Scatterometric defect measurements – uncertainty assessment by means of a virtual instrument and a statistical analysis

Abstract

Abstract Defects in nanostructured surfaces have to be detected in or close to the manufacturing process in the production environment. For this purpose, scatterometry promises a non-contact approach with in-process capability. However, the achievable measurement uncertainty with a scatterometric measurement principle is difficult to assess by means of experiments. Especially for nano-surfaces with stochastic features, a large sample size is required. In addition, the influence of the natural uncertainty due to the inherent surface stochastics, which causes an ultimate uncertainty limit, remains hidden. Therefore, a virtual experimentation in combination with a statistical evaluation is proposed for the uncertainty assessment of scatterometric defect measurements of nanostructured surface. One virtual experiment calculates the scattered light distribution from a randomized modelled surface. For the uncertainty assessment, (a) multiple defective surfaces with the same defect grade are modelled, (b) the surfaces’ scattered light distributions are simulated, (c) the signal processing is applied for obtaining the virtual measurement results of the defect grade, and (d) the uncertainty is determined. The proposed virtual method is realized and demonstrated for defective ZnO nanograss surfaces, where the vacancy of nanograss is the studied defect as an example. As central results for the exemplarily studied defect grade measurement, the determined achievable mean uncertainty due to the nanostructure randomness is 3.2 % , and the effect of the detector shot noise is negligibly small. Furthermore, the proposed method is universally applicable for any type of nanostructure/defect, and for any scatterometric principle, to clarify the respective potential for the reliable detection of nanostructure defects.