1.1.

3D Mask Effects in EUV Lithography

Figure 1(a) shows a schematic sketch of an EUV mask. The multilayer reflects the incident light from the illumination toward the projection system. The mask pattern is defined by an absorber on top of the multilayer. To separate the reflected from the incident light, the mask is illuminated with obliquely incident light that is tilted in the $yz$ plane. The tilt of the illumination introduces an asymmetry of the imaging system and a difference between the imaging behavior of $x$-parallel horizontal features (as shown in the figure) and $y$-parallel vertical features. The illumination direction of the features varies with the position in the exposure slit.

Fig. 1

Schematic of an EUV mask. (a) Geometrical representation by an absorber on the top of a reflective multilayer. (b) Double diffraction scheme, first diffraction of the incident light (green bold arrow) by the absorber pattern, backreflection from the multilayer, second diffraction from the absorber, see Ref. 7 for a more detailed discussion.

The described asymmetry of EUV imaging introduces orientation-dependent feature size, placement, and nontelecentricity (nTC), i.e., variation of feature position versus focus position.⁸ Variation of the incidence direction of the light on the mask versus the position in the illumination source causes image blur and deteriorates the contrast of the obtained images.^9,10 Deformation of the phase of the propagating light by the thick absorber causes pitch-dependent shifts of the best focus position, asymmetric process windows, and other aberration such as effects with adverse impact on the image quality.^11–13

The diffraction scheme in Fig. 1(b) highlights other important characteristics of EUV imaging. The light is twice diffracted by the EUV mask absorber. The first diffraction occurs when the incident light from the illuminator hits the absorber. The diffracted light penetrates into the multilayer and is reflected at the layer interfaces. The upward propagating light hits the absorber again and is diffracted a second time. The light in each diffraction direction that enters the entrance pupil of the EUV projector is composed of several diffraction orders. The coherent superposition of these orders depends on the reflectivity characteristics of the multilayer. Finally, the light that is reflected from the top of the absorber (not shown in Fig. 1) contributes to the image formation as well and causes a sinusoidal variation of the image metrics versus the absorber thickness.⁶ In this paper, we demonstrate that the grazing incidence of the light on the absorber edges and the formation of modes inside trenches in the absorber impact the EUV imaging characteristics as well.

Many of the described effects are already observed in EUV systems with an NA of 0.33. Some of the mentioned 3D mask effects occur in DUV lithography as well, see for example, Ref. 13. The anamorphic optics of high NA EUV systems introduces several further aspects.^14,15 Due to the $4\times /8\times$ demagnification in $x$ and $y$, respectively, the mask size of vertical features is $2\times$ smaller than that of horizontal features (for nominally identical wafer size). Smaller sizes involve also larger diffraction angles at mask level. Smaller sizes and larger diffraction angles increase the sensitivity of vertical features to mask 3D effects. Blocking of the diffracted light by the center obscuration in the high NA systems can potentially cause a further drop of the image contrast for certain pitches.¹⁶ In some of the investigated use cases in this paper, we have provoked such scenarios to investigate the mask absorber performance for extreme and critical imaging conditions.

1.2.

Paths Toward Mitigation

The most obvious solution to reduce 3D mask effects is to reduce the absorber thickness. State-of-the-art EUV masks employ about 60-nm-thick tantalum-based absorbers with typical extinction coefficients $k\approx 0.031$ to suppress the reflectivity in the nominally dark areas of a binary mask to values below 2%. Significantly thinner metal containing absorber materials with extinction coefficients up to 0.08 can provide sufficiently low reflectivity as well. Alternatively, absorber materials with appropriate combinations of refractive index $n$ and extinction $k$ can be used to devise attenuated phase shift masks (PSM) for EUV. Both approaches have been investigated for EUV systems with an NA of 0.33,^17–21 including a first experimental demonstration of improved imaging performance of high $k$ absorbers.²²

The effective thickness of EUV masks depends also on the multilayer. Presently used bilayer systems of molybdenum (Mo) and silicon (Si) reflect the incident EUV light at an effective plane $\sim 50\mathrm{nm}$ below the top surface of the multilayer. Replacement of Mo by ruthenium (Ru) with a slightly lower refractive index can help to reduce the distance between the effective reflection plane and the top of the multilayer to $<40\mathrm{nm}$.²³ The modified weighting of (double diffracted) orders in aperiodic or quasiperiodic MoSi bilayer systems can mitigate the 3D mask effects for specific pitches.^24–26 However, at the cost of the imaging performance at other pitches. This and further aspects of the multilayer impact on high NA EUV imaging, including limitations of performance improvement by multilayers, are discussed in Ref. 27.

