## Abstract

The illumination system design for high numerical aperture (NA) anamorphic objectives is a key challenge for extreme ultraviolet lithography. In this paper, a reverse design method of the off-axis mixed-conic-surface-type relay system and an automatic arrangement method of field facets are proposed to design a high NA anamorphic illumination system. The two off-axis relay mirrors are fitted into different conic surfaces based on the conjugation of the mask plane and field facet and that of the illumination exit pupil and pupil facet. To eliminate ray obscuration between neighboring field facets, the field facets are automatically arranged according to the distances that are determined by the relative tilt angles of neighboring field facets under the current illumination mode. The proposed methods are applied in the design of an illumination system matching the NA0.60 anamorphic objective. Simulation results show that the uniformity of the scanning energy distribution can reach 99% on the mask plane under different illumination modes.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

An extreme ultraviolet (EUV) lithography exposure tool with a high numerical aperture (NA) greater than 0.50 has been chosen to extend Moore’s law throughout the next decade [1]. To keep using the 6” mask and avoid an excessive productivity impact, an anamorphic objective, with an 8× magnification in the scanning direction and a 4× magnification, has been introduced to extend the single exposure EUV for advanced nodes [1]. Different magnifications of an anamorphic objective will lead to an elliptical entrance pupil with a circular aperture stop. Correspondingly, the illumination systems for anamorphic objectives must comply with the elliptical entrance pupil. What’s more, the non-uniformity across the designated illumination area on the mask plane is required to be less than 1% [2]. Several high NA anamorphic EUV projection objectives [3–10] and anamorphic illumination systems [8,11] have been designed. In our previous work, Liu [4–7] has designed two six-mirror anamorphic objectives, one with NA0.50 and the other with NA0.60, and Jiang [11] has designed an illumination system for a NA0.50 anamorphic objective with illumination uniformity of 95%–98%. Schwab et al. [8] disclosed a patent of eight-mirror anamorphic objectives with NA0.55 and the parameters of corresponding relay systems rather than the design of a whole illumination system. Thus, it is still a key challenge to design a high-performance illumination system for the anamorphic objective with a high NA to achieve higher resolution under the single exposure.

Illumination systems with fly’s eye are the industrial choice for EUV lithography [12]. There are two key parts of the illumination system, the fly’s eye and the relay system. The fly’s eye (composed of field facets and pupil facets) can provide an adjustment of illumination modes on the exit pupil of the EUV illumination system through changing the assignment relationships of the field facets and pupil facets [13]. The relay system ensures the double conjugate relations in the Köhler illumination system [14], that is, the conjugation of the mask plane and field facets and of the illumination exit pupil and pupil facets. Some EUV illumination system design methods have been published in recent years [11,15–17]. Among them, Mei et al. [17] proposed a reverse design method of ellipsoidal relay systems. Jiang [11] provided an effective design method to determine the reasonable coaxial spherical configuration of the relay system based on matrix optics, and then fitted it into an ellipsoidal relay system by Mei's method. However, a trial-and-error process must be applied to find a reasonable configuration of the two-ellipsoid-mirror relay system under some illumination design requirements (especially for the design of high NA anamorphic illumination systems). One may even fail to find such a two-ellipsoid-mirror relay system to realize the design of high NA anamorphic illumination system with high performance in some cases. Therefore, it would be much better to extend the fitting surfaces of the relay system so that the two mirrors can be fitted into different conic surfaces according to specific requirements, making the design more efficient.

Different illumination modes will cause a different distribution of the pupil facets that contribute to the illumination, so that the field facets will have different tilt angles to make sure that each illumination channel superimposes at the same position on the mask and realizes the illumination modes on the exit pupil plane [18]. In the traditional assignment method, the evenly distributed facets are grouped and assigned within each group according to principle of proximity, which is complicated and inefficient [13,17,18]. To obtain the optimal assignment of field facets and pupil facets automatically and efficiently, Jiang [11] proposed an assignment method based on combinatorial optimization. In these assignment methods, some field facets, especially those far from the pupil facets, may tilt at a large angle under some assignment conditions. However, field facets are usually closely arranged in a near circular area. It is quite easy for those field facets with large tilt angles to collide with their neighboring field facets. What’s more, in an anamorphic illumination system, the pupil facets must be arranged in an elliptical contour to match the elliptical entrance pupil of anamorphic objective, which means that the pupil facets in the scanning direction will be further away from the field facets. Thus, the possibility of collisions between neighboring field facets may be serious in the anamorphic illumination system. The collisions can cause the ray obscuration of neighboring field facets, which will do harm to the illumination uniformity. Obviously, ray obscuration or collisions of field facets are not allowed in the industrial production. Eliminating ray obscuration or avoiding the collisions between neighboring field facets is also an important design requirement of field facets in the EUV illumination system. Until now, there has been few public reports on this problem in the design of EUV illumination systems.

