OPC provides a technique to compensate or at least reduce the disturbing effects by either modifying the shape of the features or by adding adjacent subresolution geometries like serifs on the corners to improve image quality [57,58]. Simulation has proved to be a valuable tool to investigate, improve or even automatically correct optical proximity effects. Simple rule-based approaches show promise for first order optical effects and enable restricted process corrections [59,60]. More accurate models are based on Hopkins' method of partial coherent imaging (cf. Section 4.3.2) and make use of expansion techniques similar to the Fast Fourier Transform, but which are much faster and allow mask edges and sizes to have arbitrary location and sizes . For additional speed in OPC a technique of reusing precalculated lens effects over a small window and then scanning that window over the sizeable mask area of interest has been developed [62,63]. Using such advanced algorithms the computation of the aerial image for dense patterns in areas up to 400 m x 400 m has been reported .
Some second order effects are also of concern in aerial image simulation. One is accounting for propagation through lenses with high numerical apertures of 0.5 and above [65,66,67]. Here it becomes important to consider the large ray angles beyond the paraxial assumption in formulating ray path effects, to introduce obliquity factors for flux at various takeoff angles, and to investigate the rotation of the electric field component vectors with propagation angle in the transverse magnetic polarization case. The complexity of such models increases considerably and the simulation areas are therefore restricted to smaller areas.