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

Abstract

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/sup -6/[°C/sup -1/]. This value was quite comparable to those reported in previous literatures, and much more so if the specimen temperature is calibrated more exactly.