Determination Of Elastic Constants Of Piezoelectric Nano-materials Via Combination Of Finite Element Method And Nanoindentation

Piezoelectric nanobelts and piezoelectric thin films, which are usually bonded to thesubstrate, have been widely used in the microelectronic devices due to their mechanical andelectrical coupling behaviors, and their thickness ranges from a few nanometers to severalmillimeters. The mechanical properties of piezoelectric nanobelts and piezoelectric thin filmshave an important influence on the performances of the devices. Therefore, it is veryimportant to measure the mechanical properties of piezoelectric nanobelts and piezoelectricthin films. In term of flexibility, high accuracy and requirements of the small sample size,nanoindentation test commonly is an effective method to measure the mechanical propertiesof nanometer materials. However, because the indentation is influenced by the substrate, theindentation response itself can not reflect the real mechanical properties of the materialsaccurately. In this thesis, the substrate effect is considered to study the elastic mechanicalproperties of piezoelectric nanobelts and piezoelectric thin films. Firstly, based on the weightaverage method, the elastic constants of piezoelectric nanobelts can be determined bycombining nanoindentation test and finite element method （FEM）. Secondly, the relationshipbetween the indentation force and the material property parameters is established for thepiezoelectric thin film/insulating elastic substrate system, and according to the relationship,the elastic constants of piezoelectric thin films can be determined. Three main aspects of thispaper are shown as follows：（1） Based on the weight average method, the elastic constants of transversely isotropicnanobelts were determined by combining nanoindentation test and FEM. The nanoindentationtests of nanobelt/substrate system were simulated by using the purely mechanical indentation（PMI） and piezoelectric indentation （PI） modes, and then the dimensionless equations amongthe maximum indentation load, loading curve exponent and elastic constants of film/substratesystem are obtained. In the reverse analysis, the nanoindentation tests were performed on ZnSnanobelts deposited on the silicon substrate, then the experimental indentation data aresubstituted into the dimensionless equations and the weight average method to determine theelastic constants of ZnS nanobelts（2） A theoretical model about the load response of indentation, which builds up therelationship between the indentation load and material parameters of piezoelectric thin films（elastic constants, piezoelectric constants and dielectric constants） by consideringdisplacement boundary conditions, electrical boundary conditions and interface continuousconditions, was proposed for the nanoindentation test of the piezoelectric thin film/insulating elastic substrate system. The dimensionless equations between the maximum indentation load,loading curve exponent and elastic constants of film/substrate system were established bydimensionless analysis. The elastic constants of piezoelectric thin films can be determined bysolving the simultaneity of the theoretical model and the dimensionless equations.（3） Based on the theoretical model about the load response of indentation of thepiezoelectric thin film/insulating elastic substrate system, the elastic constants of transverselyisotropic piezoelectric thin films were determined by combining nanoindentation test andFEM. In the forward analysis, the dimensionless equations between the maximum indentationload, loading curve exponent and elastic constants of film/substrate system were obtained bysimulating the nanoindentation tests of film/substrate system. In the reverse analysis, thenanoindentation tests were performed on ZnO and0.95Na_0.5Bi_0.5TiO₃-0.5K0.5Bi0.5TiO3（BNKT） thin films deposited on silicon substrate respectively, then the experimentalindentation data are substituted into the dimensionless equations and the theoretical model todetermine the elastic constants of ZnO and BNKT thin films.