Increasing soft x-ray reflectance of short-period W/Si multilayers using B 4 C diffusion barriers

Short-period multilayer mirrors are used in wavelength-dispersive x-ray fluorescence to extend the wavelength range available with naturally occurring Bragg-crystals. W/Si multilayer mirrors with a period of 2.5 nm are used to reflect and disperse elements in the O-K α – Al-K α range. However, the reflectance is far from theoretical due to nanoscale W-Si intermixing and formation of WSi x . In this work, B 4 C diffusion barriers were applied in sputter deposited 2.5 nm W/Si multilayers to inhibit W – Si interaction. A peak reflectance of 45% at 9.7° grazing was measured at a wavelength of 0.834 nm — the highest reported in the literature so far. Diffuse scattering measurements revealed no change in interfacial roughness when applying B 4 C barriers compared to W/Si. A hybrid grazing incidence x-ray reflectivity and x-ray standing wave fluorescence analysis revealed an increase in W concentration of the absorber layer after the application of B 4 C barriers. Chemical analysis suggests a partial replacement of W silicide bonds with W carbide/boride bonds from the B 4 C barrier. The formed W x B y and W x C y instead of W x Si y is hypothesized to increase reflectance at 0.834 nm due to its higher W atomic density.


I. INTRODUCTION
Progress in fields of x-ray instrumentation in a variety of disciplines including space astronomy, 1 synchrotron-based optics, 2 x-ray microscopy, 3 and spectroscopy 4 increasingly depends on multilayer optics with length scales at or below several nm.In such x-ray optical schemes, a short-period multilayer is composed of two or more repeating sub-nm thin layers with alternating refractive indices to reflect photons in a Bragg mirror geometry.This is needed to efficiently reflect and disperse x rays with short wavelengths.One important application is in the field of wavelength-dispersive x-ray fluorescence (WD-XRF), where a multilayer is used as an analyzing crystal to resolve emission lines of light elements.6][7][8] In this use case, multilayer optics are favored over natural crystals because the period and bandwidth can be controlled, whereas crystals have too low d-spacing and too narrow bandwidth for light element analysis in x-ray fluorescence (XRF).
In this work, multilayers designed to cover the O-Kα-Al-Kα (2.36-0.834nm) emission lines are investigated.The key requirements are that the multilayer should be highly reflective in the entire emission range, while also providing sufficient angular dispersion to resolve specific XRF lines.Angular dispersion increases by reducing the multilayer period, but in practice, this compromises reflectance because of increasing reflectance losses from interfacial imperfections.A period of 2.5 nm was chosen as a bestcompromise between angular dispersion and reflectance for the chosen wavelength range of 2.36-0.834nm.
Multiple absorption edges of typical multilayer materials are present in this range, which limits the options for such materials.W-based multilayers in combination with Si, B, or B 4 C spacer materials are good candidates as they provide a high theoretical reflectance of 60%-62% at 0.834 nm-with reflectance saturation occurring around 200 bi-layers using an ideal, thickness optimized bi-layer structure defined in the IMD program. 9An ideal ML structure is defined as a 2-layer model with bulk material densities and steplike interfaces.][12][13] However, at higher periods (>2 nm), W/B 4 C is a less attractive material combination due to an increase in interface width. 14,15W/ B multilayers with a period of 2.5 nm have been synthesized recently using DC magnetron sputtering, 16 where the authors found strong intermixing between W and B-limiting reflectance to only 34.6% at 0.84 nm.W/C multilayers are not considered in this work due to their lower theoretical reflectance (57% @0.834 nm) in the specific working range, as well as their higher interface width relative to W/B 4 C. 17 W/Si multilayers are currently used as analyzers in WD-XRF 5,6 as the layers can be grown with relatively low interface width at 2.5 nm with 200 periods. 18owever, the same study 18 also shows that the thin W layer is completely consumed by Si to form a silicide-thereby lowering the optical contrast with Si and limiting reflectance to 40%.Mitigating the reaction between W and Si is, therefore, a key for improving the reflectance of W/Si.
A variety of techniques have been developed in order to promote smooth growth and/or reduced intermixing in bi-layer systems with short periods.For example, research on WSi 2 /Si 19 and WC/SiC 20 multilayers has shown that depositing layers directly as a compound enables a very sharp and stable interface.A similar trend is observed by using partial nitridation, where the formation of nitrides in W/B 4 C 21 and W/Si 22 multilayers creates a sharper interface.The issue for some compound materials is that they reduce the optical contrast too much in this specific wavelength range.
An alternative method used to reduce interdiffusion is to introduce an additional thin layer in between the spacer and absorber that acts as a barrier against diffusion.This so-called "diffusion barrier" usually contains B 4 C and was first applied in multilayers with a larger period like Mo/Si. 23,24Using B 4 C reduced the formation of optically unfavorable molybdenum silicide, resulting in an increased reflectance at 13.5 nm.Later, B 4 C barriers were also implemented in short-period Cr/Sc multilayers with a demonstrated increase in reflectance in the water window region. 25,26The efficacy of B 4 C barriers in a variety of material combinations has proven beneficial to reduce interdiffusion but is as of yet unexplored in short-period W/Si.
The goal of this paper is to characterize the structural changes and soft x-ray optical performance of 2.5 nm W/Si with B 4 C diffusion barriers deposited by DC magnetron sputtering.B 4 C is deposited on both the W-on-Si and Si-on-W interfaces, as well as on the W-on-Si and Si-on-W interfaces separately-with the idea to prevent the formation of optically unfavorable WSi 2 .Alongside W/ Si with B 4 C barriers, W/Si and W/B 4 C reference multilayers are deposited for comparison.The reflectance, roughness, chemical environment and W atomic distribution is characterized in each of the systems to elucidate on the physical-chemical mechanism of B 4 C barriers in W/Si.

