Casimir Arc Plate Geometry: Computational Analysis of Thickness Constraints for Gold and Silver Nanomembranes in MEMS Applications

TL;DR

This paper analyzes the Casimir interaction in arc-plate geometries relevant to MEMS, deriving thickness constraints for gold and silver nanomembranes to prevent curvature reversal due to Casimir forces.

Contribution

It introduces a theoretical framework combining PFA with NTLO corrections and Kirchhoff-Love theory to evaluate Casimir effects on nanomembranes in MEMS.

Findings

Silver nanomembranes tolerate greater thickness than gold.

Curvature reversal occurs at nanoscale thicknesses.

NTLO corrections improve Casimir force estimation.

Abstract

A theoretical analysis of the Casimir interaction between an arc and plate is conducted, which remains unexplored despite its relevance to Micro-Electro-Mechanical Systems (MEMS) fabrication. The configuration consists of a rigid finite plate and a flexible curved nanomembrane, with radius 100 micrometers, initially concave toward the rigid plate. The maximum thickness is evaluated for which the nanomembrane undergoes a change in curvature: from concave to convex with respect to the plate, due to the Casimir interaction. The Casimir energy for a curved surface is derived using the Proximity Force Approximation (PFA) with next-to-leading-order (NTLO) corrections. Kirchhoff-Love theory for a thin isotropic plate of constant thickness is used to estimate the bending energy. Material-dependent effects on the Casimir interaction are evaluated by comparing Au and Ag plates. The maximum thickness is derived where U_Casimir > U_bending for distances in the range of 0.1-1 micrometers. Results show curvature reversal occurs for nanomembranes with nanoscale thicknesses at the studied distances. Silver nanomembranes tolerate greater thickness than gold nanomembranes due to material-dependent properties. Comparison between NTLO-corrected PFA and perturbative PFA confirms the accuracy of the NTLO approach. The Casimir arc-to-plate geometry in MEMS enables Casimir-based actuation, enhances devices reliability, and prevents stiction. These findings provide thickness constraints for MEMS design and performance, accounting for the Casimir force.