Title

Nanofocusing of X-ray Free-Electron Lasers Using
Multilayer Kirkpatrick-Baez Mirrors

Author(s)金, 章雨

Citation

大阪大学, 2016, 博士論文

Version Type VoR
URL

https://doi.org/10.18910/55976

rights
Note

Osaka University Knowledge Archive : OUKA
https://ir.library.osaka-u.ac.jp/
Osaka University

Doctoral Dissertation

Nanofocusing of
X-ray Free-Electron Lasers Using
Multilayer Kirkpatrick-Baez Mirrors

Jangwoo Kim
January 2016

Department of Precision Science & Technology
Graduate School of Engineering
Osaka University

ABSTRACT
X-ray free-electron lasers (XFELs) produce unprecedented high brilliance, excellent spatial
coherence, and ultrafast pulse durations. In recent years, several XFEL facilities have achieved
lasing in the hard X-ray regime. The use of focusing optics enables enhancement of X-ray
intensity, which expands the range of possible XFEL applications. Several optical devices, suchas Fresnel zone plates, refractive lenses, and reflective mirrors, have been utilized for thispurpose. Amongst these devices, reflective mirrors can achieve the highest focusing efficiencies
with long working distances; therefore, they provide significant advantages for various
applications.
The principle aim of the investigation described herein was to generate an extremely intense
X-ray field to explore nonlinear phenomena in the hard X-ray regime. To meet this requirement,
the usage of an XFEL and its focusing are critically important. To achieve power densities ofaround 1022 W/cm2, a XFEL sub-10-nm focusing system was developed in this study using twostage reflective focusing optics. The development of this system required studies of thefabrication and measurement of mirror substrates with steeply curved surfaces, deposition ofmultilayers with high reflectivities and sufficient X-ray irradiation tolerances, and techniques
for single-shot measurement of focused wavefronts.
XFEL sub-10-nm focusing mirrors have steeply curved surfaces that are difficult to measureusing conventional shape testing methods. The minimum radius of curvature is a few meters,
and the slope range is several dozen milliradians. Furthermore, the required accuracy, orRayleigh criterion, of the mirror surface is 1 nm peak-to-valley. A laser autofocus microscope
system featuring a position correction mechanism utilizing three heterodyne interferometers
was developed to provide measurements at this level of accuracy. This apparatus successfullymeasured the surface shapes of sub-10-nm focusing mirrors with the accuracy required by theRayleigh criterion.
In XFEL optical design, the utilization of multilayer mirrors may be considered, since the
iii

iv

Abstract

grazing incidence angle is much greater than the critical angle at which total reflection occurs.
However, one of the critical requirements of the optical elements used in XFELs is sufficienttolerance to intense X-ray irradiation. Therefore, we investigated the X-ray damage thresholds
of multilayer films consisting of Pt and C, a suitable combination for this optical design, ingrazing incidence conditions. We determined that the threshold value was 0.051 μJ/μm2, which
is sufficiently higher than the energy densities that are practically employed. Additionally, thefocusing efficiency is related to the X-ray reflectivity of the multilayer film. We improved the
X-ray reflectivity of a Pt/C multilayer by approximately 10% through slight C-doping into thePt layers.
To investigate the focused state of the XFEL nanobeam, a wavefront measurement method
was developed, utilizing single-grating interferometry based on the Talbot effect. This method
can be used to measure the wavefront phase error, which includes the alignment and surface
shape errors of the mirror optics, from a single image. Correct mirror alignment was achieved
using this method, and the residual errors could be corrected through deferential deposition with
sub-nanometer accuracy.
Use of the above results facilitated initial commissioning of the XFEL sub-10-nm focusing
optics at SPring-8 Angstrom Compact free-electron LAser. We found that phase errors ofseveral radians were caused by the shape error of the multilayer mirror, and the focused beam
size was approximately 10 nm, which is the smallest reported to date in XFEL focusing. Then,
we endeavor to focus the XFEL to sub-10-nm size with a power density greater than 1022 W/cm2,
by using shape-error-corrected multilayer mirrors. Such X-ray field intensities will enable theexploration of nonlinear phenomena in the hard X-ray regime.

ACKNOWLEDGEMENT
Completing this Ph.D. has been a collaborative process, and I would like to thank the following
people for their gracious help and support.
First and foremost, I would like to express sincere gratitude to my supervisor Prof. Kazuto
Yamauchi of Osaka University for his advice, constant support, and encouragement throughout
the course of my studies. I would also like to express my great appreciation to Assist. Prof.
Satoshi Matsuyama, Assoc. Prof. Yasuhisa Sano, and Assoc. Prof. Yukio Takahashi of Osaka
University for their suggestions and discussions. I would additionally like to thank Prof.
Kiyoshi Yasutake, Prof. Mizuho Morita, Prof. Yuji Kuwahara, Prof. Yoshitada Morikawa, Prof.
Heiji Watanabe, and Prof. Katsuyoshi Endo, and all of the other professors and technicians of
the Department of Precision Science & Technology, Osaka University.
I would like to express my sincere acknowledgements to Director Dr. Tetsuya Ishikawa,Group Director Dr. Makina Yabashi, Team Leader Dr. Kenji Tamasaku, Unit Leader Dr. Yoshiki
Kohmura, and Researcher Dr. Yuichi Inubushi of the RIKEN SPring-8 Center (RSC), andDivision Director Dr. Shunji Goto, Group Reader Dr. Haruhiko Ohashi, Team Reader Dr.
Kensuke Tono, and Researcher Dr. Takahisa Koyama, Dr. Hirokatsu Yumoto, and Dr. Yasunori
Senba of the Japan Synchrotron Radiation Research Institute (JASRI), for their valuable andeffective advice and suggestions in preparing this thesis.
In particular, I would like to express my gratitude to Prof. Hidetsugu Yagi of Ehime
University for his guidance and encouragement throughout my overseas studies in Japan. I
would also like to express my appreciation to Prof. Keiji Ogi of Ehime University for his advice
throughout my undergraduate years.
I am grateful to Ayaka Nagahira, Hikaru Yokoyama, Ryosuke Fukui, Akihiko Nishihara,
and Shogo Kawai of the X-ray focusing group, and all the members of Ultra-Precision
Machining Laboratory. Also, I am grateful to the secretaries; Yumiko Tachibana, Eriko Kubo,
and Kanako Terai for their administrative and clerical support. I also heartily thank Ph.D.
v

vi

Acknowledgement

candidate Taito Osaka and Ph.D. candidate Akihiro Suzuki for their friendship, kindness,
support, and encouragement during our time studying together.
I would like to express appreciation to JTEC Corporation, Motion Trust Co., Ltd., andMitaka Kohki Co., Ltd. for developing surface shape measurement system.
This research was mainly supported by a Grant-in-Aid for Scientific Research (S) no.
2322604, a Grant-in-Aid for JSPS Fellows no. 25-129, and the Global COE program (H08)from the Ministry of Education, Sport, Culture, Science and Technology, Japan. It was also
supported by CREST from the Japan Science and Technology Agency. The use of BL29XULat SPring-8 and BL3 at SPring-8 Angstrom Compact free-electron LAser (SACLA) was
supported by RSC and JASRI. I am grateful to the staff at SPring-8 and SACLA beamline for
their help during the beam time. I also heartily appreciate scholarships granted by Korea-Japan
Joint Government Scholarship Program and Kato Asao International Scholarship Foundation.
Finally, I would like to express my gratitude to my family for their lasting love and support.
In particular, I would like to thank my lovely wife and my cute daughter for always being there
for me, and for helping me improve. Without their love and support, I would not be here
completing this study. Thank you for being there.

Jangwoo Kim
January 2016

CONTENTS
Abstractiii

Acknowledgementv

List of Figuresix

List of Tablesxiii

1. Introduction

1

2. Reflective Focusing Optics for X-ray Free-Electron Lasers

5

2.1 X-ray Focusing with Reflective Optics ·················································· 5
2.2 Multilayer Films for X-ray Focusing ····················································· 9
2.3 Reflective Focusing Optics Used at SACLA ············································ 16

3. Preparation and Measurement of Mirror Substrates

19

3.1 Reflective Mirrors for XFEL Focusing ·················································· 19
3.2 Development of Surface Shape Measurement System ································· 24
3.2.1 Apparatus Overview ································································ 24
3.2.2 Repeatability Test using Planar Mirror ··········································· 27
3.3 Fabrication and Measurement of XFEL Sub-10 nm Focusing Mirrors ·············· 29
3.4 Summary ····················································································· 32

4. Tolerance of Multilayer Films to X-ray Free-Electron Laser Irradiation 33
4.1 Development of Thin Film Deposition System ········································· 33
4.1.1 Apparatus Overview ································································ 33
4.1.2 Differential Deposition Test for Mirror Shape Modification ················· 36

vii

viii

Contents

4.2 Evaluation of Breakdown Threshold using Focused XFEL ··························· 40
4.3 Evaluation in Actual Operating Conditions using Unfocused XFEL ················ 46
4.4 Summary ····················································································· 51

5. Improvement of X-ray Reflectivity in Multilayer Films

53

5.1 Determination of Critical Pt Layer Thickness ··········································· 53
5.2 X-ray Reflectivity Improvement in Pt/C Multilayers by C-Doping of Pt Layers ·· 55
5.2.1 Roughness Improvement by Crystallization Suppression ····················· 57
5.2.2 X-ray Reflectivity Improvement ·················································· 60
5.3 Summary ····················································································· 63

6. Nanofocusing of X-ray Free-Electron Lasers

65

6.1 XFEL Sub-10 nm Focusing Optics and Focusing Strategy ··························· 65
6.2 Measurement of Focused X-ray Wavefront ············································· 71
6.3 Experimental Evaluation of Multilayers at SPring-8 ··································· 74
6.4 Nanofocusing Experiment at SACLA ···················································· 77
6.5 Summary ····················································································· 80

7. Conclusions

83

Bibliography

87

List of Publications

97

List of Presentations

101

LIST OF FIGURES
Fig. 1.1.

Peak brilliances of X-ray sources. ························································ 2Fig. 2.1.

Schematic of Kirkpatrick-Baez mirror geometry. ······································ 6Fig. 2.2.

Ellipsoidal focusing mirror geometry. ···················································· 7Fig. 2.3.

Multilayer mirror schematic. Differences between total reflection from singlelayer mirror and Bragg reflection from multilayer mirror. ···························· 8Fig. 2.4.

Schematic of transmitted and reflected plane electromagnetic waves insidemultilayer. ··················································································· 11

Fig. 2.5.

Calculated X-ray reflectivities versus grazing incidence angle. ····················· 13

Fig. 2.6.

Calculated X-ray reflectivities of first- and second-order Bragg diffractions
versus γ. ······················································································ 14

Fig. 2.7.

Calculated X-ray reflectivities of first- and second-order Bragg diffractions
versus multilayer period. ·································································· 14

Fig. 2.8.

Calculated X-ray standing wave field-intensity distributions in multilayer
structure. ····················································································· 15

Fig. 2.9.

Schematic of optical configuration of XFEL 1 μm focusing system at SACLA. · 17

Fig. 2.10. Schematic of optical configuration of XFEL 50 nm focusing system at SACLA. · 18
Fig. 3.1.

Height error corresponding to λ/4 phase error at photon energy of 10 keV. ······· 20

Fig. 3.2.

Surface shape profiles of 1 μm, 50 nm, and sub-10 nm XFEL focusing mirrors. 22

Fig. 3.3.

Surface shape profiles of XFEL sub-10-nm focusing mirrors. ······················ 23

Fig. 3.4.

Schematic of shape measurement apparatus. ··········································· 24

Fig. 3.5.

Principle diagram of laser autofocus microscope. ····································· 25

Fig. 3.6.

Angular dependence of laser autofocus microscope.·································· 26

Fig. 3.7.

Schematic of probe table. ································································· 26ix

x

List of Figures

Fig. 3.8.

Results of the repeatability test. ·························································· 28

Fig. 3.9.

Conceptual diagram of elastic emission machining. ·································· 30

Fig. 3.10. Schematic diagram of processes using nozzle-type and rotating-ball-type
machining heads. ··········································································· 30
Fig. 3.11. Residual shape errors of horizontal and vertical direction focusing mirrors.·········· 31
Fig. 4.1.

Schematic of thin film deposition apparatus. ··········································· 35

Fig. 4.2.

Photograph of thin film deposition apparatus. ········································· 35

Fig. 4.3.

Thickness distribution of Pt deposition spot. ··········································· 37

Fig. 4.4.

Thickness distribution of C deposition spot. ··········································· 37

Fig. 4.5.

Thickness distribution of Pt deposition spot for differential deposition. ··········· 38

Fig. 4.6.

Designed and measured thickness distributions. ······································· 39

Fig. 4.7.

Residual errors of differential deposition with and without low-pass filter. ······· 39

Fig. 4.8.

Schematic of experimental system for evaluation of breakdown threshold of
Pt/C multilayer. ············································································· 40

Fig. 4.9.

Photograph of experimental system for evaluation of breakdown threshold of
Pt/C multilayer. ············································································· 40

Fig. 4.10. Change in reflectivity versus irradiation fluence.······································ 42
Fig. 4.11. Changes in reflectivity versus number of pulses. Optical microscopy images ofsample surface after 100 pulses of irradiation. ········································· 42
Fig. 4.12. Bragg angle shift measurement by θ-2θ scan. Cross-sectional bright-fieldtransmission electron microscopy images of irradiated and non-irradiated areas. ·· 43
Fig. 4.13. Calculated X-ray standing-wave field-intensity distribution in the multilayer
structure. ····················································································· 45
Fig. 4.14. Schematic of X-ray reflectometer. ······················································· 46
Fig. 4.15. X-ray reflectivities of Pt/C multilayer samples versus grazing incidence angle. · 48
Fig. 4.16. X-ray reflectivity versus time, with measured first-order Bragg peak angles atvarious times. ··············································································· 49
Fig. 4.17. Cross-sectional bright-field transmission electron microscopy images. ··········· 50
Fig. 5.1.

Calculated X-ray reflectivities of Pt/C multilayers with varying d and N as

List of Figures

xifunctions of γ. ··············································································· 54
Fig. 5.2.

Critical Pt layer thickness measured by X-ray reflectivity of Pt/C multilayers. ·· 55

Fig. 5.3.

Calculated and measured X-ray reflectivities of Pt/C multilayers.·················· 56

Fig. 5.4.

Atomic force microscopy images of surfaces of deposited Pt and PtC films. ····· 58

Fig. 5.5.

Root-mean-square film surface roughness versus C concentration in PtC film. ·· 59

Fig. 5.6.

X-ray diffraction spectra of Pt and PtC films.·········································· 59

Fig. 5.7.

Electron beam diffraction patterns. Bright-field and dark-field transmission
electron microscopy images of single-layer films. ···································· 61

Fig. 5.8.

Calculated and measured X-ray reflectivities of Pt/C and PtC/C multilayers. ···· 62

Fig. 5.9.

Interface roughness calculated using Debye-Waller factor for Pt/C and PtC/C
multilayers. ·················································································· 62

Fig. 6.1.

Schematic of optical configuration of two-stage XFEL sub-10-nm focusing
system. ······················································································· 66

Fig. 6.2.

Calculated horizontal and vertical focusing beam waists. ···························· 68

Fig. 6.3.

Calculated horizontal and vertical focusing beam profiles. ·························· 68

Fig. 6.4.