A. Deposition
The multilayers were deposited on 25 × 25 mm 2 single side polished Si(100) wafers with ∼1 nm native oxide and a roughness of 0.13 ± 0.05 nm rms measured with AFM.For the deposition, a DC magnetron sputtering system (MS1600 designed by Roth & Rau) was used with a base pressure <1.0 × 10 −8 mbar.During deposition, Kr gas was used at a working pressure of 1.5 × 10 −3 mbar.Kr was chosen over Ar as the sputter gas to reduce the number of high-energy reflected neutrals during the deposition of W. 27 The magnetrons with targets of size 381 × 89 mm are situated in front of a passing substrate holder at a distance of 8 cm (illustrated in Ref. 18).The Si substrates are mounted on a 35 cm diameter circular substrate holder at a radius of 7.5 cm.During deposition, the substrate holder is rotated at 1.5 revolutions per second while moving over each target by a substrate arm.The deposited film thickness scales with the inverse of the substrate arm velocity.In order to achieve a stable deposition flux, the magnetrons are power regulated.The sputter powers used for W, Si, and B 4 C are 30, 260, and 260 W, respectively, with corresponding voltages of 328, 640, and 560 V.The powers are chosen such that the smallest required thickness can still be deposited without exceeding the maximum speed of the substrate arm, while also keeping the power high enough to minimize deposition time.
Full stack multilayers with 200 periods and model structures of 20 periods were deposited with a period of 2.5 nm.The diffusion barrier structures, illustrated in Fig. 1

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and W/B 4 C stacks containing three different thicknesses of the to-be-calibrated material.To prevent oxidation, all multilayers except W/B 4 C are capped with ∼2 nm Si.W/B 4 C was capped with ∼2 nm B 4 C.

