We have evaluated the prospects of phosphorus-based compounds in extreme ultraviolet multilayer optics. Boron phosphide (BP) is suggested to be used as a spacer material in reflective multilayer optics operating just above the L-photoabsorption edge of P (λ ≈9.2 nm). Mo, Ag, Ru, Rh, and Pd were considered for applications as reflector materials. Our calculations for multilayer structures with perfect interfaces show that the Pd/BP material combination suggests the highest reflectivity values, exceeding 70% within the 9.2 – 10.0 nm spectral range. We also discuss the potential of fabrication of BP-based multilayer structures for optical applications in the extreme ultraviolet range.
© 2015 Optical Society of America
Multilayer interference mirrors are the key optical elements enabling numerous research studies in the soft x-ray and extreme ultraviolet wavelength ranges. These are the basis for applications in optical imaging systems, e.g. for short wavelength microscopy, astronomy, optical beamline systems for synchrotron and free-electron laser radiation, high-harmonics generating sources [1–3], etc. Multilayer mirrors make use of the constructive interference of waves reflected from their multiple interfaces. In most cases, multilayers are composed of two alternating materials. Parameters of a multilayer structure can be optimized to achieve a required angular or spectral response of a designed mirror. Tuning geometrical parameters of the layered structures, like layer thicknesses, provides high flexibility for angular and spectral shaping . However, the most fundamental issue in designing multilayer mirrors is the proper choice of materials. As a general optical criterion for the material selection it is stated that the most favorable pair of materials should have maximum possible difference in refractive indices and minimum possible absorption . The material with the lower absorbance is usually referred to as spacer, and the other material is referred to as reflector or absorber. Besides the criteria dealing with optical properties of materials there are a few others which are of no less importance – proper materials are required to have (a) good layer growth properties, i.e. to form continuous and smooth layers when deposited, (b) low miscibility due to interdiffusion and compound formation at interfaces, (c) low chemical reactivity with standard ambient gas species, (d) minimal health hazard, and (e) low cost.
The choice of spacer and reflector materials is typically conducted by analyzing the absorption spectra of various materials. In this respect spectral features such as absorption edges of elements corresponding to ionization potentials from K, L, M, ... electron shells are of interest . Just above (wavelength-wise) an absorption edge of an element its extinction coefficient can be small enough and its refractive index can be close to unity, so this element can be used as a spacer. The important examples of such materials that have been applied as spacers to the moment are the elements of the 2nd period of the periodic table: beryllium (Be), boron (B) and carbon (C) that are used as spacers just above their K absorption edges; elements of the 3rd and 4th period: magnesium (Mg), aluminum (Al), silicon (Si), scandium (Sc) and titanium (Ti) that are used just above their L2,3 absorption edges; elements of the 5th period: strontium (Sr) and yttrium (Y) that are used just above their M4,5 absorption edges. When moving along each period (increasing atomic number) spectral position of the interesting absorption edge shifts towards the shorter wavelength. The application of different spacers allows to cover different parts of the shortwavelength spectrum.
In this paper we considered elements from the 3rd period of the periodic table that to the best of our knowledge have not been previously explored for EUV applications. We mainly focus on the properties of phosphorus-based multilayer mirrors operating at around the L2,3 absorption edge of phosphorus (P). Reflective optics operating at around the photo absorption edge of P is of interest for several applications, including extreme ultraviolet astronomy [4–7] and high-harmonic generation [8,9]. Here we theoretically examine reflective properties of planar multilayer structures with BP spacer and different reflector materials that suggest high reflectivity values. Our calculations show that Pd/BP material combination suggests the highest reflectivity values, exceeding 70% within 9.2 – 10.0 nm spectral range. We also show that BP-based multilayer structures suggest higher reflectivity values than Y-based and B-based multilayer structures suggesting maximal reflectivity below 70%. Finally, we discuss the possibility of fabrication of BP-based multilayer structures and stress that the recent progress in simple and cost-effective production of BP material  makes its applications in EUV optics feasible.
2. Material selection
In this section we considered elements from the 3rd period of the periodic table that have not been previously explored for EUV applications. These could be phosphorus (P) and sulfur (S) having L2,3 absorption edges situated in between the K absorption edge of B and M absorption edge of Sr (see Fig. 1). Below we focus only on P. As for S, our calculations revealed that stable compounds of S result in maximum predicted reflectivity similar to that of multilayers with B applied as spacer .
