Photon Factory Activity Report 2017 #35 (2018)

BL-11D/2016G144

High-Diffraction-Efficiency Wide-Acceptance-Angle
Laminar-Type Diffraction Gratings Overcoated with Oxide Films forBoron-K Emission Spectroscopic Measurements
Masato KOIKE1,*, Tadashi HATANO2, Alexander S. PIROZHKOV1,Ryuichi UKITA3, Hiroaki NISHIHARA3, Hiroyuki SASAI3, and Tetsuya NAGANO3
1Kansai Photon Science Institute, Quantum Beam Sciences Directorate,
National Institutes for Quantum and Radiological Science and Technology
8-1-7 Umemidai, Kizugawa, Kyoto 619-0215, Japan
2Institute of Multidisciplinary Research for Advanced Materials, Tohoku University2-1-1 Katahira, Aoba-ku, Sendai, Miyagi 980-8577, Japan
3Device Department, Shimadzu Corporation
1 Nishinokyo-Kuwabaracho, Nakagyo-ku, Kyoto, Kyoto 604-8511, Japan
Theoretical and experimental studies have been performed to explore the enhancement of diffraction efficiency ofdiffraction gratings around B-K emission (6.76 nm, 184 eV) spectrum based on overcoating with materials having highreflectivity and small extinction coefficient (T layer) on conventional metal layer (M layer) coated gratings. In theprevious study we confirmed this effect with a laminar-type Ni-coated diffraction grating overcoated with diamond-likecarbon (DLC). In this report the authors examine this effect using TiO2 or CeO2 layer as the T layer and Ni as the M layer
by numerical calculations and measurements by use of the reflectometer at the PF-BL11D beamline. As the results, theenhancements of diffraction efficiency at 6.76 nm are 2.2 and 3.4 times with the T layers having optimum thickness of
22.0 and 30.2 nm at the incident angles of 85.262° and 84.492° for TiO2 and CeO2 layers, respectively, compared with aconventional Ni coated grating used at an incidence angle of 87.070°.
1 Introduction
There has been a great demand from both academic
and industrial communities in highly sensitive
spectroscopic measurement in the soft X-ray region
containing emission and absorption associated with theinner shell transitions of light elements. Especially boron
is the critical trace element due to the advantage ofimproving quenching characteristics in steel. To detect theB-K emission band at around 6.76 nm more efficiently we
performed a feasibility study to enhance the diffraction
efficiency of laminar-type diffraction grating based on a
newly discovered physical phenomenon in the region oftotal reflection. The phenomenon is embodied byovercoating a transparent high-density material on a metallayer on grating grooves. We have found that theovercoating material should have middle refractive index
between those of vacuum and the metal layer, and small
extinction coefficient, i. e. high transparency. We havealready found that tetrahedral amorphous carbon, namely
diamond-like carbon (DLC), in which sp3 hybrid orbital(diamond structure) is dominant, is a suitable material forthis purpose by numerical calculations [1]. The DLC
layer can be produced by use of a filtered arc method [2].
The enhancement of diffraction efficiency by means of
this technique was confirmed by the measurements at asynchrotron radiation facility [3].
The purpose of this report is to show simulation andexperimental results which demonstrate that similar
enhancement of diffraction efficiency can be obtained byuse of well-known TiO2 and CeO2 layers. Our efforts arealso extended to the optimizations of the thickness of theoxide layer as well as the incidence angle which increases
spectral flux due to widening of the acceptance angle of
the grating.
2 Experiment
Figure 1 shows a schematic diagram of the crosssection of the new laminar-type diffraction grating having
a rectangular groove shape. Geometrical parameters of
the base Ni-coated grating used throughout this study are
as follows: grating constant, of /1200 mm; duty ratio,
D = a/, of 0.41; groove depth, h, of 14.0 nm; diffraction
order, m, of +1. Also assumed was a metal layer of Nilayer (M layer) having a thickness, d1, of 30 nm. Thexyd2
d1O z



TiO2 orCeO2
NihSiO2aFig. 1: Schematic diagram of a new laminar-type gratingcoated with Ni and TiO2 or CeO2.

