Analysis of contributions of nonlinear material constants to temperature-induced velocity shifts of quartz surface acoustic wave resonators

• TOEs were found to contribute most significantly to the temperature-induced shifts.
• The contributions from the TOD and EL constants were found to be negligible.
• The TOPs were found to make a good contribution to the temperature-induced shifts for some cases.
• For X-cut SAW resonators, c222 and c134 contribute maximum and minimum compared with other TOEs.

In this paper, we examine the significance of the various higher-order effects regarding calculating temperature behavior from a set of material constants and their temperature coefficients. Temperature-induced velocity shifts have been calculated for quartz surface acoustic wave (SAW) resonators and the contributions of different groups of nonlinear material constants (third-order elastic constants (TOE), third-order piezoelectric constants (TOP), third-order dielectric constants (TOD) and electrostrictive constants (EL)) to the temperature-induced velocity shifts have been analyzed. The analytical methodology has been verified through the comparison of experimental and analytical results for quartz resonators. In general, the third-order elastic constants were found to contribute most significantly to the temperature-induced shifts in the SAW velocity. The contributions from the third-order dielectric constants and electrostrictive constants were found to be negligible. For some specific cases, the third-order piezoelectric constants were found to make a significant contribution to the temperature-induced shifts. The significance of each third-order elastic constant as a contributor to the temperature-velocity effect was analyzed by applying a 10% variation to each of the third-order elastic constants separately. Additionally, we have considered the issues arising from the commonly used thermoelastic expansions that provide a good but not exact description of the temperature effects on frequency in piezoelectric resonators as these commonly used expansions do not include the effects of higher-order material constants.