Introduction
Scientific Reports
5: Article number: 861810.1038/srep08618; published online: 03
02
2015; updated: 07
11
2016
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 qz (4π sinθ/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/ΔE ≅ 670),
smaller vertical angular divergence (0.5 mrad), larger photon flux (~1.4 × 1010) 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 B4C layer (40 Å) in Si thin
film of thickness 300 Å. The samples are fabricated using electron beam evaporation.
Elementary boron is incorporated into B4C layer by co-deposition. B4C 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. Prior to R-SoXR measurements,
hard XRR measurements are done using Cu K
α
source. Hard XRR profile of all three samples are measured and fitted up to qz = 0.42 Å−1
(theta = 3 degree). However, hard XRR profile are plotted up to qz = 0.22 Å−1 (theta = 1.545
degree) [Figure 1(a,b)]. Measured profiles of three samples with varying position
of B4C layer in Si clearly appear very similar [Figure 1(a)]. Inset of Figure 1(a)
shows nearly identical electron density profiles (EDP) obtained from best-fit results
of XRR of S1, S2 and S3 [Figure 1(b)]. The fitted profile matches the measured curve
by considering Si and B4C as a single layer. The total thickness of (Si + B4C) is
350 ± 1, 352 ± 1 and 353 ± 1 Å; and mass density is about 95 ± 2% of bulk value of
Si with rms roughness = 7.5 ± 0.5, 6.5 ± 0.5 and 7 ± 0.5 Å; for samples S1, S2 and
S3, respectively. W layer thickness is ~10 Å having rms roughness = 3.5 ± 0.5, 4 ± 0.5
and 4.5 ± 0.5 Å; for samples S1, S2 and S3, respectively. The rms roughness of the
substrates is 4.5 ± 0.5 Å. A silicon oxide layer of thickness ~15.5 Å is considered
above the silicon substrate. Thus, conventional XRR is not sensitive to Si/B4C interface
having low electron density contrast (EDC), ∆ρ/ρ = 0.5%, and to compositional variation
in the film, due to low contrast and lack of element-specificity.
Sensitivity of resonant reflectivity to low contrast interface
Sensitivity of resonant reflectivity to low contrast Si/B4C interface is demonstrated
by performing measurements at a selected energy of 191.4 eV (B K-edge of B4C) [Figure
2(b)]. Soft x-ray reflectivity measurements are carried out in the s-polarization
geometry using the Optics Beamline at the BESSY-II storage ring1
2. The measurements were done with a better energy resolution, photon flux, accessible
q-space and lower angular divergence than the measurements presented in the original
paper. For the soft x-ray measurements, the data are collected up to theta = 89.2
degree. The reflectometer used was specially designed for measurements in near-normal
incidence geometry. A GaAsP-photodiode 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 B4C layer. To understand the observed scattered profiles for
chemically selective atomic distribution analysis, the measured atomic scattering
factor (ASF) of B, B4C and B2O3 near boron K-edge are shown in Figure 3. At this specified
energy of 191.4 eV, ASF of B4C has a strong variation [Figure 3]. The strong modulations
in reflected spectra [Figure 2(b)] is due to major reflection contribution from Si/B4C
interface apart from contributions from other interfaces. Due to the contribution
of the reflection from the Si/B4C 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 B4C layer changes in Si film.
Two vertical dotted lines mark how the period of oscillations gets modulated as position
of the B4C 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 XRR3.
