Dissipation dilution-driven topology optimization for maximizing the Q factor of nanomechanical resonators
H.J. Algra (Technion Israel Institute of Technology)
Zichao Li (TU Delft - Dynamics of Micro and Nano Systems)
M Langelaar (TU Delft - Computational Design and Mechanics)
Farbod Alijani (TU Delft - Dynamics of Micro and Nano Systems)
AM Aragon (TU Delft - Computational Design and Mechanics)
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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.
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