Electronic stopping of Si from a three-dimensional charge distribution

We describe an electronic stopping model for low-energy ions, a necessity for an accurate prediction of the penetration depths of energetic ions in materials, especially in crystal channels. With the use of molecular dynamics simulations and calculating the electronic stopping from a three-dimensional charge distribution without using any free parameters, we obtain accurate range distributions on a realistic physical basis. Our electronic stopping model is based on the Brandt-Kitagawa (BK) [W. Brandt and M. Kitagawa, Phys. Rev. B 25 5631 (1982)] theory. For heavy ions $(Z>1)$ we also include a version of the Firsov inelastic energy loss model. We test our model for silicon, where plenty of experimental data are available. We first test the model for the ranges of hydrogen, to determine the accuracy of the scaling hypothesis used in the BK theory, and then for other ions. The results are compared with experimental range profiles and, with the exception of the $〈110〉$ direction, show good agreement, comparable to that achieved with models employing free parameters. We also show that a model using an averaged electron distribution is a promising method to overcome the shortcoming in the $〈110〉$ direction.