Resonant Frequencies of a Nanoscale Fractal Resonator

Vassil Tzanov1, Jordi Llobet2, Francesc Torres1, Francesc Perez-Murano3, Nuria Barniol1
1Universitat Autonoma de Barcelona, Barcelona, Spain
2Iberian Nanotechnology Laboratory, Braga, Portugal
3Institut de Microelectronica de Barcelona, Spain
Published in 2020

A top-down nanosize mechanical resonator has been fabricated with a shape of a fractal. The self-similar structure consists of star-polygons and it is suspended over a 10 μm trench and has width of 12 μm. Its thickness of 0.040 μm is defined by the fabrication process and prescribes Young’s modulus of 76 GPa (fit by COMSOL Multiphysics®) which is significantly lower than the value of the bulk material. The mechanical resonator is electrostatically excited and the resulted multiple resonant peaks spread between 2 MHz and 24 MHz. The COMSOL Multiphysics® MEMS Module has been used to vary material properties and residual stress in order to fit the eigenfrequencies of the model with the resonance peaks detected experimentally. Moreover, by using COMSOL Multiphysics®we show how the symmetry of the device and the residual stress affect the order at which the vibration modes appear in the spectrum. Furthermore, by using our model, the possibility for an electrical read out of the device was successfully tested. The experimental measurements and simulations proved that the device can resonate at many different excitation frequencies allowing multiple operational bands.

https://doi.org/10.3390/nano10040811

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