A Helium Bubble Damage Model Based on Population Balance Equation for Focused Helium Ion Beam Processing

Focused helium ion beam allow for precise processing of materials on the nanoscale, but inevitably causes damage to the substrate. Therefore, developing a damage model is essential. The damage caused by helium ions to the substrate primarily includes the amorphization damage to the crystalline materials and helium bubble formation due to helium accumulation inside the material. In this paper, a helium bubble damage model is proposed which utilizes the population balance equation to solve for the helium bubble distribution, enabling simulation of helium bubble growth and aggregation within the substrate under specific ion energies and doses. Simultaneously, silicon was subjected to focused helium ion beam implantation, followed by sample preparation and observation using Transmission Electron Microscopy (TEM). Finally, the simulation results were compared with the experimental observations to verify the accuracy of the model.