In this paper, a design method of the off-axis mixed-conic-surface-type relay system and an automatic arrangement method of field facets are proposed to design a high NA EUV illumination system. According to the optical characteristics of conic surfaces and the imaging requirements of the mask plane and the exit pupil, the initial spherical relay mirrors are fitted to different off-axis conic surfaces. The relay system designed by this proposed method can meet the requirements on the location and size of the facets. To avoid the collision between neighboring field facets and to eliminate ray obscuration, the field facets are automatically arranged according to the distances that are determined by the relative tilt angle of neighboring field facets under the current illumination mode. An illumination system with a collision-free arrangement of field facets is designed by the proposed methods to match the NA0.60 anamorphic projection. Simulation results show that the uniformity of the scanning energy distribution can reach 99% on the mask plane under different illumination modes.

## 2. Design method of the relay system

The relay system is a key subsystem of a EUV illumination system. It determines the location and size of field facets and pupil facets. Since the illumination system matches the objective, the parameters of the exit pupil and illumination area can be obtained from the objective. Thus, the illumination system can be designed in the reverse optical path. In the reverse optical path, the mask plane is treated as the object plane and the illumination exit pupil acts as the aperture stop. And in our method, the first relay mirror encountered along the forward optical path is denoted as Relay 1, and the second relay mirror as Relay 2.

#### 2.1 Calculation of spherical relay systems

The relay system is designed by the restriction of the double conjugate relations. The coaxial spherical relay system will be calculated by the method in Ref. [11]. After that, the two spherical mirrors are tilted and decentered to eliminate ray obscurations.

#### 2.2 Fitting of the mixed-conic-surface-type relay systems

After the off-axis spherical relay system is determined, the two mirrors need to be fitted into off-axis conic surfaces to reduce the imaging aberrations. Based on the optical characteristics of conic surfaces, there are three feature points required to fit the conic surfaces: two focal points of the conic surface and one point on the surface, the coordinates of which can be obtained by real ray tracing in CODE V.

Figure 1 illustrates the fitting of the conic mirror Relay 2 in the reverse optical path. The exit pupil center of the illuminator is one of the focal points of Relay 2, which is treated as the first feature point, marked by F21 in Fig. 1. The image of the first feature point through Relay 2 forms another focal point and is considered as the second feature point. Furthermore, there are three possible positions of the second feature point, respectively marked by F22, F22′, and F22′′ in Fig. 1. Then, the intersection of the chief ray and the Relay 2 mirror is considered as the third feature point, marked by A2. According to the positions of these feature points, Relay 2 will be fitted into an ellipsoid, a hyperboloid or a paraboloid. In the first case, the image of the exit pupil center is a real image point, as shown at point F22 in Fig. 1. It means that the two focal points locate on the same side of the conic surface, so that Relay 2 will be fitted into an ellipsoid. In the second case, as shown at point F22′, the image of the exit pupil center is a virtual image point, which means the two focal points locate on the different sides of the conic surface. Accordingly, Relay 2 will be fitted into a hyperboloid. In the third case, as shown at point F22′′, the image of the center of the exit pupil is at infinity. It means that the object is imaged at infinity by the conic mirror, which is exactly in line with the imaging properties of parabolic mirrors. Consequently, Relay 2 will be fitted into a paraboloid.

The fitting of the conic mirror Relay 1 is illustrated in Fig. 2. The image of the mask center through Relay 2 is one of the focal points of Relay 1 and treated as the first focal point. The first feature point has two possible positions, marked by F11 and F11′ in Fig. 2. The image of the mask center through the two-mirror relay system is another focal point, which is treated as the second feature point. There are three possible positions of the second feature point, marked by F12, F12′, and F12′′ in Fig. 2. The third feature point, marked by A1, is the intersection of the chief ray and Relay 1. Similar with the fitting of Relay 2, Relay 1 can be fitted into an ellipsoid, a hyperboloid and a paraboloid.

