Analytical extraction of residual stresses and gradients in MEMS structures with application to CMOS-layered materials

Abstract

Accurate thin-film characterization is a key requirement in the MEMS industry. Residual stresses determine both the final shape and the functionality of released micromachined structures, and should therefore be accurately assessed. To date, a number of techniques to characterize thin-film materials have been developed, from substrate curvature measurement to methods that exploit the post-release deformation of test structures. These techniques have some major drawbacks, from high implementation costs to accuracy limitations due to improper boundary condition modeling. Here, we present a new technique for the characterization of multilayered, composite MEMS structures that uses easily accessible experimental information on the post-release deformation of microbridges only, with no need for multiple beam lengths. The method is based on an analytical solution of the (post-)buckling problem of microbridges, including the effect of residual stresses (both mean and gradient) and non-ideal clamping (boundary flexibility). The method allows simultaneous characterization of both the mean and the gradient residual stress components, as well as the effective boundary condition associated with the fabrication process, yielding approximately one order of magnitude improvement in resolution compared to extant methods using the same type and number of test structures. The higher resolution is largely attributable to proper accounting for boundary flexibility by our method, with the boundary condition for the structures in this work being ∼90% as stiff in bending relative to the commonly assumed perfectly clamped condition. Additional enhancement can be achieved with post-release deformation measurements of simple cantilevers in addition to the microbridges. The method is useful as it ensures very low stress extraction uncertainty using a limited number of microbridge test structures, and it is transferrable to package-stress characterization. The analytical approach can also be extended to device design, quantifying the effect of residual stresses and boundary flexibility on a structure's post-release state.