Gompertz type dechanneling functions for protons in 〈1 0 0〉, 〈1 1 0〉 and 〈1 1 1〉 Si crystal channels

In this work the energy dependences of the Gompertz type sigmoidal dechanneling function parameters for protons in 〈1 0 0〉, 〈1 1 0〉 and 〈1 1 1〉 Si crystal channels is investigated theoretically. The proton energy range considered is between 1 and 10 MeV. The original dechanneling functions are generated using a realistic Monte Carlo computer simulation code. We show that the Gompertz type dechanneling function, having two parameters, lc and k, representing the dechanneling range and rate, respectively, approximate accurately the original dechanneling function. It is also shown that the energy dependences of parameters lc and k can be approximated by a linear function and a sum of two exponential functions, respectively. The results obtained can be used for accurate reproduction of experimental proton channeling spectra recorded in the backscattering geometry.