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<p><em>In this paper we present four simple analytical threshold voltage model for short- channel and length of saturation velocity region (LVSR) effect that takes into account the built – in potential of the source and drain channel junction, the surface potential and the surface electric field effect on double – gate graphene nanoribbon transistors. Four established models for surface potential, lateral electric field, LVSR and threshold voltage are presented. These models are based on the easy analytical solution of the two dimensional potential distribution in the graphene and Poisson equation which can be used to obtain surface potential, lateral electric field, LVSR and threshold voltage. These models give a closed form solution of the surface potential and electrical field distribution as a function of structural parameters and drain bias. Most of analytical outcomes are shown to correlate with outcomes acquired by Matlab simulation and the end model applicability to the published silicon base devices is demonstrated.</em></p>

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