Understanding characteristic EUV image variations in full-field exposure tools

Peter Brooker, Lena Zavyalova, Synopsys, Mountain View, CA USA

A clear understanding of the physical origin of image CD and placement variations will make it possible for EUV users and optical proximity correction (OPC) vendors to develop OPC strategies at the 22nm and 16nm device nodes to effectively compensate for them.

Given the recent technical progress of extreme ultraviolet (EUV) technology [1] and the existence of full-field EUV alpha tools at customer sites, it is necessary for all potential EUV users to understand the origin of the sources of image critical dimension (CD) and placement variations that are unique to EUV. EUV scanners are fundamentally different from current optical scanners. These fundamental differences result in changes of image CDs unique to EUV optics, which have hidden rotational symmetry, and that must be addressed by OPC. To gain insight into the fundamental differences, idealized versions of optical and EUV scanners will be presented. After a brief discussion of EUV lithography simulation concepts, we discuss the expected image CD variations from effects that will have to be corrected by OPC:

– image CD and image placement difference between vertical and horizontal lines in the mask due to mask shadowing,
– the image differences due to changing mask illumination conditions as one moves towards the edge of the ring slit, and
– the change in image CD due to expected amounts of flare.

Rigorous lithography simulation of the EUV imaging process, including complete solution of Maxwell’s electromagnetic field (EMF) equations for the reflective EUV mask – with topography – will be used to accurately predict the magnitude of the expected CD variations. Such predictions are a necessary first step in developing field and pattern orientation sensitive OPC strategies to compensate for the expected CD variations.

Idealized representations of EUV and optical scanners

The idealized representation of an optical scanner using transmissive optical elements is shown in Fig. 1.

Figure 1: Idealized representation of an optical scanner using transmissive optical elements. The image of the source appears at the aperture (system) stop in the Köhler illumination scheme.
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Referring to Fig. 1, we see that the mask is illuminated with light from the source that is parallel to the optical axis for both the on-axis and off-axis image points. As the light passes through the mask, diffraction orders are formed. Only the diffraction orders that make it through the scanner slit are collected by lens 1. Lens 2 images these diffraction orders so that an image of the mask is formed in the resist layer at the wafer plane. (Both these “lenses” actually consist of many lens elements.) Note also that the optics is arranged so that the source is imaged at the aperture stop. With this Köhler illumination arrangement, one can see from the diagram that the diffraction orders from the off-axis mask point pass through the stop at roughly the same location as the on axis field point. This means that as the diameter of the stop is reduced, the diffraction orders of the off axis points are attenuated in the same fashion as the on axis points.

In a similar fashion, let us consider an idealized EUV system that is catoptric. To do this, lenses 1 and 2 are replaced by curved (multi-element) mirrors, and the mask must be reflective as illustrated in Fig. 2.

The scanner ring slit and curved mirrors M1 and M2 share the z-axis as their optical axis, resulting in rotational symmetry. The angle Θ defines the position in the ring-slit of the local XΘYΘ coordinate system as in figure 2c. The views shown in 2a and 2b are characteristic of the XΘYΘ plane and change very little for different locations on the ring slit (Θ values) because of the rotational symmetry of the optical system about the z-axis. The source (Fig. 2c and 2d) illuminates the ring slit with light whose direction is also rotationally symmetric about the z-axis. The value of Θ thus can be used to define both the illumination angle and the position in the ring slit.

Figure 2: An Idealized EUV system for rotationally symmetric illumination of the ring slit. The ZΘZ side view is shown in a) and b) is the top XΘZ view. The view down the Z-axis showing the ring slit and the reticle behind it appears in c). This view also defines the rotated XΘYΘZ local coordinate system. The illumination angles Φ and Θ are defined in d). Angle Φ is a polar angle measured from the positive Z-axis, while angle Θ is an azimuthal angle measured from the positive X-axis. With illumination that is rotationally symmetric around the Z-azis at the ring slit, Θ can be used as a slit-position coordinate, as well as a direction coordinate for the source illumination.
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The aperture stop defined in Fig. 2 also needs to be discussed. As in the optical system, we see that the stop is located where the image of the source occurs. The rotational symmetry about the z-axis assures that diffraction orders from different parts of the slit will traverse the stop at the same location.

Having presented the fundamentals of an idealized reflective EUV system, we can now look at a few points regarding lithography simulation of an EUV scanner.