From a modeling perspective, various forms of (alternating) PSM that employ etched multilayers^28–31 or buried shifters³² offer the largest degree of freedom for the design of EUV masks with reduced 3D mask effects. However, the manufacturing, characterization, handling, and repair of such masks are very challenging.

The goal of this paper is to identify the optical properties of the most promising absorber materials for high NA EUV lithography from a modeling perspective and to understand important effects that determine this selection. The equally important discussion of technical requirements for the experimental realization and use of absorbers in actual manufacturing is beyond the scope of this study.

Section 2 presents a parametric study of the impact of the extinction coefficient $k$, of the refractive index $n$, and of the thickness of the absorber on the local contrast or normalized image log slope (NILS) for selected critical use cases. The results of this study exhibit important physical effects in high NA EUV imaging and their impact on the selection of absorber materials. Section 3 employs multiobjective optimizations of selected exemplary material systems to derive conclusions for more practical use scenarios. The analysis of the resulting data provides further insights into the selection of the most promising absorber materials for high NA EUV lithography. The paper ends with conclusions and an outlook to future work.

2.1.

Impact of Absorber Extinction and Thickness on Imaging of Line-Space Patterns

Figure 2 shows the simulated NILS of 16-nm L/S with a pitch of 32 nm versus the extinction coefficient $k$. The NILS is extracted at the threshold-to-size (THRS) to print a 16-nm trench. The circle indicates the reference value for a 60-nm-thick TaBN absorber with $k=0.031$. Simultaneous variation of the absorber thickness according to $0.031\times 60\mathrm{nm}/k$ result in a nominally constant reflectivity of the multilayer stack with absorber. The reported data are extracted at the best focus position, which is the focus position that provides the highest NILS.

The data in Fig. 2 confirm the expected improved performance of high $k$ absorber materials. Absorbers with increased extinction and appropriate thickness offer a better imaging performance. The nonmonotonous behavior of NILS versus extinction can be attributed to the thickness variation and interference effects in the absorber stack.⁶

To understand the reason of this observation, we simulate near fields and aerial images that are obtained with individual poles of the leaf dipole illuminator. Figures 3 and 4 show data for the TaBN reference absorber with a thickness of 60 nm. The near fields are computed with the rigorous electromagnetic field solver using the waveguide method in Dr. LiTHO for illumination with $y$-polarized incident plane waves that emerge from the centers of the left and right poles, respectively. The rigorous solver enables a separate presentation of the incident downward propagating fields, which are shown in the upper and lower rows of Fig. 3.

Fig. 3

Rigorously simulated near-field intensities of $4\times 16\mathrm{nm}$ vertical trenches with a pitch of $4\times 32\mathrm{nm}$ in the vicinity of a 60-nm-thick TaBN absorber on top of a MoSi multilayer. Left/right columns: illumination with a plane wave emerging from the center of the left/right pole. Upper/lower row: incident downward propagating and reflected upward propagating light. The blue rectangles indicate the geometrical contour of the absorber. The top of the multilayer is at $z=0\mathrm{nm}$.

Fig. 4

Simulated aerial image cross sections at best focus for illumination with (a) single poles and (b) total image as obtained by the incoherent superposition of the images that are obtained by the individual poles. All parameters as specified in Fig. 3 and at the beginning of Sec. 2.

