Impact of thermal expansion coefficient on the local tilt angle of extreme ultraviolet pellicle

Abstract. Background: A local tilt angle of <300  mrad results in a critical dimension uniformity (CDU) impact below 0.1 nm when a pellicle is used for extreme ultraviolet (EUV) lithography. However, the thermomechanical property guidelines satisfying this specification have not yet been established. Aim: We present the thermomechanical property guidelines that yield a CDU impact below 0.1 nm. Approach: The peak temperature ranges of the EUV pellicle, as a function of the emissivity, were calculated through experimental, numerical, and finite element method analyses. The wrinkle profiles were evaluated as a function of the coefficient of thermal expansion (CTE) within these temperature ranges. The emissivity and CTE values satisfying the specifications were obtained using the CDU impact caused by the wrinkled EUV pellicle. Results: The wrinkle amplitude in the EUV pellicle exhibited 45% attenuation with a twofold decrease in the CTE. The maximum local tilt angles for the 17, 16, and 15 nm half-pitch patterns were 290.2, 286.1, and 272.3 mrad, respectively. CTE below 2  ×  10  −  5  K  −  1 and emissivity above 0.1 are suggested for the EUV pellicle. Conclusions: The CTE and emissivity guidelines satisfying the CDU impact specifications can be used for developing next-generation EUV pellicles.


Introduction
Even though the extreme ultraviolet transmittance (EUVT) and thermal stability of EUV pellicles have been improved, it is necessary to confirm the effect on the imaging performance when a EUV pellicle is employed in the lithography process. 1 As the temperature of the EUV pellicle increases under EUV exposure, the corresponding slit area expands and forms a wrinkle. 1,2 This wrinkle induces EUVT nonuniformity because of the different EUV-light paths through the wrinkled EUV pellicle, ultimately impacting the imaging performance. 3 It was reported that, because of the wrinkles formed in the EUV pellicle during the exposure, the critical dimension uniformity (CDU) impact can be limited to 0.1 nm by maintaining the local tilt angle below 300 mrad. 4 Although the value of the local tilt angle has been specified, the corresponding thermomechanical property guidelines have not been reported. 5 Previous studies assumed a twodimensional wrinkle profile and an arbitrary period independent of the material properties of the EUV pellicle. 2,6 *Address all correspondence to Jinho Ahn, jhahn@hanyang.ac.kr We performed experimental, numerical, and finite element method (FEM) analyses to present the guidelines for the thermomechanical properties of the EUV pellicle according to the CDU impact specifications. 7 The wrinkle profile of the pellicle was studied under EUV exposure, and the imaging performance was simulated using a wrinkled EUV pellicle under various values of emissivity and coefficients of thermal expansion (CTE) (Fig. 1). We present the guidelines of thermomechanical properties for the next-generation EUV pellicles, which meet the CDU specification.

Experimental and Numerical Analyses for Evaluating the Peak Temperature of the Pellicle Under EUV Exposure
Silicon-rich silicon nitride (Si 6 N 7 ) was used as the EUV pellicle for experimental analysis to confirm the feasibility of the numerical and FEM analyses. 8 Figure 2(a) shows the transmission electron microscopy (TEM) cross-sectional image of a 19-nm-thick Si 6 N 7 EUV pellicle, which exhibits 90% single-pass transmittance at a wavelength of 13.5 nm. 9 The thickness of Si 6 N 7 EUV pellicle used for subsequent analysis was extracted from the TEM result. Figure 2(b) shows the schematic of the heat-load test apparatus used to emulate the thermal load during EUV scanning. 10 The heat flux of the 355-nm UV laser can be matched with that of the EUV using Eq. (1), considering the absorbance of the pellicle at two different wavelengths. 11 The absorbance (0.1) at a wavelength of 13.5 nm was used for the 19-nm-thick Si 6 N 7 pellicle according to the center for x-ray optics database. 12 α 355 nm was set to 0.0344 based on the spectrophotometer results, and A 355 nm was set to 0.283 cm 2 , corresponding to the area of a 0.6-cm-diameter beam. A two-channel pyrometer was used to eliminate the effect of emissivity changes during the measurement of the EUV pellicle temperature: 13,14 Fig. 1 Analysis flow for evaluating the ranges of the emissivity and CTE and the limit of the local tilt angle of the EUV pellicle for a CDU impact below 0.1 nm. Kim, Kim, where α is the absorbance, P is the power, A is the beam size, and each subindex is the wavelength of the light source. The change in the temperature of the EUV pellicle over time (dT∕dt), with the varying the emissivity and specific heat, was calculated using the Stefan-Boltzmann equation, considering radiation to be the only heat dissipation mechanism [Eq. (2)]. 2,15,16 The material properties of the EUV pellicle and the exposure conditions for numerical analysis were considered to be independent of the temperature and were approximated by rounding to the fourth decimal place (Table 1)

