Vibrational Modes of thin Silicon Membranes

Membranes with thicknesses in the range of hundred nanometers and macroscopic lateral size are interesting systems to study the mechanical properties of solids on various length scales. In our experiment a piezo is used to couple in vibrations, which can be observed with a phase-shift interferometer using stroboscopic light. With this technique we image transverse modes of frequencies up to 12 MHz. In general, the observed wave pattern of the membrane deflection will be a superposition of the mode corresponding to the excitation frequency and several higher harmonics. Using a Fourier transformation in time, it is possible to separate these contributions. This way eigenmodes up to the 8th harmonic of the excitation frequency can be imaged. The influence of strain on the dispersion relation is investigated by applying a pressure difference between both sides of the membrane. The results are compared to finite-elements simulations.