Ionization region model of high power impulse magnetron sputtering of copper

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The ionization region model (IRM) is applied to model a high power impulse magnetron sputtering discharge with a tungsten target. The IRM gives the temporal variation of the various species and the average electron energy, as well as internal discharge parameters such as the ionization probability and the back-attraction probability of the sputtered species. It is shown that an initial peak in the discharge current is due to argon ions bombarding the cathode target. After the initial peak the W+ ions become the dominating ions and remain as such to the end of the pulse. We demonstrate how the contribution of the W+ ions to the total discharge current at the target surface increases with increased discharge voltage for peak current density JD,peak in the range 0.33 – 0.73 A/cm2. For the sputtered tungsten the ionization probability increases, while the back-attraction probability decreases with increasing discharge voltage. Furthermore, we discuss the findings in terms of the generalized recycling model and compare to experimentally determined deposition rates and find good agreement.

Section: Model Resultssupporting

confidence: 67%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Modeling of high power impulse magnetron sputtering discharges with tungsten target

Babu

Rudolph

Lundin

et al. 2022

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“…Despite significant progress in recent years [11][12][13][14][15][16][17][18][19][20][21][22], comprehensive modeling and simulation of HiPIMS is still in its infancy. Given the complex mechanisms which are involved, this statement may not be very surprising.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic quasi-equilibria in high power magnetron discharges: a generalized Poisson–Boltzmann relation

Köhn

Krüger

Eremin

et al. 2023

The Poisson-Boltzmann equation is a nonlinear partial differential equation that describes the equilibria of conducting fluids. Using a thermodynamic variational principle based on the balances ofparticle number,entropy, and electromagnetic enthalpy, it can also be justified for a wide class of unmagnetized technological plasmas [Köhn et al., Plasma Sources Sci.~Technol.~\textbf{30}, 105014 (2021)].This study extends the variational principle and the resulting Poisson-Boltzmann equation to high power magnetron discharges as used in planar high power pulsed magnetron sputtering (HiPIMS). The example in focus is that of a circular high power magnetron.The discharge chamber $\mathcal{V}$ and the \LB magnetic field are assumed to be axisymmetric. The plasma dynamics need not share the symmetry.The domain $\mathcal{V}$ is split into the ionization region $\mathcal{V}_\mathrm{ir}$ close to the cathode where electrons are confined,i.\,e., can escape from their magnetic field lines only by slow processes such as drift and diffusion, and the outer region $\Vor=\mathcal{V}\!\setminus\!\mathcal{V}_\mathrm{ir}$, where the electrons are largely free and the plasma is cold. \LBWith regard to the dynamics of the electrons and the electric field, a distinction is made between a fast thermodynamic and a slow dissipative temporal regime.The variational principle established for the thermodynamic regime is similar to its counterpart for unmagnetized plasmas but takes magnetic confinement explicitly into account by treating the infinitesimal flux tubes of $\mathcal{V}_\mathrm{ir}$ as individual thermodynamic units.The obtained solutions satisfy a generalized Poisson-Boltzmann relation and represent thermodynamic equilibria in the fast regime. However, in the slow regime, they must be interpreted as dissipative structures.The theoretical characterization of the dynamics is corroborated by experimental results on high power magnetrons published in the literature. These results are briefly discussed to provide additional support.

“…The IRM proposed in [26][27][28] for HiPIMS discharges is taken to study the electrical and kinetic properties of s-and us-HiPIMS plasma. The IRM is a time-dependent, spatially averaged model based on the simultaneous solution of ordinary differential equations for neutral and charged particles (continuity equations for number density) with the power balance equation for the electron temperature.…”

Section: Model Descriptionmentioning

confidence: 99%

Ion current density on the substrate during short-pulse HiPIMS

Oskirko

Kozhevnikov

Работкин

et al. 2023

The probe method for the ion current density measurements and a theoretical calculations of the dynamics of neutral and charged plasma particles by ionization region model (IRM), are used to study high-power impulse magnetron sputtering (HiPIMS) short and ultra-short pulse discharges. The paper studies reasons for the increase in the average ion current density on the substrate at shorter pulses, when the average discharge power does not change. HiPIMS pulses are applied to the copper target at constant values of the average discharge power (1000 W) and the peak current (150 А), respectively, while the pulse time of the discharge voltage ranges from 4 to 50 µs. A power supply with low output inductance is designed to generate ultra-short pulses. It is shown that the discharge pulse time reduction leads to a multiple growth (from 2 to 7 mA/cm2) in the average ion current density onto the substrate and the growth in the peak intensity of Ar+, Cu+ and Cu2+ recorded by optical emission spectroscopy. A theoretical model of this effect is based on the spatially averaged IRM, which takes into account afterglow effects. According to theoretical calculations, the increase in the average ion current density onto the substrate is determined by the plasma dissipation in the ionized region after the pulse end. Also, explained is the decrease in the copper deposition rate from 180 to 60 nm/min with decreasing pulse time from 40 to 4 µs. A comparison of the experimental data and those obtained earlier, shows that the suggested dependences of the ion current density and deposition rate on the HiPIMS pulse time, are typical for discharge systems with different cathode materials and configurations, i.e., for single- and dual-magnetron systems. This indicates to a common nature of the phenomena observed and additionally confirms the results obtained.