B. Characterization
The soft x-ray reflectance of full stack multilayers was measured at 0.834 nm around the first Bragg maximum-corresponding to a ∼9.7°grazing angle-using the storage ring BESSY II at Physikalisch-Technische Bundesanstalt (PTB) in Berlin.To reduce the beam footprint on the sample, a 0.5 mm exit slit at the source side was used.The footprint is kept as small as possible to avoid any broadening of the reflectance peak as a result of small, picometer sized lateral gradients on the sample.A detailed description of the soft x-ray beamline can be found in Ref. 28.
For in-lab x-ray diffuse scattering and x-ray reflectivity measurements a Malvern Panalytical Empyrean diffractometer is used at Cu-Kα radiation (λ ¼ 0:154 nm).A hybrid monochromator consisting of a parallel beam x-ray mirror and a 2-bounce Ge(220) monochromator was used at the source side.To qualitatively assess the interfacial roughness, x-ray diffuse scattering rocking curves were measured around the 2nd Bragg peak.An in-depth explanation of multilayer rocking curves is presented in Ref. 29.GI-XRR was measured in the θ À 2θ geometry from 0°to 10°grazing.
To analyze the chemical bonding of elements, non-destructive x-ray photoelectron spectroscopy (XPS) was used.A Thermo Scientific Theta Probe instrument with monochromatic Al-Kα radiation (1486.7 eV) was used with a base pressure of 5 × 10 −10 mbar.The energy resolution was better than 0.8 eV, with an average probing depth of 6 nm.All multilayer samples were measured after exposure to air, without surface treatment.A thick W metal film was cleaned by 1 keV Ar ion bombardment until the oxygen content dropped below 1 at.%, to serve as reference sample for the binding energy (BE) of clean W. The photoelectron signal was evaluated at a takeoff angle of 34.25°with respect to the surface normal.Peak fitting of the measured W4f spectra was performed using Thermo Avantage software by fitting Gaussian-Lorentzian peaks, with asymmetry parameters based on a fit of a sputter cleaned W reference sample.
To find the atomic distribution of W in the multilayer, a hybrid GI-XRR and x-ray standing wave fluorescence (F-XSW) approach was used. 30Simultaneous GI-XRR and F-XSW of the W-M emission line was measured using the Empyrean diffractometer mentioned earlier (λ ¼ 0:154 nm).The angular-dependent W-M fluorescence was measured with an Amptek energy dispersive XR-100SDD silicon drift detector by scanning the 1st Bragg peak in the θ À 2θ geometry.An angular step of 0:004 around the Bragg peak and 0:01 outside of the Bragg peak was used, with an accumulation time of 5 min per angular step.The measurements were performed on model structures with 0.5 nm W and 20 periods.The number of periods is deliberately kept low to decrease sensitivity to Bragg broadening-induced by random layer thickness errors-which allows for more reliable reflectance and fluorescence fitting in comparison to structures with 200 periods.The obtained W-M spectrum for each angle was analyzed and fitted using the PyMCA software 31 to get the angular-dependent fluorescence yield.
The simultaneous fitting of GI-XRR and W fluorescence yield was performed using a free-form approach, described in more detail in Ref. 32.A free-form approach allows for more freedom in modeling of the interface profile, whereas classical modeldependent approaches model the interface using a limited error function interface profile.The free-form approach is especially beneficial in modeling short-period multilayers, where the interface profile extends into the full thin film layer thickness.The reconstruction was done by dividing the periodic part of the multilayer into 15 sublayers, each with a given chemical composition and density.Each sublayer is used as a fitting parameter and varied to get an elemental concentration profile.To reduce the cumulative mismatch between measured and simulated data of GI-XRR and F-XSW, a minimizing procedure was applied as described in Ref. 32.

A. Soft x-ray reflectance
The reflectance at 0.834 nm measured at the 1st Bragg peak (∼9.7°grazing) is shown in Fig. 2(a).For each multilayer design, four samples were produced at different gammas and measured to find the maximum reflectance.The results show an optimal gamma value of 0.20 for W/B 4 C, while the optimum for the other multilayers is 0.15.In all cases, the optimal gamma is lower than predicted for an ideal W/Si and W/B 4 C multilayer (Γ ¼ 0:25), shown in Fig. 2(b).This effect has been reported before in Ref. 18  and we hypothesize that this is related to expansion of the W layer from interaction with Si and/or B 4 C.
Table I shows the peak reflectance and bandwidth for each structure at the gamma optimum.At the gamma optimum, a 3% increase in peak reflectance is observed for Si/B 4 C/W and Si/B 4 C/ W/B 4 C relative to W/Si.This corresponds to an increase in integrated reflectance of around 10%.For Si/W/B 4 C, the increase in peak reflectance is slightly lower at 2%.Interestingly, the maximum reflectance of W/B 4 C is only 39%.Although applying a diffusion barrier has resulted in a reflectance of 45%, it is still substantially lower than the reflectance of an ideal W/Si multilayer (61%) or an ideal W/B 4 C multilayer (60%). 9This can be due to two mechanisms: interfacial roughness (Sec.III B) or intermixing of W with Si and/or B 4 C (Secs.III C and III D).W/Si with B 4 C barrier layers, W/Si and W/B 4 C are analyzed further and compared to each other in order to understand the differences in reflectance.

