Electronic stopping of Si from a three-dimensional charge distribution

We describe an electronic stopping model for low-energy ions, a necessity f or an accurate prediction of the penetration depths of energetic ions in ma terials, especially in crystal channels. With the use of molecular dynamics simulations and calculating the electronic stopping from a three-dimension al charge distribution without using any free parameters, we obtain accurat e range distributions on a realistic physical basis. Our electronic stoppin g model is based on the Brandt-Kitagawa (BK) [W. Brandt and M. Kitagawa, Ph ys. Rev. B 25 5631 (1982)] theory. For heavy ions (Z>1) we also include a v ersion of the Firsov inelastic energy loss model. We test our model for sil icon, where plenty of experimental data are available. We first test the mo del for the ranges of hydrogen, to determine the accuracy of the scaling hy pothesis used in the BK theory, and then for other ions. The results are co mpared with experimental range profiles and, with the exception of the [110 ] direction, show good agreement, comparable to that achieved with models e mploying free parameters. We also show that a model using an averaged elect ron distribution is a promising method to overcome the shortcoming in the [ 110] direction.