Validity of the thin mask approximation in extreme ultraviolet mask roughness simulations

In the case of extreme ultraviolet (EUV) lithography, modeling has shown that reflector phase roughness on the lithographic mask is a significant concern due to the image plane speckle it causes and the resulting line-edge roughness on imaged features. Modeling results have recently been used to determine the requirements for future production worthy masks yielding the extremely stringent specification of 50 pm rms roughness. Owing to the scale of the problem in terms of memory requirements, past modeling results have been based on the thin mask approximation in this application. EUV masks, however, are inherently three-dimensional (3D) in nature and thus the question arises as to the validity of the thin mask approximation. Here, we directly compare the image plane speckle calculation results using the fast two-dimensional thin mask model to rigorous finite-difference time-domain results and find the two methods to agree to within 10% in the computation of the speckle magnitude and 20% in the computation of the line-edge roughness limited depth of focus. For both types of computation, the two-dimensional method provides a conservative estimate. The 3D modeling is also used to show that layer-to-layer correlated roughness is indeed the roughness metric of most concern.