Improved Theoretical Reflectivities of Extreme Ultraviolet Mirrors

Transcription

1 Proceedings of the 5 th SPIE Symposium on Microlithography, Santa Clara, 7 Feb.-3 Mar.,. Proc SPIE, 3997, () Improved Theoretical Reflectivities of Extreme Ultraviolet Mirrors Mandeep Singh and Joseph J.M. Braat Optics Research Group, Faculty of Applied Sciences, Delft University of Technology, Lorentzweg 1, 68 CJ Delft, The Netherlands ABSTRACT We show that the theoretical reflectivities of multilayered Mo/Be and Mo/Si extreme ultraviolet (EUV) mirrors tuned for the nm spectral region can be enhanced significantly by incorporating additional materials within the stack. The reflectivity performance of these quarter-wave multilayers can be enhanced further by global optimization procedures by which the layer thicknesses are varied for optimum performance. By incorporating additional materials of differing complex refractive indices - e.g. Rh, Ru and Sr - in various regions of the stack we calculate peak reflectivity enhancements of up to ~5% for a single reflector compared to standard unoptimized stacks. For an EUV optical system with nine near-normalincidence mirrors, the theoretical optical throughput may be increased by up to 1%. We also show that protective capping layers such as Rh and Ru, in addition to protecting the mirrors from environmental attack, may serve to improve the reflectivity characteristics. Keywords: Thin film optics, multilayers, distributed Bragg reflectors, extreme ultraviolet lithography, optimization 1. INTRODUCTION The considerable interest in mirrors with high reflectivity at near-normal incidence tuned for the extreme ultraviolet (EUV) nm spectral range is driven by the potential of EUV proection lithography as the basis for the next generation of high throughput semiconductor lithographic tools for delineating structures at 7 nm and below [1,]. For the EUV spectral region high reflectivity normal incidence mirrors are necessarily multilayered thin film designs. Examples of high reflectivity EUV mirrors for near-normal incidence operation are Mo/Be and Mo/Si multilayer systems that exhibit particularly high reflectivities in the nm and nm spectral regions, respectively [3-5]. The motivation behind this work is the pressing need for optical throughput enhancement in an EUV proection lithographic system. The predominant designs are composed of distributed Bragg reflectors resembling quarter wavelength stacks with constant film thicknesses. The typical designs that have been fabricated thus far are 8 periods of Mo/Be and 4-5 periods of Mo/Si. [4, 5] These designs yield maximum theoretical reflectivities of R~.75 for the Mo/Be stack, and R~.73 for the Mo/Si stack (taking into account a highly absorbing ~-3 nm native oxide on the surface Be and Si layers). These reflectivity values (which are amongst the best for multilayer reflectors in the EUV region), whilst adequate for optical systems with a few reflectors, will dramatically diminish the output optical intensity to 6-1% of that directly before the first mirror in a nine-mirror EUV lithographic system. It is therefore evident that even an increase of 1-% in the peak reflectivity of a single mirror will yield a significant light throughput enhancement in the overall optical system. A particular problem in the EUV region is that all useful materials absorb the radiation to a certain extent. To reduce the effect on the reflectivity response of the absorption losses, the thicknesses of the two components of the stack are adusted to deviate slightly from the optical path length of λ/4. The thickness of the high absorption (absorber) layer d h is set slightly lower than that of the low absorption (spacer) layer d l, thus the partition ratio Γ = d h /(d h +d l ) of the multilayer is defined. Vinogradov and Zeldovich [6] have calculated Γ as a function of absorption - a value of Γ =.4 is commonly used. It is well known for general thin-film mirror designs with absorbing films [7], and for EUV designs [3, 8-1], that a gradual variation of the partition ratio through the stack - with Γ =.3-.4 at the surface to Γ =.5 near the substrate can increase the peak reflectivity. Carniglia and Apfel [7] showed that if the ratio of the thicknesses of the "spacer" and "absorber" are adusted for each period to give the largest increase in reflectivity, there is a transition from the ideal quarterwave stack near the substrate to thinner "absorber" layers near the surface. Their optimized design exhibited significantly higher reflectivity than the periodic stack. In the case of EUV mirrors an increase in peak reflectivity of.5-.% may be achieved. Such optimized stacks would yield significant throughput enhancements in a nine-mirror optical system. singh@optica.tn.tudelft.nl