Rigorous lithography simulation of EUV

The mask in an EUV system is reflective. Incident light from the source will scatter from the mask topography, and a portion of the scattered light will enter the EUV projection optics. To capture all physical effects, a simulator must calculate the electric “near” fields of the mask by rigorously solving the Maxwell’s EMF equations for the reflective EUV, multilayer topographic mask. Once the electric fields are known, the diffraction orders scattered from the mask can be calculated. The simulator will then use the numerical aperture (NA) of the system to determine which diffraction orders make it through the system, and the ones that do will be used to construct the far field at the wafer. For this work, Synopsys’ Sentaurus Lithography commercial simulator with the EUV Module was used [4]. This type of rigorous simulator can be used to model all aspects of the imaging process, as well as the formation of the 3D resist profiles.

It’s important to understand the simulation results for the effects unique to EUV that result in changes in the image CD for which OPC will have to compensate: mask-shadowing effects, CD variation vs. ring slit position, and the CD variation for expected flare levels.

The simulation setup will use the parameters of an EUV alpha demo tool [2, 3], which are NA=0.25, sigma = 0.5, Φ=6° and the ring slit extending to ± 24°. The ring slit angular extension means that the source illumination angle Θ goes from 66° at one edge of the ring slit to 114° at the other edge of the ring slit. The multilayer EUV mask simulated consisted of 40 molybdenum silicon (MoSi) pairs with a 70nm tantalum nitride (Ta6N4) absorber on top of the multilayer stack.

3D mask shadowing effects

Consider the specific case of mask illumination at the center of the ring slit. For this location, Φ=6° and Θ = 90°. Now consider a “vertical” mask line/space (L/S) pattern that is parallel to the Y-axis and a “horizontal” L/S pattern that is parallel to the X-axis (Fig. 3).

Figure 3: Horizontal and vertical mask line/space patterns located at the center of the ring slit. The vertical pattern with the lines parallel to the y-axis is shown in a) and horizontal orientation is shown in b). Also shown are the mask illumination angles of Φ=6 degrees and Θ=90 degrees.
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In Fig. 3, the vertical and horizontal L/S patterns can be seen at the center of the ring slit. By looking at the illumination direction in the figure, it is obvious that the shadowing will be at a minimum for the vertical case. On the other hand, we expect a significant amount of image shift due to shadowing for the horizontal lines. Simulation results for the two cases are presented in Fig. 4.

Figure 4: Aerial image in resist at the center of the ring slit for horizontal and vertical line patterns. For the “3D Vert” curve, the “position (nm)” axis is the x-axis. For the “3D horiz” curve the “position (nm)” axis is the y-axis. The “2D” curve refers to the result in which a non-topographic Kirchhoff mask is assumed.
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Figure 4 shows that the “3D Vert” curve is clearly centered about the “position” axis. This is expected since no mask shadowing should occur for this orientation (Fig. 3). The horizontal orientation, on the other hand, clearly shows a shift in position as well as attenuation. The amount of shift is ~5nm, which is significant and is one of the largest effects that will need to be compensated for by OPC. It is also possible to consider vertical and horizontal patterns at the edge of the ring slit as shown in Fig. 5.

Figure 5: Horizontal and vertical L/S patterns at the edge of the ring slit. As shown in the diagram, angle Θ=114 degrees defines the field location at the edge of the ring slit.
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By inspecting Fig. 5, it becomes apparent that at the edge of the ring slit, even the vertical lines should pick up some image shift, and the image shift should reverse when compared to the other edge. The image intensity profiles for different values of Θ are presented in Fig. 6.

Figure 6: Comparison of image intensity vs. position for 35nm vertical and horizontal patterns. Cases considered are at the right edge of the ring slit (Θ=66°), the center (Θ=90°) and the left edge(Θ=114°).
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Inspection of Fig. 6 indicates that there is ~1nm image shift for the vertical line pattern as one moves through different values of Θ across the ring slit. The horizontal lines show much less image shift variation for different values of Θ.

All results presented up to this point were for 35nm dense line/space features. Let us now compare image CD variation of dense line to isolated lines. Simulation results for image CD values are presented in Table 1 for different values of Θ. Values of Θ=66°, 90° & 114° correspond to the right edge, center and left edge of the ring slit, respectively.

Table 1: Image CD for horizontal and vertical L/S patterns for different values of Θ. The Θ values considered correspond to edge and center slit positions.

From Table 1, the following conclusions can be drawn:

– The largest CD variation for vertical vs. horizontal patterns occurs at the center of the field (Θ =90 deg) for the isolated pattern. This HV bias is ~2.1nm. The HV bias at the edge of the field is ~1nm.
– The largest CD change as Θ is varied is ~0.6nm and occurs for the vertical lines of the dense pattern.

Finally, the amount of pattern shift is also a function of mask plane defocus. For a further discussion of the origin of this effect and its minimization the reader is referred to [5].

