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Gallium oxide (G a 2 O 3 ) is a promising ultra-wide bandgap material offering a large bandgap (> --> 4.7 eV) and high critical electric fields. The increasing demand for electronic devices for high-power applications in electric automobiles, high-performance computing, green energy technologies, etc., requires higher voltages and currents with enhanced efficiency. Vertical transistors, such as fin-shaped field-effect transistors (FinFETs) have emerged to meet the growing need with improved current handling capabilities, reduced resistance, and enhanced thermal performance. However, to fully exploit the Ga 2 O 3 power transistors, precise and reliable physics-driven models are crucial. Therefore, a comprehensive surface potential model has been developed in this work for a vertical Ga 2 O 3 FinFET. The electric potential across the channel is explained by analyzing the two-dimensional (2D) Poisson equation employing parabolic approximation. Such a surface potential model is instrumental in determining the performance of the Ga 2 O 3 FinFET as it affects the threshold voltage, the drain current, and fringing capacitance. Exploiting the surface potentials, a fringing capacitance model is derived which is crucial in analyzing the speed of the device in compact integrated circuits. In addition, statistical analysis of the Ga 2 O 3 FinFET using the Monte Carlo simulation technique is performed to determine the leakage current fluctuation due to doping variations. The validation of the analytical model with experimental results confirms the effectiveness and prospects of the developed models in the rapid development and characterization of next-generation high-performance vertical Ga 2 O 3 power transistors. [ABSTRACT FROM AUTHOR]