Photon Factory Activity Report 2017 #35 (2018)

=0.00

1.0ta-Ca-C

=0.05

0.8

=0.10

Reflectanceinitially designed incident angle, , of the Ni-coatedgrating is 87.070°.
It is a common practice to coat the grating with ahighly reflective material to enhance the diffraction
efficiency of a grating for any spectral region. Table 1
shows the list of common and newly investigatedmaterials, and their theoretical density, ρ, complex
refractive index parameters defined by n = (1– δ) + iβ (β:extinction coefficient), and θ/θ C, i.e., glancing angle ofincidence, θ (= 90° – α), divided by critical angle
measured from the surface, θC [4]. Here, a-C and ta-C
stand for amorphous graphite and DLC.
Figure 2 shows the reflectance curves for δ /β=0, 0.05,0.10, 0.20, 0.40, 0.80, and 1.00. The abscissa indicates thevalue of θ normalized to θC. In the figure the calculated
reflectance of Ni, □, Au, ■, Si, ◇, SiC, △, SiO2, ▲, a-C,●, ta-C, ○, TiO2, ☆, and CeO2, ◎, at = 6.76 nm and = 5.5° are plotted against respective values of C.
Carbon based a-C and ta-C show high reflectance as seenin this figure. From this figure it is found that TiO2 andCeO2 would exhibit high diffraction efficiency as well asta-C and a-C comparing with conventional metals, Ni andAu, and silicides, if the grating grooves could be ruled in
TiO2 and CeO2 substrates. However, it is difficult torealize with both mechanically ruled and holographic
gratings from various practical reasons. Therefore it is themost realistic solution to coat the oxide layer having highreflectance on the conventional metal coated grating.
Assuming Ni as the M layer we have searched theoptimum layer thickness of the oxide layer (T layer) and
incident angle simultaneously which attains maximum
diffraction efficiency at the B-K emission by use of asimulation code based on rigorous coupling method [5].
Finally we found that the optimum thicknesses were 25.8
and 31.5 nm at the incident angles of 84.360° and 82.840°
for TiO2 and CeO2 layers, respectively.
Fabrications of laminar-type grooves and coatings ofboth M and T layers were performed at Shimadzu Corp.,
Kyoto, Japan. The measurements of absolute diffraction
efficiencies of the gratings were carried out at the BL-

=0.20

0.6

Ni

0.4
0.2
0.00.0=0.40

Au
SiCB-KE = 183.3 eV = 6.76 nm = 84.5º = 5.5º

0.2

0.4

SiO2

=0.80Si1.00
0.6

0.8

1.0

1.2

1.4

1.6

/CFig. 2: Calculated reflectance of Ni, □, Au, ■, Si, ◇,SiC, △, SiO2, ▲, a-C, ●, ta-C, ○, TiO2, ☆, and CeO2,◎, at λ= 6.76 nm and glancing angle of incidence θ =5.5°. Reflectance curves for δ/β = 0.0, 0.05, 0.10, 0.20,0.40, 0.80, and 1.00 are also shown.
11D beamline at the Photon Factory, KEK, Tsukuba,Japan.
3 Results and Discussion,Figure 3 shows the relation of the incidence angle withdiffraction efficiency of the first order light (m = + 1) at λ= 6.76 nm for the gratings coated with Ni(30.0), Ni(30.0)/
TiO2(22.0), and Ni(30.0)/CeO2(30.2). The numbers in theparentheses show the thickness of the layer in nm. The
diffraction efficiencies of the grating coated with Ni, Ni/TiO2, and Ni/CeO2 layers were 0.139, 0.173, and 0.191 at
the incidence angle of 87.070°, respectively. The
corresponding maximum diffraction efficiencies were0.173, 0.206, and 0.282 at the incidence angles of
84.420°, 85.262°, and 84.492° for the gratings coatedwith Ni, Ni/TiO2, and Ni/CeO2 layers, respectively. For
the case of the width of the diffraction grating in view of
the incident light direction is proportional to theamount of incident flux (∝ cos α), the gains of theTable 1: Density and optical constants of common andinvestigated coating materials. Here is density,  and are defined by complex refractive index, n = (1-iCis critical angle measured from the reflecting surface at = 6.76 nm, and θ = 5.5° is glancing angle of incidence.

