# Multilayer mirrors in the soft x-ray and extreme ultraviolet ranges

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## Chapter 2 Analysis techniques

In this chapter we will present the main characterization methods used in our work. Basic principle of each technique and description about experiments as well as setup will be presented.

X-ray reflectometry in hard x-ray range

X-ray reflectometry (XRR) is a non-destructive and non-contact technique for thickness determination between 2-200 nm with a precision of about 0.1-0.3 nm. This method can also be employed to determine the roughness of thin films and the density of a material which is calculated from the electron density. The principle of x-ray reflectometry setup is shown in Figure 2.1. An x-ray tube produces x-rays; a monochromator gives a monochromatic light; a slit is mounted after it collimates the light beam. A slit is also mounted before the detector for minimizing the aberration. In XRR measurements the intensity of the x-ray beam reflected by a sample as a function of the grazing angle is monitored. The mode of operation is θ-2θ mode in which the incident angle is always half of the diffraction angle, i.e., the specular reflection condition is satisfied. The reflectivity, which is defined as a ratio between the intensity of reflected beam and that of incident beam, is related to the value of refractive index and x-ray wavelength. Structural parameters of multilayers can be obtained by fitting the reflectivity data. Informations provided by the x-ray reflectivity curves are shown in Figure 2.2. From the reflectivity curves, we can obtain information on the thickness, the density and the roughness of each layer.
In this work, all the hard x-ray reflectivity measurements were performed with Cu Kα emission line (0.154 nm, 8048 eV) in Tongji University (China) with a reflectometer. The incident beam is monochromatized with a Si (220) crystal. The angular resolution is 5/1000°. The reflected beam travels through two slits and the photons are counted by a scintillation detector. The alignment is checked for each sample. After that we performed the fitting of reflectivity curves with Bede Refs software (genetic algorithm) [55] to estimate the thickness of individual layer and interface roughness as well as density of materials.

X-ray diffraction (XRD)

X-ray diffraction as a non-destructive technique is commonly used to determine the structural properties of solid materials. Diffraction effects are observed when electromagnetic radiation impinges on periodic structures with geometrical variations on the length scale of the wavelength of the radiation. The interatomic distances in crystals and molecules amount to 0.15-0.4 nm which correspond in the electromagnetic spectrum at of x-rays having photon energies between 3 and 8 keV. Analysis of diffraction peak can provide the following information: identification of compound or phase, crystallinity, strain, crystallite size, orientation.
In this work all the XRD experiments were performed by using a PANalytical X’Pert Pro diffractometer with Cu Kα radiation (0.154 nm) from an x-ray tube operating at 45 kV and 40 mA. The scan angle range starts at 10° and ends 80° with a step of 0.01°. The XRD patterns of the reference of Co/C multilayers were also performed as a comparison to the results of the Co/Mo2C multilayers.

Description of the BEAR beamline

The BEAR (Bending magnet for Emission, Absorption and Reflectivity) [56] beamline is installed at the right exit of the 8.1 bending magnet at Elettra, Trieste in Italy. The beamline is designed to satisfy the following requirements: (a) a spectral range of approximately 3-1600 eV, (b) an energy resolution ≥ 3000 over the whole energy range, (c) a final spot size of the order of 10×100 µm2 and (d) the availability of elliptically polarized radiation with the possibility of ellipticity selection from linear to near circular polarization, all with an appreciable flux (Figure 2.3). The functions of the beamline can be employed to determine the performance of optical elements (e.g. mirrors and multilayers), optical devices and detectors.
The beamline is equipped with a device for selecting the polarization of light. There are three monochromators. Their parameters are listed in Table 2.1.

