A bending beam method has been developed to measure the elastic modulus E, the coefficient of thermal expansion (CTE) and the Poisson ratio ν for on-wafer dielectric films with thicknesses in the submicron range. The method was demonstrated for 0.5 μm thick silicon dioxide films made from tetraethylorthosilane (TEOS). First, the biaxial elastic modulus E/(1-ν) and CTE were measured on blanket TEOS on Si and GaAs substrates and found to be 77 GPa and 1.0 ppm/°C, respectively. The Poisson ratio ν was determined by combining the finite element calculation and the experimental result of the thermal stresses of TEOS fine lines on the Si substrate. The Poisson ratio of TEOS was determined to be 0.24 and, as a consequence, the Young’s modulus was 59 GPa. Fourier transform infrared spectra were obtained for TEOS films on the Si and GaAs substrates to ensure that the chemical structure of the film is independent of the substrate.
The thermal stress of thin and ultrathin polystyrene (PS) films on Si substrate has been studied and the glass transition temperature (Tg) is determined from the thermal stress data. Tg of PS turned out to be thickness independent for thick films but decreases when the film thickness is comparable to the end-to-end distance of the polymer chains (<100 nm). The thermal stress level and the slope of the stress temperature curve of the film also decrease as the film thickness decreases. The slope reduction indicates that the product of the biaxial modulus E/(1−ν) and the coefficient of thermal expansion (CTE) of the film decreases with film thickness. Assuming that the CTE increases for ultrathin films, the modulus is found to decrease significantly with respect to the bulk value.
A method of measuring the Yong’s modulus, Poisson ratio, and coefficient of thermal expansion (CTE) is presented. The method uses a wafer curvature technique to measure thermal stresses of thin films of the same material deposited on two different substrates, one isotropic and the other thermomechanically anisotropic. By analyzing the thermal stress data as a function of temperature, the Young’s modulus, Poisson ratio and CTE can be simultaneously determined. The method is demonstrated for Al (0.5 wt % Cu) and Cu thin films by performing measurements on (100) Si wafers and Y-cut single-crystal quartz wafers. The CTE, Young’s modulus, and Poisson ratio are found to be 24.3 ppm/°C, 58.9 GPa, and 0.342, respectively, for Al (Cu) thin film, and 17.7 ppm/°C, 104.2 GPa, and 0.352, respectively, for Cu thin film. They are in good agreement with those measured by other methods. This method is generally applicable to other on-wafer films with in-plane isotropy.
Although polymer-based materials are widely used in microelectronics packaging and viscoelasticity is an intrinsic characteristic of polymers, viscoelastic properties of polymeric materials are often ignored in package stress analyses due to the difficulty in measuring these properties. However, it is necessary to consider the viscoelastic behavior when an accurate stress model is required. Viscoelastic properties of materials can be characterized in either the time or the frequency domain. In this study, stress relaxation experiments were performed on a molding compound in the time domain. A thermorheologically simple model was assumed to deduce the master curve of relaxation modulus using the time-temperature equivalence assumption. A Prony series expansion was used to express the material's relaxation behavior. Two methods to determine the Prony pairs and shift factors were compared. After they were determined, the master curve at a reference temperature was shifted to every measured temperature for comparison with experimental data.
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