Impact of different stochastic line edge roughness patterns on measurements in scatterometry - A simulation study

The impact of line edge roughness (LER) on measured light diffraction pattern of photo masks is investigated. This is relevant for scatterometry as an accurate, indirect method in wafer metrology to determine geometry parameters of periodic surface structures from scattered light intensities. The sensitivity to roughness increases the smaller the wavelength of the incident light is. For EUV scatterometry at 13.5 nm, the efficiencies of many higher diffraction orders can be measured. In the nanometer range they are sensitive to deviations from the ideal periodic straight line structure such as LER. Applying the Fraunhofer approximation, we calculate the far field diffraction pattern of an illuminated 2D aperture plane composed of many rough slits by its 2D-Fourier transform. The rough edges of the aperture gaps are created by means of power spectrum density (PSD) functions used with a random complex exponential phase term. A simple theory neglecting correlation in the roughness profile predicts for the intensities an exponential decrease with the diffraction order and the standard deviation of the roughness amplitude which can be tested by our numerical solutions. The calculated light intensities for a rough aperture are compared with the ones found for an ideal periodic aperture whose edges are straight lines. Ensembles of rough apertures with different values for the imposed standard deviation of the roughness amplitude σ, the linear correlation length ξ, and the roughness exponent α were examined. The validity of the exponential decrease was investigated for correlation lengths ξ from 5 nm up to 1000 nm and roughness exponents α from 0.3 to 1.0. It was found that the results for the exponential correction factor deviate substantially from the mentioned theoretical value for large correlation lengths and small roughness exponents.