Chapter 1 Introduction

Extreme ultraviolet and soft x-ray regions

The visible light is a very small part of the electromagnetic spectrum, with wavelengths from 380 to 780 nm. The extreme ultraviolet (EUV) range extends from the photon energy of about 30 eV to about 250 eV, with corresponding wavelengths from about 5 nm to 40 nm. The energy of soft x-rays extends from 250 eV to several keV. The application of these spectral regions consists of two sides:

1. The resolution of an optical system is limited by the well-known Rayleigh criterion: Δ ~ λ/NA, where NA is the numerical aperture of the optical system and λ the working wavelength. Because the wavelengths are relatively shorter, it is possible to see smaller structures as in EUV microscopy [1] and soft x-ray microscopy [2], and to write smaller patterns as in EUV lithography [3].

2. These spectral regions cover the main atomic resonances and absorption edges of most low and intermediate atomic number elements. This provides mechanisms for elemental and chemical identification. Many analysis methods of spectroscopy are developed, such as emission spectroscopy and absorption spectroscopy etc. These in turn lead to new scientific understandings, for instance in materials science [4], EUV and X-ray astronomy [5,6] and plasma diagnosis [7,8]. The optical elements working at EUV and soft x-ray ranges are required in these applications mentioned above. In terms of function, there are imaging elements (spatial resolution), dispersive elements (spectral resolution) and some elements with both functions. At these wavelength ranges, the refractive index of all the materials is close to unity, thus the transmissive lenses cannot be used as optical elements because of the their weak optical contrast with air or vacuum. On the other hand, the strong absorption limits the application of single reflective interfaces as mirrors. An exception for achieving high reflectivity is the total external reflection at grazing incident angle [9,10]. The shortcoming of this optics is their large image aberrations, small collection solid angle and bad spectral resolution. The diffraction elements such as grating and zone plate can offer good spectral resolution. However, they also suffer from strong absorption of materials thus from low diffraction efficiency [11].

Bragg reflection of radiation by the lattice planes of crystalline structures is a well-known phenomenon. It can serve as a technique to analyze crystalline materials and it also can be used to monochromatize x-ray radiation and to design x-ray optics. However, the wavelength ranges are determined by the lattice spacing of the available natural crystals, which are too small to reflect EUV and soft x-ray radiations. This limitation can be overcome by the use of synthetically produced layered structures of alternating materials with a high optical contrast. A multilayer system is composed of alternative layers of two materials. The multilayers permit the achievement of high reflectivity, with a modest spectral bandwidth at EUV and soft x-ray wavelengths. It has been proposed and experimentally demonstrated that it is possible to improve the resolution by making multilayer grating at the detriment of a loss of reflectivity [12][13][14]. The multilayer gratings can be prepared by multilayer deposition onto a structured substrate or lithographically etching a flat multilayer structure. In summary, multilayers nowadays play an important role for optical applications from the EUV to x-rays ranges.

Multilayer mirrors 1.2.1 Theory of multilayers mirrors

We consider the case of a multilayer structure deposited on a thick substrate, as shown in Figure 1.2. The N layers having the thickness The zeroth layer represents the ambient for incident plane wave. The ambient may be vacuum or air. The (N+1) th layer is the substrate.

The equation of a plane electromagnetic wave in the j th layer at a position r can be expressed as:

( ) ikj r j j

E r E e   ikj r ikj r  ikj r ikj r ikj r (1.1) Figure1. 2 The electric field at j th interface of a multilayer.

where j E is the amplitude of the field at the top of layer j and j k k is the of the wave vector of the j th layer. Its component in z direction is given by: 2 2 s i n 2 2

j z j j j k i         (1.2)
where θ is the grazing angle of incidence, λ is the wavelength of the x-rays. The refractive index of j th layer is

1 j j j n i    
, where δ j is the deviation of real part of the refractive index from unity and β j , the imaginary part, denotes the absorption of x-rays into this material.

The electric field in a layer can be calculated for both s and p polarizations. However, in EUV and x-ray region and usually in grazing incidence and normal incidence condition, the s and p polarizations are almost identical. Here we only consider s-polarization and the boundary conditions at j th layer are:

1 1 1 ( ) j j j T R T j j j j j z T R z T E E E k E E k E             (1.3)
where j T E and j R E are the transmitted and reflected x-ray field amplitudes, at the top of j th layer.

The complex coefficients of reflection r j and transmission t j at the j th interface can be given from Fresnel's formula:

1 , 1 1 1 , 1 1 2 j j j R z z jj j j j T z z j j T z jj j j j T z z E k k r E k k E k t E k k                     (1.4)
Form equation 1.3 and 1.4, the electric field amplitude of reflection and transmission can be solved as:

1 1 1 1 1 1 1 1 1 1 , 1 , 1 1 1 , 1 , 1 1 ( ) 1 (
)

j j z j z j j j z j z j ik d ik d j j j R R T j j j j ik d ik d j j j T T R j j j j E E e E r e t E E e E r e t                                    (1.5)
The reflectance from the top of the j th ayer, including multiple reflections is now calculated.

The recursive relation can be seen from the calculation of reflectance of the next layer up, which is called Parratt recursive method: For periodic multilayers, all reflected radiation at all interfaces should be added in phase.

When the phase factor of one period where m is the order of Bragg reflection. Considering the refraction of material, the Bragg law should be modified as: Maximum of reflectivity for a multilayer mirror occurs when its period satisfies equation (1.8).

It can be describe as an analogy of reflection of crystal as shown in Figure 1. From the Bragg law, it is clear that multilayer mirrors can be dispersive elements: at a particular angle, one wavelength is reflected for each Bragg order. The resolving power of a multilayer is given by the kinematical theory of x-ray diffraction [15]:

max E mN E     (1.10)
where E is the photon energy and N max is the maximum number of periods that contribute to the overall reflection. We can conclude that a large number of effective periods increase the resolution of a multilayer mirror. N max is corresponding to the penetration depth of incident

x-rays into the multilayer and determined by the incident angle and the absorption coefficient of materials.

Taking absorption into account, the reflectivity of the multilayer can be increased by reducing the thickness of the absorber layer. The optimum value of the thickness ratio Г=d A /d is given by [16]:

tan B opt opt AB            (1.11)

Material selection for multilayers

Multilayer for EUV and x-rays can also be seen as an extension of traditional optical coatings to shorter wavelengths. However, the absorption of materials in this wavelength range should be considered. The most important choice of material selection is that of the spacer (low Z) material. To obtain a maximum reflectance, this should be a material with as low absorption as possible at the working wavelength. The absorption coefficient of a material is quite small when the required wavelength is slightly larger than the absorption edge, and the refractive index has greater contrast with another material because of anomalous dispersion [17]. Thus the selection of spacer is dependent on the absorption edges in EUV and X-ray ranges. For example, boron-based multilayers perform well above the boron K-edge at 6.6 nm and Mg-based multilayers are for applications in the range close to the Mg L-edge at 25nm. Selection of the absorber material should be based on a maximum difference in refractive index, specifically in real part. Generally, heavy metals such as Mo, Ru, Cr, W etc. are choosing as absorber layers.

Furthermore, in EUV and x-ray ranges, individual lagers are each about a few nanometers thick, i.e. made of 10 to dozens of atomic layers. That is to say that the quality of interfaces greatly affects the optical performance of a multilayer. Thus in addition to optical contrast and absorption, chemical diffusion or reaction of the materials should also be considered while choosing the materials.

The imperfection of interfaces

The interfaces of a multilayer in practice are far from perfect. The optical performance of a multilayer mirror however depends critically on the interface quality which is defined by the morphological roughness and interdiffussion of the two materials at the interfaces. For the diffused interfaces, the refractive index profile perpendicular to the interfaces traces the composition gradient. For rough interfaces, there is discontinuous change in refractive index at the interface. However, the laterally average profile of a rough interface also presents a gradient, as shown in Figure 1.4. Thus the morphological roughness (σ r ) and diffusion (σ d ) affect the specular reflectivity in the same way: the imperfect interfaces reduces the reflectivity by lowering the optical contrast of the two materials.

In most cases, the imperfection of an interface is taken into account as a Gaussian distribution through a Debye-Waller factor:

22 exp( / 2) k   ,
where k is the amplitude of wave vector and σ can be described by [START_REF] Clift | Improved reflectance and stability of Mo-Si multilayers[END_REF] =+ rd    [18]. For the calculation of reflectance with imperfect interfaces, equation (1.4) should be multiplied by the Debye-Waller factor.

Thus the reflectance is given by:

2 2 -4 sin -2 0 0 = exp( ) exp( ) m d R R R      (1.12)
where R 0 is the reflectance from ideal interfaces. According to this equation, the shorter the wavelength, the more the interface width will have a negative impact on the optical performance of multilayer mirrors. The interface width of multilayers is typically several atom layers thick. Interdiffusion in these nanoscale multilayers is a phenomenon not as well understood as diffusion in bulk materials. It attracts considerable research interest, not only in understanding of the phenomenon itself, but also in so-called "interface engineering" to improve of the interface quality, thermal stability and stress property in practical applications. The interface engineering methods include diffusion barrier layer, nitrogen incorporation, ion assistance, etc.

For example, researchers revealed that Mo/Si multilayers consist of layers of polycrystalline Mo and amorphous Si that are separated with interdiffusion regions of mixed composition.

Diffusion at Mo-on-Si interface was found to be much larger than that at Si-on-Mo interface.

Because it is easier for Si to penetrate into the amorphous growing Mo layer at Mo-on-Si interface than for Si to penetrate into textured Mo grains at Si-on-Mo interface [START_REF] Bajt | Investigation of the amorphous-to-crystalline transition in Mo/Si multilayers[END_REF][START_REF] Yulin | Interlayer transition zones in Mo/Si superlattices[END_REF]. Using sub-nanometer carbon or B 4 C as diffusion barriers, the reflectance of Mo/Si multilayers can be enhanced [START_REF] Yulin | Interface-engineered EUV multilayer mirrors[END_REF][START_REF] Clift | Improved reflectance and stability of Mo-Si multilayers[END_REF]. Such an increase was reported from 68.8% at 13.4 nm for magnetron sputtered Mo/Si multilayers, to 70% at 13.5 nm by using B 4 C at both interfaces. Reactive sputtering with N 2 was used to deposit Co/C, W/B 4 C and Cr/Sc X-ray multilayers [START_REF] Ghafoor | Incorporation of nitrogen in Cr/Sc multilayers giving improved soft x-ray reflectivity[END_REF][START_REF] Windt | Reduction of stress and roughness by reactive sputtering in W/B4C multilayer films[END_REF][START_REF] Bellotti | Depth-graded Co/C multilayers prepared by reactive sputtering[END_REF]. In comparison to films deposited non-reactively, reactively-sputtered films show lower stress and lower roughness. Moreover, ultra-thin (d<1.7nm) Cr/Sc and Cr/Ti multilayers show severe roughness and layer distortions. By using ion-assisted growth (ion energy range of 21 eV to 37 eV and an ion flux of 10 ions per deposited atom), the intermixing, flattening and abruptness of interfaces were improved [START_REF] Eriksson | Atomic scale interface engineering by modulated ion-asssted deposition applied to soft x-ray multilayer optics[END_REF][START_REF] Ghafoor | Effects of ion-assisted growth on the layer definition in Cr/Sc multilayers[END_REF].

Thermal stability

The other parameter, which is crucial for the application of multilayer mirrors, is the stability. Multilayers usually are exposed to high heat-load and large flux radiation for long time, such as in application of synchrotron radiation and astronomy [START_REF] Ziegler | Multilayers for high heat load synchrotron applications[END_REF][START_REF] Ziegler | Stability of multilayers for synchrotron optics[END_REF][START_REF] Mitsuda | The high-resolution x-ray microcalorimeter spectrometer system for the SXS on ASTRO-H[END_REF]. The as-deposited multilayer may not be in thermal equilibrium which generates chemical and physical instabilities. It is known that the structure and interfaces of multilayers can change during heat treatment, e.g. period expansion, interdiffusion and crystallization [START_REF] Vitta | Thermal stability of 2.4 nm period Ni-Nb/C multilayer x-ray mirror[END_REF][START_REF] Böttger | Thermal stability of Mo/Si multilayers with boron carbide interlayers[END_REF]. Roughness and interdiffusion lead to formation of compounds and interlayers at the interfaces. The two-layer periodic stack may become a three-or four-layer periodic system [START_REF] Wu | Interlayer microstructure of sputtered Mo/Si multilayers[END_REF][START_REF] Zhong | Optical and structural performance of the Al (1% wtSi)/Zr reflection multilayers in the 17-19nm region[END_REF]. Therefore it is necessary to study the possible thermal changes in multilayers when they are in the extreme environments. It helps in not only predicting the optical performance, but also understanding the physical-chemical environment of interfaces in the multilayers in order to improve their stability.

For convenience, the thermal-induced change mechanisms in multilayer are often investigated by thermal annealing instead of real intense radiation. For example, thermal annealing studies of Mo/Si multilayers have shown that the crystallization of layers and silicides such as MoSi 2 and Mo 5 Si 3 grow from room temperature to 800°C [START_REF] Nedelcu | Thermally enhanced interdiffusion in Mo∕ Si multilayers[END_REF]. Another feature of annealed Mo/Si system is the reduction of period due to the formation of denser silicides [START_REF] Holloway | Interfacial reactions on annealing molybdenum-silicon multilayers[END_REF]. In a metal/carbon system, the annealing process usually induces an increasing in the period thickness due to expansion of carbon layers [START_REF] Tu | Structural Changes Induced by Thermal Annealing in Cr/C Multilayers[END_REF][START_REF] Jiang | Improvement of the thermal stability of W/C multilayers[END_REF] or the crystallization of metal layers [START_REF] Lodha | Thermally induced structural modification in Pt/C X-ray multilayer mirrors fabricated by electron beam evaporation[END_REF].