The direct application of the solid allotropes of P in multilayer structures is unlikely because of its high reactivity – phosphorus forms solid compounds (phosphides) with nearly all the elements in the Periodic Table . Also the deposition of pure P nanolayers with the conventional thin film deposition techniques like magnetron sputtering or electron beam evaporation might be challenging. At least this has not been tested so far to the best of our knowledge. For that reason instead of pure phosphorus some stable P-based compounds should be considered for applications in multilayer structures. This is in spite of the fact that in this situation the increased chemical stability is achieved at the expense of the optical performance. Compounds of P with any material have higher absorbance for EUV radiation than that of pure phosphorus in the wavelength range where the application of P is favorable. Hence the elements to form compounds with P should be chosen using the two following criteria: 1) high chemical stability of the resulting compound; 2) optical constants of the resulting compound close to those of pure P. The analysis of the CXRO database of the optical constants  indicates that the most promising candidates are boron (B), yttrium (Y) and strontium (Sr). Obviously phosphorus-reach compounds are still the most attractive – these are BP, YP and Sr3P2. However the two latter compounds are decomposed by water with the release of phosphine (PH3), which is a flammable and toxic gas. Hence they do not meet the criterion of stability. For that reason we exclude YP and Sr3P2 from the consideration and focus on BP. BP is a stable covalent compound with relatively low enthalpy of formation (ΔHform ≈– 100 kJ mol–1) . Low intrinsic absorption of boron in the wavelength range of interest and low density of BP (2.9 g·cm–3) results in optical properties suitable for the applications in reflective multilayer structures as discussed below.
3. Layer design
We used the transfer matrix formalism to calculate spectral properties of multilayer structures . All the calculations were performed with the assumptions of zero interface roughness and sharp interfaces between adjacent layers, i.e. the intermixing of materials is neglected. Optical constants, refractive index n and extinction coefficient k, for the considered materials were calculated using the tabulated atomic scattering factors from the CXRO database. Only periodic multilayer structures are considered here. All calculations were performed for normal incidence irradiation of the multilayer structures.
Since the applications of EUV optics requires high-reflective mirrors we characterize the considered here multilayer structures by the value of the maximal achievable reflectivity at a given wavelength. In order to calculate maximum achievable reflectivity for a periodic multilayer structure we applied local optimization technique based on the Powell's algorithm that is implemented in SciPy library for scientific calculations in Python language . For a periodic multilayer structure composed of selected materials and a fixed number of periods the optimization procedure is based on the variation of the thicknesses of elementary layers constituting the period. The value of maximal reflectivity increases with number of periods, but due to attenuation of electromagnetic wave inside the multilayer structure the number of periods, Neff, that effectively contribute to the constructive interference is limited. Figure 2 exemplifies the calculated dependence of the maximal reflectivity for Pd/BP multilayer structure at the wavelength of 9.5 nm versus the number of periods. The calculations show that for Pd/BP multilayer Neff ≈100 at 9.5 nm. But this value can be larger (depending on the target wavelength) for the other considered below material combinations. For that reason in the calculations of maximal reflectivity spectra we set the number of periods to 200 in order to ensure the reflectivity at a given wavelength reaches its saturation.
For a multilayer structure with parameters optimized for the maximal reflectance at a given wavelength an important characteristics is reflectivity spectrum and the bandwidth of the reflectivity peak. Figure 3 exemplifies the calculated EUV reflectivity spectrum for a Pd/BP multilayer structure with parameters optimized for maximal reflectance at the wavelength of 9.5 nm. We define here and discuss below the bandwidth of the reflectivity peak as its full width at the half of maximum (FWHM) as shown in Fig. 3.
4. Results of calculations
The application of BP as a spacer material in EUV reflective multilayer optics requires selection of proper reflector materials. The analysis of the database of the optical constants indicates that Tc, Ru, Rh, Pd and Ag provides high optical contrasts with respect to BP while their absorbance is relatively low. We exclude Tc from the consideration because of its radioactivity. But we also added Mo for the consideration since it is widely used as a reflector material in multilayer optics operating in the spectral range of our interest [5–7, 16]. For that reason in the calculations we considered Mo/BP, Ru/BP, Rh/BP, Ag/BP, and Pd/BP periodic multilayer structures. The number of periods was set to 200 for each structure. Figure 4(a) compares the calculated spectral dependence of maximum achievable reflectivity for these structures. The calculations show that Ru/BP, Rh/BP, Ag/BP, and Pd/BP structures provide reflectivity values exceeding 70% for the wavelengths just above the photoabsorption edge of P, unlike Mo/BP structures with maximum reflectivity just below 70%. The highest reflectivity values are predicted for Pd/BP multilayer structures up to around 9.9 nm. The reflectivity reaches 77.3% at the wavelength of 9.2 nm. For longer wavelengths Rh/BP structures suggest the highest reflectivity from around 10 nm up to around 11.3 nm where it becomes inferior to Ru/BP structures. Figure 4(b) compares spectral dependencies of the reflection peak bandwidths corresponding to the multilayers in Fig. 4(a). From Fig. 4(b) it is seen that Pd/BP multilayer structures suggest the highest reflection peak bandwidth values above the photoabsorption edge of P.