The simulated downward propagating near fields in the upper row of Fig. 3 indicate the excitation of a mode inside the space between the absorber. The obliquely incident light hits one of the absorber sidewalls almost at grazing incidence and is reflected back into the space—an observation that was already reported by others.³⁵ Adam and Neureuther³⁶ interpreted a similar phenomenon at edges of DUV masks as Cherenkov radiation. The opposite absorber sidewall is located in the geometrical shadow of the incident light. The shape of the propagating light inside the space depends on the width of the space, on the optical properties of the absorber, and on the excitation by the incident light—a typical behavior that is observed for waveguides. Similar waveguide effects for EUV masks were already described in publications on EUV imaging for 4-nm feature size.³⁷

The shape of the upward propagating light in the lower row of Fig. 3 looks different. The upward propagating light is not excited by a incident plane wave, but by the reflected light from the multilayer. The amplitude and phase of the reflected light depend on the properties of the multilayer. Typical MoSi-multilayers can be characterized by an effective reflection plane at a location about 50 nm below the top surface of the multilayer.^25,27 Both the near-field simulations and simple geometrical arguments suggest that no light is excited from locations of the multilayer below the shadowed side of the absorber space. This explains the strong asymmetry of the upward propagating light of the left and right poles, respectively. Investigations of the phase of the reflected light from the multilayer and its impact on the image can provide further insights.

The shown near-field plots and additional simulations indicate that the intensity (and phase) of the light within the absorber opening depends strongly on material, geometry, and incidence direction. More detailed investigations on this phenomenon will be discussed in future publications.

The aerial image cross sections in Fig. 4 are computed for an illumination with all relevant incidence angles inside the poles, i.e., with partially coherent light. They demonstrate that the asymmetry of the upward propagating reflected light is transferred into the lithographic images. The peak intensity positions of the left and right pole cross sections are shifted by about 10 nm. Superposition of the partial images results in a significantly blurred image with a very small NILS. Such blur phenomenon was also described by others.^9,10,12,13

Figure 5 shows how the near fields and cross sections change versus the extinction and thickness of the absorber. The intensity distributions and NILS plot in Fig. 2 are dominated by the effective mask height. Thinner absorbers with higher extinction $k$ help to reduce the difference between the upward propagating near fields for illumination with the left/right pole, to lower the shift between the corresponding image cross sections and to mitigate the blur of the total image. High $k$ materials can provide a better NILS—an observation that is consistent with previous work.²⁴

Fig. 5

Simulated near-field intensities and aerial image cross sections for selected values of absorber extinction $k$ and thickness. (a) Intensity of upward propagating reflected field for left/right pole and magnitude of intensity difference between the poles. (b) Aerial image cross sections of left/right pole. (c) Total image and NILS value. All parameters as described in Figs. 3 and 4.

2.2.

Impact of Absorber Refractive Index on Imaging of Line-Space Patterns

Next, we describe a less obvious phenomenon: the impact of the refractive index $n$ of a binary mask on the image quality. In the classical Kirchhoff model, the refractive index of the absorber or the phase of completely dark mask features on a binary mask has no impact on the image at all. The following simulations show that this is fundamentally different for EUV masks.

Figure 6 shows the simulated NILS of 16-nm L/S with a pitch of 32 nm versus the refractive index. The reflectivity of the 60-nm-thick absorber with an extinction of $k=0.031$ is about 2% and represents a (very) weak attenuated PSM that should behave similar to a binary mask. Contrary to the expectations from the classical Kirchhoff model, the data in Fig. 6 suggest a significant impact of the refractive index on the NILS. This impact is even stronger than that of the extinction $k$. A low refractive index absorber enables NILS values above 3, whereas the best high $k$ material provides only NILS values below 2.

Fig. 6

Simulated NILS of 16-nm vertical L/S with a pitch of 32 nm versus refractive index of the absorber $n$. Absorber thickness: 60 nm, extinction $k=0.031$, circle: 60-nm-thick TaBN absorber. The figure inset on the right exhibits a pupil diagram—see Fig. 2 for details.

The small circle in Fig. 6 indicates the reference value of a 60-nm-thick TaBN absorber with $n=0.95$ and $k=0.031$. That value is close to the minimum of the NILS versus $n$ curve. In other words, the presently used TaBN absorbers represent the worst choice of refractive index.

The simulated near fields and cross sections for different refractive index values in Fig. 7 provide an explanation of the described phenomenon. In contrast to Fig. 5, where the difference of the near-field intensities of the poles is shown, here we have plotted the average near-field intensities. This highlights the combination of shift and blur effects that is important for the understanding of the following observations. For the reference refraction value of 0.95, the upward propagating reflected fields of the two poles are significantly shifted and blurred. This explains the image shift and blur of the cross sections—see discussion of Fig. 5 above. Absorbers with increased refractive index provide less or no guiding of the light inside the absorber spaces. The intensity distributions of the near fields are more blurred, but less shifted, resulting in increased NILS values compared to that of the reference material.

