Quantitative signal extraction in the dynamic range of nanomechanical systems by free and constrained fitting

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We present a free and a constrained fitting procedure for determining the intrinsic response of a nanomechanical systems subject to noise and other environmental influences. We demonstrate that applying the free fitting procedure to the measured frequency response of amorphous silicon nitride (SiN) nanomembranes at varying pressure enables us to disentangle the intrinsic membrane vibration properties from the system response. This approach gives quantitative access to the eigenfrequency, quality factor, coupling strength to the excitation system as well as to system noise. The validity of physical models for quantities such as excitation, fluctuations, and damping can be verified with the help of the constrained fitting procedure that implies additional mathematical relationships between the fit parameters. We verify the performance of the constrained fitting procedure for amorphous SiN membrane resonators tested in various experimental setups.

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ISO 690YANG, Fan, Reimar WAITZ, Mengqi FU, Elke SCHEER, 2023. Quantitative signal extraction in the dynamic range of nanomechanical systems by free and constrained fitting. In: Sensors and Actuators A: Physical. Elsevier. 2023, 354, 114307. ISSN 0924-4247. eISSN 1873-3069. Available under: doi: 10.1016/j.sna.2023.114307
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@article{Yang2023Quant-67209,
  year={2023},
  doi={10.1016/j.sna.2023.114307},
  title={Quantitative signal extraction in the dynamic range of nanomechanical systems by free and constrained fitting},
  volume={354},
  issn={0924-4247},
  journal={Sensors and Actuators A: Physical},
  author={Yang, Fan and Waitz, Reimar and Fu, Mengqi and Scheer, Elke},
  note={Article Number: 114307}
}
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    <dcterms:abstract>We present a free and a constrained fitting procedure for determining the intrinsic response of a nanomechanical systems subject to noise and other environmental influences. We demonstrate that applying the free fitting procedure to the measured frequency response of amorphous silicon nitride (SiN) nanomembranes at varying pressure enables us to disentangle the intrinsic membrane vibration properties from the system response. This approach gives quantitative access to the eigenfrequency, quality factor, coupling strength to the excitation system as well as to system noise. The validity of physical models for quantities such as excitation, fluctuations, and damping can be verified with the help of the constrained fitting procedure that implies additional mathematical relationships between the fit parameters. We verify the performance of the constrained fitting procedure for amorphous SiN membrane resonators tested in various experimental setups.</dcterms:abstract>
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