Modeling of Continuous Physical Vapor Deposition

Abstract

Physical Vapor Deposition (PVD) is the resublimation of a substance on a cold surface coating it with a thin solid layer. PVD coatings are utilized in industry to modify surface properties and appearance. Since the industrial process requires vacuum conditions, it has been mainly conducted in a batch process. Recently, PVD is considered a promising alternative coating technology to the hot-dip galvanization in order to apply a corrosion protective coating on steel. However, a continuous process is missing to manufacture protective coatings for strip steel on an industrial scale using PVD.

First approaches suggest the following process: The steel strip is pulled into a vacuum chamber through air-tight seals to ensure a non-reactive coating atmosphere and avoid impurities; then its surface is treated to obtain high adhesion during the coating process; afterwards it passes a Vapor Distribution Box (VDB) from which vapor jets (or plumes) emerge and coat the steel surface; eventually the strip leaves the vacuum chamber again via air-tight seals, is coiled and shipped.

To make this process usable on a large scale - or even superior to galvanization - multiple challenges need to be overcome: ensuring the tightness of the seals, cleaning the strip, preventing stray coating of the vacuum chamber, guaranteeing a uniform coating thickness, and providing a uniform high vapor mass flow to maintain a high speed of the production line.

This thesis tackles the last challenge by modeling the vapor transport both inside the VDB and inside the vacuum chamber.

First the flow inside the VDB is modeled using a SIMPLE-/PISO-based algorithm for transsonic flows. To account for the evaporation at the melt surface, a boundary condition for the inlet pressure is implemented based on the Hertz-Knudsen equation. The total mass flow rate for different melt temperatures is compared to experimental values as well as an analytical, isentropic estimation. Furthermore, the sensitivity of the model to material properties and process conditions is studied.

The total mass flow rate of the system is found to depend on evaporation and choking. With higher melt temperatures the total mass flow rate increases. The trend found in the simulations resembles the one from the experiment. Both yield only 33%-54% of the mass flow rate estimated by the analytical isentropic relation. This low efficiency improves with higher melt temperature. A comparison of the pressure loss across the VDB reveals that the main losses appear due to the viscous boundary layer in the nozzles connecting the VDB with the vacuum chamber. The simulation overpredicts the experimental result by a factor of 1.3. This may be due to the used assumption of an idealized value of unity for the evaporation coefficient; a value of approximately 0.3 would produce a better match between simulations and experiments. Impurities found in the experiment may cause this reduction of the evaporation coefficient.

When expanding from the nozzles into the vacuum chamber, the flow accelerates to supersonic speeds and rarefies. We study the interaction of two planar sonic plumes that causes a shock next to the interaction plane. This in turn produces peaks in deposition rate and thus in the coating. Direct Simulation Monte Carlo (DSMC) method is applied for the flow which ranges from continuum at the nozzles to rarefied and free molecular flow downstream. The results are compared to the analytical effusion solution and the inviscid continuum solution from a Riemann solver. The expansion and shock regions of the DSMC simulation are visualized by the Method of Characteristics (MOC). The mass flow distribution as a function of the degree of rarefaction, the nozzle-separation-distance and the inclination of the nozzles is studied.

The DSMC result of plume interaction outside the VDB closely resembles the inviscid continuum solution at low degrees of rarefaction. The flow structure with expansions and shocks coincides, deviations are apparent in the actual number density, velocity and temperature especially in the shock region. With higher rarefaction, the shock structure diminishes and the flow field approaches the free molecular flow field. However, the rarefied flow field is not within the limits of the inviscid continuum and the free molecular flow field, but may exceed them in both deposition peaks and temperature peak in the shock region.
Using the MOC for visualization reveals that with higher rarefaction the shock bends away from the interaction plane which can be explained by the increased temperature in the secondary expansion. While the shock location shifts with the nozzle-separation distance, it merges to one location when scaling it with the nozzle-separation distance. Bending the nozzle outlets towards each other produces a stronger shock starting further upstream, which in turn causes a stronger secondary expansion and thus smoother deposition.

In addition to studying the impact of geometry changes in the PVD setup, the effect of adding a light, inert carrier gas on the plume interaction and the resulting deposition uniformity is investigated. To this end, the carrier-gas mole fraction is varied at a given Knudsen number. Species separation focuses the heavy species along the primary axes, whereas the light inert carrier gas is scattered towards the periphery. Due to the higher mean molecular weight, the speed of sound decreases and consequently the interaction shock occurs farther downstream, is less bent and weaker producing a more uniform deposition profile. Desirable side effects of the carrier-gas are less stray deposition and a higher conductance of the coating material from the inlet nozzle.

The last part of the thesis focuses on the numerical method, since DSMC is accurate but computationally costly. The substitution of the collision step in DSMC with a kinetic relaxation using the Bhatnagar-Gross-Krook (BGK) operator is implemented in order to speed up the algorithm. The choice of the target distribution for the relaxation is crucial. The Maxwellian velocity distribution produces an incorrect Prandtl number; the Ellipsoidal-Stochastical BGK (ES-BGK) corrects for the Prandtl number by taking the stress into account; the Shakov model (S-BGK) corrects by considering the heat flux vector. The implemented models are verified against literature data and evaluated for their accuracy in simulating the interacting plumes case. In addition, we evaluated a hybrid coupling of the various kinetic relaxation models in dense, near-continuum regions with DSMC for rarefied and non-continuum regions. The switching criterion for the hybrid coupling was the gradient-length local Knudsen number. The implemented kinetic models compare well to literature data for rarefied Poiseuille flow. The lower resolution criteria lower the computational cost to approximately 30% of the one of DSMC. For the planar jet interaction, the BGK model (using the Maxwellian target distribution) overestimates the shock strength, the S-BGK model overpredicts the diffusion of the shock, whereas the ES-BGK models results are in good agreement with the DSMC results. This indicates that the velocity sorting and breakdown of temperature isotropy in the expansions have a more significant influence on the flow field than the shock, which skews the velocity distribution. Coupling the kinetic models with DSMC in the highly rarefied regions improves the flow field for the BGK and S-BGK model, but not significantly.

In short, this thesis examines the influence of process conditions, geometry and carrier-gas use on the mass flow rate and deposition uniformity in continuous PVD for coating steel strips with anti-corrosive coatings. It provides modeling tools for the mass transport both inside and outside the VDB which can be used for further investigation and optimization.