arXiv subjects

Vittorio Romano

Publications and source records attributed to Vittorio Romano.

16 recordsLinked to original sources

arXiv2025

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 tick. 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 & Romano, IEEE TED (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 adopting as mathematical model the semiclassical Boltzmann transport equations (BTEs) in the bipolar case, coupled with the Poisson equation for the electric field. The system is solved by means of a discontinuous Galerkin (DG) approach (see Cockburn & Shu, J. Comp. Phys. (1998); Hesthaven & Warburton, 2008) with linear elements in the spatial coordinate and constant approximation for the wave-vector space, discretized with a polar mesh. The correct physical range for the distribution function is preserved with the maximum-principle-satisfying scheme introduced in Zhang & Shu, J. Comp. Phys. (2010). The adopted 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 results for suspended monolayer graphene and GFET constitute benchmark solutions for a rigorous assessment of the validity of macroscopic models, such as drift-diffusion and hydrodynamic ones.

math-ph↗

arXiv2025

Ballistic electron transport described by a generalized Schr\"{o}dinger equation

We propose a Schr\"odinger 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 Schr\"odinger 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 Schr\"odinger 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

Selective decoupling in multi-level quantum systems by the SU(2) sign anomaly

We investigate dynamical decoupling operated by $2\pi$-pulses in a two-level subspaces of a multilevel system showing that it may leads to selective decoupling. This provides a flexible strategy for decoupling transitions in a quantum network, when control to directly address them is not available which can be use to control internode interaction or actively suppress decoherence

quant-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 Schr\"odinger equation

A fourth-order Schr\"{o}dinger 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) Schr\"{o}dinger 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 Schr\"{o}dinger equation in the effective mass approximation.

math-ph↗

arXiv2024

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↗

arXiv2023

Wigner equations for phonons transport and quantum heat flux

Starting from the quantum Liouville equation for the density operator and applying the Weyl quantization, Wigner equations for the longitudinal and transversal optical and acoustic phonons are deduced. The equations are valid for any solid, including 2D crystals like graphene. With the use of Moyal's calculus and its properties the pseudo-differential operators are expanded up to the second order in $\hbar$. The phonon-phonon collision operators are modelled in a BGK form and describe the relaxation of the Wigner functions to a local equilibrium function, depending on a local equilibrium temperature which is definite according to \cite{MaRo1}. An energy transport model is obtained by using the moment method with closures based on a quantum version of the Maximum Entropy Principle. An explicit form of the thermal conductivity with quantum correction is obtained under a suitable scaling.

math-ph↗

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↗

arXiv2021

Design and characterization of effective solar cells

We propose a two-stage multi-objective optimization framework for full scheme solar cell structure design and characterization, cost minimization and quantum efficiency maximization. We evaluated structures of 15 different cell designs simulated by varying material types and photodiode doping strategies. At first, non-dominated sorting genetic algorithm~II (NSGA-II) produced Pareto-optimal-solutions sets for respective cell designs. Then, on investigating quantum efficiencies of all cell designs produced by NSGA-II, we applied a new multi-objective optimization algorithm~II (OptIA-II) to discover the Pareto fronts of select (three) best cell designs. Our designed OptIA-II algorithm improved the quantum efficiencies of all select cell designs and reduced their fabrication costs. We observed that the cell design comprising an optimally doped zinc-oxide-based transparent conductive oxide (TCO) layer and rough silver back reflector (BR) offered a quantum efficiency ($Q_e$) of $0.6031.$ Overall, this paper provides a full characterization of cell structure designs. It derives a relationship between quantum efficiency, $Q_e$ of a cell with its TCO layer's doping methods and TCO and BR layer's material types. Our solar cells design characterization enables us to perform a cost-benefit analysis of solar cells usage in real-world applications

physics.app-ph↗

arXiv2021

The Pauli principle and the Monte Carlo Method for charge transport in graphene

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.

cond-mat.mes-hall↗

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↗

arXiv1998

The Case for Hyperbolic Theories of Dissipation in Relativistic Fluids

In this paper we highlight the fact that the physical content of hyperbolic theories of relativistic dissipative fluids is, in general, much broader than that of the parabolic ones. This is substantiated by presenting an ample range of dissipative fluids whose behavior noticeably departs from Navier-Stokes'.

gr-qc↗