There are many different situations in which special attention to color choices provide the potential to improve the manufacturing results of multi-patterned masks.

BY DAVID ABERCROMBIE and ALEX PEARSON, Mentor Graphics, Wilsonville, OR

Multi-patterning design rules don’t care about color (mask assignments). As long as all the spacing and alternation constraints are met, any coloring arrangement is legal. In the beginning of multi-patterning, all possible color combinations that passed the design rule checks (DRC) were considered and treated as equal. As the technology moves into more advanced nodes, however, that is no longer the case.

As it turns out, one legal coloring choice can, in fact, be significantly better than another when it comes to manufacturing success and chip performance. Designers working on multi-patterned layouts need to understand the issues and conditions that affect their color choices, so they can determine the optimal coloring scheme for their designs.

Color density

In multi-patterned designs, each color assignment represents a different manufacturing mask. Each mask is processed through a lithography operation, and the pattern is etched onto the wafer. Once all the masks are processed, the goal is to have all the shapes created from all the masks act as if they were all generated from one mask, with very similar process biases and variations.
To ensure that type of consistency, all the masks need to resemble each other in terms of the total area and distribution of shapes. Clumping shapes in one area of one mask, while distributing shapes evenly across another, is going to result in very different process bias behavior and results. Balancing the color density across each mask provides the best manufacturing result.

To explain why, let’s look at a standard cell library design. Because power rails are typically much wider than the routing tracks inside the cells, they constitute a large portion of the polygon area inside the standard cell design block. The number of tracks in the library force the power rails into certain color pairings (FIGURE 1). In the first case, the power rails are forced to opposite colors, while in the second, they are forced to the same color.

The color ratio distribution charts tell the story of the two designs. When the power rails alternate color, the distribution of the color density ratio is well-centered around the 50% point. However, forcing the power rails to be a single color can dramatically shift the color ratio towards that single color. This distribution is more problematic to manufacture.

But uniform color density isn’t just a chip-wide, global issue—even local differences can have negative impacts, because local areas with excessive or insufficient color density can impact the biases of nearby shapes during processing. In FIGURE 2, both coloring options are legal, but the polygons within each connected component are not equal in area, so the choice of G-B-G-B vs. B-G-B-G affects how much area of each color ultimately exists within this local region. The second coloring choice results in a more uniform area density of each color.

However, some layouts contain polygon configurations that inherently make it almost impossible to balance colors simply by changing color choices. For example, sometimes you have a very large area polygon in the midst of your layout (FIGURE 3). No matter what color you assign to the large polygon, it will dominate the color density in this region. Changing color selections in the nearby polygons doesn’t help, because they can’t all be assigned to the other color.

In this case, a new (and perhaps unexpected) solution is needed. Placing evenly distributed polygons of the opposite color in a grid on top of the large area polygon (known as reverse tone overlay fill) adds shapes to the opposite color mask in a region that would otherwise have been empty (FIGURE 4). The smaller polygons on top don’t create openings (they merely “double” block the etch), so they have no real purpose in terms of the final wafer shape. In that regard, they are similar to dummy fill. This technique ensures the two masks have more similar color densities in this region.

Color regularity

Specific configurations, such as those found in memory applications, may also need strongly controlled, repetitive coloring patterns to help the optical proximity correction (OPC) process generate more consistent results. FIGURE 5 shows three vertical instantiations of a repetitive pattern with horizontal color alternation constraints. On the left, a density-balanced legal coloring assignment is shown. However, by adding a few extra coloring constraints, you can also achieve a regular repetitive coloring pattern, as shown on the right. By introducing this color regularity, you can increase the chances of consistency in the post-OPC results.

Layout symmetry is another aspect of design that benefits from color regularity. When there is a significant amount of symmetry around a central point, such as a sensitive analog circuit, the most desirable coloring solution maintains x and y axis symmetry around the central point. In FIGURE 6, the constrained coloring solution on the right adds constraints for x and y axis symmetry to generate a mirrored coloring pattern.

DFM-aware coloring

In design for manufacturing (DFM) optimization, weak lithographic configurations are often captured as process hotspot patterns, which can be used with DFM and/or resolution enhancement technology (RET) processes to minimize the chance of a hotspot forming during manufacturing. As it turns out, the coloring of these patterns in multi-patterned designs can influence whether or not a pattern becomes a hotspot, or actually change the hotspot severity or impact of a particular pattern. If a hotspot pattern is consistently colored in all its instantiations, it may prevent that hotspot from forming, or allow a carefully tuned OPC recipe to be applied.

In FIGURE 7, a different, but still legal, coloring is applied to a rotated/reflected pattern. Because the OPC process will now affect each instance differently, the rotated pattern may become a lithographic hotspot, while the original pattern does not.

FIGURE 8 shows the same legal coloring applied to both pattern instances, which allows the same OPC to be applied to the layout in both locations, because the coloring is the same, and the polygons that end up on each mask are consistent.

Sometimes there are cases where information from other layers indicate a color preference for certain shapes. These preferences are typically the result of analysis on another layer, or from information the designer provides, such as for critical or high voltage nets. While these preferences may sometimes conflict with each other for neighboring shapes in the same component, applying these preferences whenever possible helps drive an optimal coloring solution. In FIGURE 9, the red markers indicate a preference for placing those shapes on the green mask. In this case, there is one component that cannot comply, but placing three of the four tagged polygons on the preferred mask maximizes the preferred placements, making this optimal coloring solution.

Conclusion

In advanced process nodes, achieving the best performance and yield requires moving beyond the minimum requirements of the design rules to optimizing the layout. This optimization is a fundamental principle of all design for manufacturing (DFM) activities, including multi-patterning decomposition. There are many different situations in which special attention to color choices provide the potential to improve the manufacturing results of multi-patterned masks. Designers involved with generating the decomposed mask data before tapeout can expect to see more emphasis on color optimizations as the industry continues to refine and enhance multi-patterning processes.