Generalized damage profile function for subsurface damage in SiC induced by helium focused ion beam under line scanning at different energies and doses

Silicon carbide is receiving increasing attention as a substrate due to its stability in harsh environments. At the same time, further minimization of sensors and micro devices requires new techniques for nanofabrication. In this context, the helium focused ion beam (He-FIB) is a promising candidate, due to its high resolution and capability of sub-10 nm fabrication, as well as its ability to modify the properties of the substrate via ion implantation. In this work, we consider previously reported experimental images of subsurface damage in both SiC and Si, as induced by He-FIB under line scanning, and provide a summary of the resulting amorphous and bubble regions as a function of the beam energy and dose. Based on empirical relations collectively encapsulated into a damage profile function (DPF) that was previously used to describe the contour of the amorphous region in Si, we focus on presenting a generalized damage profile function (GDPF) that enables describing the contours of both the amorphous and bubble regions in SiC simultaneously. In particular, the role of swelling, as a relatively small protruding region from the initial surface that eventually restricts the upward expansion of the bubble region, is fully considered. The parameters of the resulting mathematical model are related to measurements from the experimental cross-sectional images and are eventually optimized by using an evolutionary algorithm. Comparison to the experimental profiles concludes that the proposed GDPF captures both the amorphous and bubble region profiles with good precision.