Mechanics of thin films on compliant substrates with applications in stretchable electronics

Stretchable electronics can flex and stretch while function and therefore can fully conform to their surroundings. Electronic systems with large stretchability have many applications such as flexible displays, electronic eye camera, conformable skin sensors, smart surgical gloves, and structural health monitoring devices. Current electronics are silicon-based, which cannot be stretched since silicon is a brittle material. Although organic semiconductor materials are promising in developing stretchable electronics, their poor electrical performance limits their applications. A feasible approach is to still use inorganic semiconductor material (e.g., silicon) but change the structures and profiles to make electronics stretchable. Several designs have been developed through buckling to realize stretchability: One dimensional nanoribbon, two dimensional nanomembrane, precisely controlled big wave, and non-coplanar mesh design. Mechanics plays a key role in the development of these designs to ensure the stretchability of electronics without failure.;In this dissertation, several mechanics issues are studied associated with these designs, including.;(1) Controlled buckling of thin film on elastomeric substrate in large deformation.;A new mechanics model is developed to study the deformation of buckled thin film by discarding the assumption of the sinusoidal form for buckled profile. The non-vanishing rotation at the ends due to the substrate is accounted by two torsional springs. The maximum mid-span deflection and curvature of the beam are obtained analytically. The film geometric effect on spring constant is discussed. Previous small deformation model overestimates the results. Analytical results in the new model agree well with numerical simulations.;(2) Lateral buckling of interconnects in a non-coplanar mesh design.;We have derived analytical solutions for lateral buckling of interconnects under shear in a non-coplanar mesh design for stretchable electronics. The critical buckling load and mode are obtained analytically by solving the equilibrium equations, and they agree well with finite element simulations. The postbuckling behavior is studied by energy minimization of the potential energy including up to 4th power of the displacement. A simple expression of the amplitude to characterize the magnitude of deformation is obtained and it agrees well with the finite element simulations without any parameter fitting. The models in this chapter may provide a route to study complex buckling modes of interconnects such as diagonal compression/stretching involving both compression and shear.;(3) Secondary buckling of thin films on compliant substrates.;Finite element models are established to study the secondary buckling of a stiff thin film on a compliant substrate. The finite element simulations agree well with experiments in wavelength and amplitudes. An analytical out-of-plane displacement function is proposed for future theoretical modeling of secondary buckling. (4) Buckling of piezoelectric films with and without compliant substrates We have developed an energy model to investigate the buckling of piezoelectric beam under an electric field. The critical voltage and buckled amplitude are obtained analytically for the buckled lead zirconate titanate (PZT) beam. The substrate thickness effect is obtained from finite element simulations for the buckled PZT thin films on compliant substrates. The results clearly show that the substrate thickness has significant effects on the critical voltage and amplitude but a negligible effect on the wavelength.;Surface effects must be considered when the film thickness reduces to below 100 nm. We have developed an energy model to investigate the surface effects on the buckling of piezoelectric nanobeam. The critical voltage and buckled amplitude are obtained analytically. These results might be helpful for the design of the film/substrate system for the stretchable piezoelectrics.