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In this paper, by solving the 1-D Poisson equation using appropriate boundary conditions, we report a closed-form surface potential solution for all the three surfaces (gate oxide-silicon film interface, silicon-film-buried oxide interface, and buried oxide-substrate interface) of fully depleted silicon-on-insulator (SOI) MOSFETs by considering the effect of substrate charge explicitly. During the model derivation, it is assumed that the silicon film is always fully depleted and the back silicon film surface is never inverted. The calculated values of the surface potentials obtained from the proposed model agree well with the iterative solution of exact Poisson equation with a maximum relative error bound of 0.3%. In the entire model, only two square roots, one exponential, and two logarithm terms are used and the continuity and differentiability of the resultant surface potential solutions are ensured making the proposed model computationally efficient.