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Polarising Hyper-NA models

It is becoming apparent that the future of lithography is to use Hyper-NA (Numerical Appeture) 193nm immersion systems to handle needs up to the 32nm node. Such systems can have NA > 1.2. At such hyper-NA values, correct modelling of polarisation effects is critical to understanding the benefits as well as limitations of polarisation choices. Peter Brooker and John Lewellen of SIGMA-C and Yuri Aksenov of Philips Research Leuven investigate different source polarisation and chrome biasing options for printing 45nm lines through pitch in resist

It is becoming apparent that the future of lithography is to use Hyper-NA (Numerical Appeture) 193nm immersion systems to handle needs up to the 32nm node. Such systems can have NA > 1.2. At such hyper-NA values, correct modelling of polarisation effects is critical to understanding the benefits as well as limitations of polarisation choices. Peter Brooker and John Lewellen of SIGMA-C and Yuri Aksenov of Philips Research Leuven investigate different source polarisation and chrome biasing options for printing 45nm lines through pitch in resist.

A problem facing all Integrated Device Manufacturers (IDMs) is estimating what tool sets will be needed for the next technology node. In this context, lithography simulation is indispensable in modelling tool capability even if the tools do not exist yet. To make an informed decision, extensive analysis can be done using simulation. Variables typically explored include chrome bias, source design, mask design (binary, altPSM, attPSM), scattering bar width and placement, etc.). Typically, a great investment is made in extensive "batch" routines for this exhaustive analysis. Often, thousands of individual simulations are run to characterise the capability of a given exposure tool to print a given technology node.

Optimising source design and mask bias for printing 45nm lines through pitch need not be separate issues. Printing the same line width through pitch, batch files are not needed for such analysis. The authors chose rather to investigate the built in analysis capabilities of the SOLID-C simulator.

The investigative process tackled the problem of source and chrome bias optimisation for printing resist lines through pitch, starting with a 100nm pitch. The maximum overlapping process window for both polarised and unpolarised dipole sources could then be determined. The investigation was then expanded from the mask to a 2D test cell. This test cell contained L/S patterns in both the X and Y directions at various pitches. Chrome bias necessary for process window overlap can be determined and the benefit of using an azimuthally polarised quadrupole source versus an unpolarised source was explored.


Simulation

In a single simulation set-up, the chrome width, source radius and offset were varied. SOLID-C automatically performed a Focus-Exposure Matrix (FEM) analysis and calculated the Depth of Focus (DOF) for the maximum process window for each set of chrome width, radius and offset. The DOF parameter can then be displayed versus the other parameters. The analysis was performed for both an unpolarised source and with the source polarisation vector parallel to the y-axis. This orientation of the polarisation vector results in TE polarisation since the polarisation vector is parallel to the L/S pattern.

A single simulation run for 400nm pitch, unpolarised was configured to vary chrome width, source radius and source offset for an unpolarised source case. The DOF analysis output is shown in figures 2 a and b as well as the exposure dose that is at the centre of the process window.

The first thing to notice from fig. 2 is that the maximum DOF is only between 55nm and 75nm. We also see that as the chrome width is increased, the exposure dose at the centre of the process windows increase also. This is expected. Lastly, as the chrome width increases, the DOF decreases slightly. Another observation is that the very maximum DOF occurs for the smallest source radius and the smallest line width.

Comparing results of the 100nm pitch case to the 400nm pitch case will determine what the optimum amount of chrome bias is along with a source configuration. From fig. 3 we immediately see that the DOF values for the 100nm pitch lines can be as large as 600nm. This is 8 times greater than typical values of 70nm for the 400nm lines. This clearly means that the width in focus of the common process window between 400nm and 100nm pitches will be limited by the 400nm pitch.

The comparisons showed that that for any given chrome width, the centre exposure dose for the 100nm pitch is always higher than that of the 400nm pitch, as expected. Comparing 100nm and 400nm pitch allows us to determine what chrome bias is necessary for the process windows to overlap.

