Microbridge tests on multi-layer thin films

My PhD study was focused on the continuous development of microbridge tests on thin films. We developed a microbridge testing method to characterize the mechanical properties of a symmetrical trilayer thin film composed of two kinds of materials. Theoretically, taking the substrate deformation into account, we analysed the deformation of the symmetrical trilayer microbridge sample with a deformable boundary condition and derived load-deflection formulas in closed-form. The symmetrical condition was satisfied by fabricating the same material layer with the same conditions. In a symmetrical trilayer sample, there is no residual moment and hence no residual deflection in the film, thereby eliminating the effect of residual deflection on the measurement of the load-induced deflection. On the other hand, a zero value of the tension and bending coupling stiffness makes it possible for us to evaluate the Young's modulus of two kinds of materials and the average residual stress of the trilayer thin film simultaneously. The slope of a load-deflection curve under small deformation gives the relationship of the bending stiffness and the residual force, which reduces the number of the parameters to be evaluated from the load-deflection curve under large deformation to two. The designed experiment on the symmetrical SiO2/Si3N4/SiO2 thin films, which were fabricated by using the MEMS technique and tested by Nanoindentation with a wedge indenter, verifies the novel microbridge testing method. The crucial measurement in the microbridge test is the thickness measurement of each layer in the trilayer film because a small error in the thickness measurement will lead to a large error in the determination of Young's modulus and residual stress. The error analysis indicates that enhancing the measurement precision of the sample geometry will greatly improve the experimental accuracy. The microbridge test was applied to characterize mechanical properties of asymmetrical trilayer thin films by taking the initial deflection into account. To increase the measurement accuracy, we re-calculated the spring compliances as functions of the film thickness and the thickness-averaged Young's modulus. In general, a residual moment is induced in an asymmetrical trilayer microbridge sample and results in an initial deflection. The profile of the initial deflection provides information about the mechanical properties of the trilayer film, which can be utilized in the mechanical characterization of the film. With the addition information provided by the slope of a load-deflection curve under small loads, which gives the relationship of the equivalent bending stiffness and the initial resultant force, we are able to determine the tension stiffness, the bending stiffness, the residual moment, and the residual force, from the profile of the initial deflection on a single sample based on the beam theory without other assumptions. Then, if two of the four parameters are used as input data, we can verify the other two parameters from fitting the entire load-deflection curve under large deformation. It should be emphasized that although an asymmetrical trilayer thin film was used here to demonstrate the extended microbridge testing method, the extended microbridge testing method holds actually for multilayer films because only the four parameters, the tension stiffness, the bending stiffness, the residual moment, and the residual force, determine the response of a multilayer microbridge sample in the test. We also developed a microbridge testing method for a bilayer microbridge beam initially buckled by residual compressive resultant force and residual moment. A multilayer beam with a compressive residual resultant force will be buckled if the compressive residual resultant force exceeds a critical value. If there co-exist a residual moment and a compressive residual resultant force in a multilayer beam, the residual moment may change the critical value of compressive residual resultant force for buckling due to substrate deformation. The large absolute net moment determines the buckling direction. Measuring the buckling profile and the slope of deflection to load, we determine the four parameters, which govern the buckling and bending behaviors of the multilayer beam. For bilayer beams, the Young's modulus and the residual stress of each layer can be uniquely ascertained from the microbridge test without any further assumptions. In addition, we adopted the microbridge testing method to characterize the interface stress and the interface stiffness in a bilayer thin film. Considering the interface, we analysed the deformation of a bilayer microbridge with the deformable boundary condition and derived a load-deflection formula in closed-form. We fabricated silicon oxide and silicon nitride bilayer films. By maintaining the underneath layer thickness unchanged and varying the thickness of the upper layer, we determine the interface stress and the interface stiffness