Grazing incidence angle and multilayer period distributions. ······················· 69

Fig. 6.5.

X-ray reflectivity distributions. ·························································· 69

Fig. 6.6.

Schematic of XFEL sub-10-nm focusing strategy. ···································· 70

Fig. 6.7.

Schematic of single-grating interferometer system. ··································· 72

Fig. 6.8.

Reconstructed wavefront aberration. ···················································· 73

Fig. 6.9.

Typical relationship between grazing incidence angle error and phase differenceof cubic function from wavefront shape. ··············································· 73

Fig. 6.10. Relationship between multilayer period error and reflectivity. ······················ 74
Fig. 6.11. Experimental setup for multilayer evaluation at SPring-8. ··························· 75
Fig. 6.12. X-ray reflectivities at various grazing incidence angles and X-ray photon energyof 9.1 keV. ··················································································· 76
Fig. 6.13. X-ray reflectivities at various X-ray photon energies and ideal grazing incidence
angle. ························································································· 76
Fig. 6.14. Experimental setup for XFEL sub-10-nm focusing. ·································· 77
Fig. 6.15. Horizontal and vertical focused-beam profiles measured using wire scan method. ·· 78

xii

List of Figures

Fig. 6.16. Measured phase errors resulting from shape errors of sub-10-nm focusing
mirrors. ······················································································· 79
Fig. 6.17. Focusing beam waists expected based on measured phase errors. ·················· 79
Fig. 6.18. Focusing beam profiles expected based on measured phase errors. ················ 80

LIST OF TABLES
Table 2.1. Optical parameters of XFEL 1 μm focusing system at SACLA. ···················· 17
Table 2.2. Optical parameters of XFEL 50 nm focusing system at SACLA. ··················· 18
Table 3.1. Designed parameters of XFEL sub-10-nm focusing mirrors. ························ 21
Table 3.2. Conditions for testing measurement repeatability using planar mirror. ············ 27
Table 4.1. Deposition conditions for Pt and C deposition spots. ································· 36
Table 4.2. Details of Pt/C multilayer samples. ······················································ 46
Table 4.3. Multilayer periods and ratios of Pt layer thickness to multilayer period of Pt/C
multilayer samples.········································································· 47
Table 6.1. Optical parameters of XFEL sub-10-nm focusing system at SACLA. ············· 66
Table 6.2. Phase grating parameters. ································································· 71

xiii

Chapter 1

INTRODUCTION
In 1895, a new form of radiation was discovered by W. C. Rӧntgen [1], when he experimentallydischarged a Crookes tube [2] to produce radiation of a wavelength that had not been observed
previously. This new radiation was subsequently named “X-ray” to signify its unknown nature.
Rӧntgen went on to research his discovery further and was able to ascertain some of the typicalcharacteristics of X-rays, such as their deep penetration abilities, their fluorescence, and that
their trajectories are unaffected by electric and magnetic fields. Then, in 1912, M. von Laue
discovered the diffraction of X-rays by atoms in a crystal structure [3,4]. Moreover, in 1913, W.
H. Bragg and W. L. Bragg observed the diffraction of X-rays by crystal planes and determined
the relationship between X-ray reflection angle and crystal lattice spacing, called Bragg’s law[5]. Since these discoveries, X-rays have played important roles in a wide range of scientificfields, including the physical sciences, the medical sciences, and engineering. In the fields ofmaterials and life sciences, the high penetration of X-rays through materials and their mutualinteractions with crystals and atoms have been effectively utilized, and they have been
instrumental in groundbreaking discoveries such as that of the double helix structure of DNA[6]. Consequently, X-rays are widely recognized as irreplaceable analytical tools.
However, X-ray sources remained essentially explored until the 1960s. Synchrotron
radiation was theoretically predicted in 1946 [7] and was observed using an electron accelerator
in 1947 [8]. However, at that time, synchrotron radiation, which was produced by firstgeneration facilities, was considered to be only the energy lost from accelerators in elementary
particle experiments. In the 1970s, a second-generation synchrotron radiation facility was built,
which was designed primarily as an X-ray source. It was then found that synchrotron radiation
is much more powerful and more widely applicable than radiation from conventional X-ray
1

2

Chapter 1. Introduction

sources.
In recent years, various advanced analytical technologies have been developed by utilizing
the high-brilliance and low-emittance properties of third-generation synchrotron radiation
sources [9], which began operation in the 1990s. The increase in the peak brilliances of the Xray sources over time is shown in Fig. 1.1. The development of X-ray free-electron lasers(XFELs) [9] is expected to enable further advances in the field of X-ray analytical technology.
High-brilliance X-ray sources are effective for providing high photon densities at their focal
points and can yield both high spatial resolution and high throughput when used in scanningtype X-ray microscopes. Therefore, the competition to improve focusing states via advances in
optical element performance has intensified since the 2000s, and the use of Fresnel zone plates,
refractive lenses, reflective mirrors, and various other X-ray optical elements has yielded focus
spot sizes of 100 nm or less [10–16]. Of these optical elements, mirrors greatly surpass theothers due to their high focusing efficiencies, long working distances, and small chromaticaberrations. Furthermore, since ablation damage induced by intense X-rays, such as thoseFig. 1.1. Peak brilliances of X-ray sources.

Background and Purpose of This Study

3

produced by XFELs, cannot be avoided in normal incidence optical elements, the use of mirrors
in grazing incidence optics is advantageous.
The principle aim of this study was to generate an extremely intense X-ray field to explore
nonlinear phenomena in the hard X-ray regime. To meet this requirement, the usage of an XFEL
and the control of its focusing are critically important. In SPring-8 Angstrom Compact freeelectron LAser (SACLA) [17], a 50 nm focusing beam with a power density of 1020 W/cm2 hasbeen achieved using total reflection mirror optics [18]. This focused beam has been applied tostudies of nonlinear X-ray optical phenomena such as two-photon absorption [19], saturable
absorption [20], and Cu-atomic inner-shell lasers [21]. To achieve higher power densities ofaround 1022 W/cm2, XFEL sub-10-nm focusing is needed. With the objective of developing
such a focusing system, we performed studies of the fabrication and measurement of mirror
substrates with steeply curved surfaces, deposition of multilayers with high reflectivities andsufficient X-ray irradiation tolerances, and development of a technique for single-shotmeasurement of focused wavefronts.
The remainder of this thesis is organized as follows.
In Chapter 2, the fundamentals of reflective X-ray focusing optics are described. The focal
spot sizes achievable by reflective optics, the limitations of total reflection, and the need for
multilayer films to overcome their limitations are described. Then, the existing reflective XFEL
focusing optics at SACLA are introduced.
In Chapter 3, the mirror substrate fabrication and measurement methods used to produce
the sub-10-nm focusing mirrors for this study are described. To create the desired mirror shapes
accurately, precise shape measurements were necessary; therefore, a new measurement system
was developed, as explained in this chapter.
In Chapter 4, the thin film deposition system developed to fabricate Pt/C multilayers andits tolerance to XFEL irradiation are described. Then, evaluations of the Pt/C multilayers
obtained using focused and unfocused XFEL beams are described.
In Chapter 5, various methods of improving the reflectivities of Pt/C multilayers are
discussed, and the results of Pt layer thinning and C-doping tests are presented.
In Chapter 6, XFEL sub-10-nm focusing optics and focusing strategies are described, andthe wavefront measurement method developed to examine the focused state of the XFEL
nanobeam is discussed. The results of using this method for accurate mirror alignment and the4Chapter 1. Introduction

measured residual surface shape errors of the mirror optics are presented. Then, the initialcommissioning of the XFEL sub-10-nm focusing optics at SACLA is described.
Finally, in Chapter 7, the conclusions of this study are summarized.

Chapter 2

REFLECTIVE FOCUSING OPTICS FOR
X-RAY FREE-ELECTRON LASERS
XFELs produce unprecedented high brilliance, excellent spatial coherence, and ultrafast pulse
duration. The Linac Coherent Light Source [22] in the USA and SACLA [17] in Japan haverecently achieved lasing in the hard X-ray regime. Additional hard XFEL facilities are underconstruction in many countries, e.g., the European XFEL in Germany, the Pohang Accelerator
Laboratory XFEL in South Korea, and the SwissFEL in Switzerland. These X-ray sources, inconjunction with analysis methods, provide unique capabilities, and their application to
exploring new frontiers of science can be advanced by using focusing optics.

2.1 X-ray Focusing with Reflective Optics
The use of focusing optics enables further enhancement of X-ray intensity, expanding the range
of applications of XFELs. Several optical focusing devices, such as Fresnel zone plates [23,24],
refractive lenses [25], and reflective mirrors [18,26], have been utilized in XFEL facilities.
Amongst these, reflective mirrors achieve the highest focusing efficiencies with long working
distances; therefore, they provide significant advantages in various applications. In this section,
X-ray focusing with reflective optics and the focal spot sizes achievable by using this method
are described.
X-rays are high-frequency electromagnetic waves. Therefore, the diffraction-limited focal
5

6

Chapter 2. Reflective Focusing Optics for X-ray Free-Electron Lasers

spot size D of an X-ray beam, based on Fraunhofer diffraction theory [27], is given by

D=

l
,
2 NA

(2.1)

in the case of a rectangular aperture, where λ and NA are the X-ray wavelength and numericalaperture of the incoming beam, respectively. NA is given by

NA = n sin q ,(2.2)

where θ and n are the convergent angle of the incoming beam and the refractive index (n ≤ 1usually in the X-ray regime), respectively. If the spot size is defined by the full width at half
maximum (FWHM) of the intensity on the focal plane, the spot size DFWHM is given by

DFWHM = 0.44

l
.
NA

(2.3)

The essential lower limit of the spot size is comparable to λ, since NA is generally smaller than
1.
However, large convergent angles, NA ≈ 1, are currently impossible to attain in the X-ray
regime, since transmission without reflection occurs when the incidence angle becomes large.
Therefore, the fundamental upper limit of NA is severely restricted by the effective value of NA,
which is optical-element dependent. Attempts to estimate the theoretically available lower limitof the focal spot size, i.e., the upper limit of NA, in diffraction-limited conditions have beenreported. For example, in the Kirkpatrick–Baez (KB) optical system [28] (see Fig. 2.1), whichis the typical X-ray reflective focusing system, the upper limit of NA is the equivalent to thecritical angle of the surface material of the total reflection mirror. Therefore, D is given by

D³

l
,
2q c

Fig. 2.1. Schematic of KB mirror geometry, where two concave mirrors arearranged orthogonally.

(2.4)

2.1 X-ray Focusing with Reflective Optics

7

since the critical grazing incidence angle is sufficiently small, sinθc ≈ θc. In the total reflection
condition, θc is restricted by the surface material. Even for high-density materials, such as Pt(21.45 g/cm3), θc is only 8 mrad at a photon energy of 10 keV. In contrast, employing a
multilayer coating enables the use of a large grazing incidence angle 3–4 times larger than thecritical angle at which total reflection occurs, thus allowing spot sizes 3–4 times smalleraccording to Eq. (2.4).
The geometry of an ellipsoidal focusing mirror is depicted in Fig. 2.2, showing that the two
focal points of the ellipse become the source and the focus. Typically, the major and minor axes
are several tens of meters and several tens of millimeters long, respectively. The grazing
incidence angle on the optical axis is θ2, with θ1 ~ θ3, where θ1 < θ3.
A schematic of a multilayer mirror, and the difference between the total reflection conditionof a single-layer mirror and the Bragg refraction condition of a multilayer mirror, are shown in
Fig. 2.3. If the influence of refraction is ignored, the shape of each interface of the multilayer
film follows part of the ellipse, each with a slightly different eccentricity. Moreover, to design
multilayer mirrors, it is necessary for the difference of each optical path to be an integral
multiple of the X-ray wavelength. The light impinging on each interface will then be reflected
towards the focal point, and the ideal diffraction-limited focusing conditions, such as
constructive interference at the focal point, will be satisfied. The multilayer period is nonuniform at each point on the mirror surface since the incidence angle changes, resulting in alaterally graded multilayer mirror. The advantage of replacing the single-layer mirror with amultilayer mirror is the large convergent angle of the incident X-rays, as shown in Fig. 2.3(b).

Fig. 2.2. Ellipsoidal focusing mirror geometry.

8

Chapter 2. Reflective Focusing Optics for X-ray Free-Electron Lasers

Fig. 2.3. (a) Multilayer mirror schematic: thick black lines represent multilayerinterfaces. (b) Differences between total reflection from single-layer mirror andBragg reflection from multilayer mirror.

2.2 Multilayer Films for X-ray Focusing

9

2.2 Multilayer Films for X-ray Focusing
A multilayer film is an X-ray optical element utilizing Bragg diffraction from an artificial
periodic structure consisting of alternating layers of two or more optically dissimilar
components. Bragg diffraction from the constructive interference of the multilayer film canoccur at large grazing incidence angles, which are sufficiently larger than the critical angle atwhich total reflection occurs.
X-rays can penetrate substances easily when the incidence angle is larger than the criticalangle. Therefore, periodically layered structures inside the material will cause reflected waves
to interfere with each other. When the optical path difference between the reflected waves isequal to an integer multiple of the wavelength, a high reflectivity will be obtained. Thiscondition is Bragg’s law [5] and can be written as

ml = 2d sin q ,(2.5)

where m, λ, d, and θ are the Bragg index, incident X-ray wavelength, multilayer period, andgrazing incidence angle, respectively. Considering refraction inside the materials, Eq. (2.5) canbe written as

ml = 2d sin q m 1 -2d - d 2,
sin 2 q m

(2.6)

where θm is the mth-order grazing incidence Bragg angle, and δ is the real part of the complex
refractive index n. Equation (2.7) defines n to ben = 1 - d - ib ,(2.7)

where δ and β are related to the real (refraction) and imaginary (absorption) parts of n,
respectively, and are given byr l 2 N A r m f1
2p A

(2.8)

r l 2 N A rm f2
,
2p A

(2.9)

d= e
and

b= e

where re, NA, ρm, and A are the classical electron radius, Avogadro’s constant, the material
density, and the atomic weight, respectively. The variables f1 and f2 represent the real and10

Chapter 2. Reflective Focusing Optics for X-ray Free-Electron Lasers

imaginary parts of the anomalous dispersion factors, respectively.
Multilayer films have artificial periodic structures, consisting of alternating layers of two
optically dissimilar components. A material with a high atomic number (Z) is used to obtain ahigh reflectivity, and a low-Z material is used as the spacer. Various material combinations havebeen researched for use as focusing mirrors and monochromators in the hard X-ray regime.
Predominately, Cr, Ni, Mo, W, and Pt have been used as high-Z materials, while B4C, C, and Si
have been used as low-Z materials [29–38]. In this study, Pt was used as the high-Z element
because it exhibits adequate reflectivity and chemical stability, and C was used as the low-Z
element because it possesses sufficiently low absorptivity in the hard X-ray regime and isresistant to thermal interdiffusion.
A brief theoretical background of X-ray reflection and X-ray standing waves (XSWs) in aperiodical multilayer is as follows. The multilayer structure consists of N bilayers of alternating
high- and low-Z materials, as shown in Fig. 2.4. A plane electromagnetic wave of frequency ωin the jth layer of a medium, at a position r, can be described by [39]E j (r ) = E j exp éë -i ( k j × r - wt ) ùû ,(2.10)

where Ej is the field amplitude at the top of the jth layer, and kj is the wave vector in the materialof the jth layer. The z-component of the wave vector is given by

k jz =

2ple j - cos 2 q ,(2.11)

where θ is the grazing incidence angle, and λ is the incident X-ray wavelength. The dielectric
function in the jth layer, εj, is given by

e j = 1 - 2d j - i 2 b j .

