The paper deals with 2D numerical modeling of Si-SiO<sub>2</sub> MOSFET for considering the field dependent mobility of the carriers in the surface channel. The fundamental device equations have been numerically solved to obtain various characteristics and parameters. The surface potential and electric field profile in the channel have been numerically estimated to have indepth analysis. The model enables one to estimate various parameters which determine the potential use of this device for various applications. The noise analysis of the device has been carried out to study the performance of the device. The exact solution of the 2D Poisson's equation for the S<sub>i</sub>-S<sub>i</sub>O<sub>2</sub> MOSFET's is derived by using Liebmann's iteration method. Based on the derived 2D potential distribution, the surface potential distribution in the S<sub>i</sub> film is numerically obtained and their accuracy is verified by 2D analytical analysis. The calculated minimum surface potential and its location are used to analyze the drain-induced barrier-lowering effect and further to develop numerical threshold - voltage model. It is shown that excellent agreements are obtained for wide ranges of device structure parameters and applied biases.