We are presenting a convergence study of the evanescent model and the polynomial model with and without the Effective Conduction Path Effect. These analytic models of the electric potential in the channel are used to analyze the short channel effect for the submicronic SG FD SOI MOSFET. Hereby, we figure out the 2D Poisson equation and we analytically write the surface potential, the threshold voltage, the DIBL and the sub-threshold slope. The results show a good agreement of the evanescent model and the polynomial model including the Effective Conduction Path Effect with measures done by simulation tools.