We compare BP with Y and B that can be alternatively considered for the application as spacer materials at the considered spectral range [5,16]. Figure 5(a) compares the calculated spectral dependencies of maximum achievable reflectivity for Pd/BP, Pd/Y and Pd/B periodic multilayer structures. The number of periods was set to 200 for each structure. It is seen that the calculations predict reflectivity of Pd/BP structures to be higher than that of Pd/Y in around 9.2-11.2 nm range, where Y-based multilayers are typically used [4, 5]. The same is valid for all other abovementioned reflector materials. Figure 5(b) shows that Pd/BP multilayer structures also provide higher reflection peak bandwidth values than Pd/Y and Pd/B structures. Thus BP can be considered as the most promising spacer material for the production of high-reflective multilayer optics operating at around the photoabsorption edge of P.
As shown by Larruquert  for the multilayer structures containing absorbing materials, the total reflection can be increased by introducing sub-quarter wavelength thick interlayers into the period structure. Our calculations showed that using three- or four-component multilayer structures could be beneficial for the BP-based systems. Extra materials can be introduced both at the reflector-on-spacer interfaces, e.g. Pd-on-BP, and at the spacer-on-reflector interfaces, e.g. BP-on-Pd.” Below we consider some examples of both cases for three-component structures. But in practice for the maximum gain one would need to combine and use extra materials at both interfaces. The material selection was performed by analyzing the CXRO database of the optical constants and using the empirical material selection rules derived by Larruquert . For the reflector-on-spacer interfaces we have found that the introduction of molybdenum nitride (MoN) provides up to 1% reflectivity gain for Mo/BP multilayers above the absorption edge of P. The other possible candidates as the third material, like e.g. RuN, PdN, RhN could be considered to work with Ru, Pd, Rh reflectors correspondingly. But because of a lack of published data about their properties we were not able to evaluate their potential. For the spacer-on-reflector interfaces we have found that the introduction of B, B4C, C and Y provides gains in reflectivity for all the considered spacers. Our calculations indicate that among the three materials the introduction of B layers provides the highest reflectivity gain for all multilayer structures considered; the introduction of C layers provides the lowest reflectivity gain. For the Pd/BP system, the introduction of the third material at the BP-on-Pd interface results in the smallest reflectivity gain as compared to the other systems considered, yet its total reflectivity value is the highest of all. Figure 6(a) compares the maximum achievable reflectivity for Pd/BP multilayer structures with and without B interlayers at the BP-on-Pd. It is seen that above 9.2 nm the introduction of B layers provides some reflectivity increase, ΔRmax = 0.8-2%, depending on the wavelength. Figure 6(b) shows the optimal layer thicknesses of multilayer structures corresponding to Fig. 6(a). From Fig. 6(b) it is seen that above 9.2 nm wavelength the optimal B thickness is within 0.7-1.2 nm range. Note that the state-of-art deposition technologies allow to use ≈0.3 nm thick interlayers [18,19], hence the calculated optimal B thickness values are feasible for real applications. In Fig. 6(b) it is also seen that below 9.2 nm B will better operate as the spacer material, with BP being efficient as a sub-quarter wavelength thick layer. Finally, only some examples of possible candidates for extra materials to be used as reflectivity enhancing interlayers have been considered here. More extensive research is needed to find the best candidates, which is out of scope of this work.
The presented above results of calculations indicate that BP can be considered as a competitive spacer material to Sr and Y that were previously considered as spacers for multilayer mirrors operating at around 9 nm wavelength [4–7]. However vast application of Sr-based mirrors is unlikely since they were demonstrated to deteriorate within a few hours when exposed to air due to interaction with the ambient gases , For Y-based mirrors interaction with ambient gases is less critical but it is still the case - oxidation of yttrium causes significant discrepancy between the measured reflectivity values for the manufactured structures and the theoretical predictions .
The presented above calculation results show that BP-based, e.g. Pd/BP, multilayer structures have a potential for applications in production of high-reflective EUV optics operating above the photoabsorption edge of P. Figure 7 shows maximum reflectivity spectrum for Pd/BP material combination together with other material combinations (La/B, Mo/Si and Mo/Be) suggesting high reflectivity values at different spectral ranges. It is seen that BP-based multilayer structures could partially bridge the spectral gap between B-based and Be-based high-reflectivity mirrors as presented in Fig. 6 that makes the former attractive for the further studies.
