Measurement of Steep Surfaces Using White Light Interferometry

Abstract:  Scanning white light interferometry (SWLI) is an increasingly popular method to measure the surface profile of miniature components. Although it is tolerant to step changes in profile, its capability to measure the large surface gradients that are characteristic of high-aspect-ratio surfaces is limited. This is in part due to the numerical aperture of the objective lens which restricts the spatial frequency content of both the illumination and recorded fields. More fundamentally, though, SWLI instrumentation neglects the effects of multiple scattering and assumes that the field which illuminates the object is that which would be present if the object were absent. Although this is a reasonable approximation for slowly varying surfaces, it is generally not true for those with steep gradients. In this paper the 3D theory of SWLI is presented and the approximations made by current instrumentation are discussed in this context. Using finite element methods (FEM), SWLI interferograms are calculated, for the cases of 2D Silicon V-grooves and step artefacts, and the effects of multiple scattering are illustrated. Methods to improve the capability of SWLI to measure large surface gradients, first by tilting the sample and subsequently by using an iterative FEM model to provide improved estimates of the illuminating conditions are introduced.