The Surface potential model based on 2D Poisson's equation of heterojunction Selective Buried Oxide (SELBOX) TFET has been predicted with appropriate boundary conditions in the rectangular coordinates. The device has been bifurcated into rectangular regions to perform an analysis of the electrostatic potential of the device. The potentials in the source and drain regions have been considered constant. The potential model is utilized to derive the mathematical relations for the electric field. Moreover, the affectability of drain voltage and gate voltage on capacitance has been explored by formulating the analytical model for capacitance. The charge model has also been articulated. The capacitance model considers depletion capacitances, inversion capacitances, and fringing capacitances of the proposed device. The total charge is modeled by considering the depletion charge and inner fringing charge at the source region with the dominancy of inversion charge at the channel region. Further, subthreshold swing (SS) based on band to band tunneling (BTBT) has been derived. The device behavior has been studied by incorporating quantum correction (QC). The analytically modeled results agree well with the TCAD simulation results.