By the conjugate relationship between the exit pupil and pupil facets, the configuration of pupil facets can be obtained easily. Similarly, the configuration of field facets is determined by the conjugate relationship between the mask and field facets. The method in Ref. [11] can be applied to determine the optimal facet mapping relationships under different illumination modes.

## 3. Automatic arrangement method of the field facets

The field facet is a key component of the fly’s eye for a EUV illumination system to achieve high uniformity and different illumination modes. The tilt angle of each field facet will be determined when the assignment relationship of each field facet and the corresponding pupil facet is obtained according to the required illumination mode. To avoid the collision of neighboring field facets and eliminate ray obscuration, an automatic arrangement method of field facets will be proposed in this section.

#### 3.1 Calculation of neighboring field facets’ critical distances

For a single field facet, there are two possible distributions of its surrounding field facets, as shown in Fig. 3. The key of the automatic arrangement of field facets is to find the critical row distance, $\Delta {y_{crirow}}$, and critical column distance, $\Delta {x_{cricol}}$, between each pair of neighboring field facets.

As shown in Fig. 3, whether it is the alignment arrangement or misalignment arrangement, two neighboring field facets within a row are always in the case of left and right neighboring. Therefore, to facilitate the calculation, each field facet only needs to calculate the critical column distance $\Delta {x_{cricol}}$ to its left neighboring field facet. Similarly, the two neighboring field facets within a column are always upper and lower neighboring, and each field facet only needs to calculate the critical column distance $\Delta {y_{crirow}}$ to its lower neighboring field facet.

Since each field facet differs in tilt angles, we will split the tilt process of the two neighboring field facets into three steps. First, establish the two initial neighboring field facets, as shown in Fig. 4(a). Suppose that the reference field facet (the left field facet in the left and right neighboring case, the lower field facet in the upper and lower neighboring case) is Field Facet #1 and the tilt angle of Field Facet #1 is ${\theta _\textrm{1}}$ and that of Field Facet #2 is ${\theta _\textrm{2}}$. Second, tilt the two field facets by the angle ${\theta _\textrm{1}}$. The two neighboring field facets are kept parallel, as shown in Fig. 4(b). Third, tilt Field Facet #2 from the red dotted position (in this position the two field facets are parallel) to the position where the two field facets are exactly tangent (the tilt angle $\Delta \theta = {\theta _2} - {\theta _\textrm{1}}$), as shown in Fig. 4(c). Then calculate the critical distances of the two neighboring field facets.

In what follows, we will calculate the critical row distances and the critical column distances under different tilt situations by this three-step process.

### 3.1.1 Calculation of the critical row distances

In this section, we will take two upper and lower neighboring field facets in the *YZ* plane as an example to illustrate the calculation of the critical row distance.

The critical row distance $\Delta {y_{crirow}}$ can be calculated by the difference between the coordinates of center points *O* and $O^{\prime}$ of the two neighboring field facets’ reflective surfaces when the two field facets are tangent. Figure 5 illustrates the calculation of the critical row distance between the upper and lower field facets in *YZ* plane based on the tilt angle $\alpha $ (the definition of the tilt angle $\alpha $ is consistent with the optical design software LightTools). According to our three-step tilt model, the relation between ${\alpha _{upper}}$, ${\alpha _{lower}}$ and $\Delta \alpha $ is:

Through analyzing Fig. 5, the critical row distance between these two neighboring field facets can be calculated as:

*h*represents the height of the field facet;${O_Z}$ and $O^{\prime}_{Z}$ represent the coordinates of the tilt centers of lower field facet and the upper field facet, respectively;${\alpha _{ref}}$ represents the tilt angle of the reference field facet, which refers to the angle of the lower field facet here; and $\Delta {Y_{\Delta \alpha }}$ represents the distance between the lower field facet and the upper field facet (where the upper field facet is in the red dotted position).

In Eq. (2), all variables are known except the variable $\Delta {Y_{\Delta \alpha }}$, which can be calculated by the vertex of the field facet in the local coordinate of the upper field facet (when in the red dotted position). As shown in Fig. 6, the calculation of $\Delta {Y_{\Delta \alpha }}$ is related to the collision vertex of the upper field facet. The tilted vertex $A^{\prime}$ may collide to the lower field facet, so that $\Delta {Y_{\Delta \alpha }}$ can be obtained by:

where $A_{y^{\prime}}$ represents the $y^{\prime}$ coordinate of the non-tilted vertex*A*, ${A^{\prime}_{y^{\prime}}}$ represents the $y^{\prime}$ coordinate of the vertex $A^{\prime}$.

