Influence of asymmetric grating structures on measurement accuracy in integrated phase grating interference-based metrology

We present an analysis of the position error caused by asymmetry in phase grating measurement systems, demonstrating that such error is dependent on the structure of the grating and the measurement order. The asymmetry-induced error varies as a function of diffraction order, with the nature of this variation depending on the grating structure. We verify our analysis by comparing the average error obtained with a multiorder interferometer to the error simulated using an atomic force microscopy scanning profile. The deviations of different orders of asymmetry-introduced error are less than ±3  nm. This result provides an explanation of diffraction fields and measurement errors from asymmetric gratings.