An algorithm for fast calculation of ion range and damage distributions based on the boltzmann transport equation

Boltzmann transport equation (BTE) method using large energy intervals in ion scattering calculations can lead to significant errors in the calculation of ion and damage distributions. We pointed out that the inaccuracy is caused by the fact that the flux distribution in a transited energy state is not uniform. The flux is higher at its higher energy end because of a relatively higher cross section for a small energy transfer. Neglecting this difference and assuming an evenly distributed flux will lead to significant errors. The issue can be alleviated by using small energy intervals which inevitably increases computational times. We proposed to redistribute the flux among neighboring energy states around a transited energy state, with the redistribution weighted by their proximities to the mean value of transited energy. Therefore, ion range distributions can be calculated accurately with large energy intervals, thus significantly improving computational efficiency, i.e. by at least one order of magnitudes for 100 keV Si self ion irradiation.