On the use of PCE based surrogate models in SXR Scatterometry

Abstract

Scatterometry is a non-destructive metrology technique widely used in the semiconductor industry for the reconstruction of periodic structures from diffraction measurements. This involves solving a so-called inverse problem, which can be done by tuning the geometry parameters of a forward model such that the discrepancy between the measured diffraction pattern and the diffraction pattern computed using a Maxwell solver, are minimized. In order to meet with current semiconductor metrology demands, soft x-ray (SXR) scatterometry has been introduced. In SXR a short wavelength and broad band illumination source is used, allowing for the reconstruction of smaller and more complex structures. However, this does require the use of a computationally expensive forward model. This also complicates the assessment of the sensitivity of the measurement setup to the various grating parameters and whether the parameters can be determined independently. The current approach to this problem is strictly local. In order to address these issues, the use of a surrogate model for the Maxwell solver based on Polynomial Chaos Expansion (PCE) is investigated in this report. The performance of the PCE based surrogate model is accessed for the SXR metrology application on a simple 1D line grating.