Modeling of a continuous physical vapor deposition process: Mass transfer limitations by evaporation rate and sonic choking

Abstract

• Novel evaporation boundary condition is proposed to consider Hertz-Knudsen limitation. • A comprehensive numerical model for continuous PVD processes in OpenFoam is presented. • Non-isentropic losses reduce discharge; this effect decreases with melt temperature. • The isentropic overestimate is 110%–150%, that of the new CFD model only 30%. • Numerical model predictions are relatively insensitive to unknown process parameters. In recent years, Physical Vapor Deposition has been advanced to a continuous process which makes it amenable for in-line, high-quality and energy-efficient galvanization. To achieve the high and uniform mass flow required for in-line production, a Vapor Distribution Box is used, in which the zinc is evaporated. The zinc fills the Vapor Distribution Box at a relatively high pressure and leaves into the coating chamber via nozzles. A reliable modeling approach that can be used in the design and optimization of Vapor Distribution Boxes is as yet not available in the literature. The present paper analyses which phenomena play a major role and therefore have to be included in a simulation model of continuous Physical Vapor Deposition processes, and identifies process parameters which have a significant impact on deposition rate and uniformity. To this end, a model for the flow and heat transfer is developed based on the numerical solution of the compressible Navier–Stokes-Fourier equations in combination with the Launder and Sharma low-Reynolds k- ∊ turbulence model, using the open-source CFD-library OpenFOAM. To account for the vapor mass flow to be limited by both evaporation and sonic choking, a novel inlet boundary condition is proposed based on the Hertz-Knudsen condition. Results from the CFD model are compared to those of analytical models based on isentropic flow, the influence of various modeling parameters is evaluated against experiments, and sensitivity of the process to various process parameters studied. The proposed numerical model predicts mass flow rates with a much better accuracy than analytical models previously proposed in the literature. The latter overpredict the mass flow rate by a factor of 2.1–2.5, whereas the proposed numerical model overpredicts only by a factor of 1.3. Next to the novel Hertz-Knudsen boundary condition, the inclusion of viscous effects is found to be crucial to achieve this improvement, since viscous effects – especially in the boundary layer inside the nozzles – severely reduce the mass flow. The numerical model is shown to be only weakly sensitive to uncertainties in the evaporation coefficients and metal vapor viscosity. For the device studied, the mass flow discharge efficiency was found to be relatively low ( ≈ 40 % ). To increase this efficiency, viscous losses in the nozzle boundary layers have to be reduced, for instance by employing shorter or a bigger radius nozzles (possibly impairing nozzle-to-nozzle uniformity) or by employing a higher melt temperature and vapor pressure.