Analytical Solution for the Potential Distribution in the Channel of A Graphene Field-Effect Transistor Validated with a Custom-Fabricated Test Platform

A comprehensive analytical framework for computing the potential distribution in graphene-based field-effect transistors (GFETs) is presented. The work introduces a pioneering set of self-consistent and explicit closed-form expressions that enable an accurate description of the internal potential profiles along the graphene channel. The proposed models are experimentally validated using a custom-fabricated test platform based on global back-gated GFETs incorporating two in-channel terminals, which allow direct measurement of the local potential drop at different channel positions and provide unique experimental access to the internal electrostatics of the device. Experimental drain current characteristics and in-channel potential measurements are systematically compared with model predictions, showing excellent agreement over a wide range of bias conditions and validating the analytical framework in both unipolar and ambipolar operating regimes. The extracted potential distributions enable a clear physical interpretation of key transport phenomena in GFETs, including the onset of channel pinch-off associated with maximum transconductance and the transition between unipolar and ambipolar transport regimes. Owing to their analytical nature and computational efficiency, the proposed pioneering models provide a powerful tool for rapid device evaluation, optimization, and interpretation, with direct relevance to graphene-based analog and radio frequency electronics, sensing, flexible electronics, and thermoelectric applications.