Application of multilayer monochromator

DuMond and Youtz reported the first positive results of multilayers in 1940 [START_REF] Dumond | An X-Ray Method of Determining Rates of Diffusion in the Solid State[END_REF]. By evaporation, they made periodic structures composed of alternate layers of Au/Cu, with a period of 10 nm, and observed diffraction of x-rays from the superlattice. However, the diffracting power decayed to zero in just about a month as the interdiffusion of two metals. In 1967, Dinklage found that Fe/Mg structures with a period of 3-5nm can last for more than one year [START_REF] Dinklage | X-Ray Diffraction by Multilayered Thin-Film Structures and Their Diffusion[END_REF]. The peak diffracted intensity for soft x-rays is comparable to that from a lead stearate soap film multilayer structure made by the Langmuir-Blodgett technique. In 1985, Mo/Si multilayers were fabricated by using magnetron sputtering [START_REF] Jr | Molybdenum-silicon multilayer mirrors for the extreme ultraviolet[END_REF]. The measured peak reflectance was 50% at 17 nm. Because of the potential application in semiconductor industry, Mo/Si multilayers were widely studied by many groups all over the world. With the development of micro-machining and high-precision deposition technology, the Mo/Si multilayer reflectors can show reflectance (70% at 13.5nm) very close to theoretical performance. Nowadays, the first machine to produce computer chips using Mo/Si multilayer optics is commercially available [43].

In some science facilities, multilayers provide a modest spectral bandpass with a relatively high throughput, which can be used a monochromator. In the following we will give examples from solar astronomy, EUV and x-ray spectrometry, plasma phyics and synchrotron radiation.

Solar astronomy

The temperature range of solar atmosphere is 10 4 -10 7 K. A lot of emission lines lie in the EUV and soft x-ray ranges. High-resolution imagers comprising normal-incidence telescope mirrors coated with multilayers tuned to specific coronal or transition-region emission lines have been used in a variety of missions, such as the SOHO [START_REF] Kohl | UVCS: an Ultraviolet Coronagraph Spectrometer for SOHO. The SOHO Mission[END_REF], TRACE [START_REF] Golub | A new view of the solar corona from the transition region and coronal explorer (TRACE)[END_REF] and SDO [START_REF] Podgorski | SDO-AIA mirror performance[END_REF] satellite instruments. Mo/Y (9.4 nm) and SiC/Mg (30.4, 33.5 nm) multilayers. Thus seven EUV channels can be selected in order to observe the solar corona at specific temperatures corresponding to Fe and He ion lines [START_REF] Soufli | Development and testing of EUV multilayer coatings for the atmospheric imaging assembly instrument aboard the Solar Dynamics Observatory[END_REF].

The multilayer-coated normal incidence optics can provide a powerful tool capable of achieving high spatial resolution, wide field of view, broad wavelength coverage, and moderate spectral resolution (λ/Δλ≈10-100). The other parameters which are crucial for the application of reflecting mirrors using in outer space, are the thermal and life stabilities. Additional, shorter period multilayers, such as Mo/B4C, Cr/Ti, Cr/Sc,Co/Mo2C, W/B4C and others may lead to the development of narrow-band imagers operating in the soft x-ray, specifically near the Si VII (7.3 nm), C VI (3.4 nm), O VII (2.2 nm), O VIII (1.9 nm), and Fe XVII (1.7 and 1.5 nm) lines [START_REF] Windt | EUV multilayers for solar physics[END_REF].

EUV and x-ray spectrometry

Characteristic emissions available for the analysis of the light elements (Li, Be, B, C, N) are the EUV and soft x-ray K emission bands. The measurement of these radiations is difficult because of their relatively weak intensities arising from the low fluorescence yield and the strong absorption inside the sample. To compensate for these physical effects, it is necessary to use good x-ray monochromators. Lead stearate, made by the Langmuir-Blodgett technique, can be used to analyse these emissions. Multilayers are nowadays widely used to perform wavelength dispersive spectrometry. Compared to Langmuir-Blodgett soap-films, multilayers have some advantages: 1) they have a larger integrated reflectivity, 2) they offer good stability under thermal and radiation loads and under vacuum; 3) they let one choose the material and structures and thus optimize the energy and reflectance.

Mo/B 4 C and La/B 4 C multilayer monochromators have been reported for the detection of the boron K emission at a large Bragg angle close to 45 o [START_REF] Hombourger | Use of layered synthetic microstructures for the quantitative x-ray analysis of light elements[END_REF] . In the water window, a bent Cr/ Sc multilayer mirror has been used to study the emissions as monochromators for spectroscopy [START_REF] Guen | X-ray spectroscopic application of Cr/Sc periodic multilayers[END_REF]. The use of these multilayers in a curved-crystal or double-crystal spectrometer lead to a spectral resolution good enough to distinguish the chemical state of the emitting B, N or Sc atoms.

With multilayers as monochromator elements, the quantitative analysis is often difficult or even impossible, in particular in case of two close emission lines because multilayers suffer from moderate spectral resolution due to their large diffraction patterns. In 1993, the principle of a multilayer grating monochromator with an improved resolution was given [START_REF] Sammar | Monochromateur multicouche á bande passante e´troite pour le rayonnement X[END_REF]. The device was fabricated by means of combining deposition of thin films on a nanometer scale, UV lithography and reactive ion etching [START_REF] Häussler | Quantitative TEM characterizations of La/B 4 C and Mo/B 4 C C ultrathin multilayer gratings by the geometric phase method[END_REF]. It was possible to improve the resolution by factor 2-3 to the detriment with a small loss of reflectivity [13].

Plasma diagnosis

Multilayer mirrors are widely used for the diagnostics of hot plasmas. By using an assembly of multilayer monochromators, multi-channel polychromators can be realized for spectrally selective radiometry of high-temperature plasmas. A polychromator channel includes a streak camera, a filter cutting off the long-wavelength radiation and a multilayer mirror.

Providing a moderate spectral selectivity, multilayer-based devices offer a high sensitivity and relatively easy way to obtain time and spectral resolution simultaneously. For example, a polychromator for the tokamak facility has five channels at the FOM Institute for Plasma Physics. For measurements of time and spatial distributions of impurity ions in the plasma three spectral lines were chosen: B V (4.86 nm), C VI (3.37 nm) and O VII (2.164 nm) [START_REF] Andreev | Multilayer dispersion optics for X-ray radiation[END_REF].

Researchers in Tongji University have improved this polychromator so that time and spectral resolved one dimensional x-ray imaging can be realized to study implosion dynamics in laser inertial confinement fusion. This facility uses the new optical design of the multi-channel Kirkpatrick-Baez (KB) microscope to obtain high-throughput high-resolution

x-ray images at multi-keV energy bands. It consists of a total reflection mirror in the sagittal direction and two multilayer mirrors in the tangential direction. The two multilayer mirror providing two channels as follow: Cr/C multilayers with d=8 nm at 2 o grazing incidence for 2.5 keV channel (E/ΔE=12),Cr/C multilayer with d=6.8 nm at 1.9 o for 3.0 keV channel (E/ΔE=15). Figure 1.6 shows an image of laser irradiated target in a period of 1 ns obtain from this system. Multilayers are also used for x-ray optical elements in-between single reflective mirrors and crystals at beamlines of synchrotron radiation. The single reflective mirrors work below the critical angle as a low-pass energy filter. The crystal monochromators, using Bragg reflection at much higher incident angles, ha ve typical energy bandwidth (∆E/E) of 10 -4 [START_REF] Freund | Synchrotron hard x-ray beam optics[END_REF].

The typical energy band width of a multilayer is much larger than that of a crystal. In this way the multilayer reflects a larger portion of the energy spectrum leading to increased integral intensity. Thus multilayer is suitable for some application where medium resolution optics with high throughput is required, for instance x-ray imaging and fluorescence [START_REF] Bilderback | Wide bandpass monochromator for synchrotron radiation[END_REF][START_REF] Kazimirov | Multilayer X-ray optics at CHESS[END_REF], where the narrow bandwidth of the crystal optics is not required. Typical multilayer x-ray optical elements, based on materials such as W/B4C, W/Si or Ni/B4C, yield a relative spectral resolution of the order of a few percents.

The multilayer period can be adjusted to arbitrary values, in particular to wavelengths above 1 nm that are hardly or not accessible by crystals. In this wavelength range, multilayer are used to provide a tool for controlling and measuring the polarization properties. The incidence angle is the Brewster angle at which the polarizing power has a maximum. The multilayers are used as polarizers and polarimeters. For example, the multilayer phase retarder are studied at both an SR beam and a laser plasma source near 97 and 277 eV [START_REF] Kortright | Soft x-ray phase retardation using transmission multilayers[END_REF] and in the range 390-570 eV [START_REF] Schäfers | Cr/Sc multila yers for the soft-x-ray range[END_REF]. For the water window spectral range, Cr/Sc have been developed [START_REF] Schäfers | At-wavelength Metrology on Sc-based Multilayers for the UV and Water Window[END_REF] to be incorporated into a high precision polarimeter. Using this setup, the full polarization state of the light from the beamline could be determined at energies around 400 and 570 eV.

Curved geometries can be manufacteasily with multilayers that are deposited on bent or curved substrates than bending a crystal to small radii of curvature. Focusing or collimating multilayer optics generally require a lateral thickness gradient to meet with Bragg conditions with varying angle of incidence along the whole length of the mirror [START_REF] Morawe | Double gradient multilayers for broadband focusing[END_REF]. An x-ray beam has been focused in one direction to a width of 7 nm in SPring-8 synchrotron radiation facility by using a Pt/C multilayer coated on a elliptically curved substrate [START_REF] Mimura | Breaking the 10 nm barrier in hard-X-ray focusing[END_REF].

Another application of multilayers in synchrotron radiation is quantitative analysis of the high order spectral purity in a soft X-ray beamline output. A multilayer is used as a bandpass filter for order sorting with the angle of incidence changing. An example is given in reflectometry of a normal incidence Cr/C multilayer mirror for use around 282 eV [START_REF] Hatano | Multilayer reflectometry and quantitative analysis of higher order diffraction impurities of grating monochromator[END_REF].

The contribution of this thesis

As mentioned in 1.2.3 and 1.2.4, for the research of multilayer coatings, great effort can be expected in two areas of : 1) research for new material combinations for multilayer mirrors with improved optical performances; 2) study of interface engineering methods to improve the interface quality and thermal and radiation stabilities. Our work focuses on several material combinations as follows:

Mg-based multilayer mirrors are promising in the 25-40 nm range for Mg L absorption edge lies in 25nm. Co/Mg multilayers are found with minor diffusion and roughness. Besides, Co/Mg multilayers have a slightly better thermal stability than traditional SiC/Mg multilayers.

In chapter 3, barrier layers are considered to further improve the optical performance and stability of Co/Mg multilayers. Zr barrier layer can significantly increase the thermal stability of Mg/Co to 400°C without optical performance degradation. Additionally, analysis of fluorescence induced by soft x-ray standing waves, which can yield valuable information about the depth profiles of specific elements in the multilayers, is discussed in this chapter.

The most important problem for the multilayer working in the range of "water window" is the extremely high sensitivity to interface imperfections. The interest in multilayers containing C and Ti are called for by their high theoretical reflectivity in the range of the anomalous dispersion at their absorption edges. In chapter 4, a comparative study of the thermal stability of Co/C and Cr/C multilayers is described firstly. In chapter 5, two interface engineering methods are used to improve the interfaces of Ti-based multilayers. We intentionally incorporated B and C into Cr/Ti multilayers by depositing ultra-thin B 4 C at the interfaces and using reactive sputtering with N 2 to deposit Co/Ti multilayers. We show that the interfaces and soft x-ray reflectivity of Ti-based multilayers are enhanced by interface engineering.

As Co is a ferromagnetic material, the multilayer containing Co can be analyzed by magnetic techniques, for instance nuclear magnetic resonance spectroscopy. In chapters 3 and 4, this characterization technique is used for Co/Mg, Co/Ti and Co/C multilayers to understand the behavior of Co atoms in these multilayers.

Boron-based multilayers are expected to perform well above the Boron K-edge at 6.6nm.

Mo/B 4 C multilayers are promising for the wavelengths near 6.7-7nm because of its good thermal stability and it is easy to handle. The shortcoming of Mo/B4C system is its asymmetric interfaces and high intrinsic stress. The research presented in chapter 6 shows that replacement of molybdenum by molybdenum carbide (Mo 2 C) can limit the reaction and diffusion of boron and carbon atoms with molybdenum ones. The thermal stability and stress are also improved by Mo 2 C/B 4 C multilayer system.

Chapter 2 Experimental

Sample preparation

High performance EUV and X-ray multilayer mirrors have been successfully deposited with different physical deposition techniques including evaporation [START_REF] Spiller | Controlled fabrication of multilayer soft x-ray mirrors[END_REF], sputtering [START_REF] Barbee | Multilayers for X-ray Optics[END_REF] and pulsed laser [START_REF] Gaponov | Multilayer mirrors for soft x-ray and VUV radiation[END_REF]. Magnetron sputtering and electron beam evaporation are the most widely used. Magnetron sputtering is a plasma vapor deposition (PVD) process in which the plasma is created and where positively charged ions from the plasma are accelerated by an electrical field superimposed on the negatively charged target. The positive ions are accelerated by potentials ranging from several hundred to several thousand electron volts and strike the negative electrode with sufficient force to dislodge and eject ato ms from the target. These atoms will be ejected in a cosine distribution from the face of the target and will condense on surface of substrate that is placed close to the sputtering target. The targets are fabricated from materials that one wishes to deposit. Usually, conductive materials can be deposited using a direct current (DC) power supply and insulators can be deposited by using a rad io frequency (RF) power supply.

