**Fan Jiang**, Mentor Graphics, Wilsonville, OR

*EUV’s off-axis mask illumination introduces a special problem in EUV OPC – the shadowing effect.*

While there is debate about when extreme ultraviolet lithography will be ready for production, there continues to be active research and development into making every part of an EUV system work, including optical proximity correction (OPC). That’s right, there is no break from the pattern distortions seen in sub-wavelength lithography. In fact, EUV introduces significant new pattern-distorting effects. As EUV has developed over the last few years, the models for these new EUV-specific effects have also developed and improved. Now that pre-production EUV scanners are in foundries and being rigorously tested, tools to correct for EUV-specific optical effects are being fully integrated and tested. This article covers the impact on OPC caused by one of those new distortions, the EUV shadowing effect, and looks at a model-based solution for managing the shadowing effect.

Scaling down to a wavelength of 13.5nm for EUV lithography requires dedicated optics, materials, and above all reflective reticles. An EUV optical system is built completely from reflective components (mirrors) because everything absorbs 13.5nm EUV wavelength. The reflective mask stack and off-axis mask illumination required with EUV induces new imaging effects, like mask shadowing, that need to be carefully captured through computational lithography. At the wafer level, the mask shadowing effect causes CD variation through the illumination scanner slit, with the amount of distortion depending on the orientation and position of the feature. Currently, the angle of incidence is 6° from normal with a changing azimuthal angle. This angle varies across the scanner’s illumination slit and ranges from 67° to 123°.

This off-axis illumination causes a shadowing effect because the mask has a thickness, as illustrated in FIGURE 1. Theoretically, the shift of the image in this case can be written in terms of the total thickness and the incident angle: shift = total thickness x tan (6°).

In order to simulate this correctly, we need to use 3D mask simulation. What is more difficult is when we try to look at this issue through the scanner’s illumination slit. We depict the position in the scanner slit as a combination of two parameters: radius, intersection of the optical axis with the mask plane, and the azimuthal angle 0, varying from 66° to 114°, where 0=90° corresponds to the slit center. At the slit center, vertical oriented lines are not subjected to the mask shadowing effect. Horizontal oriented lines, which are perpendicular to the plane of incidence, fully capture the mask shadowing effect. FIGURE 2 shows that as the azimuthal angle changes through slit, the impact on the mask varies.

To evaluate topology-aware mask modeling for EUV imaging, we collected a large set of wafer CD data and compared the data to simulation data. FIGURE 3A shows the error between the wafer data and the simulation data without shadowing effect considered for different patterns. The simulation only uses 3D mask calculation at the center of the slit, so there is no simulation of the shadowing effect at the other slit locations. The result shows a parabola trend through slit, which is caused by the change of azimuthal angle.

We used 90° as the azimuthal angle in the 3D mask calculation. This is the correct azimuthal angle at the center of the slit. So the simulation data matches wafer CD data best at the center. When the azimuthal changes from 90°, the 3D mask calculation becomes less and less accurate. So the error gets bigger towards the edge. Error is calculated as measurement minus simulation, so the negative numbers shown in FIGURE 3 mean that the simulation gave a larger number than did the wafer CD. The data in FIGURE 3a does not capture the through-slit shadowing effect, only the center effect. To have a correct simulation result, we have to add the through-slit shadowing effect into our model. We used a rule-based bias table to include it. The rule-based bias table could come from the following formulas, using the incident angle/azimuthal angle and the thickness of the mask:

where h is the total thickness of the mask, 0 is the incident angle and ϕ is the azimuthal angle. The relation between azimuthal angle and the location in the scanner slit direction is:

where R is the radius of the illumination slit, and y is the location. These equations link the location and bias together, and serve as a guideline for generating a bias table for the ideal theoretical shadowing effect. Sometimes the shadowing effect is not the only through-slit change we want to consider. For example, the aberration and the illumination may also change. When you have a set of experiment data at several slit locations, without any shadowing effect compensation, you could measure the difference between the wafer data and the target. This difference gives a bias table for through-slit change that includes shadowing bias change and also aberration and illumination change.

In the data shown in FIGURE 3b, the bias table comes directly from experiment data rather than theoretical formulas, which includes all the through-slit changes. When we applied this bias table in our simulation, we re-calculate the CD error.

We see in FIGURE 3b that at each slit location, the average errors between simulation and measured CD are significant decreased compared to the results in Figure a, However, the RMS error calculated from the data points in FIGURE 3b does not improve. This is because the shadowing effect seen varies between different patterns. The rule-based bias table considers the change through slit, but it considers the change for all different patterns the same. However, the change through slit is pattern dependent. To get a more accurate simulation result, we need to use model-based method to predict and correct for the shadowing effect.

As an example, there are 7 slit locations in FIGURES 3a and 3b. If we use 3D mask modeling at all these locations, we should be able to calculate the shadowing effect correctly. The CD error result when using a model-based method instead of a rule-based bias table is shown in FIGURE 3c.

Comparing the RMS error calculated from the data in FIGURE 3b and FIGURE 3c at different slit locations, we see a significant benefit of using a model-based method for determining shadowing effect through slit.

These experiments showed us that in order to simulate shadowing effect with the most accuracy, model-based method may be necessary. Hence, when we talk about compensating for shadowing effect, we could use either a rule-based bias table for faster computation time or a model-based method for better accuracy.

The asymmetric illumination of EUV lithography also causes another problem—asymmetry of the SRAF pattern. The first question is when do we need to use SRAF in EUV? You might recall a similar situation in KrF and ArF. SRAF was first used with the 130 nm technology node with KrF, and recently, with a 0.39 k1 factor. In ArF, we started to use SRAF for the 90 nm node, with 0.35 k1 factor. For the 7 nm process node, the half pitch is 16 nm and the k1 factor is 0.41. This k1 number is close enough to what it was in KrF and ArF when we introduced SRAF that we can consider using SFRAF in EUV lithography. The next question for using SRAF in EUV is how to place scattering bars. We made a simple example with an isolated contact in a 7 nm node wafer. By applying symmetric SRAF, we get the process window in FIGURE 4a, and the depth of focus (DOF) is 98 nm. Also, we moved the SRAF around and looked for the best setting for DOF. The best DOF we found in this case is 167 nm, shown in FIGURE 4b, accomplished by using a set of asymmetric SRAF. By comparing the two process windows, we see that the process window of symmetric SRAF placement is not symmetric, which decreases the DOF. We conclude from this that to obtain the best process window, asymmetric SRAF placement may be needed due to EUV’s non-telecentric imaging system.

EUV’s specific off-axis mask illumination introduces a special problem in EUV OPC – the shadowing effect. This effect can be adequately compensated for by using a rule-based bias table, which gives faster runtime than the model-based simulations. But because not all the patterns at the same location require the same bias value, the model-based (3D mask simulation) compensation has a better prediction of the shadowing effect, and therefore gives a more accurate repair of shadowing errors. Finally, we found the best SFRAF placement is also asymmetric, as judged by DOF, because of the asymmetric nature of the incident angle. The shadow modeling results were verified on the pre-production ASML NXE:3100 EUV lithography tool. As EUV gets closer to production use, the OPC tools needed to correct for EUV-specific patterning effects are well developed, integrated, and tested.

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