Near field modeling of the Moiré interferometer for nanoscale strain measurement

In this study, we propose a new method to validate the basic assumptions used in Moiré Interferometry (MI) measurement using exact electromagnetic (EM) theory; and simulate the EM fields in a few microns region above the surface of the diffraction grating. Proving that spatial frequency of EM field matches the spatial frequency of strain field is critical to ensure accuracy of MI measurement at nanoscale resolution. The EM simulations for a deformed diffraction grating structure were performed by introducing a single defect that acts as a variation on the periodic diffraction grating. The spatial frequency of simulated EM field was quantified using Continuous Wavelet Transform (CWT) algorithm. The results were compared with the strain field to show the correlations between the two. The study shows that there is a strong correlation (correlation factor R=0.869) of spatial frequency response between EM field and strain field at the nanoscale. The study shows that using the traditional MI assumptions for nanoscale strain measurement introduces an error in the order of 2.7%. We demonstrate that MI measurement can be used for nanoscale strain measurement within acceptable measurement errors using the proposed method. The proposed method can help to evaluate the MI instrument design to enhance the measurement performance.

► We validated the near field correlation of spatial frequencies between diffracted electromagnetic field. ► The validation is based on quantitative Continuous Wavelet analysis. ► It is shown that traditional MI assumptions for nanoscale strain measurement introduces an error of 2.7%. ► The study indicates that accuracy of state-of-art MI with image processing is sufficient for nano-scale strain measurement. ► The study provides a validate scheme for design diffraction grating for MI application.