Study of Silicon Cantilevers by the Photoacoustic Elastic Bending Method

Rectangular silicon cantilevers are studied by the photoacoustic (PA) elastic bending method. Experimental signals versus modulation frequency of the excitation optical beam are measured and analyzed in a frequency range from 20 Hz to 50 000 Hz. The procedure for experimental signal correction to eliminate the frequency characteristics of the measuring system is given. The corrected experimental signal shows a good correlation with theoretically calculated PA signal at frequencies below 32 000 Hz. The corrected experimental PA elastic bending signals for cantilevers with different thicknesses are analyzed. The experimental results allow identifying the resonant frequency (the first resonant mode) of the cantilever vibrations. These values are in good agreement with the theoretically computed values. A theoretical model of the optically excited Si cantilever is derived, taking into account plasmaelastic, thermoelastic, and thermodiffusion mechanisms. Dynamic relations for the amplitude and phase of electronic and thermal elastic vibrations in optically excited cantilevers are derived. The theoretical model is compared to the experimental results.