2.1.

Preparation of the Qz Substrate with Various Shapes of Space Patterns

The cross-sectional angles of the space patterns on the quartz (Qz) substrate were designed to be 90 deg, 60 deg, and 30 deg. The 90 deg space pattern was fabricated by applying a standard resist patterning on Qz, followed by a dry etching process. The space patterns with 60 deg and 30 deg angles were fabricated by applying scratch markers on the Qz substrate using an AFM tip with the tip angles of 60 deg and 30 deg as shown in Fig. 1(a). By pressing the tip against the Qz surface, five scratch lines were drawn as shown in Fig. 1(b). A cross-sectional profile of Fig. 1(b) along a line between two illustrated arrows is shown in Fig. 1(c).

Fig. 1

(a) Schematic view of the cantilever used in the scratching process. The tip angles were 60 deg and 30 deg. (b) Schematic model of the scratching process. The tip made five scratching lines on quartz (Qz) substrate. (c) Cross-sectional profile of the scratched Qz substrate along the line between two arrows indicated in the image (b).

Figure 2(a) shows the mask design. Space patterns with their etching angles of 90 deg were arrayed in a $7\times 7$ matrix with a pitch of 22 mm on the Qz substrate. Each block has 150-nm-wide space patterns with their orientation angles of 0 deg, 45 deg, 90 deg, and 135 deg forming an asterisk symbol [Fig. 2(b)]. The 60 deg and 30 deg of the space patterns were fabricated on the blocks from A to H. The cross-sectional transmission electron microscope (TEM) images of the fabricated space patterns after their multilayer coating, are shown in Figs. 3(a) and 3(b). Not only the 90 deg of the space pattern but also the 30 deg and 60 deg of the space patterns were robustly fabricated with their etching depths of about 10 nm. The nonflatness of the blank before and after the multilayer coating was $<20\mathrm{nm}$ and $-800\mathrm{nm}$ (center of the multilayer surface was higher than the corners of the blank), respectively.

Fig. 2

(a) Arrangement of the test pattern. (b) Magnified image of the each block which has 150 nm of space patterns, forming an asterisk symbol and two types of the scratched patterns.

Fig. 3

Cross-sectional TEM images of the space pattern with multilayer (ML). The cross-sectional etching angles were (a) 90 deg. (b) 30 deg and 60 deg.

2.2.

Simulation Condition for the Analysis of the Inclination Angle on the Printed Image

A simulator known a LAIPH™ EUV Defect Printability Simulator (Luminescent technologies, California) was employed to predict the impact of the inclination angle of the PD on wafer printed image in this work. The parameters for the simulations were as follows: numerical aperture $(\mathrm{NA})=0.33$, $\mathrm{sigma}=0.8/0.4$ (dipole), chief $\mathrm{ray}\mathrm{angle}=6\mathrm{deg}$, $\mathrm{demagnification}=4$, and $\mathrm{wavelength}=13.5\mathrm{nm}$. The blank structure was Ru-capped multilayer ($\mathrm{Ru}=2.5\mathrm{nm}$, 40 pairs of $\mathrm{Si}/\mathrm{Mo}=2.8/4.2\mathrm{nm}$). The defect sizes were 4, 6, and 8 nm in depths and 50 nm in full-width at half-maximum. The inclination angles of the PDs were set from $-8\mathrm{deg}$ to 8 deg.

3.1.

Influence of the Defect Location on the Inclination Angle and its Direction

To determine the cause of the inclined growth of the PD, space patterns with the etching angles of 90 deg in the blocks A, B, C, D, and G [shown in Fig. 2(a)] were prepared for TEM observation. Figure 4(a) describes a schematic view of the TEM observation direction. Each TEM observation sample was cut perpendicular to the space pattern using a focused ion beam. The TEM images and the inclination angles of the PDs are shown in Fig. 4(b). The inclination angle was defined as the angle between two lines where one line is normal to the substrate surface, and the other is a line defined by connecting the center of the etched substrate to the center of the depressed region (representing a defect image) on the surface of the multilayer. These TEM images clearly show a tendency that the direction of propagation of PDs, starting from the bottom surface of the etched Qz and ending at the top surface of the multilayer, leans toward the center of the mask.

