The rapid growth of microelectromechanical systems ͑MEMS͒ industry has introduced a need for the characterization of thin film properties at all temperatures encountered during fabrication and application of the devices. A technique was developed to use MEMS test structures for the determination of the difference in thermal expansion coefficients ͑␣͒ between poly-Si and SiO 2 thin films at high temperatures. The test structure consists of multilayered cantilever beams, fabricated using standard photolithography techniques. An apparatus was developed to measure the thermally induced curvature of beams at high temperatures using imaging techniques. The curvatures measured were compared to the numerical model for multilayered beam curvature. The model accounts for the variation in thermomechanical properties with temperature. The beams were designed so that the values of Young's moduli had negligible effect on beam curvature; therefore, values from literature were used for E Si and E SiO 2 without introducing significant error in curvature analysis. Applying this approximation, the difference in thermal expansion coefficients between ␣ Si and ␣ SiO 2 was found to increase from 2.9ϫ10 Ϫ6 to 5.8ϫ10 Ϫ6°CϪ1 between room temperature and 900°C. These results suggest that the ␣ for poly-Si thin films may be significantly higher than values for bulk, crystalline Si.
An innovative system was designed to optically measure the curvature of microelectromechanical system at high temperatures. The system takes advantage of the limited numerical aperture of the imaging system to detect the curvature of cantilever beams. Images of the beam are used to determine beam curvature at high temperatures of up to 850°C by analyzing the apparent change in beam length as seen by the camera during an experimental trial. The system is designed to operate at very high temperatures, which is difficult in conventional microscale curvature measurement techniques such as scanning electron microscopy or stylus profilometry due to excess heating of peripheral equipment. The system can measure curvatures as small as 300 m Ϫ1 , which corresponds to tip deflections of 1.5 m for a 100 m beam. The resolution of the system is limited by the image resolution of the charge-coupled device camera, and increases at large curvatures. The maximum curvature that can be measured by the system is limited by the increase in system resolution, and is estimated to be 4500 m Ϫ1 , corresponding to 22 m deflection for a 100 m beam. The apparatus was demonstrated to measure the thermally induced curvature of multilayered thin-film cantilever beams. The beams bend at high temperatures due to mismatch in thermal expansion coefficients between the layers. One innovative application of such curvature measurement is the determination of thermophysical properties of thin films at elevated temperatures. This article presents the experimental setup and operational theory of apparatus, as well as curvature measurements obtained by the system. The thermal expansion coefficient of polycrystalline silicon, determined from the curvature measurements, are also discussed.
Microelectromechanical systems (MEMS) have potential application in high temperature environments such as in thermal processing of microelectronics. The MEMS designs require an accurate knowledge of the temperature dependent thermomechanical properties of the materials. Techniques used at room temperature often cannot be used for high-temperature property measurements. MEMS test structures have been developed in conjunction with a novel imaging apparatus designed to measure either the modulus of elasticity or thermal expansion coefficient of thin films at high temperatures. The MEMS test structure is the common bi-layered cantilever beam which undergoes thermally induced deflection at high temperatures. An individual cantilever beam on the order of 100 νm long can be viewed up to approximately 800°C. With image analysis, the curvature of the beam can be determined; and then the difference in coefficient of thermal expansion between the two layers can be determined using numerical modeling. The results of studying silicon nitride films on silicon oxide are presented for a range of temperatures.
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