Flare effects

The origin of flare is undesired light scattering due to surface roughness of the optical surfaces, as well as other multiple scattering mechanisms. Current systems have 16% scatter level that must be reduced to 5% for high-volume manufacturing [1]. For the EUV systems, high levels of flare mean that an L/S pattern on a brightfield mask will print very differently than the L/S pattern on a darkfield mask. Generally, features in a brightfield mask will suffer more from stray light compared to the darkfield. More specifically, each layout will have a unique flare signature that will depend on the mask layout density. Due to the far-reaching nature of flare, spanning a submicron-to-millimeter scale, the flare effect will extend over the entire exposure area.

Flare can be measured experimentally via disappearing pad tests [6] in addition to the mirror’s surface roughness measurements. These measurements are used to determine the power spectrum density (PSD) function of the projection system. Once the PSD is known, it can be used by the rigorous simulator and by the OPC tool to calculate the flare-modified image. The calculation uses the PSD as well as the surrounding mask area. The effect of flare on the image intensity is shown in Fig. 7.

Figure 7: Image intensity vs. position for different values of flare. The case considered was a 35nm line at a pitch of 160nm.
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From Fig. 7, we can see that current levels of flare (16%) can significantly degrade the image, and consequently, the actual CDs in resist can change significantly depending on the surrounding mask pattern. From the image intensity plots, such as those in Fig. 7, it is possible to calculate the rate of change in image CD values versus flare. Image CD versus flare level is presented in Fig. 8.

Figure 8: Impact of flare on image CD for dense and isolated mask patterns. The flare sensitivity is above 1nm/%, signaling that flare-induced CD variation is significant and the inclusion of stray light into imaging and OPC models is necessary.
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Looking at Fig. 8, one can see that at the current 16% level, the flare has changed the image CD by 11nm for the 25nm 1:1 pattern. For the production-tool level of 5%, the CD change is still significant at 3nm, indicating that a flare compensation strategy is required. Moreover, flare levels are not constant and will vary as a function of field position. CD variation due to localized flare fluctuation is expected to be severe, even in the nominally dark field regions, and a correction scheme is required in order to compensate for very long range and substantial percentage layout dependent flare effects. Calculation of a full-chip flare map is a major new and integral step in the overall OPC flow [7] designed to accurately predict CD variations arising from density variation across the chip.


This article introduced the idealized EUV scanner and used this example to emphasize the inherent rotational symmetry of an EUV system. In particular, it outlined how the ring slit is illuminated with light from the source that is rotationally symmetric about the z-axis, and provided exact definitions for the illumination angles Θ and Φ.

With the definitions of Θ and Φ clear, major effects were presented that result in CD variations for which OPC would have to compensate. The effects presented were those associated with mask shadowing, variations with the ring slit angle Θ, and flare. Simulation was used to quantify the magnitude of these variations. The largest effects that will have to be compensated for by OPC in future production systems are the horizontal-to-vertical CD bias and the horizontal image shift, which was 5nm at the center of the ring slit for 35nm dense lines. This field-position dependent CD bias compensation is a paradigm brought about by the annular ring slit systems that are a new component to the overall OPC flow. Across-field localized flare calculations and subsequent compensation is also critical to achieving the across-slit CD uniformity control.


[1] O. Wood, “Learning from the EUVL Alpha Demo Tool 45nm Device Demonstration,” SEMATECH Litho Forum, May 13, 2008.
[2] H. Kang et al., “EUV Simulation Extension Study for Mask Shadowing Effect and its Correction,” Proc. of SPIE Vol. 6921, 69213I, (2008).
[3] H. Meiling et al., “Performance of the Full-Field EUV Systems,” Proc. of SPIE Vol. 6921, 69210L, (2008).
[4] Sentaurus Lithography EUV lithography simulation software, Synopsys Inc. http://synopsys.com/products/tcad/lits_ds.html.
[5] T. Schmoeller, T. Klimpel, “EUV Pattern Shift Compensation Strategies,” Proc. of SPIE Vol. 6921, 69211B, (2008).
[6] J. Kirk, “Scattered Light in Photolithographic Lenses,” Proc. of SPIE Vol. 2197, 566-572, (1994).
[7] Proteus full-chip optical proximity correction (OPC) software, Synopsys Inc. http://www.synopsys.com/products/avmrg/proteus_ds.html


Peter Brooker received his PhD in nuclear engineering and engineering physics from the U. of Wisconsin and is a corporate applications engineer for the Synopsys Sentaurus Lithography product at Synopsys, Inc., 700 E. Middlefield Rd., Mountain View, CA 94043 USA; ph 650/584-5000, e-mail: brooker@synopsys.com.

Lena Zavyalova received her BS and MS degrees in microelectronic engineering and imaging science from RIT and will complete her PhD in imaging science in 2008; she is a corporate applications engineer for the OPC modeling group at Synopsys Inc.


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