Fig. 4

(a) Explanation of the cutting directions of the space patterns and TEM observation directions. (b) Cross-sectional TEM images of the phase defects (PDs) in the blocks A, B, C, D, and G.

To confirm the tendency of the defect propagation direction, the block H located in the upper-right corner of the mask was prepared for TEM observation. The center-directed space pattern and another space pattern normal to the center-directed space pattern, were both cut perpendicular to the space patterns [Fig. 5(a)]. Figure 5(b) shows the TEM images of the space patterns. The terms TEM-1 and -2 describe the observation directions 1 and 2 depicted in Fig. 5(a). When the space pattern was observed along the direction 1, the inclination angle of the PD was almost 0 deg. However, the space pattern with its direction was normal to the radial direction and was apparently inclined toward the center of the mask (TEM-2). These results indicate that the inclination angle of the PD through the multilayer is not random, but there is a tendency of its propagation direction to lean toward the mask center.

Fig. 5

(a) Explanation of the cutting direction of the space patterns and TEM observation direction. (b) Cross-sectional TEM images of the PDs in the block H.

Figure 6 represents a relationship between the inclination angles of the PDs [Figs. 4(b) and 5(b)] and the distances of the space patterns on Qz substrate from the mask center. The inclination angle increased in proportion to the distance from the mask center. The maximum inclination angle was 5.9 deg (93.3 mm away from the mask center).

Fig. 6

Inclination angle of the PD through the multilayer as a function of the distance from the mask center.

3.2.

Influence of the Qz Etching Shape on the Propagation Angle of the PD

To fully understand the defect propagation direction and angle from the bottom to the top of the multilayer, we conducted an investigation to determine the influence of the shapes of the defect seeds on the propagation direction and angle of the PD. Figures 7(a) and 7(b) show the cross-sectional TEM images of the PDs with various shapes of the seeds in the blocks D and A, respectively. The observation results of block D, which were located in the center of the mask, apparently showed that the center of the defect at the bottom and top were completely matched. Furthermore, the observation results of block A, which was located 66 mm from the mask center, also showed that not only the propagation direction but also the inclination angles were independent of the shapes of the seeds on the Qz substrate.

Fig. 7

Cross-sectional TEM images of the (a) block D and (b) block A. The etching angles of the Qz substrate are 30 deg, 60 deg, and 90 deg.

3.3.

Inclination Angle Versus Positional Shift of the Minimum Intensity of PD Image on Wafer

The impact of the inclination angel of the PD on the wafer printed image was calculated by a lithography simulator. The simulated mask models were the Ru-capped multilayer with several shapes and sizes of pit-type PDs as described in Sec. 2.2. Figure 8(a) shows the schematic cross-sectional mask structures with vertical-type and inclined-type pit PDs. The defects were 6-nm deep and 50-nm wide with their inclination angles of 0 deg and 8 deg. The calculated wafer printed images are shown in Fig. 8(b). Compared with the wafer printed image of the vertical-type PD, the inclined-type PD image shifted about 8 nm on the mask scale, which corresponded to 2 nm on the wafer scale.

Fig. 8

(a) Cross-sectional schematic view of the masks with vertical-type PD and inclined-type PD. (b) Calculated wafer printed images of the PDs.

The calculated positional shift of the PD image on the wafer due to the inclination angles are summarized in Fig. 9. The plus or minus of the inclination angles are defined as shown in Fig. 9(a) with a definition of EUV incident direction and angle. Figure 9(b) shows the positional shifts of the PD images on the wafer as a function of the inclination angle of the PDs. The results show that the image shift values are independent of the depths of the pit-type defects. The image of the inclined PD on wafer shifts about $1\mathrm{nm}/\mathrm{deg}$ to the inclined direction compared with the vertical-types one.

Fig. 9

(a) Definition of the plus and minus directions of the inclination angles of the PD. (b) Relationship between the inclination angles of the PDs and the positional shift of the defect image on the wafer. The defect sizes are 4, 6, and 8 nm in depth and 50 nm in width.