Evaluation of elastic properties and temperature effects in Si thin films using an electrostatic microresonator

Laterally driven microresonators were used to estimate the temperature-dependent elastic modulus of single-crystalline Si for microelectromechanical systems (MEMS). The resonators were fabricated through surface micromachining from silicon-on-glass wafers. They were moved laterally by alternating electrostatic force at a series of frequencies, and then a resonance frequency was determined, under temperature cycling in the range of 25°C to 600°C, by detecting the maximum displacement. The elastic modulus was obtained in the temperature range by Rayleigh´s energy method from the detected resonance frequency. At this time, the temperature dependency of elastic modulus was affected by surface oxidation as well as its intrinsic variation: a temperature cycle permanently reduces the resonance frequency. The effect of Si oxidation was analyzed for thermal cycling by applying a simple composite model to the measured frequency data; here the oxide thickness was estimated from the difference in the resonance frequency before and after the temperature cycle, and was confirmed by field-emission scanning electron microscopy. Finally, the temperature coefficient of the elastic modulus of Si in the <110> direction was determined as -64×10^-6[°C^-1]. This value was quite comparable to those reported in previous literatures, and much more so if the specimen temperature is calibrated more exactly.