And the coordinate of the vertex $A^{\prime}$ can be calculated by:

*A*.

According to Eqs. (1)–(4), the critical row distance between the upper and lower field facets in the *YZ* plane can be determined. What’s more, the calculations of other relative tilt relationships of the upper and lower neighboring field facets are similar.

### 3.1.2 Calculation of the critical column distances

In this section, we will take two left and right neighboring field facets in the *XZ* plane as an example to illustrate the calculation of the critical column distance.

Similar to the calculation of $\Delta {y_{crirow}}$, the critical column distance $\Delta {x_{cricol}}$ is also calculated by the difference between the coordinates of center points of the two neighboring field facets’ reflective surfaces when the two field facets are tangent. Figure 7 illustrates the calculation of the critical column distance between left and right field facets in the *XZ* plane based on the tilt angle $\beta $ (the definition of the tilt angle $\beta $ is consistent with the optical design software LightTools). According to our three-step tilt model, the relation between ${\beta _{left}}$, ${\beta _{right}}$ and $\Delta \beta $ is:

By analyzing Fig. 7, the critical column distance between these two neighboring field facets can be calculated as:

*l*represents the length of the field facet; ${\beta _{ref}}$ represents the tilt angle of the reference field facet, which refers to the angle of the left field facet here; and $\Delta {X_{\Delta \beta }}$ represents the distance between the left field facet and the right field facet (where the right field facet is in the red dotted position).

In Eq. (6), all variables are known except the variable $\Delta {X_{\Delta \beta }}$, which will be calculated by the vertex of the field facet in the local coordinate of the right field facet (when in the red dotted position). As shown in Fig. 8, the calculation of $\Delta {X_{\Delta \beta }}$ is related to the collision vertex of the right field facet. The tilted vertex $B^{\prime}$ of the right field facet may collide to the left field facet, so that $\Delta {X_{\Delta \beta }}$ can be obtained by:

where $B_{x^{\prime}}$ represents the $x^{\prime}$ coordinate of the non-tilted vertex $B$ and $B^{\prime}_{x^{\prime}}$ represents the $x^{\prime}$ coordinate of the vertex $B^{\prime}$.And the coordinate of the vertex $B^{\prime}$ can be calculated by:

According to Eqs. (5)–(8), the critical column distance between the left and right field facets in the *XZ* plane can be determined. What’s more, the calculations of other relative tilt relationships of the left and right neighboring field facets are similar.

#### 3.2 Arrangement of field facets

By the method described in Section 3.1, we have calculated the critical row and column distances required for each field facet at its current tilt angle ($\alpha $, $\beta $, $\gamma $) under the given illumination mode. Now, the minimum row and column distance of each field facet required to avoid the collision with its neighboring field facets can be determined by:

*N*is the total number of field facets.

Since $(\Delta x/l) \ll (\Delta y/h)$, the column distance will have little impact on the arrangement while the row distance will have a major impact on the arrangement. Therefore, for a better arrangement, each column has the same column distance and only each row distance is varied. The column distance for the whole field facets can be obtained as:

while the row distance for each row required can be obtained as: where $\Delta {y_k}$ represents the row distance of the ${k^{th}}$ row; $\Delta {y_{kj}}$ represents the row distance of the ${j^{th}}$ field facet in the ${k^{th}}$ row, $k = 1,2,3,4,\ldots .,K$;*K*is the total number of rows, $j = 1,2,3,4,\ldots .,J$; and

*J*is the total number of field facet in the ${k^{th}}$ row.

Since the column distance and row distances for arrangement have been determined, we will arrange the field facets from bottom to top as follows. First, as shown in Fig. 9, the white field facets and below have already been arranged. Then, choose the upper row distance (depicted in orange). Second, a row of field facets (depicted in green in Fig. 9) is placed at the remaining space. Third, choose the upper row distance (depicted in blue in Fig. 9) of this row. Fourth, judge whether the remaining space (upper blue row distance in Fig. 9) meets the placement requirements of a row of field facets. The arrangement is complete when the remaining space could not place a row of field facets. Repeat the process above until the arrangement is complete.

