Photothermal Study of Free and Forced Elastic Vibrations of Microcantilevers

Dynamic free (spontaneous) and forced (optically excited) elastic vibration spectra of a cantilever (CL) were studied. The amplitude and phase elastic displacements of silicon CLs were measured as a function of the modulation frequency with and without optical excitation. Typically, four obvious peaks can be observed in the elastic vibration spectrum. The first peak represents the forced vibrations at the same frequency as the modulation of laser excitation, while two other peaks are the third and fifth harmonics. One small peak is the first natural resonance of the CL (free vibrations, spontaneous vibrations). The amplitude of elastic vibrations without optical excitation changes with frequency, and it is possible to distinguish two frequency regions. In the high frequency range above 10 kHz, the amplitude elastic vibration spectra are not a function of the frequency which is typically for white noise. The white noise level, which corresponds to the thermomechanical noise, was found. The forced vibrations are precisely studied by modulated optical excitation where the frequency is varied from 3 kHz to 45 kHz and by measuring the response with a lock-in-amplifier (measuring the amplitude and phase of the elastic vibrations). The optically excited elastic vibrations are the consequence of thermal and electronic elastic effects in the silicon CL. The mechanical response of the optically excited CL was modeled with good approximation by a damped harmonic oscillator. The experimental amplitude and phase spectra were fitted with theoretical curves, and the quality factor near the natural (resonance) frequency was obtained.