Particle-in-Cell Techniques for Simulations of Magnetron Sputtering

Variable grid spacing, energy-conserving particle-in-cell (EPIC), and speed-limited particle-in-cell (SLPIC) techniques are investigated to speed up fully-kinetic simulations of magnetron sputtering. Fully-kinetic simulations of magnetron sputtering are needed to optimize the sputter-coating of thin films. Traditional PIC simulations of magnetron sputtering are computationally slow because the Debye length (~10^-5 m) is much smaller than the centimeter size device, and the plasma period (~10^-11 s^-1) is much shorter than the microsecond long dynamics. Variable grids speed up simulations by resolving the bulk of the plasma with larger cells and the high-density cathode sheath with small cells. EPIC speeds up simulations by relaxing the requirement to resolve the Debye length, which enables larger grid cells. SLPIC speeds up simulations by limiting the speeds of the fastest electrons, which enables larger timesteps. We have shown that SLPIC can quickly simulate electric discharge, collisions, and wall interactions, which are relevant to magnetron sputtering. We plan to compare these different PIC techniques and benchmark our results to both simulation and experimental data before exploring device optimization.