MechE PhD Prospectus Defense: Hagen Gress

TITLE: Stochastic and Deterministic Dynamics of Polymeric and Solid-State Micro-/Nano-Mechanical Resonators

ABSTRACT: Micro- and nano-electromechanical systems (MEMS/NEMS) resonators con-stitute a key component in a wide range of sensing applications. Maximizing MEMS/NEMS sensitivity requires precise characterization of their mechani-cal properties, a thorough understanding of the resolution limits imposed by noise, and robust mechanisms to actuate and detect oscillatory motion. With recent advances in polymer science and additive manufacturing, polymeric res-onators have emerged as a viable alternative to their solid-state counterparts. In this thesis work, we provide a comparative study of polymeric and solid-state MEMS/NEMS resonators. We focus on the stochastic dynamics of their thermal displacement fluctuations, the distinct mechanical properties of poly-meric systems, and the development of polymeric resonators with integrated electromechanical transducers. First, we investigate the Brownian motion of nanomechanical solid-state res-onators immersed in a viscous fluid. We optically measure the thermal displace-ment fluctuations of the first 12 eigenmodes of doubly-clamped silicon nitride beams in vacuum, air, and water. By matching the measured eigenfrequencies in vacuum to a tensioned Euler-Bernoulli beam theory, we extract the Young’s modulus and tension. We then combine the hydrodynamic function of an os-cillating cylinder in a viscous fluid with the fluctuation-dissipation theorem to predict the power spectral densities (PSDs) of all modes in air and water. The excellent agreement between theoretical predictions and measurements leads us to conclude that, within our experimental parameter range, the Brownian force noise exhibits a colored PSD due to the “memory” of the fluid, while remaining mode-independent and spatially uncorrelated. Next, we extend our investigation of thermal displacement fluctuations to polymeric resonators. Analogous to our analysis of silicon nitride beams, we measure the eigenfrequencies of several eigenmodes and match them to a ten-sioned plate theory to extract the Young’s modulus and tension of molecularly thin polyaramid membranes. Complementary experiments, where membranes are quasi-statically deflected by gas pressure, reveal how polymer-substrate ad-hesion affects mechanical resonances. Our devices represent a convincing path toward molecular-scale polymeric NEMS with high mechanical strength, low density, and synthetic processability. Finally, we address the challenge of integrating electromechanical transduc-ers into polymeric systems. Using direct laser writing, we fabricate doubly-clamped beam resonators with sub-micrometer resolution. A stencil mask is in-corporated into the design, enabling the formation of conductive electrodes for electrothermal actuation and piezoresistive sensing through a single-step gold deposition on top of the printed geometry. These self-actuating, self-sensing structures are characterized in terms of their resonance frequencies, quality fac-tors, and electromechanical transduction efficiency. Additionally, we investigate the effect of Joule heating on our devices and measure the frequency response to changes in the surrounding fluid. In conclusion, we present a comprehensive investigation into the stochas-tic and deterministic dynamics of MEMS/NEMS resonators, with a particu-lar focus on the characterization, actuation, and signal detection of polymeric resonators. By bridging the gap between conventional solid-state devices and highly adaptable polymeric systems, our findings contribute to the development of next-generation sensing applications.

COMMITTEE: ADVISOR Professor Kamil Ekinci, ME/MSE; CHAIR Professor Katherine Yanhang Zhang, ME/BME/MSE; Professor J. Scott Bunch, ME/MSE; Professor Joerg J. Werner, ME/MSE; Professor Mark Paul, Virginia Tech Department of Mechanical Engineering