Compared with electron beam evaporation, magnetron sputtering have several advantages: 1) the deposited atoms have higher kinetic energy (about 10 eV, two orders of magnitude higher than electron beam evaporation) so that the deposited films are denser and smoother 2) the thickness of individual layers can be precisely controlled by the sputtering time; 3) it is possible to deposit laterally gradient multilayers on figured substrate.

All the samples in our work are deposited by DC magnetron sputtering system (JGP560C6, SKY Inc., China) with high-purity targets of Co, Mg, Zr, Mo, B 4 C, C, Mo 2 C, Cr and Ti targets. The working gas is argon (purity 99.999%). The base pressure is 1×10 -4 Pa and the sputtering gas pressure is 0.13 Pa (1 mtorr). The multilayers are deposited onto ultra-smooth polished Si substrate with surface roughness of 0.3 nm.

A large part of this thesis involves the research of multilayers at elevated temperatures, enabling the study of thermally induced change of structure and interfaces. The samples are mounted on a holder heated by a wire-wound furnace in a vacuum chamber with a base pressure of 3×10 -4 Pa. The samples are heated at temperatures in the range 200-600°C keeping for 1 hour. A thermocouple enables the temperature reading from the holder.

X-ray measurments

The physical properties of multilayer samples, such as interdiffusion, roughness and crystallinity can be studied by X-ray measurements using X-ray diffractometry at 0.154 nm (Cu Kα emission at 8048 eV). The structural qualities of all multilayers have been checked by us ing X-ray reflectivity using of a grazing incidence X-ray reflectometer (D1 system, Bede Ltd.). The principle of grazing incidence x-ray reflectivity (XRR) at specular direction is mentioned in section 1.2.1. Bragg law corrected for refraction is used to obtain the multilayer period. We can determine individual layer thickness, interface width and layer density by fitting the XRR curves. The fitting process utilizes recursive equation (1.4) for calculating the reflection curve and genetic algorithm for optimization [START_REF] Windt | IMD-Software for modeling the optical properties of multilayer films[END_REF].

An additional method to analyze the correlated morphological roughness is diffuse scattering (off-specular). Rocking curves are measured by using the same diffractometer with the detector fixed at the angle of first order Bragg peak, while the detector is scanned around it. In this work, we performed rocking curves measurement for the Co/Mg, Co/Ti and Co/C multilayers. We can know the morphological roughness of the interface by fitting the rocking curve by a kinetic theory (distorted wave Born approximation) [START_REF] Savage | Determination of roughness correlations in multilayer films for x-ray mirrors[END_REF] with some interface parameters (fractal exponent, correlation length) which can obtained from the X-ray scattering diagram in the out-of-plane geometry [START_REF] Li | Integration method for directly analyzing interface statistics of periodic multilayers from X-ray scattering[END_REF]. This study is only performed for Co/Mg multilayers. For other multilayers, we can only see the variation of the correlated morphological roughness.

In the condition of grazing incidence, the Bragg diffraction in mainly come from multilayer structures. When the grazing incident angle increases (generally, larger than 20 o ), the Bragg diffraction is due to reflection of radiation by the lattice planes of crystalline structures. Thus X-ray diffraction (XRD) at large angle is a technique which can be used to determine the crystallinity of metal layers or their compounds. Analysis of XRD peak can give some information such as crystallite size, orientation of lattice planes, and identification of compounds. In this thesis, the XRD experiments for Co/Mg, Co/C are performed in the symmetric (θ-2θ) geometry by using a Rigaku-Dmax-2550V powder diffractometer.

The reflectivity of multilayers at working wavelength can be made by scanning the wavelength at an incident angle or by scanning the incident angle at a wavelength. The intensity measurements are made by a silicon photodiode which can convert lights into electric currents. The reflectivity is calculated by the ratio of the two currents corresponding to the reflected and direct incident beams. The Co/Mg multilayers are measured on BEAR beamline at the Elettra synchrotron facility, Italy. The measurements of Cr/Ti multilayers are made in on beamline I06 at the Diamond Light Source, United Kingdom, and the Mo/B4C and Mo2C/B4C multilayers on beamline 3W1B at the Beijing Synchrotron Radiation Facility (BSRF), China.

Fluorescence induced by x-ray standing wave

Angle-dependent X-ray fluorescence (XRF) analysis is an important tool which has been used to investigate the depth profile of impurity atoms in surfaces, thin films and absorbed molecules. Grazing incidence XRF was demonstrated by Becker for the first time in 1983 [START_REF] Becker R S | X-ray evanescent-wave absorption and emission[END_REF]. Barbee applied the angle-dependent GIXRF to the study of periodic multilayer [START_REF] Barbee | X-ray evanescent-and standing-wave fluorescence studies using a layered synthetic microstructure[END_REF].

X-ray standing waves generated by the multilayers are a sensitive probe to obtain the depth profile of impurity elements and interdiffusion at the interfaces [START_REF] Mény | Satellite structure of 59Co NMR spectra in some Co alloys[END_REF]. The fluorescence intensity of a selected element depends not only on the depth profile of the specific atoms inside the sample, but also on the electric filed in the multilayer structure, which can be controlled by changing the grazing incidence angle. Compared with XRF, XRR technology is more sensitive to the density variations and surface/interfacial roughness in multilayers. The combined analysis of XRR and XRF permits the determination of consistent micro structural parameters of multilayers.

Theory of Fluorescence induced by x-ray standing wave

Using the model mentioned in section 1.2, the normalized x-ray intensity ( , ) jj Iz  in j th layer at depth z j of a multilayer is given by:

      2 2 2 , , , (0)
(0) ( , ) (0)
(0) (0) exp 2 exp 2 2 cos ( ) 2 (0) (0) jj TR jj j T jj RR j z j j z j j z j jj TT EE Iz E EE k z k z k z EE                  (2.1)
where (0)

() (0) (0) (0) (0) jj i RR jj TT EE e EE  
(2.

2)

The XRF yield from element A in a multilayer, ()

A Y  is given by: 1 , , 11 , , ,A j 0 ( / ) ( ) exp ( ) sin ( / ) ( ) ( ) ( , z ) exp sin j j N n E n n A j A jn d jE j A j j j j j j d YY Y C z I z dz                                (2.3)
where , () jA Y  is the emitted fluorescence intensity by atoms of element A distributed in the j th layer.

()

A
Y  is calculated by the sum of the contributions from each layer corrected by the absorption from the upper layers.

,A () jj Cz is the concentration profile of element A in the j th layer. j  is the density of j th layer.

, ( / ) jE  is mass attenuation coefficient of j th layer at the energy of emitted fluorescence.  is the take-off angle of the emitted fluorescent x-rays from the surface.

Experimental

On the BEAR beam line at Elettra synchrotron radiation facility. We perform In the GIF case, the resolution is governed by the divergence of the incident beam, which is generally quite small on synchrotron beam lines. A 50 µm wide slit is put into the path of incident beam to further decrease the divergence of the beam. In the GEF case, the angular resolution is governed by the aperture of the detector. The original aperture of the detector is 0.9 o . In order to decrease the aperture of the detector, a 0.5 millimeter wide slit is put between the detector and the sample. The fluorescence radiation is detected by using a silicon drift detector cooled to around -15 °C. For each experiment, two different energies of incident beam are used: 807.6 eV for Co Lα emission and 1332 eV for Mg Kα emission.

Nuclear magnetic resonance spectroscopy

Nuclear magnetic resonance (NMR) spectroscopy is based on the fact that nuclei of atoms have magnetic moment that can be utilized to yield chemical information. The NMR allows the observation of specific quantum mechanical magnetic properties of the atomic nucleus. There are two possible measurement techniques. One is the conventional NMR where the sample needs to be placed in a high magnetic field. The applied magnetic field serves several purposes. Most nuclei have two states: spin-up and spin-down. When nuclei are placed in a magnetic field, the spin-down state is at a higher energy level than the spin-up state. The sample is excited by radio waves and then we measure the energy absorbed or emitted when nuclei flip between the two states. The same nuclei in different parts of a molecule have slightly different transition frequencies. Thus measuring these frequencies allows determining the environment of particular atoms in the molecule. The other one is the zero-field NMR; in this mode no external field is applied and the nuclei are excited by the oscillation of the hyperfine field which is created by the spontaneous magnetic moment in the magnetic materials.

The zero-filed NMR spectroscopy for magnetic material probes primarily the hyperfine field, which is arising from local magnetic moments around the observed nuclei. The hyperfine field determines the NMR frequency and its strength depends on the local symmetry and chemical environment of the probed nuclei [START_REF] Mény | Satellite structure of 59Co NMR spectra in some Co alloys[END_REF][START_REF] Malinowska | The anisotropic first-neighbour contribution to the hyperfine field in hexagonal-close-packed Co: a nuclear magnetic resonance study of diluted alloys and multilayers[END_REF]. This analysis yields the fractions of atoms involved in the various atomic configurations or structural components in a sample. In the materials which contain magnetic and non-magnetic composites, these are mainly the bulk of the magnetic phase and its interfaces with the other phase. For a perfect Co/X multilayer, the spectrum should exhibit two peaks: one for the bulk part of Co layers and another for Co atoms at the interfaces because the alien atoms as nearest neighbor of the probed atoms shift the resonance frequency. In real multilayers, there are a certain amount of interdiffusion and admixture at the interfaces. Thus the peaks usually become broad since the NMR reflects the probability distribution of all nearest neighbor configurations in the samples (each configuration giving rise to a characteristic structure in the spectrum) .

In The energy of the emitted photoelectrons is determined using an analyzer and this gives a spectrum with a series of photoelectron peaks. The binding energy of the peaks are characteristic of each element. The peak areas can be used (with appropriate sensitivity factors) to determine the composition of the materials surface. Normally, in the outmost several nanometer of thin films surface XPS can identify all elements (at concentration larger than 0.1 atomic %) except H and He [START_REF] Vickerman | Surface Analysis-The Principal Techniques[END_REF]. The detailed information of each element in the thin film can be obtained from the narrow scan spectrum of XPS.

XPS measurements are carried out for the Cr/Ti and Cr/C multilayer. The measurements are performed on a Thermo Scientific K-Alpha system with an Al Kα source. The binding energy scale is calibrated from hydrocarbon contamination using the C 1s peak at 284.6 eV.

The surfaces of samples are removed by argon ions (3 keV) sputtering until we can get the information of the interface before the measurements. Narrow scan spectra are analyzed using a nonlinear Shirley-type background. The peak positions and areas are optimized by a weighted least-squares fitting method using 70% Gaussian, 30% Lorentzian lineshapes.

Transmission electron microscopy

Cross-section transmission electron microscopy (TEM) can provide 2D analysis for a 3D specimen and magnifications of hundreds of thousands times can be routinely obtained for many materials making it an ideal method for the study of multilayers [START_REF] Stearns | TEM and x-ray analysis of multilayer mirrors and beamsplitters[END_REF]. A focused high energy electron beam (40 to 400 keV) penetrates a thin perpendicular slice of the multilayer.

It contains information about the structure of the slice that is magnified by an objective lens system. From the TEM images, darker areas of the image show that the sample is thicker or denser in these areas, so we can observe the different components and structures of the specimen from a grayscale. TEM provide a high resolution image for nanomaterials but also it can distinguish each layer within a nanostructured material. Additionally, the selected-area electron diffraction SAED can be performed for a part of the specimen. It is similar to XRD, but unique as areas as small as several hundred nanometers in size can be examined, whereas XRD typically samples areas having several centimeters in size.

The Cr/Ti, Mo/B4C, Mo2C/B4C multilayers are measured by using high resolution TEM (FEI-TECNAI G2 F20) operated at 200 kV. For preparation of sliced sample, the multilayers are thinned by dimpling that followed by ion milling to get a large electron transparent area.

Ion milling is carried out using a 5 keV Ar ion beam at 5° grazing angle.

Raman scattering

Raman scattering (RS) is a standard nondestructive tool for the characterization of crystalline, nanocrystalline, and amorphous carbon since it is sensitive to changes in translational symmetry in materials [START_REF] Ferrari | Raman spectroscopy of amorphous, nanostructured, diamondlike carbon, and nanodiamond[END_REF]. The RS spectra of disordered graphite show two sharp modes: the G peak around 1580 cm -1 and the D peak around 1360 -1 , usually assigned to zone center phonons of E 2g symmetry and K-point phonons of A1 g symmetry, respectively.

The unusual fact is that G and D peaks, of varying intensity, position, and width, continue to dominate the RS sprctra of nanocrystalline and amorphous carbons, even tho se without widespread graphitic ordering. The visible RS spectra depend formally on the configuration of the sp 2 sites in sp 2 -bonded clusters.

In this thesis, we made the RS on Cr/C multilayers, both un-annealed and annealed, which have (for those annealed to 600°C ) period expansion. The RS are carried out with a HORIBA JOBIN YVON HR-800 Raman instrument using an argon-ion laser operating at 514.5 nm. Considering the balance between the signal-to-noise ratio and the measuring time,

we chose an integration time of 5 s and took 10 accumulations for each spectrum. The RS are made in a backscattering mode at room temperature. The RS spectra can be decomposed into two Gaussian lines, where the line position and full width at half maximum are given with a fitting error lower than 10 cm -1 .