2 In this computational study we go a step further and show that unprecedented reflectivity enhancements in the standard Mo/Be and Mo/Si stacks can be achieved by (1) incorporating additional materials within the basic stack, () utilizing global optimization routines, based on optimal control theory, to vary the partition of each period within the stack for optimum peak reflectivity, and (3) by selecting certain relatively inert materials as capping layers to avoid the formation of highly absorbing surface oxide films. We show that optimized multicomponent multilayer stacks are a prerequisite if significant optical throughput enhancement is to be realized in EUV proection lithography. The various materials considered in this study, in addition to molybdenum, silicon and beryllium, are mainly from period 5 of the periodic table: strontium, ruthenium and rhodium.. NUMERICAL METHODS The computations were performed using the thin film design program TFCalc (Software Spectra Inc.), which is based on the characteristic matrix methodology [11], and verified using LPro (4D Technology Ltd.), based on the 4 4 matrix formulation [1]. The characteristic matrix of the -th layer of the stack is given by: M cos φ = iη sin φ i sin φ η cosφ, = 1,,, J (1) where ϕ = π n λ d cosθ () is the phase thickness expressed in terms of the refractive index n and the physical thickness d of the layers, wavelength λ, and the angle of internal refraction θ. The optical admittances: η η = n cosθ n = cosθ (TE pol.) (TM pol.) (3) depend on the polarization of light at non-normal incidence. The assumptions inherent in these programs are that the interfaces between the adacent layers are perfect i.e. that there is no interfacial interdiffusion and no scattering loss. The optimization methods for thin film multilayered structures are based on the general principles of optimal control theory. In many thin film design methods there is a point at which the performance of the system can no longer be improved. In optimal control theory, one way to overcome such problems is to increase the number of design variables so that a system with a better performance i.e. with a lower minimum in a multidimensional parameter space can be found. In thin-film design this can be accomplished, for example, by globally modifying the relative thicknesses of the layers in the multilayer stack until the target optical performance is attained. For further convergence to the target value (of reflectivity) additional materials were introduced into the standard stack with initial thicknesses set to zero. Multicomponent stacks were thus engineered for near-normal incidence operation. Target reflectivities at one or more wavelengths around the central wavelength were then entered into the optimization routine, which optimally varied the thicknesses, until the target reflectivity values are approached for each wavelength. The merit (obective) function (common in optimal control theory) is of the form [13]: m 1 R( λ ) ˆ i Ri F = m i= 1 δri 1/ (4)

3 which represents the root-mean-square error between the calculated reflectance R(λ i ) and the target value Rˆi ± δr i where δr i is a tolerance, and m is the number of target values. In a previous paper [14] we have described in detail how esoteric optimization procedures such as needle optimization [15,16] can be employed to further enhance the reflector performance. However, in this work, we confine the discussion to a few relatively easily realizable designs. In sections 3 and 4 we shall show that the thin-film optimization techniques outlined here are essential for achieving reflectivity improvements in EUV multilayer reflectors. Global optimization procedures employed in this work are an integral part of the TFCalc software package. The notation that we have adopted to represent a period in a multicomponent stack is based on the commonly used notation for a -component stack e.g. Mo/Si where Mo is the low, and Si the high refractive index material. A typical needle-optimized stack is represented as Ru-Mo/Si which represents a single period with a total optical path difference of λ/. The sequence of the components is written as manifested within the stack, i.e. Ru is on the substrate side and Si on the top (vacuum) side. It should be noted that each distinct entity is separated by a hyphen in this notation. The optical constants of the various materials, namely the complex refractive index N = n ik are derived from atomic scattering factors by Henke et. al. and were obtained from the CXRO WWW server at Berkeley [17]. The values of n and k for the materials used in this study were downloaded as functions of wavelength from 1 nm to 4 nm and as such the wavelength dependence of n and k is implicit in all calculations. The values of n and k at the two wavelengths of particular technological interest are tabulated in Table 1. The main aim of this study is to demonstrate the performance enhancement of the reflectors and therefore we assume ideal white light illumination. Table 1: Values of n and k at 11.3 and 13.4 nm 11.3 nm 13.4 nm n k n k Be BeO Mo Rh Ru Si Si Sr