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Abstract
A method to optimize the spectral performance of 193 nm antireflective (AR) coating with a broad range of angle of incidence (AOI) on strongly curved spherical substrates is described. In this method, the actual film thickness on test plates for single-layer LaF3 and MgF2 films are corrected by measuring the relationship between the film thickness on test plates and that on quartz crystal microbalance. Interface roughness in multi-layer AR coating is obtained from atomic force microscopy measurements and its effect on the spectrum of the multi-layer is taken into account in this method by being simulated as a homogeneous sublayer. Porosities of the sublayers in AR coatings are obtained by reversely engineering the residual reflectance of the coatings/substrate/coating stacks. The obtained refractive indices and thicknesses in the multilayer are then used for analysis and optimization of the spectrum of 193 nm AR coatings. For strongly curved spherical surfaces, spectrum uniformity of the AR coating is optimized by taking into consideration simultaneously the merit functions at different positions of spherical substrates. This work provides a general solution to the performance optimization of 193 nm AR coatings with broad AOI range and on strongly curved spherical substrates.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The advances of high transistor density in integrated circuits impose requirements of photo-lithography systems with short working wavelengths and high numerical apertures (NA) [1]. To achieve a high NA, some optical components of the projective lenses are designed to have strongly curved concave or convex shapes. The large steepness results in wide range of angle of incidence (AOI) that can vary from 0° for near-axis rays to over 60° for off-axis rays [2]. Design and fabrication of high-performance antireflective (AR) coatings with such wide AOI range on these strongly curve-shaped components are critical yet technique-demanding steps toward successful manufacturing of high-NA photo-lithography systems, as in these high-NA systems both high illumination uniformity and low wavefront error at the pupil are required. To satisfy these requirements, AR coatings deposited on the strongly curved substrates have to be uniform in optical performances, which can be controlled via correction of film thickness uniformity [3–7] and designs of AR coatings with broad AOI range and wide working bands [2,3].
Currently, 193 nm excimer laser is still one of the most widely used optical sources for photo-lithography systems. Metal fluorides [8–11] such as lanthanum fluoride (LaF3) [12–15] and magnesium fluoride (MgF2) [16,17] prepared by thermal evaporation are normally used as high and low refractive index sublayers for AR coatings of projective lenses in 193 nm photo-lithography systems, respectively. Previous studies have revealed that LaF3 and MgF2 films prepared by thermal evaporation present columnar micro-structures and rough surfaces, which generally lead to increasing porosity of single-layer films with increasing thickness [18,19]. This thickness dependent film porosity makes it difficult to describe performance of fluoride AR coatings with homogeneous multi-layer model and to design accurately the coatings with commercial software [20]. In addition, since 193 nm AR coatings with broad AOI ranges usually consist of as many as 7 sublayers, the influence of thickness-dependent refractive index inhomogeneity on their optical performance will be amplified.
Moreover, the micro-structures and the related optical properties of fluoride films closely depend on their radial positions on a strongly curved spherical substrate [11]. Previously we have reported that the columnar tilting angles of LaF3 and MgF2 films increased from the center to the rim of a strongly curved spherical substrate with the increase of refractive index inhomogeneity by approximately one order of magnitude [21], which leads to severe spectral non-uniformity of AR coatings on strongly curved spherical substrates. For example, residual reflection of an AR coating at 193 nm is only 0.2% at the center region but reaches as high as 1% at the rim region of the spherical substrate [21]. Although it is possible to optimize the performance of fluoride coatings via trial and error, a directly theoretical design method to fabricate AR coatings with the desired spectral uniformity is of great technical importance for the overall performance optimization of high-NA photo-lithography systems.
In this paper, several factors that influence the spectra of fluoride multilayers are considered to optimize the spectral performance of 193 nm AR coatings with broad AOI range and on strongly curved spherical substrate. The film thickness is precisely controlled by experimentally establish the relationship between film thicknesses on quartz crystal microbalance and that on planetary rotation substrates. The interface roughness of the multilayers is obtained from atomic force microscopy (AFM) measurement and simulated as homogeneous sublayers in the multilayer design. Finally, the thickness and refractive index profiles of the multilayer are obtained from reversely engineering the spectra of the AR coatings and are taken into account in the AR coating design. 193 nm AR coatings designed with the optimized model taking into account the factors mentioned above yield theoretical and experimental spectra in well agreement. Furthermore, refractive index and thickness profiles at different positions of a strongly curved spherical substrate are obtained, and the spectral uniformity along the radial direction of the spherical substrate is improved by optimizing simultaneously the spectra at different positions.
