Charge transport and mobility in monolayer graphene (original) (raw)
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Ricerche di Matematica, 2016
The aim of this work is to simulate the charge transport in a monolayer graphene on a substrate. This requires the inclusion of the scatterings of the charge carriers with the impurities and the phonons of the substrate, besides the interaction mechanisms already present in the graphene layer. As physical model, the semiclassical Boltzmann equation will be assumed. Two approaches will be used for the simulations: a numerical scheme based on the Discontinuous Galerkin method for finding deterministic (non stochastic) solutions and a new Direct Monte Carlo Simulation formulated in Romano et al. (J Comput Phys 302:267-284, 2015) in order to deal in the appropriate way with the Pauli exclusion principle for degenerate Fermi gases. A cross validation of the deterministic and stochastic solutions shows the robustness and accuracy of both the approaches.
Comparing Kinetic and MEP Model of Charge Transport in Graphene
Journal of Computational and Theoretical Transport, 2020
Graphene has attracted the attention of several researchers because of its peculiar features. In particular, the study of charge transport in graphene is challenging for future electron devices. Usually, the physical description of electron flow in graphene given by the semiclassical Boltzmann equation is considered to be a good one. However, due to the computational complexity, its use in simulation tools is not practical and, as already done for traditional semiconductors such as Si or GaAs, simpler models are warranted. Here we will assess the validity of a class of hydrodynamical models based on the maximum entropy principle (MEP), by comparing, in the case of suspended monolayer graphene, the direct solution of the semiclassical Boltzmann equation for electrons, obtained by employing a discontinuous Galerkin approach, with the MEP distribution function. A reasonable agreement is observed.
Communications Physics
Pristine graphene and graphene-based heterostructures can exhibit exceptionally high electron mobility if their surface contains few electron-scattering impurities. Mobility directly influences electrical conductivity and its dependence on the carrier density. But linking these key transport parameters remains a challenging task for both theorists and experimentalists. Here, we report numerical and analytical models of carrier transport in graphene, which reveal a universal connection between graphene’s carrier mobility and the variation of its electrical conductivity with carrier density. Our model of graphene conductivity is based on a convolution of carrier density and its uncertainty, which is verified by numerical solution of the Boltzmann transport equation including the effects of charged impurity scattering and optical phonons on the carrier mobility. This model reproduces, explains, and unifies experimental mobility and conductivity data from a wide range of samples and pro...
Pauli principle and the Monte Carlo method for charge transport in graphene
Physical Review B, 2021
The attempt to include the Pauli principle in the Monte Carlo method by acting also on the free flight step and not only at the end of each collision is investigated. The charge transport in suspended monolayer graphene is considered as test case. The results are compared with those obtained in the standard Ensemble Monte Carlo technique and in the new Direct Simulation Monte Carlo algorithm which is able to correctly handle with Pauli's principle. The physical aspects of the investigated approach are analyzed as well.
Monte Carlo studies of low-field electron transport in monolayer silicene and graphene
physica status solidi (a), 2016
Electron mobility and diffusion coefficients in monolayer silicene and graphene are calculated by Monte Carlo simulations using a simplified band structure with linear energy bands. Temperature evolution of the low-field mobility and diffusion coefficients is presented. Calculated characteristics of the low-field mobility in silicene exhibit a 1/T 3 dependence for nondegenerate electron gas conditions, which is attributed to dominant acoustic phonon scattering and to the linear band structure of the material. In degenerate conditions, a 1/T dependence is found in silicene. In graphene, there is no such simple power relation since optical and acoustic phonon scattering have comparable influences on electron transport. It is also found that electron-electron scattering only slightly modifies the low-field electron mobility in a degenerate electron gas.
arXiv: Materials Science, 2020
Pristine graphene and graphene-based heterostructures exhibit exceptionally high electron mobility and conductance if their surface contains few electron-scattering impurities. Here, we reveal a universal connection between graphene's carrier mobility and the variation of its electrical conductance with carrier density. Our model of graphene conductivity is based on a convolution of carrier density and its uncertainty, which reproduces the observed universality. Taking a single conductance measurement as input, this model accurately predicts the full shape of the conductance versus carrier density curves for a wide range of reported graphene samples. We verify the convolution model by numerically solving the Boltzmann transport equation to analyse in detail the effects of charged impurity scattering on carrier mobility. In this model, we also include optical phonons, which relax high-energy charge carriers for small impurity densities. Our numerical and analytical results both c...