Spectroscopic information using resonant reflectivity
To determine the spectroscopic information using R-SoXR, elementary boron is introduced
in B4C 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(a) demonstrates experimental evidence of the presence
of chemical changes in sample S1. The measurements are performed at B K-edge of both
elementary B (~189.5 eV) and B2O3 (~194.1 eV). Near B K-edge of B2O3, four energies
of 193.7, 194, 194. 3 and 194.6 eV are chosen across the edge. At these energies the
ASF undergoes strong variation for B2O3 but elementary boron exhibits nearly a flat
optical response [Figure 3]. If the film contains B2O3 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 B2O3 [Figure 4(a)]. This observation corroborates that no B2O3 is
present in sample S1. Similarly, to confirm the presence of B in sample S1, R-SoXR
measurements are performed across the B K-absorption edge of B at selected energies
of 185, 186,187, 188, 189, 190.7 and 191.4 eV [Figure 4(a)]. At these energies the
ASF undergoes strong variation for boron but not for B2O3 [Figure 3]. Near the edge,
B provides enhanced and tunable scattering. B4C 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 B4C due to stronger resonance enhancement of elementary
B than B in B4C. 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 B4C 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 B4C 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 B4C 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 B4C 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 B4C layer with different
thicknesses and atomic compositions to account for a spatial variation of at. % of
B within B4C 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 B4C layers
are 294 Å (5 Å) and 42 Å (13 Å), respectively. An intermixing layer at the Si/B4C
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 B4C
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 B4C 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 optical contrast by varying with atomic percent
of B. The changes in the values of atomic scattering factor/optical constant (δ and
β) by incorporation of different percent of B in B4C layer are as follows: At 190.7 eV,
the values of δ and β of B4C layer with 0%, 10%, 15%, 20%, 25% and 40% of B are as
follows: −3.17 × 10−3 and 2.29 × 10−3, −4.72 × 10−3 and 4.09 × 10−3, −5.49 × 10−3
and 4.99 × 10−3, −6.27 × 10−3 and 5.89 × 10−3, −7.04 × 10−3 and 6.78 × 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 B4C layer, which brings significant changes in the
reflected spectra as well. The scattering contrast at interface,
, 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 B4C 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/B4C interface. The
EDP profiles clearly show that the position of B4C layer is at top of Si in sample
S1. The EDP of B4C 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 B4C) 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) (B4C-on-Si),
B4C 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 B4C layer is composed of 80 ± 3% of B4C
and 20 ± 3% of B. The interlayer (mixed layer) is composed of 80% of Si and 20% of
(80% B4C + 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 B2O3 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 B2O3 [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 B2O3 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 B4C 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 (B4C-on-Si), B4C, interlayer II (Si-on-B4C) 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 B4C layer is composed of 80± 3% of B4C and 20 ± 3% of B. The
interlayer (mixed layer) is composed of 80% of Si and 20% of (80% B4C + 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, B4C, interlayer
(Si-on-B4C) 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 B4C layer is composed of 80± 3% of B4C and 20 ± 3% of B. The interlayer (mixed
layer) is composed of 80% of Si and 20% of (80% B4C + 20% B).
Energy resolution of the measurements
The energy resolution (E/ΔE) for the energy scan to determine (f0 + 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 B2O3 (Figure 4(a) in the original paper) although the energy resolution
was not optimum, we compare the changes in the value of (f0 + 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, (f0 + f′) and f″ of
B2O3 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 (f0 + f′) and f″ in energy interval of 0.3 eV is small.
However, near the edge, (f0 + f′) and f″ of B2O3 are −30.46 and 13.89 at 193.7 eV,
−16.3 and 49.25 at 194 eV, and 25.5 and 39.78 at 194.3 eV, respectively. Taking into
account the broadening of the resonance for the angular scan in the original paper,
near the edge, (f0 + f′) and f″ of B2O3 are −27.77 and 17.53 at 193.7 eV, −15.93 and
40.44 at 194 eV, and 18.25 and 38.91 at 194.3 eV, respectively. Near the edge, the
change in (f0 + f′) and f″ in energy interval of 0.3 eV is significant. The variation
of the atomic scattering factor of B2O3 near the B2O3 edge provides changes in the
reflectivity profile as observed in the original paper.
A. Sokolov and F. Schäfers have been added to the author list because they contributed
to the experiments reported in this Corrigendum. This has now been corrected in the
HTML versions of the Article. The Author Contributions section in the HTML version
now reads:
M.N. took part in conceiving the idea and performed experiments in the original paper;
M.N., G.S.L. and P.C.P. discussed the results; M.N. wrote the manuscript; All authors
reviewed the manuscript; In the corrigendum, A. S. 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.