Experiments at the BEAR beamline

1) Reflectivity measurements
The measurements of reflectivity at the soft x-ray and EUV ranges can be made by scanning the photon energy at a fixed incidence angle or by angle scanning at fixed photon energy. During the experiment, the incident and reflected photon flux are collected by a silicon photodiode connected to a picoammeter. A tungsten grid continuously measures the flux after the monochromator to take into account any variation of the current in the storage ring.
To perform a reflectivity measurement, we firstly measured the currents ( ) in the photodiode corresponding to the direct incident beam and the electron current ( ) in the tungsten grid. Then, the currents ( ) in the photodiode corresponding to the reflected beam and the electron current ( ) in the grid were measured. The absolute reflectivity is calculated by the ratio of the two currents of the reflected and direct incident beams normalized to the electron current in the tungsten grid
2) Rocking curve (off-specular) measurements
Rocking curve analysis is a good method to study the degree of preferred orientation in the crystals. This method is performed by rocking the sample (ω scan) while the detector is kept a fixed angle of 2θ with respect to the incident beam to record the diffraction intensities from the preferentially-oriented lattice planes. This method can also be applied to study multilayers. The scheme of this measurement is shown in the Figure 2.4.
When a multilayer structure is characterized by this method, it yields wide rocking curves compared to the perfect crystal. Lateral and vertical correlation lengths of the roughness of layers can be obtained by fitting the rocking curves. Before doing this experiment, we first need to determine the position of the Bragg peaks by making angle scan with fixed photon energy. Then we fix this angle between incidence beam and sample surface and rotate the sample around this Bragg angle. In this work, we performed rocking curves measurements for the Co/Mo2C system to observe the lateral and vertical correlation lengths of the roughness layers upon annealing.
3) Fluorescence measurement induced by x-ray standing wave
It is known that a periodic multilayer illuminated under Bragg conditions is an XSW generator because of the strong interference between the incident and reflected waves (Figure 2.5). This standing wave field can be used to excite or generate the emission of photoelectrons, Auger electrons or characteristic x-ray emissions of elements from a thin sample deposited onto the multilayer or from the multilayer itself. X-ray photoemission spectroscopy (XPS) studies photoelectrons whose mean free path at some hundreds of eV is about 1~2 nm, while fluorescence detects photons coming from some hundreds of nanometers and thus is sensitive to many buried interfaces. Fluorescence requires doing the modelization of the whole sample, while XPS allows investigating in particular the first interface and then it is a good choice for the analysis of the evolution of the multilayer capping layer. In this specific case, XSW is a powerful technique to investigate the internal modifications of the multilayer induced by thermal treatment.
In this thesis, we used the standing wave XPS to study the evolution of first buried interface between capping layer B4C and first Mo2C layer of the samples annealed at different temperature. We also used the x-ray standing wave technique to explore the study of either the center of the layers or their interfaces and obtain the depth distribution of the various species in the sample.

Reflectivity with MONOX apparatus

The MONOX apparatus consists of three different parts located in separated vacuum chambers [58]. A scheme is shown in Figure 2.6. The first part is an x-ray tube; the second one is a two-crystal monochromator and the third one is the θ-2θ goniometer. The whole apparatus works under a pressure of 5×10-7 Torr.
The radiation used for the experiments is either the Bremsstrahlung coming from a target of high atomic number (tungsten, gold, …) or a characteristic emission line: K line of light element (B to Si), Lα line of transition elements (Cr to Pd). Thus, these lines cover the spectral range between 12.9 and 0.3 nm. The maximal excitation conditions in the x-ray tube are 10 kV, 100 mA.
There are three working modes: spectrometric mode, dispersion mode and reflectometric mode. In our case, we used the reflectometric mode working the Lα line emission of copper (1.33 nm). Two W/C multilayer mirrors are used as monochromators. We firstly need to do alignment and put the detector in the centre of incident beam from the monochromator. We measure the intensity of incident beam . After that we place the sample at the position where the detector receives the intensity of ⁄ . Then we make the alignment of sample, which means that the surface of the sample is coincidence with the plane of incident beam. We noted down the height of sample. Once again we measure the intensity of incident beam without sample and then we put the sample on the right position and measure the reflected intensity. The reflectivity is obtained by making the ratio between the reflected and incident intensities. The error on the reflectivity is less than 5%.

#### X-ray emission spectroscopy (XES)

The principle of XES

X-ray emission spectroscopy (XES) is a technique to study the electronic structure of bulk sample. It can probe the depth information up to few hundreds nanometres without sample damage. The schematic of the principle is shown in Figure 2.7. When high energy photons or electrons ionize atoms in a target sample, an x-ray emission process can be described as the transition of a valence electron or an electron from high energy level into a core hole. Local density of states for one type of atom can be measured separately from the others because the core states are well separated in energy. Electrons transitions between empty and filled levels are determined by the quantum selection rules. For the most intensive x-ray lines the electrical dipole transitions are followed:
where l and j are the orbital quantum number and total angular momentum quantum number respectively.
X-ray emission spectra reflect partial occupied density of electronic states. The position of peak and its chemical shift, the shape of spectrum as well as any satellites are important characteristics for analysing buried interfaces within the sample. The probed thickness can be determined by selecting the incident electron energy. In our experiment, we used the Monte Carlo CASINO program [59] to simulate the depth distribution of ionizations in a material subjected to electron bombardment and hence to determine the probed thickness. A model of the emission study is created and allows us to choose the angle and the appropriate incident electron energy.

