Extending the two-substrate method for characterization of thermo-mechanical properties to polymer thin films with non-uniform thickness

In the context of a growing interest in characterizing the thermoelastic properties of polymer thin films, namely the biaxial modulus ($M_f$) and the thermal expansion coefficient (TEC), accurate estimations of their mechanical response is mandatory. We present a method based on the measurement of temperature-dependent curvature of a polymer film deposited on two different substrates (two-substrate method) to identify these characteristics ($M_f$ and TEC). The interest and feasibility are illustrated for three different thermoset films (epoxide resins) exhibiting a non-uniform film thickness. The film thicknesses are in the micrometer range. The predictions with the proposed method are cross-compared with temperature-dependent ellipsometry, atomic force microscopy (AFM), and nanoscale dynamic mechanical analysis (nDMA). The thermal expansion coefficients estimated from ellipsometry data are in agreement with the curvature method. AFM nano-DMA data show some discrepancy, but confirm the range of values for $M_f$. A sensitivity analysis shows a larger dependence of the method on the experimental uncertainties in the case of polymer films on semiconductor substrates compared to the case of metal or oxide films. This originates from the larger thermoelastic contrast. The study also shows quantitatively how the accuracy of the measurement of curvature is critical and that the measurement of the spatial distribution of the radial and angular curvatures is necessary when the film thickness distribution is non-uniform. Quantitative limits are also provided for using the proposed method. In conclusion, the study proposed practical guidelines and theoretical advances to improve the curvature method and apply it to a wider variety of materials deposited in the form of films on substrates.