In the unpolarised case the process windows are for 60nm chrome width for the 400nm pitch and 40nm chrome width for the 100nm pitch. The rectangle is for an exposure latitude of 4%. The focus width of the rectangle is 84nm. From figure 5 we see that the common DOF at 4% exposure latitude is only 84nm. Note also that the height in dose is determined by the 100nm pitch and the width in focus of the common process window is determined by the 400nm pitch.

Polarizing

So far we have reviewed unpolarised sources. By using a polarised source, the process window can be significantly increased. With the Solid-C simulator one can choose a common global polarisation over the entire source, Azimuthal, Radial or alternatively, one can specify the polarisation at each point in the source using an external file.

With the "Azimuthal" polarisation option chosen, the polarisation vector is parallel to the y-axis at the locations of the dipole. Since the L/S pattern is also parallel to the y-axis we have TE polarisation. For an X-dipole source, very similar results to azimuthal polarisation would be obtained for the choice of uniform polarisation over the source with the polarisation vector parallel to the Y axis.

We see then that using an azimuthally polarised X-dipole source increased the 4%EL DOF to 109nm from 84nm. This represents an increase of 30%. Other polarisation choices such as radial would have resulted in process windows smaller than the unpolarised case. The same holds to true for a global polarisation of the source where the polarisation vector is parallel to the X-axis.

Analysis was required for a pattern that contains features oriented in both the X and Y directions. For this reason a quadrupole source made up of an X and Y dipole was required. In order for both the horizontal and vertical lines to be resolved it will be necessary to use quadruple illumination.

From Figure 7 we see that in order to print the 100nm lines simultaneously it is necessary to use the quadrupole source. In figure 7 we have presented the case for azimuthal polarisation of the quadrupole. The XY-quadrupole source shown will optimally print horizontal and vertical line/space patterns at the finest resolution. A much more common pattern is a quadrupole rotated by 45¡.

Once the polarised and unpolarised sections had been explored there was a need to observe overlapping process windows for the polarised and unpolarised cases. The first thing to notice about Fig. 8 is that the exposure latitude of the 100nm vertical lines has been greatly reduced. Note also that the 4%-EL DOF of the common process window has decreased to only 64nm. This compares to a DOF of 109nm for the polarised dipole source. This represents a decrease of 41% due to the addition of the Y-dipole. Note also that the maximum EL is about 6%.

The reason the common process window has decreased so dramatically is due to the addition of the Y-dipole, which is needed to print the horizontal lines. Unfortunately, adding the Y-dipole greatly decreased the image contrast for the vertical lines.

The first thing to note about Fig. 9 is that the maximum height in dose of the common process window has decreased by 30% to 3.6% as compared to 6% for the polarised source. Azimuthal polarisation has a clear benefit of increasing the exposure latitude of the dense lines pattern.

Cpk ANALYSIS

So far we have shown that with proper chrome biasing and source design it is possible to obtain overlapping process windows for 45nm resist CDs at 100nm and 400nm pitches. A metric that was quoted was the DOF at 4% exposure latitude. Such metrics are useful but they do not take into account any information that may be known about the process variation. In particular, knowing the DOF alone does not estimate how "capable" the process is.

Process capability is measured by Cpk. This process capability index Cpk can be viewed in its entirety on the website. In particular, if Cpk >1, the process is deemed to be manufacturable. In order to calculate Cpk, one must specify what we are measuring and also what are the upper spec limit (UL) and the lower spec limit (LL). In our specific application we were measuring the resist line width CD. The target CD is 45nm. Our limits are set to +/- 10%. This means UL= 49.5nm and LL=40.5nm.

Let's now make the assumption that focus and exposure dose are normally distributed with variations _E and _F. Since lithography simulation tells us how resist CD varies with focus and exposure, and we know the probability distribution of both focus and exposure, we can then calculate Cpk for any specific values of _E and _F .


