Thin films and multilayers are widely used in many applications, ranging from X-ray optics to microelectronic devices. In service, the X-ray optics elements are exposed to the X-ray beam, which heats up the structure resulting in the thermal deformations, and consequently in distortions of the reflective surface. In addition, the excessive heating may activate interdiffusion in the multilayers coatings and result in degradation of their reflective performance and even film cracking. Therefore, analysis of the thermally-induced deformations and stresses in the X-ray optical elements is important. The presented work is organized in two major parts. The first part examines formation of the peculiar periodic crack patterns observed in the thermally loaded Mo/Si multilayers. Film stress evolution during thermal cycling of the multilayers on Si substrate is analyzed. Results of the high-speed microscopic observations of crack propagation in the annealed Mo/Si multilayers are presented. The observations provide experimental evidence of the mechanism underlying formation of the periodic crack patterns. In the second part, thermal deformations and the resulting surface curvature changes in the X-ray optics elements are analyzed. Finite element modeling is used to assess the potential to thermally control curvature in the X-ray mirrors consisting of the Mo/Si multilayers on a Si substrate. Influence of heating due to the X-ray beam irradiation on thermal deformations in the X-ray mirror bonded to a thick substrate is analyzed in-depth. The detailed consideration includes analysis of the thermal and structural mechanics simulations. Based on simulations of different model configurations, influence of structural composition on thermal distortions of the optics elements is addressed. Results of this analysis can be used to mitigate distortions of the X-ray optics caused by the X-ray beam and provide basis for further studies of thermally controlling surface curvature in the optical elements.

The exploitation of the soft x-ray/extreme ultra-violet (EUV) region of the electromagnetic spectrum is possible mainly due to the development of multilayer (ML) mirrors. This region of the electromagnetic spectrum offers great opportunities in both science and technology. The shorter wavelength allows one to see smaller features in microscopy and write finer features in lithography. High reflectivity with moderate spectral bandwidth at normal/near-normal incidence can be achieved in soft x-ray/ EUV spectral range using these ML mirrors, where natural crystals with the required large periodicity are not available. These MLs are generally artificial Bragg’s reflectors, which consist of alternative high and low density materials with periodicity in the nanometer range. The main advantages of ML optics stem from the tunability of layer thickness, composition, lateral gradient, and the gradient along the normal to the substrate; these can be tailored according to the desired wavelength regime. They have the great advantage of being adaptable to figured surfaces, enabling their use as reflective optics in these spectral regions, for focusing and imaging applications. Broadband reflectivity and wavelength tunability are also possible by using MLs with normal and lateral gradient, respectively. However, fabrication of these ML mirrors requires the capability to deposit uniform, ultra-thin (a few angstroms-thick) films of different materials with thickness control on the atomic scale. Thus, one requires a proper understanding of substrate surfaces, individual layers, chemical reactivity at interfaces and, finally, of the ML structures required for particular applications. The performance of these MLs is limited by (the lack of) contrast in optical constants of the two materials, interfacial roughness, the chemical reactivity of two materials and, finally, errors in the thickness of individual layers. Soft x-ray/extreme ultra-violet ML mirrors have found a wide range of applications in synchrotron radiation beam lines, materials science, astronomy, x-ray microscopy, x-ray laser, x-ray lithography, polarizers, and plasma diagnostics. The Indus–1 synchrotron radiation (SR) source is an operational 450 MeV machine, which produces radiation up to soft x-rays. Indus-2 is a 2.5 GeV machine, which has been commissioned recently to produce hard x-rays (E > 25 keV). The combination of Indus-1 and Indus-2 will cover a broad energy spectrum from IR to hard x-rays. Therefore, there is a significant need and opportunity to study MLs of different pairs of materials, with different parameters such as periodicity and optimum thickness of individual layers. The goal of the present thesis is to fabricate MLs for soft x-ray optics and to study their physics for application as polarizers in the wavelength range from 67 Å to 160 Å on the Indus-1 synchrotron source. To accomplish this task, a UHV electron beam evaporation system has been developed indigenously for the fabrication of MLs. Three different ML systems viz., Mo/Si, Fe/B4C and