(2.12)

Here, δj and βj are the real and imaginary parts of the complex refractive index of the jth layer,
respectively.
In the X-ray regime, there is no significant difference between s and p polarizations [40];thus, the expression for s polarization can be adopted. The Fresnel equations for the reflection
and transmission coefficients, rj and tj, respectively, at the interface between layers j and j+1
are given by2.2 Multilayer Films for X-ray Focusing

Fig. 2.4. Schematic of transmitted (Et) and reflected (Er) plane electromagnetic
waves inside multilayer.

11

12

Chapter 2. Reflective Focusing Optics for X-ray Free-Electron Lasers

rj =k jz - k j +1, z(2.13)

k jz + k j +1, z

and
tj =

2k jz
k jz + k j +1, z.

(2.14)An expression to consider attenuation due to the interface roughness σj, the root-mean-square(RMS) deviation at the interface of layers j and j+1, was previously derived [41,42]. Here, rj
and tj are multiplied by factors Sj and Tj, respectively, which are given by
S j = exp éë -2s 2j k jz k j +1, z ùû

(2.15)

2
T j = exp éês 2j ( k jz - k j +1, z ) / 2 ùú .
ë
û

(2.16)

andThe behavior of electromagnetic waves in a multilayer system consisting of multiple interfaces
can be calculated by recursive [40,43] or matrix [42] methods. In the following derivation, therecursive method is used. The amplitudes of the transmitted and reflected plane waves at the
top of the jth layer, Etj and Erj, respectively, are given by

E rj = exp éë -2ik jz d j ùû Aj E tj

(2.17)

and
E

t
j +1

=

exp éë -ik jz d j ùû E tj t jT j

1 + exp éë -2ik j +1, z d j +1 ùû Aj +1rj S j,(2.18)

where

Aj =

rj S j + exp éë -2ik j +1, z d j +1 ùû X j +1

1 + exp éë -2ik j +1, z d j +1 ùû Aj +1rj S j(2.19)and dj is the thickness of the jth layer.
The X-ray reflectivity R can be calculated from the ratio of the field amplitudes at the
sample surface:2.2 Multilayer Films for X-ray Focusing

13

2

E0r
R (q ) = t .
E0(2.20)The XSW field intensity at each interface of the multilayer can be obtained using Eqs. (2.17)–(2.19), and the inside of the jth layer can be interpolated to be an interface between thetransmitting and reflecting plane waves as [44,45]

I (q , z ) = E tj exp éë -2k ¢¢jz z ùû + E rj exp éë 2k ¢¢jz z ùû + 2 E tj E rj cos (n + 2k ¢jz z ) ,22(2.21)

where z and ν are the depth from the top of the jth layer and the phase difference between Erj
and Etj, respectively. The variables k'jz and k"jz are the real and imaginary parts of the component
kjz, respectively.
The calculated X-ray reflectivities and XSW field intensities of the Pt/C multilayers areshown in Figs. 2.5–2.7 and Fig. 2.8, respectively, for an X-ray photon energy of 10 keV (λ =0.124 nm). The X-ray reflectivities were calculated as functions of three quantities: the grazing
incidence angle (Fig. 2.5); γ (= dhigh/d), the ratio of the thickness of the high-Z layer to the total
thickness of the bilayer (Fig. 2.6); and the multilayer period (Fig. 2.7). In Fig. 2.5, it can beseen that high reflectivity peaks were obtained in the Bragg condition (Eq. (2.6)). The vibrationsof the reflected intensity, which are called Kiessig fringes [46], enable determination of theFig. 2.5. Calculated X-ray reflectivities versus grazing incidence angle (fixedparameters γ = 0.25, N = 50).

14

Chapter 2. Reflective Focusing Optics for X-ray Free-Electron Lasers

thickness of the multilayer period. In Fig. 2.6, the γ range from 0.2 to 0.5 is optimal for the firstorder Bragg diffraction, with a small dependence on N. For the second-order diffraction, thereflectivity is approximately 0 at γ = 0.5. The XSW field intensities were calculated as functionsof the grazing incidence angle and the depth of the multilayer medium, as shown in Fig. 2.8.

Fig. 2.6. Calculated X-ray reflectivities of (a) first- and (b) second-order Bragg
diffractions versus γ (fixed parameter d = 3 nm).

Fig. 2.7. Calculated X-ray reflectivities of (a) first- and (b) second-order Bragg
diffractions versus multilayer period (fixed parameter γ = 0.25).

2.2 Multilayer Films for X-ray Focusing

Fig. 2.8. Calculated XSW field-intensity distributions in multilayer structure, asfunctions of grazing incidence angle and depth of multilayer medium. Dashed whitelines represent first-order Bragg angle. (a) d = 2.5 nm, γ = 0.5, N = 40; (b) d = 6 nm,
γ = 0.25, N = 40.

15

16

Chapter 2. Reflective Focusing Optics for X-ray Free-Electron Lasers

2.3 Reflective Focusing Optics Used at SACLAAt SACLA, 1 μm [26] and 50 nm [18] XFEL focusing has previously been demonstrated byutilizing total reflection focusing mirrors. The schematics of the optical configurations and theoptical design parameters used to obtain 1 μm and 50 nm focusing are shown in Fig. 2.9 andTable 2.1 and in Fig. 2.10 and Table 2.2, respectively.
The 1 μm focusing system [26] realized an FWHM beam size of 0.95 μm (horizontal
direction, H) × 1.20 μm (vertical direction, V), at a photon energy of 10 keV. The photon flux
density of the focused beam was 4 × 104 times higher than that of the unfocused beam. A peak
power density of 6 × 1017 W/cm2 was achieved, at a pulse energy of 98 μJ and a pulse durationof 20 fs [47]. To reduce XFEL-induced irradiation damage, sufficiently long mirror substrates
and small grazing incidence angles were utilized. The mirror surfaces were coated with 50 nm
of C so that they would be highly reflective, since C and quartz have reflectivities ofapproximately 99.9% and 99%, respectively, up to photon energies of 20 keV. The resulting
high-intensity focused beams are appropriately sized for various applications, such as X-ray
coherent diffraction imaging [48–51] and observations of other physical phenomena [52,53].
The 50 nm focusing system [18] realized an FWHM beam size of 55 nm (H) × 30 nm (V)at a photon energy of 9.9 keV. The peak power density achieved was 1.2 × 1020 W/cm2, whichis 200 times higher than that of the 1 μm focused beam, at a pulse energy of 11 μJ and a pulse
duration of 7 fs [47]. To obtain a large NA, and a long working distance with small beam
divergence, a two-stage reflective focusing system was used. In the first (upstream) stage, an
uncoated total reflection KB mirror was used for beam expansion. In the second (downstream)
stage, a single-layer metal-coated KB mirror focused the expanded beam. Beams focused using
this method have been applied to studies of nonlinear X-ray optical phenomena, such as twophoton absorption [19], saturable absorption [20], and Cu-atomic inner-shell lasers [21].

2.3 Reflective Focusing Optics Used at SACLA

17

Fig. 2.9. Schematic of optical configuration of XFEL 1 μm focusing system at
SACLA.

Table 2.1. Optical parameters of XFEL 1 μm focusing system at SACLA.
Vertical direction

Horizontal direction

focusing mirror

focusing mirror

Surface shape

Elliptical cylinder

Elliptical cylinder

Substrate material

QuartzQuartzCoating material

CarbonCarbonCoating thickness (nm)50

50

Substrate size (mm3)420 × 50 × 50

420 × 50 × 50

1.55

1.50

Focal length (m)

2.00

1.55

Distance from source (m)120.00120.45Semi-major axis (m)51

51

Semi-minor axis (mm)

21.9

18.7

Grazing incidence angle
on mirror center (mrad)

18

Chapter 2. Reflective Focusing Optics for X-ray Free-Electron Lasers

Fig. 2.10. Schematic of optical configuration of XFEL 50 nm focusing system at
SACLA.

Table 2.2. Optical parameters of XFEL 50 nm focusing system at SACLA.
Upstream focusing mirrors

Downstream focusing mirrors

VerticalHorizontal

Horizontal

Verticaldirection

direction

direction

direction

Elliptical

Elliptical

Elliptical

EllipticalcylindercylindercylindercylinderSubstrate material

QuartzQuartzQuartzQuartzCoating material

None

None

Platinum

Platinum

Coating thickness (nm)

None

None

50

50

Substrate size (mm3)

400×50×50

400×50×50

500×50×50

465×50×50

1.5

1.5

5.5

5.0

Focal length (m)

6.520

6.070

1.115

0.582

Distance from source (m)120.00120.4572.24772.780Semi-major axis (m)120.000

120.450

36.68

36.68

Semi-minor axis (mm)

42.0

40.6

49.4

32.6

Surface shape

Grazing incidence angle
on mirror center (mrad)Chapter 3

PREPARATION AND MEASUREMENT OF
MIRROR SUBSTRATES
Mirrors are among the most widely used optical devices, and the surface shape of a mirror
significantly affects the quality of X-rays at the sample position. Planar or nearly planar
surfaces can be measured using interferometry (e.g., microstitching interferometry (MSI) [56]and relative-angle determinable-stitching interferometry (RADSI) [57,58]), slope profilers (e.g.,long trace profilers (LTPs) [59,60] and nanometer optical component measuring machines(NOMs) [61]), and coordinate measuring machines (CMMs) [62]. However, the focusing
mirrors used for soft X-ray focusing and single-nanometer hard X-ray focusing have minimum
radii of curvature of a few meters. Thus, it is difficult to measure the surfaces of these mirrors
using conventional methods. We developed a new measurement system that uses a laser
autofocus microscope as a probe to measure steeply curved mirrors.

3.1 Reflective Mirrors for XFEL Focusing
Reflective mirrors are the most widely used optical elements in synchrotron radiation facilities
and are employed to collimate and focus X-rays and to filter high-order light frequencies. The
shapes of X-ray mirrors must be more accurate than those of visible light mirrors because Xrays have wavelengths much shorter than those of visible lights. Mirror surface shape errors are
the factors that most significantly degrade the focusing of X-rays. The phase error φ of a19

20

Chapter 3. Preparation and Measurement of Mirror Substrates

reflected X-ray that originates from the shape error is

j = 2hk sin q ,(3.1)

where h and θ are the peak-to-valley (PV) height shape errors of the mirror surface and thegrazing incidence angle, respectively, and k is the X-ray wavenumber, which is given by

k=

2p

l

,

(3.2)

where λ is the X-ray wavelength. The degree of constructive interference is significantly
influenced by the phase error. According to Rayleigh’s criterion [27], an image is not
significantly degraded unless it has wavefront aberration of greater than λ/4 in the imaging
optical system. The height error of a mirror surface corresponding to a λ/4 phase error (i.e. π/2rad) ishl /4 =

l.
8sin q(3.3)

For example, in the case of an X-ray wavelength of 0.124 nm (i.e., a photon energy of 10 keV),
the required shape accuracy is as shown in Fig. 3.1.
The required shape accuracies of the 1 μm and 50 nm focusing mirrors whose opticalFig. 3.1. Height error corresponding to λ/4 phase error at photon energy of 10 keV.

3.1 Reflective Mirrors for XFEL Focusing

21

parameters were described in Tables 2.1 and 2.2 are approximately 10 nm and 2.8 nm (PV),respectively, because the grazing incidence angles are 1.5 mrad and 5.5 mrad, respectively. The
designed optical parameters of XFEL sub-10-nm focusing mirrors, which were the target opticalsystems of this study, are shown in Table 3.1.
Table 3.1. Designed parameters of XFEL sub-10-nm focusing mirrors.
Horizontal direction

Vertical direction

380

100

14.6

13.2

Focal length (m)

0.380

0.070

Distance from source (m)79.07272.372Semi-major axis (m)39.69636.221Semi-minor axis (mm)73.43829.710Mirror length (mm)Grazing incidence angle
on mirror center (mrad)

The grazing incidence angles of the sub-10-nm focusing mirrors are greater than those for otheroptics. Correspondingly, the required shape accuracy is ~1 nm (PV), which is higher than theaccuracies required by the other optics. Furthermore, as the surface shape steepness increases,
measurement becomes more difficult. The surfaces of the sub-10-nm focusing mirrors are thesteepest among the three optical systems shown in Fig. 3.2.
The surface shape profiles of the sub-10-nm focusing mirrors are shown in Fig. 3.3. The
lengths of the horizontal and vertical mirrors are 100 mm and 380 mm, respectively. In Fig. 3.3,
the black, red, and blue lines represent the heights, radii of curvature, and slopes of these mirrors,
respectively. The vertical focusing mirror has a wide slope range of 14 mrad and a small radiusof curvature of 1.62 m. The horizontal focusing mirror also has a wide slope range of 11 mradover a long range of 380 mm. Therefore, a new system is necessary that can measure a wideslope range and small radius of curvature with an accuracy of nearly 1 nm.
The typical measurement methods for X-ray mirrors involve using slope profilers, stitchinginterferometers, and CMMs. Recently, slope profilers [59–61] and stitching interferometers[56–58] have been primarily used. Slope profilers can perform highly accurate measurements

22

Chapter 3. Preparation and Measurement of Mirror Substrates

Fig. 3.2. Surface shape profiles of 1 μm, 50 nm, and sub-10-nm XFEL focusing
mirrors, whose optical parameters are given in Tables 2.1, 2.2, and 3.1, respectively.
because they do not have reference planes. Interferometers are used to measure high spatial
frequencies in two dimensions. On the other hand, CMMs are not currently used to measure Xray optics, as their accuracies are insufficient to determine shape errors with the accuracy
required in X-ray mirror substrate measurements. However, if their accuracies are improvedand become acceptable, CMMs could be very useful for measuring steeply and twodimensionally curved mirrors, since their dynamic ranges are more extensive than those of theother methods. Therefore, we are developing a new system that uses the CMM method.
Additionally, after developing this system, we will cross-check its results with those obtainedusing other methods in order to advance X-ray optics measurements.

3.1 Reflective Mirrors for XFEL Focusing

Fig. 3.3. Surface shape profiles of XFEL sub-10-nm focusing mirrors of the (a)horizontal and (b) vertical directions.

23

24

Chapter 3. Preparation and Measurement of Mirror Substrates

3.2 Development of Surface Shape Measurement System
3.2.1 Apparatus Overview
The surface shape measurement system developed to measure steeply curved surfaces is shownin Fig. 3.4. The main components of this apparatus are a main probe to perform steeply curved
surface measurements, sub-probes to measure the posture error of the main probe, and akinematic stage. In this study, the apparatus was placed in a temperature-controlled room inside
a class-1 cleanroom, whose temperature was also controlled. The graph in Fig. 3.4(b) depicts
the temperatures outside and inside the room, both of which are very stable. In particular, thetemperature stability inside is very high, exhibiting variations of less than ±0.01 °C. A counterbalance is used to prevent center-of-gravity movement and to suppress the elastic deformationof the metrology frame.

Fig. 3.4. Schematic of shape measurement apparatus.