Some common characterization methods mentioned above are listed in Table 2.1:

Table 2.1: Lists all the analysis techniques used in our work and their advantages and From the phase diagram, the Mg-Co system is stable in the solid state up to a high temperature. The only possible compound is MgCo 2 [START_REF] Clark | The Co-Mg (cobalt-magnesium) system[END_REF]. Mg/Co can be stable at 200°C [START_REF] Zhu | Comparison of Mg-based multilayers for solar He II radiation at 30.4 nm wavelength[END_REF] and further investigation on the heat resistance of this multilayer is rare.

X-ray diffuse Scattering

The X-ray scattering diagram of the as-deposited sample in the out-of-plane geometry is showed in Figure 3.2 (a). The integration method was used to analyze the measured diagrams.

A detailed description of the methods can be found in Ref. [START_REF] Li | Integration method for directly analyzing interface statistics of periodic multilayers from X-ray scattering[END_REF]. There is no obvious change for the annealed samples thus they are not presented here. The red area represents the high intensity and the blue area represents the low intensity. There are four Bragg sheets in the diagram. The black area between the first and second Bragg sheets is the beamstop which is inserted to shade the reflected beam. According to Stearns [START_REF] Stearns | X-ray scattering from interfacial roughness in multilayer structures[END_REF], the full width at half-maximum (FWHM) of the m th Bragg sheet (q z direction) is proportional to ξ⊥, the vertical correlation length, i.e. FWHM≈2mπ/ξ⊥. The analyzed result of vertical correlation length is shown in Figure 3.2 (b). The power spectral density (PSD) function is shown in The results of XDS (rocking curve) are presented in Figure 3.3. After 300°C annealing, the XRD curve is similar with the one of as-deposited sample but the intensity of scattering decreases at 350°C. We can know the geometrical roughness of the interface by fitting the XDS curve by using the parameter (ξ⊥, ξ‖ and α) obtained from the X-ray scattering diagram.

After 350°C annealing, the geometrical roughness decreases.

The roughness deduced from the fitting of XRR (σ t ) is an overall imperfection of interfaces, including the contributions from both geometrical roughness (σ r ) and interdiffusion (σ d ). According to the equation σ t 2 = σ r 2 +σ d 2 , the interface width can be calculated. These values are collected in Table 3.1. They show that σ t increases with the increasing of temperature but σ r has a decreasing tendency. That is to say, the deterioration of the interface is due to the interdiffusion of the layers of Co and Mg. However, introducing a Zr layer at one or at the other interface or at both interfaces of Mg/Co does not induce an equivalent effect on the optical performances. We are interested in understanding this asymmetrical behavior by correlating the mirror reflectivity to the quality of its interfaces.

Samples

We prepare two sets of Co/Mg-based multilayers. The first is designed for high reflectivity at 25.1nm at 45 o incidence angle. This set is performed for NMR measurements.

The thickness is expressed in nm: Mg (14. for Mg Kα emission.

Nuclear magnetic resonance spectroscopy

The NMR spectra of all samples are presented in Figure 3. For the grazing exit mode, no geometrical factor has been taken into account since this correction is generally significant only for the very small incident angles. On the other hand, during the deposition of Zr on Co, no such chemical driving force exists;

therefore the intermixing at Zr-on-Co interface would take place as a result of random thermal motions only and hence concentration profile is expected to be an error function.

Conclusion

We have probed the interface quality through NMR and XRF induced by x-ray standing wave measurements. The Zr-on-Co interface is found quite sharp while a strong intermixing process is evidenced at Co-on-Zr interface and mixing layer exists with approximate composition of Co 4 Zr. This difference in the structure of the two interfaces is the cause of different diffusivities at the two interfaces.

Chapter 4 Study the thermal stability of carbon-based multilayers

Carbon-based multilayers exhibit a high reflectivity near the carbon K-edge at 4.47 nm where the absorption of carbon is low. Co/C and Cr/C multilayers show high theoretical reflectivity [START_REF] Takenaka | Soft X-ray reflectivity and structure evaluation of CoCr/C multilayer X-ray mirrors for spectral region around 6nm[END_REF] and state-of-the-art Cr/C [START_REF] Hatano | Multilayer reflectometry and quantitative analysis of higher order diffraction impurities of grating monochromator[END_REF] and Co/C [START_REF] Artyukov | Carbon window soft x-ray imaging using multilayer optics[END_REF] multilayers have near normal reflectance of about 18.7% and 14.8% respectively. In this chapter, we present the interfacial 4.1. When Γ is smaller than 0.5, the period and carbon layer thicknesses decrease. When Γ is larger than 0.5, the opposite situation occurs after annealing.

For all samples, the chromium layer thickness decreases and the interlayer thickness increases after annealing. The Cr-on-C interfacial layers are about 0.3 nm-thick for the as-deposited samples and increase to about 0.4 nm. The C-on-Cr interfacial layers grow from 0.6 nm to 0.9 nm after annealing. From the results of RS, we confirm the initial states of the amorphous carbon in Cr/C multilayers. After annealing at 600°C, the further graphitization of the carbon layers can be observed. I(D)/I(G) is related to the size of the graphite planes in the carbon films [START_REF] Robertson | Properties of diamond-like carbon[END_REF] and this has been used to analyze the thermal stability. [START_REF] Funada | Thermal properties of DLC thin films bombarded with ion beams[END_REF] However, Cho et al. [START_REF] Cho | Effects of substrate temperature on chemical structure of amorphous carbon films[END_REF] have observed that when the value is larger than 1.1, the linear relationship between I(D)/I(G) and the inverse of the microcrystalline size 1/L a may no longer hold. They attribute the increase of the I(D)/I(G) ratio to the increase of the number of graphite microcrystallites wit h defects.

This also explains the increase in the intensity of D peak for most amorphous films after annealing at a higher temperature [START_REF] Dillon | Use of Raman scattering to investigate disorder and crystallite formation in as-deposited and annealed carbon films[END_REF]. The D peak intensity usually increases after annealing above 300°C and this phenomenon is generally due to the conversion of sp 3 bonds to sp 2 bonds and the change of the carbon structure to nanocrystalline graphite [START_REF] Funada | Thermal properties of DLC thin films bombarded with ion beams[END_REF]. For our results, the intensity of the D peak increases after annealing and this shows that the structure of the carbon is at the beginning stage of the graphitization process. Full graphitization should be obtained over 2000°C [START_REF] Jiang | Raman scattering from carbon in tungsten/carbon multilayer films[END_REF]. The sp 3 fraction in carbon layers decreases after annealing with the density of carbon changes linearly [START_REF] Ferrari | Interpretation of Raman spectra of disordered and amorphous carbon[END_REF]. That is to say, the density of carbon should decrease and the thickness of the carbon layers should increase upon annealing. It is in agreement with the change of carbon layer thickness and density listed in Table 4.1 obtained from the fitting of XRR curves. The NMR spectrum of the Co/C 300°C annealed sample also shows no defined peak, meaning that Co and C atoms are still strongly mixed in CoC x layers. There is a broad structure at 110 MHz showing that some atomic motion occurred during annealing but the exact origin of this signal is difficult to identify. However, compared to the result of as-deposited samples, Co and C may have a tendency of demixing at a temperature of 300°C.

X-ray photoelectron spectroscopy

The demixing process between the Co and C atoms increases the x-ray optical contrast of the Co/C multilayers. That is why the X-ray reflectivity is improved at temperature of 300°C.

The spectrum of the Co/C 600°C annealed sample shows a well-defined peak at about 220 MHz which corresponds to bulk hcp like Co [START_REF] Mény | Satellite structure of 59Co NMR spectra in some Co alloys[END_REF][START_REF] Malinowska | The anisotropic first-neighbour contribution to the hyperfine field in hexagonal-close-packed Co: a nuclear magnetic resonance study of diluted alloys and multilayers[END_REF]. This means that pure Co regions appear and the diffusion decreases at the interfaces. We infer from these results that Co and C layers in the Co/C stack are strongly mixed during deposition and then demixing occurs upon annealing.

X-ray diffuse scattering

The NMR results confirm the decrease of intermixing after annealing. Thus we attribute the deterioration of the interfaces to the increase of correlated morphological roughness.

Therefore, X-ray diffuse scattering measurements are performed. The reduction in reflectivity induced by interface roughness becomes more significant as the multilayer period thickness decreases, because the ratio of the interface roughness to the multilayer period thickness directly affects the reflectivity according to the Debye-Waller factor. Crystallization of metal layers in multilayers can cause an increase of geometrical roughness [START_REF] Bajt | Investigation of the amorphous-to-crystalline transition in Mo/Si multilayers[END_REF]. Crystallites can nucleate at some points during annealing. They have a size limited to the metal layer thickness in the growth direction and are also small in the in-plane

Chapter 5 Improvement of Ti-based multilayers

Introduction

Multilayers for use in the so-called "water window" between the oxygen K-absorption edge at 2.34 nm (529.9 eV) and the carbon K-absorption edge at 4.38 nm (283.1 eV) have important applications for high-resolution microscopy [23, 25, 92], x-ray polarimetry [START_REF] Schäfers | Cr/Sc multila yers for the soft-x-ray range[END_REF] and spectrometry [START_REF] Guen | X-ray spectroscopic application of Cr/Sc periodic multilayers[END_REF]. Many efforts are being put into realizing highly reflective multilayer mirror in this wavelength range. Ti-based multilayers are promising for application in this range close to Ti-2p absorption edge at λ=2.74 nm (452 eV). Cr/Ti and Co/Ti multilayers are two of the suitable candidates because their theoretical near-normal incidence reflectivity is as high as 64% at wavelengths just above 2.74 nm. However the reported experimental reflectivity of these multilayers at near-incidence angles is lower than 3%. According to the Debye-Waller term [105] in the reflectance ,the performance of a multilayer is increasingly influenced by the interface imperfections with a decrease in wavelength and a corresponding decrease in period of multilayers. That is to say, the most important problem for the multilayer working at the range of "water window" is the extremely high sensitivity to interface imperfections. A possible solution for this problem is to prepare compound multilayers instead of elemental multilayers. Both the absorber and the spacer can be made of relatively stable compounds so that the tendency of interdiffusion and reaction at the interface can be minimized.

In The Co/Ti multilayers are optimized for the highest reflectivity at 450 eV at 22.5 o grazing incident angle. They are designed with bilayer number N=20, period Λ=3.7 nm, and thickness ratio Γ=0.55 (Ti layer thickness to period thickness, Γ= d Ti /d). The calculated reflectance with ideal interface is 26.4%.

Argon gas at 1.5 mTorr is used for non-reactively sputtered films, while a small amount of N 2 (99.9995% purity) is added (maintaining the same 1.5 mTorr gas pressure) for reactively sputtered films. The N 2 gas fraction, defined as the N 2 gas flow rate (units of sccm) divided by the total Ar + N 2 gas flow rate, is respectively set to 5%, 10%, 15% and 20% for the reactively sputtered films.

Characterization of structure and interfaces 1. X-ray reflectivity

The grazing incident XRR curves of the Co/Ti multilayers are presented in Figure 5.1 (a).

All the curves are fitted to obtain the interface width and thickness of individual layers. The fitted values are listed in Table 5.1. The reactively sputtered samples show three Bragg peaks while the non-reactively sputtered sample exhibits only two peaks and a relative ly broader first peak than the reactively sputtered ones. That is to say that the interface width decreases remarkably by reactive sputtering (from about 0.8 nm to 0.3 nm from fitting). According to the fitted values of XRR curves, the reactively sputtered samples have a similar interface width. Thus the reduction of soft X-ray reflectivity for the samples which prepared with higher N 2 fraction may be due to the increase of concentration of nitrogen in multilayers.

The absorption effect of nitrogen cannot be ignored at the applicable wavelength range of Co/Ti multilayers which is slightly lower than the nitrogen K edge (410 eV,3.02 nm) 3. Zero-field nuclear magnetic resonance (NMR) spectroscopy NMR spectra for the Co/Ti multilayers are presented in Figure 5.3. To compare the shape of the spectra, all the data are normalized to their total surface area. The spectrum of the nonreactively sputtered sample shows a weak signal without any defined feature in the frequency range of pure Co. This indicates that the Co layers are not pure and alien titanium atoms are mixed with Co over the total Co thickness. The as-deposited multilayers are actually CoTi x /Ti multilayer with probably some concentration gradient at the interface with the Ti layers. In addition some Co atoms are most probably also situated into non-ferromagnetic phases (and therefore give no NMR signal) with a large content of Ti.

For the 5% N 2 fraction samples, an intense peak is observed around 217 MHz. This intense line at 217 MHz corresponds to bulk fcc or hcp Co according to the reference [START_REF] Mény | Satellite structure of 59Co NMR spectra in some Co alloys[END_REF][START_REF] Malinowska | The anisotropic first-neighbour contribution to the hyperfine field in hexagonal-close-packed Co: a nuclear magnetic resonance study of diluted alloys and multilayers[END_REF].

This means the pure Co regions appear and the diffusion decreases at the interfaces. There is a satellite shoulder at 185 MHz showing that some Co atoms still mix with alien atoms (titanium or nitrogen) but the exact origin of this signal is difficult to identify because of the lack of appropriate reference samples. For the 10% N 2 fraction samples, the peak of Co decreases and its position shifts to lower frequency. This peak vanishes for the sample deposited at 15% N 2 fraction. The change of the bulk Co peak is consistent with the change of soft X-ray reflectivity which can be attributed to the increase in the concentration of nitrogen in Co layer and more nitrogen atoms mixed with Co. We did not plot the result of the sample deposited at 20% N 2 fraction because the signal is almost zero for all the frequency range.

That means the Co atoms mixed with nitrogen atoms completely. We infer that the reactively sputtered multilayer consists of under-stoichiometric fcc TiN x layers. Although the distribution of N could not be determined, it can be expected that TiN x will be closer to stoichiometric due to titanium high affinity for nitrogen. The TiN x formation limits the diffusion between the Co and Ti layers.

