Determination of the temperature coefficient piezoelectric constant TCe<inf>33</inf> to improve thermal 1D acoustic tool for BAW resonator design

This paper presents a full characterization of the thermal parameters to improve the thermal Mason's model for BAW resonator design, in particular, the temperature dependence of the velocity TC(V), the elasticity TC(C ₃₃ ^D ), the piezoelectric coefficient TC(e ₃₃ ) and the permittivity TC(¿ ₃₃ ) for the AlN film. These parameters associated with the piezoelectric theory assesses the TC(e ₃₃ ) coefficient. To do so, the temperature piezoresponse force microscopy (PFM) technique is used to measure the temperature dependence of the (d _33eff ) coefficient. The thermal RF measurement is used to characterize the TC(¿ ₃₃ ) and the ultrasonic picosecond tool with its heating system is used to characterize the TC(C ₃₃ ^D ). Finally, the thermal Mason's model is compared with the experimental response of the BAW resonator.