Showing papers by "Vittorio Romano published in 2019"

Improved mobility models for charge transport in graphene

Abstract: Abstract Charge transport in graphene is crucial for the design of a new generation of nanoscale electron devices. A reasonable model is represented by the semiclassical Boltzmann equations for electrons in the valence and conduction bands. As shown by Romano et al. (J. Comput. Phys., 2015), the discontinuous Galerkin methods are a viable way to tackle the problem of the numerical integration of these equations, even if efficient DSMC with a proper inclusion of the Pauli principle have been also devised. One of the advantages of the solutions obtained with deterministic approach is of course the absence of statistical noise. This fact is crucial for an accurate estimation of the low field mobility as proved by Majorana et al. (J. Math. Industry, 2016) in the case of a unipolar charge transport in a suspended graphene sheet under a constant electric field. The mobility expressions are essential for the drift-diffusion equations which constitute the most adopted models for charge transport in CAD. Here the analysis by Majorana et al. (J. Math. Industry, 2016) is improved in two ways: by including the charge transport both in the valence and conduction bands; by taking into account the presence of an oxide as substrate for the graphene sheet. New models of mobility are obtained and, in particular, relevant improvements of the low field mobility are achieved.

High-field mobility in graphene on substrate with a proper inclusion of the Pauli exclusion principle

Abstract: The aim of this work is to simulate charge transport in a monolayer graphene on different substrates. This requires the inclusion of the scatterings of charge carriers with impurities and phonons of the substrate, besides the interaction mechanisms already present in the graphene layer. As mathematical model, the semiclassical Boltzmann equation is assumed and the results are based on Direct Simulation Monte Carlo (DSMC) method. A crucial point is the correct inclusion of the Pauli Exclusion Principle (PEP). Most simulations use the approach proposed by Jacoboni e Lugli which, however, allows an occupation number greater than one with an evident violation of PEP. Here the Monte Carlo scheme devised by Romano et al. (J. Comput. Phys. 302 , 267--284, 2015) is employed. It predicts occupation numbers consistent with PEP and therefore is physically more accurate. Two different substrates are investigated: SiO 2 and hexagonal boron nitride (h-BN). We adopt the model for charge-impurities scattering described by E. H. Hwang and S. Das Sarma (Phys. Rev. B 75 , 205418, 2007). In such a model a crucial parameter is the distance d between the graphene layer and the impurities of the substrate. Usually d is considered constant. Here we assume that d is a random variable in order to take into account the roughness of the substrate and the randomness of the location of the impurities. Our results confirm that h-BN is one of the most promising substrate also for the high-field mobility on account of the reduced degradation of the velocity due to the remote impurities. This is in agreement with results shown by Hirai et al. (J. Appl. Phys. 116 , 083703, 2014) where only the low-field mobility has been investigated.

An improved 2D–3D model for charge transport based on the maximum entropy principle

Abstract: To study the electron transport in a some tens of nanometers long channel of a metal oxide field effect transistor, in order to reduce the computational cost of simulations, it can be convenient to divide the electrons into a 2D and a 3D population. Near the silicon/oxide interface the two populations coexist, while in the remaining part of the device only the 3D component needs to be considered because quantum effects are negligible there. The major issue is the description of the scattering mechanisms between the 2D and the 3D electron populations, due to interactions of electrons with nonpolar optical phonons and interface modes. Here, we propose a rigorous treatment of these collisions based on an approach similar to that used in Fischetti and Laux (Phys Rev B 48:2244–2274, 1993), in the context of a Monte Carlo simulation. We also consider all the other main scatterings, which are those with acoustic phonons, surface roughness, and impurities.