Buckling analysis of stiff thin films suspended on a substrate with tripod surface relief structure

A wavy configuration is a simple yet powerful structural design strategy, which has been widely used in flexible and stretchable electronics. A buckled structure created from a prestretch-contact-release process represents an early effort. Substrates with engineered surface relief structures (e.g., rectangular islands or tripod structure) have enabled stretchability to the devices without sacrificing their electric performance (e.g., high areal coverage for LEDs/photovoltaics/batteries/supercapacitors). In particular, the substrate with a tripod surface relief structure allows wrinkled devices to be suspended on a soft tripod substrate. This minimizes the contact area between devices and the deformed substrate, which contributes to a significantly reduced interfacial stress/strain. To uncover the underlying mechanism of such a design, we exploit the energy method to analytically investigate the buckling and postbuckling behaviors of stiff films suspended on a stretchable polymeric substrate with a tripod surface relief structure. Validated by finite element analysis, the predications from such an analytical study elucidate the deformed profile and maximum strain in the buckled and postbuckled stiff thin device films, providing a useful toolkit for future experimental designs.