2. Experiment
The coatings were prepared with a SYRUSpro-DUV coating plant (Leybold Optics, Germany) equipped with a planetary rotation system without inclination of substrates holders. Fused silica plates with surface roughness approximately 0.1 nm, thickness 4 mm and diameter 25 mm were used as the substrates. The plates were manually cleaned with mixed ethanol and ether and then transferred to the vacuum chamber for film deposition. The chamber was pump down by combination of drypump, cryopump and a polycold system to a base pressure of 2.0 × 10−6 mbar. The substrates were then heated with a set of ceramic heaters to 300 °C and kept at 300 °C for two hours, and then cleaned by ion bombardment with mixed Ar and O2 plasma (100V) for 5 minutes before film deposition. LaF3 and MgF2 were deposited on the substrate plates at 0.6 nm/s and 0.5 nm/s deposition rates, respectively, monitored by a quartz-crystal microbalance. Optical spectra of the coating samples were measured using a ML-6500 spectrophotometer (Laser Zentrum Hannover, Germany) at an incident angle of 10°. The spectrophotometer was working under vacuum condition with pressure of 2.0 × 10−6 mbar. A deuterium lamp (L7296, Hamamatsu Photonics, Japan) was used as the optical source and two photomultipliers were used as detectors for measurements of reference and signal intensities respectively. The light beam size was approximately 1 mm × 2 mm for reflectance spectrum measurements. The angle-resolved reflectance was measured by adjusting AOI of the sample and correspondingly the positions of the signal detector. Optical absorption and scattering losses were measured with a 193 nm laser calorimeter and an integrated scattering measurement instrument at 193 nm (both were developed by Laser Zentrum Hannover, Germany), respectively. Surface roughness was measured by an AFM (NaniteaAFM-110UM, Switzerland), which was operated in atmosphere and tapping mode. The scanning area was 2 μm × 2 μm. The scan lines were fitted with polynomial function. Five positions on the test samples were measured and the rms roughness was obtained by averaging over the measured results. The surface roughness, absorptance, scattering loss and reflectance spectra were measured at the center regions of the test plates.
Three groups of samples were prepared and characterized in this work. The first group was single MgF2 and LaF3 films deposited on fused silica plates and on strongly curved spherical substrates. The monitored thicknesses ranged from 20 nm to 35 nm for deposition on the test plates and were 80 nm for deposition on the spherical substrates, respectively. The thicknesses and refractive indices of the single films were reversely engineered from their optical spectra. The second group of samples was used for determination of interface roughness of AR coatings with AFM. The roughness of the ith interface was analyzed using a sample with multi-layer structure of Sub/ L1/ L2/ .../ Li/ air, where Sub denotes the fused-silica substrate and Li denotes the thickness of ith sublayer of the AR coating, respectively. The third group of samples was coating/substrate/coating stacks (substrate with both sides AR-coated). Refractive indices of sublayers were obtained from reversely engineering the residual reflectance spectra of the stack. The second and third groups of samples were prepared both on the test plates and on the spherical substrates. For film preparation on the test plates, the fused silica substrates were placed at the center of the substrate holders and no shadowing masks was used. The spherical substrate was simulated by a convex jig with clear aperture 220 mm and radius of curvature 155 mm. Holes with diameter 25 mm for holding the test plates were distributed on four positions of the jigs: the center and the positions with radius of 45 mm, 75 mm and 105 mm, referred as P1- P4, respectively. It is noted that the coating geometry for the test plate is the same as the coating geometry for the spherical substrate at the center of the holes. A group of shadowing masks was positioned approximately 10 mm below the substrate to improve film thickness uniformity on the spherical substrate. With correction of the shadowing masks, it is expected that the film thicknesses and refractive indices of the films were approximately uniform in the center regions of test plates located on the convex jig to simulate the spherical substrate.
