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А.А. TSELYKOVSKIY, E.V. MELNIK Scientific adviser – G.I. ZEBREV Moscow Engineering Physics Institute (State University) GRAPHENE FIELD EFFECT TRANSISTOR CURRENTVOLTAGE CHARACTERISTICS MODELING TAKING INTO ACCOUNT VELOCITY SATURATION IN THE CHANNEL It has been proposed a model of I-V characteristics for bulk graphene based fieldeffect transistors with taking into account the carrier velocity saturation effects due to high-field driven electric field in the graphene channel. The fabrication of the first field-effect zero-bandgap graphene-based transistor with pronounced current saturation [1] led to an increase of interest in the bulk graphene based devices. It was found in [1] that effect of velocity saturation of carriers plays a major role in graphene channel transport. Maximum drift velocity is of order vSAT ~ 0.06-0.6 v0 (v0 108 cm/s is the universal Fermi velocity in graphene) due to strong scattering in the channel. Using ideal graphene statistics we have been developed a model of I-V dependencies taking into account aforementioned effect. Total channel carrier sheet density (electrons plus holes) can be expressed in ideal graphene as exact poli-logarithm functions of chemical potential [2] 2 2 k BT kBT k BT . (1) eN S ene nh Li 2 e Li 2 e v0 Quantum capacitance through the charge imbalance reads as e d ne nh 2 e2 k BT . (2) CQ ln 2 2 cosh d v0 v0 k BT Current-voltage characteristics of graphene transistor can be described taking into account maximum drift velocity vSAT based on results of [3, 4] by a following expression CQ VD W 0 e 2 N S2 1 , (3) ID 1 exp L CQ 1 enC 1 0 VDS vSAT L where 0 is channel carrier mobility (almost independent on NS), is the ratio of the diffusion component of the channel current to the drift one which can be derived from electroneutralty condition [3] Cox C ox CQ (4) For a sufficiently large dimensionless parameter 0 VDS vSAT L we have saturation current restricted by maximum drift current (5) I D WeN S vSAT Fig.2. Comparison of simulation results (line) Fig.1. Simulated drain current dependence as function of drain voltage VD and gate voltage VGS and experimental data [1] (dots) All parameters in Eq.3 can be expressed as explicit and exact (for a case of ideal graphene) function of chemical potential in graphene. Solving 1D Poisson equation the same procedure can be done for gate voltage VG () that allows to simulate graphene transistor drain current as function of the gate and drain-source biases (see Figs.1,2). This work is considered as a step to development of comprehensive models for simulation of emerging graphene field devices. References [1] I. Meric, M. Han et al. “Current saturation in zero-bandgap, top-gated graphene field-effect transistors”, 21 September 2008; doi:10.1038/nnano.2008.268 [2] G.I. Zebrev, “Graphene nanoelectronics: electrostatics and kinetics”, Proceedings of the SPIE, Volume 7025, p. 70250M-9 (2008). [3] G.I. Zebrev, “Electrostatics and diffusion-drift transport in graphene field effect transistors”, MIEL 2008. 26th International Conference on Microelectronics 2008, pp. 159-162. [4] G.I. Zebrev, “Current-voltage characteristics of a metal-oxide-semiconductor transistor calculated allowing for the dependence of the mobility on a longitudinal electric field”, Soviet physics. Semiconductors, 1992, vol. 26, no.1, pp. 47-49 , 1992.