Thickness Dependence of crack initiation and propagation in stacks for piezoelectric microelectromechanical systems

Piezoelectric thin films are vulnerable to fracture, which results in degradation of the structural integrity and device performance in piezoelectric microelectromechanical systems (PiezoMEMS). This work explains the fracture process as a combination of a crack initiation event in the piezoelectric film followed by crack propagation through the remaining layers. Biaxial bending tests using the Ball-on-three-Balls (B3B) technique were performed on stacks containing Pb(Zr_0.52Ti_0.48)O₃ (PZT) thin films of varying thicknesses grown on Si wafers (coated with thin LaNiO₃/SiO₂ layers). The fracture initiates in the PZT film, arrests in the compressive SiO₂ layer, prior to failure of the Si substrate. Weibull analyses show a significant effect of the thin film thickness on the stack's strength; the characteristic strength and Weibull modulus being σ₀ ∼1110 MPa and m ∼28, σ₀ ∼1060 MPa and m ∼26, and σ₀ ∼880 MPa and m ∼10 for the 0.7 µm, 1.3 µm, and 1.8 µm film stack, respectively and σ₀ ∼ 1820 MPa and m ∼3 for the Si wafer. A stress-energy criterion using finite fracture mechanics explains the dependence of crack initiation load on the PZT layer thickness, whereas linear elastic fracture mechanics is employed to rationalize crack propagation through the stack.