arXiv subjects

Giovanni Nastasi

Publications and source records attributed to Giovanni Nastasi.

14 recordsLinked to original sources

arXiv2026

A discontinuous Galerkin approach for simulating graphene-based electron devices via the Boltzmann transport equation

Electron devices based on graphene have lately received a considerable interest; in fact, they could represent the ultimate miniaturization, since the active area is only one atom thick. However, the gapless dispersion relation of graphene at the Dirac points limits the possibility of using pristine graphene instead of traditional semiconductors in Field Effect Transistors (FET). For such a reason very accurate simulations are needed. In Nastasi and Romano (IEEE Trans. Electron Devices 68, 2021) a graphene field effect transistor (GFET) has been proposed and simulated adopting a drift-diffusion model. Here, electron devices whose active area is made of monolayer graphene are simulated taking as mathematical model the complete semiclassical Boltzmann transport equation (BTE) retaining the full complexity of the collision operator which includes all the electron-phonon scatterings along with the Pauli exclusion principle. The transport equation is coupled with the Poisson equation for the electric field. The Boltzmann equation is solved by means of a discontinuous Galerkin (DG) approach with linear elements in space and piecewise constant approximation in the wave-vector. The correct physical range for the distribution function is preserved with a maximum-principle-preserving scheme. Finite differences for the Poisson equation, and a TVD Runge-Kutta scheme for time discretization are adopted. The method reveals very robust and possesses a good degree of accuracy, making it particularly well suited for capturing the complex charge transport dynamics inherent to graphene-based devices. The kinetic approach reveals new features which are caught by the standard drift-diffusion equations; in particular, the presence of a boundary layer at the contacts.

math-ph↗

arXiv2026

Second order unfitted ghost-FEM for elliptic interface problems with applications to low-dimensional semiconductor devices

We develop an unfitted ghost finite element method for elliptic interface problems with discontinuous diffusion coefficients and apply it to the electrostatic simulation of low-dimensional semiconductor devices. The proposed approach is based on a fixed Cartesian grid and represents the geometry by level-set functions, avoiding mesh generation and remeshing even in the presence of interfaces. A snapping-back-to-grid strategy is used to control the small-cut-cell issue, while interface conditions are weakly enforced by a symmetric Nitsche formulation. The method is first validated on benchmark elliptic interface problems with different geometries and coefficient jumps, showing second-order accuracy for the solution and first-order accuracy for its gradient. As an application, we consider a graphene field-effect transistor described by a self-consistent drift-diffusion-Poisson model. The electrostatic potential is computed in a two-dimensional oxide/graphene/oxide structure, while charge transport in the graphene layer is modeled by one-dimensional bipolar drift-diffusion equations in the degenerate case and by including a field-dependent mobility model. The coupled nonlinear system is solved by a damped fixed-point iteration combined with a domain-decomposition treatment of the three-layer geometry. Numerical simulations reproduce transfer characteristics with a clear transition from an OFF state to an ON state and show the influence of the gate voltage on the two-dimensional electrostatic potential. The results also indicate that the effective thickness and discretization of the graphene layer affect the transverse potential profile, supporting the use of a full two-dimensional electrostatic description with explicit oxide/graphene interface conditions.

math.NA↗

arXiv2026

Low-noise Pauli-consistent ensemble Monte Carlo for graphene with electron-electron scattering

We investigate Pauli-consistent ensemble Monte Carlo simulations of graphene with explicit intraband electron-electron scattering. To reduce the cost of electron-electron proposal-rate evaluation, we introduce a sampled-partner approximation that replaces the full partner-cell sum by uniform sampling from the instantaneous ensemble, while leaving the event-level collision step unchanged. Comparison with the full-sum reference shows close agreement together with a substantial reduction in computational cost, enabling large-ensemble low-noise simulations. In this regime, systematic oscillatory components become clearly resolved in ensemble-averaged time traces. We show that these oscillations are numerical and originate from deterministic drift on the discretized momentum-space grid. We also discuss a procedure for reducing their impact in recorded observables without modifying the underlying Monte Carlo dynamics.

math-ph↗

arXiv2026

Ballistic electron transport described by a generalized Schrödinger equation

We propose a Schrödinger equation of arbitrary order for modeling charge transport in semiconductors operating in the ballistic regime. This formulation incorporates non-parabolic effects through the Kane dispersion relation, thereby extending beyond the conventional effective mass approximation. Building upon the framework introduced in G.E. Aliffi, G. Nastasi, V. Romano, {ZAMP} {76}, 155 (2025), we derive a hierarchy of models, each governed by a Schrödinger equation of increasing order. As in the standard second-order case, the problem is formulated on a finite spatial domain with suitable transparent boundary conditions. These conditions are designed to simulate charge transport in a quantum coupler where an active region -- representing the electron device -- is connected to leads acting as reservoirs. We investigate several analytical properties of the proposed models and derive a generalized expression for the current, valid for any order. This formula includes additional terms that account for interference effects arising from the richer wave structure inherent in higher-order Schrödinger equations, which are absent in the effective mass approximation. Numerical simulations of a resonant tunneling diode (RTD) illustrate the key features of the solutions and highlight the impact of the generalized formulation on device behavior.