Conclusion

Co/Ti multilayers are deposited by reactive magnetron sputtering with a nitrogen-argon gas mixture. The reactive sputtering has positive effects on the interfaces of Co/Ti multilayers, effectively forming crystalline fcc TiN x multilayer structures. The reactively sputtered sample with 5% N 2 fraction exhibits 24% higher soft x-ray reflectance than the conventional Co/Ti multilayer. This is attributed to more abrupt interfaces and reduced interdiffusion by reactive sputtering. With the increase of N 2 fraction, the strong absorption of nitrogen in the applicable wavelength range causes a loss to the soft X-ray reflectivity. This is in consistent with the results of NMR. Thus, other light element such as boron or carbon is a better choice than nitrogen in the wavelengths of "water window". Only the first order Bragg peak could be observed for each multilayer because of the ultra-short period. We show the peak reflectivity as a function of the grazing incident angle in

Transmission electron microscopy

Encouraged by the results above, two Cr/Ti multilayers, one without B4C and the other with 0.13 nm of B4C at both interfaces, with periodic number N=600 and period Λ=1.38 nm are deposited. They are designed as high reflection mirrors for wavelength λ=2.73 nm. Figure

Conclusion

We have shown that pure Cr/Ti multilayers with ultra-short period (Λ~1. X-ray and EUV reflectivities are measured and then a qualitative observation and analysis of high-resolution cross-sectional TEM images are presented to study the structure and interfaces of the as-deposited and annealed multilayers. Before and after deposition, the radius of surface curvatures of substrates are measured using a stylus profiler and then the film stress can be calculated. To investigate the thermal behavior of these multilayers, all the samples are annealed at 600°C for one hour in a furnace with a base pressure o f 3×10 -4 Pa. After annealing, the samples are cooled down to room temperature naturally. The measured x-ray reflectance curves of Mo/B 4 C_2 before and after annealing are shown in Figure 6.1 on a logarithmic scale. Four sharp Bragg peaks are observed in the as-deposited sample. The second and fourth peaks almost vanish as Г is close to 0.5. In the annealed curves, the second peak becomes higher demonstrating the variation of Г. All Bragg peaks become broader and slightly shift towards lower angles, which correspond to an expansion of period thickness and to an increase of interdiffusion. We extract the in-depth intensity profile of multilayers along a few periods from the bright field image of each sample. The period thickness is determined by calculating the distance between two peaks. In order to minimize the aberration, we take the average value obtained over almost all the periods of stack. The thickness of one period is determined to be 3.76 nm and 3.81 nm corresponding to the as-deposited and annealed samples, respectively.

To obtain the detailed information of each layer in one period and interface between layers, in-depth intensity profile of one period is magnified and shown in Figure 6.

EUV reflectivity

The measured curves of the EUV reflectance as a function of the wavelength at 10° incidence are shown in Figure 6.5 as black dots. For Mo/B 4 C multilayers, the as-deposited multilayers have a peak reflectance of 22.3%. Annealing to 600°C reduces the reflectance to 17.5%. For Mo 2 C/B 4 C multilayer, the as-deposited multilayers have a peak reflectance of 28.5%. After annealing, the reflectance remains as high as 27.0%. Mo 2 C/B 4 C multilayers present not only a reflectivity higher than Mo/B 4 C ones with same multilayer structure, but also a better thermal stability. This behavior coincided well with XRR and TEM measurements.

The Mo 2 C/B 4 C system provides high reflectivity because of good symmetry of the optical index profile and small interface width. We fitted the EUV curves and the data of interface width are listed in Table 6.2 with the data obtained from the XRR and TEM. All the fitted curves show reasonable accordance with the measured ones. To measure the stress of different mono-layer thin films and multilayers, the radius of surface curvature of substrates are measured before and after deposition using a stylus profiler (Dektak 6M). To ensure the reliability of results , each sample is measured in two perpendicular directions repeatedly.

Results and discussion

Before deposition, the deformations of substrates are almost flat as shown in Figure where t s is the thickness of the substrate and t f is the thickness of the films. In order to avoid or minimize the problem coming from the variation of the optical indices as a function of the incident energy, it would be better to work with a characteristic emission whose energy is far from the energy of the involved core level. For Co-based multilayers, in order to identify the Co x X y (X is the element of Co/X multilayers) compounds at the interfaces, some reference Co x X y disordered alloys and Co/X thin layer with different thickness of X layers when thickness of Co layers are fixed should be prepared and NMR, XES and XPS used to improve the analysis of the Co-based system.

Conclusion

A 27 μm-thick multilayer Laue lens with an outermost layer thickness of 10 nm was designed and fabricated. The focusing property of the MLL was measured at the SSRF. The measured results show that a focusing resolution of 92 nm was achieved at 14 keV. Up to now, this is the best results for MLL in the hard X-ray region in China. More efforts should be made to improve the fabrication process and the nano-focusing experiment system to further decrease the resolution of the MLL.

Figure 1 . 1

 11 Figure 1.1 The electromagnetic spectrum from the infrared to the γ-ray region.

  reflectivity in the ambient can be calculated. Thus the reflectivity of the multilayer is given by 2 0 R  .

  is the thickness of one period), interference enhancement occurs, i.e. Bragg condition:

  average real part of the refractive index for one period: d A and d B are the thickness of the two layers (absorber and spacer, respectively) in one period.

  3.

Figure 1 . 3

 13 Figure 1.3 Reflection scheme of a crystal lattice (left) and a multilayer stack (right).

Figure. 1 . 4

 14 Figure.1.4 Schemes of the interface profile, which describes a rough or diffuse interface.

Figure 1 . 5

 15 Figure 1.5 EUV images of the solar atmosphere at four wavelengths (17.1, 30.4, 33.5 and 9.4 nm, from left to right) The use of multilayer coated optics to obtain astronomy images is illustrated in Figure 1.5. This shows images of the solar corona obtained at nominal 17.1 nm, 30.4 nm, 33.5 nm and 9.4 nm (from left to right) [47,48]. The image was obtained by Atmospheric Imaging Assembly (AIA) instrument aboard the Solar Dynamics Observatory mission (SDO). Four Cassegrain telescopes were coated with Mo/Si (for wavelength at 13.1, 17.1, 19.4, 21.1 nm),

Figure 1 . 6

 16 Figure 1.6 Time resolved image of plasma obtained from Cr/C multilayer coated KB mirror

  and reflected amplitudes of electromagnetic field at the top of j th layer. , jz k and , jz k are the real and imaginary part of k j, the z-component of the wave-vector k. ()  is the phase of the electric field ratio and expressed as:

  angle-dependent XRF measurements induced by x-ray standing waves (XSW) in Co/Mg based periodic multilayers. The incident beam and detector are fixed and the sample is rotated. The angle between the incident beam and the fluorescence detector is about 60 o due to mechanical constraints. Two different experiments are done as a function of the glancing angle: 1) grazing incidence fluorescence (GIF), the grazing incident angle are varied in the range of the Bragg peak of the incident radiation, 2) grazing exit fluorescence (GEF), the grazing exit angle are varied in the range of the Bragg peak of the fluorescence radiation. In this case, the incident angle is large (between 110 and 120°) and the sample surface is very close to the direction of detector, as shown in Figure 2.1.

Figure 2 . 1

 21 Figure 2.1 Scheme of the x-ray fluorescence experiments in the (a) grazing incidence and (b) grazing exit (b) modes.

  this thesis, zero-field NMR spectra of the Co-based (Co/Mg, Co/C, Co/Ti) multilayers are performed with the homemade automated broadband NMR spectrometer of IPCMS, Strasbourg. All the multilayer samples are made measured at 2K since the NMR signal increases as the inverse of the measurement temperature according to Curie's law. All spectra have been recorded for different values of radio frequency field strengths allowing for correcting the NMR intensities with a frequency dependent enhancement factor. The NMR spectra represent the distribution of Co atoms versus their resonance frequency. 2.5 X-ray photoelectron spectroscopy X-ray photoelectron spectroscopy (XPS) is an important surface characterization method which combines surface sensitivity with the ability to obtain elemental and chemical state informations. In the area of thin films, XPS is a widely used analytical tool to give useful information such as composition, chemical state, and thickness etc. of thin films. The principle of XPS is based on the photoelectric effect proposed by Einstein in 1905. This process can be expressed by the equation [74] : binding kinetic E h E     , where binding E is the binding energy of the electron in the atom (a function of the type of atom and its environment), h is the photon energy of x-ray source, kinetic E is the kinetic energy of the emitted electron that is measured in the XPS spectrometer and φ is the work function dependent on both the spectrometer and the detected material. Al Kα (1486.6eV) or Mg Kα (1253.6eV) are common the photon energies. The XPS technique is highly surface sensitive due to the short inelastic mean free path of the photoelectrons that are excited from the solid.

Chapter 3

 3 Study of barrier layers in Co/Mg multilayers

3. 2 . 2

 22 Figure 3.1(a). It shows slight decrease at 300 °C and then, notable decline at 350°C, while no reflectance is obtained after 400°C annealing. Figure3.1(b) presents the XRR curves of Mg/Co multilayers. After 300°C annealing, despite that the Bragg peaks remained intense, the 8 th and higher Bragg orders have shifted a little and broadened, indicating a slight period thickness contraction and the development of interdiffusion. When it comes to 350°C, the multilayer encountered a significant change and the high Bragg orders were not so well-defined compared to the unannealed sample. The roughness of interface increased remarkably and the individual thickness change notably after 300 °C annealing. After 400°C annealing, no Bragg peaks is obtained by the XRR measurements indicating that the annealed sample had no periodic structure. Mg/Co multilayer stayed constant below 300°C and the multilayer structure and reflectance changed when being annealed at 300°C or higher temperatures. After 400°C heat treatment, the multilayer structure has been destroyed and the

Figure 3 .

 3 Figure 3.1 (a) EUV reflectance curves of Mg/Co multilayers before and after annealing (b) XRR curves of Mg/Co multilayers before and after annealing,each curve has been shifted vertically by 4 orders-of magnitude for better discrimination, scatter and solid lines represent measured and fitted XRR curves, respectively.

Figure 3 .

 3 Figure 3.2 (c). It shows a linear feature in the log-log plot at high q y values, thus indicates the power-law asymptotic behavior. The exponent γ is found to be -3.85 by power-law fit and this exponent is associated with the static roughness exponent (also called the fractal exponent) α= 0.928. The autocorrelation function (ACF) which is the Fourier transformation of PSD function, is shown in Figure 3.2 (d). The lateral correlation length ξ‖ is equal to 16.7 nm, deduced by fitting the ACF. The vertical correlation length, lateral correlation length and fractal exponent is 123 nm, 16.5 nm, 0.915 for the 300°C annealed sample and 118 nm, 16.3 nm, 0.922 for the 350°C annealed sample, respectively.

Figure 3 .

 3 Figure 3.2 (a) X-ray scattering diagram of Co/Mg multilayer, as-deposited; (b) the curve of vertical correlation length;(c) PSD and the fitting curve; (d) ACF and the fitting curve.

Figure 3 . 3 X

 33 Figure 3.3 X-ray diffuse scattering (rocking curve) of Mg/Co multilayer, (left) as-deposited sample, measured and fitted curve; (right) as as-deposited and annealed sample.

3 .

 3 X-ray Diffraction Results of XRD are illustrated in Figure 3.4. For the as-deposited sample, two obvious diffraction peaks can be observed around 34.6° and 44.5° which correspond to Mg hcp (002) and Co hcp (002) planes respectively. When annealing to 350°C , the intensity of the two peaks reduces, which is attributed to the diffusion between the Co and Mg layers during annealing. The peaks shift slightly toward low angles, meaning that the lattice constant of Co and Mg increases after annealing. After 400°C annealing, it shows only one strong peak around 44.57°. This peak can be related to MgCo 2 hcp (201) plane and Co hcp (002) plane. In our previous studies [87], for the 400°C annealed sample, the NMR results showed a well-defined line at 226 MHz which corresponds to Co atoms lying in the bulk of the Co layers with an hcp structure. However, the contribution of the Co atoms at the Co/Mg interfaces (156 MHz) vanishes after annealing. That is to say, Co and Mg layers mix completely and the multilayer structure is destroyed after 400°C annealing, which is consistent to XRR curves. The films are converted into crystalline compound MgCo 2 with embedded Co grains, which contribute to the XRD peaks.

Figure 3 . 4

 34 Figure 3.4 XRD curves of Mg/Co multilayers before and after annealing

3. 3

 3 Introduction of Zr in Co/Mg multilayersOur previous study shows that the introduction of Zr barriers can not only enhance the promising optical performance of the Mg/Co system but also improve the thermal stability from 200°C to 400°C[START_REF] Zhu | Thermal stability of Mg/Co multilayer with B 4 C, Mo or Zr diffusion barrier layers[END_REF]. The experimental EUV reflectivity at 25.1 nm and 45° of grazing incidence for Mg/Co, Mg/Zr/Co, Mg/Co/Zr is equal to 42.4%, 41.4%, 50.0%, and 40.6%, respectively. The addition of Zr at the only Mg-on-Co interface has been proven to be an efficient combination to enhance the reflectance. The Mg/Zr/Co/Zr multilayer almost kept its abrupt interfaces and high EUV reflectance when heated up to 400°C. Despite that a slight decrease of EUV reflectance can be noted after 400°C annealing, the multilayer structure has no obvious changes according to the XRR measurement.

5 .

