Effects of stress on the temperature coefficient of frequency in double clamped resonators

This paper presents a theoretical framework for evaluating the temperature coefficient of frequency (TCf) of double clamped resonators due to stresses induced by the die and through die packaging. It is desirable to have a zero TCf such that the resonator frequency is stable over a broad temperature range. The TCf depends on how the resonator's material properties, dimensions, and stresses change with temperature. A passive method of using thin film induced stresses in an encapsulated resonator to compensate for material softening is explored. By using a combination of finite element and analytical models it is possible to predict the TCf and improve thermal frequency stability of micromachined resonators.

[1]  Cam Nguyen,et al.  Micromechanical Signal Processors , 1994 .

[2]  Wan-Thai Hsu,et al.  Geometric stress compensation for enhanced thermal stability in micromechanical resonators , 1998, 1998 IEEE Ultrasonics Symposium. Proceedings (Cat. No. 98CH36102).

[3]  Kenneth Meade Lakin,et al.  Temperature compensated bulk acoustic thin film resonators , 2000, 2000 IEEE Ultrasonics Symposium. Proceedings. An International Symposium (Cat. No.00CH37121).

[4]  Wan-Thai Hsu,et al.  Stiffness-compensated temperature-insensitive micromechanical resonators , 2002, Technical Digest. MEMS 2002 IEEE International Conference. Fifteenth IEEE International Conference on Micro Electro Mechanical Systems (Cat. No.02CH37266).

[5]  D. J. Gorman.  Free vibration analysis of beams and shafts , 1975 .

[6]  M. Madou.  Fundamentals of microfabrication , 1997 .