3. Design consideration
3.1 Calibration of film thickness
In our coating plant, the position of the quartz crystal for film thickness monitoring is different from the position of the planetary-rotation substrate. Therefore, the monitored thickness generally differs from the actual film thickness on the substrate. Experimentally, the film thickness on the substrates is obtained by reversely engineering the optical spectra of the films deposited on test plates placed at the same positions as the substrates. Figures 1(a) and 1(b) show the reflectance spectra of single-layer LaF3 and single-layer MgF2 films deposited on one side of fused silica plates with monitored thicknesses ranging from 20 nm to 35 nm, respectively. The spectra are reversely engineered using homogeneous single-layer model with refractive index dispersions described by Cauchy formulas [21]. Refractive indices and thicknesses of the films on the test plates are shown in Figs. 1(c) and 1(d), respectively. The refractive indices at 193 nm are 1.718 for LaF3 and 1.432 for MgF2, close to the value of the bulk materials [21]. Film thicknesses deposited on the test plates (td) show linear dependence on the monitoring thicknesses (tm) of the single-layer films, which is described by
From linear fitting of the experimental data, I and tooling are determined to be 2.33 and 0.96 for MgF2 and −0.8 and 0.98 for LaF3, respectively. The non-zero I is caused by severe oscillations of quartz crystal at the initial monitoring period. Similar phenomena have also been reported previously in monitoring the oxide coatings by quartz crystal microbalance [22]. From Eq. (1) the actual film thickness can be accurately determined from the monitoring thickness.
Fig. 1 Residual reflectance of (a) single-layer LaF3 and (b) single-layer MgF2 films. The dots are from experimental measurements and the solid lines are from theoretical calculations. The red, blue, black, and green lines are for single-layer films with monitored thicknesses of 20 nm, 25 nm, 30 nm and 35 nm, respectively. (c) Refractive index dispersions of LaF3 (red cycles) and MgF2 (black square) from reversely engineering the experimental reflectance spectra. (d) The film thicknesses deposited on the test plate for single-layer LaF3 (square) and single-layer MgF2 (cycle) with respect to the monitored thickness. The lines are linear fits.
3.2 Effect of interface roughness
It is well known that interface roughness is an important factor that influences the spectra of coatings, and that mean-medium theory works well for simulating the effect of interface roughness on optical spectra of single-layer metal-fluoride film, such as MgF2 [23], GdF3 [24], LaF3 [25] and multi-layer coatings [26]. Here we model the ith interface, formed between the ith and (i + 1)th sublayers of a fluoride multilayer, by a homogeneous layer with thickness
and refractive indexwhere σi is the roughness of the ith interface, ns,i and ns,i + 1 denote refractive indices of the two materials inclining to the ith interface. Due to the artificial interface sublayer, the thicknesses of both the ith and (i + 1)th sublayers have to be decreased by σi accordingly in order to keep the total deposited amount unchanged. It is noted that the ith sublayer of the fluoride coatings contributes to both ith and (i-1)th interfaces, After taken both the interfaces σi and σi-1 into consideration, thickness (ti0) of the ith sublayer with deposited thickness tdi will be changed toHere σ0 (that is, σi-1 with i = 1) denotes the surface roughness of the substrate for calculation of the thickness of the first sublayer.3.3 Effect of film porosity
It has been recognized that film porosities influence the refractive indices of the sublayers in 193 nm AR coatings [21]. In our study, the influence of porosity on refractive index of the film is described by [24]:
where ni and pi are the refractive index and porosity of the ith sublayer, ns,i is the refractive index of the corresponding bulk material, respectively. The porosity also influences the thicknesses of the sublayers. For material with bulk density, the film density is determined approximately by . Because the thickness is measured directly by deposited mass on quartz crystal, the monitored thickness is for bulk materials. When the presence of porosity in the film is considered, the actual film thickness (ti) on the test plate should be corrected to4. Design, fabrication and characterization of AR coatings
In this work, 193 nm AR coatings with AOI from 0° to 60° are realized by fluoride multilayers that yield residual reflectance below 0.2% for double-side AR coated fused silica substrate. We firstly design the AR coating with commercial software (Macleod). Traditional multilayer model is used in the design, where all the sublayers are homogeneous and the interfaces are ideal. The refractive indices of LaF3 and MgF2 sublayers are taken from Fig. 1(c). A typical coating design meeting the requirements is Sub/ 22.6 nm L/ 13.9 nm H/ 27.3 nm L/12.8 nm H/ 37.2 nm L/ 29.3 nm H/ 38.2 nm L/ air, where H and L represent LaF3 and MgF2 sublayers, respectively. The black dashed line in Fig. 2(a) shows the reflectance spectrum of the coating/substrate/coating stack from theoretical calculation. The reflectance is well below 0.2% between 193 nm and 215 nm. The angle-resolved reflectance, as shown by dashed (blue) line in the inset, is below 0.2% for AOI below 30°. However, the measured residual reflectance of the stack, prepared on test plate without shadowing masks for thickness correction, reaches approximately 0.5% from 193 nm to 208 nm as shown in Fig. 2(a). Correspondingly, the measured reflectance (0.5%) at 193nm is much higher than theoretical prediction for incident angle from 0° to 30°, as shown in the inset of Fig. 2(a). The significant difference between experiment and theory indicates that the performance of 193 nm AR coating designed with the traditional multilayer model cannot meet the technical requirements experimentally. In addition, the optical scattering and absorption losses at 193nm are measured to be 0.04 ± 0.01% and 0.71 ± 0.05%, respectively.
