Uncertainty evaluation of thickness and warp of a silicon wafer measured by a spectrally resolved interferometer

Evaluation of uncertainty of thickness and gravity-compensated warp of a silicon wafer measured by a spectrally resolved interferometer is presented. The evaluation is performed in a rigorous manner, by analysing the propagation of uncertainty from the input quantities through all the steps of measurement functions, in accordance with the ISO Guide to the Expression of Uncertainty in Measurement. In the evaluation, correlation between input quantities as well as uncertainty attributed to thermal effect, which were not included in earlier publications, are taken into account. The temperature dependence of the group refractive index of silicon was found to be nonlinear and varies widely within a wafer and also between different wafers. The uncertainty evaluation described here can be applied to other spectral interferometry applications based on similar principles.