Tzu-Hou Chan¹, Wen-Yi Tai¹, Chang-Ze Hong¹, Yao-Kuang Yang¹, Chien-Jen Tang^2
1Dah Young Vacuum Equipment Co., Ltd., Taichung, Taiwan
²Feng Chia University, Taichung, Taiwan
As curved optical components and freeform surface designs are increasingly adopted in automotive displays and advanced optical systems, achieving thickness uniformity in multilayer interference coatings on non-planar substrates has become critical to overall optical performance. In sputtering processes, the angular distribution of sputtered particles, combined with local variations in surface normal orientation and geometric shadowing effects, leads to spatial variations in deposition flux across three-dimensional (3D) substrates. These factors make film thickness distribution difficult to predict and control, thereby affecting optical performance and manufacturing yield. In multilayer interference coatings, thickness deviations can accumulate layer by layer, amplifying spectral shifts and color non-uniformity. Conventional process optimization typically relies on iterative trial-and-error deposition and measurement, lacking a predictive thickness model that simultaneously accounts for substrate geometry and deposition flux distribution. Consequently, systematic thickness compensation and mask design remain challenging.
In this study, a thickness simulation framework, implemented in Film-thickness Accurate Simulation Tool (FAST), is established based on geometric view-factor analysis and particle flux distribution modeling. The computational model incorporates substrate geometry, sputtering target configuration, and mask geometry to predict film thickness distribution on 3D substrates within a sputtering system. The framework further enables correlation analysis between thickness deviations and the resulting variations in optical performance. Experimental validation was carried out using the ARMS Coating Machine developed by Dah Young Vacuum. The system features a 1650 mm inner-diameter vacuum chamber equipped with a high-density ICP plasma source and four pairs of 750 mm cylindrical sputtering cathodes, enabling multi-material deposition for both high- and low-refractive-index films (e.g., Si-, Ti-, Nb-, and Al-based materials) under mass-production conditions. The maximum deviation between simulated and measured thickness distributions was controlled within ±0.5%. For a high-curvature substrate with dimensions of approximately 200 mm × 126 mm and a radius of curvature of ~97 mm, mask optimization based on the simulation reduced in-plane thickness non-uniformity from 34% to 9% and significantly improving the uniformity of multilayer reflectance peaks.
The predictive and compensation framework implemented in FAST provides a practical approach for assessing process feasibility in curved optical designs prior to fabrication, thereby reducing trial-and-error costs and enhancing controllability and production stability of sputtering processes for complex 3D geometries.