<title>Efficient computational techniques for aerial imaging simulation</title>

Abstract

We discuss computational techniques for calculating aerial image intensity distributions from large GDS II files recently implemented in Depict, a photolithography simulator for projection imaging, resist exposure, post-exposure bake and development. In particular, an algorithm for rapid and accurate evaluation of the mask Fourier transform over large domains containing non-uniformly positioned mask elements is implemented. By controlling aliasing errors within the context of a multiple level scheme, this algorithm renders feasible the simulation of aerial images across large portions of integrated circuits. The algorithm also allows overlapping phase mask elements obeying multiplicative transmission rules, and mask element merging. Accuracy for integration of the extended light source is also reported.

Using advanced simulation to aid microlithography development

“…These models extend microlithography aerial image simulation capability beyond the simple "threshold energy model" [87], [79], [88] that is often used for obtaining a rough prediction for how an optical mask prints. Here, we will examine general features of these models and try to explain why they achieve good results, as well as discuss their inherent limitations.…”

“…Fortunately, over the past eight years or so, several groups have made significant advances in algorithmic approaches to enable rapid calculation of this quantity [24], [25], [89], [81], [88]. Instead of roughly scaling with the square of the area for such calculations, as was the case with the original algorithms [23], [90], the fast algorithms available today roughly scale with the area [25].…”

“…A third observation is that the resist bias models that have been developed and reported on so far in the literature [79]- [86] are generally intended to act as a perturbation to the familiar "threshold model" [87], [79], [88]. This threshold model essentially makes the approximation that any point at the top surface of the resist that receives an incident amount of energy above some threshold value will either develop away, or remain, depending on whether the photoresist is positive or negative.…”

Challenges for patterning process models applied to large scale

“…Rieger and Stirniman reported fast large area simulation using zone-sampling behavioral modeling in 1994. 17 Convolution-based imaging was introduced shortly thereafter, 18 and Cobb's seminal paper in 1996 introduced a mathematical framework for full-chip proximity correction. 19 This work used a Sum of Coherent Systems (SOCS) approximation to the Hopkins optical model, and a simple physically-based, empirically parameterized resist model.…”

The evolution of patterning process models in computational lithography

“…Rieger and Stirniman reported fast large area simulation using zone-sampling behavioral modeling in 1994 10 . Convolution-based imaging was introduced shortly thereafter 11 , and Cobb's seminal paper in 1996 introduced a mathematical framework for full-chip proximity correction. This work used a Sum of Coherent Systems (SOCS) approximation to the Hopkins optical model, and a simple physically-based, empirically parameterized resist model 12 .…”