The effect of thermoelastic internal friction on the Q of micromachined silicon resonators

Abstract

Resonator damping measurements made on flexural beams micromachined from single-crystal silicon are described. A theoretical analysis of thermoelastic internal friction that accurately predicts the measurements that were taken is described. The results of these tests show that thermoelastic internal friction is a fundamental damping mechanism that can determine the quality of high-Q resonators over a range of operating conditions. Single-crystal silicon beams were tested under vacuum conditions over a range of frequencies from 80 kHz to 1.6 MHz and over a range of temperatures from 300 K to 400 K. measured values of Q varied from 10000 to more than 70000 and showed good agreement with theoretical estimates of thermoelastic internal friction. It is concluded that thermoelastic internal friction is a measurable phenomenon in micromachined flexures and should be considered when designing, testing, and evaluating miniature resonators for solid-state sensors.