Calculation of average projected range and range straggling of charged particles in solids

Abstract

Based on the KRAL equations (Ashworth et al., 1991. J. Phys. D 24, 1376-1380), which take into account second order energy loss moments, projected ranges and range moments of ions in mono-atomic targets were calculated. For this purpose, the set of three coupled differential equations of second order was first reduced to a set of differential equations of first order, and solved afterwards numerically, using initial Values with respect to the electronic stopping power according to Montenegro et al. (1981) which are valid at non-relativistic velocities in all solid targets and are consistent with experimental data for a wide range of energies. The numerical solution of the KRAL equations was performed by applying a continuous Runge-Kutta method of seventh-eighth order and a Fehlberg Runge-Kutta method of fourth-fifth order. The results with respect to the projected ranges of Xe ions in amorphous Si are in a good agreement with measured data, and those with respect to the projected ranges and range straggling of H or B ions in amorphous Si with data calculated by the standard theories TRIM, PRAL 97 and WS (Wang and Shi, 1990. J. Phys. D 23, 1282-1289). (C) 2001 Elsevier Science Ltd. All rights reserved.