B. X-ray diffuse scattering
To find the impact of B 4 C diffusion barriers on the interfacial roughness of the multilayer, x-ray diffuse scattering was measured by performing rocking scans at λ ¼ 0:154 nm.The rocking scan was measured by fixing the detector at the 2nd Bragg peak (∼3.5°g razing) and rocking the sample around ω from 0°to 7°grazing.The rocking curves were measured for multilayers with maximum reflectance/optimal gamma, corresponding to Γ ¼ 0:20 for W/B  29 An attempt was made to correlate x-ray diffuse scattering results with atomic force microscopy (AFM) by measuring the surface roughness of the deposited multilayers.Measurements revealed that the different multilayer structures did not show any significant difference in surface roughness; all exhibiting an RMS roughness of 0:21 + 0:05 nm.Assuming that the surface roughness is an accurate representation of the interfacial roughness, the change in reflectance at 0.834 nm for σ ¼ 0:205 nm and σ ¼ 0:215 nm nm is calculated at ∼11% absolute (using a 2-layer W/Si IMD model 9 and inserting the AFM roughness 0:21 + 0:05 nm as the interface width σ).This means that the reflectance in these structures is extremely sensitive to sub-angstrom changes in the interface width -which is typically below the detection limit of the AFM instrument.Additionally, the presence of surface oxidation from the ambient air can potentially modify th e roughness of the cap layer, which is the only thing that is observed with AFM.Based on these considerations, we conclude that AFM is not reliable in this case.To reliably extract quantitative interfacial roughness values, other x-ray techniques next to diffuse scattering would be needed such as GISAXS, 33 but this is outside the scope of the work presented here.

C. GI-XRR and F-XSW free-form analysis
To reveal if the application of B 4 C barriers modified the atomic distribution of W in the multilayer, i.e., by reducing

Journal of Applied Physics
interdiffusion, a hybrid GI-XRR and F-XSW free-form analysis was performed on 2.5 nm model multilayers with 20 periods.The model multilayers were deposited at Γ ¼ 0:2.A free-form fit of the GI-XRR and F-XSW data allows us to reconstruct the interface profile freely, without a priori knowledge of the sample structure. 34his has advantages over the classical model-dependent approach, 9 where the interface profile is modeled by a Debye-Waller or Nevot-Croce attenuation factor.The interface profile of real structures can be more complex, which requires a more flexible model-independent approach to fit experimental data.
The combined GI-XRR and F-XSW free-form approach allows for both sensitivity to changes in electron density and elemental concentration in-depth, 32 causing a reduction in the number of cross correlations between the model parameters and increasing the uniqueness of the reconstructed W profile. Simultaneous measurements of the reflectance and fluorescence spectra were taken using Cu-Kα radiation (λ ¼ 0:154 nm) around the 1st Bragg peak, corresponding to an angular range of 1.5°-2.1°g razing.
An example of a measured fluorescence spectrum at a grazing angle of 1.8°is shown in Fig. 4. To fit the spectra, a model is used in PyMCA; taking into account emission energies of elements, escape peaks and background (SNIP) in the 0-3 keV range.The simulated W-M lines are then fitted to the measured data.The integrated intensity of the fitted W-M lines in the 1.9-2.5 keV range is used as a data point for the angular-dependent fluorescence yield.This is done for each angle to obtain the fluorescence yield of W. The Si fluorescence yield is not obtained due to a strong contribution of the Si substrate to the Si-K intensity.
The obtained fits for the W fluorescence yield and GI-XRR for W/Si, Si/W/B 4 C, Si/B 4 C/W, and Si/ B 4 C/W/B 4 C model structures are shown in Figs. 5 and 6, respectively.For the GI-XRR curves, the fit right before the critical angle region (θ ¼ 0 À0:3 ) was omitted due to inadequate modeling of geometric effects (e.g., sample curvature, beam footprint, etc.) in the software.For both GI-XRR and W fluorescence, a good fit to the measured data is obtained.
The combined analysis of GI-XRR and F-XSW results in a set of W concentrations per sub-layer.The concentration of each sublayer is fitted with a line to give the final reconstructed W concentration profile.In order to validate the final profile, several reconstructions were performed using different W starting profiles such as a steplike profile and a linear profile.The addition of F-XSW data allows retrieval of phase-sensitive information of the reflected waves, thereby reducing the number of profiles that fit both F-XSW and GI-XRR data sets.The reconstructed concentration profiles of W/Si, Si/W/B 4 C, Si/B 4 C/W, and Si/B 4 C/W/B 4 C are shown in Fig. 7.
As can be seen from the figure, the W concentration does not reach 1-even in the center of W layers.The profiles show a W concentration of around 60%-65%, depending on the structure, meaning that the remaining 35%-40% is Si and/or B and C. Another observation is that the W concentration profiles are smooth and continuous, which means that there is no sharp interface present between the W and the spacer.The W profiles show symmetric interfaces, which means that either no interface asymmetry is present or the asymmetry is too small to be resolved using this analysis.There are also areas in the profile where there is almost no tungsten.From this we infer that-contrary to W-there is pure Si and/or B 4 C present in the multilayer.

