Modeling and Validation of Anisotropic Thin-Film Deposition on Cylindrical Substrates for Predictable Resistance Control in MEMS Fabrication

Precise control of electrical properties in conductive micro-structures is essential for the performance and reliability of micro-electro-mechanical systems (MEMS). However, the nature of anisotropic physical vapor deposition (PVD), such as electron-beam or thermal evaporation on curved or wire-like substrates, complicates the prediction of thin-film morphology and resulting electrical properties. This study develops and validates a geometrically explicit deposition model describing film growth on cylindrical substrates using a generalized pseudo-Lambertian cosine emission profile. Analytical expressions for local film thickness are derived as functions of deposition time, substrate geometry, and source collimation. Monte Carlo simulations confirm that the model accurately reproduces the deposition profile observed with simulated data ($R^2=0.99$). A closed-form expression for resistance as a function of deposition parameters was also derived, integrating the Fuchs–Sondheimer and Mayadas–Shatzkes (FS-MS) frameworks to account for thin-film electron scattering and grain-boundary effects. Experimental validation was performed via electron-beam evaporation of gold onto cylindrical glass-core wires, with measured resistances spanning $10\space \Omega$ to $1 \space k\Omega$ across films $70$ to $3000$~nm thick. The FS-MS predicted resistances exhibited a Pearson correlation of $R=0.983$ ($p<0.001$) with empirical measurements, confirming the model’s predictive accuracy. Additionally, this study develops an empirical mathematical model that captures the anisotropic behavior of PVD deposition on cylindrical surfaces. The model enables predictive control of thin-film resistivity in MEMS and bio-MEMS structures and offers a simulation framework that generalizes conventional planar thin-film modeling to complex, three-dimensional microfabrication topographies.