Analysis and design of kinked (bent) beam sensors

This paper describes microfabricated freestanding 'v'-shaped beams, which may be used for a wide variety of sensing applications, e.g., temperature, residual stress arising from microfabrication and surface stresses generated by molecular adsorption. Analytical solutions are derived that connect structural deformation (i.e. output displacement) to physical driving forces and geometry. Various asymptotic limits are presented to illustrate the range of geometries for which bending and axial deformation can be neglected. An intriguing implication of the analysis is that the most sensitive device is only slightly kinked, with a kink angle close to the width-to-length ratio of the beams. For such structures, the displacements produced by buckling-type deformation can be much larger than those produced by purely axial elongation of structures with larger kink angles. The paper concludes with a discussion of the implications for designing highly sensitive devices, with an emphasis on the advantages of exploiting nonlinear behavior and constructing polymeric structures.