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The profiles show that the application of B 4 C diffusion barriers results in an increased W concentration in the center, which is most evident for the two-barrier system Si/B 4 C/W/B 4 C.This means that there a reduction in W intermixing with the spacer, relative to W/Si.For the one-barrier structures Si/B 4 C/W and Si/W/B 4 C, the W concentration is slightly lower.Interestingly, the interfaces (from the center of the W layer to zero W) seem relatively unaffected for structures with B 4 C barriers, compared to W/Si.This result suggests that the higher reflectance at 0.834 nm is not from a reduction of the interface width between W and Si, but rather from an increased optical contrast from the increase in W concentration at the center.
It should be noted that the model structures used to obtain the W profiles have a slightly different W thickness and a different number of periods (20 bi-layers) compared to the full stack multilayers used for the analyses provided in Secs.III A and III B. This could clarify why, for example, Si/B 4 C/W/B 4 C and Si/B 4 C/W have the same reflectance at 0.834 nm but Si/B 4 C/W/B 4 C has a higher W concentration.In any case, the differences between Si/B 4 C/W, Si/W/B 4 C, and Si/B 4 C/W/B 4 C structures are rather small in both the N = 200 and N = 20 multilayers.Mechanisms responsible for their similarities are discussed later.

D. X-ray photoelectron spectroscopy (XPS)
The reconstructed W concentration profiles in Fig. 7 have shown that W is intermixed in all structures, with a slight decrease in W intermixing for structures containing B 4 C diffusion barriers with respect to W/Si.To investigate if the application of B 4 C diffusion barriers modified the chemical environment of W, XPS was used on the same N = 20 model structures as in Sec.III C. The signal was collected from two top periods and the intensity normalized to the W4f 7/2 peak.Samples were measured within the same measurement run to ensure shifts in binding energy between samples could not be attributed to a temporal drift in the binding energy scale of the instrument.Figure 8 shows the W4f 7/2 peaks for W/Si, Si/W/B 4 C, Si/B 4 C/W, and Si/B 4 C/W/B 4 C multilayers.Additionally, W4f was measured for a sputter cleaned pure W film.The figure is zoomed in on the W4f 7/2 peak from the W4f doublet to better illustrate the shift of the peaks.
The XPS spectra in Fig. 8 show shifts in the binding energy for the W in the multilayers with respect to a pure W film, as well as broadening of the peak.The peak broadening in the multilayers is caused by the presence of many different W-Si and/or W-C/W-B chemical bonds, whereas in a pure W metal reference only W-W bonds are present.Comparing the chemical shifts, the largest shift is found for W/Si (31.2 eV) and W/B 4 C (31.7 eV); which is 0.5 eV.Previous work from our group 16 has compared W4f binding energies in 2.5 nm W/B and W/Si multilayers and observed a shift of 0.6 eV.They found a negative shift of 0.2 eV in W/Si relative to the pure W layer reference, which was associated with formation of W silicide.Additionally, for W/B, a positive shift of 0.2 eV was found relative to the pure W layer reference, which was associated with W boride formation.In this work, a slightly larger positive shift of 0.3 eV was found for W/B 4 C.The fact that the shift in W/B 4 C is similar to that of W/B 16 shows that part of the B 4 C from the multilayer must have formed a bond with W to form carbides and/or borides.The preferential binding of B 4 C to metals rather than itself has also been demonstrated in Mo/Be, where insertion of a B 4 C barrier resulted in the formation of MoB and Mo 2 C. 35 When analyzing the W/Si structures with B 4 C barriers [