SILICON-BASED MULTILAYERS FOR 13.4 nm OPERATION The standard Si-based multilayer stack is considered to be an unoptimized 5-period Mo/Si system grown on a Zerodur glass substrate, with a partition ratio Γ =.4 yielding d Mo =.8 nm and d Si =4.1 nm. In addition, it is assumed that the top 4.1 nm Si layer will undergo oxidation and effectively form a ~ nm capping layer of native oxide (SiO ). Analysis of such a stack yields a peak reflectivity at ~13.4 nm of R =.73. This is the first stack in Table and will be regarded as the reference and standard Mo/Si stack throughout this work. Furthermore, for a 9-reflector system, a more useful measure of optical throughput is the value of R 9. The relative values of the integrated reflectivities to the 9th power are also tabulated in Table. R 9 int is the area under the curve in the R 9 vs. λ spectrum. Optical thickness nd (nm) Si 3.1 Optimized two-component stacks The second design in Table represents an optimized Mo/Si stack again with a -nm native oxide layer at the surface. A 16% gain in R 9 int is observed - the maority of this increase is a result of the increase in the top Si layer. A further increase in R may be obtained by selecting Rh or Ru as capping layers and optimizing the stack. A gain of % in R 9 int is possible for a two-component Mo/Si multilayer stack with a -nm Rh capping layer as tabulated in Table. The optimization of the Mo/Si stack results in a gradual, smooth variation of the layer thicknesses through the stack while the period optical thickness remains nominally constant at ~ nm as.5 Substrate Mo Layer number Figure 1: The layer thickness profiles in a 5-period optimized Mo/Si stack with a nm Rh capping layer. 3

4 Optimized Capping Layer R (Peak) R 9 int (Rel.Units) Mo/Si No nm SiO Mo/Si Yes nm SiO Mo/Si Yes nm Rh Ru-Mo/Si Yes nm Rh Mo/Sr-Si Yes nm Rh Table : Silicon-based 5-period multilayer stacks tuned for 13.4 nm indicating the peak reflectivity (R) and the relative values of R 9 (integrated). shown in Fig. 1. Near the substrate, d Mo d Si 3.5 nm, varying to d Mo.7 nm and d Si 4. nm near the surface. A salient feature of the layer profile data in Fig. 1 is that the partition ration of ~.4 is maintained for the first periods from the surface and thereafter gradually changes to ~.5 at the substrate (close to the ideal λ/4 value). Thus for an optimum reflectivity response, the higher the absorption in the material, the lower the thickness near the surface. Furthermore, the increased thickness of Mo at the substrate side would indicate that near the substrate, optical contrast rather than absorption within the layer is the prerequisite for optimum performance, and hence the optical thicknesses approach the quarter wavelength value as for non-absorbing multilayers [6]. This phenomenon is discussed further in section 5. A selection of R 9 spectra for the 13.4 nm region is presented in Fig.. R 9.1 d e 5 Si.8 c b a Optical Thickness nd (nm) 3 Mo. 1 Ru Wavelength (nm) Layer Number Figure : R 9 spectra of various Si-based multilayers: (a) Standard unoptimized Mo/Si, (b) optimized Mo/Si, (c) optimized Mo/Si with Rh capping layer, (d) optimized Ru-Mo/Si and (e) Mo/Sr-Si. Figure 3: Layer profiles in a 5-period Ru-Mo/Si stack with a nm Rh capping layer. The predominance of Ru over Mo near the substrate (Layer ) is clearly observed. 3. Three-component stacks The three component system is set up initially as a two-component Mo/Si stack with the third material interleaved between the Mo and Si layers with its initial thickness set to zero. In the case of Ru-Mo/Si, Mo is favored near the surface and Ru near the substrate (Fig. 3). In this case, Ru is introduced throughout the 5-period stack with its initial thickness set to zero 4

5 with a layer order given by [S 5(Ru-Mo-Si) Rh V] where S is the substrate, a -nm Rh capping layer and V is the vacuum. The layer profile data for the Ru-Mo/Si multilayer stack is shown in Fig. 3 and clearly indicates the preference of Ru over Mo close to the substrate and vice-versa near the surface; in fact Mo is absent in the first 1 layers closest to the substrate. The sum of the optical thicknesses of the adacent Ru and Mo layers of this stack is identical to the optical thickness profile of Mo in Fig. 1 i.e. the quasi-quarter-wave character of the stack is maintained. The main increase in R 9 int in the Ru-Mo/Si system appears to be from the higher optical contrast obtained near the substrate as a consequence of the lower value of n for Ru as compared to Mo (Table 1). It is evident that the influence of optical contrast dominates near the substrate and therefore the higher absorption in Ru is not critical. Also, thin (~1 nm) interleaved Ru layers persist to the surface. This is a result of a high optical contrast between Ru and Si - the absorption is kept in check by maintaining very thin Ru layers. A 36% gain in 9-reflector computed throughput is observed for the Ru-Mo/Si system over the standard Mo/Si