Ionization of Atoms and the Thomas-Fermi Model for the Electric Field in Crystal Planar Channels

The electric field in the crystal planar channels is studied by the Thomas Fermi method. The Thomas-Fermi equation and the corresponding boundary conditions are derived for the crystal planar channels. The numericalsolution for the electric field in the channels between (110) planes of the single crystal silicon and the critical angles ofchannelling protons in them are shown. Reasonable agreements with the experimental data are obtained. The resultsshow that the Thomas-Fermi method for the crystal works well in this study, and a microscopic research of the channelelectric field with the contribution of all atoms and the atomic ionization being taken into account is practical.