NiAu
Si
SiC
SiO2
a-C
ta-C
TiO2
CeO2

 (g/cm3)

C

8.9
19.32
2.33
3.22
2.2
2.2
3.1
4.26
7.3

0.025200
0.014819
0.008062
0.011704
0.009525
0.008900
0.012550
0.015919
0.0221300.018933
0.008417
0.009647
0.009662
0.005422
0.000757
0.001066
0.004000
0.003725

0.428
0.558
0.756
0.627
0.695
0.720
0.606
0.537
0.456

Fig. 3: The measured diffraction efficiencies for thegratings coated with Ni, Ni/TiO2, and Ni/CeO2 layers vs.
incidence angle at  = 6.76 nm.

Photon Factory Activity Report 2017 #35 (2018)that TiO2 layer circumvents the phenomenon of seizure
attributed to residual contaminants on the surface of the
optical elements including diffraction gratings in theultra-high vacuum apparatus such as a synchrotron
radiation beamline.

Fig. 4: Diffraction efficiency vs. wavelength for Ni,Ni/TiO2 and Ni/CeO2 coated gratings obtained bynumerical calculations and experiments. For details seetext.
incidence flux are 1.51, 1.61, and 1.88 times, and finallythe enhancements of diffracted spectral flux are 1.87, 2.39
and 3.81 times compared to those of the Ni coated gratingused at the incidence angle of 87.070°, respectively.
Figure 4 shows wavelength dependence of thediffraction efficiencies of the gratings coated with the Ni,Ni/TiO2, and Ni/CeO2 for the incidence angles of87.070°, 85.262° and 84.492°, respectively. The grating
overcoated with CeO2 shows high diffraction efficiency inthe vicinity of B-K. However, it is found that thediffraction efficiency significantly decreases toward 11
nm, which is considered to be attributed to the absorptionof 4d104f→ 4d94f2 transition [6]. The deviations between
the calculated and experimental peak positions and valuesof diffraction efficiencies appeared for Ni/TiO2 and Ni/
CeO2 coated gratings are considered to be due to theoptical constants and thickness of the coatings
assumed for the calculations as well as the surface
roughness, and required to perform further investigations.
It is well known that TiO2 is a unique material having
photocatalyst effect [7], therefore, it could be expected

Acknowledgements
This work was partly supported by CAMS Project
2016 of “Development of high diffraction efficiency
coating method of extreme ultraviolet diffraction
gratings,” IMRAM, Tohoku University. A part of thisresearch was carried out as a joint research“Development of low incident angle high efficiency
gratings in extreme ultraviolet region” of Shimadzu Corp.,
Tohoku University, and National Institutes for Quantum
and Radiological Science and Technology. The
measurements of absolute diffraction efficiencies wereperformed as a part of the PF synchrotron radiation joint
experiment of “Development of low incidence angle andhigh efficiency diffraction gratings in extreme ultravioletregion,” (2016G144, April 2016- March 2018).
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[4] D. Attwood, Soft X-rays and extreme ultraviolet(Cambridge Univ. Press, New York, 1999), pp.55–80.
[5] GSOLVER V4.2c, Grating Solver Development Co.,
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[6] H. W. Wolff, R. Bruhn, K. Radler, and B. Sonntag,
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* koike.masato@qst.go.jp