Fig. 7

Simulated near-field intensities and aerial image cross sections for selected values of absorber refractive index $n$. (a) Intensity of upward propagating reflected field for left/right pole and average intensity of both poles. (b) Aerial image cross sections of left/right pole. (c) Total image and NILS value. All other parameters as described in Figs. 3 and 4.

Absorbers with smaller refractive index values than the reference material provide an improved guiding of the light inside the space. The intensity distributions of the near fields become more distinct and cause sharper and less shifted cross sections of the individual pole images. The sharpening of the partial images results in a significantly increased NILS at refractive indices between 0.88 and 0.92.

2.3.

Impact of Absorber Refractive Index on Imaging of Contact Arrays

Next, we investigate the impact of the refractive index of an attenuated PSM on the imaging characteristics for an array of regular 12-nm square contacts with a pitch of 28 nm on a bright field mask. An optimized quasar illumination with a source filling of 20% is used. The nominal reflectivity of the reference absorber with a thickness of 39 nm, a refractive index 0.95, and extinction 0.02 is about 20% and represents a high transmission/reflection attenuated PSM. Such types of attenuated PSM for EUV can provide good imaging performance for contact arrays.²¹ All other settings are identical to those for the L/S simulations in the previous sections.

Figure 8 shows simulated NILS values for the described case. Again, a pronounced impact of the absorber refractive index on the local image contrast can be seen. Varying the refractive index from $n=1.0$ to $n=0.89$ increases the NILS by a factor of 4. The root causes of this phenomenon are explained by the simulated near fields and aerial images for different refractive index values in Fig. 9. To simplify the graphical representation and discussion, the averaged near-field intensities of the reflected light for illumination from the four pole centers are shown. The near fields are shown on mask scale with the stretching of the $y$ axis due to the anamorphic projection system.

Fig. 8

Simulated NILS of an regular array of 12 nm square contacts with a pitch of 28 nm on a bright field attenuated PSM versus refractive index $n$ of the absorber. 39-nm-thick absorber with extinction $k=0.02$, optimized quasar illumination with a source filling of 20%. The shown NILS data are extracted at the feature center along an $x$-parallel cut. All other parameters identical to the settings of the L/S simulations in the previous sections.

Fig. 9

Simulated near-field intensities and aerial image for selected values of absorber refractive index $n$. (a) Averaged near-ield intensities of the reflected light for illumination from the centers of the four poles of the quadrupole, (b) aerial images, and (c) $x$-parallel aerial image cross sections at the feature center and NILS value. All parameters as described in Fig. 8.

The computed near-field data indicate that the light is not only absorbed by the features in the center but also scattered back from the absorber edges into the absorber-free areas. The amount of the backscattered light increases with the refractive index disparity ($\mathrm{\Delta }n$) between absorber and vacuum. The contrast of the averaged near-field intensities increases for low refractive index absorbers.

The computed aerial images and cross sections in Fig. 9 are not based on the averaged near-field intensities. Instead, they are computed from complex scattering data for all relevant illumination directions and incoherent superposition of the resulting images, as described by the Abbe imaging model. The improvement of contrast and NILS for low index materials is clearly seen.

2.4.

Summary of Observations and Learnings

The results of the simulations for the selected cases in the previous sections suggest several first learnings and hypothesis for further investigations:

3.1.

Investigated Use Cases and Optimization Strategy

A good absorber has to provide good lithographic performance for at least a large group of use cases. To investigate and compare the lithographic performance of the material option from Fig. 10, we define several one- (1D) and two-dimensional (2D) use cases. These use cases, variable parameters, and the used optimization strategy are explained below.