Fig. 2 Reflectance spectra and angle-resolved reflectance (inset) of 193 nm AR coatings in coating/ substrate/ coating stacks. The black (dashed) line in Fig. 2(a) is from theoretical design with Macleod software. The red dots are reflectance from the measurement and the solid (green) lines depict the reversely engineered spectra taking the interface roughness and varying porosity of the sublayers into account. The solid (green) lines and red dots in Fig. 2(b) are reflectance of the stack designed with the optimized model and from experimental measurements, respectively.
The above-mentioned three factors that influence the refractive indices and thicknesses of the sublayers have to be taken into consideration for the design and fabrication of the 193nm AR coatings with low residual reflectance (therefore high transmittance). As summarized in Table 1, the actual deposition thicknesses (td) on the test plates are calculated from the monitoring thicknesses (tm) via Eq. (1). Interface roughness (σ) is measured with AFM, and its influences on the structure of the multilayer are described with Eqs. (2)-(4).
Table 1. Parameters for Each Sublayer of the 193 nm AR Coating
Accurate determination of the refractive indices of the sublayers is the major challenge in analyzing the spectrum of AR coatings. In this work, the refractive indices and corresponding film porosities of the sublayers are obtained by reversely engineering optical spectrum of the multilayer. In the reversely engineering process, refractive index inhomogeneity within each sublayer is negligible because the sublayers in the 193 nm AR coatings are thin [21,27]. However, the refractive indices for the sublayers fabricated by the same coating materials are different as a result of refractive index inhomogeneity. Therefore the film porosity in each sublayer is taken as fitting parameters during reversely engineering the reflectance spectrum of the 193nm AR coating with Eqs. (1)-(6). A simulated annealing algorithm was employed for the multi-parameter optimization. The fitted spectrum is presented by solid green lines in Fig. 2(a). Table 1 summary the effective refractive index at 193 nm and film porosity for each sublayer from reversely engineering results. The porosity of LaF3 film increases much faster than MgF2, which is consistent with higher porosity of LaF3 single films than MgF2 single films [21,28].
AR coating is optimized with the knowledge of refractive index and thickness profiles of the fluoride multilayer. Performance of a coating design is evaluated with merit function (MF)
where num is the total points in the optimization target, Ti, Ai and wi denote the target, theoretically calculated value of the multilayer coating, and weight of the ith point of the target, respectively. A typical coating design with this optimizing method is Sub/ 34.4 nm L/ 11.1 nm H/ 25.1 nm L/15.3 nm H/ 37.3 nm L/ 29.5 nm H/ 36.0 nm L/ air. Here the thicknesses have been changed into monitoring thicknesses. The symbol- and solid- lines in Fig. 2(b) show the theoretical and experimental residual reflectance spectra of the coating/substrate/coating stack, respectively. Compared to reflectance spectrum presented in Fig. 2(a), the coating with optimizing design presents excellent AR performance between 193 nm and 215 nm. The angle-resolved reflectance spectrum, as shown in the inset of Fig. 2(b), is also in good agreement with the theoretical calculation. The scattering and absorption losses of this double-side AR coated sample at 193 nm are measured to be 0.05 ± 0.01% and 0.75 ± 0.05%, respectively, slightly different to the measured values of the sample with traditional design due to small difference in film thicknesses (181.3nm versus 188.7nm). It is noticed that if the thicknesses of the sublayers derivate drastically from the initial design, the interface roughness may differ greatly from the values presented in Table 1. The interface roughness should be re-measured again for theoretical reflectance spectrum calculations. The method has been used for design and fabrication of other coatings, which all yield well accordance between experimental spectra and theoretical calculation.5. Results and discussion
In our experiment, shadowing masks are used to correct film thickness non-uniformity on the strongly curved spherical substrate. With shadowing masks, the film thickness deposited on the substrate are related to the monitoring thickness via
where the factor f describes the influence of shadowing masks. To ensure that tooling and I are the same as in Eq. (1) before using masks, the height of the spherical substrate is adjusted so that its center is at the same height as deposition on the test plates. Then the factor f is determined from the monitored thicknesses of single films on crystal quartz microbalance and the deposited thicknesses at the center of the spherical substrate after using shadowing masks. Even with shadowing masks for film thickness correction, the properties of single-layer LaF3 and MgF2 films are still position dependent. Figure 3(a) presents the uniformity of refractive indices and thicknesses of single-layer MgF2 and LaF3 films with thickness approximately 40nm at positions P1- P4 of the spherical substrate. Here the uniformity is defined by the thicknesses and refractive indices relative to their values at the center of the substrate. The LaF3 film thickness increases gradually from 1 at the center to approximately 1.03 at the edge region, and the MgF2 film thickness decreases gradually from 1 at P1 to 0.99 at P4. The refractive indices at 193nm decreased from the center to the rim of substrate, especially for single-layer LaF3 film. This is consistent with the micro-structures and optical properties of thick single films in our previous work [21].Fig. 3 (a) Uniformity of thickness and refractive index of single LaF3 and MgF2 film on the spherical substrate. (b) Reflectance spectrum of double-side AR coated samples from experiments (symbol) and reversely engineering (solid line) on four positions of the spherical substrate. (c) and (d) present the position-dependent interface roughness and porosity for each sublayer, respectively.