math-ph↗

arXiv2025

Spatially Mapping Phonon Drag in Ultrascaled 5-nm Silicon Nanowire Field-Effect Transistor Based on a Quantum Hydrodynamic Formalism

The growing demand for better performance and lower thermal energy dissipation in nanoelectronic devices is the major driving force of the semiconductor industry's quest for future generations of nanotransistors. Over the past 15 years, the miniaturization of silicon-based nanoelectronics predicted by Moore's law has driven an aggressive scaling down of transistor structures, including materials, design, and geometries. In this regard, the electronic device community has expanded its focus to ultrascaled transistors targeting the 7 nm technology node and beyond. However, these emerging nanodevices also present thermal challenges that can limit carrier transport as a result of strong electron-phonon coupling. In this work, we investigate the physical origin of self-heating effects in an ultrascaled 5 nm silicon nanowire field-effect transistor. Based on a quantum hydrodynamic approach, we also provide an explanation of the phonon drag contribution to thermal conductivity. We report the impact of the phonon drag effect on the electrical and thermal performance of 5 nm gate-all-around silicon nanowire field-effect transistors. Our findings provide new insight into the origin of self-heating as a result of mutual electron-phonon coupling. Furthermore, we demonstrate that the phonon drag effect significantly reduces thermal conductivity by nearly 50% under high-bias conditions.

cond-mat.mes-hall↗

arXiv2025

Ballistic electron transport described by a fourth-order Schrödinger equation

A fourth-order Schrödinger equation for the description of charge transport in semiconductors in the ballistic regime is proposed with the inclusion of non-parabolic effects in the dispersion relation in order to go beyond the simple effective mass approximation. Similarly to the standard (second order) Schrödinger equation, the problem is reduced to a finite spatial domain with appropriate transparent boundary conditions to simulate charge transport in a quantum coupler (Lent and Kirkner in J Appl Phys 67:6353, 1990; Ben Abdallah et al. in ZAMP 48:135-155, 1997; Ben Abdallah in J. Math. Phys. 41:4241-4261, 2000), where an active region representing an electron device is coupled to leads which take the role of reservoirs. Some analytical properties are investigated, and a generalized formula for the current is obtained. Numerical results show the main features of the solutions of the new model. In particular, an effect of interference appears due to a richer wave structure than that arising for the second-order Schrödinger equation in the effective mass approximation.

math-ph↗

arXiv2025

Uncertainty quantification for charge transport in GNRs through particle Galerkin methods for the semiclassical Boltzmann equation

In this article, we investigate some issues related to the quantification of uncertainties associated with the electrical properties of graphene nanoribbons. The approach is suited to understand the effects of missing information linked to the difficulty of fixing some material parameters, such as the band gap, and the strength of the applied electric field. In particular, we focus on the extension of particle Galerkin methods for kinetic equations in the case of the semiclassical Boltzmann equation for charge transport in graphene nanoribbons with uncertainties. To this end, we develop an efficient particle scheme which allows us to parallelize the computation and then, after a suitable generalization of the scheme to the case of random inputs, we present a Galerkin reformulation of the particle dynamics, obtained by means of a generalized Polynomial Chaos approach, which allows the reconstruction of the kinetic distribution. As a consequence, the proposed particle-based scheme preserves the physical properties and the positivity of the distribution function also in the presence of a complex scattering in the transport equation of electrons. The impact of the uncertainty of the band gap and applied field on the electrical current is analysed.

physics.comp-ph↗

arXiv2023

A System of ODEs for Representing Trends of CGM Signals

Diabetes Mellitus is a metabolic disorder which may result in severe and potentially fatal complications if not well-treated and monitored. In this study, a quantitative analysis of the data collected using CGM (Continuous Glucose Monitoring) devices from eight subjects with type 2 diabetes in good metabolic control at the University Polyclinic Agostino Gemelli, Catholic University of the Sacred Heart, was carried out. In particular, a system of ordinary differential equations whose state variables are affected by a sequence of stochastic perturbations was proposed and used to extract more informative inferences from the patients' data. For this work, Matlab and R programs were used to find the most appropriate values of the parameters (according to the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC)) for each patient. Fitting was carried out by Particle Swarm Optimization to minimize the ordinary least squares error between the observed CGM data and the data from the ODE model. Goodness of fit tests were made in order to assess which probability distribution was best suitable for representing the waiting times computed from the model parameters. Finally, both parametric and non-parametric density estimation of the frequency histograms associated with the variability of the glucose elimination rate from blood were conducted and their representative parameters assessed from the data. The results show that the chosen models succeed in capturing most of the glucose fluctuations for almost every patient.

