Observation and Spectrum of Mesoscopic Buckling Modes

Classical Euler buckling of a rod or beam is a familiar phenomenon. For clamped-clamped boundary conditions the expected eigenfunction has a single antinode midway between the endpoints [1]. Recently we have observed stable higher-order buckling modes of suspended mesoscopic SiO2 beams [2], where the beam dimensions are approximately 200 nm x 500 nm in cross-section and 5 um to 60 um in length. Starting with a silicon wafer with 500 nm of thermal oxide, the suspended structures are fabricated by e-beam lithography and plasma etching. During the plasma etching of the underlying silicon, the structures buckle due to the residual strain from the thermal oxide growth. We have analyzed the observed elastic buckling spectrum in terms of clamped eigenfunctions with mode numbers n=1 through n=6 using image processing of the SEM micrographs. The observed spectrum exhibits several interesting features, including significant mode-mode interaction and the appearance of a geometrical constraint involving a sum over all modes. Ideal Euler buckling theory cannot account for the stability and interaction of the higher-order modes. We are investigating the applicability of a mulitmode Ginzburg-Landau description which includes ideal Euler buckling as a limiting case [3]. [1] S.M. Carr and M.N. Wybourne, Applied Physics Letters 82 709 (2003). [2] S.M. Carr, W.E. Lawrence, and M.N. Wybourne, submitted (2003). [3] W.E. Lawrence, APS March Meeting Bulletin (2004).