3.2 Development of Surface Shape Measurement System

25

A laser autofocus microscope (MP-3P, Mitaka Kohki), which is optimal for measuring
steeply curved surfaces, is used as the main probe in this system. A principle diagram is shownin Fig. 3.5. First, light emitted from the laser irradiates the sample surface through an objective
lens. Then, the light reflected from the sample surface goes to the center of an auto-focus (AF)sensor through the objective and imaging lenses. If the distance between the objective lens andthe sample is varied, the position of the light on the AF sensor also varies. To maintain theposition of the light on the sensor, the objective lens moves upwards and downwards. The
surface shape is determined based on the magnitude of movement of the objective lens. The
elemental parts were upgraded from the commercially available machine (MP-3, Mitaka Kohki[63]) to increase the sensitivity of the AF sensor. The linear scale was also upgraded to a
resolution of 0.034 nm. The angular dependence of the laser autofocus microscope is measured
by MP-3. In this study, the sample was a 5-mm-diameter glass sphere, whose measured surface
profile is shown in Fig. 3.6(a). The error with respect to an ideal spherical surface is shown in
Fig. 3.6(b), as a function of the surface angle. There is no angular dependence within ±30° (~0.5rad), which is sufficiently large to measure the surfaces of focusing mirrors (Fig. 3.3).

Fig. 3.5. Principle diagram of laser autofocus microscope.

26

Chapter 3. Preparation and Measurement of Mirror Substrates

Fig. 3.6. Angular dependence of laser autofocus microscope measured using 5-mmdiameter glass sphere: (a) measured surface profile and (b) error compared to ideal
spherical surface.

Fig. 3.7. Schematic of probe table.

3.2 Development of Surface Shape Measurement System

27

Three heterodyne interferometers (Zygo ZMI 4000) are used as sub-probes and are locatedon the same table as the main probe to measure the posture of the main probe. The schematicof the probe table is shown in Fig. 3.7. The laser autofocus microscope is positioned at thecenter of the table, and the heterodyne interferometers are positioned at the three indicatedlocations. A reference mirror is placed under each heterodyne interferometer. The heterodyne
interferometers are used to measure the posture of the probe table and to correct the value
measured by the main probe accordingly.

3.2.2 Repeatability Test using Planar Mirror
The measurement repeatability of the shape-measurement apparatus was tested using a nearlyflat surface mirror as a measurement object. The size of the mirror was 400 mm (length) × 50
mm (width) × 50 mm (height), and it was composed of Si. The testing conditions are shown in
Table 3.2.
Table 3.2. Conditions for testing measurement repeatability using planar mirror.
Step length

Number of steps

Speed

1 mm

380

1 mm/sAveraging
50 at each point
20 lines

The average number of measurements at each point was 50, and the average number of lines
was 20. Therefore, the total number of measurements taken and averaged at each point was
1,000. The repeatability was tested by comparing two independent measurements, and theresults are shown in Fig. 3.8. The solid and dashed black lines represent the first and second
measurements, respectively, and the solid red line represents the difference between the firstand second measurements. Figure 3.8(a) is the result measured using only the laser autofocus
microscope. This profile includes the surface profiles of the measured object and the postureerror of the probe table due to the bending of the stage guide, etc. Figure 3.8(b) shows themeasurements made using only the heterodyne interferometers. This profile includes the surface
profiles of the reference mirrors and the posture error of the probe table due to the same factors.

28

Chapter 3. Preparation and Measurement of Mirror Substrates

Fig. 3.8. Results of repeatability test: (a) surface profile of measured object, (b)surface profiles of reference mirrors, and (c) repeatability error.

3.2 Development of Surface Shape Measurement System

29

Both figures show the same posture error. Therefore, the error could be eliminated bysubtracting the results in Fig. 3.8(b) from those in Fig. 3.8(a). If the errors of the results shownin Figs. 3.8(a) and 3.8(b) were equal, the repeatability error would become zero. Figure 3.8(c)shows conclusive evidence that the developed apparatus can achieve measurements that are
repeatable to within ~2 nm (PV). This value is not small; however, high-frequency fluctuations
can be reduced by the interferometer.

3.3 Fabrication and Measurement of XFEL Sub-10-nm Focusing
Mirrors
To fabricate XFEL sub-10-nm focusing mirrors with highly precise elliptical shapes, numericalcontrol machining was performed by using elastic emission machining (EMM) [64–66],
stitching interferometers (MSI [56] and RADSI [57]), and the newly developed instrument.
EEM is a processing method utilizing a solid chemical reaction between particles, such as
metal oxides, and the workpiece surface. Figure 3.9 shows a conceptual diagram of EEM. Whenthe reactive particles are supplied to the surface by a flow of ultrapure water, the atoms of theworkpiece surface and the particles are chemically coupled via oxygen. Atom-by-atom removal
can be realized by carrying away the particles using ultrapure water, which can chemicallycouple to the atoms of the workpiece surface. Figure 3.10 presents schematic diagrams ofprocesses using nozzle-type and rotating-ball-type machining heads. In nozzle-type EEM, theworkpiece is processed by using slurry jet from the nozzle with an appropriate pressure, suchas 0.2 MPa. The removal spot shape can be easily controlled in this type of machining bychanging the nozzle shape, supply pressure, and particle size. In rotating-ball-type EEM, bygenerating physically stable elastohydrodynamic lubrication conditions between the workpieceand the surfaces of the rotating spheres, the particles are fed to the workpiece surface. Byutilizing the parallel flow generated in this area, rotating-ball-type EEM was found to besuitable for automatic smoothing of regions with the spatial wavelengths shorter than 0.1 mm.

30

Chapter 3. Preparation and Measurement of Mirror Substrates

Fig. 3.9. Conceptual diagram of EEM.

Fig. 3.10. Schematic diagrams of processes using (a) nozzle-type and (b) rotatingball-type machining heads. Arrows indicate direction of water flow.
To perform the surface shape measurements, MSI using a Michelson-type white lightinterferometer (Zygo NewView 5000) was employed in the high spatial frequency range, and
RADSI using a Fizeau-type phase-shifting interferometer (Zygo GPI-XD/D) and the newly
developed instrument were employed in the low spatial frequency range. The residual shapeerrors obtained after deterministic figuring are shown in Fig. 3.11. The obtained shape accuracy
is ~3 nm (PV) and includes some ambiguity because of the high curvature of the surface. We
confirmed the final shape using wavefront measurements, which will be described later.

3.3 Fabrication and Measurement of XFEL Sub-10-nm Focusing Mirrors

Fig. 3.11. Residual shape errors of (a) horizontal and (b) vertical direction focusing
mirrors.

31

32

Chapter 3. Preparation and Measurement of Mirror Substrates

3.4 Summary
XFEL sub-10-nm focusing mirrors have steeply curved surfaces that are difficult to measureusing conventional shape measurement methods. Their minimum radii of curvature are a few
meters, and their slope ranges are several dozen milliradians. Furthermore, the required
accuracy, or Rayleigh criterion, of the surfaces of such mirrors is ~1 nm (PV). Therefore, wedeveloped a laser autofocus microscope system featuring a position correction mechanism
utilizing three heterodyne interferometers to provide measurements at this level of accuracy.
The apparatus could be consistently adjusted to within 2 nm (PV), as demonstrated by arepeatability test.
The sub-10-nm focusing mirrors used in this study were fabricated by EEM and measured
by MSI, RADSI, and the newly developed instrument. The residual shape errors typicallyobtained after deterministic figuring of the sub-10-nm focusing mirrors were ~3 nm (PV). Theseerrors are somewhat high; however, we confirmed the final shape using wavefront
measurements, which will be described later.

Chapter 4

TOLERANCE OF MULTILAYER FILMS
TO X-RAY FREE-ELECTRON LASERIRRADIATION
One of the critical requirements of the X-ray optical elements for XFELs is sufficient tolerance
to intense X-ray irradiation. Therefore, the X-ray damage thresholds of various opticalmaterials in normal and grazing incidence conditions have been extensively investigated. The
damage threshold in the normal incidence condition was theoretically estimated using theamount of absorption energy per atom, while in the grazing incidence condition, it wasevaluated by considering the energetic photoelectrons that can remove deposited energy froman interaction region [68]. These models have been experimentally verified [69–77]. However,the damage to multilayers induced by XFEL exposure has not been investigated in the hard Xray regime. In order to investigate this damage in this study, focused and unfocused XFELs
were used at a photon energy of 10 keV to provide a sufficiently high intensity and actual
operating conditions.

4.1 Development of Thin Film Deposition System
4.1.1 Apparatus Overview

33

34

Chapter 4. Tolerance of Multilayer Films to X-ray Free-Electron Laser Irradiation

The thin film deposition system developed to fabricate a laterally graded multilayer is shownin Figs. 4.1 and 4.2. Our X-ray focusing mirror design requires optical thin film deposition in aregion elongated in the longitudinal direction of the mirror substrate. A mirror substrate that islong in the longitudinal direction is required to allow for the small divergence of the XFEL.
The deposition apparatus was therefore designed for deposition over an elongated area of 500
mm (length) × 50 mm (width), sufficient to produce XFEL focusing mirrors.
As shown in Fig. 4.1, three direct current (DC) magnetron sputtering cathodes (Kurt J.
Lesker Company) with 2-inch targets were mounted in this apparatus. Magnetron sputtering isa widely used deposition method and is generally considered to enable reproducible subnanometer control of the deposition thickness [78]. Two targets can be used concurrently in one
deposition area to allow the mixing of two materials. The mixing ratio is controlled by adjusting
the sputtering cathode power, since the deposition rates are proportional to the input power.
Slits and shutters were mounted between the substrate and the sputtering cathode to limit theparticle flux to a local deposition area. The substrate was placed on a speed-controlled
horizontal scanning stage, and the distance from the target to the substrate was approximately
100 mm.
The elemental performance of the deposition apparatus was tested by depositing Pt and C
single-layer thin films. To achieve highly accurate thickness control, it was necessary to
determine the spatial distributions of the sputtered atoms accurately. The thickness distributionsof the deposited Pt and C films were measured precisely under predetermined conditions by a
Fizeau interferometer (ZYGO GPI XP/D). The interferometer method is not suitable for direct
measurements of the thickness distributions of thin films, but rather is intended formeasurements of the surface shapes of homogeneous substrates. The shape profiles obtained
might not accurately represent the shape of the outermost surface, due to the influences of thedifference between the reflectivities of the thin film and the substrate and the light reflectedfrom the interface between the thin film and the substrate. To overcome these problems, asufficiently thick Pt film of ~50 nm was deposited on the substrate in advance.
A spatially limited Pt film was deposited thereon, and the surface shape was then precisely
measured by the interferometer. The deposition thickness distribution was calculated from thedifference between the surface shape profiles before and after film deposition. Measurement of
the C film was performed after deposition of another sufficiently thick Pt film on the C surface.

4.1 Development of Thin Film Deposition System

Fig. 4.1. Schematic of thin film deposition apparatus.

Fig. 4.2. Photograph of thin film deposition apparatus.

35

36

Chapter 4. Tolerance of Multilayer Films to X-ray Free-Electron Laser Irradiation

The measured film thickness distributions of the Pt and C films are shown in Figs. 4.3 and 4.4,
which were obtained using the deposition conditions listed in Table 4.1.
Table 4.1. Deposition conditions for Pt and C deposition spots.
DC input power (W)Deposition time

Ar flow rate (sccm)

Ar pressure(Sputter gun 1 / 2 / 3)(min)

(Sputter gun 1 / 2 / 3)

(Pa)

Pt

10 / 0 / 040

16 / 10 / 10

0.11

C

0 / 120 / 120

40

16 / 10 / 10

0.11

SampleIn Figs. 4.3 and 4.4, the horizontal direction corresponds to the longitudinal direction of thesubstrate. The slit used to limit the extent of the deposition region had dimensions of 30 mm(length direction) × 10 mm (width direction). The measured deposition distributions give
deposition rates of Pt and C of 2.53 nm/min and 1.71 nm/min, respectively. The deposition rateof C was significantly lower than that of Pt, even at higher input powers, due to the difference
between the Pt and C sputtering rates and the different responses of Pt and C to the Ar atom
impacts [78,79]. At the C deposition spot, the entire substrate was distorted convexly, as can beseen in Fig. 4.4, due to the film stress caused by the subsequent Pt deposition. This substratedeflection should be corrected when evaluating the C deposition distribution, and the correcteddistribution is shown by the dashed line in Fig. 4.4(a).

4.1.2 Differential Deposition Test for Mirror Shape Modification
XFEL sub-10-nm focusing mirrors must have extremely accurate surface shapes. As describedin Chapter 3, the required shape accuracy across the entire mirror substrate is typically ~1 nm(PV). In addition, the spatial wavelength components of several parts of the mirror length areparticularly important to obtain an ideally focused beam. The remaining residual shape errors
from the mirror manufacturing process distort the reflected wavefronts and ultimately
determine the quality of the focused beam. Therefore, it was planned to obtain the final shapecorrection by the differential deposition of a Pt thin film, since it has very high reliability and4.1 Development of Thin Film Deposition System

Fig. 4.3. (a) Thickness distribution of Pt deposition spot. (b) Thickness profile along
center line of (a).

Fig. 4.4. (a) Thickness distribution of C deposition spot. (b) Thickness profile along
center line of (a). In (b), dashed line represents correct profile after correcting
substrate deflection.

37

38

Chapter 4. Tolerance of Multilayer Films to X-ray Free-Electron Laser Irradiation

precision despite the relative simplicity of the method.
A differential deposition test was performed using the deposition apparatus. In this test, thespatial wavelengths of the created shape were set to 10–20 mm with a slit size of 2 mm (length
direction) × 10 mm (width direction). The creation of shapes with shorter spatial wavelengths
is also possible by using narrower length direction slits. The scan speed of the substrate stage
was calculated by deconvoluting the deposition spot and the designed film thickness
distribution. The thickness profile of the Pt deposition spot for the differential deposition isshown in Fig. 4.5. The deposition conditions were a 20 W input power and 20 sccm Ar flowrate for a deposition time of 20 min. As shown in Fig. 4.5, a sufficiently short horizontal
distribution was obtained. The designed and measured thickness distributions agree well, as
shown in Fig. 4.6. The residual errors are 1.46 nm (PV) and 0.28 nm (RMS), without low-passfiltering, which include measurement errors, as shown in Fig. 4.7. Eventually, the deposition
error was considered to be less than 1 nm (PV), as can be seen from the data obtained by using
a 200 Hz low-pass filter (LPF) that are shown in Fig. 4.7.

Fig. 4.5. Thickness distribution of Pt deposition spot for differential deposition. (a)Thickness distribution of deposition spot. (b) Thickness profile along center line of(a).

4.1 Development of Thin Film Deposition System

Fig. 4.6. Designed and measured thickness distributions.

Fig. 4.7. Residual errors of differential deposition with and without LPF. PV and
RMS errors are represented.

39

40

Chapter 4. Tolerance of Multilayer Films to X-ray Free-Electron Laser Irradiation

4.2 Evaluation of Breakdown Threshold using Focused XFEL[80]An experiment was performed at SACLA using 1 μm focusing optics [26] at a photon energyof 10 keV, a pulse duration of <10 fs [47], and a repetition rate of 10 Hz. The experimental
system is shown in Figs. 4.8 and 4.9. The test sample was a Pt/C multilayer with 40 bilayers
having a multilayer period of 3 nm with a ratio of the Pt layer thickness to the multilayer period
γ = 0.5, deposited on a commercially available Si (100) wafer using a DC magnetron sputteringsystem. The sample was placed at the focal point and was pre-aligned to the first-order Bragg
condition at a reduced X-ray intensity. The irradiation tests were performed using 100-shot
exposures in a fluence range of 0.01–10 μJ/μm2 using Si attenuators of various thicknesses. The
pulse energy fluctuation over 100 shots was approximately 10%.

