Modeling and Simulation of High Power Magnetron Discharges

• Applicants: Professor Dr. Ralf-Peter Brinkmann; Dr. Denis Eremin
• Subject Area: Communication Technology and Networks, High-Frequency Technology and Photonic Systems, Signal Processing and Machine Learning for Information Technology
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 550860775

Physical vapor deposition technology via magnetron sputtering represents one of the primary methods used for thin film deposition in industrial applications. A recent modification of this method, known as High Power Impulse Magnetron Sputtering (HiPIMS), involves sustaining the magnetron discharge with short pulses of high power. This modification allows operation with any type of target and substrate and results in a high degree of ionization of the sputtered material, leading to substantial improvements in the film properties. However, understanding such discharges remains challenging in many aspects, primarily due to their extreme plasma densities, rendering many experimental diagnostics inapplicable. Numerical modeling also faces difficulties due to the high plasma densities. Because of the low pressures in such discharges, they must be modeled using a kinetic and nonlocal method. The explicit momentum-conserving particle-in-cell (PIC) algorithm, commonly employed for this purpose, becomes impractical due to inherent numerical limitations. We propose two different approaches to address this issue, complementing each other and increasing the likelihood of successfully developing a numerical tool capable of comprehensively modeling HiPIMS discharges. The first approach involves utilizing an energy-conserving implicit PIC method in combination with noise reduction techniques. This method has more relaxed numerical limitations compared to the conventional one and is expected to be universally applicable to any type of ExB plasma. However, it needs to address the increased numerical noise resulting from the high plasma densities in HiPIMS. The second approach relies on scale separation and quasi-thermodynamic arguments to reduce the problem's dimensionality and produce a system of formally two-dimensional parabolic equations that model the discharges under consideration. This approach should provide not only fundamental insight, but deliver results much faster than the PIC simulations. However, the underlying assumption of strong Coulomb collisions might limit its applicability at the low power boundary of the HiPIMS regime. Enhanced with plasma chemistry and target models, the first approach will create a "digital twin," a versatile numerical tool capable of realistically simulating key physics phenomena in HiPIMS discharges and delivering spatially and energy-resolved fluxes of ions and neutrals onto the substrate. The second approach is expected to deliver a "digital junior" numerical tool for modeling HiPIMS discharges much faster but within a narrower range of parameters. These tools are intended to be utilized to gain insights into the fundamental principles of HiPIMS physics, specifically focusing on the formation and sustainment of large-scale spokes, fine-scale instabilities, their potential interactions, and their impact on electron and ion physics relevant to technological applications.

• DFG Programme: Research Grants
• Co-Investigator: Professor Dr.-Ing. Jan Trieschmann