AG Scheer
Mesoscopic Systems

Login |

The study of interaction, nonlinear and dissipation effects in nanomembranes by investigating the dispersion relations of bending waves

Fan Yang

Funding by SFB 767 (A3)

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.

Bending Waves in thin Silicon Membranes

Time dependent surface profile
Time dependent surface profile measured on a silicon membrane vibrating at a frequency of 1 MHz. Click for animation.
R. Waitz, S. Nößner, M. Hertkorn, funding by SFB767

We study the vibrational behavior of membranes with thicknesses in the range of a hundred nanometers and macroscopic lateral size. A piezo is used to couple in vibrations, which we monitor with a phase-shift interferometer using stroboscopic light. With this technique we image transverse modes of frequencies up to 12 MHz. The influence of pre-stress is investigated by applying a pressure difference between both sides of the membrane. Depending on frequency and pre-stress, the membranes show stressed membrane and thin plate behavior.

The experiments identify the eigenfrequencies, mode shapes and the dispersion relation of the bending waves. These results are compared to finite-elements simulations and an analytical model.

Please click the figure for animation.