stack (Table ). The discontinuities in the Mo profile are a result of the optimization process, whereby Mo wholly replaces Ru at random locations in the stack. In the Mo/Sr-Si system, Sr was introduced into the standard stack ust in the 15 periods near the surface. Strontium, with high n and low k (Table 1), acts predominantly like a "spacer" and partially substitutes for Si as can be seen in the abrupt transition in the Si layer profile in Fig. 4. However, another subtle effect also takes place. A very small decrease in the optical thickness of Mo of ~.nm at the point where Sr is introduced into the stack. This amounts to ~9-1% of the optical thickness of the "absorber" Mo being replaced by Sr - predominantly the "spacer". The imperative of low photon absorption near the surface takes precedence; with the value of k for Sr lower than that of Si, a significant proportion (~4%) of the "absorber" part of the period is Sr. However, the value of n for Sr is sufficiently lower than that of Si for a proportion of Sr to be incorporated into the low index "absorber" layer, mediated strongly by the low absorption in Sr. The incorporation of Sr leads to a peak reflectivity of R=.766 and a 41% increase in R 9 int. 4 4 Si Be Optical thickness nd (nm) 3 1 Substrate Mo Sr Optical thickness nd (nm) 3 1 Substrate Rh Sr Layer number Figure 4: Layer thickness profiles of the Mo/Sr-Si stack. Layer number Figure 5: Layer thickness profiles of the Rh/Sr-Be stack. 4. BERYLLIUM-BASED MULTILAYERS FOR 11.3 nm OPERATION The standard Be-based multilayer stack is considered to be an unoptimized 8-period Mo/Be system grown on a Zerodur glass substrate, with a partition ratio Γ =.4 yielding d Mo =.3 nm and d Be =3.4 nm. The top Be layer is assumed to undergo oxidation such that a -nm BeO layer is formed. This is the standard two-component system entered in Table 3 and all other 5

6 stacks are referred to it. Upon optimization of the stack (again with a -nm BeO surface layer) the peak reflectivity increases by ~3% resulting in a 4% enhancement in R 9 int. Further significant increases in R and R 9 int occur upon coating the multilayer with a -nm Rh capping layer as tabulated in Table 3. However, the most striking feature of the data in Table 3 is that Mo appears not to be the optimal material for the 11.3 nm window. The Rh/Be stack exhibits enhanced 9-reflector relative optical throughput of 77%. However, factors such as high interdiffusion may favor Mo over Rh, though we are not aware of any studies on Rh-Be interface chemistry. The layer profiles of the optimized Mo/Be and Rh/Be are qualitatively identical to those shown in Fig. 1 for the Mo/Si system. The optical thickness profiles of the Rh/Sr-Be system are shown in Fig. 5. Strontium is incorporated in periods nearest the surface by a similar manner to that described for the Mo/Sr-Si system above and results in a 117% increase in R 9 int. Due to their similar optical constants, Be and Sr behave in a similar manner within the stack. Indeed the Rh/Sr-Be stack is uncannily similar to the Mo/Sr-Si stack and the explanation provided in section 3. applies here as well. Selected spectra of Be-based multilayers are shown in Fig. 6. Optimized Capping Layer R (Peak) R 9 int (Rel.Units) Mo/Be No nm BeO Mo/Be Yes nm BeO Mo/Be Yes nm Rh Rh/Be Yes nm Rh Rh/Sr-Be Yes nm Rh Table 3: Beryllium-based 8-period multilayer stacks tuned for 11.3 nm indicating the peak reflectivity R and the relative values of R 9 (integrated). 5. DISCUSSION From our computational analysis of the various multilayer systems for the EUV region between 11 nm and 14 nm it would appear that drastic enhancements in peak and 9-reflector integrated reflectivities are possible. A combination of capping layer, global optimization procedures and, most importantly, the incorporation of additional materials within the stack R e d c b a Wavelength (nm) Figure 6: R 9 spectra of various Be-based multilayers: (a) Standard unoptimized Mo/Be, (b) optimized Mo/Be, (c) optimized Mo/Be with Rh capping layer, (d) optimized Rh/Be and (e) Rh/Sr-Be. appear to be necessary conditions for reflectivity enhancement. We have in the past [14] found that in the nm region, in addition to Mo, the "absorber" materials that show promise are Pd, Rh and Ru. In addition to Si and Be, the viable "spacer" materials from the numerical point of view are Sr and RbCl. These findings are consistent with the selection criteria based on Fresnel reflection coefficients discussed by Yamamoto et. al. [18]. In the case of the Be-based multilayers, we have found that Rh/Be yields superior performance to that of Mo/Be. Issues such as interface chemistry may preclude the viability of Rh/Be, however, we are not aware of any studies in the literature on this issue. Multilayers of Rh/Si and Ru/Si have been investigated in the past in relation to polarizer and filter design for the 4-13 nm spectral region [18-], and interface imperfection [1]. Yanagihara et. al [] have investigated the performance of Rh/Si and Ru/Si as a function of synchrotron radiation dose. Also, binaryalloy/carbon-based grazing incidence multilayers such as RhRu/C and ReW/C have been studied in the past [3,4]. In this study, we have shown unequivocally that near-normal incidence numerically optimized - component and multicomponent multilayers yield substantially better theoretical reflectivities. We point out that we cannot say for certain that the optimization 6

