In the present study, we determine exact analytical expression of the current flow through a Schottky barrier diode as a function of the input voltage. The Schottky diode is modeled by an electronic circuit containing four physical parameters: a series resistance Rs, a shunt resistance Rsh, a Schottky diode reverse saturation current Is and a Schottky diode ideality factor ??. Firstly, we solve the characteristic equation and determine the analytical expression of the input current I as a function of the input voltage of the Schottky diode V using the LambertW Function. Secondly, We present two different methods to extract the four physical parameters appearing in the electronic circuit. These methods are applied for two junctions: Iridium-Silicon Carbide Schottky barrier diode at 200 K and Gold-Gallium Arsenide at 300 K. Finally, we compare the results obtained via the two methods presented.