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Description of IRIS setup

Experimental setup IRIS (instrument for research on interface and surface) consists of three main chambers [60]:
(1) Preparation chamber: it is equipped with slot to insert devices for preparing thin layers. heating, annealing, cleaning samples. The chamber is connected to another chamber where the samples can be stored.
(2) Source chamber: In this chamber, there is an electron gun to bombard the sample which is the radiation source. The energy and the incident angle of electron beam determine the penetration depth of the electrons in the sample. The inclination angle of the sample is the results of compromise between maximizing of probed thickness and minimization of the phenomenon of reabsorption. The kinetic energy of the electrons may vary from 0 to 10 keV. We work with high focusing voltage that adjusts the size of the beam on the sample. The electron current density can be set from 0 to10 mA/cm2. A sample holder cooled by water is used.
(3) Spectrometer chamber: The scheme of the spectrometer is shown in Figure 2.8(a). This room is equipped with dispersive spectrometer and curved crystal working in reflection mode. The focusing spectrometer is of Johann type [61], whose principle is shown schematically in Figure 2.8(b).
In Figure 2.6(b), the beam reflected by the bend cylindrically (2R) crystal is focused on a cylinder of radius R, which is called focusing cylinder. The radius of curvature of 2R is 500 mm. The detector, placed behind an adjustable slit, is a gas (90% Ar and 10% CH4) flow meter operating in the Geiger field.

Nuclear magnetic resonance (NMR) spectroscopy

Nuclear magnetic resonance (NMR) spectroscopy is based on the fact that nuclei of atoms have magnetic properties that can be utilized to yield chemical information. Quantum mechanically subatomic particles (protons, neutrons and electrons) have spin. In some atoms (12C, 16O, 32S) these spins are paired and cancel out each other so that the nucleus of the atom has no overall spin. However, in many atoms (1H, 13C, 31P, 59Co), the nucleus does possess an overall spin. To determine the spin of a given nucleus one can use the following rules: if the number of neutrons and the number of protons are both even, the nucleus has no spin. If the numbers of neutrons plus the number of protons is odd, then the nucleus has half-integer spin (i.e. 1/2, 3/2, 5/2). If the number of neutrons and the number of protons are both odd, then the nucleus has an integer spin (i.e. 1, 2, 3).
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 direct yield of a zero-field NMR experiment in magnetic materials is the hyperfine field produced by the electron spin polarization at the observed nuclei. As such, the measurement provides a direct insight, element and site specific, onto the electron moment values and possible magnetic structure. The hyperfine field is sensitive to the local environment of atoms, which can be used to study the local atomic structure of individual layers and the interfaces topology of metallic multilayers and superlattices. Indeed, the hyperfine field distribution (the NMR spectrum) reflects the occurrence probability distribution of all nearest neighbour configurations in the samples (each configuration giving rise to a characteristic line in the spectrum). In our work we use zero-field NMR to characterize the Co-based multilayers. In multilayers where there are several mixed planes at interfaces. The analysis of the interface concentration profile yields also the average hyperfine field for each atomic plane. This reflects the magnetization profile at the interfaces.
In this work, all the NMR experiments are carried out on the home-made NMR instrument in IPCMS (Institut de Physique et Chimie des Matériaux de Strasbourg). A spectrometer with 20-750 MHz wide band is used to receive the signal. To improve the sensitivity, the measurement temperature is 2 K for all the multilayers and 4.2 K for the disordered alloy reference. We measured the spin echo intensity of Co atoms surrounded by others atoms in the Co/Mo2C and Co/Y/Mo2C systems. Meanwhile the NMR spectra of some references Co3Mo, CoMo1 %( at.) disordered alloys and Co/C multilayers were measured.