Figure 11 shows the target sizes of spaces in a 1D L/S pattern versus the hp. The best focus position is determined by the focus where the L/S pattern with the largest hp exhibits the highest NILS. A variable bias is applied to the smallest hp space. The widths of all other features are adapted to print at the THRS of the smallest hp feature. A leaf-shaped dipole with a minimum source filling of 20% and a variable intensity center pole, as shown in the inset of Fig. 11, is used. Both vertical and horizontal lines with adapted rotation of the dipoles are considered. Simulations are done at the center and at the edge of the exposure slit. To reduce the computation time of the rigorous mask diffraction and image simulations for several thousands mask and source parameters, the simulations are limited to pitches of 16, 24, 32, and 60 nm. The data points in the figures of this section report the smallest THRS, the smallest NILS, and the largest nTC that is obtained for certain mask and source parameters. The goal of the optimization is to make the smallest THRS and NILS values (over all pitches) as large as possible and the largest nTC as small as possible. See Ref. 7 for a more detailed description of the imaging settings and for a comprehensive discussion of the imaging effects for such exposure scenario.

Fig. 11

Definition of 1D use case: target size of space in an L/S pattern versus hp. The figure inset exhibits the used leaf-shaped dipole with variable size of the leafs (identical for all leafs) and variable intensity of the inner leaf.

The 2D use cases with different arrays of square and long contacts on bright and dark field masks are presented in Fig. 12. Besides from the given rectangular features and pitches of the mask and the shown source shapes, all imaging settings are identical to the 1D use case. The THRS and best focus position are obtained for $x$-parallel cuts of the feature with a variable bias along $x$. The feature size in $y$ direction is adapted to print on target. The applied source shapes with variable intensity center poles and minimum source filling of 20% are shown in the bottom column of the figure.

Fig. 12

Definition of 2D use cases. From left to right: regular squares (SQU), $x$- and $y$-parallel hexagonal arrays of square contacts (HEX X, HEX Y), $x$- and $y$-parallel long rectangular vias (VIAS X, VIAS Y). From top to bottom: bright field images, dark field images, source shapes, and wafer scale target sizes and pitches.

A multiobjective genetic algorithm⁴⁰ is used to identify the most appropriate absorber parameters for the investigated use cases. The optimization variables include the composition of the alloys, an absorber thickness between 20 and 60 nm, a variable size bias, and illumination shapes as discussed above. The vector merit function consists of THRS (as defined above, to be maximized), NILS (smallest value over all pitches and orientations, to be maximized), and nTC (largest value over all pitches and orientations, magnitude to be minimized). The used multiobjective optimization algorithm does not require a weighting of the individual components of the merit function. The result of a multiobjective optimization is not a single solution, but a group of solutions that provide an appropriate tradeoff between the components of the merit vector. The achieved performance and parameters of these Pareto optimal solutions are discussed in the next sections.

3.2.

Lines-Spaces Pattern Example

Figure 13 shows simulated Pareto data of vertical L/S at the slit edge for different absorber options. The data in the plots show the achievable NILS versus THRS. Each data point (colored circle) represents a combination of mask and illumination parameters to achieve the predicted NILS/THRS performance. The color of the data points expresses the nTC ranging from magnitudes below 10 mrad (green), via medium nTC (yellow) to magnitudes of nTC around 30 mrad or larger (red).

Fig. 13

Plot of simulated Pareto data of the L/S use case with vertical spaces at the slit edge: NILS versus THRS for TaBN, high $k$ alloy, and attenuated PSM absorber. nTC values (in mrad) are indicated by the color.

The data in Fig. 13 indicate a tradeoff among NILS, THRS, and nTC for all mask material options. Although not directly visible from the plotted data, there are various physical reasons for such tradeoff. For example, thicker absorbers tend to exhibit higher contrast (NILS) but absorb more light and reduce the THRS. Thin absorbers with larger THRS tend to exhibit smaller values of nTC. Figure 13 shows that both the high $k$ alloy and the attPSM alloy can provide much better tradeoffs than the TaBN absorber, which suffers from high nTC and cannot achieve NILS values better than 2.2.

Alternative plots of the Pareto data in Fig. 14 provide further insights. The points in these scatter plots include only data with $\mathrm{nTC}\le 25\mathrm{mrad}$ and $\mathrm{THRS}\ge 0.15$. The used material options are differentiated by colors and symbols. The plot on the upper left of Fig. 14 provides a similar message as Fig. 13: Both the high k alloy and the attPSM alloy offer a significantly better NILS/THRS tradeoff than TaBN. There is only a small difference between the achievable performance of the alloys.

