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

We present a free and a constrained fitting procedure for determining the intrinsic response of a nanome-chanical 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.

Automated summary

We propose a free and constrained fitting procedure to determine the intrinsic response of nanomechanical systems subjected to noise and other environmental influences. The free fitting procedure allows us to separate the intrinsic vibration properties from the system response by analyzing the measured frequency response of amorphous silicon nitride nanomembranes at different pressures. The constrained fitting procedure, which includes additional mathematical relationships between fit parameters, can be used to validate physical models for excitation, fluctuations, and damping.