Dissipation Dilution-Driven Topology Optimization for Maximizing the $Q$ Factor of Nanomechanical Resonators

TL;DR

This paper introduces a topology optimization approach for designing nanomechanical resonators with maximized $Q$ factors by leveraging dissipation dilution, considering nonlinear modal stiffness, and applying the method to various geometries.

Contribution

It develops a novel topology optimization framework based on modal stiffness ratios to enhance dissipation dilution in nanomechanical resonators.

Findings

Optimized geometries achieve high $Q$ factors comparable to existing designs.

Trade-offs between resonance frequency and $Q$ factor are characterized.

Full mesh optimization yields symmetric designs with four tethers.

Abstract

The quality factor ($Q$ factor) of nanomechanical resonators is influenced by geometry and stress, a phenomenon called dissipation dilution. Studies have explored maximizing this effect, leading to softly-clamped resonator designs. This paper proposes a topology optimization methodology to design two-dimensional nanomechanical resonators with high $Q$ factors by maximizing dissipation dilution. A formulation based on the ratio of geometrically nonlinear to linear modal stiffnesses of a prestressed finite element model is used, with its corresponding adjoint sensitivity analysis formulation. Systematic design in square domains yields geometries with comparable $Q$ factors to literature. We analyze the trade-offs between resonance frequency and quality factor, and how these are reflected in the geometry of resonators. We further apply the methodology to optimize a resonator on a full hexagonal domain. By using the entire mesh -- i.e., without assuming any symmetries -- we find that the optimizer converges to a two-axis symmetric design comprised of four tethers.