FREQUENCY-DEPENDENCE OF THERMAL EXCITATION OF MICROMECHANICAL RESONATORS

A theoretical and experimental study is presented on thermal excitation of micromechanical resonators. It is shown that there is a turnover frequency, omega-t, which is related to the square of the ratio of the penetration depth of the thermal wave into the structure and its thickness. For constant power dissipation at the surface of the structure, the bending moment is independent of the frequency omega at omega << omega-t, while at omega >> omega-t, it is proportional to omega-1. At high frequency we obtain a phase shift of - pi/2. Vibration amplitudes and turnover frequencies measured on clamped beam structures agree well with the theory.