Guy Buyle

Computer modelling of magnetron discharges

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.

Recapture of secondary electrons by the target in a DC planar magnetron discharge

Abstract In this paper we describe a simple two-dimensional model that allows the study of the individual secondary electron orbits in a DC planar magnetron discharge. Emphasis is on the recapture of secondary electrons by the target, which is enabled by their small initial energy, because this reduces the effective secondary electron yield as seen by the discharge. This reduction depends strongly on both the position along the race track and the gas pressure and it can be substantial for typical planar magnetron operating conditions. Our simple model allows to conclude that because of the sensitivity of the discharge on the secondary electron yield, the current–voltage characteristic, the spatial distribution as well as the pressure dependence of the planar magnetron discharge will be influenced by recapture.

Hysteresis behavior during reactive magnetron sputtering of Al2O3 using a rotating cylindrical magnetron

Rotating cylindrical magnetrons are used intensively on industrial scale. A rotating cylindrical magnetron on laboratory scale makes it possible to study this deposition technique in detail and under well controlled conditions. Therefore, a small scale rotating cylindrical magnetron was designed and used to study the influence of the rotation speed on the hysteresis behavior during reactive magnetron sputtering of aluminum in Ar∕O2 in dc mode. This study reveals that the hysteresis shifts towards lower oxygen flows when the rotation speed of the target is increased, i.e., target poisoning occurs more readily when the rotation speed is increased. The shift is more pronounced for the lower branch of the hysteresis loop than for the upper branch of the hysteresis. This behavior can be understood qualitatively. The results also show that the oxidation mechanism inside the race track is different from the oxidation mechanism outside the race track. Indeed, outside the race track the oxidation mechanism is only...

Influence of the geometrical configuration on the plasma ionization distribution and erosion profile of a rotating cylindrical magnetron: a Monte Carlo simulation

The ionization distribution of a small scale rotating cylindrical magnetron discharge is simulated by a Monte Carlo based program. The simulation describes the high energy electron trajectories and the interaction between these electrons and the sputtering gas, which finally leads to the ionization distribution. By radial projection of the ionization positions on the target surface, the erosion track dimensions can be correctly simulated. The discrepancy between the simulation and the experiments shows the need to modify the experimental design and to control the alignment between the central axis of the target tube and the magnet configuration in a better way.

Investigation of the sustaining mechanisms of dc magnetron discharges and consequences for I–V characteristics

The influence of the starting conditions and sheath thickness on the magnetron discharge is investigated using a Monte Carlo program. The average number of ionizations caused by an electron emitted from the cathode is calculated. It is shown that the sheath thickness plays a crucial role in the generation of ions and the sustainment of the discharge. An analytical formula is obtained which relates discharge voltage, sheath thickness and ion-induced secondary electron coefficient. From it, a natural explanation for the very steep current-voltage (I-V) characteristic in magnetron discharges follows. Comparison with experiment suggests an anomalous diffusion of electrons across the sheath. The simulations were done for a rotatable cylindrical magnetron, but the results should be valid for planar magnetrons as well.

Simplified model for calculating the pressure dependence of a direct current planar magnetron discharge

A simplified model for the direct current planar magnetron discharge allowing one to simulate the pressure dependence over a wide range is presented. For sufficiently strong magnetic fields, the high energy electrons (HEE), the electrons that are responsible for the ionization, move predominantly in arch shaped regions in between interactions with the discharge gas. This allows one to model the discharge as being built up by arches. The influence of the interactions of the HEE on their motion is modeled by calculating the probabilities for transfer of HEE among the arch shaped regions. In this way the ionization distribution of the electrons emitted at a certain position at the target surface can be calculated. The results of this approach agree well with Monte Carlo results. This modeling of the HEE motion combined with simple schemes for determining the ionization and target erosion forms the core of the simplified model. The model is made self-consistent through iteration. It appears that for a given m...

Calculation of the effective gas interaction probabilities of the secondary electrons in a dc magnetron discharge

In sputter magnetrons the electrons emitted from the target, the so-called secondary electrons (SE), can be recaptured by the target. As a result, not all emitted SE will interact with the discharge gas. The effective gas interaction probability (EGIP) is the probability that an emitted SE interacts with the discharge gas, and thus is not recaptured by the target. To calculate the EGIP an analytical model is developed. The model is verified by comparing its results with those of a Monte Carlo model.The EGIP of an individual SE is strongly, and in a complex manner, dependent on the electric and magnetic field to which the electron is subjected and on its initial starting conditions. Therefore, it is useful to introduce the average EGIP of the discharge which is a weighted average of the individual EGIP values. The influence on the EGIP of different parameters, such as the initial energy of the SE, the electron reflection coefficient and the electric and magnetic field is discussed. For typical discharge conditions at a pressure of 0.5 Pa values for the average EGIP in the range of 0.25–0.35 are found. This means that the recapture probability lies typically between 65% and 75%, showing that it is necessary to take into account this process to accurately model and simulate the magnetron discharge.

Low pressure behaviour of the sputter magnetron discharge

Summary form only given. For successful simulation of the complete magnetron sputter deposition process, the modelling of the plasma is crucial. This is because the position and extension of the plasma, more specific its ionisation distribution, determines the erosion profile, i.e. the area on the target (cathode) from where the atoms are removed due to argon ion bombardment. The pressure dependence of the width of the erosion profile was experimentally studied: it is nearly constant above a certain pressure (0.51 Pa), but below this pressure, the width increases strongly with decreasing pressure. The width of the ionisation distribution, and thus also of the plasma, along the direction parallel with the target surface has the same pressure dependence. As the ionisation of the argon gas is primarily due to the secondary electrons (SE), which are released from the target by impinging ions, we developed a model for simulating the orbits of these SE. This is done by solving the Lorentz equation of motion for charged particles. The magnetic field is calculated analytically, and the electric field is assumed to vary linearly over a known distance. Our simulations show that the arch shaped ionisation region of a single SE, emitted at a certain position at the cathode surface, does not change with pressure. Thus, the change in the plasma must be due to a change of emission profile of the SE. For explaining this change we investigated the SE movement: due to its arch shaped orbit, a SE is brought back towards the surface after one cycloidal bounce. If the initial energy of the SE is set to zero, as is common practice, it is reflected by the combined influence of the electric and magnetic field. However, if the initial energy is given a realistic value (typical 4 eV), the SE can interact with the cathode which can lead to recapture of the SE. This recapture is only possible before a SE undergoes any interaction with the discharge gas. As a result, the effect only appears at low pressures and affects the SE emitted near the centre of the erosion profile more than the ones close to the edge because the first have a shorter cycloidal bounce. Consequently, lowering the operating pressure favours the SE emitted near the edge and they will relatively be more present. This effect causes the change in SE emission profile and the resulting increase in plasma and erosion profile width. Hence, for modelling the magnetically confined plasma of a magnetron discharge at low pressures the small initial energy of the SE has to be taken into account, and should not be set to zero as is usually done in such simulations.