All the presented above results are based on the calculations where we assumed perfect interfaces in multilayer structures. However, when fabricating real structures interface imperfections limit optical performance of multilayer optics. To understand an impact of interface roughness on the mirror reflectivity it is required to study morphology of the experimentally grown multilayer structures as it was done for Mo/Si optics . Another issue is to study diffusion of multilayer components at interfaces and compound formation processes that are also crucial for the optical performance. Our preliminary analysis of thermochemical data indicates that BP is more stable (in terms of formation enthalpies) than the phosphides of the considered above reflector materials that may form at the interfaces (see Table 1).
Introducing B, C or B4C as sub-quarter wavelength thick interlayers at the spacer-on-reflector interfaces showed gains in reflectivity. We note here that these materials are also potentially able to add further benefits to the structures acting as diffusion barrier layers. This is connected to the fact that B and C are less reactive with the considered reflector materials than P (see Table 1). Therefore depositing interlayers of these materials is expected to both increase reflectance and result in thinner interfaces.
The potential of practical application of P-based multilayer mirrors is primarily determined by the possibilities of their fabrication, i.e. by the possibilities of the controlled deposition of nanometer-scale BP layers. Thin films of phosphide materials are usually fabricated using deposition techniques that implies heating of the substrate receiving material up to a few hundred degrees; these can be chemical vapor deposition or molecular beam epitaxy [21–24]. For instance, BP coatings are produced by chemical vapor deposition at substrate temperatures above 600°C . However, such deposition techniques are mostly not compatible with the growth conditions for multilayer structures with individual layer thicknesses in the nanometer scale, since heating of the deposited structures activates the processes of diffusion and compound formation at the interfaces and, consequently, damages the deposited structures. For that reason physical vapor deposition techniques, such as magnetron sputtering or electron beam evaporation, are required. A possible way is to use co-evaporation techniques, which was proven to work for BP deposition . Alternatively, the deposition of BP films by reactive magnetron sputtering using boron target in PH3/Ar sputtering medium can be applied . This can also be done using magnetron sputtering of B target in combination with ion treatment of the growing layers during its deposition using an ion gun. However these two deposition techniques imply utilization of the toxic and flammable gas PH3 that poses strong limitations on its applications. Alternatively, magnetron sputtering can be done using phosphide targets like it is done for gallium phosphide infrared antireflective coatings . For the latter approach the availability of BP sputtering targets is the most critical issue. Until very recent the lack of relatively simple and cost-effective methods of BP production was the main limitation for the use of BP while this is also of interest for many other applications including thermoelectricity, neutron detectors, light emitting diodes and laser diodes, and ultra-durable antireflection coatings [28–30]. The standardly used techniques [31–34] of BP production have several disadvantages: the use of toxic and aggressive reagents, rather complicated technical implementation, high labor intensity and time consumption. In 2013 Mukhanov et al. proposed a new simple and rapid technique for the production of BP submicron powders using readily available and cheap reagents according to the reaction of boron phosphate reduction with magnesium . We assume this technique of BP production should enable the availability of BP sputtering targets that are required for the fabrication of BP-based multilayer coatings.
We have evaluated the prospects of phosphorus compounds in extreme ultraviolet multilayer optics optimized for wavelengths above the absorption edge of P corresponding to photoionization from the L2,3 electron shell. By analyzing the optical constants of different compounds of P and their chemical stability we concluded that BP is the most promising for the application in multilayer optics as a spacer material. For the promising reflector materials Mo, Ag, Ru, Rh, and Pd were selected. Optical performance of BP-based multilayer mirrors was evaluated theoretically using the transfer matrix approach for the calculation of multilayer reflection. Our calculations show that Pd in combination with BP suggests the highest reflectivity values as compared to the other considered reflector materials. The predicted maximum reflectivity for Pd/BP multilayer mirrors reaches 77.3% at a wavelength of 9.2 nm. We have also considered three-component multilayer mirrors and found that introduction of B, B4C, C or Y thin interlayers at the spacer-on-reflector interface provides gains in reflectivity for all the considered reflectors. Finally the potential of fabrication of BP-based multilayer optics have been discussed.
This work is part of the research program “Controlling photon and plasma induced processes at EUV optical surfaces (CP3E)” of the “Stichting voor Fundamenteel Onderzoek der Materie (FOM)” which is financially supported by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO). The CP3E programme is cofinanced by Carl Zeiss SMT GmbH (Oberkochen), ASML (Veldhoven), and the Agentschap NL through the Catrene EXEPT program.
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