Fig. 4.8. Schematic of experimental system for evaluation of breakdown thresholdof Pt/C multilayer.

Fig. 4.9. Photograph of experimental system for evaluation of breakdown thresholdof Pt/C multilayer.

4.2 Evaluation of Breakdown Threshold using Focused XFEL41

The damage threshold was determined by comparing the reflectivities, measured in
reduced intensity conditions, before and after the 100 shots of fluence-controlled irradiation.
The changes in reflectivity during the 100-shot exposure were also monitored.
The reflectivities before and after the fluence-controlled irradiation are presented in Fig.
4.10. As shown, the reflectivity does not change at fluences less than 0.051 μJ/μm2; however, anotable decrease is apparent as the fluence exceeds this value, corresponding to the damage
threshold of the Pt/C multilayer.
Typical reflectivity changes during the 100-shot exposures in different fluence conditions
are shown in Fig. 4.11(a). Images of the sample surfaces after exposure were obtained with an
optical microscope (OM) and are shown in Fig. 4.11(b). At a fluence of 0.051 μJ/μm2, nodamage is apparent in either the reflectivity data or the OM image. However, at fluences
considerably greater than the damage threshold, a scratch is noticeable in the OM image, witha corresponding rapid decrease to almost zero reflectivity. Interestingly, only the first pulse
exhibits the original reflectivity because the temporal duration of the X-ray pulses was much
faster than the changes in the multilayer structure. At a fluence of 0.11 μJ/μm2, just slightly
larger than the damage threshold, there is a slight decrease in the reflectivity, with little damage
observable in the OM image.
To investigate the detailed mechanisms behind the changes observed at the last condition,
θ-2θ scans were performed before and after irradiation at a reduced intensity and indicated ashift of the Bragg angle from 22.05 mrad to 21.98 mrad, together with a decrease in thereflectivity, as shown in Fig. 4.12(a). This shift corresponds to an expansion of the multilayer
period by approximately 0.3% on average over the irradiated area. Cross-sectional transmission
electron microscopy (TEM) images of a central part of the footprint were obtained before andafter irradiation and are shown in Figs. 4.12(c) and 4.12(b), respectively, indicating that themultilayer expanded by approximately 10% and that the expansion was widely distributed
across its footprint. The expansion may originate from intermixing at the interface and theintroduction of vacancies into the Pt layer, although further investigation is required to clarify
this phenomenon.
The damage threshold fluence Fth can be converted to the damage threshold dose Dth for asingle atom using the following expression [68,81,82]:

42

Chapter 4. Tolerance of Multilayer Films to X-ray Free-Electron Laser Irradiation

Fig. 4.10. Change in reflectivity versus irradiation fluence.

Fig. 4.11. (a) Changes in reflectivity versus number of pulses at each irradiation
fluence. (b)–(d) OM images of sample surface after 100 pulses of irradiation.

4.2 Evaluation of Breakdown Threshold using Focused XFEL

Fig. 4.12. (a) Bragg angle shift measurement by θ-2θ scan near first-order Bragg
angle. Measured pre- and post-irradiation Bragg angles were 22.05 mrad and 21.98
mrad, respectively. (b), (c) Cross-sectional bright-field TEM images of irradiatedand non-irradiated areas, respectively. Dark and bright layers correspond to Pt andC layers, respectively.

43

44

Chapter 4. Tolerance of Multilayer Films to X-ray Free-Electron Laser Irradiation

Dth =Fth (1 - R ) sin q
,
dQPt

(4.1)

where R and θ are the reflectivity and grazing incidence angle, respectively. In this study, R andθ were estimated to be 0.76 and 21.6 mrad, respectively, which were theoretically determinedbased on the multilayer design parameters. Here, QPt is the approximate quantity of Pt atoms,
which is given by

QPt =N A r Pt
N r
r
g + A C (1 - g ) C ,
APt
AC
r Pt

(4.2)

where NA, ρ, and A are Avogadro’s constant, density, and atomic weight, respectively, and thesubscripts Pt and C denote the Pt and C layers, respectively. The quantity of C atoms is included
as a converted quantity using a ratio of the general electron penetration depth, which isapproximately inversely proportional to the density [83]. Moreover, the energy deposition depth
d is given byd = d x2 + d e2 ,(4.3)

where dx and de are the X-ray penetration depth and electron collision range [84], respectively.
In this case, de was assumed to be 70 nm, which is twice the de value of a Pt single layer (35nm [85]), because electrons penetrate the C layers more easily than the Pt layers. An estimateof dx was obtained using an XSW field intensity of 1/e. The XSW field intensity was calculatedusing Eq. (2.21), with the assumption that the sample was surrounded by a vacuum and that theparameters of the materials retained their bulk properties [86]. The calculated XSW field
intensity is shown in Fig. 4.13, where Fig. 4.13(b) shows dx to be 22.5 nm at the Bragg angle.
According to Eq. (4.1), Dth was calculated to be 0.58 eV/atom, which is in reasonable agreementwith the measured threshold dose of a Pt single layer (0.52 eV/atom [74]).
The typical beam size of SACLA at a photon energy of 10 keV is 200 μm in diameter(FWHM), with a pulse energy of 400 μJ, implying that the fluence should reach 0.01 μJ/μm2.
This fluence is sufficiently lower than the damage threshold of the Pt/C multilayer. Thus, we
confirmed the feasibility of utilizing multilayered Pt/C films as optical components in XFELs.

4.2 Evaluation of Breakdown Threshold using Focused XFEL

Fig. 4.13. Calculated XSW field-intensity distribution in multilayer structure versus(a) grazing incidence angle and depth of multilayer medium and (b) line profile atfirst-order Bragg angle.

45

46

Chapter 4. Tolerance of Multilayer Films to X-ray Free-Electron Laser Irradiation

4.3 Evaluation in Actual Operating Conditions using Unfocused
XFEL[87]
Two Pt/C multilayer samples, fabricated by the DC magnetron sputtering system on Si (100)wafer substrates, were evaluated. Number of bilayers N, designed and measured multilayer
periods d, and designed and measured ratio γ of the Pt layer thickness to the multilayer periodof the multilayer samples are shown in Table 4.2.
Table 4.2. Details of Pt/C multilayer samples.
Measured (Cu-Kα)

DesignSampleNd (nm)γd (nm)

γ

A

45

5.0

0.5

4.78

0.508

B

45

2.5

0.5

2.45

0.527

An X-ray reflectometer (Rigaku SmartLab) was used to estimate the thicknesses, since X-ray
reflectrometry is a non-destructive and non-contact method for thickness determination of thinfilms. The experimental setup consisted of a Cu-Kα X-ray source (λ = 0.154 nm) and a θ-2θ
goniometer stage to change the grazing incidence angle on the sample surface, as shown in Fig.
4.14. The intensities of the X-rays reflected by the sample were monitored at various grazing

Fig. 4.14. Schematic of X-ray reflectometer.

4.3 Evaluation in Actual Operating Conditions using Unfocused XFEL

47

incidence angles.
To ensure that the multilayer films would function in typical operating conditions,multilayer films A and B were evaluated with the non-monochromatic XFEL at a photon energyof 10 keV, a pulse duration of <10 fs [47], a repetition rate of 10 Hz, a mean pulse energy of
130 μJ, and a beam diameter (FWHM) of 300 μm. In this evaluation, the fluence of the incident
beam was designed to be ~0.0014 μJ/μm2. In the first-order Bragg angle, the change ofreflectivity of film B was determined after X-ray irradiation for 5 hours. Irradiation damage
was expected to be induced in the B multilayer due to its very large first-order Bragg angle.
Post-irradiation, the cross-section of an irradiated region of film B was compared with that ofa non-irradiated region by TEM.
Figure 4.15 shows the measured X-ray reflectivities of samples A and B as functions of thegrazing incidence angle of the XFEL. The solid lines represent the measured reflectivities, andthe dashed lines show the curve fitting results. The experimental data from samples A and B
show that their reflectivities of the first-order Bragg peak were 78.3% and 51.8%, respectively.
Since sufficiently high reflectivities were obtained, these samples function well as multilayer
films. The periods of the multilayers and the ratios of Pt layer thickness to multilayer period
were estimated by using the curve fitting results and are shown in Table 4.3.
Table 4.3. Multilayer periods and ratios of Pt layer thickness to multilayer periodof Pt/C multilayer samples. Thicknesses of fabricated samples were measured byusing X-ray reflectometer and XFEL.
Measured (Cu-Kα)

Measured (XFEL)d (nm)γd (nm)

γ

multilayer period (%)

A

4.78

0.508

4.74

0.513

0.84

B

2.45

0.527

2.42

0.528

1.22

SampleDeviation of

The calculated multilayer periods agree with the results obtained from the X-ray reflectometerto within 1%.
The reflectivity of film B in the first-order Bragg peak is shown in Fig. 4.16, with no change
during the 5 hours of measurements. After 50 min, 100 min, 200 min, and 300 min, the angle

48

Chapter 4. Tolerance of Multilayer Films to X-ray Free-Electron Laser Irradiation

first-order
Bragg peakfirst-order
Bragg peakFig. 4.15. X-ray reflectivities of Pt/C multilayer samples (a) A and (b) B versus
grazing incidence angle. Solid and dashed lines show experimental data andcalculated fit curves, respectively. X-ray reflectivities of first-order Bragg peaks are(a) 78.3% and (b) 51.8%.

4.3 Evaluation in Actual Operating Conditions using Unfocused XFEL

49

Fig. 4.16. X-ray reflectivity versus time, with annotations indicating measured firstorder Bragg peak angles of sample B at various times.
of the first-order Bragg peak was measured, and the results are presented in Fig. 4.16. As shown,
the angle of the first-order Bragg peak also did not change.
Figure 4.17 depicts the cross-sectional TEM images of the surface and substrate sides of
the non-irradiated and irradiated regions of film B. The dark and bright layers correspond to thePt and C layers, respectively. No evidence of XFEL irradiation damage is evident. The
multilayer periods and the ratios of Pt layer thickness to multilayer period were estimated fromthese images. The resulting values were somewhat larger than those obtained from the X-ray
reflectometer and the XFEL, possibility due to slight inclination of the cross-sections.
The reflectivity and TEM images do not display any observable changes throughout the 5hours irradiation period. Thus, the unfocused XFEL irradiation did not seriously damage themultilayer film samples.

50

Chapter 4. Tolerance of Multilayer Films to X-ray Free-Electron Laser Irradiation

Fig. 4.17. Cross-sectional bright-field TEM images of film B. (a) and (b) show nonirradiated and irradiated sections, respectively, and “-1” and “-2” in figure partnames denote surface side and substrate side, respectively. Dark and bright layers
correspond to Pt and C layers, respectively. davg is average multilayer period, andγavg is average ratio of Pt layer thickness to multilayer period.

4.4 Summary

51

4.4 Summary
In hard X-ray focusing, multilayer mirrors are required, because reflection at high grazing
incidence angles is necessary. To fabricate laterally graded multilayer mirrors for X-ray
focusing, a thin film deposition system was developed in this study. Then, an arbitrarily shaped
mirror was fabricated using the differential deposition technique to estimate the accuracy of thedeposition apparatus. The deposition apparatus was found to be capable of sub-nanometer
accuracy, which is sufficiently high for multilayer mirror fabrication and mirror shapemodification.
We also evaluated the feasibility of using Pt/C multilayers for XFEL focusing applications.
The X-ray reflectivity, surface, and cross-section of a multilayer film were measured to observe
the irradiation damage. We determined the damage threshold of the Pt/C multilayer using a 1
μm focused hard XFEL beam with a photon energy of 10 keV and found that the damage
threshold of the Pt/C multilayer with a bilayer period of 3 nm was 0.051 μJ/μm2, confirmingthat it could be employed in XFEL focusing optics. Moreover, no damage to the multilayer wasobserved during testing in the conditions in which it was designed to be used. Our calculated
value of the threshold atomic dose in the multilayer was similar to that of the bulk material. The
obtained threshold should be a useful criterion for designing multilayer optics in XFEL sub-10nm focusing and related fields.

Chapter 5

IMPROVEMENT OF X-RAY
REFLECTIVITY IN MULTILAYER FILMS
The achievement of high photon densities using reflective optics requires the use of multilayer
films in the hard X-ray regime. One important property of multilayer films used as opticalelements is X-ray reflectivity, which is related to focusing efficiency. Since the X-ray reflectivityof a multilayer film is mainly related to the X-ray wavelength and the composition of the film,
it is necessary to design multilayer films in accordance with the wavelength to be used, by
varying the base materials, component ratio, and number of layers [88]. Additionally,
compatibility between the different materials in a multilayer film is important to suppress
interdiffusion and interface roughness between the layers. To improve the reflectivities of Pt/C
hard X-ray multilayers, we evaluated the effects of thinning and C-doping their Pt layers.

5.1 Determination of Critical Pt Layer Thickness
To confirm the Pt/C multilayer reflectivity improvements realized by thinning their Pt layers,
the changes in reflectivity with varying period d and number of bilayers N were calculated asfunctions of the ratio γ of the Pt layer thickness to the total bilayer thickness, and the results areshown in Fig. 5.1. A Cu-Kα X-ray source was used with a photon energy of 8.048 keV. The
multilayer period of such a laterally graded multilayer is typically in the range of 3–9 nm [89].
At least 30 bilayers are required since the reflectivity of short-period multilayers is saturated.
53

54

Chapter 5. Improvement of X-ray Reflectivity in Multilayer Films

Fig. 5.1. Calculated X-ray reflectivities of Pt/C multilayers with varying d and N as
functions of γ at photon energy of 8.048 keV.
In the case of a long-period multilayer, as the Pt layer thickness is reduced, the reflectivity
improves if there are a sufficient number of bilayers to reflect the incident X-rays.
Pt layer thinning can increase the reflectivities of long-period multilayers. However, since
it is not possible to reduce the Pt layer thickness indefinitely, the critical Pt layer thickness wasevaluated by using the reflectivities of Pt/C multilayers. Although the reflectivity can beincreased by reducing the Pt layer thickness, caution must be exercised so that a continuous
film is not formed when the Pt layers are too thin.
The measured thicknesses of the Pt layers used in this study were 1.0 mm, 1.1 mm, 1.2 mm,
and 1.4 nm; the multilayer period was 4 nm; and the number of bilayers was 30. The measured
and calculated X-ray reflectivities are shown in Fig. 5.2. Initially, the calculated reflectivity
increases as the Pt thickness decreases; however, when the Pt thickness becomes less than 1.2
nm, the measured reflectivity drops off significantly. The reason for this reflectivity reductionis that continuous Pt layers are not formed when their thicknesses are less than 1.2 nm. Thus,
we confirmed that the critical Pt layer thickness is 1.2 nm, which is reasonably comparable to
the results of previous research [33], in which the critical thickness was determined by5.1 Determination of Critical Pt Layer Thickness

55

Fig. 5.2. Critical Pt layer thickness measured by X-ray reflectivity of Pt/C
multilayers in 30-bilayer stack with d = 4 nm.
measuring the electrical resistance of a single Pt layer. To obtain the highest reflectivity, theoptimal Pt layer thickness in the Pt/C multilayer structure was 1.2 nm.
The reflectivities of Pt/C multilayers with fixed Pt layer thickness dPt = 1.2 nm or with fixed
γ = 0.5 were calculated and measured at various incidence angles, and the results are comparedin Fig. 5.3. Again, 30 bilayers were used, and the X-ray wavelength was 0.154 nm. As shown,the calculated reflectivity is higher with dPt = 1.2 nm than with γ = 0.5. The experimentallymeasured reflectivity also increases when the theoretically obtainable reflectivity increases.

