Quantitative evaluation of manufacturability and performance for ILT produced mask shapes using a single-objective function

The continuous scaling of semiconductor devices is quickly outpacing the resolution improvements of lithographic exposure tools and processes. This one-sided progression has pushed optical lithography to its limits, resulting in the use of well-known techniques such as Sub-Resolution Assist Features (SRAF’s), Source-Mask Optimization (SMO), and double-patterning, to name a few. These techniques, belonging to a larger category of Resolution Enhancement Techniques (RET), have extended the resolution capabilities of optical lithography at the cost of increasing mask complexity, and therefore cost. One such technique, called Inverse Lithography Technique (ILT), has attracted much attention for its ability to produce the best possible theoretical mask design. ILT treats the mask design process as an inverse problem, where the known transformation from mask to wafer is carried out backwards using a rigorous mathematical approach. One practical problem in the application of ILT is the resulting contour-like mask shapes that must be “Manhattanized” (composed of straight edges and 90-deg corners) in order to produce a manufacturable mask. This conversion process inherently degrades the mask quality as it is a departure from the “optimal mask” represented by the continuously curved shapes produced by ILT. However, simpler masks composed of longer straight edges reduce the mask cost as it lowers the shot count and saves mask writing time during mask fabrication, resulting in a conflict between manufacturability and performance for ILT produced masks1,2. In this study, various commonly used metrics will be combined into an objective function to produce a single number to quantitatively measure a particular ILT solution’s ability to balance mask manufacturability and RET performance. Several metrics that relate to mask manufacturing costs (i.e. mask vertex count, ILT computation runtime) are appropriately weighted against metrics that represent RET capability (i.e. process-variation band, edge-placement-error) in order to reflect the desired practical balance. This well-defined scoring system allows direct comparison of several masks with varying degrees of complexities. Using this method, ILT masks produced with increasing mask constraints will be compared, and it will be demonstrated that using the smallest minimum width for mask shapes does not always produce the optimal solution.