Why the mask world is moving to curvilinear
If you’ve been to a lithography or photomask technology conference
lately, you’ve likely noticed a trend: many papers and talks on
curvilinear masks, curvilinear OPC, curvilinear ILT, curvilinear mask
process correction (MPC), and curvilinear mask formats. The photomask
industry is experiencing a fundamental shift from Manhattan masks to
curvilinear masks. Part 2.
By Leo Pang, D2S, Inc.
Manhattanizing curvilinear ILT mask shapes creates two issues. First, there is the issue with VSB shot count discussed in Part 1 of this article in SiS Issue 6. The other issue is mask dose margin. Just as the wafer print on the scanner has process window, mask writing on an eBeam mask writer also has process window. In the case of wafer process window, the two variables are focus and dose. In mask writing, since the eBeam writer has infinite or very large depth of focus, the main variable is dose. Instead of calling it dose latitude (as they do in the lithography world), the mask world calls it dose margin. Dose margin is particularly bad for 90-degree corners. Manhattanizing curvilinear mask shapes creates a lot of 90-degree corners, as shown in Figure 11.
Figure 11. Dose margin is poor for 90-degree corners. Manhattanized
curvilinear shapes have many 90-degee corners and so have poor dose
margin in comparison to the smooth curvilinear shape.
In Figure 12, on the right, we show the dose margin for Manhattan and curvilinear contact arrays. Dose margin is represented by a pseudo color: the red represents bad dose margin and the green represents good dose margin. The 90-degree corners of the Manhattan contacts clearly have worse dose margin than the smooth curvilinear contacts. On the left of Figure 12, is a study done in 2019[16], demonstrating that while the edges of the square contact had good dose margin, the corners had unacceptable dose margin. At the same time, it shows that circles at any angle have good dose margin.
Figure 12. While edges of Manhattan features have good dose margin,
90-degree corners have very poor dose margin, as shown by the red
pseudo color. Circles have acceptable dose margin at any angle, as
shown by the green/yellow pseudo color[16]. Source: D2S.
In addition, curvilinear shapes have less variation on wafer or smaller mask error enhancement factor (MEEF). A 2022 study found that in comparing the MEEF of a Manhattanized diagonal line to a curvilinear diagonal line, the smooth curvilinear line had ~28% improvement in MEEF over the stair-stepped Manhattanized line [17] (Figure 13).
This is the fundamental reason why curvilinear is better. Imagine moving the edge of a shape by a unit of 1, as shown in Figure 14. If it is a Manhattan shape, such as a square, the edges in the X and Y direction are moved by 1, but the corners are moved by 1.4. In a curvilinear shape, such as a circle, the edge in every place on the circle is moved by 1. This means the same change on mask will cause more variations on wafer with the Manhattan shape than the curvilinear shape.
For the same reason as the explanation above, curvilinear shapes have less variation in the mask process as well. In the mask process, which involves bias processes such as etching, curvilinear shapes are created more faithfully. Figure 15 summarizes the findings of a joint study of contact arrays with Micron and D2S. We created contact arrays, both curvilinear and Manhattan [18], and made 6 copies on each array on the mask. We took measurements every four nanometers from four locations on each contact array (left edge, center, a corner, and the bottom), including hundreds of contacts each for a total of millions of measurements.