Nondestructive determination of Young’s modulus, coefficient of thermal expansion, Poisson ratio, and thickness of a thin film has long been a difficult but important issue as the film of micrometer order thick might behave differently from that in the bulk state. In this paper, we have successfully demonstrated the capability of determining all these four parameters at one time. This novel method includes use of the digital phase-shifting reflection moire´ (DPRM) technique to record the slope of wafer warpage under temperature drop condition. In the experiment, 1-um thick aluminum was sputtered on a 6-in silicon wafer. The convolution relationship between the measured data and the mechanical properties was constructed numerically using the conventional 3D finite element code. The genetic algorithm (GA) was adopted as the searching tool for search of the optimal mechanical properties of the film. It was found that the determined data for Young’s modulus (E), Coefficient of Thermal Expansion (CTE), Poisson ratio (ν), and thickness (h) of the 1.00 um thick aluminum film were 104.2Gpa, 38.0 ppm/°C, 0.38, and 0.98 um, respectively, whereas that in the bulk state were measured to be E=71.4 Gpa, CTE=23.0 ppm/°C, and ν=0.34. The significantly larger values on the Young’s modulus and the coefficient of thermal expansion determined by this method might be attributed to the smaller dislocation density due to the thin dimension and formation of the 5-nm layer of Al2O3 formed on top of the 1-um thick sputtered film. The Young’s Modulus and the Poisson ratio of this nano-scale Al2O3 film were then determined. Their values are consistent with the physical intuition of the microstructure.
Estimation of Young's Modulus for Polysilicon Thin Film by Finite Element Analysis