7 procedure finds a global minimum of the merit function in our designs. However, due to the severe constraints on the control variables imposed by high photon absorption in the materials and the relatively low optical contrast between the materials, we consider the designs presented in this work to be near-optimal. In for instance the Ru-Mo/Si stack where the optimization procedure invariably prefers to locate Ru near the substrate and Mo near the surface (Fig. 3), we suggest a qualitative explanation as follows. At 13.4 nm Ru exhibits a higher optical contrast with Si than does Mo. Additionally, the extinction coefficient k and therefore the absorption within the layer is lower for Mo than Ru. Near the surface of the stack, it is important that there be low absorption so that the incident radiation penetrates as deep into the stack as possible such that phasor addition is maximized. However, deep within the stack where the intensity is low, increased optical contrast is favored for the intensity of the Fresnel reflection to be maximized, i.e. the absorption is not critical and therefore the partition ratio tends towards the ideal quarter-wave limit as for non-absorbing multilayers. When Sr is incorporated in the structure it is preferentially located in the near-surface region of the stack and predominantly substitutes for Si (Fig. 4). This can be explained by similar arguments: the value of n for Sr is lower than that of Si and therefore whilst the optical contrast with the low-n materials is lowered, the lower value of k for Sr compared with Si (Table 1), means that the absorption within the layer is lower - thus favoring Sr near the surface of the stack. There is also a partial (~9-1%) substitution of Sr for Mo or Rh qualitatively explained in section 3.. This subtle effect is a product of the optimization process in which a small trade-off between n and k and the thicknesses of the various materials are made for optimum reflectivity performance. Similar arguments are consistent with data obtained for Be-based stacks for 11.3 nm operation. An analysis of variable partition ratio stacks for EUV was carried out by Spiller [3] and Meekins et. al. [1] who concluded that the periodic designs exhibit only slightly lower reflectivities than the fully optimized designs for a large (semi-infinite) number of layers. Whilst we agree that the change in the peak reflectivity is small (~.5-1.%) for a 5- period Mo/Si stack, and tends to zero for a quasi-infinite stack, this increase becomes significant when the throughput of a 9-reflector system is considered. We have shown that the peak reflectivity of optimized 5-period Mo/Si stacks with suitable capping layers can be increased significantly such that the optical throughput of a 9-reflector optical system can be enhanced by as much as ~3%. Significantly, the insertion of additional components into the stack, and subsequent optimization, serves to enhance further the value of R 9 int. In the case of the Mo/Be system, the gain in R 9 int is more pronounced and the inclusion of additional components within the stack and the choice of capping layer is crucial - yielding R 9 int enhancement of 5-1%. We would like to point out that despite our only having modeled idealized multilayer stacks, we believe that similar enhancement can be achieved in real multilayers by partition ration optimization and oxygen-free low n capping layer deposition. It is evident that our idealized Mo/Si stack is in reality a MoSi x /Mo/MoSi x /Si due to inevitable interfacial silicide formation. Our new multicomponent structures may include e.g. Ru and Rh, and astonishingly, despite the overwhelming suitability of these metals for the nm spectral region, there is only limited experimental data available on interfacial interdiffusion and scattering at, for example, the Ru/Si boundary [1]. Indeed more data is required regarding the Ru/Mo and the Rh/Mo interface. We shall concentrate future work on experimentally realizing the multilayer structures numerically modeled in this work. 6. CONCLUSION We have shown that theoretical reflectivity enhancements for EUV reflectors tuned for the nm spectral region can be acquired by numerical global optimization techniques, in conunction with the incorporation of additional materials interleaved in the standard stack layers such that the quarter-wavelength character of the stack is maintained. 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