Finite Element Modeling of Back-Gated Monolayer Graphene FETs with Carrier-Dependent Transport and Residual Density Effects

• A finite element modeling framework for back-gated monolayer graphene FETs is developed and validated. • Carrier-dependent transport with residual density effects near the Dirac point is incorporated. • Excellent agreement between analytical and FEM results is achieved, with current deviation below 0.1%. • Drain current scaling with channel length and effective graphene thickness is accurately reproduced. • The model provides a computationally efficient tool extensible to complex GFET geometries and layouts. This work develops and validates a finite element modeling framework for back-gated monolayer graphene field-effect transistors (GFETs) using COMSOL Multiphysics and a macroscopic conductivity-based transport model. The analytical formulation incorporates gate-voltage-induced carrier modulation, a residual carrier density near the Dirac point, and field- and density-dependent mobility, enabling a realistic description of charge transport in the low source–drain bias regime. Finite element simulations of devices with varying channel lengths and effective graphene thicknesses are systematically benchmarked against the analytical model for rectangular channels, showing excellent agreement with deviations in maximum drain current below 0.1%. The framework reproduces the expected inverse scaling of drain current with channel length, linear dependence on effective graphene thickness, and a pronounced resistance peak near the Dirac point arising from residual carriers. By representing graphene as a surface-conducting layered shell, the model captures essential GFET physics while remaining computationally efficient and is readily extensible to complex channel geometries, multi-finger gate architectures, and realistic layouts beyond the reach of closed-form analytical solutions.