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assume that almost all W silicide bonds are replaced by W carbide/ boride bonds in this structure.For both Si/B 4 C/W (31.5 eV) and Si/W/B 4 C (31.4 eV), the binding energy is in the middle of W/Si and W/B 4 C, as well as almost overlapping with the peak of the pure W layer reference.In these structures, at least part of the W silicide bonds seem to be replaced by W boride/carbide bonds.
To find out whether the XPS peak of Si/B 4 C/W and Si/W/B 4 C could be explained by a combination of bonds from W/Si and W/ B 4 C reference multilayers, peak fitting was applied.This was done by adding two peaks; one with a fixed binding energy and full width half maximum (FWHM) obtained from W/Si (BE: 31.2 eV; FWHM: 0.69 eV) and one with a fixed binding energy and FWHM obtained from W/B 4 C (BE: 31.7 eV; FWHM: 0.79 eV).These two peaks could then be varied in intensity such that the area under the measured curves is fitted.The result of these fits is shown in Fig. 9.In both cases, the peaks could not properly fit the measured data.We conclude from this that the structure we formed is not simply a mixture of W-Si bonds from W/Si and W-B/W-C bonds from W/ B 4 C. Three scenarios are proposed to explain the residual area.
(1) There is pure W present in the multilayer (2) Formation WSi x with lower x relative to the WSi x from the W/Si multilayer (3) Formation of WB x /WC x with lower x relative to the WB x /WC x from the W/B 4 C multilayer It is reasonable to expect that the position of the W metal peak will depend on the x in WSi x (scenario 2), since this was previously demonstrated for MoSi x . 36A similar dependence of the position of the W peak on the x in WB x /WC x (scenario 3) is assumed.
If pure W is to be expected from these structures (scenario 1), then Si/B 4 C/W/B 4 C should contain at least the same amount of pure W as the one-barrier systems Si/B 4 C/W and Si/W/ B 4 C.However, from Fig. 8(c), we see that the W4f 7/2 peak is very close to W4f 7/2 of W/B 4 C; meaning Si/B 4 C/W/B 4 C can only contain a very small amount of pure W. Therefore, scenario 2, 3, or a combination of both seem most likely to explain these results.
An attempt was made to analyze the Si2p, C1s, and B1s peaks in the model structures.However, in all cases no significant shift of the binding energies could be identified between W/Si, W/B 4 C and W/Si with B 4 C-meaning the peaks were either too broad, the shifts too weak, or the elements had similar bonding states.This work has therefore been limited to analysis of the W4f peak.

IV. DISCUSSION
The application of 0.3 nm B 4 C in 2.5 nm W/Si multilayers systemically increases reflectance at 0.834 nm.However, the reconstructed W profiles in Fig. 7 show only a small increase in W concentration. Therefore, the W atomic density is only marginally