5.2 X-ray Reflectivity Improvement in Pt/C Multilayers by CDoping of Pt Layers
The X-ray reflectivity of a multilayer film depends strongly on the quality of the interfaces
between the individual layers [90–93]. Furthermore, the reflectivity reduction induced by

56

Chapter 5. Improvement of X-ray Reflectivity in Multilayer Films

Fig. 5.3. Calculated and measured X-ray reflectivities of Pt/C multilayers with fixed
γ = 0.5 (black) or fixed dPt = 1.2 nm (red).
interface roughness becomes more significant as the multilayer period decreases because theratio of the interface roughness to the multilayer period directly affects the reflectivity throughthe Debye–Waller factor (DWF) [94]. One reason for interface roughness is crystallization
during multilayer deposition [92,93]. In a short-period multilayer (shorter than several
nanometers), the metal layer, e.g., the Pt layer, retains its amorphous structure. However, Pt
atoms tend to form closely packed structures and are covered by surfaces with relatively low
surface energies, such as (111) surfaces, which is the most significant cause of interface
roughening. Crystalline metals can generally be made amorphous by the addition of non-metals
or metalloids such as B, C, P, or Si [95]. Thus, in this section, we address whether the dopingof C atoms into Pt layers at concentrations of 1–15 v/v % can effectively reduce theirroughnesses; we also discuss the controllability that can be achieved by this method.

5.2 X-ray Reflectivity Improvement in Pt/C Multilayers by C-Doping of Pt Layers

57

5.2.1 Roughness Improvement by Crystallization Suppression[96]Pure Pt and C-doped Pt (PtC) films were fabricated by DC magnetron sputtering. The Pt and
PtC films were deposited on Si (100) substrates. To confirm the crystallization suppression, thesurface morphologies of the Pt and PtC films were measured by an atomic force microscope(AFM, Digital Instruments D3100) in air. Scan areas of 500 nm × 500 nm and 5 μm × 5 μm
were used for both types of film. The thickness of each film was 50 nm; this relatively large
thickness was chosen to enhance the difference between the surface roughnesses of the Pt films
with and without C-doping. Figure 5.4 presents AFM images of the deposited Pt films with C
concentrations of 0–15 v/v %. Figure 5.5 shows the relationship between the RMS roughnessof the film surface and the C concentration; the surface roughness decreases with increasing C
concentration. A level of C-doping as low as 1 v/v % can reduce the RMS roughness by 0.1 nm.
The surface roughness of the PtC film with 15 v/v % C is equivalent to that of the substrate, so
the roughness induced by crystallization during deposition is almost completely suppressed.
The X-ray diffraction spectrum of each film was measured using a Cu-Kα X-ray source;
the results are shown in Fig. 5.6. The sharp diffraction peak is from the Si substrate, while the
X-ray diffraction spectra of the deposited Pt and PtC films have high-intensity peaks at (111)and (222). The films with lower C concentrations are more likely to have their (111) orientations
parallel to their surfaces. This result clearly shows that C-doping can effectively suppress Pt
crystallization during film deposition.
The grain sizes of the polycrystalline Pt and PtC films were estimated from the widths of
their diffraction peaks at (111) by applying the Scherrer equation [97,98],

D=

0.9l
,
b cos q

(5.1)

where D is the grain size, λ is the X-ray wavelength, β is the line broadening at FWHM inradians, and θ is the Bragg angle (θ of Pt(111) is 0.347 rad). The FWHM of the Pt film is 30.1
mrad, which is almost the same as those of the PtC films. The grain size is 5 nm, which is nearly
the same as the spatial wavelength of the AFM image shown in Fig. 5.6.
To obtain the electron diffraction patterns and TEM images of the Pt and PtC films, a 10nm-thick C film was deposited on a NaCl (100) substrate, and 50-nm-thick Pt and PtC films
were deposited on this film. Then, the thin film formed on the NaCl substrate was peeled off

58

Chapter 5. Improvement of X-ray Reflectivity in Multilayer Films

Fig. 5.4. AFM images of surfaces of deposited Pt and PtC films with 0–15 v/v % C.
Scanned areas are (a) 500 nm × 500 nm and (b) 5 μm × 5 μm.

5.2 X-ray Reflectivity Improvement in Pt/C Multilayers by C-Doping of Pt Layers

Fig. 5.5. RMS film surface roughness versus C concentration in PtC film.

Fig. 5.6. X-ray diffraction spectra of Pt and PtC films.

59

60

Chapter 5. Improvement of X-ray Reflectivity in Multilayer Films

and placed on the TEM grid. Electron diffraction patterns, bright-field TEM images, and darkfield TEM images were obtained and are shown in Fig. 5.7. The electron diffraction patterns of
the deposited Pt and PtC films have significant high-intensity peaks at (220), most likely
because Pt has its (111) orientation parallel to its surface. Moreover, the intensity of the (220)peak decreases as the C concentration increases. This result shows that C-doping can effectively
suppress Pt crystallization during film deposition. From the bright-field TEM images, it can beseen that the grain size becomes smaller as the C content increases. The dark-field TEM images
depict only the grains of Pt (220). The grains of the C-doped samples are smaller than those of
the Pt film, and the grains were evenly distributed.

5.2.2 X-ray Reflectivity Improvement[99]The reflectivities of the Pt/C and PtC/C multilayers were compared when dPt was 1.2 nm. The
C concentration in the PtC layer was 4 v/v %, which is sufficient to suppress Pt layer
crystallization. The calculated and measured reflectivities are shown in Fig. 5.8, which was
obtained using 30 bilayers and an X-ray wavelength of 0.154 nm. The calculated reflectivitiesof the films are similar. However, the measured reflectivity is higher for the PtC/C multilayer.
The interface roughness of each sample was calculated using the DWF,é æ 2p ms ö2 ù
DWF = exp ê - ç÷ ú,ëê è d ø ûú

(5.2)

where m is the Bragg index, d is the multilayer period, and σ is the RMS interface roughness[94]. The DWF is essentially the relative reflectivity (the ratio of the measured and theoreticalvalues). The calculated interface roughnesses are presented in Fig. 5.9, which shows that the
average interface roughness of the PtC/C multilayer is lower than that of the Pt/C multilayer.

5.2 X-ray Reflectivity Improvement in Pt/C Multilayers by C-Doping of Pt Layers

Fig. 5.7. Electron beam diffraction patterns (-1) and bright-field (-2) and dark-field(-3) TEM images of single-layer films. (a), (b), and (c) refer to pure Pt, PtC (3v/v %), and PtC (11 v/v %) samples, respectively.

61

62

Chapter 5. Improvement of X-ray Reflectivity in Multilayer Films

Fig. 5.8. Calculated and measured X-ray reflectivities of Pt/C and PtC/C multilayers
using N = 30, Pt (or PtC) thickness of 1.2 nm, and C concentration in PtC of 4 v/v %.

Fig. 5.9. Interface roughnesses calculated using DWF for Pt/C and PtC/C
multilayers.

5.3 Summary

63

5.3 Summary
To develop a Pt/C multilayer film with improved X-ray reflectivity, we evaluated the effects of
Pt layer thinning and C-doping of the Pt layers.
Pt layer thinning effectively reduced the absorption of hard X-rays by the Pt, especially inthe long-period multilayers. In this study, the critical Pt layer thickness was determined by using
the X-ray reflectivity of the Pt/C multilayer because it is not possible to reduce the Pt layer
thickness indefinitely. We determined the critical Pt layer thickness to be ~1.2 nm, at which thetheoretically obtainable X-ray reflectivity was increased, and the measured X-ray reflectivity
was increased by ~10%.
Since admixtures of metals and nonmetals, or metalloid elements such as C, generally
suppress the crystallization of metal films during deposition, we compared single-layer filmsof pure Pt to single-layer films of C-doped Pt to evaluate the effectiveness of C-doping insuppressing Pt crystallization. C concentrations ranging from 0 v/v % to 15 v/v % were
employed, and the surface roughnesses, X-ray diffraction spectra, and electron beam diffraction
spectra of the resulting films were measured. We concluded that the surface roughness
decreased with increasing C concentration in the Pt layers and that the Pt crystallization during
deposition was also suppressed; these factors can be used to achieve improvements in interface
quality and reflectivity. Furthermore, we found that C-doping effectively increased thereflectivity of the total X-ray reflection optical system.

Chapter 6

NANOFOCUSING OF
X-RAY FREE-ELECTRON LASERS
The use of focusing optics enables enhancement of X-ray intensity, which can expand the range
of applications of XFELs. At SACLA [17], a 50 nm focusing beam with a power density of 1020
W/cm2 has been achieved using total reflection mirror optics [18]. To achieve higher power
densities of ~1022 W/cm2, multilayer mirrors have been developed for use as XFEL sub-10-nm
focusing optics. To investigate XFEL nanobeam focusing, a wavefront measurement method
was developed. Using this method, correct mirror alignment was achieved, and the residual
surface shape errors of the mirror optics were measured. Then, the XFEL sub-10-nm focusing
optics were commissioned at SACLA.

6.1 XFEL Sub-10-nm Focusing Optics and Focusing Strategy
The optical configuration and parameters of a sub-10-nm focusing system are shown in Fig.
6.1 and Table 6.1, respectively. To achieve a sub-10-nm spot size, a shorter focal length andlarger numerical aperture are theoretically required. However, short focal lengths have several
demerits, such as the risk of incurring debris from samples and limited application variations.
For the focal length to be sufficiently long, the incident beam must be several millimeters indiameter. However, such a large numerical aperture cannot be obtained by using theconventional single-stage focusing system due to the small divergence of the XFEL beam,65

66

Chapter 6. Nanofocusing of X-ray Free-Electron Lasers

Fig. 6.1. Schematic of optical configuration of two-stage XFEL sub-10-nm focusing
system.

Table 6.1. Optical parameters of XFEL sub-10-nm focusing system at SACLA.
Upstream focusing mirrors

Downstream focusing mirrors

VerticalHorizontal

Horizontal

Verticaldirection

direction

direction

direction

Elliptical

Elliptical

Elliptical

EllipticalcylindercylindercylindercylinderSubstrate material

QuartzQuartzQuartzQuartzCoating material

None

None

[Pt/C]30[Pt/C]30

Coating thickness (nm)

None

None

93.6–217.5

86.1–273.0

Substrate size (mm3)

400×50×50

400×50×50

380×50×50

100×50×50

1.50

1.50

14.6

13.2

Focal length (m)

10.10

2.70

0.320

0.070

Distance from source (m)176.30176.7579.07272.372Semi-major axis (m)93.20089.72539.69636.221Semi-minor axis (mm)63.29632.76873.43829.710Surface shape

Grazing incidence angle
on mirror center (mrad)6.1 XFEL Sub-10-nm Focusing Optics and Focusing Strategy

67

which is on the order of microradians. At SACLA, which is a compact facility, the maximum
beam size is ~500 μm (FWHM) at the farthest experimental hutch. To overcome this limitation,
this focusing system has adopted a two-stage reflective focusing system, which was also
adopted for the 50 nm focusing at SACLA. In the first (upstream) stage, non-coated totalreflection KB mirrors are used to pre-focus and expand the incident beam. In the second(downstream) stage, multilayer coated KB mirrors focus the expanded beam. The geometric
reduction ratios of the horizontal and vertical directions are 1/16175.8 and 1/18046.9,
respectively. Therefore, if the XFEL source size is 100 μm (FWHM), the obtainable spot size
becomes 6.2 nm (H) × 5.5 nm (V). Then, the theoretically obtainable diffraction-limited focal
spot size is 5.3 nm (H) × 4.2 nm (V) at a photon energy of 9.1 keV, which was calculated byusing wave-optics analysis. A photon energy of 9.1 keV was used to enable the application of
nonlinear phenomena [20] for optical system alignment, such as astigmatism, and to confirm
the focusing power density. The calculated focusing beam waists and profiles of the horizontal
and vertical directions are shown in Figs. 6.2 and 6.3, respectively.
The grazing incidence angle and multilayer period of the sub-10-nm optics have the
distributions shown in Fig. 6.4. The grazing incidence angle ranges of the second KB mirrors
are 11.58–22.88 mrad (H) and 10.09–24.68 mrad (V). These grazing incidence angles
significantly exceed the critical angle of Pt at which total reflection occurs (8.97 mrad) at a
photon energy of 9.1 keV. In this optical design, the multilayer mirror is essential. The required
accuracy of total multilayer film thickness is the same as that of the mirror shape, ~1 nm (PV),as was described in Chapter 3. The multilayer period ranges were calculated to be 3.12–7.25
nm (H) and 2.87–9.10 nm (V) by using Eq. (2.6). The ratio of the thicknesses of the Pt and C
layers was chosen to be 1:1 to facilitate phase control of the reflected beam. A high-reflectivity
C-doped Pt/C multilayer, which was introduced in Chapter 5, will be adopted for the second
commissioning because the purpose of the first commissioning was primarily to measure theshape errors of the focusing mirrors.
Figure 6.5 shows the calculated multilayer X-ray reflectivity distribution for an interface
roughness of 0.2 nm (RMS). The X-ray reflectivity continually increases towards its saturation
value with increasing number of multilayers. Moreover, uniform and high X-ray reflectivity isevident across the entire mirror surface. However, practically, it is desirable to select theminimum number of multilayers within the range capable of obtaining a certain degree of68

Chapter 6. Nanofocusing of X-ray Free-Electron Lasers

Fig. 6.2. Calculated (a) horizontal and (b) vertical focusing beam waists.

Fig. 6.3. Calculated (a) horizontal and (b) vertical focusing beam profiles.

6.1 XFEL Sub-10-nm Focusing Optics and Focusing Strategy

Fig. 6.4. Grazing incidence angle and multilayer period distributions of (a)horizontal and (b) vertical direction focusing mirrors.

Fig. 6.5. X-ray reflectivity distributions of (a) horizontal and (b) vertical direction
focusing mirrors.

69

70

Chapter 6. Nanofocusing of X-ray Free-Electron Lasers

uniformity and high reflectance from the entire mirror surface. Multilayer films with fully
saturated reflectivity may have adverse effects, such as increasing the film stress and the shapeerror of the outermost surface due to the increased amount of film and changes in the deposition
rate resulting from increased deposition time. We chose to use 30 multilayers based on thesimulation results to obtain the reflectivity of 99.5% to the saturation value.
In this sub-10-nm focusing system, an at-wavelength wavefront measurement method,which will be described in the next section, was used to measure the final surface shape error,
because it would have been difficult to define the absolute shape errors of the second KB
mirrors by using only ex-situ measurements. The at-wavelength wavefront measurement
method is an in-situ measurement method and is useful for determining the shape error, which
degrades the focusing. In the first commissioning, the final shape error will be measured byusing the X-ray wavelength that is actually used. Then, as shown in Fig. 6.6, the error will becorrected by using differential deposition on the surfaces of the second KB mirrors, because therepeatability of the multilayer deposition and the accuracy of the differential deposition are
sufficiently high, as mentioned in Chapter 4. Finally, ideal sub-10-nm focusing will be achievedby using shape-error-corrected multilayer KB mirrors.

