Deciphering the mode shapes of vibrations of nanopatterned membrane is paving the way for the applications of nanoscale membrane which rely on particular properties of the vibrational excitations.

The mode shape of bending waves in thin silicon, silicon carbide and silicon nitride membranes is measured as a function of space and time, using a phase-shift interferometer with stroboscopic light. The vibrations are excited by a piezoelectric actuation system that has resonances in the same frequency range as the membranes. We developed a method to separate the contribution of the excitation system from the measured amplitude in order to obtain contribution of the membrane itself. After this disentanglement we retrieve the well-known resonance curves of a damped driven harmonic oscillator. The eigenfrequencies and the Q factor of the membrane can be obtained as well. Contributions of a superposition of the mode corresponding to the excitation frequency and several higher harmonics have been separated and been imaged up to the eighth harmonic of the excitation frequency. With this method we are able to determine the dispersion relation of membrane oscillations in a frequency range up to 12 MHz revealing that depending on the actual frequency the nature of the vibrations may change from a drum-head behavior to a bending -plate behavior. For membranes with non-uniform stress either intrinsically or created by the fabrication procedure), a simple algorithm to obtain a map of the lateral tensor components of the prestress is presented.Here systematic studies of the influence of manufacturing parameters (temperature, surface tension and film thickness) by installing a variable temperature system would be desirable. Also the attenuation of sound emission at the silicon nitride membranes can be investigated further. By the designed micro-structured membranes a two-dimensional phononic crystals can be produced. Further, we can construct membrane waveguides and the scattering of the wave at the defects also can be investigated.


  1. X. Zhang, R. Waitz, F. Yang, et al., Appl. Phys. Lett. 106, 063107 (2015).
  2. R. Waitz, S. Noeßner, M. Hertkorn, O. Schecker, and E. Scheer, Phy. Rev. B 85, 035324 (2012).
  3. Waitz, R., et al. Phy. Rev. Applied 3(4): 044002 (2015).
  4. Yang, F., et al. "Quantitative Determination of the Mechanical Properties of Nanomembrane Resonators by Vibrometry In Continuous Light." arXiv preprint arXiv:1704.05328 (2017). 
  5. Yang F, Rochau F, Huber J S, et al. Spatial modulation of nonlinear flexural vibrations of membrane resonators[J]. Physical review letters, 2019, 122(15): 154301.

Information

Contributors: Fan Yang
Former Contributors: Dr. Reimar Waitz
External Cooperations: Prof. Dr. Weig in Uni Konstanz, Prof. Dr. Gölzhäuser in Uni Bielefeld, Dr. Rastelli, Dr. Blick in Uni Hamburg
Funding: SFB 767 A1
Period: since 2014