Corrigendum: Determining Chemically and Spatially Resolved Atomic Profile of Low Contrast Interface Structure with High Resolution

It was brought to the authors’ attention that the original paper contains the following errors. (i) We reported a 0.05% electron density contrast between silicon and boron carbide. There was a calculation error in computing this number and the correct contrast is 0.5%. This is one order of magnitude lower than what can be studied using hard x-ray reflectivity. Therefore, with this revised electron density contrast value, the proposed methodology is still valid. (ii) Numerical errors were made during the conversion of the measured angular reflectivity to q z (4 π sin θ / λ ). To revalidate the proposed methodology, we have performed fresh measurements on similar new samples. The fresh soft x-ray resonant reflectivity measurements were done using the Optics Beamline at the BESSY storage ring which has a better energy resolution (E/ Δ E ≅ 670), smaller vertical angular divergence (0.5 mrad), larger photon flux (~1.4 × 10 10 ) and accessible q-space compared to the measurements reported in the original paper using the Indus -1 reflectivity beamline. The results are presented below and the methodology and the conclusion reported in the original paper still stand. Hard x-ray reflectivity . Thin film samples are fabricated with varying position of B 4 C layer (40 Å) in Si thin film of thickness 300 Å. The samples are fabricated using electron beam evaporation. Elementary boron is incorporated into B 4 C layer by co-deposition. B 4 C is at top, middle and bottom of Si layer for sample 1 (S1), sample 2 (S2) and sample 3 (S3), respectively. In all samples, a W layer of thickness 10 Å is deposited just above the Si substrate to provide an optical contrast between substrate and the film

Scientific RepoRts | 6:27322 | DOI: 10.1038/srep27322 of 4 × 4 mm2 acceptance area, surrounded by a support of 2 mm diameter at a distance of 310 mm from the sample was used. The minimum angle to normal is thus atan(4/310) = 0.74°, corresponding to 89.26° grazing angle. Figure 2(a) illustrates schematic of three deposited samples S1, S2 and S3 with different spatial positions of B 4 C layer. To understand the observed scattered profiles for chemically selective atomic distribution analysis, the measured atomic scattering factor (ASF) of B, B 4 C and B 2 O 3 near boron K-edge are shown in Figure 3. At this specified energy of 191.4 eV, ASF of B 4 C has a strong variation [ Figure 3]. The strong modulations in reflected spectra [ Figure 2(b)] is due to major reflection contribution from Si/B 4 C interface apart from contributions from  other interfaces. Due to the contribution of the reflection from the Si/B 4 C interface, the three different layer structures of three samples (S1, S2 and S3) exhibit significantly different measured profiles with a strong modulation, as the spatial position of B 4 C layer changes in Si film. Two vertical dotted lines mark how the period of oscillations gets modulated as position of the B 4 C layer varies in Si film. This provides an experimental evidence for sensitivity of resonant soft x-ray reflectivity (R-SoXR) to the spatial variation of a low contrast interface. The results demonstrated here with ∆ρ/ρ = 0.5% as an example, has one order of magnitude better EDC sensitivity compared to conventional hard XRR 3 .

Spectroscopic information using resonant reflectivity.
To determine the spectroscopic information using R-SoXR, elementary boron is introduced in B 4 C layer by co-deposition using electron beam evaporation method. R-SoXR measurements are performed at selected energies near the respective absorption edges of boron and the compounds of boron. Figure 4 At these energies the ASF undergoes strong variation for B 2 O 3 but elementary boron exhibits nearly a flat optical response [ Figure 3]. If the film contains B 2 O 3 within penetration depth of x-ray, it will produce a strong modulation in reflected spectra as incident energy is varied in these ranges. The measured reflection spectra clearly appear very similar near B K-edge of B 2 O 3 [ Figure 4 Figure 3]. Near the edge, B provides enhanced and tunable scattering. B 4 C also exhibits variation of ASF with energy towards higher side with respect to elementary B. However, the magnitude of variation of ASF is more in B than B 4 C due to stronger resonance enhancement of elementary B than B in B 4 C. The observed changes in the reflected profile at the selected energies across the B K-edge of elementary boron can be due to contribution of both kinds of atoms. At the lower energy side, the variation in the measured profiles is dominated by the contribution of elementary boron. The contribution of B 4 C starts at higher energy along with elementary boron. This corroborates the presence of B in sample S1. In the original paper, the elementary boron was not detected in S1, as elementary boron is fully oxidized when exposed to ambient condition. Whereas in the fresh sample S1 (in corrigendum), the elementary boron in the top B 4 C layer is not oxidized because of a contaminated carbon layer at the top. This contaminated carbon layer most likely prevents elementary boron in the top B 4 C layer to be oxidized in fresh sample S1.