q-bio.QM↗

arXiv2022

Mathematical aspects and simulation of electron-electron scattering in graphene

Some properties of the electron-electron collision operator in graphene are analyzed along with the evaluation of collision rate. Monte Carlo simulations complete the study and highlight the non-negligible role of the electron-electron scattering for an accurate evaluation of the currents and, as a consequence, of the characteristic curves.

math-ph↗

arXiv2021

Continuous-time stochastic processes for the spread of COVID-19 disease simulated via a Monte Carlo approach and comparison with deterministic models

Two stochastic models are proposed to describe the evolution of the COVID-19 pandemic. In the first model the population is partitioned into four compartments: susceptible $S$, infected $I$, removed $R$ and dead people $D$. In order to have a cross validation, a deterministic version of such a model is also devised which is represented by a system of ordinary differential equations with delays. In the second stochastic model two further compartments are added: the class $A$ of asymptomatic individuals and the class $L$ of isolated infected people. Effects such as social distancing measures are easily included and the consequences are analyzed. Numerical solutions are obtained with Monte Carlo simulations. Quantitative predictions are provided which can be useful for the evaluation of political measures, e.g. the obtained results suggest that strategies based on herd immunity are too risky.

q-bio.PE↗

arXiv2020

Mathematical modelling of charge transport in graphene heterojunctions

A typical graphene heterojunction device can be divided into two classical zones, where the transport is basically diffusive, separated by a "quantum active region" (e.g., a locally gated region), where the charge carriers are scattered according to the laws of quantum mechanics.In this paper we derive a mathematical model of such a device, where the classical regions are described by drift-diffusion equations and the quantum zone is seen as an interface where suitable transmission conditions are imposed that take into account the quantum scattering process. Numerical simulations show good agreement with experimental data.

cond-mat.mes-hall↗

arXiv2020

An efficient GFET structure

A graphene field effect transistor, where the active area is made of monolayer large-area graphene, is simulated including a full 2D Poisson equation and a drift-diffusion model with mobilities deduced by a direct numerical solution of the semiclassical Boltzmann equations for charge transport by a suitable discontinuous Galerkin approach. The critical issue in a graphene field effect transistor is the difficulty of fixing the off state which requires an accurate calibration of the gate voltages. In the present paper we propose and simulate a graphene field effect transistor structure which has well-behaved characteristic curves similar to those of conventional (with gap) semiconductor materials. The introduced device has a clear off region and can be the prototype of devices suited for post-silicon nanoscale electron technology. The specific geometry overcomes the problems of triggering the minority charge current and gives a viable way for the design of electron devices based on large area monolayer graphene as substitute of standard semiconductors in the active area. The good field effect transistor behavior of the current versus the gate voltage makes the simulated device very promising and a challenging case for experimentalists.

physics.app-ph↗

arXiv2017

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

The aim of this work is to simulate the charge transport in a monolayer graphene on different substrates. 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 is assumed and the results are based on Direct Simulation Monte Carlo (DSMC). A crucial point is the correct inclusion of the Pauli Exclusion Principle (PEP). Two different substrates are investigated: SiO$_2$ and hexagonal boron nitride (h-BN). In the adopted model for the charge-impurities scattering, 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. We confirm, where only the low-field mobility has been investigated, 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.

cond-mat.mes-hall↗

arXiv2017

Monte Carlo Simulation of Charge Transport in Graphene (Simulazione Monte Carlo per il trasporto di cariche nel grafene)

Simulations of charge transport in graphene are presented by implementing a recent method published on the paper: V. Romano, A. Majorana, M. Coco, "DSMC method consistent with the Pauli exclusion principle and comparison with deterministic solutions for charge transport in graphene", Journal of Computational Physics 302 (2015) 267-284. After an overview of the most important aspects of the semiclassical transport model for the dynamics of electrons in monolayer graphene, it is made a comparison in computational time between MATLAB and Fortran implementations of the algorithms. Therefore it is studied the case of graphene on substrates which it is produced original results by introducing models for the distribution of distances between graphene's atoms and impurities. Finally simulations, by choosing different kind of substrates, are done. ----- Le simulazioni per il trasporto di cariche nel grafene sono presentate implementando un recente metodo pubblicato nell'articolo: V. Romano, A. Majorana, M. Coco, "DSMC method consistent with the Pauli exclusion principle and comparison with deterministic solutions for charge transport in graphene", Journal of Computational Physics 302 (2015) 267-284. Dopo una panoramica sugli aspetti più importanti del modello di trasporto semiclassico per la dinamica degli elettroni nel grafene sospeso, è stato effettuato un confronto del tempo computazionale tra le implementazioni MATLAB e Fortran dell'algoritmo. Inoltre è stato anche studiato il caso del grafene su substrato su cui sono stati prodotti dei risultati originali considerando dei modelli per la distribuzione delle distanze tra gli atomi del grafene e le impurezze. Infine sono state effettuate delle simulazioni scegliendo substrati di diversa natura.

cond-mat.mtrl-sci↗