Cumulative energy analysis of thermally-induced surface wrinkling of heterogeneously multilayered thin films

Wrinkling is a well-known example of instability-driven surface deformation that occurs when the accumulated compressive stress exceeds the critical value in multilayered systems. A number of studies have investigated the instability conditions and the corresponding mechanisms of wrinkling deformation. Force balance analysis of bilayer systems, in which the thickness of the capping layer is importantly considered, has offered a useful approach for the quantitative understanding of wrinkling. However, it is inappropriate for multilayer wrinkling (layer number > 3) consisting of heterogeneous materials (e.g. polymer/metal or inorganic), in which the thickness variation in the substrate is also crucial. Therefore, to accommodate the additive characteristics of multilayered systems, we thermally treated tri- or quad-layer samples of polymer/metal multilayers to generate surface wrinkles and used a cumulative energy balance analysis to consider the individual contribution of each constituent layer. Unlike the composite layer model, wherein the thickness effect of the capping layer is highly overestimated for heterogenously stacked multilayers, our approach precisely reflects the bending energy contribution of the given multilayer system, with results that match well with experimental values. Furthermore, we demonstrate the feasibility of this approach as a metrological tool for simple and straightforward estimation of the thermomechanical properties of polymers, whereby a delicate change in the Young's modulus of a thin polymeric layer near its glass transition temperature can be successfully monitored.