Structure of DC magnetron sputtering discharge at various gas pressures: a two-dimensional particle-in-cell Monte Carlo collision study

Abstract

We report the results of a particle-in-cell Monte-Carlo collision simulation of an axially symmetric DC magnetron discharge with a 5 cm diameter flat cathode in argon at pressures from 1 to 10 mTorr at a constant discharge current of about 0.5 A. Calculations show that the cathode region, where almost the entire discharge voltage drops, consists of a cathode sheath 0.1–0.2 mm wide and a presheath about 2 cm wide, where most of the ionizations occur, separated by a region 0.25–0.35 mm wide, where the plasma potential remains almost unchanged and the plasma density reaches its maximum value. Most of the discharge voltage drops in the presheath at low gas pressure, and in cathode sheath at high pressure. The ratio of sheath to presheath voltages increases linearly with pressure. The distribution of the ionization rate has two maxima: near the cathode sheath and in the presheath. The fraction of ionizations near the cathode sheath increases with pressure. The electron energy distribution function (EEDF) is generally a two-temperature function. At low pressures at a distance of less than 1 cm from the cathode, the EEDF becomes one-temperature. A high-energy tail is observed on the EEDF near the cathode; the fraction of electrons in the tail (in the order of tenths of a percent at 10 mTorr) and their energy, determined by the sheath voltage, increase with pressure. The electron temperature decreases with pressure due to a decrease of the electric field in the presheath, which leads to a decrease of energetically accessible regions of collisionless electron motion and to a corresponding decrease in the energy that electrons can obtain in these regions. The dependence of the discharge voltage on the gas pressure has a minimum at about 3 mTorr, which occurs due to the competition of two processes on pressure increase: a decrease in the electron temperature and a decrease in the fraction of electrons returning back to the cathode. Plasma density waves are observed in the presheath region at pressures of 1–3 mTorr.

Spoke-resolved electron density, temperature and potential in direct current magnetron sputtering and HiPIMS discharges

“…The electron density found here is in good agreement with previously reported, time-averaged values [32][33][34].…”

Influence of the magnetic field on the discharge physics of a high power impulse magnetron sputtering discharge

“…In section 3.3 the probability of target species ionization is discussed and related to the discharge current. In the following, we will derive equations (11) and (12). Starting with equation (10) and using t Ti + = 1/(n e,peak k Ti + ) from the discussion above, yields…”

“…Summarizing again the constants into k 2 = t 0 k 1 /t cross and k 3 = t 0 k 1 k rare /t cross yields equation (12).…”

“…The key to understanding the changes in the discharge voltage and current waveforms lies in how the discharge voltage V D is split between the cathode sheath and the ionization region (IR). The presence of a transverse magnetic field enables a potential drop to exist outside the cathode sheath [9][10][11][12]. In sputtering magnetrons, this potential outside the sheath is denoted as V IR , where the subscript IR signifies the ionization region in the vicinity of the cathode target.…”

Speeding-up direct implicit particle-in-cell simulations in bounded plasma by obtaining future electric field through explicitly propulsion of particles

“…The damped explicit method may be useful in certain specific plasma studies, such as magnetron discharges, where a small time-step ω ce ∆t = 0.2 is required to capture the dynamics of the system accurately, [36] where ω ce represents electron cyclotron frequency. In this case, the advantages of traditional direct implicit methods are limited since a very large timestep ω ce ∆t 0.2 is not allowed.…”