#### 3.3 Iterative process

With the method in Section 3.1 and Section 3.2, we can obtain the reasonable arrangement of field facets of each illumination mode. Based on the current arrangement of field facets, we can determine the assignment relationships of each field facet and the corresponding pupil facet by the method in Ref. [11] under the current illumination mode. After that, the new arrangement of field facets can be calculated by the method in Section 3.1 and Section 3.2 based on the current assignment relationship. Then, it can be judged whether the new arrangement is the same as the previous arrangement. If they are different, the previous arrangement of field facets will be replaced by the new arrangement, and this new system is taken as the initial system to redetermine the new assignment relationship of each field facet and the corresponding pupil facet. And then the new arrangement can be regenerated based on the new assignment relationship. The iteration process is complete when the new arrangement of field facets is the same as the previous arrangement. The flow diagram of the iterative process is shown in Fig. 10.

## 4. Design of a high NA anamorphic EUV illumination system

An illumination system matching the NA0.60 anamorphic projection objective is designed by the methods above. Table 1 shows the parameters of the NA0.60 anamorphic projection objective [6].

The layout of the illumination system matching the NA0.60 anamorphic projection objective is shown in Fig. 11. The parameters of the relay system are listed in Table 2, in which the distance *d* represents the distance between the two relay mirrors along the ray path. As indicated by the conic constants, Relay 1 is fitted into a hyperboloidal mirror and Relay 2 is fitted to an ellipsoidal mirror.

Figure 12 shows the initial arrangement of field facets, which is used as the initial system to implement the arrangement method of field facets described above. From Fig. 12, field facets are arranged in a near circular contour, while pupil facets are arranged in an elliptical contour to match the elliptical entrance pupil of the anamorphic projection objective. The field facets and pupil facets are all rectangular-shaped and spherical surfaces, the radius of which can be worked out by geometric optics. The dimension of each field facet is 70mm×5.5mm, and that of each pupil facet is 4mm×3mm.

Figure 13 shows the distribution of pupil facets under each illumination mode. Only those pupil facets depicted in orange color will illuminate the mask plane under each illumination mode. The number of pupil facets illuminating the mask plane under each illumination mode always equals that of field facets.

Figure 14 gives the number of rows that meet the arrangement requirements with the number of iterations. The iterations end when the new arrangement is the same as the previous. For most illumination modes, the arrangement of field facets can converge quickly.

Figure 15 shows the corresponding arrangement of field facets after iterations under each illumination mode above. It can be seen that the field facets’ arrangement under each illumination mode is quite different from each other. And the field facets above the field facet plate tend to have larger row distances (which are clearly shown in Fig. 15(b)), which means these field facets have a large tilt angles so that they need more space to avoid the collisions and ray obscuration with their neighboring field facets.

Usually, the performance of the EUV illumination system is evaluated by the integrated illumination uniformity on the mask plane under different illumination modes, defined as:

The illumination uniformity under the four illumination modes have been evaluated, i.e., annular illumination mode, dipole illumination mode, quasar illumination mode and leaf illumination mode. The illumination uniformity under each illumination mode is simulated by Monte-Carlo ray tracing in LightTools and calculated by Eq. (12). The parameters of the illumination modes and the illumination uniformity are listed in Table 3, in which ${\sigma _{in}}$ is the inner partial coherence factor, ${\sigma _{out}}$ is the outer partial coherence factor and $\theta $ is the opening angle.

The illumination area under each illumination mode is shown in Fig. 16. Results show that this illumination system matching the NA0.60 anamorphic objective can achieve uniformity greater than 99% (which means the non-uniformity is less than 1%) on the designated illumination area of the mask plane under the four illumination modes.

## 5. Conclusion

In this paper, a reverse design method of the off-axis mixed-conic-surface-type relay system and an automatic arrangement method of field facets are proposed to design a high NA anamorphic EUV illumination system. According to the optical characteristics of conic surfaces and the imaging requirements of the mask plane and the exit pupil, the initial spherical relay mirrors are fitted to different off-axis conic surfaces. The relay system designed by this proposed method can meet the requirements on the location and size of facets. To avoid collisions between neighboring field facets and to eliminate ray obscuration, the field facets are automatically arranged according to the minimum distances that are determined by the relative tilt angle of neighboring field facets under the current illumination mode. An illumination system with the collision-free arrangement of field facets is designed by the proposed method to match the NA0.60 anamorphic projection. In this illumination system, Relay 1 is fitted to a hyperboloidal mirror and Relay 2 is fitted to an ellipsoidal mirror. The reasonable arrangement of field facets of each illumination mode can be obtained automatically and quickly. Simulation results show that the uniformity of the scanning energy distribution can reach 99% on the mask plane under different illumination modes.

## Funding

National Natural Science Foundation of China (61675026).

## Disclosures

The authors declare no conflicts of interest.

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