 5 On one hand, the Mg/Co and Mg/Co/Zr spectra are both characterized by a well-defined and intense line at 226 MHz due to bulk hcp Co and a shoulder at 156 MHz related to the Co/Mg interface. In the spectrum of Mg/Co/Zr, we note the additional presence of a shoulder at 180 MHz corresponding to the Co/Zr interface. On the other hand, the 226 MHz line is no more observed in the spectra of Mg/Zr/Co and Mg/Zr/Co/Zr: they are made of a wide and flat feature covering the whole frequency domain. From this distinction, we can deduce that: 1) the Co layers and related interfaces are well-defined in Mg/Co and Mg/Co/Zr, giving evidence in Mg/Co/Zr system that the Zr-on-Co interface is sharp. 2) no more pure Co layers remain within Mg/Zr/Co as a consequence of an intermixing between upper Co and lower Zr layers at the Co-on-Zr interface. A careful look at the Mg/Co/Zr and Mg/Co spectra shows significant differences: lower amplitude and broadening of the hcp Co bulk line and larger intensity in the low-frequency range. This suggests that the Zr-on-Co interface in Mg/Co/Zr is not as sharp as the Co-Mg interface in Mg/Co.

Figure 3 . 5

 35 Figure 3.5 NMR spectra of the Mg/Co, Mg/Zr/Co, Mg/Co/Zr, and Mg/Zr/Co/Zr multilayers.

Figure 3 . 6 X

 36 Figure 3.6 X-ray fluorescence spectrum excited at photon energy of 1332 eV.

Figure 3 .

 3 Figure 3.7 shows the measured XRR curves of samples of Mg/Co, Mg/Zr/Co and Mg/Co/Zr multilayers at x-ray photon energy of 8 keV. The XRR curves are fitted based on the genetic algorithm in order to derive the actual layer thickness and interface roughness. The fitted results agree quite well with the experimental data, which are shown in Table 3.2.The measured XRF yields of the multilayer samples are shown in the following. The number of counts under the Co Lα or Mg Kα emission is integrated during a given time and plotted as a function of the glancing angle i and is normalized to the current of a gold mesh inserted in the incident beam in order to correct for its intensity variations.

Figure 3 . 7

 37 Figure 3.7 Measured (circles) and fitted (red line) XRR curves of Co/Mg, Mg/Co/Zr and Mg/Zr/Co samples.

Figure 3 . 8

 38 Figure 3.8 XRF curves of Mg/Co sample, experimental (circles) and calculated (solid line), obtained at 807.6 eV for the Co Lα emission ((c) and (d)) and 1332 eV for the Mg Kα emission ((a) and (b)). (a) and (c), (b) and (d) correspond to the grazing incidence mode and the grazing exit mode, respectively.The calculated and experimental results fit well for the Mg Kα emission except for a shoulder at 119 o for grazing exit mode which may due to the oxidation of Mg layers close to the surface. This means the Co/Mg multilayers have sharp interfaces which is consistent with NMR results. The disagreement between experiment and theory of Co Lα emission can be attributed mainly to the difference between the values of the tabulated optical indices. We note that there is a small energy difference, 1.7 eV, between the Co Lα emission and the Co L3 absorption edge whereas there are about 50 eV between the Mg Kα emission and the Mg K

Figure 3 . 9

 39 Figure 3.9 XRF curves of Mg/Co/Zr and Mg/Zr/Co samples, experimental (circles) and calculated (solid line), obtained at 807.6 eV for the Co Lα emission ((c) and (d)) and 1332 eV for the Mg Kα emission ((a) and (b)). (a) and (c), (b) and (d) correspond to the grazing incidence mode and the grazing exit mode, respectively.

  structure and thermal stability of carbon-based multilayers. Two systems Cr/C and Co/C are studied. In Section 4.1, we investigate thermal induced structural modifications of Cr/C multilayers. Section 4.2 presents the interface changes of Co/C multilayers upon annealing. Cr/C and Co/C multilayers show different changes at the interfaces upon annealing. 4.1 Structural changes induced by thermal annealing in Cr/C multilayers 4.1.1 Samples Three sets of Cr/C multilayers whose period is about 5 nm are deposited by using DC magnetron sputtering with 30 bi-layers and thickness ratio (thickness of the carbon layer to the period, d C /d) Γ= 0.29, 0.51 and 0.65. To investigate their thermal behavior of Cr/C, all the samples are annealed at 600°C for one hour in a furnace with a base pressure of 3×10 -4 Pa. After annealing, the samples are cooled down to room temperature naturally. 4.1.2 Characterization of structure and interfaces 1. X-ray Reflectivity XRR results are shown in Figure 4.1 as black dots. In Fig.1(a), for the sample with carbon layer thickness ratio Γ=0.29, upon annealing, the Bragg peaks shift to higher grazing incident angle which means that the period decreases. The intensity of 5 th order peak (at 4.7°) vanishes, suggesting that Γ changes to about 0.2.

Figure 4 .

 4 1(b) shows slight shift of the Bragg peaks before and after annealing for the sample whose carbon layer thickness ratio is Γ=0.51.In Figure4.1(c), contrary to that in Figure 4.1(a), the Bragg peaks of annealed sample shift to lower angle meaning that the period increases for the multilayer with Γ=0.65. Before and after annealing, all three samples show sharp Bragg peaks, indicating slight changes in interface quality. All the XRR curves are fitted to obtain the interlayer thickness, individual layer thickness and layer density. The fitted curves are plotted in Figure 4.1 as red thin lines. The fitted values are listed in Table

Figure 4 . 1 Figure 4 . 2

 4142 Figure 4.1 Measured XRR curves of as-deposited and annealed Cr/C multilayers with initial carbon thickness ratios of (a) Γ=0.29; (b) Γ=0.51; (c) Γ=0.65; dashed and solid lines represent measured and fitted XRR curves, respectively.

Figure 4 . 2

 42 Figure 4.2 Measured Raman spectra decomposed in Gaussian lines of as-deposited and annealed Cr/C multilayers. Initial carbon ratio (a) Γ=0.29; (b) Γ=0.51; (c) Γ=0.65; Black lines are for the measured curves and red lines are for the fitted curves;Blue dotted and green dotted lines are for the fitted G peak and D peaks, respectively.

Figure 4 .

 4 Figure 4.3 shows the high-resolution regional scans of as-deposited and annealed samples with Γ=0.51. The C 1s peak shape of both samples shows distinct regions which can be assigned to C-O (286.2 eV), C-C sp 2 (284.3 eV), sp 3 (285.3 eV) and C-Cr (283.2 eV)bondings. After annealing, the ratio of sp 3 /sp 2 decreases from 0.11 to 0.06 implying the decrease in sp 3 fraction in carbon layers, which is consistent with the RS results. The C-Cr compound exists at the interfaces of both as-deposited and annealed Cr/C multilayers.Compared to the ratio of sp 2 , there is a transition to higher C-Cr bonding after annealing.The XPS results indicate that the interfaces of Cr/C multilayer are mixture composed of carbon, chromium and C-Cr bondings. The annealing process causes increase of inter-diffusion and denser C-Cr compound forms at the interfaces. Thus the thickness of chromium layers decreases and the thickness of interlayers increases after annealing.

Figure 4 . 3

 43 Figure 4.3 Carbon 1s peak XPS scan in for the samples with Γ=0.51. When annealed up to 600°C, the graphitization of carbon and the formation of compounds at the interfaces play simultaneously important role in the structure change of Cr/C multilayers. Based on the Miedema's macroscopic atom model [100], the mixing enthalpy of Cr-C system can be calculated, and the results are shown in Figure 4.4. It can be seen that the value of mixing enthalpy is negative at carbon concentration below 0.6 (mole ratio) and after increases sharply. That is to say, the mixing of Cr-C is easy when the carbon thickness ratio equals to 0.29 and 0.51 (carbon concentration equals to 0.34 and 0.56) thus the reduction of period caused by formation of carbide exceeds the expansion of residual carbon. When the carbon thickness ratio equals to 0.64 (carbon concentration equals to 0.7), the interface shows small possibility of Cr-C mixing and the graphitization carbon layers dominate the expansion of period. The calculated enthalpy of Cr-C mixing also shows that the most possible Cr-C compounds formed in multilayers is Cr 3 C 2 because it has the largest negative value of enthalpy of formation (C concentration equals to 0.4). This is confirmed by Wilson et.al [101]. They have observed that the Cr-C sputtering coating had a Cr:C ratio of 3:2, suggesting Cr 3 C 2 composition.

Figure 4 . 4

 44 Figure 4.4 Calculated enthalpy of mixing for the Cr-C system.

Figure 4 . 5

 45 Figure 4.5 Measured (black circle) and fitted (red solid line) XRR curves of as-deposited and annealed Co/C multilayers.

Figure 4 . 6

 46 Figure 4.6 Zero-field NMR spectra of as-deposited and annealed Co/C multilayers. Based on the Miedema's macroscopic atom model [100], the mixing enthalpy of Co-C system is calculated and the results are shown in Figure 4.7. It can be seen that the value of mixing enthalpy is positive at any carbon concentration. This indicates that the Co-C system

Figure 4 . 7

 47 Figure 4.7 Calculated mixing enthalpy of the Co-C system.

Figure 4 .

 4 8 shows the rocking curves measured around the first Bragg peak for the three samples. For the as-deposited and 300°C annealed sample there is no significant change of the intensity except a slight shift of peak position. After annealed at 600°C, a high intensity of diffuse scattered x-rays is observed, indicating significant increase of the correlated interfaces roughness.

Figure 4 . 8

 48 Figure 4.8 Rocking curves around the first Bragg peak of as-deposited and annealed Co/C multilayers.

  direction. The spatial distribution of crystallites in the metal layer is replica ted as a modulation of the surface height. Since the metal layer becomes rougher, the nonmetal layer on top of the metal layer also becomes rougher. For the Co/C multilayers annealed up to 600°C, the crystallization of Co layers increases the geometrical roughness and aggravates the overall imperfection of the interfaces.

Figure 4 . 9

 49 Figure 4.9 Diffraction patterns of as-deposited and annealed Co/C multilayers. The curves are shifted vertically for the sake of clarity.

  recent years there has been a huge efforts to develop techniques that can reduce the interface width of multilayers. One recent attempt involved the intentional incorporation of light-element impurities such as N into multilayers. It has been shown that the incorporation of nitrogen in Cr/Sc or La/B4C multilayers can form nonstoichiometric nitride multilayers with reduced interdiffusion or reaction between the layers and leads to major improvements in the x-ray reflectivity. In this chapter, two interface engineering methods are used to improve the interfaces of Ti-based multilayers. In Section 5.2, Co/Ti multilayers are deposited by using reactive sputtering with N 2 . Section 5.3 shows that boron and carbon are incorporated into Cr/Ti multilayers by depositing ultra-thin B 4 C at the interfaces. The interfaces and soft x-ray reflectivity of Ti-based multilayers are enhanced by interface engineering. 5.2 Co/Ti multilayers prepared by reactive sputtering 5.2.1 Samples

Figure 5 .

 5 Figure 5.1 (a) Measured (black circle) and fitted (red solid line) XRR curves of Co/Ti multilayers. (b) Soft X-ray reflectivity of Co/Ti multilayers. The measured curves of soft X-ray reflectivity as a function of the photon energy at 22.5 o grazing incidence are shown in Figure 5.1 (b). The non-reactively sputtered multilayer has a peak reflectance of 9.5%. The sample deposited at 5% N 2 fraction shows the highest reflectance, 11.8% and then the reflectance decreases with the increase of N 2 fraction. The improvement of reflectivity is attributed to improved interfaces and reduced interdiffusion.

2 .

 2 X-ray diffuse scattering XDS measurement is performed to determine the change of correlated morphological roughness of interfaces. As shown in Figure 5.2, rocking curves around the first Bragg peak are measured for the non-reactively and reactively sputtered samples. Apart from a slight shift in the specular peak position due to variation of period, no other change is noticed on reactively sputtered samples. For clarity, we plot only results from the non-reactively sputtered sample and the sample deposited at 5% N 2 fraction. The FWHM of the specular peak for the non-reactively sample is larger than the one of the reactively sputtered one. This indicates reduction of interdiffusion at the interfaces by reactive sputtering. However, the diffuse signal around the specular peak does not decrease, which we interpret as negligible change in correlated roughness of interfaces with reactively sputtered samples.

Figure 5 . 2

 52 Figure 5.2 Rocking curves around the first Bragg peak of Co/Ti multilayers.

Figure 5 . 3

 53 Figure 5.3 Zero-field NMR spectra of Co/Ti multilayers.

Figure 5 . 4

 54 Figure 5.4 Cross-section TEM images and selected area electron diffraction patterns of Co/Ti multilayers (a) non-reactively sputtered (b) reactively sputtered.

