Browsing by Author "Hanay, M. S."

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    Mode-dependent scaling of nonlinearity and linear dynamic range in a NEMS resonator
    Ma, M.; Welles, N.; Svitelskiy, O.; Yanik, C.; Kaya, I. I.; Hanay, M. S.; Paul, Mark R.; Ekinci, K. L. (AIP Publishing, 2024-08-20)
    Even a relatively weak drive force is enough to push a typical nanomechanical resonator into the nonlinear regime. Consequently, nonlinearities are widespread in nanomechanics and determine the critical characteristics of nanoelectromechanical systems' (NEMSs) resonators. A thorough understanding of the nonlinear dynamics of higher eigenmodes of NEMS resonators would be beneficial for progress, given their use in applications and fundamental studies. Here, we characterize the nonlinearity and the linear dynamic range (LDR) of each eigenmode of two nanomechanical beam resonators with different intrinsic tension values up to eigenmode n = 11. We find that the modal Duffing constant increases as n4, while the critical amplitude for the onset of nonlinearity decreases as 1 / n . The LDR, determined from the ratio of the critical amplitude to the thermal noise amplitude, increases weakly with n. Our findings are consistent with our theory treating the beam as a string, with the nonlinearity emerging from stretching at high amplitudes. These scaling laws, observed in experiments and validated theoretically, can be leveraged for pushing the limits of NEMS-based sensing even further.
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    Multimode Brownian dynamics of a nanomechanical resonator in a viscous fluid
    Gress, H.; Barbish, J.; Yanik, C.; Kaya, I. I.; Erdogan, R. T.; Hanay, M. S.; Gonzalez, M.; Svitelskiy, O.; Paul, Mark R.; Ekinci, K. L. (American Physical Society, 2023-10-24)
    Brownian motion imposes a hard limit on the overall precision of a nanomechanical measurement. Here, we present a combined experimental and theoretical study of the Brownian dynamics of a quintessential nanomechanical system, a doubly clamped nanomechanical beam resonator, in a viscous fluid. Our theoretical approach is based on the fluctuation-dissipation theorem of statistical mechanics: we determine the dissipation from fluid dynamics; we incorporate this dissipation into the proper elastic equation to obtain the equation of motion; and the fluctuation-dissipation theorem then directly provides an analytical expression for the position-dependent power spectral density (PSD) of the displacement fluctuations of the beam. We compare our theory to experiments on nanomechanical beams immersed in air and water and obtain excellent agreement. Within our experimental parameter range, the Brownian-force noise driving the nanomechanical beam has a colored PSD due to the "memory"of the fluid; the force noise remains mode independent and uncorrelated in space. These conclusions are not only of interest for nanomechanical sensing but also provide insight into the fluctuations of elastic systems at any length scale.