Damage profile evolution model based on the Boltzmann transport equation for silicon micromachining with the focused helium ion beam

Abstract

In this work, a damage profile evolution model based on the Boltzmann transport equation was developed for silicon micromachining using the focused helium ion beam. The energy grouping method, the spherical harmonic function expansion method, and the discrete ordinate method were used to solve the model numerically to obtain the implanted ion distribution and the amorphous damage profile. The influence of the ion beam energy and the ion dose on the evolution of the amorphous damage profile and the helium ion distribution in the silicon substrate were investigated. The implantation depth of the ions was positively correlated with the beam energy, and the influence of the ion dose on the implantation depth of the ions was very slight. The amorphous damage profiles predicted by the model were in good agreement with the experimental transmission electron microscope images. The results showed that the amorphous damage profile evolved into an approximately cylindrical shape for low beam energy (<10 keV), and an approximate “vase” shape for high beam energy (>10 keV). For the specified beam energy, the maximum amorphous width increased linearly and the amorphous depth first increased rapidly and then slowly increased with the increasing ion dose, and there was a limit on the amorphous depth. The computational efficiency of the model was not limited by the number of particles, which made up for a common shortcoming of the Monte Carlo and molecular dynamics methods.