Chemically selective quantitative atomic profile. To quantify the atomic percentage of B and the spatial distribution in B 4 C layer of sample S1, R-SoXR measured data along with fitted profiles with different models are shown in Figure 4(b). The measured data are fitted by slicing B 4 C layer with different thicknesses and atomic compositions to account for a spatial variation of at. % of B within B 4 C layer. However, the best-fit data matches well with the experimental data with uniform distribution model. The layer thickness and roughness obtained by simultaneous fitting measured data at different selected energies near B K-edge of B are kept constant. The optimized value for thickness (roughness) of Si and B 4 C layers are 294 Å (5 Å) and 42 Å (13 Å), respectively. An intermixing layer at the Si/B 4 C interface is considered with thickness 11.5 Å and roughness 7.5 Å. A carbon contaminated layer with thickness 11.5 Å and roughness 6.5 Å is also considered at the top of B 4 C layer. Figure 4(b) shows the variation of fitted profiles with the measured R-SoXR curve (at energy 190.7 eV) when the content of atomic % of B in B 4 C layer is varied. As B is varied from 0 to 40%, the reflected profile undergoes strong modulation producing changes in both the amplitude and shape of the oscillations envelope. Here, it is mentioned that while structural parameters are linked to the periods of the oscillations in the reflected profile, parameters of the atomic composition of the resonating atom/compound are closely related to the amplitudes and shape of the oscillations envelope. Resonant x-ray reflectivity has excellent chemical sensitivity to the resonating atom along with their spatial distribution. This high sensitivity determines the chemically and spatially resolved atomic profile within the nanometer range with a very tiny volume of contributing material. The significant change in reflectivity profile at around q = 0.05 Å −1 by varying percent of elementary B in Figure 4(b) could be due to type of layer structure chosen in the thin film for the case study, the optical properties of the resonating atom and change in .78 × 10 −3 , and − 9.36 × 10 −3 and 9.48 × 10 −3 , respectively. Even by mixing 5% of B, brings significant changes in the optical properties of the B 4 C layer, which brings significant changes in the reflected spectra as well. The scattering contrast at interface, δ β ∆ + ∆ ( ) ( ) 2 2 , which is proportional to scattering intensity undergoes significant and tunable enhancement. In Figure 4(b), the fitted profile with 20 atomic % of B in the B 4 C layer matches the measured curve well. The result clearly reveals resonant reflectivity is a highly sensitive technique to quantify atomic composition within a few atomic % of the precision.
The effective EDP [bottom panel of Figure 5] is obtained from the best-fit R-SoXR curve [top panel of Figure 5] at three different selected energies. The EDP undergoes gradual variation at the interfaces and is sensitive to the Si/B 4 C interface. The EDP profiles clearly show that the position of B 4 C layer is at top of Si in sample S1. The EDP of B 4 C layer containing B undergoes significant changes as the energy is tuned near the B K-edge of elementary boron due to the contribution of both types of B atoms (i.e. elementary B and B in B 4 C) at these energies. A schematic model of the vertical atomic composition distribution in different layers obtained from best-fit R-SoXR results is shown in the right hand side of Figure 5. The best-fit results of sample S1 are: average thickness (roughness) of W, Si, interlayer (mixed layer) (B 4 C-on-Si), B 4 C and the top contaminated carbon layers as 8 ± 1 Å (3.5 ± 0.5 Å ), 294 ± 1 Å (5 ± 0.5 Å ), 11.5 ± 1 Å (7.5 ± 0.5 Å), 42 ± 1 Å (13 ± 0.5 Å) and 11.5 ± 1 Å (6.5 ± 0.5 Å), respectively. The best-fit results also reveal that the B 4 C layer is composed of 80 ± 3% of B 4 C and 20 ± 3% of B. The interlayer (mixed layer) is composed of 80% of Si and 20% of (80% B 4 C + 20% B).
