On Temperature Effects in a MEMS Ring Gyroscope

We report on experimental and analytical investigation of temperature effects in a 3.2mm-diameter, 57kHz ring gyroscope equipped with 16 capacitive stress sensors. According to the well-known ~-60ppm/°C temperature dependency of Young's modulus of silicon, the temperature coefficient of frequency (TCF) is expected to be ~-30ppm/°C. Our experimentally observed TCFs, however, tend to be ~-14ppm/°C, pointing to thermal stresses as the countering factor. To find the root cause of the measured TCFs, we develop an analytical framework that enables us to calculate the temperature-induced stiffness variations, considering both thermal and mechanical strains. The model successfully predicts changes and hysteretic behavior of frequency over temperature using the measured stress and temperature data.