A discussion of the regression of physical parameters for photolithographic process models

摘要

All models currently used for Optical Proximity Correction and related Resolution Enhancement techniques are comprised of an analytical description of the modeled system with coefficients determined by data collected from the physical process. The analytical model is normally based on the Hopkin's approximation of the system because this approximation allows the reticle to be a variable in the exposure system. The analytical component of the model contains terms such as numerical aperture, partial coherence, and wavelength, all of which are physical parameters that can be directly read from the equipment used to generate the empirical process data. Therefore, these physical parameters can be directly used in the process model and do not need to be modified. One case example of a physical parameter is the illuminator shape. In an annular exposure system, the center of the exposure system is blocked to allow illumination by high order illumination components. The annular shape can be achieved in different manners. The scanner manufacturer can use a shape cut in a metal form to achieve an annular illumination condition or the scanner manufacturer can use a lens system to achieve the same illumination condition. Both of these systems have the same inner and outer diameters, resulting in the same annulus and therefore the same illumination technique. However, experimental data show that for the exact same setting values, the annular illumination shape is detectably different. This is a first order system difference that is the result of different implementation methods. Further differences can be found due to scanner to scanner variations in either lens shape or aperture shape. These differences create a need for physical parameters to be regressed during fitting of empirical data to the analytical model. This paper will discuss the need to regress what initially appear to be constant physical parameters during the model fitting process. The study will use equipment variability information to demonstrate the range of physical constant impact upon the accuracy of a process model.