In this paper, we present a formulation of the Sub-Resolution Assist Feature (SRAF) placement problem as a geometric optimization problem. We present three independent geometric methodologies that use the above formulation to optimize SRAF placements under mask and lithographic process constraints. Traditional rules-based methodology, are mainly one dimensional in nature. These methods, though apparently very simple, has proven to be inadequate for complex two-dimensional layouts. The methodologies presented in this paper, on the other hand, are inherently two-dimensional and attempt to maximize SRAF coverage on real and complex designs, and minimizes mask rule and lithographic violations.
Optical Rule Checking (ORC) is an important vehicle to predict the failure of wafer shapes due to the process proximity effects. Optical Proximity Correction (OPC) if not aided by ORC may cause severe failures affecting the yield in manufacturing. However, it is fairly complicated to do ORC on mask shapes that are pre-corrected either by rules-based or by model-based OPC. ORC is also a good tool to capture the problems that may occur at multi-layer interactions. We present a methodology to use both geometric directives and limited optical simulation to detect potential failures using ORC. We extend our methodology to multi-layer interactions. In case of multi-layer ORC, we present several approaches that deal with how to judiciously mix the geometric directives and the optical simulations for different layers. We show the ORC can help us design better rules for OPC.
We describe how to generate better Optical Proximity Corrections (OPC) for line-ends and corners by using rounded anchors and serifs. These rounded serifs and anchors can be made smaller in size and shape than the traditional rectilinear anchors and serifs. The smaller size of the serifs tend to have less problems in satisfying mask-rule constraints. They also have less adverse effects on the printability of neighboring shapes. We refer to these rounded anchors and serifs as Mouse-Ears. The rounding is done by circles which are regular octagons with Ortho-45 straight lines. The main idea of this paper stems from the physical description of the lithographic process, which can be conceptualized as a low-pass filter. The low-pass filter eliminates the sharp corners of the feature which are made of high spatial-frequency components and retains the low spatial-frequency components. Since the rounded anchors and serifs have fewer high-frequency components than their rectilinear counterparts they get less deformed in the lithographic process.