Compact Mask Models for Optical Projection Lithography

The transfer of micro and nano patterns into a photosensitive material has a large number of technological applications. One of this techniques is known as optical lithography and is widely used in the fabrication process of integrated circuits (IC). The exposure, as one of the most important steps of a lithography process, has a critical influence on the dimension of the features in the fabricated IC. A mask contains the pattern that has to be replicated into the photosensitive material, which is coated on the top of a semiconductor wafer. A light source illuminates the mask, where diffraction phenomena occur. Then, the diffracted light is guided by means of an optical system to create a demagnified image of the mask. Modeling and simulation allow a deeper understanding of the image formation, in particular at small scales in the range of few wavelengths and below. One of the most important aspects for the image formation is the appropriate modeling of the light diffraction from the mask. When the mask features are larger than the wavelength of light, the scalar diffraction theory (Kirchhoff approach) yields sufficiently accurate results in the computation of the diffraction spectrum. With feature sizes smaller than or comparable to the wavelength, the scalar approximation exhibits a serious limitation. It does not account for the three-dimensional mask geometry and related mask topography effects. That is why a rigorous description of the light diffraction from the mask is required. The propagation of the light through the mask can be rigorously computed using the Maxwells equations. The effort to accomplish a highly accurate description of the diffracted field, introduces a huge computational expense. As a consequence, innovative modeling techniques are challenged to compromise accuracy and speed in the computation of the diffracted field, as well as in the computation of the imaging. So-called compact mask models speed up the mask diffraction spectrum and imaging computation, considering the threedimensional mask geometry and related mask topography effects. These compact mask models introduce methods to improve the accuracy of the Kirchhoffbased imaging model. This is done by means of a systematic modification of the scalar diffraction spectrum or the mask geometry, in order to yield similar results as the fully rigorous simulations. In this work, three novel compact mask models are formulated. These approaches are considered in the spatial frequency domain. First, a Jones pupil function is introduced in the projector to describe amplitude, phase and polarization effects, which are introduced by the mask (pupil filtering model). Second, a correction is performed directly on the scalar diffraction spectrum, to tune the diffraction orders that are captured by the pupil of the optical projection system (spectrum correction model). Finally, an artificial neural network approach is considered. The artificial neural networks are trained using the scalar diffraction spectrum as input and the rigorous spectrum as target. The outcome of this training process is a neural network capable of reproducing a diffraction spectrum that approximates the rigorous spectrum, which is obtained from electromagnetic field simulations. The proposed compact mask models account for and compensate mask topography- induced effects even at image planes out of focus. This allows to preserve the accuracy of the image computation in lithography simulations, at a reasonable computational cost compared to the rigorous mask model.