FEM Simulation of a Wrinkle in the Slit Area of the EUV Pellicle
Several studies performed FEM analysis using the ANSYS workbench to evaluate the wrinkles in the membrane. [19][20][21][22] We also used ANSYS 2021R1 to simulate the wrinkle profile in a fullsized (110 mm × 143 mm) pellicle under EUV exposure. 23  The simulation was performed using steady-state thermomechanically coupled analysis. The experimental results were compared with the FEM results using the parameters in Table 1 to confirm the effectiveness of the FEM thermal analysis. The temperature of the pellicles under EUV scanning was calculated using the conditions in Table 1, except for the exposure time (0.01 s) and incident heat flux (7.925 W cm −2 considering 65% reflection from the mask). 2,[24][25][26] The thermal analysis assumed uniform heat flux in a 10 mm × 110 mm rectangular slit and radiation as the only mechanism for heat dissipation. Tensile residual stress and gravity were applied to the EUV pellicle before applying the temperature load during the structural analysis. 27 The wrinkle profile of the EUV pellicle was simulated at different emissivity values (0.025, 0.05, 0.1, 0.2, and 0.4) and CTEs (0.5 × 10 −5 , 1 × 10 −5 , 2 × 10 −5 , and 4 × 10 −5 K −1 ). 17,[28][29][30][31] The CTE range was set according to the change in the CTE due to heating and oxidation. [32][33][34][35][36][37] The EUV pellicle deformation was assumed to be elastic, and nonlinear analysis was performed for large deflections. 38

Numerical Analysis of the EUV-Light Path and EUVT Non-Uniformity in a Wrinkled EUV Pellicle
The biaxial wrinkle profile in the rectangular plate used for numerical modeling 39 is given by the following equation: E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 3 ; 1 1 6 ; 5 0 3 where w is the out-of-plane deformation in the Z direction at the ðx; yÞ coordinate, A is the wrinkle amplitude, m and n are the number of half-wavelengths in the X and Y directions, and a and b are the lengths of the slit in the X direction (10 mm) and Y direction (110 mm), respectively. The number of half-wavelengths and the average wrinkle amplitude of the simulated results were substituted in Eq. (3). Wrinkles within 3 mm of the border were excluded as they did not affect the imaging performance owing to the black border of the mask, 40 and the modeled wrinkle profiles were plotted as a 10 mm × 100 mm XY-plane contour graph with a grid size of 100 μm.
The EUV-light path length through the wrinkled pellicle, calculated using MATLAB R2020b, was used to evaluate the EUVT nonuniformity of the wrinkled region in the EUV pellicle. The single-pass EUVT through the pellicle membrane was calculated using Eqs. (4) and (5) 41 with fixed values of the refractive index η p (0.983) and extinction coefficient κ p (0.006) at wavelength λ (13.5 nm). The length of the EUV-light path through the wrinkled pellicle is l, and the proportional coefficient used for calculating the EUVT is D.
The effect of wrinkles on the imaging performance was evaluated using a double-pass EUVT, which is the product of the EUVT in the first and second passes, and the EUVT nonuniformity was calculated as the difference between the maximum and minimum double-pass EUVT in the slit area: 3 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 4 ; 1 1 6 ; 2 3 0 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 5 ; 1 1 6 ; 1 7 4

CDU Impact Due to the Double-Pass EUVT Nonuniformity in a Wrinkled EUV Pellicle
The CDU impact of the wrinkles in the EUV pellicle during patterning was simulated using Panoramic Hyperlith, and the parameters used for imaging performance simulation are listed Kim, Kim, and Ahn: Impact of thermal expansion coefficient on the local tilt angle of extreme ultraviolet pellicle in Table 2. 12,42,43 The refractive index and extinction coefficient were approximated by rounding to the fourth decimal place. The aerial images through pellicles with different EUVT were simulated separately for the 17, 16, and 15 nm half-pitch (HP) L/S patterns because Hyperlith cannot accommodate the wrinkles in the EUV pellicle. The threshold intensity that meets the target CD without the pellicle ("no pellicle" condition) was used as the reference intensity, and the CD after double-pass through the EUV pellicle was obtained. The CDU impact owing to the double-pass EUVT in the wrinkled EUV pellicle was then calculated using the derived equation. 3 3 Results and Discussion

