Improving optical metrology by subpixel reference imaging simulations

High-precision optical metrology is often limited by intrinsic errors of the measurement system, such as aberrations, or by the optical resolution itself. We show that many of these errors can be reduced by a reference image simulation that considers the appropriate effects. For this we developed a polygon-based forward model for imaging based on modern differentiable programming. The model-based optimization approach directly leads to the desired metrology results like placement errors, material coefficients or layer thickness without being affected by known errors of the measurement optics. The procedure is demonstrated by the example of photomask registration metrology, which is an essential part of the modern semiconductor production process.