Critical thickness for cracking of Pb(Zr_0.53Ti_0.47)O₃ thin films deposited on Pt/Ti/Si(100) substrates

This paper reports on the critical thickness for residual stress–induced cracking of Pb(Zr_0.53Ti_0.47)O₃ (PZT) thin films deposited on 150 nm Pt and 30 nm Ti/Si(100) substrates. The PZT thin films were deposited on the substrate using the sol–gel technique, baked at 110 °C for 3 min, pyrolyzed at 350 °C for 10 min and finally annealed at 650 °C for 60 min. Film cracks were examined at room temperature after the annealing. The experimental results show that there exists a critical film thickness of about 0.78 °m for PZT film cracking in the PZT/Pt/Ti/Si systems. No cracking was observed, if the PZT film thickness was smaller than the critical value. When the film thickness was larger than the critical thickness, the crack density, defined as the reciprocal of the crack spacing, increased rapidly with increasing film thickness. An elastic–plastic multi–crack shear lag model is developed to explain the experimental results. The model has the ability to calculate the interaction between cracks even when the crack spacing is almost three orders of magnitude larger than the film thickness. The theoretical results predict both the critical thickness for film cracking and the crack density, and the predictions agree with the experimental observations.