Topology optimization of nanomechanical resonators

Abstract

Nanomechanical resonators are used in high-precision sensing and emerging quantum experiments, where performance strongly depends on achieving a very high Quality Factor (Q), i.e., minimal energy loss. One way of achieving high Q is dissipation dilution, where tensile prestress reduces the relative losses through bending. This thesis investigates how topology optimization can be improved to design resonator geometries with enhanced dissipation dilution. A key challenge in conventional density-based optimization is the appearance of “grey” regions (intermediate volume fractions): these regions can temporarily boost performance during optimization, but are typically forced out to obtain manufacturable solid-void designs. In this work, these intermediate volume fractions are given a physical meaning by assigning them a manufacturable microstructure through homogenization, leading to designs that are not restricted to purely solid-void layouts. Using this homogenization based optimization approach, the optimized designs achieve 20% - 40% higher Q factor compared to solid-void results under comparable setting. The thesis also studies how volume and frequency constraints influence the final topology, and analyses instability issues related to localized compressive stresses, and proposes mitigation strategies. Finally, the thesis explores graphene resonators as an alternative to silicon nitride resonators, motivated by graphene’s ultra-low mass and strong tensile properties, and discusses practical design strategies to obtain a high performing resonator.