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increased.This means B 4 C does indeed function as a barrier against W-Si interaction, but is far from ideal.We propose that the B 4 C works via partial substitution of W-Si bonds with W-B and W-C bonds-as evidenced by XPS.The W atomic density of the formed structure increases because of two possible scenarios.
(1) The formed W x B y /W x C y has a more W-rich stoichiometry compared to the W x Si y in W/Si.(2) W x B y and W x C y tend to form higher density structures compared to W x Si y , even at equal W concentration.For example, WB (ρ ¼ 15:3 g cm 3 ) and WC (ρ ¼ 15:6 g cm 3 ) both have a higher atomic density than W 5 Si 3 (ρ ¼ 14:6 g cm 3 ), even though W 5 Si 3 contains more parts of W.
It should be noted that the sub-nm thickness of the materials and the deposition at room temperature do not allow the formation of ordered compound (bulk) structures.We can only talk about disordered or amorphous sub-stoichiometric structures.
The increase in W concentration of the W profile in Fig. 7 would support scenario 1, although a contribution from scenario 2 cannot be excluded based on the presented data.However, in both scenarios the result is an increase in W atomic density-leading to an increase in reflectance.Conclusively, the formation of higher density and/or stoichiometry W x B y and W x C y instead of W x Si y by applying sub-nm B 4 C barriers plays a key role in the increased reflectance at 0.834 nm.
It is also necessary Reflectance is expected to be higher for Si/B 4 C/W/B 4 C due to the presence of more (presumably higher density or higher stoichiometry) W x B y and W x C y .Instead, the reflectance saturates when the remaining W-Si bonds are replaced by W-C and W-B bonds.An explanation for this apparent saturation could be that the remaining W x Si y present in Si/B 4 C/W has a higher density compared to the W x Si y formed in W/Si.The Si in Si/B 4 C/W can only form limited bonds with W because they have to be shared with C and B. In this scenario further addition of B 4 C replaces the higher density W x Si y with W x B y and W x C y , but the reflectance of the structure is not significantly affected.
Finally, we note that the obtained peak reflectance of 45% is still far from an ideal multilayer (61%).Although applying a thin B 4 C layer has improved reflectance by 3%, the W concentration profile in Fig. 7 shows that the absorber density is not close to bulk.Furthermore, the W concentration profile shows a large transition region, instead of a sharp step, which affects the reflectance of the multilayer.The effect of such a transition region on the peak reflectance of 2.5 nm multilayers can be estimated using a basic 2-layer W/Si IMD model with error function interfaces-defined by a roughness/interdiffusion parameter σ. 9 First, the Al-Kα reflectance of the full stack Si/B 4 C/W multilayer from Fig. 2(b) is fitted with this model (obtained fit parameters: ρ w ¼ 15:3 g cm 3 ; σ w ¼ 0:25 nm; d w ¼ 0:70 nm; ρ Si ¼ 2:33 g cm 3 ; σ si ¼ 0:23 nm; d Si ¼ 1:8 nm).Then the roughness/interdiffusion parameter σ of W and Si is set to 0 to estimate the reflectance gain of a sharp interface transition.When this is done, a peak reflectance of 55% is obtained-10% higher than currently achieved, and 6% below an ideal W/Si multilayer.The remaining 6% is explained by the lower refractive index of the W absorber.The focus of future research should therefore be on finding optically favorable materials that have a lower chemical affinity, resulting in a reduction of optically unfavorable compounds and intermixing.

V. CONCLUSIONS
We have demonstrated an increase in soft x-ray reflectance of 2.5 nm W/Si multilayers deposited by DC magnetron sputtering by the addition of 0.3 nm B 4 C diffusion barriers.Si/B 4 C/W, Si/W/B 4 C, and Si/B 4 C/W/B 4 C multilayers were deposited and analyzed alongside W/Si and W/B 4 C reference multilayers.A peak reflectance of 45% (at 9:7 grazing) for both Si/B 4 C/W and Si/B 4 C/W/B 4 C was measured at λ = 0.834 nm.This represents a 3% increase relative to W/Si and a 6% increase relative to W/B 4 C. Diffuse scattering measurements revealed that the interfacial roughness in W/Si did not change significantly by applying B 4 C barriers, while interfacial roughness in W/B 4 C was substantially higher compared to the other structures.A GI-XRR and F-XSW hybrid analysis revealed that the W concentration increased by the introduction of B 4 C barriers, while the smooth varying transition from W to the spacer was not significantly affected.XPS analysis revealed a shift of the W4f binding energy in structures with B 4 C barriers relative to W/ Si, suggesting that the W silicide bonds present in W/Si are partially replaced by W carbide/boride bonds from the B 4 C barrier.The formed W x B y and W x C y instead of W x Si y is hypothesized to increase the W atomic density, and hence reflectance.The 3% increase in peak reflectance corresponds to a 10% increase in integrated reflectance, meaning a 10% increase in the detection of the Al-Kα line in WD-XRF.

