A Reduced Order Model for Plasma-Surface Interactions

A digital twin for plasma tools in semiconductor processing requires bidirectional interactions between the physical system and its computational representation evolving over time.¹ Essential to this is a reduced order model (ROM) for plasma-surface interactions. Previously, we developed a well-mixed site balance ROM simulating Atomic Layer Etching (ALE) of Si with Cl/Ar+ using ordinary differential equations (ODEs).² Here, we extend this ROM by incorporating spatial and temporal atomic concentration variations via diffusion-convection-reaction partial differential equations (PDEs). This advanced model addresses cases where the well-mixed assumption fails, such as physical sputtering of fluorocarbon layers or oxide films.³

We first present a PDE-based ROM for ALE of Si with Cl and Ar⁺, capturing complex spatial-temporal dynamics beyond ODE capabilities. Additionally, we introduce a specialized ROM for physical sputtering of Alumina (Al₂O₃). Molecular Dynamics (MD) simulations of Al₂O₃ sputtering with Ar⁺ ions were validated experimentally and used to parameterize the ROM. Both ROM implementations effectively reproduce MD results, demonstrating computational efficiency and accurately modeling transient sputtering processes.

1. National Academies of Sciences, Engineering, and Medicine. 2024. Washington, DC: The National Academies Press.

2. Vella et al. Plasma Sources Sci. Technol. 2024, 33 (7), 075009.



3. Shim et al. Journal of Vacuum Science & Technology A 2024, 42 (2), 023207.