Modeling the role of secondary electron emission in direct current magnetron sputtering using explicit energy-conserving particle-in-cell methods

We present results from particle-in-cell (PIC) simulations of direct current magnetron sputtering (dcMS) in a 2D cylindrically symmetric geometry. The PIC model assumes an electrostatic approximation and includes the Monte Carlo collision method to model collisions between electrons and the neutral gas. A newly implemented explicit energy-conserving PIC algorithm (EC-PIC) is also exercised by the model, and results are compared with the standard momentum-conserving PIC (MC-PIC) method. We use these simulation tools to examine how changes in ion-induced secondary electron yield (SEY) and the external circuit impact the steady-state current, voltage, and plasma density of dcMS discharges. We show that in general, higher ion-induced SEY and lower external resistance values lead to larger currents, smaller voltages, and larger plasma densities. Simulation results presented in this paper related to the ion-induced SEY demonstrate similar trends that have been observed in previous experimental work and theory. Finally, we demonstrate that EC-PIC maintains numerical stability up to cell sizes as large as ten times the electron Debye length. While we have not performed a comprehensive stability study of MC-PIC, this paper demonstrates improved stability over the standard practice often assumed in MC-PIC. We therefore demonstrate that EC-PIC allows for modeling a wide range of plasma currents and densities using modest computational resources compared with PIC models that require resolution of the electron Debye length.