than the characteristic dissipation lengths, such as the mean free path or phase relaxation length, that is, as in the cases of ballistic transport. On the other hand, the latter is a more convenient method to calculate the physical properties of samples connected to electrodes, especially for systems with broken phase coherence, dealing more rigorously with physical processes that become important in quantum transport, such as scattering due to impurities and structural defects. In view of the great practical interest for the development of new technologies and combined with the fact that new lamellar materials prove to be quite promising in the design of nanoscale devices, in this work we investigate the transport properties in isotropic and anisotropic two-dimensional (2D) semiconductor materials in the presence of a superlattice generated by a sequence of potential barriers with rectangular and linear profiles. The anisotropic transport signatures with respect to the number of potential barriers, as well as the height and width of the barriers and their orientation in the crystal are analyzed. To do so, we first present the concepts and basic physical properties related to the transfer matrix method, using Hamiltonians within the effective mass approximation, and the formalism of the equilibrium Green's function combined with the equation of motion technique. In addition, we discuss (i) the calculation of the transmission through an arbitrarily profiled quantum potential via the transfer matrix method; and (ii) the calculation of the density of states and the transmission coefficient, via the recursive method of the equilibrium Green's function, in 1D and 2D discrete lattices of non-interacting electrons described by tight-binding Hamiltonians, exemplifying with the cases of few-sites lattice (1, 2 and 3), finite and infinite linear chains, and 2D lattices (square, graphene and phosphorene).