Simulation of bipolar charge transport in graphene on h-BN
COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, 2020
Purpose The purpose of this paper is to simulate charge transport in monolayer graphene on a substrate made of hexagonal boron nitride (h-BN). This choice is motivated by the fact that h-BN is one of the most promising substrates on account of the reduced degradation of the velocity due to the remote impurities. Design/methodology/approach The semiclassical Boltzmann equations for electrons in the monolayer graphene are numerically solved by an approach based on a discontinuous Galerkin (DG) method. Both the conduction and valence bands are included, and the inter-band scatterings are taken into account as well. Findings The importance of the inter-band scatterings is accurately evaluated for several values of the Fermi energy, addressing the issue related to the validity of neglecting the generation-recombination terms. It is found out that the inclusion of the inter-band scatterings produces sizable variations in the average values, like the current density, at zero Fermi energy, ...
Physical Review B, 2013
Charge carrier transport in single-layer graphene with one-dimensional charged defects is studied theoretically. Extended charged defects, considered an important factor for mobility degradation in chemically vapor-deposited graphene, are described by a self-consistent Thomas-Fermi potential. A numerical study of electronic transport is performed by means of a time-dependent real-space Kubo approach in honeycomb lattices containing millions of carbon atoms, capturing the linear response of realistic size systems in the highly disordered regime. Our numerical calculations are complemented with a kinetic transport theory describing charge transport in the weak scattering limit. The semiclassical transport lifetimes are obtained by computing scattered amplitudes within the second Born approximation. The transport electron-hole asymmetry found in the semiclassical approach is consistent with the Kubo calculations. In the strong scattering regime, the conductivity is found to be a sublinear function of electronic density and weakly dependent on the Thomas-Fermi screening wavelength. We attribute this atypical behavior to the extended nature of one-dimensional charged defects. Our results are consistent with recent experimental reports.
Ballistic versus diffusive transport in graphene
Physical Review B, 2013
We investigate the transport of electrons in disordered and clean graphene devices. We consider a geometry where the graphene flake is contacted by narrow metallic leads. Plotting the conductance as a function of the position of one of the leads, we can approximate the probability density function of the charge flow at the edge which is used to analyze the transport properties with increasing length of the device. Moreover, we simulate scanning probe microscopy (SPM) measurements for the same devices, which can be seen as a measure for the flow of charge inside the device, thus complementing the transport calculations. We compare our analysis to theory describing transport in clean and disordered systems.
Monte Carlo Study of Electronic Transport in Monolayer InSe
Materials
The absence of a band gap in graphene makes it of minor interest for field-effect transistors. Layered metal chalcogenides have shown great potential in device applications thanks to their wide bandgap and high carrier mobility. Interestingly, in the ever-growing library of two-dimensional (2D) materials, monolayer InSe appears as one of the new promising candidates, although still in the initial stage of theoretical studies. Here, we present a theoretical study of this material using density functional theory (DFT) to determine the electronic band structure as well as the phonon spectrum and electron-phonon matrix elements. The electron-phonon scattering rates are obtained using Fermi’s Golden Rule and are used in a full-band Monte Carlo computer program to solve the Boltzmann transport equation (BTE) to evaluate the intrinsic low-field mobility and velocity-field characteristic. The electron-phonon matrix elements, accounting for both long- and short-range interactions, are consid...