The process of de-channeling for electrons of energy 2 GeV channeled in the (110) plane of silicon and tungsten single crystals has been studied. The dynamics of the particle distribution density has been investigated in dependence on both the energy and scattering distribution of the initial electron beam. The influence of de-channeling on the spectral intensity of channeling radiation has been investigated by solving the Fokker-Planck equation. A non-conventional positron source is described based on the generation of radiation by relativistic electrons channeled along different crystallographic planes or axes of W, Si, Ge and C (diamond) single crystals and the subsequent conversion of the radiation into e+e−-pairs in an amorphous tungsten target. The simulation of channeling radiation and its dependence on the incidence angle into the crystal has been carried out by means of our Mathematica codes. The conversion of the radiation into e+e−-pairs and the energy distribution of positrons have been simulated using the GEANT4 package.