In figures 10 and 11, contours of Cpk are presented for the case of the 100nm pitch lines on the 2D mask for a polarised and unpolarised source. Examining Fig. 11 we see that the Cpk contours are closer to the origin for the unpolarised case. The largest effect is observed on the _E axis where the Cpk values are half that as compared to the polarised case.


Conclusion

Lithography simulation was used to explore the effect of dipole offset, dipole radius and chrome bias for printing 45nm lines at 100nm and 400nm pitches. Through inspection of the data we were easily able to determine an appropriate source design and chrome bias necessary to obtain overlapping process windows for the case of printing 45nm lines in resist at 100nm and 400nm pitches. This efficient exploration of parameters was accomplished using options available within the simulator rather than having to resort to the complication of batch analysis.

When investigating printing with a 2D mask we saw that in order for lines at 100nm pitch to print simultaneously in both the vertical and horizontal directions, a quadrupole source was needed. We then saw that the DOF at 4%-EL decreased by 40%. This decrease was due to the degradation of the image contrast caused by the addition of the Y-dipole. We also observed that for the 2D mask pattern, the maximum EL of the common process window for the polarised source was 6% as compared to only 3.7% for the unpolarised source.

In the limit of an ideal ARC layer, we showed that it is possible to obtain a non-zero common process window. In the process, we have demonstrated that lithography simulation is an invaluable tool in investigating critical issues associated with printing such aggressive geometries. Although we only addressed source design and Cr biasing, many other design aspects could have just as easily been optimised. One that immediately comes to mind is the addition of non-printing scattering bars to the 400nm pitch lines to increase the DOF at the isolated pitch. Proper modelling of these effects requires solving for the electromagnetic near fields exactly in the mask. An advanced lithography simulator such as SOLID-C can easily handle such tasks and will be the subject of future work.

The full article including Cpk Process Capability Index appendix can be viewed on the website.

Figure 1: X-Dipole source specification. Offset is distance from center. Radius is radius of pole

 

Figure 2: Analysis results for 400nm pitch, unpolarised source. In a), the DOF is plotted and in b), the exposure dose at the center of the process window is displayed. The horizontal axis in both plots is the width of the chrome. All data is displayed for a source offset of 0.4. As is shown by the drop down menu in a), data is also available for many other offset values

 

Figure 3: Results for 100nm pitch for an unpolarised source. The process window DOF values are presented versus chrome width for different source offset values

 

Figure 4: Process windows for 400nm pitch is shown in a). In b), the 100nm pitch process window is displayed. The line widths are 60nm for the 400nm pitch and 40nm for the 100nm pitch

 

Figure 5: The overlapping process windows for the unpolarised case. The process windows are for 60nm chrome width for the 400nm pitch and 40nm chrome width for the 100nm pitch. The rectangle is for an exposure latitude of 4%. The focus width of the rectangle is 84nm

 

Figure 6: Overlapping process window for azimuthally polarised source. Rectangle drawn is for 4% exposure latitude. From the rectangle we see that the DOF is 109nm at 4% exposure latitude

 

Figure 7: Resulting resist patterns for X-Dipole and quadrupole sources. Note that the 3D resist profile is only created for the area defined by the green box on the mask. This section includes the horizontal and vertical lines at 100nm pitches

 

Figure 8: Process windows for the 2D mask. The rectangle drawn is for 4% exposure latitude. From the graph we see that the 4% EL-DOF is 64nm

 

Figure 9: 2D mask pattern with unpolarised quadrupole source. The rectangle has a height of 3.6% EL and the focus width is 61nm

 

Figure 10: Cpk contours for 100nm pitch pattern on test cell mask for a polarised source. The process is deemed to be manufacturable if Cpk >1

 

Figure 11: Cpk contours for the 100nm pitch for an unpolarised source

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