XFEL

Differential
deposition
Intermediate
focus

Multilayer mirror
Final
focus

Phase grating

Total reflection mirror

Fig. 6.6. Schematic of XFEL sub-10-nm focusing strategy.

CCD6.2 Measurement of Focused X-ray Wavefront

71

6.2 Measurement of Focused X-ray Wavefront
The achievable focal spot size is significantly degraded by mirror shape errors and grazing
incidence angle misalignment. For sub-10-nm focusing optics, to satisfy Rayleigh’s criterion,
the mirror shape and grazing incidence angle errors must not exceed 1 nm (PV) and 0.1 μrad,respectively. Generally, the alignment accuracy is evaluated by monitoring the beam profile
using knife-edge scanning methods [100,101]. In this way, the alignment is optimized by an
iterative procedure of beam profiling and grazing incidence angle adjustment. This procedure
is very time-consuming and frequently introduces significant profiling error due to shapeimperfections and/or vibrations of the scanned object. Accordingly, the grazing incidence anglealignment often determines the achievable focal spot size. To evaluate XFEL nanofocusing, a
shot-by-shot method is essential to reduce the influence of focal position fluctuations during
beam profiling.
To meet this requirement, we used single-grating interferometry [102–116], based on the
Talbot effect [117]. Therefore, we tested the sensing capability of the coma aberration generated
by the grazing-incidence-angle error of a focusing mirror. A schematic of the single-gratinginterferometer system is shown in Fig. 6.7, and the phase grating parameters are listed in Table
6.2.
Table 6.2. Phase grating parameters.
Parameters
Material

Tantalum

Thickness

2.25 μm

Pitch

3.0μm

Phase shift

λ/2 (at 9.1 keV)Transmission

80.5% (at 9.1 keV)The energy of the X-rays was 9.1 keV. A tantalum phase grating (3.0 μm pitch; NTT Advanced
Technology Corporation) fabricated on a thin SiC membrane (thickness <1 μm) was used, andthe grating thickness (2.25 μm) was chosen such that the grating would behave as a π/2 phase

72

Chapter 6. Nanofocusing of X-ray Free-Electron Lasers

Fig. 6.7. Schematic of single-grating interferometer system.
shifter for 9.1 keV X-rays. The grating was placed 8.34 mm downstream from the final focal
point. The formed self-image was recorded by a charge-coupled device (CCD) camera (C9300124, Hamamatsu Photonics) placed 820 mm downstream of the final focal point. The effective
pixel size and field of view of the camera were 9.0 μm and 36.00 mm × 24.05 mm, respectively.
Self-images were obtained by single-shot irradiation.
To detect the coma aberration caused by grazing incidence angle error, we intentionallyvaried the grazing incidence angle around the optimal angle and measured the resulting
wavefront shapes, which are shown in Fig. 6.8. To evaluate only the coma aberration inducedby the grazing incidence angle error, best-fit quadratic functions were removed from thereconstructed wavefront shapes. The obtained wavefront shapes appear to be cubic functions,with no significant higher-order polynomial components below λ/10. We measured the PV
heights of the cubic functions by changing the grazing incidence angle (pitched at 1 μrad) from
-5 μrad to 5 μrad and found that the heights increased with increasing grazing incidence angle
error. Figure 6.9 depicts the experimental and calculated results, which agree well. The phasedifference at the minimum, for which the grazing incidence angle is optimal, is sufficiently
small to satisfy Rayleigh’s criterion. Single-grating interferometry is the only available method
for evaluating aberration shot-by-shot.

6.2 Measurement of Focused X-ray Wavefront

Fig. 6.8. Reconstructed wavefront aberration.

Fig. 6.9. Typical relationship between grazing incidence angle error and phasedifference of cubic function (PV) from wavefront shape measured by gratinginterferometry.

73

74

Chapter 6. Nanofocusing of X-ray Free-Electron Lasers

6.3 Experimental Evaluation of Multilayers at SPring-8
To measure the mirror shape by using the wavefront measurement method, it is necessary tocoat the multilayer on the mirror surface. If the multilayer film has multilayer period error, therelationship between the grazing incidence angle and the multilayer period (Bragg condition)is broken, and the reflectivity is reduced. When the multilayer period error is the range of -4–2%, more than 90% of the designed reflectivity can be achieved, as shown in Fig. 6.10. To
evaluate the deposition accuracies of the multilayer films, their reflectivities were measured at
SPring-8 BL29XUL using the experimental setup shown in Fig. 6.11. The intensities of theincident and reflected beams were measured by using an ion chamber and a PIN photodiode,respectively. The evaluated multilayer films were the same as those used for XFEL sub-10-nm
focusing.
Figure 6.12 presents the measured reflectivities as functions of the grazing incidence angle
at an X-ray photon energy of 9.1 keV. Grazing incidence angles that deviated from the ideal
grazing incidence angle by between -0.5 mrad and 0.5 mrad were used. The reflectivity of theFig. 6.10. Relationship between multilayer period error and reflectivity.

6.3 Experimental Evaluation of Multilayers at SPring-8

75

Fig. 6.11. Experimental setup for multilayer evaluation at SPring-8.
horizontal direction focusing mirror increases when the grazing incidence angle is shifted to thenegative side, as shown in Fig. 6.12(a), because the multilayer period became longer than thedesign value. On the other hand, the reflectivity of the vertical direction focusing mirror is thehighest at the ideal grazing incidence angle, as shown in Fig. 6.12(b), indicating that themultilayer period was fabricated at a value close to the design value.
Figure 6.13 depicts the measured reflectivities at the ideal grazing incidence angle and at
X-ray photon energies ranging from 8.1 keV to 10.1 keV. The lines indicate the reflectivities at
an arbitrary mirror position. Figures 6.13(a) and 6.13(b) show that the photon energies at which
the horizontal and vertical direction focusing mirrors reflectivities are maximized are 8.909 keV
and 9.096 keV, respectively. The corresponding multilayer period errors were determined to be+2.1% (H) and -0.4% (V). Thus, we succeeded in fabricating the multilayer within the allowableerror range.

76

Chapter 6. Nanofocusing of X-ray Free-Electron Lasers

Fig. 6.12. X-ray reflectivities of (a) horizontal and (b) vertical direction focusing
mirrors at various grazing incidence angles and X-ray photon energy of 9.1 keV.

Fig. 6.13. X-ray reflectivities of (a) horizontal and (b) vertical direction focusing
mirrors at various X-ray photon energies and ideal grazing incidence angle.

6.4 Nanofocusing Experiment at SACLA

77

6.4 Nanofocusing Experiment at SACLAThe first commissioning of the sub-10-nm XFEL focusing system was performed at SACLA
using the setup shown in Fig. 6.14. The mirror and sample chambers were divided to protect
the mirror from debris and to increase the range of potential applications.
To investigate the focused beam profiles roughly, wire scan and knife-edge methods wereapplied, which are capable of micron-order evaluations. These methods are not suitable forsub-10-nm focusing, in which the beam profile would be estimated to be significantly larger
because of focal point fluctuations. The measured results are shown in Fig. 6.15. The measured
focused-beam size was 65 nm (H) × 49 nm (V) at a photon energy of 9.1 keV; this beam sizeis larger than the predicted focal spot size. As mentioned above, the knife-edge scan method is
not suitable for evaluating sub-10-nm focusing optics. Grating interferometry, using a shot-byshot method, was employed to understand the exact wavefront aberration. In this case, thecubic function corresponding to the coma aberration was minimized by precisely aligning thegrazing incidence angle, and higher-order polynomial elements were extracted to investigate

Fig. 6.14. Experimental setup for XFEL sub-10-nm focusing.

78

Chapter 6. Nanofocusing of X-ray Free-Electron Lasers

Fig. 6.15. (a) Horizontal and (b) vertical focused-beam profiles measured using
wire scan method.
the wavefront error due to mirror shape imperfections. The results of this test are shown in
Fig. 6.16. The mirror imperfections led to errors of several radians in both the horizontal andvertical directions, which exceed the errors allowed by Rayleigh’s criterion. In two-stage optics
for sub-10-nm focusing, the grazing incidence angles of the downstream mirrors are about 10
times larger than those of the upstream mirrors, which means that the shape errors of thedownstream mirrors affect the wavefront error 10 times more than those of the upstream mirrors.
Accordingly, we concluded that the wavefront error originated from the imperfections of thedownstream mirrors. Meanwhile, using the obtained phase errors, the focusing beam waists andprofiles were calculated and are shown in Fig. 6.17 and Fig. 6.18, respectively. The theoretically
expected beam size is ~10 nm, which is the smallest beam size reported to date in XFEL
focusing. Then, in the second commissioning, we endeavor to focus the XFEL to sub-10-nm
size with a power density greater than 1022 W/cm2, by using shape-error-corrected multilayer
mirrors.

6.4 Nanofocusing Experiment at SACLA

Fig. 6.16. Measured phase errors resulting from shape errors of sub-10-nm focusing
mirrors.

Fig. 6.17. (a) Horizontal and (b) vertical focusing beam waists expected based on
measured phase errors.

79

80

Chapter 6. Nanofocusing of X-ray Free-Electron Lasers

Fig. 6.18. (a) Horizontal and (b) vertical focusing beam profiles expected based on
measured phase errors.

6.5 Summary
To achieve X-ray fields with higher power densities, sub-10-nm XFEL focusing was developed
using a two-stage reflective focusing system. In the second (downstream) stage, multilayer
coated KB mirrors were adopted, and the focused XFEL beam profiles were obtained. Usingsuch optics, the theoretically obtainable diffraction-limited focal spot size is 5.3 nm (H) × 4.2
nm (V) at a photon energy of 9.1 keV. To investigate the focused state of the XFEL nanobeam,a wavefront measurement method was developed. In this way, the alignment was optimized by
iterative beam profiling and grazing incidence angle adjustment. However, this procedure isvery time-consuming and frequently introduces significant error in the beam profile due toshape imperfections and/or scanner vibrations. Accordingly, the grazing incidence angle error
often determines the achievable focal-spot size.
The first commissioning of the sub-10-nm XFEL focusing system was performed at
SACLA. To investigate the focused beam profiles roughly, wire scan and knife-edge methods
were applied. The measured focused-beam size was 65 nm (H) × 49 nm (V), which includes
imperfections and scanner vibrations. Therefore, grating interferometry, using a shot-by-shot6.5 Summary81

method, was employed to understand the exact wavefront aberration. The mirror imperfections
led to errors of several radians in both the horizontal and vertical directions. The beam size wastheoretically determined to be ~10 nm based on the obtained phase errors, which is the smallest
beam size reported to date in XFEL focusing. Then, in the second commissioning, we endeavor
to focus the XFEL to sub-10-nm size with a power density greater than 1022 W/cm2, by using
shape-error-corrected multilayer mirrors.

Chapter 7

CONCLUSIONSIn this study, to generate extremely intense X-ray fields that can be used to explore nonlinear
phenomena in the hard X-ray regime, a sub-10-nm XFEL focusing system was developed using
multilayer KB mirror optics. The design of this system required studies of the fabrication andmeasurement of mirror substrates with steeply curved surfaces, deposition of multilayers withhigh reflectivities and sufficient X-ray irradiation tolerances, and techniques for single-shotmeasurement of focused wavefronts. The main conclusions can be summarized as follows.

XFEL Sub-10-nm Focusing Mirror Fabrication
XFEL sub-10-nm focusing mirrors have steeply curved surfaces that are difficult to measureusing conventional shape measurement methods. The minimum radius of curvature is a few
meters, and the slope range is several dozen milliradians. Furthermore, the required mirror
surface accuracy, or Rayleigh criterion, is ~1 nm (PV). A laser autofocus microscope system
was developed to provide measurements at this level of accuracy, featuring a position correction
mechanism utilizing three heterodyne interferometers. A repeatability test demonstrated that theapparatus could be consistently adjusted to within 2 nm (PV).
The sub-10-nm focusing mirrors were fabricated using EEM and measured using MSI,RADSI, and the newly developed instrument. The residual shape errors typically obtained after
deterministic figuring of the sub-10-nm focusing mirrors were ~3 nm (PV).

83

84

Chapter 7. Conclusions

Pt/C Multilayers with XFEL Irradiation Tolerance
In hard X-ray focusing, multilayer mirrors must be used because reflection at high grazing
incidence angles is necessary. To fabricate laterally graded multilayer mirrors for X-ray
focusing, a thin film deposition system was developed. An arbitrary shape was fabricated using
the differential deposition technique to estimate the accuracy of the deposition apparatus. We
confirmed that the deposition apparatus was capable of sub-nanometer accuracy, which is
sufficiently high for the fabrication of multilayer mirrors and mirror shape modification.
We then evaluated the applicability of Pt/C multilayer films in XFEL focusing. The X-ray
reflectivities, surfaces, and cross-sections of the multilayer films were measured to observe theirradiation damage. We measured the damage threshold of a Pt/C multilayer using a 1 μm
focused hard XFEL beam with a photon energy of 10 keV and found that the damage thresholdof the Pt/C multilayer film, which had a bilayer period of 3 nm, was 0.051 μJ/μm2, indicatingthat it could be employed in XFEL focusing optics. Moreover, damage to the multilayer was
not observed in the conditions in which it was designed to be used. Our calculated value of thethreshold atomic dose of the multilayer was similar to that of the bulk material. The obtained
threshold should be a useful criterion for designing multilayer optics in sub-10-nm XFEL
focusing and related fields.

Pt/C Multilayers with High X-ray Reflectivities
To develop Pt/C multilayers with improved X-ray reflectivities, we evaluated the effects of Pt
layer thinning and C-doping of the Pt layers.
Pt layer thinning effectively reduced the absorption of hard X-rays by the Pt, especially in
long-period multilayers. The critical Pt layer thickness of ~1.2 nm was determined by using the
X-ray reflectivity of the Pt/C multilayer because it is not possible to reduce the Pt layer
thickness indefinitely. With this thickness, the theoretically obtainable X-ray reflectivity wasincreased, and the measured X-ray reflectivity was increased by ~10%.
Since admixtures of metals and nonmetals, or metalloid elements such as C, generally
suppress the crystallization of metal films during deposition, we compared single-layer filmsof pure Pt to single-layer films of C-doped Pt to evaluate the effectiveness of C-doping inSummary and Prospects

85

suppressing Pt crystallization. C concentrations ranging from 0 v/v % to 15 v/v % were used,
and the surface roughness, X-ray diffraction spectra, and electron beam diffraction spectra were
measured. We concluded that the surface roughness decreased with increasing C concentrationin the Pt layers, and that Pt crystallization during deposition was also suppressed, which can
explain the observed improvements in interface quality and reflectivity. Furthermore, C-doping
effectively heightened the reflectivity of the total X-ray reflection optics.

