New trends in charge and phonon transport in low dimensional structures

This workshop is related to the activities of the project PRIN 2022 provided by the Italian Ministry of University and Research. The network comprises five nodes: Università di Catania (UNICT), Politecnico di Milano (POLIMI), Università di Firenze (UNIFI), Università di Palermo (UNIPA), Università di Salerno (UNISA). The research activity is split into several work-packages (WP). The carrying out of the project will be performed by the units according to the objectives of the WPs. UNICT will be in charge of coordinating the activity of the whole network.

Title: Transport phonema in low dimensional structures: models, simulations and theoretical aspects

Abstract: The project tackles relevant issues concerning the mathematical modeling and simulation of electrostatics and charge transport in 2D crystals, e.g. graphene and TM dichalcogenides, and structures such as nanoribbons and nanowires or polymeric nanofibers and tubes, where the presence of confinement effects allows the formal description of the carrier flow as a two- or one-dimensional electron gas. Due to the peculiar electrical and mechanical properties, graphene and TMD are considered very promising materials for future electron devices and important components for composite functional materials. While for electron devices based on standard semiconductor materials the efficiency of off-the-shelf commercial simulation tools is well established, the same does not hold for the mentioned 2D materials. Besides, by increasing the miniaturization of devices, hot-spots are observed, that are zones with very high crystal temperature due to the release of energy by highly energetic electrons. This makes thermal effects of primary importance. Moreover, composite functional materials consisting of blends of different polymers or of a mix of polymeric materials and nanoparticles made of graphene or other semi-conducting materials have also been recently considered for their promising electrical and thermal properties (polymeric insulators including graphene nanoparticles and graphene-polymer composites).
The main goals of the project are the following. The analytical properties of the Schrödinger equation in confined structures and open systems will be investigated. Efficient stochastic Monte Carlo schemes for the Wigner equation will be developed including collisions. Direct solutions of the semiclassical Boltzmann equations will be obtained by developing and employing advanced numerical schemes based on the discontinuous Galerkin methods for studying the electron-electron interaction and the charge transport in nanoribbons, nanowires and quantum dots. Similarly, phonon transport with coupling to the electron flow in graphene will be tackled. Thermal effects will be introduced along with the piezoelectric ones and mechanical stresses. Macroscopic models will be deduced from the transport equations by using the moment method and obtaining the needed closure relations by means of the Maximum Entropy Principle. The obtained models will be used to simulate graphene field effect transistors. In order to allow efficient simulations of nanocomposites, numerical methods for coupling models with different dimensionality will be developed, focusing in particular on Finite Element/Embedded Interface to simulate interfaces with complex geometries that are not aligned to the bulk mesh; upscaling techniques will be applied to evaluate macroscopic material properties from nanoscale modeling of nanostructured materials. For disordered materials, effective macroscopic transport models and techniques to infer model parameters from experimental data will be developed.

Duration: 24 months

Main ERC field: PE - Physical Sciences and Engineering

ERC subfields: PE1_12 Mathematical physics, PE1_19 Scientific computing and data processing, PE1_21 Application of mathematics in sciences

Project code: 2022TMW2PY