# AMaSiS 2021 - Abstract

**Romano, Vittorio**

*Simulation of graphene field effect transistors by directly solving the semiclassical Boltzmann equation*

Università degli Studi di Catania, Italy

In the last years an increasing interest has been devoted to graphene field effect transistors (GFETs) as potential candidates for high-speed analog electronics, where transistor current gain is more important than ratio current ON/current OFF. Several types of GFETs have been considered in the literature [1]: top-gated graphene based transistors, obtained synthesizing graphene on silicon dioxide wafer, and double gate GFETs. The current-voltage curves present a behaviour different from that of devices made of semiconductors, like Si or GaAs, because of the zero gap in monolayer graphene. The current is no longer a monotone function of the gate voltage but there exists an inversion gate voltage [1]. As a consequence, there is a certain degree of uncertainty in the determination of the current-off regime which requires a rather well tuning of the gate-source voltage.

Lately, some attempts to simulate Graphene Field Effects transistors (GFETs) have been performed (see for example [2, 3, 4, 5]) with simplified models like drift-diffusion. The latter contains several functions to be fitted by experimental data such as mobilities and generation-recombination terms. Often adaptations of the expressions used for standard semiconductors are adopted and a reduced 1D Poisson equation is coupled to the equations for the charge transport. It is therefore warranted to have a confirmation of the obtained results by a direct solution of the semiclassical Boltzmann equation for charge transport in graphene. Here a discontinuous Galerkin method, already developed in ([6, 7]), is used to simulate some challenging geometry for future GFETs by numerically solving the Boltzamnn equations for electrons and holes in graphene.

**Acknowledgments**: The authors acknowledge the financial support from Universitá degli Studi di Catania, *Piano della Ricerca 2020/2022 Linea di intervento 2* “QICT”. G. N. acknowledges the financial support from the National Group of Mathematical Physics (GNFM-INdAM) *Progetti Giovani GNFM 2020*.

**References**

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[5] G. Nastasi and V. Romano, A full coupled drift-diffusion-Poisson simulation of a GFET, *Commun. Nonlinear Sci. Numer. Simulat.* **87** (2020), 105300.

[6] V. Romano, A. Majorana and M. Coco, DSMC method consistent with the Pauli exclusion principle and comparison with deterministic solutions for charge transport in graphene, *J. Comp. Physics* **302** (2015), 267--284.

[7] A. Majorana, G. Nastasi and V. Romano, Simulation of bipolar charge transport in graphene by using a discontinuous Galerkin method, *Commun. Comput. Phys.* **26** (2019), 114--134.