Peak Temperature of the EUV Pellicle at Various Emissivity and Specific Heat Values
The peak temperatures obtained from the numerical and FEM analyses were compared with the experimental values obtained by irradiating the pellicle using a 355-nm laser equivalent to 5 W cm −2 EUV for 0.1 s [ Fig. 3(a)]. The average peak temperature of the EUV pellicle (1752 K) measured by the heat load apparatus is consistent with the results of the numerical (1830 K) and FEM analyses (1834 K). The small deviation (4.5%) from the experimental data confirms that the numerical and FEM analyses can be used for calculating the peak temperature of the pellicle. The peak temperature was calculated while varying the emissivity and specific heat of the EUV pellicle under the double-pass with an EUV incident power of 5 W cm −2 and a 65% mask reflection [ Figs. 3(b) and 3(c)]. The average peak temperature decreases by 15%, 34%, 56%, and 82% as the emissivity increased by a factor of 2, 4, 8, and 16 from 0.025, respectively. The average peak temperature decreases by 1.3% and 4.3% with a two-and three-factor increase in the specific heat, respectively. The density of potential EUV pellicle materials ranges from 1000 to 6000 kg m −3 , limiting the effect of the specific heat on the peak temperature. [44][45][46] Consequently, only the emissivity was considered during the analysis of the thermal properties of the EUV pellicle.

FEM Analysis of the Wrinkle Profile and Numerical Analysis of the
Double-Pass EUVT Nonuniformity in the Slit Area Figure 4(a) shows the isometric view of the wrinkle profile in the exposed slit area when EUV heat flux of 7.925 W cm −2 is applied to the center of the 19-nm-thick EUV pellicle for 10 ms. The EUVT, emissivity, and CTE of the EUV pellicle were set to 90%, 0.1, and 1 × 10 −5 K −1 , respectively. When the applied compressive stress is higher than the critical buckling stress of the membrane, a wrinkle is formed along the direction of the applied tensile stress. 47 Compressive stress is formed along the X and Y directions because of restrained thermal expansion due to the heat flux applied to the membrane. However, the compressive stresses along two directions are different as the magnitude of the compressive stress is proportional to the stiffness of the constraint. 48 Although the compressive stress along the X direction is low due to the freestanding membrane, the compressive stress along the Y direction compensates for the residual stress of the membrane owing to the rigid border. Therefore, tensile stress is formed along the X direction, while compressive stress is formed along the Y direction, as shown in Fig. 4(a). 47 The maximum wrinkle amplitude (71.2 μm) was obtained at emissivity and CTE values of 0.025 and 4 × 10 −5 K −1 , respectively, whereas the minimum amplitude (15.6 μm) was obtained at emissivity and CTE values of 0.4 and 5 × 10 −6 K −1 , respectively [ Fig. 4(b)]. The attenuation ratios of the emissivity and the CTE of the wrinkle amplitude were calculated at an emissivity of 0.025 and CTE of 4 × 10 −5 K −1 [Figs. 4(c) and 4(d), respectively]. The wrinkle amplitude attenuates with the increase in the emissivity and decrease in the CTE. However, the attenuation ratios of the two properties are not compared at the same level because emissivity determines the peak temperature of the pellicle, whereas the CTE determines the wrinkle profiles in the pellicle under temperature gradients. However, an appropriate combination of the emissivity and CTE can yield a wrinkle profile satisfying the CD specifications.
The color bars in Fig. 5 represent the amount of deformation in the Z direction at each grid coordinate while varying the CTE of the pellicle. The numerically modeled wrinkle profile was    5 Contour plot of the modeled wrinkle profiles using MATLAB R2020b when EUV pellicles, with a single-pass EUVT of 90%, emissivity of 0.05, and various CTEs (5 × 10 −6 , 1 × 10 −5 , 2 × 10 −5 , and 4 × 10 −5 K −1 from left to right), are exposed to EUV heat flux of 7.925 W cm −2 for 10 ms.
used to calculate the EUV-light length through the wrinkled pellicle owing to its similarity with the simulation results. Figure 6(a) shows the cross-section of the modeled wrinkle, which is divided by the XZ plane, corresponding to an arbitrary y 1 on the wrinkled surface. The EUV-light path is denoted by a black arrow with a 6-deg chief ray angle at the object (CRAO) along the X direction. 49 The bottom surface (w bot ) of the wrinkle is expressed using Eq. (3) and the top surface ðw top Þ is the sum of h∕ sinðθ nx Þ (θ nx is the slope of the line normal to the wrinkle bottom) and w bot because the perpendicular distance between w bot and w top denotes the EUV pellicle thickness (h). The incident angle (θ ix ) of the EUV-light at w bot was calculated by subtracting θ nx from the slope of the incident line with 6-deg CRAO (84 deg). The diffraction angle (θ dx ) was calculated using Eq. (6), which was derived from Snell's law, with the refractive indices of vacuum and the EUV pellicle set to 1 and η p , respectively. 50 The value of x 2 was calculated using Eq. (7), assuming that the EUV-light incident on the bottom of the wrinkle at ðx 1 ; y 1 ; z 1 Þ passes through the pellicle and contacts the top surface at ðx 2 ; y 1 ; z 2 Þ: E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 6 ; 1 1 6 ; 2 5 0 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 7 ; 1 1 6 ; 1 7 8 Figure 6(b) shows the cross-section of the wrinkled EUV pellicle divided by a plane, with a line in w bot when x ¼ x 1 and a line in w top when x ¼ x 2 . The sum of ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ðx 2 − x 1 Þ 2 þ ðz 2 − z 1 Þ 2 p and w bot gives w top . The diffraction angle of the YZ-plane (θ dy ) was calculated by substituting the slopes of the line perpendicular to the bottom of the wrinkle (θ ny ) and that of the incident line (θ iy ) into Snell's law. Assuming that the EUV-light incident on the bottom at ðx 1 ; y 1 ; z 1 Þ contacts Fig. 6 (a) Schematic of the diffracted EUV-light path in the X direction incident at 6 deg on the pellicle and (b) in the Y direction incident normally on the pellicle. Kim, Kim, and Ahn: Impact of thermal expansion coefficient on the local tilt angle of extreme ultraviolet pellicle the top of the wrinkle at ðx 2 ; y 2 ; z 3 Þ due to refraction in the X and Y directions within the pellicle, the distance between the two points gives the EUV-light length within the wrinkled pellicle. Equation (8) was used to calculate y 2 and the single-pass EUVT was calculated by substituting the total length of the EUV-light in Eq. (4). Figure 7 shows the plot of double-pass EUVT nonuniformity according to the wrinkle amplitude:   show the aerial images through the EUV pellicles with an 88% to 98% singlepass EUVT for the 17, 16, and 15 nm HP L/S patterns, respectively. It can be inferred from the results that the CDU depends on the EUVT of the EUV pellicle.
The CD values at the threshold intensity were fitted linearly with the above equations [ Fig. 9(a)]. The CDU impact depends on the nonuniformity of the double-pass EUVT in the pellicle, and the slopes corresponding to the 17, 16, and 15 nm HP L/S patterns are shown in Fig. 9(b). The nonuniformity of the double-pass EUVT should be less than 0.4973%,

