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In modeling direct current (dc) discharges, such as dc magnetrons, a current-limiting device is often neglected. In this study, it is shown that an external circuit consisting of a voltage source and a resistor is inevitable in calculating the correct cathode current. Avoiding the external circuit can cause the current to converge (if at all) to a wrong volt-ampere regime. The importance of this external circuit is studied by comparing the results with those of a model without current-limiting device. For this purpose, a 2d3v particle-in-cell/Monte Carlo collisions model was applied to calculate discharge characteristics, such as cathode potential and current, particle fluxes and densities, and potential distribution in the plasma. It is shown that the calculated cathode current is several orders of magnitude lower when an external circuit is omitted, leading to lower charged particle fluxes and densities, and a wider plasma sheath. Also, it was shown, that only simulations with external circuit can bring the cathode current into a certain plasma regime, which has its own typical properties. In this work, the normal and abnormal regimes were studied.

In this paper, some modelling approaches to describe direct current (dc) magnetron discharges developed in our research groups will be presented, including an analytical model, Monte Carlo simulations for the electrons and for the sputtered atoms, a hybrid Monte Carlo-fluid model and particle-in-cell-Monte Carlo collision simulations. The strengths and limitations of the various modelling approaches will be explained, and some characteristic simulation results will be illustrated. Furthermore, some other simulation methods related to the magnetron device will be briefly explained, more specifically for calculating the magnetic field distribution inside the discharge, and for describing the (reactive) sputtering.

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In this paper, an overview is given of different modeling approaches used for describing gas discharge plasmas, as well as plasma‐surface interactions. A fluid model is illustrated for describing the detailed plasma chemistry in capacitively coupled rf discharges. The strengths and limitations of Monte Carlo simulations and of a particle‐in‐cell–Monte Carlo collisions model are explained for a magnetron discharge, whereas the capabilities of a hybrid Monte Carlo–fluid approach are illustrated for a direct current glow discharge used for spectrochemical analysis of materials. Finally, some examples of molecular dynamics simulations, for the purpose of plasma‐deposition, are given.

‘Bohm diffusion’ causes the electrons to diffuse perpendicularly to the magnetic field lines. However, its origin is not yet completely understood: low and high frequency electric field fluctuations are both named to cause Bohm diffusion. The importance of including this process in a Monte Carlo (MC) model is demonstrated by comparing calculated ionization rates with particle-in-cell/Monte Carlo collisions (PIC/MCC) simulations. A good agreement is found with a Bohm diffusion parameter of 0.05, which corresponds well to experiments. Since the PIC/MCC method accounts for fast electric field fluctuations, we conclude that Bohm diffusion is caused by fast electric field phenomena.

A combined Monte Carlo (MC)/analytical surface model is developed to study the plasma processes occurring during the reactive sputter deposition of TiO x thin films. This model describes the important plasma species with a MC approach (i.e. electrons, Ar + ions, O + 2 ions, fast Ar atoms and sputtered Ti atoms). The deposition of the TiO x film is treated by an analytical surface model.The implementation of our so-called multi-species MC model is presented, and some typical calculation results are shown, such as densities, fluxes, energies and collision rates. The advantages and disadvantages of the multi-species MC model are illustrated by a comparison with a particle-in-cell/Monte Carlo collisions (PIC/MCC) model. Disadvantages include the fact that certain input values and assumptions are needed. However, when these are accounted for, the results are in good agreement with the PIC/MCC simulations, and the calculation time has drastically decreased, which enables us to simulate large and complicated reactor geometries.To illustrate this, the effect of larger target-substrate distances on the film properties is investigated. It is shown that a stoichiometric film is deposited at all investigated target-substrate distances (24, 40, 60 and 80 mm). Moreover, a larger target-substrate distance promotes film uniformity, but the deposition rate is much lower.

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