A novel spatial-distribution-function of electron beam-induced vapor plume for analyzing EBPVD thickness

Ching-Yen Ho,Long-Gen Li,Xiao-Qiong Yu,Bor-Chyuan Chen,Si-Li Fan,Chang-Wei Xiong,Song-Feng Wan,Yu-Feng Shu

doi:10.1063/1.5037826

Abstract

This paper investigates the thickness distribution of substrate coating of electron-beam physical vapor deposition (EBPVD) using a novel spatial-distribution-function, which is different from the empirical modified law. The Knudsen cosine law and empirical modified law were usually used for predicting coating thickness in EBPVD. However, these two laws obtained from experiments and geometric concepts cannot provide the elucidation for physical point of view and all-inclusive spatial-distribution-functions. Therefore, instead of the spatial-distribution-functions based on the Knudsen cosine law for low evaporation rates and empirical modified law for the higher evaporation rates, the spatial distribution function based on the mass diffusion theory is proposed to analyze the coating thickness of EB-induced physical vapor deposition. The coating thicknesses predicted by these spatial-distribution-functions are compared with the data measured by the published papers. The results reveal that the coating thicknesses predicted by the spatial distribution function of the diffusion theory are more consistent with the measured data than these obtained from the spatial distribution function of the empirical modified law. The spatial distribution function proposed by this study is validated by correctly predicting the measured coating thickness for EBPVD of titanium and aluminum.

Highlights

Electron beam has many processing applications such as welding,[1] cutting, drilling, coating,[2] micrstructuring, etc
This paper proposed a spatial distribution function derived from the diffusion theory instead of the Knudsen cosine law and the empirical modified law for the coating thickness prediction of electron beam (EB)
The coating thicknesses are predicted using the distribution function based on the diffusion theory and are compared with the predictions of other models

Summary

INTRODUCTION

Electron beam has many processing applications such as welding,[1] cutting, drilling, coating,[2] micrstructuring, etc. In the Schiller’s model,[12] the coating thickness at a given element directly above and facing the source, which is the reference value for a coating thickness in other elements, can be provided by using the Pulker’s model.[13] Piot et al conducted a Monte Carlo simulation study of the atom emission from the vapour source for the coating thickness distribution using non-Maxwell form of the distribution of vapour atom velocities.[6] Fan et al utilized the direct simulation Monte Carlo (DSMC) method to study the three-dimensional electron beam physical vapor deposition process of yttrium in a vacuum chamber.[14] The paper employed the inverse-power model to describe the interaction between atoms of metal vapors. The experimental data of the coating thickness were employed to validate the spatial distribution function from the diffusion theory for EB-induced physical vapor deposition

ANALYSIS

RESULTS AND DISCUSSION

CONCLUSION