Evaluation of engineering/piezoelectric constants of piezoelectric thin film by combining nanoindentation test with FEM

Based on the weight averaged method, the variety of the PZT thin film is determined by combining nanoindentation test with finite element method (FEM) simulation, and the piezoelectric constitution is used to establish the supplemental equation, in which the piezoelectric strain constants are related with the piezoelectric stress constants, so that all of the piezoelectric constants of piezoelectric thin film can be determined by combining nanoindentation test and FEM. In the forward analysis, the numerical loading curves at the broad spectrum of possible material combinations are simulated by using ABAQUS software to extract the numerical maximum indentation loads and loading curve exponents, and they are used to establish two dimensionless equations related with the engineering/piezoelectric constants of film/substrate system. In the reverse analysis, the loading part of experimental indentation curves performed on PZT thin film in nanoindentation test are fitted as the power function to obtain the maximum indentation loads and the loading curve exponents, and the engineering constants can be solved by using the simultaneity of dimensionless and supplemental equations. In order to verify the validity, the optimized engineering constants are inputted into ABAQUS software to obtain the numerical loading curves, and they are compared with the engineering constants of PZT thin film measured by the previous method to determine the variety of the PZT thin film. The piezoelectric constants of the certain variety are determined by combining forward analysis and inverse analysis. The engineering constants of the PZT thin film are determined as ET = 142 GPa, EL = 137 GPa, GL = 52 GPa, and the PZT thin film is determined as PZT-6B. The piezoelectric constants of the PZT-6B are determined as e15 = 4.75 C/m2, e31 = −0.85 C/m2, e33 = 7.08 C/m2. The proposed method is effective to determine the engineering/piezoelectric constants of piezoelectric thin film.