Example Buckling wavelength for a glass substrate

s film that is 35nm in thickness is transferred from its Si substrate onto the surface of a borophosphorosilicate glass without reduction in mismatch strain. The structure is then heated to the temperature of 800°C. Determine the wavelength of the buckhng pattern that is expected to develop and the characteristic time for its formation. Base the estimate on the assumed properties E = 124 GPa, P = 0.26 and r]s = 10 Pa- s. 

The mismatch strain between the SiGe film and its Si substrate is approximately Cm = —0.012. From (5.54), the ratio of the wavelength of the fastest growing buckhng mode to the film thickness is 

For hi = 35 nm, this wavelength is roughly 1pm. From the differential equation 

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