The electron density of states near the semiconductor-insulator interface is calculated using the Feynman's path-integral method. Statistical interface charge distribution properties have been taken into account and the Fourier transform of the binary correlation function of the random potential has been computed. Finally the electron density of states in the band tail in a first cumulant approximation is obtained. The exponential dependence of the density of states on the energy is similar to that obtained for the three-dimensional screened Coulomb potential at a limit of weak screening. The exponent b(v) of the density of states is the same and the pre-exponential factor a(v) are approximately two orders of magnitude smaller than those obtained using the screened Coulomb model random potential. Some numerical results have been presented for the system Si-SiO2.