Fig. 14

Alternative plots of simulated Pareto data of the L/S use case with vertical spaces at the slit edge. Only data points with $\mathrm{nTC}\le 25\mathrm{mrad}$ and $\mathrm{THRS}\ge 0.15$ are included.

The NILS versus thickness plot of the same data in the upper right of Fig. 14 suggests that the best NILS performance is obtained for certain thickness values with a period of about 7 nm, i.e., $\lambda /2$. This observation is consistent with the NILS values versus extinction with adapted absorber thickness in Fig. 2 and can be attributed to interference effects in the absorber stack. Both the high $k$ alloy and the attPSM alloy offer solutions with NILS values above 2.0 and absorber thickness values in the range between 20 and 40 nm. About 41- and 48-nm-thick high $k$ absorber alloys offer NILS values above 2.4. The best NILS values of the attPSM alloy are about 2.3. Conversely, the TaBN absorber has to be at least 50 nm thick and achieves NILS values close to 2.0 only.

The NILS versus $k$ plot in the lower left of Fig. 14 confirms that the best NILS values are obtained for alloys with extinction coefficients above 0.06. This requirement is fulfilled by all high $k$ alloys and by attPSM alloys that mainly consist of the component with the larger value of $k$—see Fig. 10. The largest NILS values are obtained for the high $k$ alloy with the maximum achievable $k\approx 0.08$. All TaBN absorbers have the same extinction $k=0.031$. The corresponding data in the figure differ only in the mask thickness, bias, and illumination setting and the resulting NILS value.

The NILS versus reflectivity plot in the lower right of Fig. 14 highlights that the best lithographic performance for vertical L/S can be only achieved for binary masks with absorber reflectivity below 1%. Additional analysis of the simulated data shows that potential attPSM solutions with larger reflectivity and thickness fail due to insufficient contrast or unacceptable nTC.

3.3.

Contact Array Example

Figures 16 and 15 show plots of typical Pareto data for hexagonal arrays of square contacts on bright- and darkfield masks, respectively. The NILS versus THRS plots in the upper left of these figures demonstrate the advantage of attenuated PSM for these types of patterns. High $k$ alloys perform only slightly better than TaBN absorbers. The NILS versus refraction plots in the upper right of the figures confirm the advantages of absorber materials with low refractive index.

Fig. 15

Alternative plots of simulated Pareto data of $x$-parallel hexagonal arrays of contact holes (see HEX X in Fig. 12) on a dark field mask. Only data points with $\mathrm{THRS}\ge 0.15$ are included.

Fig. 16

Alternative plots of simulated Pareto data of $x$-parallel hexagonal arrays of contact holes (see HEX X in Fig. 12) on a bright field mask. Only data points with $\mathrm{THRS}\ge 0.15$ are included.

The reflectivity and phase values in the lower columns of Figs. 16 and 15 are computed from the $n$, $k$, and thickness of the absorber. Only attPSM alloys can provide well-performing solutions with reflectivity above 4%. The best NILS data are achieved with absorbers with high reflectivity values up to $\sim 30\%$. Such high reflectivity absorbers are prone to sidelobe printing. Further investigations are required to investigate the risk of sidelobe printing for larger pitches.

The phase values of the solutions with the largest NILS values are different from 180 deg. The optimum phase values of dark field attenuated PSM in Fig. 15 are in the range between 200 deg and 230 deg. This observation was already made in previous studies²¹ and confirmed by studies of others.⁴¹ The data of Fig. 16 indicate a wider range of appropriate phase shift (and thickness) values of bright field attenuated PSM compared to that of dark field masks. Additional simulations confirm that bright field attenuated PSM are less sensitive to variations of the absorber thickness than their dark field counterpart. Bright field attenuated PSM with a phase around 150 deg tend to exhibit higher THRS and lower losses, whereas phase values around 200 deg offer a higher NILS.

This special characteristic of PSM can be attributed to double diffraction effects and to total reflection of light at the absorber edges. Further investigations are required to investigate the dependencies of the optimum phase shift from the mask geometry, from absorber/multilayer parameters, and from the illumination.

The simulated Pareto data of all other 2D use cases suggest similar observations. Notably, the nTC for all investigated 2D use cases is below the critical level of 10 mrad.