IEEE TRANSACTIONS ON ELECTRONDEVICES, VOL. 61, NO. 5, MAY 2014 1567 Simulation of the Performance of Graphene FETs With a Semiclassical Model, Including Band-to-Band Tunneling Alan Paussa, Gianluca Fiori, Pierpaolo Palestri, Matteo Geromel, David Esseni, Giuseppe Iannaccone, and Luca Selmi Abstract— We assess the analog/RF intrinsic performance of graphene FETs (GFETs) through a semiclassical transport model, including local and remote phonon scattering as well as band-to-band tunneling generation and recombination, validated by comparison with full quantum results over a wide range of bias voltages. We found that scaling is expected to improve the f T , and that scattering plays a role in reducing both the f T and the transconductance also in sub-100-nm GFETs. Moreover, we observed a strong degradation of the device per- formance due to the series resistances and source/drain to channel underlaps. Index Terms— Band-to-band tunneling (BTBT), Boltzmann transport equation, graphene FET (GFET), graphene monolayer, nonequilibrium Green’s function (NEGF), RF transistors, WKB approximation. I. I NTRODUCTION D UE TO its high carrier mobility, graphene is being widely investigated as an alternative channel material for future MOSFETs. Much of the attention has recently shifted to the use of graphene in RF transistors, where the OFF-current is less critical than in digital circuits and the high carrier velocity allows to achieve large cutoff frequencies ( f T ) [1]–[6]. Numerical models for accurate simulation of realistic, large area graphene devices are necessary to understand experi- mental results and optimize device performance, in particular, in view of analog/RF applications [7], [8]. Semiclassical transport models are well justified to this purpose, since they naturally incorporate the scattering mechanisms responsible for mobility degradation [9], [10]. However, band-to-band tunneling (BTBT), which is a purely quantum mechanical effect, causes large output conductance, excess OFF-current, and ambipolar behavior [8], [11]. Quantum transport models Manuscript received November 8, 2012; revised February 18, 2014; accepted February 20, 2014. Date of publication March 12, 2014; date of current version April 18, 2014. This work was supported in part by the FP7 C. A. Guardian Angels under Grant IST-285406 and in part by the GRADE under Grant 317839 through the IUNET consortium. The review of this paper was arranged by Editor A. C. Seabaugh. A. Paussa, P. Palestri, M. Geromel, D. Esseni, and L. Selmi are with the Dipartimento di Ingegneria Elettrica Gestionale e Meccanica, University of Udine, Udine 33100, Italy (e-mail: alanfromsl@gmail.com; palestri@uniud.it; matteo.geromel@gmail.com; esseni@uniud.it; luca.selmi@uniud.it). G. Fiori and G. Iannaccone are with the Dipartimento di Ingeg- neria dell’Informazione, Università di Pisa, Pisa 56126, Italy (e-mail: g.fiori@iet.unipi.it; giuseppe.iannaccone@unipi.it). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TED.2014.2307914 based on the nonequilibrium Green’s functions (NEGFs) with a tight-binding (TB) Hamiltonian [12] provide a rigorous treat- ment for the BTBT and ballistic transport in graphene devices; some scattering mechanisms (for instance, inelastic phonons) have been added as well [13]. Compared with the NEGF, the semiclassical approach is computationally more efficient in the simulation of long-channel devices and allows for an easier and less computationally demanding implementation of a large variety of scattering mechanisms [10], [14], [15]. In this paper, we first present (Section II) an original implementation of the BTBT in a Monte Carlo (MC) model to solve the semiclassical transport in graphene FETs (GFETs) with large width and arbitrary gate length, improving the one presented in [14]. Second, in Section III, we validate our BTBT model by comparison with state-of-the-art TB-NEGF simulations and we identify the region of operation, where the model is more reliable. Finally, in Section IV, we evaluate the IV characteristics and RF figures of merit of intrinsic GFETs with different channel lengths and source/drain (S/D) to channel underlaps. II. MODELS’DESCRIPTION As for the semiclassical MC model, we have extended to short-channel GFETs, the MC simulator for uniform transport presented in [10]. In particular, we have coupled in a self- consistent loop the Boltzmann transport equations for electrons and holes (solved with a MC technique) to the nonlinear Poisson equation. The gapless energy dispersion relation E =¯ h v f |k| is assumed, which is adequate for wide devices as those considered for analog/RF applications. Translational invariance is assumed along the width direction. We have modeled the acoustic and optical phonons of the graphene as in [16] and the remote phonons originating in surrounding dielectrics using the remote phonon model presented in [10] and [17]. The degeneracy of the carriers has been taken into account with a careful numerical implementation of the rejection technique originally proposed in [18]. The carriers are injected in the simulation domain adapting the approach of [19] to graphene as described in [14]. The derivatives of the potential at the source and the drain edges have been set to zero in the Poisson equation, similarly to what is done in the NEGF solvers [20]. We have validated the semiclassical transport model at low electric field by comparison with experimental 0018-9383 © 2014 IEEE. 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