Time-of-flight secondary ion mass spectrometry (ToF-SIMS)

Time-of-flight secondary ion mass spectrometry (ToF-SIMS) is a surface-sensitive analytical method that uses a focused and pulsed particle beam (typically Cs or Ga) to sputter chemical species on a material surface. The resulting secondary ions are then accelerated into a flight path on their way towards a detector. The lighter ones arrive before the heavier ones. Their mass is determined by measuring their time of flight from the sample surface to the detector and a mass spectrum is recorded. There are three different modes of analysis in ToF-SIMS: (a) mass spectra are acquired to determine the elemental and molecular species on a surface; (b) images are acquired to visualize the distribution of individual species on the surface; and (c) depth profiles are used to determine the distribution of different chemical species as a function of depth.

Chapter 1 Multilayer mirrors in the soft x-ray and extreme ultraviolet ranges
1.1 Soft x-ray and extreme ultraviolet light
1.2 Multilayer mirrors
1.2.1 Theory and principle of multilayer mirrors
1.2.2 Design of multilayer mirrors for the soft x-ray and EUV ranges
1.3 Applications of multilayer mirrors
1.3.1 Astronomical observation with multilayer mirrors
1.3.2 Extreme ultraviolet lithography
1.3.3 Photoemission microscope
1.3.4 X-ray standing wave
1.3.5 Other applications
1.4 Multilayer fabrication
1.5 Thermal stability of multilayer mirrors
1.6 Development of tri-layer multilayer optics
1.7 Proposal of Co-based multilayers
1.8 Outline
Chapter 2 Analysis techniques
2.1 X-ray reflectometry in hard x-ray range
2.2 X-ray diffraction (XRD)
2.3.1 Description of the BEAR beamline
2.3.2 Experiments at the BEAR beamline
1) Reflectivity measurements
2) Rocking curve (off-specular) measurements
3) Fluorescence measurement induced by x-ray standing wave
2.4 Reflectivity with MONOX apparatus
2.5 X-ray emission spectroscopy (XES)
2.5.1 The principle of XES
2.5.2 Description of IRIS setup
2.6 Nuclear magnetic resonance (NMR) spectroscopy
2.7 Time-of-flight secondary ion mass spectrometry (ToF-SIMS)
2.8 Transmission electron microscopy
2.8.1 Principle of TEM
2.8.2 Preparation of sliced sample
2.8.3 Description of the TEM experiments
Chapter 3 Study of Co/Mo2C multilayers
3.1 Investigation of the reflectivity of Co/Mo2C multilayer upon thermal treatment
3.1.1 Introduction
3.1.2 Experimental details
3.1.3 Results and discussion
3.1.4 Conclusions
3.2 Evaluation of structure and optical parameters of Co/Mo2C multilayer upon annealing
3.2.1 Introduction
3.2.2 Results and discussion
1) Fitting of reflectivity curves
2) Enhanced Fluorescence by XSW
3) Simulation of the electric field within the multilayer stack
3.2.3 Conclusions
3.3 Observation of the first buried interfaces within Co/Mo2C multilayers studied by soft x-ray standing wave enhanced photoemission spectroscopy
3.3.1 Introduction
3.3.2 Results and discussion
3.3.3 Conclusions
3.4 Interface analysis of heat-treated Co/Mo2C multilayers
3.4.1 Introduction
3.4.2 Experimental methods
3.4.3 Results and discussion
1) X-ray emission spectroscopy
2) Zero-field nuclear magnetic resonance spectroscopy
3) X-ray diffraction
4) Time of flight-secondary ions mass spectroscopy
5) Transmission electron microscopy
3.4.4 Discussion
3.4.5 Conclusions
Chapter 4 Study of Co/Mo2C/Y multilayers
4.1 Optical and structural characterization of the Co/Mo2C/Y system
4.1.1 Introduction
4.1.2 Experimental details
4.1.3. Results and discussion
1) X-ray reflectometry at 0.154 nm
2) Extreme ultra-violet reflectivity with synchrotron radiation
3) Zero-field nuclear magnetic resonance spectroscopy
4) X-ray diffraction
4.1.4 Discussion
4.1.5 Conclusions
4.2 Transmission electron microscopy observation of Co/Mo2C/Y system
4.2.1 Introduction
4.2.2 Experimental details
4.2.3 Results and discussion
1) Scanning transmission electron microscopy
2) In-depth intensity profiles
3) Energy dispersive x-rays spectrometry (EDS)
4) High-resolution images and selected-area electron diffraction
4.2.4 Conclusions
Chapter 5 Conclusions and perspectives
Appendix І: Miedema’s model
References
Appendix П: other publications

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