Naulleau Patrick P, George Simi A
Center for X-Ray Optics, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.
Appl Opt. 2011 Jul 1;50(19):3346-50. doi: 10.1364/AO.50.003346.
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.
在极紫外（EUV）光刻的情况下，建模表明，光刻掩模上的反射器相位粗糙度是一个重大问题，这是由于它会导致像平面散斑以及成像特征上产生的线边缘粗糙度。建模结果最近已被用于确定未来可用于生产的掩模的要求，这些掩模要满足均方根粗糙度为50皮米这一极其严格的规格。由于该问题在内存需求方面的规模，过去的建模结果在此应用中基于薄掩模近似。然而，EUV掩模本质上是三维（3D）的，因此薄掩模近似的有效性就出现了问题。在这里，我们将使用快速二维薄掩模模型计算的像平面散斑结果与严格的时域有限差分结果直接进行比较，发现在散斑幅度计算中两种方法的结果相差在10%以内，在线边缘粗糙度受限焦深计算中相差在20%以内。对于这两种类型的计算，二维方法都提供了一个保守的估计。三维建模还用于表明层间相关粗糙度确实是最值得关注的粗糙度指标。
