The influences of transverse loads on electrothermal post-buckling microbeams

We report on a nonlinear equation-based closed-form solution for a spring-loading-enclosed electrothermal post-buckling microbeam that expresses (a) the relation between the compressive loads and its corresponding lateral deflections and (b) the threshold loads required to trigger the buckling phenomenon, under the condition of a variety of transverse loads. Our theoretical research reveals that the post-buckling behavior varies considerably under different transverse load ranges. Three types of double-clamped microbeams connected to microsprings with different dimensions and compliances representing transverse loads were fabricated and measured using microelectromechanical systems (MEMS) technology. Excellent agreement was found between our theoretical analysis and experimental results to confirm our exact solutions. It proves that the influences on thermal post-buckling behavior are dependent on different microbeam dimensions and microspring compliances (i.e., transverse loads). Therefore, an electrothermal buckling/post-buckling beam under external transverse loads can be accurately predicted using our theoretical model, which can be applied to either existing microdevices that are based on similar principles or other potential applications.