HW9 solution

# HW9 solution - EEL5225 Principles of MEMS Transducers HW9...

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Principles of MEMS Transducers Page 1 of 7 Prepared by D. Arnold December 10, 2010 EEL5225 Principles of MEMS Transducers HW9 Fall 2010 Semester Assigned: Monday, 12/6 Due: Monday, 12/13 1. The following two questions relate to residual stress. a.) Explain why thermally grown oxide is compressive, and estimate the stress (at room temp.) in an oxide layer grown at 1025°C. Hint: α Si = 2.3 x 10 -6 K -1 , α SiO2 = 0.5 x 10 -6 K -1 , E SiO2 = 50 GPa The stress in thermal SiO 2 arises from the differences in thermal expansion between Silicon and SiO 2 . SiO 2 is grown at a much higher temperature than room temperature, and a layer of SiO 2 is formed over the silicon. Following this, it is cooled to room temperature. Silicon, having a higher co-efficient of thermal expansion (CTE) than SiO 2 contracts much more. Hence, SiO 2 also contracts as it is attached to the Si substrate, resulting in a large compressive stress being developed in the oxide. Further reading can be done in an early paper: E. P. EerNisse, “Stress in thermal SiO2 during growth,” Applied Physics Letters , Vol. 35, pp. 8- 10, 1979. b.) A common method for measuring stresses in thin-films is using wafer bow measurements. Typically, a laser-based interferometer system is used to measure the deflection at the center of a wafer. The bow of the wafer is related to the thin film stress, σ , by the Stoney equation, , where δ is the center deflection, R is the wafer radius, T is the substrate thickness, t is the film thickness, and E and ν are the Young’s modulus and Poisson ratio for the film, respectively. Assume you just deposited a 1 μm PECVD nitride layer on a 525 μm thick, 125 mm diameter

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## This note was uploaded on 01/17/2011 for the course EEL 5225 taught by Professor Arnold during the Fall '08 term at University of Florida.

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HW9 solution - EEL5225 Principles of MEMS Transducers HW9...

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