Advanced determination of piezoelectric properties of AlN thin films on silicon substrates

Piezoelectric deformations of thin, aluminum nitride (AlN) layers, on top of a silicon substrate, were studied by numerical calculations and interferometric measurements. Our calculation by finite element method demonstrates that substrate deformation under the top electrode may be comparable to the electric field induced deformation in the thin AlN layer, for a given applied voltage. Simulations also show the effect of a clamped or free substrate condition and the relative contributions of d₃₃ and d₃₁ piezoelectric constants. A Laser scanning vibrometry technique was used to measure deformations in the top surface with sub-picometer vertical resolution. By comparing calculations and experimental data, quantitative information about both d₃₃ and d₃₁ constants can be obtained.