Roughness influence on periodic gratings and application to optical metrology of roughness

In the field of microelectronic industry, periodic structures are produced with spatial dimensions that can be less than 100 nm. Because of the material and process effects, these structures will most likely present some additional roughness. The optical far field characterization of these structures usually allows to deduce the shape parameters of the periodic structure. Measurements are performed thanks to an ellipsometric apparatus, associated with modelling and inversion algorithms. In this configuration the technique is called "scatterometry". This method does not permit to directly extract roughness parameters. This paper aims at describing how model and experimental tools can be used to characterize the roughness of gratings. The study needs a complete three-dimensional electromagnetic modelling of the structure but the calculations are very time consuming. Here, different theoretical models are associated in order to reduce the calculation time: rigorous numerical differential theory and Born approximation theory. The exact numerical model allows to treat the periodic part of the structure while the roughness is viewed as a perturbation and treated using a first order approximation. From an experimental point of view, the information on the periodic part of the structure lies in the diffraction orders, while the roughness signature is mainly found between diffraction orders. Practically, this model could be used in the semiconductor industry for a detailed roughness characterization, based on an optical measurement using the same test structures used for scatterometry.