With shadowing masks for thickness correction, AR stacks following the optimizing coating design are prepared on strongly curved spherical substrates. Reflectance spectra of the stacks at P1-P4 of the spherical substrate are plotted in Fig. 3(b). It is revealed that the spectral performance of the AR coating is strongly position dependent. The difference is most obvious at P4, where the residual reflectance reaches as much as 0.4%. Figure 3(c) shows the interface roughness of the AR coatings at the corresponding positions. It is noted that the interface roughness at the rim are larger than that at the center of the substrate. For example, surface roughness of S7 at P1 and P4 is 1.05 ± 0.05nm and 1.84 ± 0.07nm, respectively. The porosity of the sublayers along the radial direction is presented in Fig. 3(d). For the same sublayer, the film porosity also increases from center to the rim of the substrate. The increase of film porosity from center to the rim of the substrate is caused by increasing columnar tilting angles as revealed in single fluoride films [21,29].
It is possible to improve the spectral uniformity of AR coating on strongly curved substrates by optimizing simultaneously AR performance at different positions. The overall performance of AR coating on spherical substrates is evaluated by a MF
where N is the number of investigated positions over the spherical substrate. It is important to limit the thickness variation of each sublayer to ensure that the interface roughness in Fig. 3(c) can also be applied in the optimizing design. One of the obtained design is Sub/ 33.2 nm L/ 11.5 nm H/ 26.0 nm L/17.6 nm H/ 39.2 nm L/ 31.5 nm H/ 36.4 nm L/ air. The solid and symbol- lines in Fig. 4 show the theoretical and experimental residual reflectance spectra of AR coating at the four positions of the spherical substrate, respectively. The reflectance is below or around 0.2% in the wavelength regions for all four positions, which are much better than that presented in Fig. 3(b), indicating the importance of taking into account the thickness error, interface roughness, and film porosity in the design of AR coatings with broad AOI range and on strongly curved spherical substrates.Fig. 4 Reflectance spectra for double-side AR coated fused silica substrates from the optimized design (solid line) and experiments (symbol) on the four positions of the spherical substrate. The dashed cyan line denotes the reflectance of 0.2%.
6. Conclusions
In conclusion, a general method for analyzing and optimizing the spectral performance of 193 nm AR coating for high-NA photo-lithography applications was described. Reverse engineering of reflectance spectrum showed that thickness error, interface roughness and refractive index inhomogeneity of sublayers lead to derivation of optical spectra between theoretical design and experimental results. The position-dependent refractive index profile of sublayers and interface roughness lead to spectrum non-uniformity of AR coatings on steep spherical substrate. By taking the detailed information of each sublayer into account in the coating design, AR coatings with optimized performance and high spectral uniformity were fabricated on strongly curved spherical substrates. In principle, by setting the transmittance and light polarization at different incident angle as optimization target, the method described in this paper could be directly applied to the design and fabrication of 193nm coatings with polarization illumination in immerse systems, and so on.
Funding
Youth Innovation Promotion Association, Chinese Academy of Sciences (2016337).
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28. It is shown that the porosity of the sixth sublayer (LaF3) is higher than porosity of the seventh sublayer (MgF2). This is induced by the higher refractive index inhomogeneity of LaF3 single films.
29. It is important to note that the coating geometry for position P1 is the same as coating on small test plates except the utilization of shadowing masks. However, surface roughness of AR coating of P1 is over twice of AR coating on small test plates. The results clearly demonstrated the influence of shadowing masks on properties of single films.
