| Background, Motivation Objective Resonating beam structures using Microelectromechanical Systems (MEMS) technology have been receiving strong attention to obtain miniature high performance resonators for timing and sensing applications [1][2]. Piezoelectric materials are gaining an increasing interest because of better capacitance ratio (Co/Cm) and impedances suitable for circuits. Increasing the Q-factor is a key to improve phase noise performance for frequency references and to improve the signal-to-noise ratio for sensors. For beams thermo elastic damping (TED) is often the dominant energy loss mechanism that limits the device Q-factor. The effect of TED for a vibrating beam is shown in Fig.1 (a). Within the beam cross section the opposite sign of the axial strain causes a temperature gradient which leads to an irreversible heat flux. The understanding of TED including the effect of piezoelectricity and pyroelectricity are crucial for an optimized design. Statement of Contribution/Method In this study we introduce a thermo piezo elastic damping (TPED) analytical model for piezoelectric beams. Starting from the Euler Bernoulli theory for simple thermo elastic beams developed by Lifshitz and Roukes [] we consider the Piezo Thermo Elastic constitutive equations and derive a closed-form expression for the Q-factor of a beam. Results We applied the theory to beams of aluminum nitride (AlN), a c-axis oriented piezoelectric and pyroelectric material, because of its CMOS compatible properties. The model shows that the piezoelectric and pyroelectric effects, for a fixed-fixed beam, reduce the Q-factor by an amount of 15%. We confirm that by setting the piezoelectric and pyroelectric coefficients to zero, our model coincide with the solution derived by Lifshitz and Roukes. Discussion and Conclusion Our results demonstrate the importance of the TPED as energy loss mechanism for miniature resonators. The theory shows that the effect of TPED can be minimized by selecting for resonating beam based structures such as Double-ended Tuning Fork (DETF) the optimal geometrical dimensions. [1] A. Isobe, K. Asai, H. Matsumoto, and N. Shibagaki, IEEE Ultrasonics Symposium 2006, pp. 560-563 [2] Ron Lifshitz and M. L. Roukes, Physical review B, Vol.61, n. 8, pp. 5600-5609 |