Diffusion-reaction modeling of atomic layer etching

We present a diffusion-reaction model of plasma-assisted atomic layer etching (ALE) of silicon (Si) with alternating exposure to chlorine gas (Cl₂) and argon ions (Ar^þ). The model is an extension of a previous transient site-balance model [Vella et al., Plasma Sources Sci. Technol. 33, 075009 (2024)], which was parameterized using molecular dynamics (MD) simulations but assumed perfect mixing within the near-surface “mixed layer.” In contrast, the diffusion-reaction model, also parameterized using MD data, provides a continuum description that resolves transient spatial gradients of Cl concentration within the near-surface region during Ar^þ ion bombardment. The model conceptualizes the near-surface region as liquidlike, where Cl atoms mix and diffuse within the region during ion bombardment. The model is shown to accurately capture the evolution of the Cl concentration profiles during the ALE ion bombardment step. It also correctly reproduces the etch product distributions. This approach can be generalized to more complex chemistries and materials and could serve as a powerful foundation for future reduced-order models (ROMs) of surface modification during plasma-assisted processing.