Mo/Y have been fabricated, and their surfaces and interfaces were investigated thoroughly for the polarizer application. X-ray reflectivity (XRR) has been used extensively in the investigations of these MLs. This is because XRR is a highly sensitive non-destructive technique for the characterization of buried interfaces, and gives microscopic information (at atomic resolution) over a macroscopic length scale (a few microns). Numerical analysis of XRR data has been carried out using computer programs. Depth-graded x-ray photoelectron spectroscopy (XPS) has been used for compositional analysis at interfaces for some of the ML structures, as a technique complementary to XRR. The performance of some of these MLs has been tested in the soft x-ray region, using the Indus-1 synchrotron radiation (SR) source. Prior to studying the MLs, a detailed study of the surfaces and interfaces of thin films, bi-layers, and tri-layers was carried out using XRR and the glancing incidence fluorescence technique. The discontinuous-to-continuous transition and the mode of film growth, which are vital to the optimization of layer thickness (basically for the high-atomic number or high-Z layer) in the ML structures, were also investigated using in situ sheet resistance measurement method. Indus-1 is a soft x-ray SR source that covers atomic absorption edges of many low-Z materials. The present work demonstrates the possibilities of characterizing low-Z thin films and multilayers using soft x-ray resonant reflectivity. In one case, we have shown for first time that soft x-ray resonant reflectivity can be employed as a non-destructive technique for the determination of interlayer composition. In a second study using the Indus-1 SR source, we have shown, by observing the effect of the anomalous optical constant on reflectivity pattern when photon energy is tuned across the atomic absorption edge of the constituent low-Z element, that soft x-ray resonant reflectivity is an element-specific technique. This thesis is organized into 7 chapters. A brief summary of individual chapters is presented below. Chapter 1 gives a brief general introduction to x-ray ML optics. This is followed by a discussion of the importance of the soft x-ray region of electromagnetic radiation. The optical properties of x-rays are reviewed and optical constants are calculated for some of the important materials used for x-ray MLs. The refractive index in the x-ray region being less than unity (except absorption edges), the consequent limitation of conventional transmission lenses is discussed. The limitation of glancing angle incidence optics is presented, motivating the need for ML optics, which is discussed along with a theoretically calculated reflectivity profile. The procedure for materials for the MLs for application in different spectral regions is discussed, along with a survey of literature related to the present thesis. The importance of the quality of surfaces and interfaces on the performance of ML structures has been shown through simulations. The applications of soft x-ray MLs are discussed with emphasis on polarization. This is followed by a review of different modes of growth of thin films. Finally, the scope of the present work is highlighted. Chapter 2 provides brief descriptions of the experimental techniques used in the present investigations and of the numerical methods employed for quantitative data analysis. The XRR technique is discussed elaborately because it has been used extensively. Detailed calculations of x-ray reflectivity from single surfaces, thin films and bi-layers are presented, along with simulated values. The effect of critical angle and Brewster’s angle is also discussed. Data analysis methods for computing x-ray reflectivity from multilayer structures, based on dynamical and kinematical models, have been discussed. The effect of roughness on XRR has been discussed based on the recursion formalism of dynamical theory. Simulations of XRR and experimental XRR data fitting are carried out using computer programs. The XRR experimental set up is also outlined. A theoretical background is given for the electrical measurements on thin films. This is followed by a brief overview of x-ray photoelectron spectroscopy (XPS) and interpretation of spectra. Finally, the glancing incidence x-ray fluorescence (GIXRF) technique is outlined. Chapter 3 describes in detail the ultra-high vacuum electron beam evaporation system developed in house especially for the fabrication of thin films and x-ray multilayer optics. At the outset, a brief overview of different deposition techniques commonly used for the fabrication of x-ray optical elements is presented. Design, fabrication, and assembly of different accessories are discussed. The control of thickness and uniformity of the films deposited has been checked through the experiments, whose results are provided. The results obtained for ML test structures are presented to show the capability of system in carrying out fabrication of high quality x-ray ML structures. Finally, the