Simulation of bipolar charge transport in graphene on h-BN

Abstract

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, whereas, as expected, the effect of the inter-band scattering becomes negligible by increasing the absolute value of the Fermi energy. Research limitations/implications The correct evaluation of the influence of the inter-band scatterings on the electronic performances is deeply important not only from a theoretical point of view but also for the applications. In particular, it will be shown that the time necessary to reach the steady state is greatly affected by the inter-band scatterings, with not negligible consequences on the switching on/off processes of realistic devices. As a limitation of the present work, the proposed approach refers to the spatially homogeneous case. For the simulation of electron devices, non-homogenous numerical solutions are required. This last case will be tackled in a forthcoming paper. Originality/value As observed in Majorana et al. (2019), the use of a Direct Simulation Monte Carlo (DSMC) approach, which properly describes the inter-band scatterings, is computationally very expensive because the valence band is highly populated and a huge number of particles is needed. Even by simulating holes instead of electrons does not overcome the problem because there is a certain degree of ambiguity in the generation and recombination terms of electron-hole pairs. The DG approach, used in this paper, does not suffer from the previous drawbacks and requires a reasonable computing effort.

About the Definition of the Local Equilibrium Lattice Temperature in Suspended Monolayer Graphene

“…( 21) contains explicitly the temperature dependent relaxation times, and in turn the anisotropy, which instead do not enter the Eq. (23).…”

“…If high enough, Fermi levels are considered. It is possible to neglect the dynamics of the electrons in the valence bands, being that the latter ones are fully occupied in this case [ 27 ]. Such a situation is similar to n-type doping for traditional semiconductors.…”

“…Such an approach could lead to coarse approximations; for example, for a correct simulation of transport behavior of graphene when thermal effects are considered, the out-ofplane Z-phonons have to be included as a distinct population because, although they do not directly interact with electrons, their thermal inertia, particularly for the flexural acoustic ZA phonons, is not negligible [12,13,14,15,16,17]. However, the isotropic approximation, for which the in-plane acoustic and optical phonons are considered as a unique population, is often accepted for simulations (see for example [5,18,19,20,21,22,23,24], and references therein), and an exhaustive analysis of the implications of such a hypothesis is not present, at best of our knowledge, in the literature.…”

Pauli principle and the Monte Carlo method for charge transport in graphene

“…In the literature an analysis of this approach is missing (it received only a brief comment in [5]); it is the aim of this work to fill this gap and to present a coherent discussion on the inclusion of the Pauli principle in a Monte Carlo procedure. We do so by comparing the numerical results for a suspended monolayer graphene obtained with the Monte Carlo Method presented in [9] with those obtained using the standard EMC in [4] and the updated direct simulation Monte Carlo (DSMC) in [12], which are by now well established in the semiconductor field and have been cross validated with deterministic solutions, for example, those based on the discontinuous Galerkin method [12][13][14][15][16][17][18][19] or on weighted essentially non-oscillatory (WENO) schemes [20].…”