XFEL Nanofocusing
To achieve higher power densities, sub-10-nm XFEL focusing was developed using the twostage reflective focusing system. In the second (downstream) stage, multilayer coated KB
mirrors were adopted, and the focused XFEL beam profiles were obtained. Using such optics,
the theoretically obtainable diffraction-limited focal spot size is 5.3 nm (H) × 4.2 nm (V) at a
photon energy of 9.1 keV. To investigate the focused state of the XFEL nanobeam, a wavefront
measurement method was developed. In this way, the alignment was optimized by iterative
beam profiling and grazing incidence angle adjustment. However, this procedure is very timeconsuming and frequently introduces significant error in the beam profile due to shapeimperfections and/or scanner vibrations. Accordingly, the grazing incidence angle error often
determines the achievable focal-spot size.
The initial commissioning of the sub-10-nm XFEL focusing system was performed at
SACLA. To investigate the focused beam profiles roughly, wire scan and knife-edge methods
were applied. The measured focused-beam size was 65 nm (H) × 49 nm (V), which includes
imperfections and vibrations of the scanner. Therefore, grating interferometry, using a shot-byshot method, was employed to understand the exact wavefront aberrations. The mirror
imperfections led to errors of several radians in both the horizontal and vertical directions. The
beam size was theoretically determined to be ~10 nm based on the obtained phase errors, whichis the smallest beam size reported to date in XFEL focusing.

Prospects
Sub-10-nm XFEL beams with power densities greater than 1022 W/cm2 will be generated using

86

Chapter 7. Conclusions

shape-error-corrected multilayer mirrors. Such X-ray field intensities will enable theexploration of nonlinear phenomena in the hard X-ray regime. Moreover, further developmentof the elemental technologies involved can lead to the realization of focusing diameters at the
wavelength level. Then, the electromagnetic field power density could possibly reach the
Schwinger limit [118] (~1029 W/cm2), at which electron and positron pairs are generated fromthe vacuum. Additionally, in the field of biomolecular imaging, structural analyses of single
molecules of protein before destruction may become possible by using single-shot XFEL pulses[119,120].

BIBLIOGRAPHY[1]

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LIST OF PUBLICATIONS[1]

J. Kim, A. Nagahira, T. Koyama, S. Matsuyama, Y. Sano, M. Yabashi, H. Ohashi, T.
Ishikawa, and K. Yamauchi“Damage threshold of platinum/carbon multilayers under hard X-ray free-electron laser
irradiation”
Optics Express 23(22), 29032–29037 (2015).

[2]

T. Koyama, H. Yumoto, K. Tono, T. Togashi, Y. Inubushi, T. Katayama, J. Kim, S.
Matsuyama, M. Yabashi, K. Yamauchi, and H. Ohashi“Damage to inorganic materials illuminated by focused beam of X-ray free-electron
laser radiation”
Proceedings of SPIE 9511, 951107 (2015).

[3]

H. Mimura, H. Yumoto, S. Matsuyama, T. Koyama, K. Tono, Y. Inubushi, T. Togashi, T.
Sato, J. Kim, R. Fukui, Y. Sano, M. Yabashi, H. Ohashi, T. Ishikawa, and K. Yamauchi“Generation of 1020 Wcm-2 hard X-ray laser pulses with two-stage reflective focusing
system”
Nature Communications 5, 3539 (2014).

[4]

R. Fukui, J. Kim, S. Matsuyama, H. Yumoto, Y. Inubushi, K. Tono, T. Koyama, T.
Kimura, H. Mimura, H. Ohashi, M. Yabashi, T. Ishikawa, and K. Yamauchi“A Precision Grazing-incidence Angle Error Measurement of a Hard X-ray Condenser
Mirror Using Single-grating Interferometry”
Synchrotron Radiation News 26(5), 13–16 (2013).

97

98

[5]

List of Publications

T. Koyama, H. Yumoto, K. Tono, T. Sato, T. Togashi, Y. Inubushi, T. Katayama, J. Kim,
S. Matsuyama, H. Mimura, M. Yabashi, K. Yamauchi, and H. Ohashi“Damage threshold investigation using grazing incidence irradiation by hard X-ray freeelectron laser”
Proceedings of SPIE 8848, 88480T (2013).

[6]

J. Kim, T. Koyama, H. Yumoto, A. Nagahira, S. Matsuyama, Y. Sano, M. Yabashi, H.
Ohashi, T. Ishikawa, and K. Yamauchi“Damage characteristics of platinum/carbon multilayers under X-ray free-electron laser
irradiation”
Proceedings of SPIE 8848, 88480S (2013).

[7]

T. Koyama, H. Yumoto, Y. Senba, K. Tono, T. Sato, T. Togashi, Y. Inubushi, T. Katayama,
J. Kim, S. Matsuyama, H. Mimura, M. Yabashi, K. Yamauchi, H. Ohashi, and T.
Ishikawa“Investigation of ablation thresholds of optical materials using 1-µm-focusing beam at
hard X-ray free electron laser”
Optics Express 21(13), 15382–15388 (2013).

[8]

K. Ogi, J. Kim, K. Ono, and N. Uda“Impact damage and residual tensile strength of a CF-SMC composite”
Advanced Composite Materials 22(1), 29–47 (2013).

[9]

H. Yumoto, H. Mimura, S. Matsuyama, T. Koyama, Y. Hachisu, T. Kimura, H.
Yokoyama, J. Kim, Y. Sano, K. Tono, T. Togashi, Y. Inubushi, T. Sato, T. Tanaka, M.
Yabashi, H. Ohashi, H. Ohmori, T. Ishikawa, and K. Yamauchi“Micro-focusing of hard x-ray free electron laser radiation using Kirkpatrick-Baez
mirror system”
Journal of Physics: Conference Series 425(5), 052022 (2013).

List of Publications

[10]

99

T. Koyama, H. Yumoto, Y. Senba, K. Tono, T. Sato, T. Togashi, Y. Inubushi, J. Kim, T.
Kimura, S. Matsuyama, H. Mimura, M. Yabashi, K. Yamauchi, H. Ohashi, and T.
Ishikawa“Damage study of optical substrates using 1-μm-focusing beam of hard X-ray freeelectron laser”
Journal of Physics: Conference Series 463, 012043 (2013).

[11]

H. Yumoto, H. Mimura, T. Koyama, S. Matsuyama, K. Tono, T. Togashi, Y. Inubushi, T.
Sato, T. Tanaka, T. Kimura, H. Yokoyama, J. Kim, Y. Sano, Y. Hachisu, M. Yabashi, H.
Ohashi, H. Ohmori, T. Ishikawa, and K. Yamauchi“Focusing of X-ray free-electron laser pulses with reflective optics”
Nature Photonics 7(1), 43–47 (2013).

[12]

J. Kim, H. Yokoyama, S. Matsuyama, Y. Sano, and K. Yamauchi“Improved reflectivity of platinum/carbon multilayers for X-ray mirrors by carbon
doping into platinum layer”
Current Applied Physics 12(S3), S20–S23 (2012).

[13]

J. Kim, S. Matsuyama, Y. Sano, and K. Yamauchi“Improvement of interface roughness in platinum/carbon multilayers for X-ray mirrors”
Key Engineering Materials 523–524, 1076–1079 (2012).

[14]

S. Matsuyama, N. Kidani, H. Mimura, J. Kim, Y. Sano, K. Tamasaku, Y. Kohmura, M.
Yabashi, T. Ishikawa, and K. Yamauchi“Development of a one-dimensional Wolter mirror for achromatic full-field X-ray
microscopy”
Proceedings of SPIE 8139, 813905 (2011).

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[15]

List of Publications

K. Yamauchi, H. Mimura, T. Kimura, H. Yumoto, S. Handa, S. Matsuyama, K. Arima,
Y. Sano, K. Yamamura, K. Inagaki, H. Nakamori, J. Kim, K. Tamasaku, Y. Nishino, M.
Yabashi, and T. Ishikawa“Single-nanometer focusing of hard x-rays by Kirkpatrick-Baez mirrors”
Journal of Physics: Condensed Matter 23(39), 394206 (2011).

LIST OF PRESENTATIONS
Presentations in International Conferences[1]

J. Kim, A. Nagahira, A. Nishihara, S. Matsuyama, H. Yumoto, T. Koyama, Y. Sano, H.
Ohashi, M. Yabashi, T. Ishikawa, and K. Yamauchi“X-ray mirror surface metrology using optical and at-wavelength techniques for hard
XFEL single-nanometer focusing”
12th International Conference on Synchrotron Radiation Instrumentation (SRI 2015),
NY Marriott Marquis, New York, NY, USA, July 6–10, 2015 (Poster presentation, THUP-015)[2]

J. Kim, S. Matsuyama, Y. Sano, and K. Yamauchi“Development of high-precision figure measurement system for x-ray optics using laser
focus microscope”
SPIE Optics + Photonics 2014, San Diego Convention Center, San Diego, CA, USA,
August 17–21, 2014 (Oral presentation, 9160-11)[3]

J. Kim, A. Nagahira, S. Matsuyama, T. Koyama, H. Yumoto, Y. Sano, M. Yabashi, H.
Ohashi, T. Ishikawa, and K. Yamauchi“XFEL-induced damage to optical thin film for X-ray mirrors under grazing incidence
condition”
International Workshop on Atomically Controlled Fabrication Technology, Osaka
University Nakanoshima Center, Osaka, Japan, February 5–6, 2014 (Poster presentation,
P5)

[4]

J. Kim, A. Nagahira, S. Matsuyama, R. Fukui, A. Nishihara, T. Koyama, H. Yumoto, Y.
Sano, H. Ohashi, S. Goto, M. Yabashi, T. Ishikawa, and K. Yamauchi
101

102

List of Presentations“Damage characteristics of platinum/carbon multilayers for hard X-ray free-electron
laser focusing”
The 25th Synchrotron Radiation Users’ Workshop & KOSUA meeting, POSCOInternational Center, Pohang, Republic of Korea, November 21, 2013 (Poster
presentation, PP-10)[5]

J. Kim, T. Koyama, H. Yumoto, A. Nagahira, S. Matsuyama, Y. Sano, M. Yabashi, H.
Ohashi, T. Ishikawa, and K. Yamauchi“Damage characteristics of platinum/carbon multilayers under focused X-ray freeelectron laser irradiation”
SPIE Optics + Photonics 2013, San Diego Convention Center, San Diego, CA, USA,
August 25–29, 2013 (Oral presentation, 8848-26)[6]

J. Kim, S. Matsuyama, Y. Sano, and K. Yamauchi“Improvement of interface roughness in Pt/C multilayers for X-ray mirrors”
14th International Conference on Precision Engineering, Awaji Yumebutai International
Conference Center, Hyogo, Japan, November 8–10, 2012 (Oral presentation, E11)

[7]

J. Kim, A. Nagahira, S. Matsuyama, Y. Sano, and K. Yamauchi“Study of Pt/C multilayers for X-ray mirrors improvement of reflectivity”
Fifth international symposium on atomically controlled fabrication technology, Osaka
University Nakanoshima Center, Osaka, Japan, October 22–24, 2012 (Poster
presentation, P33)

[8]

J. Kim, H. Yokoyama, S. Matsuyama, Y. Sano, and K. Yamauchi“Reflectivity improvement using PtC/C multilayers for X-ray mirrors”
Fourth international symposium on atomically controlled fabrication technology, Osaka
University Nakanoshima Center, Osaka, Japan, October 31–November 2, 2011 (Poster
presentation, P13)

List of Presentations

103

Presentation in Domestic Conferences[1]

金章雨，松山智至，佐野泰久，山内和人“X 線集光ミラー形状測定のための姿勢補正機構を有する三次元測定機の開発”
2015 年度精密工学会春季大会学術講演会 (2015 JSPE Spring Conference)，Toyo
University, Tokyo, March 17–19, 2015 (Oral presentation, R37)

[2]

金章雨，長平良綾香，西原明彦，松山智至，佐野泰久，山内和人“Sub-10 nm 集光用 X 線ミラーのための高精度形状計測装置の開発”

第 28 回日本放射光学会年会放射光科学合同シンポジウム (The 28th Annual
Meeting of the Japanese Society for Synchrotron Radiation Research – JSR 15) ，Ritsumeikan University, Shiga, January 10–12, 2015 (Poster presentation, 12P015)[3]

金章雨，長平良綾香，松山智至，福井亮介，西原明彦，小山貴久，湯本博勝，佐野泰久，大橋治彦，後藤俊治，矢橋牧名，石川哲也，山内和人“硬 X 線自由電子レーザーシングルナノ集光用 Pt/C 多層膜の破壊特性評価”

第 27 回日本放射光学会年会放射光科学合同シンポジウム (The 27th Annual
meeting of the Japanese Society for Synchrotron Radiation Research – JSR 14),
International Conference Center Hiroshima, Hiroshima, January 11–13, 2014 (Oralpresentation, 3D002)[4]

金章雨 (Invited)，長平良綾香，松山智至，福井亮介，西原明彦，小山貴久，湯本博勝，佐野泰久，矢橋牧名，大橋治彦，石川哲也，山内和人“硬 X 線ナノ集光ミラー用 Pt/C 多層膜の作製と評価”
Satellite Meeting of the 12th Symposium on X-ray Imaging Optics,

Ⅹ線ナノ集光技術研究会 2013 (X-ray nano-focusing technology workshop 2013),
Osaka University Nakanoshima Center, Osaka, November 17, 2013 (Oral presentation,
p19-20)[5]

金章雨，長平良綾香，小山貴久，湯本博勝，松山智至，佐野泰久，矢橋牧名，大橋治彦，石川哲也，山内和人“X 線自由電子レーザーを用いた硬 X 線集光用 Pt/C 多層膜の特性評価”

104

List of Presentations

2013 年度精密工学会秋季大会学術講演会 (2013 JSPE Autumn Conference), Kansai
University, Osaka, September 12–14, 2013 (Oral & Poster presentations, L37 & P-36)[6]

金章雨，福井亮介，松山智至，小山貴久，湯本博勝，佐野泰久，大橋治彦，後藤俊治，矢橋牧名，石川哲也，山内和人“X 線自由電子レーザー集光用 Pt/C 多層膜の性能評価”

第 26 回日本放射光学会年会放射光科学合同シンポジウム (The 26th Annual
meeting of the Japanese Society for Synchrotron Radiation Research – JSR 13), Nagoya
University, Aichi, January 12–14, 2013 (Poster presentation, 14P021)[7]

金章雨，横山光，松山智至，佐野泰久，山内和人“PtC/C 多層膜を用いた硬 X 線集光用ミラーの反射率改善”
2012 年度精密工学会春季大会学術講演会 (2012 JSPE Spring Conference), Tokyo
Metropolitan University, Tokyo, March 14–16, 2012 (Oral presentation, O36)

[8]

金章雨，横山光，松山智至，佐野泰久，香村芳樹，玉作賢治，矢橋牧名，石川哲也，
山内和人“PtC/C 多層膜を用いた X 線集光用ミラーの反射率改善”

第 25 回日本放射光学会年会放射光科学合同シンポジウム (The 25th Annual
meeting of the Japanese Society for Synchrotron Radiation Research – JSR 12), TosuShimin-Bunka-Kaikan, Saga, January 6–9, 2012 (Poster presentation, 9P002)[9]

金章雨，横山光，松山智至，三村秀和，佐野泰久，香村芳樹，石川哲也，山内和人“硬 X 線集光用多層膜ミラーの開発”
2011 年 度 精 密 工 学 会 秋 季 大 会 学 術 講 演 会 (2011 JSPE Autumn Conference),
Kanazawa University, Ishikawa, September 20–22, 2011 (Oral presentation, I75)