Criteria determination to choose piezoelectric materials for BAW resonator applications via colored picosecond acoustics

A great number of piezoelectric materials which could be used in the fabrication of BAW resonators were investigated via colored picosecond acoustics technique in order to study the required parameters for designing and fabricating improved devices. These parameters concerns acoustic longitudinal velocity, v_L, elastic stiffness constant, C^D₃₃, intrinsic mechanical loss, tanδ, and electromechanical coupling coefficient, k²_t. We first quantify the effect of the ratio between the wavelength pulse of a femtosecond laser and the period of Brillouin oscillations, λ_p/T. It is found that C^D₃₃ depends linearly on λ_p/T. Then, we deduced novel relations for stiffness constant and mechanical coupling coefficient. Moreover, the determination of different parameters (density, refractive index and v_L) of piezoelectric film is achieved, with good agreement with literature. The optimized conditions for the parameter choice of BAW resonators are found to be: 300?GPa?<?C^D₃₃?<?500?GPa and 1.7?GPa?<?e²₃₃/ε^s₃₃?<?28.5?GPa with λ_p/T?>?37 10³?m/s where e₃₃ and ε^s₃₃ are the piezoelectric constant and the materials permittivity in the direction 3, respectively.