Monte Carlo method for simulating γ-ray interaction with materials: A case study on Si

In the present work, a Monte Carlo (MC) method has been developed to simulate various quantum mechanical processes for the energy loss of photons and fast electrons. The MC model is demonstrated by application to the interaction of photons with silicon over the energy range from 50 eV to 2 MeV and the subsequent electron cascades. The electron cascade process is commonly represented by two macroscopic parameters, the mean energy required to create an electron-hole pair, W, and the Fano factor, F, describing the electron yield and its variance. At energies lower than 5 keV, W generally decreases with increasing photon energy (from 3.96 to 3.58 eV), and it exhibits a sawtooth variation, as observed previously. However, discontinuities at the shell edges follow the photoionization cross-section, in contrast to previous results. The function, F(Ep), initially increases with increasing photon energy, Ep, to a maximum value of 0.187 around 155 eV, and then decreases at higher energies. Above the K shell edge, F has a value of 0.135. These results are consistent with experimental observations. The simulated distribution indicates that the interband transition and plasmon excitation are the most important mechanisms of electron-hole pair creation, while core shell ionization appears to be significant only at high energies.