Calculation of the Local Tilt Angle in the EUV Pellicle and Material
Property Guidelines for the EUV Pellicle to Meet the CDU Impact Specifications The maximum local tilt angle (θ max ¼ tan −1 ðA · 2π∕2 · length of half wavelengthÞÞ of the EUV pellicle was calculated according to the CD specifications. 2 Fig. 10 represents the CDU impact of 0.1 nm. 7 EUV pellicles with a CTE of 1 × 10 −5 K −1 or less satisfy the CD specification with a CDU impact of 0.013 to 0.07 nm in the emissivity range of 0.025 to 0.4. However, an EUV pellicle with a CTE of 2 × 10 −5 K −1 and emissivity of 0.1 has a CDU impact of 0.0992 nm during 15-nm HP L/S patterning. The emissivity should be greater than 0.4 for a pellicle with a CTE of 4 × 10 −5 K −1 to meet the CD specification during 15 to 17 nm HP L/S patterning. For example, an EUV pellicle with a 3-nm ruthenium capping layer, which exhibits an emissivity of 0.4, cannot be used for an HP L/S pattern below 15 nm if the CTE of the EUV pellicle exceeds 4 × 10 −5 K −1 . 29 The CDU impact specifications are satisfied when EUV pellicles with a CTE of 2 × 10 −5 K −1 or less and emissivity of 0.1 or more are used during 15 to 17 nm HP L/S patterning.

Conclusion
In this study, the peak temperature of the EUV pellicle during EUV exposure was evaluated as a function of its emissivity through experimental, numerical, and FEM analyses. In addition, the wrinkle profiles of the pellicles were modeled in three dimensions by varying the CTE. The CDU impact due to EUVT nonuniformity in the wrinkled EUV pellicle was calculated, and the emissivity and CTE range for the pellicle were calculated to satisfy the CD specifications.
Although emissivity increases the thermal stability of the EUV pellicle by lowering its peak temperature, the CTE of the pellicle should also be considered to satisfy the CDU impact specifications during exposure. These guidelines for the emissivity and CTE of EUV pellicles can be extended to next-generation EUV pellicles through subsequent studies on other materials.
Jinho Ahn received his BS and MS degrees from Seoul National University in 1986 and 1988, respectively, and his PhD from the University of Texas at Austin, in 1992, in materials science and engineering. He joined Hanyang University in 1995 as a professor of materials science and engineering. He has authored more than 160 papers and invented more than 50 patents. Currently, he is a director of the EUV-IUCC, a research center, to promote collaborative work for EUV lithography technology development.