Developments in optical modeling methods for metrology

Despite the fact that in recent years the scanning electron microscope has come to dominate the linewidth measurement application for wafer manufacturing, there are still many applications for optical metrology and alignment. These include mask metrology, stepper alignment, and overlay metrology. Most advanced non-optical lithographic technologies are also considering using optics for alignment. In addition, there have been a number of in-situ technologies proposed which use optical measurements to control one aspect or another of the: semiconductor process. So optics is definitely not dying out in the semiconductor industry. In this paper a description of recent advances in optical metrology and alignment modeling is presented. The theory of high numerical aperture image simulation for partially coherent illumination is discussed. The implications of telecentric optics on the image simulation is also presented. Reciprocity tests ate proposed as an important measure of numerical accuracy. Diffracion efficiencies for chrome gratings on reticles are one good way to test Kirchoffs approximation as compared to rigorous calculations. We find significant differences between the predictions of Kirchoffs approximation-and rigorous methods. The methods for simulating brightfield, darkfield, confocal, and,coherence probe microscope images are outlined, as are methods for describing aberrations such as coma, spherical aberration,and illumination aperture decentering.