Diffusion coefficient, correlation function, and power spectral density of velocity fluctuations in monolayer graphene

Abstract

In this paper, the diffusivity in suspended monolayer graphene at low and high electric fields is investigated. The knowledge of this quantity and its dependence on the electric field is of primary importance not only for the investigation of the electronic transport properties of this material but also for the development of accurate drift-diffusion models. The results have been obtained by means of an ensemble Monte Carlo simulation. For the calculation of the diffusion coefficient, two different methods are considered, one based on the second central moment and the other one based on the Fourier analysis of velocity fluctuations, which are directly related to the noise behaviour at high frequencies. The diffusion coefficient is analyzed considering both parallel and transversal directions with regard to the applied field. Taking into account the importance of degeneracy in this material, the calculations are properly performed by considering an excess electron population obeying a linearized Boltzmann transport equation, which allows studying in an adequate fashion the diffusivity phenomena. The results show the importance of degeneracy effects at very low fields in which transport is mainly dominated by acoustic phonon scattering. Values of the diffusion coefficient larger than 40 000 cm2/Vs are obtained for a carrier concentration equal to 1012 cm−2. The correlation function of instantaneous velocity fluctuation is explained in terms of the wavevector distribution, and their power spectral density is evaluated in the THz range, showing an important dependence on the applied field and being strongly related to microscopic transport processes.

Radio Frequency Performance Projection and Stability Tradeoff of h-BN Encapsulated Graphene Field-Effect Transistors

“…Low field carrier mobility µLF and carrier saturation velocity vsat in h-BN encapsulated graphene were obtained by a self-consistent ensemble Monte Carlo (EMC) simulator at steady-state conditions that accounts for the scattering mechanisms in this particular encapsulated graphene structure [18]- [20]. The scattering mechanisms include graphene intrinsic phonons, remote surface polar phonons from h-BN encapsulating layers, carriercarrier collisions and scattering caused by defects and charged impurities.…”

Tunable spin–orbit coupling and symmetry-protected edge states in graphene/WS 2

“…2(a)]. Figure 3(a) shows the resulting τ −1 R for WS 2 -covered graphene as a function of the momentum scattering rate τ −1 e calculated from the device mobility [34]. As τ −1 e increases, the Rashba SOC relaxation rate decreases almost monotonically, indicating that the spin relaxation is dominated by the Dyakonov-Perel mechanism [35]…”

Monte Carlo studies of low‐field electron transport in monolayer silicene and graphene

“…For degenerate conditions a modified method, assuming the study of two ensembles of background and excess particles, has been proposed . Recently, this method has been successfully applied also to the studies of two‐dimensional graphene .…”

“…Numerical simulation using the Monte Carlo method is an effective approach, often used in such situations. This method has already been used in studies of graphene and silicene .…”