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For the proper interpretation of the experimental data produced in slow positron beam technique, the positron im-plantation properties are studied carefully using the latest Geant4 code. The simulated backscattering coefficients, the implantation profiles, and the median implantation depths for mono-energetic positrons with energy range from 1 keV to 50 keV normally incident on different crystals are reported. Compared with the previous experimental results, our simula-tion backscattering coefficients are in reasonable agreement, and we think that the accuracy may be related to the structures of the host materials in the Geant4 code. Based on the reasonable simulated backscattering coefficients, the adjustable parameters of the implantation profiles which are dependent on materials and implantation energies are obtained. The most important point is that we calculate the positron backscattering coefficients and median implantation depths in amorphous polymers for the first time and our simulations are in fairly good agreement with the previous experimental results.