Thermal diffusivity measurement of polymeric thin films using the photothermal displacement technique. II. On-wafer measurement

A three-dimensional analytical solution as well as experimental verification of the thermoelastically induced deformation in a substrate-constrained thin polymeric film have been developed. In this model, the elastic deformations of the two layers are treated separately since the typical polymer has a much smaller Young's modulus but a much larger out-of-plane coefficient of thermal expansion than a silicon wafer. Results from measurements of biphenyl tetracarboxylic dianhydride-p-phenyl diamine thin films on silicon wafers agree very well with calculations based on this analysis, especially by using the sensitive frequency modulation method as outlined in part I of this two-part series. Thus, this development of a two-layer thermoelastic deformation model and measurement has advanced this technique to a thinner thickness scale with improved precision. This method is also amenable to studies of the interfacial thermal resistance R-t, and numerical analysis shows that typical interfacial thermal resistances in thin films should be detectable at high chopping frequencies. Additional results on the temperature field and thermoelastic deformation, both within the film and substrate as well as at the film surface, are also discussed. (C) 1999 American Institute of Physics. [S0021-8979(99)09923-5].