High sensitivity Moiré interferometry with phase shifting at nano resolution
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Due to insatiate demand for miniaturization of electronics, there is a need for new techniques to measure full-field strain at micro-scale structures. In addition, Micro-Electronic-Mechanical-Systems (MEMS) require a high resolution and high sensitivity material property characterization technique. In this study, a theoretic model for a high sensitivity Moire Interferometry (MI) for measuring nano-scale strain field has been developed. The study also includes the application of the proposed measurement technique for the study of reliability of next generation nano-electronics/power electronics. The study includes both theoretical and experimental work. In the theoretical part, a far field modeling of a Moire Interferometer (MI) using the mode decomposition method is proposed according to the analytical formulation from the scalar diffraction theory. The wave propagation within the defined MI far field domain is solved analytically for a single frequency surface relieved grating structure following the Rayleigh-Sommerfeld formulation under the paraxial approximation. It is shown that the far-field electrical field and the intensity interferogram can be calculated using the mode decomposition method. Furthermore, the near-field (propagation distance < 1 μm) assumptions are validated using exact electromagnetic (EM) theory; and the EM fields are simulated in a few microns region above the surface of the diffraction grating. The study shows that there is a strong correlation (correlation factor R = 0.869) of spatial frequency response between EM field and strain field at the nanoscale. Experimentally, a 164 nm/pixel spatial resolution Moiré Interferometer with automated full strain field calculation is proposed. Accurate full strain field maps are generated automatically by a combination of phase shifting technique (temporal data redundancy) and Continuous Wavelet Transform (CWT) (spatial data redundancy). A thermal experiment on BGA packaging is used to demonstrate the advantages of the proposed new design. To enhance the stability of the phase shifting process, a statistical phase shifting estimation algorithm for temporal phase shifting interferometry (PSI) based on (CWT) is proposed. The proposed algorithm explores spatial information redundancy in the intra-frame interferogram data set using the phase recovery property on the power ridge of CWT. With the proposed MI, it is able to locate and measure the temperature of the hot spots caused by Joule Heating by measuring the free thermal expansion in-plane strain. It is demonstrated that the hotspot caused by the Joule heating in a thin metal film/plate structure can be measured by Phase shifting Moiré interferometry with continuous wavelet transform (PSMI/CWT) at the microscopic scale. A demonstration on a copper film is conducted to verify the theory under different current densities. It is shown that a linear relationship exists between current density squared and normal strains.