We propose an efficient numerical method to study the transport properties of armchair graphene ribbons in the presence of a generic external potential. The method is based on a continuum envelope-function description with physical boundary condition
s. The envelope functions are computed in the reciprocal space, and the transmission is then obtained with a recursive scattering matrix approach. This allows a significant reduction of the computational time with respect to finite difference simulations.
By means of an envelope function analysis, we perform a numerical investigation of the conductance behavior of a graphene structure consisting of two regions (dots) connected to the entrance and exit leads through constrictions and separated by a pot
ential barrier. We show that the conductance of the double dot depends on the symmetry of the structure and that this effect survives also in the presence of a low level of disorder, in analogy of what we had previously found for a double dot obtained in a semiconductor heterostructure. In graphene, this phenomenon is less dramatic and, in particular, conductance is not enhanced by the addition of symmetric constrictions with respect to that of the barrier alone.
The solution of differential problems, and in particular of quantum wave equations, can in general be performed both in the direct and in the reciprocal space. However, to achieve the same accuracy, direct-space finite-difference approaches usually i
nvolve handling larger algebraic problems with respect to the approaches based on the Fourier transform in reciprocal space. This is the result of the errors that direct-space discretization formulas introduce into the treatment of derivatives. Here, we propose an approach, relying on a set of sinc-based functions, that allows us to achieve an exact representation of the derivatives in the direct space and that is equivalent to the solution in the reciprocal space. We apply this method to the numerical solution of the Dirac equation in an armchair graphene nanoribbon with a potential varying only in the transverse direction.
We report fully quantum simulations of realistic models of boron-doped graphene-based field effect transistors, including atomistic details based on DFT calculations. We show that the self-consistent solution of the three-dimensional (3D) Poisson and
Schrodinger equations with a representation in terms of a tight-binding Hamiltonian manages to accurately reproduce the DFT results for an isolated boron-doped graphene nanoribbon. Using a 3D Poisson/Schrodinger solver within the Non-Equilibrium Greens Functions (NEGF) formalism, self-consistent calculations of the gate-screened scattering potentials induced by the boron impurities have been performed, allowing the theoretical exploration of the tunability of transistor characteristics. The boron-doped graphene transistors are found to approach unipolar behavior as the boron concentration is increased, and by tuning the density of chemical dopants the electron-hole transport asymmetry can be finely adjusted. Correspondingly, the onset of a mobility gap in the device is observed. Although the computed asymmetries are not sufficient to warrant proper device operation, our results represent an initial step in the direction of improved transfer characteristics and, in particular, the developed simulation strategy is a powerful new tool for modeling doped graphene nanostructures.
We discuss the possibility of diffusive conduction and thus of suppression of shot noise by a factor 1/3 in mesoscopic semiconductor devices with two-dimensional and one-dimensional potential disorder, for which existing experimental results do not p
rovide a conclusive result. On the basis of our numerical analysis, we conclude that it is quite difficult to achieve diffusive transport over a reasonably wide parameter range, unless the device dimensions are increased up to the macroscopic scale. In addition, in the case of one-dimensional disorder, some mechanism capable of mode-mixing has to be present in order to reach or even approach the diffusive regime.
We perform a numerical investigation of the effect of the disorder associated with randomly located impurities on shot noise in mesoscopic cavities. We show that such a disorder becomes dominant in determining the noise behavior when the amplitude of
the potential fluctuations is comparable to the value of the Fermi energy and for a large enough density of impurities. In contrast to existing conjectures, random potential fluctuations are shown not to contribute to achieving the chaotic regime whose signature is a Fano factor of 1/4, but, rather, to the diffusive behavior typical of disordered conductors. In particular, the 1/4 suppression factor expected for a symmetric cavity can be achieved only in high-quality material, with a very low density of impurities. As the disorder strength is increased, a relatively rapid transition of the suppression factor from 1/4 to values typical of diffusive or quasi-diffusive transport is observed. Finally, on the basis of a comparison between a hard-wall and a realistic model of the cavity, we conclude that the specific details of the confinement potential have a minor influence on noise.
We present an investigation in the device parameter space of band-to-band tunneling in nanowires with a diamond cubic or zincblende crystalline structure. Results are obtained from quantum transport simulations based on Non-Equilibrium Greens functio
ns with a tight-binding atomistic Hamiltonian. Interband tunneling is extremely sensitive to the longitudinal electric field, to the nanowire cross section, through the gap, and to the material. We have derived an approximate analytical expression for the transmission probability based on WKB theory and on a proper choice of the effective interband tunneling mass, which shows good agreement with results from atomistic quantum simulation.
The k.p method is a semi-empirical approach which allows to extrapolate the band structure of materials from the knowledge of a restricted set of parameters evaluated in correspondence of a single point of the reciprocal space. In the first part of t
his review article we give a general description of this method, both in the case of homogeneous crystals (where we consider a formulation based on the standard perturbation theory, and Kanes approach) and in the case of non-periodic systems (where, following Luttinger and Kohn, we describe the single-band and multi-band envelope function method and its application to heterostructures). The following part of our review is completely devoted to the application of the k.p method to graphene and graphene-related materials. Following Andos approach, we show how the application of this method to graphene results in a description of its properties in terms of the Dirac equation. Then we find general expressions for the probability density and the probability current density in graphene and we compare this formulation with alternative existing representations. Finally, applying proper boundary conditions, we extend the treatment to carbon nanotubes and graphene nanoribbons, recovering their fundamental electronic properties.
We report the results of an analysis, based on a straightforward quantum-mechanical model, of shot noise suppression in a structure containing cascaded tunneling barriers. Our results exhibit a behavior that is in sharp contrast with existing semicla
ssical models for this particular type of structure, which predict a limit of 1/3 for the Fano factor as the number of barriers is increased. The origin of this discrepancy is investigated and attributed to the presence of localization on the length scale of the mean free path, as a consequence of the strictly 1-dimensional nature of disorder, which does not create mode mixing, while no localization appears in common semiclassical models. We expect localization to be indeed present in practical situations with prevalent 1-D disorder, and the existing experimental evidence appears to be consistent with such a prediction.