versatility of evaporation system incorporating in situ characterization facilities such as -situ electrical measurements for different substrate temperatures is illustrated. Chapter 4 presents a study of the growth of ultra-thin Mo films at different substrate temperatures using in situ sheet resistance measurements. First, a theoretical background is given on the different stages of island growth and on factors affecting thin film growth, followed by a discussion of the possible electrical conduction phenomena in continuous and discontinuous metal films. The nature of thin film growth and a detailed microscopic picture at different growth stages are derived from a modeling of sheet resistance data obtained in situ. The various conduction mechanisms have been identified in different stages of growth. In the island growth stage, the isotropic and anisotropic growth of Mo islands is identified from the model. In the insulator-metal transition region, experimentally determined values of critical exponent of conductivity agrees well with theoretically predicted values for a two-dimensional (2D) percolating system, revealing that Mo films on float glass substrate is predominantly a 2D structure. The minimum thickness for which Mo films becomes continuous is obtained as 1.8 nm and 2.2 nm for Mo deposited at substrate temperatures 300 K and 100 K, respectively. An amorphous-to- crystalline transition is also observed, and discussed. Chapter 5 covers the detailed study of the surfaces and interfaces studies in three different ML structures viz., Mo/Si, Fe/B4C and Mo/Y, meant for the polarizer application in the wavelength range of 67 Å to 160 Å. Multilayers with varying periodicity, varying number of layer pairs, and different ratios of high-Z layer thickness to the period, were fabricated using the electron beam system. Initially, a brief overview of the design aspects of ML structures is given, along with the theoretically calculated reflectivity at Brewster’s angle from the best material combinations. In Mo/Si MLs, the interlayer formed at the interfaces due to interdiffusion of the two elements is asymmetric in thickness, i.e., Mo-on-Si interlayer is thicker than the Si-on-Mo interlayer. To take account of these interlayers in XRR data fitting, a four layer model is considered. The effect of interlayers on reflectivity pattern was studied using simulations, and differences with respect to roughness are also discussed. The mechanism of formation of asymmetric interlayers is also discussed. The interlayer composition has determined using depth-graded XPS. The results reveal the formation of the MoSi2 composition at both the interfaces. The experimental results agree well with theoretical calculations based on solid-state amorphization reaction, which is a result of large heat of mixing. The effective heat of formation model reveals the formation of MoSi2 as the first phase. The soft x-ray reflectivity performance of the Mo/Si ML structure at Brewster’s angle is tested using Indus-1 synchrotron radiation (SR). Using XRR and GIXFR, a study of the surfaces and interfaces of bilayers of B4C-on-Fe and Fe-on- B4C, and tri-layers of Fe-B4C-Fe was carried out, with a systematic variation of Fe and B4C layer thicknesses. A sharp interface was observed in Fe-on-B4C, whereas a low density (w.r.t. Fe) interlayer is observed at the B4C-on-Fe interface. The interlayer properties fluctuates w.r.t. the bottom Fe layer thickness and is independent of the top B4C layer thickness. The nature of fluctuations has been discussed in detail. A study of the surfaces and interfaces of Fe/B4C MLs is described. Finally, a study of the surfaces and interfaces of bilayers, tri-layers, and MLs of the Mo/Y system is discussed in detail. Chapter 6 describes the application of soft x-ray resonant reflectivity for the characterization of low-Z thin films and interfaces in multilayer structures. Initially, a discussion of the energy dependence of atomic scattering factors and hence of optical constants is provided with simulations, with emphasis on the atomic absorption edge. Then, a brief overview of synchrotron radiation, with particular emphasis on the parameters of the Indus-1 synchrotron source is given. The possibilities of determining the composition of the buried interlayer with sub-nanometer scale sensitivity using soft x-ray resonant reflectivity are discussed. The methodology has been applied to study the Mo/Si interface both by simulations and by experiments on the Indus-1 SR, by tuning the photon energy to the Si L-absorption edge. Finally, direct evidence of elemental specificity of soft x-ray resonant reflectivity through the observation of the effect of anomalous optical constants on the reflectivity pattern is discussed. We demonstrate the method through simulations and experiments on the B4C material in B4C thin films and Fe/ B4C bi-layers, using Indus-1 SR tuned to the boron Kedge. Chapter 7 summarizes the main findings of the present work, and provides an outlook for further investigations in the field.