5. 3

 3 Cr/Ti multilayers prepared by co-deposition of B 4 C 5.3.1 Samples The Cr/Ti multilayers are deposited by DC magnetron sputtering with the B and C impurities incorporated by deposition of ultra-thin B 4 C at the interfaces of the Cr/Ti multilayers. Firstly, we study the effect of the amount of incorporated B 4 C and the choice of interfaces at which B4C is incorporated. Four series of Cr/Ti multilayers with period number N=50 are deposited. B 4 C is incorporated at both Cr-on-Ti and Ti-on-Cr interfaces in the first series, at only Cr-on-Ti interfaces in the second series, and at only Ti-on-Cr interfaces in the third series. The multilayers in all three series are deposited with the same thicknesses of Cr layers and Ti layers (d Ti =d Cr =0.7 nm). Each of the three series consists of six multilayers with different amounts of B 4 C. One multilayer had no B 4 C incorporated and the nominal amounts (in thickness) of B 4 C in the other five multilayers are 0.08, 0.13, 0.18, 0.22 and 0.27 nm, respectively. A fourth series containing four pure Cr/Ti multilayers without B 4 C are also deposited for comparison. The period thicknesses of the four multilayers range from 1.4 nm to 1.7 nm and their thickness ratio (Γ=d Ti /Λ) is ~0.5. 5.3.2 Characterization of structure and interfaces 1. X-ray reflectivity

Figure 5 . 2 B

 52 Figure 5.5(a), in which thicker multilayers appear toward the left (low angle) side. It can be seen from the figure that incorporating B 4 C at either or both interface leads to higher reflectivity suggesting improved multilayer quality. More specifically, it is better to incorporate B 4 C at the Cr-on-Ti interfaces than at the Ti-on-Cr interfaces, and best of all to do so at both interfaces. Another conclusion from Figure 5.5(a) is that 0.13 nm of B 4 C is good enough for the interface quality improvement. The period thicknesses deduced from the peak angles are plotted as a function of the nominal B 4 C thickness in Figure 5.5 (b). A linear relation between the period thickness and the nominal B 4 C thickness is expected and observed as the deposition times of Cr or Ti are the same for each series. The slopes determined from linear fit are 1.15, 0.58, and 0.56 for the first, second, and third series, respectively. The value of the slope in the second and third series or half of the slope in the first series (because B 4 C is deposited twice in a period in the first series) represents the ratio of the actual growth rate to the nominal B 4 C deposition rate. The large disparity between this value and unity reveals that deposited B and C do not exist in B 4 C form in the multilayers. We calculated this ratio

Figure 5 .

 5 Figure 5.5 (a) Peak reflectivity versus peak angle of the first order Bragg peaks in the XRR curves of the Cr/Ti multilayers. Symbols represent the data and solid lines are only guide for the eye. (b) Period thickness versus nominal B 4 C thickness of the Cr/Ti multilayers. Symbols represent the data and dashed lines the linear fit.

Figure 5 .

 5 Figure 5.6 (a) B 1s and (b) C 1s XPS spectra of the B 4 C monolayer and Cr/Ti multilayer with B 4 C. Open symbols represent the measured data, solid lines the fitted spectra, short dashed lines the background, and long dashed lines the peaks used in the fitting if more than one peak is involved.

5. 7

 7 shows the cross-section transmission electron microscopy (TEM) graphs for the two samples. The multilayer with B 4 C shows much better contrast between the Cr and Ti layers although the flatness is similar, confirming that the TiB x C y formation prevents diffusion of Cr.

Figure 5 . 7 11 Figure 5 . 8

 571158 Figure 5.7 Cross-section TEM graphs of Cr/Ti multilayers (a) with and (b) without B 4 C.

Figure 6 . 1

 61 Figure 6.1 Measured (black dots) and fitted (red line) XRR curves of Mo/B 4 C samples.

  2 (c) and (d). All samples exhibit an asymmetric shape. For the as-deposited multilayer, the interface width of the B 4 C-on-Mo is determined to be about 1 nm, much larger than that of Mo-on-B 4 C interfaces, about 0.1-0.2 nm. After annealing, the interface width of the B 4 C-on-Mo appears to decreases to about 0.6 nm. The real width of B 4 C-on-Mo interface may be larger since the dark layers contain Mo and MoB x C y [121]. The interface width of Mo-on-B 4 C has no obvious change upon annealing.

Figure 6 . 2 .

 62 Figure 6.2. TEM cross-sectional images (a) and (b), and in-depth intensity profiles (c) and (d) of Mo/B 4 C multilayers. (a) and (c), and (b) and (d) correspond to the as-deposited and 600°C annealed samples respectively. The thickness of the layers and interfacial widths are indicated.

2 .

 2 Figure 6.3. Compared with Mo/B 4 C, the value of Г and the width of the peaks have no obvious change upon 600°C annealing, which indicate that the Mo 2 C/B 4 C multilayers show a

Figure 6 . 3

 63 Figure 6.3 Measured (black dots) and fitted (red line) XRR curves of Mo2C/B 4 C samples.

Figure 6 . 4

 64 Figure 6.4 TEM cross-sectional images (a) and (b), and in-depth intensity profiles (c) and (d) of Mo 2 C/B 4 C multilayers. (a) and (c), and (b) and (d) correspond to the as-deposited and 600°C annealed samples respectively. The thickness of one period layers and interfacial widths are indicated.

Figure 6 . 5

 65 Figure 6.5 Measured (black dots) and fitted (red lines) EUV reflectance curves of (a) Mo/B 4 C, (b) Mo 2 C/B 4 C multilayers.

6. 3

 3 Stress of the Mo 2 C/B 4 C and Mo/B 4 C multilayersThin film stress can be mainly classified into two categories, thermal stress and intrinsic stress. Thermal stress originates from the different thermal expansion coefficients of thin films and substrates. Intrinsic stress is more complicated which is usually correlated to the growth process of thin film. Microstructure changes during growth, chemical reaction in the interfaces and bombardment of energetic particles and incorporation of impurities can all cause intrinsic stress. Here, we mainly concentrate on the intrinsic stress.6.3.1 ExperimentalThe Mo, Mo 2 C, B 4 C mono-layer thin films and Mo 2 C/B 4 C, Mo/B 4 C multilayers are all deposited by direct current (DC) magnetron sputtering technology on 0.12 mm-thick glass substrates in diameter of 30mm. The thicknesses of mono-layer thin films are all 30 nm. The period of multilayers is 3.5 nm with a thickness ratio of 0.5. The number of periods is 20. The thicknesses of mono-layer thin films and multilayers are characterized by XRR at 8 keV.

6. 6 Figure 6 . 6

 666 Figure 6.6 One dimensional surface profiles of substrates (a) before deposition and (b) after deposition.

  E s and V s are the Young's modulus and Poisson ratio of the substrate material. R o and R 1 are the radius of radius of surface curvature of substrates before and after deposition. The values of stress for all samples are shown in Figure 6.7. The negative values represent compressive stress. The two columns of every sample represent the data in two perpendicular direction.

Figure 6 . 7 1 )

 671 Figure 6.7 Comparison of stress for mono-layer films and multilayers. The stress values of B 4 C, Mo 2 C and Mo layers are about -2.5, -1.0 and -0.5 GPa, respectively. The stress values of Mo 2 C/B 4 C and Mo/B 4 C multilayers are about -0.6 and -1.1 GPa. That is to say, the intrinsic stress of Mo/B 4 C multilayers is mitigated by replacing Mo by Mo 2 C. There are two possible reasons for this phenomenon: 1) The interfaces of Mo/B 4 C multilayers are more diffused than the ones of Mo 2 C/B 4 C. For diffused interfaces, the excess B and C atoms are incorporated into the position of Mo lattice or void and grain boundaries, causing local atomic displacements and densification of the films which results in the compressive stress of multilayers [123].2) When the Mo or Mo 2 C layers are at the state of initial growth, they may show tensile stress. For example, Mo layer initially grows in apparent tension until the thickness reaches 4 nm. This behavior is typical of the Volmer-Weber growth mode in which the film grows as isolated islands. As the islands coalesce, grain boundary cohesion induces, according to Hoffman, a tensile stress in the film[124]. That is why for Mo/Si multilayers, during the growth of Si on Mo, the stress evolves in compressive direction, whereas during the growth of Mo on Si, the stress evolution abruptly changes to tensile direction. The initial stress of Mo 2 C layer may be higher than Mo, making the Mo 2 C/B 4 C multilayers show lower compressive stress than Mo/B 4 C layer. However, the assumption should be verified by some precise in situ stress measurements.

Fig. 3 (Fig. 2 .

 32 Fig.3(c) refers to the middle area of the entire multilayer. It can be seen that the multilayer structure is undamaged after the repeated grinding and polishing. All the layer interfaces keep flat and sharp. The image was converted into a binary one and the layer thicknesses were directly calculated as reported in Ref.[18]. The measured layer thickness distribution is shown in Fig.4where the designed structure is also shown for comparison. Different sub-areas from the substrate to the surface are represented by numbers 1-17 in Fig.3. Fig.3 (a)is the result of the layer structure while (b) is the relative errors between the deposited and designed layer thicknesses, (d meas -d desi )/d desi. The result demonstrates that the structure fabricated conforms to the designed one and the error of the thickness curve are less than ±7%.

  Co multilayer with Zr diffusion barrier layers are investigated. An application of NMR and fluorescence induced by x-ray standing waves in Co/Mg based multilayers is also discussed.

	3.2 Thermal stability of Co/Mg multilayers
	3.2.1 Samples
	The Co/Mg multilayers are designed with period d=16.9 nm with 30 bi-layers and
	thickness ratio (thickness of the Mg layer to the period, d Mg/ d) Γ= 0.85, achieving high
	reflectivity for 25.2 nm wavelength at 45° incident angle. To investigate the thermal behavior
	Mg/Zr multilayers show the best thermal stability in the Mg-based multilayers as they
	preserve 87% of their original reflectivity in 400°C annealing and 50% even after 600°C
	annealing [85].

To improve the thermal stability, diffusion barrier layers can be inserted between the Mg and Co layers. B 4 C is a stable ceramic and typical diffusion barrier material in multilayers. The efficiency of B 4 C barrier layer has been demonstrated for the Mo/Si multilayers [21, 22]. However, B 4 C barrier layer is disastrous in Mg/Co multilayer mainly due to the poor quality of Mg-B 4 C interface [84]. Zr is also barrier layer candidates to prevent interdiffusion in Mg/Co multilayer induced by annealing since Zr cannot chemically react and maintain relatively stable phase with Mg. Section 3.2 examines Mg/Co multilayers and their thermal stability by studying interdiffusion, interfacial compound formation and roughness development. In Section 3.3, the property of Mg/of Co/Mg multilayers, the samples are annealed from room temperature to 300 °C, 350 °C or 400 °C and for one hour in a furnace with a base pressure o f 3×10 -4 Pa. After annealing, the samples are cooled down to room temperature naturally.

Table 3 .

 3 1 Parameters of the Co/Mg multilayers deduce from fitting the XRR and XDS curves.

	Annealed temperature (°C)	Periodic thickness (nm)	XRR fitting σ t (nm) Mg on Co on Co Mg	XDS fitting σ r (nm) Mg on Co on Co Mg	σ d (nm) Mg on Co on Co Mg
	As-deposited	16.9	0.47	0.46	0.29	0.31	0.37	0.34
	300	16.7	0.52	0.53	0.29	0.30	0.43	0.44
	350	16.7	0.71	0.68	0.25	0.26	0.66	0.63

  the energy of incident light is near 807.6 eV for Co Lα emission and 1332 eV

	45)/Co (2.55); Mg (13.20) /Zr (1.50) /Co (2.50);

Mg

(13.20

) /Co (2.50) /Zr (1.50); Mg (12.00) /Zr (1.50) /Co (2.00) /Zr (1.50). For the XRF measurements, the thickness of Mg layers are reduced to 5.45 nm in order to meet the Bragg condition when

Table 4 .

 4 1 Parameters of the Cr/C multilayers deduced from fitting the GIXRR curves. The * lines correspond to the annealed samples.

	Sample			Thickness(nm)		Г(d C /d)	Carbon density
		C	Cr	C-on-Cr	Cr-on-C	Period		(g/cm3)
	S1	1.4	2.49	0.31	0.66	4.86	0.29	2.01
	S2	2.53 1.48	0.25	0.70	4.96	0.51	2.04
	S3	3.02	0.8	0.29	0.62	4.73	0.64	2.01
	S1*	0.97 2.29	0.44	0.98	4.68	0.21	1.73
	S2*	2.49 1.25	0.41	0.89	5.04	0.49	1.82
	S3*	3.22 0.73	0.36	0.71	5.02	0.65	1.76

Table 4 .

 4

	Sample	Period Λ(nm) d Co (nm) d C (nm) σ Co (nm) σ C (nm) Density ratio: Co (%), C (%)
	as-deposited	4.09	1.51	2.58	0.41	0.37	89±5, 93±5
	300°C annealing	4.14	1.53	2.61	0.40	0.35	91±5, 90±5
	600°C annealing	4.81	1.44	3.37	1.16	1.02	98±5, 80±5

3 Parameters of the Co/C multilayers deduced from fitting of the XRR curves. (The density ratio is the fitted density divided by the density of the bulk.)

  gradient at the interface with the C layers. The metal-containing layer is a Co-C alloy with the density of 6.2-6.5 g/cm3 lower than the density of massive Co and carbon enriched Co 2 C layers [102]. As a result, Co/C multilayers consist of cobalt-carbon alloy and amorphous carbon layers.

	2. Zero-field nuclear magnetic resonance spectroscopy
	NMR spectra for the Co/C multilayers are presented in Figure 4.6. The spectrum of the
	Co/C as-deposited multilayer shows a weak signal without any defined feature in the
	frequency range of pure Co. This indicates that the Co layers are not pure but that alien

carbon atoms are mixed with Co over the total Co layers. In addition some Co atoms are most probably also situated in non-ferromagnetic phases (and therefore give no NMR signal) with a large content of C. The as-deposited multilayers are actually CoC x /C multilayer with probably some concentration

Table 5 .

 5 1 Parameters of the Co/Ti multilayers deduced from fitting of the XRR curves.

