2D PIC-MCC simulations of magnetron plasma in HiPIMS regime with external circuit

Abstract

2D particle simulations of plasma evolution in high power impulse magnetron sputtering (HiPIMS) are very scarce. Short HiPIMS unipolar pulses (4 ms plateau at constant-800 V) are applied on a planar magnetron cathode with a metal target operated in pure argon at 0.4 Pa. The model begins with a pre-ionised gas before the pulse, defined as a typical direct current (DC) discharge (-280 V, 100 mA). Applying the voltage pulse leads to a sharp increase in the current. The external circuit is reduced to a simple resistance connected in series with the discharge. Both the discharge and the resistance are fed by the HiPIMS power supply. HiPIMS voltage and current evolution during the pulse and the near afterglow are self-consistently obtained from the particle-incell Monte Carlo collision (PIC-MCC) simulation. Results for three values of the external resistance (1 kω, 500 ω, and 250 ω) show that, at least for this range, the pulse current plateau value is inversely proportional to the resistance, exceeding 2.5 A for the lowest resistance for 4 cm target diameter. Comparison with experiment shows that by reducing the external resistance to 12.5 ω the pulse current exceeds 10 A, in agreement with the discharge voltage and current waveforms found in the model. The microscopic PIC-MCC approach gives access to a set of plasma parameters, some of which, close to the target, have never been explored before. Generally, the voltage drop across the ionisation region (IR) is found to be higher than the voltage in the cathode sheath (CS), in line with the prediction of the ionisation region model (IRM), emphasising the importance of Ohmic heating in HiPIMS. Additionally, the model shows that a transitory double layer separates the IR from the CS, as is also seen with probe measurements. The ambipolar diffusion feeds the diffusion region volume with a plasma density which is typically one order of magnitude below the average density in the IR that exceeds 2.5 × 1018m-3 for the 250 ω external resistance. The electron energy distribution function is composed of at least two Maxwell distributions during the pulse. The temperatures of different electron populations relax along the pulse plateau and tend to approximately the same value. The electron temperature is highest during the sharp increase in current, characterised by a peak in the electron density at this instant, even though the current is far below its plateau value. This increase in density is consistent with experimental findings by optical emission spectroscopy. The ions bombarding the target are spread out on a larger race track compared to the DC case and the typical average ion energy is approximately half of the cathode-anode voltage, due to the voltage drop being split between the CS and the IR. The evolution of the plasma parameters and the effect of the power are also discussed.