Robust Rule-Based Corrections with OPRX

Topics in this technical note:

Introduction

This technical note shows how rule-based correction with OPRX can be very robust. Some industry experts have expressed doubt that an automated rule-based correction program can be as robust as a model-based (sometimes called simulation-based) tool. Perhaps this notion derives from rule-based tools with limited rule expression capabilities which produce over-corrections in dense figure situations. OPRX, however, has a rich rule expression capability and can produce corrections equal in quality to any model- or kernel-based tools.

It is important to keep in mind that with rule-based correction it is very easy to get bad corrections if the correction rules are bad. Bad Rules --> Bad Correction; Good Rules --> Good Correction! The tools and customer support provided with OPRX help you make good rules.

Correction Demonstration

To demonstrate the robustness of OPRX's rule-based correction we will consider the interconnect-crossover sample shown in Figure 1. There are three crossovers shown with pitches of 0.4um, 0.5um and 0.6um. The electrical crossover is effected on another layer with a line segment connecting the two short vertical lines. Because of line-shortening of those two lines (Figure 1a), the integrity of that connection is at risk. It is important to compensate for that correction without over-correcting (making the line too long).

Line shortening can be compensated by lengthening the line or by placing a hammerhead at the end of the line. Hammerheads are superior in situations like this where the line-end is directly opposite and close to another figure. The robustness of the line-end correction is compromised by the tilting of the dog-leg, so correcting the dog-leg so it is not tilted is indicated as well. This is done with the use of corner serifs.

The corrections required for the three pitches (line-shortening, dog-leg tilt, and line width) are all different, with the greatest correction required for the finest pitch. Notice that the line-shortenings near the crossovers are different from the line shortenings at the tops and bottoms of the structures. This means that different sized hammerheads are requred for all these conditions. Compensating for the dog-leg tilt requires different sized serifs for each of the three pitches. Although it is difficult to discern at the magnification displayed, the line widths need to be corrected as well. The line width corrections for the inside lines are different from the two outside lines, and the line width corrections are different for the three pitches.

A lithographic model was specified using SimRule and rules were computed using the model. The specifications for correcting the entire layout are recorded in a single rule file. OPRX performed an automated correction of the layout using the rules specified in the rule file. The results of the OPRX correction are shown in Figure 1B and the corrected layout is shown in Figure 1C.

Notice how well OPRX has corrected all of the line-shortening and the dog-leg tilts without overcompensating. This is possible, because the specifications for how to make hammerheads and serifs depend on the local environment in two dimensions. Although not apparent at this magnification, the line widths have been corrected as well.
A: Uncorrected


B: Corrected with rule-based OPRX


C: Corrected Layout


Figure 1. Interconnect crossovers of different pitch, left is 0.4um pitch, middle is 0.5um pitch, right is 0.6um pitch (0.25um grid displayed): (A) Uncorrected; (B) Corrected with rule-based OPRX; (C) Corrected Layout. [Illumination is 248nm, NA=0.6, sigma=0.65, bright field, binary reticle, and a 2-Gaussian resist model]

Lithographic Robustness Over the Process Window

The main problem with the uncorrected pattern is that the line-shortening in the crossover region is significant at nominal exposure and zero focus, and it is much worse at the extremes of the process window. Figure 2 shows how the line-shortening for this process can be nearly 200nm.
A: B: C:

Figure 2. Uncorrected layout through focus with nominal and plus and minus 10% exposure contours: (A) -0.3um; (B) 0.0um; (C) +0.3um.
A: B: C:

Figure 3. Effect of no defects through focus with nominal and plus and minus 10% exposure contours: (A) -0.3um; (B) 0.0um; (C) +0.3um.
Shown in Figure 3 is the effect of focus variation (-0.3um to +0.3um) on the correction at the crossover. The structures print successfully for the entire exposure/focus range. Defocusing increases line-shortening, whereas it has no significant effect on the dog-leg correction. The maximum line shortening, which occurs at the high end of the exposure range and at the extreme focus value is only about 80nm, which is substantially less than 150nm line-shortening for the uncorrected pattern at nominal exposure and zero focus.

The situation is somewhat different if there is a defect between the line end and the dog-leg as shown in Figure 4. At nominal exposure and above, the structures print satisfactorily in spite of the defect. However, for the low end of the exposure range, there is bridging between the line end and the dog-leg. The process is not tolerant to a 50nm opaque defect at -10% exposure.
A: B: C:

Figure 4. Effect of a 50nm square defect through focus: (A) -0.3um; (B) 0.0um; (C) +0.3um.


If this kind of insensitivity to defects is a requirement, then one could achieve it by changing the specification for (1) line-shortening correction or (2) how square the corrected dog-leg corners should be, or both. For method (1) for example, one could specify that for dense regions, the line length be correct for the -10% exposure condition. This effectively undercorrects, but is still a substantial improvement over the uncorrected line. For method (2) one could allow less aggressive correction of the dog-leg. In particular, one could reduce the correction of the outside corners thereby moving the contours for the dog-leg away from the line end. The result of just such a correction (effectively eliminating the outside corner serifs) is shown in Figure 5. The defect does cause a distortion of the dog-leg contour for the -10% exposure condition, but bridging does not occur.
A: B: C:

Figure 5. Effect of a 50nm square defect through focus with less correction of the dog-leg: (A) -0.3um; (B) 0.0um; (C) +0.3um.


This page last modified September 24, 1998
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