Principles of MEMS Transducers
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Prepared by D. Arnold
December 10, 2010
EEL5225 Principles of MEMS Transducers
Fall 2010 Semester
Assigned: Monday, 12/6
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.
= 2.3 x 10
= 0.5 x 10
The stress in thermal SiO
arises from the differences in thermal expansion between Silicon and
is grown at a much higher temperature than room temperature, and a layer of SiO
formed over the silicon. Following this, it is cooled to room temperature. Silicon, having a higher
co-efficient of thermal expansion (CTE) than SiO
contracts much more. Hence, SiO
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-
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,
, by the Stoney equation,
is the center deflection,
is the wafer radius,
is the substrate thickness,
is the film
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