FIG. 1 .
FIG. 1. Schematic representation of deposited full stack multilayers.Top: Si/W/ B 4 C, Si/B 4 C/W, and Si/B 4 C/W/B 4 C. Bottom: reference W/Si and W/B 4 C multilayers.The notation represents the sequence of layers from bottom to top of the periodic part of the multilayer.
4 C and Γ ¼ 0:15 for W/Si and W/Si with B 4 C barriers.The resulting rocking curves are shown in Fig. 3.The broad wings around the Bragg peak in diffuse scattering scans are indicative of interface roughness.Comparing the diffuse scattering intensity provides a qualitative comparison of the interfacial roughness within each structure.The rocking curves reveal similar diffuse scattering of W/Si with and without B 4 C barriers.Since only interfacial roughness contributes to diffuse scatter and not interfacial interdiffusion, we can conclude that the interfacial roughness in W/Si did not change substantially by the application of 0.3 nm B 4 C barrier layers.The diffuse scattering of W/B 4 C is substantially higher compared to the other samples, which indicates that W/B 4 C has rougher interfaces.The low reflectance of W/B 4 C at 0.834 nm could, therefore, be correlated to rougher growth of the W/B 4 C multilayer system.The features seen around ∼1.75°and ∼5.25°are from resonant diffuse scattering sheets caused by correlated interface roughness.

FIG. 2 .
FIG. 2. (a) Peak reflectance at 0.834 nm ( 9:7 grazing) as a function of gamma for different multilayers.(b) Reflectance as a function of wavelength at 9:7 grazing for W/Si and Si/B 4 C/W at Γ = 0.15, compared to an ideal W/Si multilayer in IMD.

FIG. 3 .
FIG. 3. Rocking curve of full stack multilayers measured at their gamma optimum.Scan taken around the second Bragg peak ( 3:5 grazing).All curves were normalized to the maximum Bragg peak for comparison.

FIG. 4 .
FIG. 4. Example of an experimental and fitted spectrum of fluorescence emitted from a W/Si sample at a grazing angle of 1.8°using a Cu-Kα (λ ¼ 0:154 nm) source.The W-M lines from 1.9 to 2.5 keV (inset, top right) are fitted to obtain the W fluorescence yield.

FIG. 5 .
FIG. 5. Experimental (points) and fitted curves (solid lines) of the angulardependent W fluorescence yield for W/Si, Si/W/B 4 C, Si/B 4 C/W, and Si/B 4 C/W/ B 4 C N = 20 model structures.

FIG. 7 .
FIG. 7. W profile as a function of the multilayer depth for W/Si, Si/W/B 4 C, Si/ B 4 C/W, and Si/B 4 C/W/B 4 C N = 20 model structures.The dashed line shows the W concentration for an ideal W/Si multilayer with 0.5 nm W and 2 nm Si.
to discuss the individual structures Si/W/ B 4 C, Si/B 4 C/W and Si/B 4 C/W/B 4 C in more detail.The reflectance at 0.834 nm of Si/W/B 4 C is 1% lower, which could be explained by the higher amount of optically unfavorable W-silicide compared to Si/B 4 C/W [Fig.9]-although a firm conclusion cannot be made due to the small difference in W4f binding energy between Si/W/B 4 C and Si/B 4 C/W.For both Si/B 4 C/W/B 4 C and Si/B 4 C/W the reflectance is 45%, even though Si/B 4 C/W/B 4 C clearly contains more W-C and W-B bonds compared to Si/B 4 C/W [Fig.8].

TABLE I .
Peak reflectance at 0.834 nm ( 9:7 grazing) and bandwidth of each structure at the gamma optimum.