An approximate analytical expression is obtained for the non-equilibrium carrier density throughout the depletion region of a Schottky diode. This expression is used to obtain a generalized expression for the J-V characteristics of the diode. It is shown that for the case of the mean free path less than a fraction of the Debye length the current approaches the Schottky diffusion-limited result. On the other hand for the mean free path greater than this amount the current approaches Bethe's thermionic result. Furthermore, knowing the non-equilibrium carrier density permits the calculation of the transit time of the carriers through the depletion region.