Atomistic theory of transport in organic and inorganic nanostructures

Abstract

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.

Modeling inelastic phonon scattering in atomic- and molecular-wire junctions

“…The current and power are then computed as integrals over this energy grid. 9,12,13 These difficulties can be overcome if ͑i͒ the electronphonon coupling is weak, i.e., the probability for multiphonon processes is low, and ͑ii͒ the density of states ͑DOS͒ of the contacts and the device are slowly varying over a few phonon-energies around the Fermi energy E F , i.e., in the notation used below, G r ͑E͒ϷG r ͑E F ͒ and ⌫ 1,2 ͑E͒Ϸ⌫ 1,2 ͑E F ͒. These approximations are valid for systems where ͑i͒ the electron spends a short time compared to the phonon scattering time in the device and ͑ii͒ the closest resonance energy ͑E res ͒ is either far away from the Fermi energy ͉͑E res − E F ͉ ӷ⌫, eV, and ប ͒ or the broadening by the contacts is large ͑⌫ӷeV, ប , and ͉E res − E F ͉͒.…”

“…11 Phonon scattering is included in the SCBA method as self-energies to the electronic description. We use the undamped phonon Green's functions to express these selfenergies in the device subspace as 12,13,19 ⌺ ph…”

Nonequilibrium transport response from equilibrium transport theory

“…They depend on the nonequilibrium density matrix ρ, which must be calculated self-consistently for each voltage V using cumbersome and computationally very demanding NEGF techniques. 5,[7][8][9][10][11][12] We propose here that in many situations ρ and its derived H M [ρ] need only be computed at zero voltage, and that the effect of a finite bias can be accounted for by the alignment or dealignment of the molecular orbitals at the extended molecule region with the energy levels of the electrodes (which are shifted by ±e V /2 by the bias voltage). Mathematically, we apply a simple shift to the Hamiltonian matrix elements from H M to H M + eV i S M , where the local shifts V i depend on the junction nature.…”

“…1,2 However, the consistent and thorough work of a range of experimental groups has allowed researchers to reach some consensus on the conductance values and variability of a few specific junctions. [3][4][5] In addition, the development of simulation codes based on a combination of density functional theory (DFT) and the nonequilibrium Green's function formalism (NEGF) [5][6][7][8][9][10][11][12] has enabled theoreticians to assist the above experiments with theoretical insights and predictions. However, the size and complexity of the experimentally active part of the junction is typically too large, and the above codes need to assume a number of simplifications regarding the size, geometry, number of feasible atomic arrangements, and the electronic correlations.…”

Crystalline Orientation Effects on Ballistic Hole Current in Ultrathin DG SOI MOSFETs

“…The nonequilibrium Green's function (NEGF) method [1,2] allows us to calculate quantum transport characteristics in ultra-small MOSFETs. By incorporating a tight-binding approximation (TBA) into the NEGF formalism one can achieve quantum-mechanical computations with atomic resolution [3]. We have reported on atomistic modeling for one-dimensional Si nanostructures within the framework of the NEGF formalism and an empirical TBA [4,5].…”