A Monte Carlo program based on acoustic and optical phonon scattering as well as on impact ionisation of valence band electrons has advantages in description of very low energy electron scattering (in eV and meV regions) and is aimed especially to wide gap dielectrics and insulators. Thus, the rapid relaxation and the ballistic transport of excited electrons within the conduction band of a wide gap insulator occurs over femtoseconds. The field-dependent transport and trapping parameters allow us to model the selfconsistent charge transport and charging-up of SiO₂ thin layers as well as bulk Al₂O₃ samples during electron bombardment. The resulting distributions of currents, charges and electric fields within these samples explain, e.g. the phenomena of field-enhanced and field-blocked secondary electron emission. In order to prove the accessible quantity of the surface charging-up potential we have chosen the X-ray bremsstrahlung (BS) spectra, i.e. the shift of the short wavelength threshold due to the negative surface potential V₀ and respective retarding of the incident electron beam. This effect is demonstrated for a 3 mm bulk Al₂O₃ sample and E₀ = 30 keV electron beam irradiation resulting in a huge negative surface potential of V₀^exp = -17 kV.