Atomistic theory of transport in organic and inorganic nanostructures

As the size of modern electronic and optoelectronic devices is scaling down at a steady pace, atomistic simulations become necessary for an accurate modelling of their structural, electronic, optical and transport properties. Such microscopic approaches are important in order to account correctly for quantum-mechanical phenomena affecting both electronic and transport properties of nanodevices. Effective bulk parameters cannot be used for the description of the electronic states since interfacial properties play a crucial role and semiclassical methods for transport calculations are not suitable at the typical scales where the device behaviour is characterized by coherent tunnelling. Quantum-mechanical computations with atomic resolution can be achieved using localized basis sets for the description of the system Hamiltonian. Such methods have been extensively used to predict optical and electronic properties of molecules and mesoscopic systems. The most important approaches formulated in terms of localized basis sets, from empirical tight-binding (TB) to first principles methods, are here reviewed. Being a full band approach, even the simplest TB overcomes the limitations of envelope function approximations, such as the well-known k p, and allows to retain atomic details and realistic band structures. First principles calculations, on the other hand, can give a very accurate description of the electronic and structural properties. Transport in nanoscale devices cannot neglect quantum effects such as coherent tunnelling. In this context, localized basis sets are well-suited for the formal treatment of quantum transport since they provide a simple mathematical framework to treat open-boundary conditions, typically encountered when the system eigenstates carry a steady-state current. We review the principal methods used to formulate quantum transport based on local orbital sets via transfer matrix and Green's function (GF) techniques. We start from a general introduction to the scattering theory which leads to the Landauer formula, and then report on the most recent progresses of the field including the application of the self-consistent non-equilibrium GF formalism.