	N 2 Fraction	Period Λ(nm)	d Co (nm)	d Ti (nm) σ Co (nm)	σ ti (nm)
	0%	3.77	1.69	2.08	0.85	0.68
	5%	3.74	1.61	2.12	0.31	0.28
	10%	3.73	1.72	2.01	0.30	0.30
	15%	3.81	1.74	2.07	0.32	0.33
	20%	3.75	1.72	2.03	0.38	0.36

6 Study of Mo 2 C/B 4 C and Mo/B 4 C multilayers

  4 nm) have an excess of Cr located in the Ti layers due to Cr diffusion. The multilayer can be described as Cr/Cr 0.37 Ti 0.63 . We intentionally incorporated B and C into Cr/Ti multilayers by depositing ultra-thin B 4 C at the interfaces. It is found that incorporating 0.13 nm of B 4 C at both interfaces dramatically affects the structure and composition of the Cr/Ti multilayers. The B and C incorporated during deposition is mainly bonded to Ti, forming Cr/TiB 0.75 C 0.19 multilayer structures. The formation of nonstoichiometric TiB 0.75 C 0.19 composition hinders the diffusion of Cr and improves the interface quality of Cr/TiB 0.75 C 0.19 multilayers. As a result, Cr/TiB 0.75 C 0.19 multilayers (with periodic number N=600) exhibit ~250% higher near-normal incidence soft x-ray reflectivity (absolute reflectivity R=15.75%) than pure Cr/Ti multilayers. In this chapter, two systems Mo 2 C/B 4 C and Mo/B 4 C are designed for working in the EUV range at near normal incidence. In Section 4.2, we investigate the optical and structural properties of both systems by combing the XRR, EUVR and TEM techniques. Section 4.3 4 C-based multilayers are widely used as reflective elements. In EUV range, multilayers for the spectral region near wavelength of 6.7 nm is of strong interest due to the development of next generation EUV lithography [3] and the x-ray spectrometry [50]. Boron-based multilayers are expected to perform well above the Boron K-edge at 6.6 nm. Boron target is difficult to sputter owing to its low conductivity and density. Good optical performance was obtained with multilayer that utilized boron carbide, such as Ru/B 4 C, La/B 4 C and Mo/B 4 C. C multilayers. On the one hand, Barthelmess et al. [112] have shown that the interfaces of Mo/B 4 C are far from perfect: amorphous molybdenum and boron carbide layers separated by molybdenum borides exist at the B 4 C-on-Mo interfaces and the interlayer thickness grows with increasing temperature. On the other hand, Mo/B 4 C multilayers show high intrinsic stress [112, 116], which can causes undesirable distortion of the substrate figure and even lead to delamination of the coatings. To improve the interface quality and stability of Mo-based multilayers, some authors have proposed to replace the Mo by Mo 2 C, such as Mo 2 C/Si [113] and Mo 2 C/Be [114]. Choueikani et al. have studied the x-ray properties and interface of Mo/B 4 C and Mo 2 C/B 4 C multilayers [115]. Mo 2 C/B 4 C multilayers show less interdiffusion and higher reflectance at 1500 eV than Mo/B 4 C ones. However, in this study the thermal behavior and the performance in the EUV range are not considered. There are some methods to reduce the stress of multilayers. For example, controlling the gas pressure [116,117], the post-deposition annealing [118,119] and varying the material ratio Г [118,119] are commonly used techniques. However, these methods degrade the optical performance of multilayers. In this paper, we show a comparative study of interface properties and optical performance in the 6.7-7 nm range between Mo/B 4 C and Mo 2 C/B 4 C multilayers.

	Chapter presents the stress property for both systems.
	6.1 Introduction
	La/B 4 C multilayers give the highest theoretical reflectivity of 60% but lanthanum is highly
	reactive. Interface engineering, such as nitrogen or carbon treatment should be used to
	improve the interface quality [110,111]. A near-normal incidence reflectivity of up to 58.6%
	has been measured for La/B 4 C by using carbon as anti-diffusion barrier layer [110]. Mo/B 4 C
	multilayers also promising for the wavelengths near 6.7-7nm because of its good thermal
	stability and it is easy to handle [112]. In x-ray range, B 4 C-based multilayers are used as
	grazing incident monochromators in beamlines of synchrotron radiation and laboratory-based
	x-ray diffractometry and reflectometry [52]. Typical multilayer elements are based on
	materials such as W/B 4 C, Ni/B 4 C or Mo/B 4 C, yielding a relative spectral resolution (∆E/E) of
	the order of a few percents and high reflectivity.
	We choose to study Mo/B4C multilayers base on the fine contrast of optical constant
	between Mo and B 4 C, its good thermal stability and the sputtering target availability in our
	laboratory. Based on previous results, it appears that there are two main shortcomings of
	Mo/B 4

B

Table 6 .

 6 1 Designed structure of Mo 2 C/B 4 C and Mo/B 4 C multilayers

	Sample name	Period (nm)	Г B4C	Simulated reflectivity	Number of periods	Experiments
	Mo/B 4 C_1 Mo 2 C/B 4 C_1	3.41	0.45	47.5% @ 6.7nm	200	XRR,EUVR
	Mo/B 4 C_2 Mo 2 C/B 4 C_2	3.8	0.5	-	60	XRR,TEM
	6.2.2 Characterization of structure and interfaces
	1. Mo/B4C

Table 6 .

 6 2 Interface widths of Mo/B 4 C and Mo 2 C/B 4 C multilayers estimated from XRR, EUVR and TEM measurements. The values of as-deposited samples derived from EUV curves are close to their respective TEM ones, which reveals that the interfaces of Mo/B 4 C and Mo 2 C/B 4 C multilayer are dominated by interdiffusion. Actually, we have measured the X-ray diffuse scattering for all samples by rocking scan around the Bragg reflections. The scattered intensities are weak and show no obvious change after annealing. For both Mo/B 4 C and Mo 2 C/B 4 C multilayers, the interface widths derived from XRR and EUV measurements share a similar feature: they increase after annealing. However, the interface width derived from TEM images decreases slightly. This can be due to an increase in the thickness of the diffused MoB x C y interlayers The TEM images exhibit an asymmetry in the Mo/B 4 C multilayer system with sharp Mo-on-B 4 C interfaces and more diffuse B 4 C-on-Mo interfaces. The Mo 2 C/B 4 C multilayers have thinner and more symmetrical interfaces because Mo 2 C limits the reaction and diffusion of boron and carbon atoms with molybdenum ones. This makes the Mo 2 C/B 4 C multilayer more stable than Mo/B 4 C up to 600°C heat treatment. The EUV reflectivity peak at 6.7 nm measured is higher for Mo 2 C/B 4 C sample than for Mo/B 4 C one. Smooth interfaces and excellent thermal stability make Mo 2 C/B 4 C multilayers a suitable alternative to Mo/B 4 C for application in EUV and x-ray ranges.

		Mo-on-B 4 C interface (nm)	B 4 C-on-Mo interface (nm)
	Sample	XRR	TEM	EUVR	XRR	TEM	EUVR
	As-deposited	0.21	0.22	0.32	0.67	0.99	0.92
	Mo/B 4 C
	Annealed	0.24	0.19	0.36	0.81	0.57	1.23
	As-deposited	0.21	0.61	0.56	0.23	0.62	0.54
	Mo 2 C/B 4 C
	Annealed	0.19	0.45	0.61	0.22	0.35	0.58

Acknowledgement: This work was supported by National Basic Research Program of China (No.2011CB922203), and National Natural Science Foundation of China (Nos. 11375131 and U1432244).

increases by 0.26 after annealing for all samples. The value of 1546 cm -1 for the G peaks position and 1.25 for I(D)/I(G) suggest a sp 3 fraction of about 9-10%. By annealing, the intensity of G peaks increases with a corresponding increase in I(D)/I(G) implying a decrease in sp 3 fraction to about 5-6%. The sp 3 fractions are calculated using three-stage model described by Ferrari et al. [START_REF] Ferrari | Interpretation of Raman spectra of disordered and amorphous carbon[END_REF]. The Co/C multilayers are designed with bilayer number N=20, period thickness Λ=4.1 nm, and the thickness of Co layer, d Co =1.5 nm. The multilayers are deposited by using DC magnetron sputtering method. To investigate the thermal behavior of Cr/C multilayers, the samples are mounted on a plate heated by a wire-wound furnace in a vacuum chamber with a base pressure of 3×10 -4 Pa. The samples are heated from room temperature to 300 and 600°C keeping for 1 hour. The fitting results reveal that the carbon layer plays a crucial role in the period expansion.

After 600°C annealing, the thickness of C layer increases from 2.58 nm to 3.37 nm. This phenomenon is attributed to the graphitization of the amorphous carbon layers by annealing, which is confirmed by RS measurements in section 4.1. The thickness of Co layers decreases from 1.51 to 1.44 nm. This may be due to the demixing of Co and C atoms in the Co layers after annealing which will be mentioned below.

In Figure 4.5, three well-defined peaks are observed for the as-deposited and 300°C annealed samples up to 3.5°. In the case of the 600°C annealed sample, only first and second Bragg peaks are observed and the reflectance decreases. The intensity o f Bragg peaks increases slightly after 300°C, meaning that there is an interface smoothening effect in Co/C multilayers. The comparison of the reflectivity curves shows that after 600°C annealing, the roughness of interfaces increases dramatically, from 0.4 nm to about 1.0 nm. The roughness deduced from the fitting of XRR (σ) is an overall imperfection of interfaces, including the

Conclusions and perspectives

In this thesis we focus on the characterization of interfaces of multilayer monochromators. Several systems, such as Co/Mg, Co/Ti, Cr/Ti, Co/C, Cr/C and Mo/B 4 C, have been studied by combining non-destructive and destructive measurements to investigate their interface properties and interface engineering methods to improve their interface quality.

The observation of interface change of these systems upon annealing is important for improving their optical performance.

We firstly investigate the optical performance and interface properties of

Appendix: other publications

Publication as author and co-author: X-ray microscopy has been found numerous applications in materials sciences, medicine, biology, environmental sciences and many other fields by utilizing analytical techniques such as diffraction, x-ray fluorescence and spectroscopy, as well as imaging techniques using absorption and phase contrast. Among these analytical methods, the resolution, signal strength and contrast must be as high as possible and the development of a hard-X-ray focusing device is important for meeting these requireme nts [1,2]. There are many types of hard X-ray focusing devices utilizing reflection, refraction and diffraction optics. In the past decade, rapid advancement in micro-fabrication technology, high-precision surface polishing, controlled layer deposition and precision metrology have led to the realization of hard X-ray focusing to nanometer dimensions [3]. Zone plates have realized the highest resolution of 10-12 nm in the soft X-ray range [4]. Capability of focusing to 47 nm with a compound refractive lens has been experimentally demonstrated at wavelength of 0.06 nm [5]. A line focus with a width of 26nm was achieved with a planar waveguide at photon energy of 13.3 keV [6]. Reflective mirrors have shown great progress recently with the advance of precision manufacturing techniques, it breaks the 10 nm barrier in hard-X-ray focusing [7].

Diffractive optics is intrinsically well suited to achieve a high spatial resolution because a large numerical aperture (NA) can be achieved. A novel approach to making diffractive optics with high NA is Multilayer-Laue-Lens (MLL) [8]. The MLL can be considered as a special type of zone plate and used in Laue geometry. It is fabricated by depositing the depth-graded multilayer inversely on a flat substrate then slicing and thinning the multilayer sample to an ideal cross-section depth. Through this process, MLL can reach a much larger aspect-ratio (the ratio of cross section depth to the outermost layer thickness) compared with zone plates, and this make it capable of focusing hard X-rays with higher efficiency [9].

Based on this method, a line focus of 16 nm width with efficiency of 31% has been obtained at photon energy of19.5 keV [10]. To obtain the point focus that most applications require, two MLL's have to be placed in series in a crossed geometry. A nano-scale 2D imaging with 25nm × 27nm resolution was reported recently [11]. In this paper, we report the design, fabrication and characterization of a partial MLL structure with a width of 10 nm outermost zone and 1582 zones. The multilayer was fabricated by using direct current (DC) magnetron sputtering technology. Thickness of each layer was determined by scanning electron microscopy (SEM) images. The focusing property of the MLL was measured at the Shanghai Synchrotron Facility (SSRF). One-dimensional (1D) focusing resolutions of 92 nm are obtained at X-ray photon energy of 14 keV.

Design and fabrication of MLL

The MLL was designed at photon energy of 14 keV using WSi 2 and Si as the material combination. In the depth-graded multilayer, the minimum layer thickness was designed to be 10 nm, while the total multilayer thickness was 27 μm, and the number of layers was 1582.

The focusing property was calculated using the Fresnel-Kirchhoff diffraction formula [14].

During deposition a few thickest layers contributing little to the focus and can be omitted. Thus, the total thickness of the actual deposited multilayer is thinner than that of designed structure. The focal length was designed to be 7.95 mm. The calculated intensity profile in the focal plane of the MLL is shown in Fig. 1 and full width of half maximum (FWHM) of the peak is 23.5 nm. The fabrication of the MLL includes two parts. The first part is the deposition of the depth-graded multilayer. The material combination of WSi 2 /Si is selected to fabricate the MLL due to its stable stress property and sharp interfaces [15,16]. The multilayer is deposited on a super-polished silicon substrate using direct current magnetron sputtering technology.

The base pressure before deposition is 2.0×10 -4 Pa and argon is used as the working gas with a pressure of 1.5 mtorr. The layer thicknesses of the designed MLL are in the range of 10.0-48.6 nm. The outermost thinnest layer is the first layer deposited. Secondly, subsequent to deposition, the multilayer is sectioned and thinned to the requisite optical depth to form the halves of the MLL. More details have been described in Ref. [17]. It should be noted that the focus of the MLL is still not perfect. The d iscrepancy between the measured width and the theoretical value is attributed to three reasons. Firstly, the layer position errors of the depth-graded multilayer and the structural damage induced by the sampling process would broaden the focal line. Second ly, the minimal scanning step of nanometer translation-stage is 35 nm which is not very precise relative to the width of focal line. Thirdly, the wave front aberration of the incident beam and the vibration of the measurement system will also broaden the focus. If these will be improved, better resolution could be expected in the future work.