Similar to quantitative determination of the atomic profile along with microstructure for sample S1, those of samples S2 and S3 have been also determined. The procedure for data analysis for samples S2 and S3 is similar to that of S1. In order to find spectroscopic information of whether B 2 O 3 is present in the samples S2 and S3 or not, R-SoXR measurements are performed across the very strong and sharp B K-absorption edge of B 2 O 3 [ Figure 6]. However, the measured R-SoXR profiles are nearly identical in nature at four selected energies of 193.7, 194, 194.3 and 194.6 eV for both S2 and S3. This confirms that B 2 O 3 is not present in samples S2 and S3. The presence of elementary boron in sample S2 is confirmed using the procedure followed for sample S1 (discussed earlier) by performing R-SoXR measurements across the B K-edge of elementary boron at the selected energies of 185, 186, 187, 188, 190.7 and 191.4 eV. To quantify the atomic % of B and the spatial distribution in B 4 C layer of sample S2, R-SoXR measured data along with best-fit profiles at three selected energies of 188, 190.7 and 191.4 eV are shown in Figure 7. The best-fit results of sample S2 are: average thickness (roughness) of W, Si, interlayer layer I (B 4 C-on-Si), B 4 C, interlayer II (Si-on-B 4 C) and Si layers as 8 ± 1 Å (4 ± 0.5 Å ), 138 ± 1 Å (8.5 ± 0.5 Å ), 13 ± 1 Å (4 ± 0.5 Å), 41 ± 1 Å (6.5 ± 0.5 Å), 13 ± 1 Å (5.5 ± 0.5 Å) and 148 ± 1 Å (7 ± 0.5 Å), respectively. The best-fit results also reveal that the B 4 C layer is composed of 80± 3% of B 4 C and 20 ± 3% of B. The interlayer (mixed layer) is composed of 80% of Si and 20% of (80% B 4 C + 20% B). Similarly for sample S3, the best-fit results of R-SoXR measurements near the B K-edge of elementary B are obtained as: average thickness (roughness) of W, B 4 C, interlayer (Si-on-B 4 C) and Si layers as 8 ± 1 Å (5 ± 0.5 Å ), 41 ± 1 Å (5.5 ± 0.5 Å ), 12 ± 1 Å (6 ± 0.5 Å) and 301 ± 1 Å (7.5 ± 0.5 Å), respectively. The best-fit results also reveal that the B 4 C layer is composed of 80± 3% of B 4 C and 20 ± 3% of B. The interlayer (mixed layer) is composed of 80% of Si and 20% of (80% B 4 C + 20% B).
Energy resolution of the measurements. The energy resolution (E/Δ E) for the energy scan to determine (f 0 + f′ ) and f″ values is about 1000 at 200 eV. The energy resolution available for the angular scan, in the original paper is about 250 at 190 eV and in the corrigendum is ~670 at 190 eV with spectral impurity ~0.1%. In  the original paper, due to intensity reasons the energy resolution used for the angular scan was poorer than for the energy scan. This may lead to some uncertainty for the determination of the composition. In the original paper, to better understand the changes in reflectivity profile in the vicinity of the B K-edge of B 2 O 3 (Figure 4(a) in the original paper) although the energy resolution was not optimum, we compare the changes in the value of (f 0 + f′ ) and f″ in energy interval of 0.3 eV at selected energies, below the edge (away from the edge) and near the edge. For example, as per the energy scan, below the edge, (f 0 + f′ ) and f″ of B 2 O 3 are − 1.71 and 0.488 at 188.5 eV, and − 1.74 and 0.476 at 188.8 eV, respectively. Below the edge, the change in (f 0 + f′ ) and f″ in energy interval of 0.3 eV is small. However, near the edge, (f 0 + f′ ) and f″ of B 2  And F. S. played a key role in the soft x-ray measurements and optimization of the beamlines for these measurements; All the authors discussed the results in preparing the scientific contents of the manuscript; M.N. wrote the manuscript; All authors reviewed the manuscript.