Igor V. Kozhevnikov

High-resolution, high-reflectivity operation of lamellar multilayer amplitude gratings: identification of the single-order regime

High resolution while maintaining high peak reflectivities can be achieved for Lamellar Multilayer Amplitude Gratings (LMAG) in the soft-x-ray (SXR) region. Using the coupled waves approach (CWA), it is derived that for small lamellar widths only the zeroth diffraction order needs to be considered for LMAG performance calculations, referred to as the single-order regime. In this regime, LMAG performance can be calculated by assuming a conventional multilayer mirror with decreased density, which significantly simplifies the calculations. Novel analytic criteria for the design of LMAGs are derived from the CWA and it is shown, for the first time, that the resolution of an LMAG operating in the single-order regime is not limited by absorption as in conventional multilayer mirrors. It is also shown that the peak reflectivity of an LMAG can then still be as high as that of a conventional multilayer mirror (MM). The performance of LMAGs operating in the single-order regime are thus only limited by technological factors.

Analytic theory of soft x-ray diffraction by lamellar multilayer gratings

An analytic theory describing soft x-ray diffraction by Lamellar Multilayer Gratings (LMG) has been developed. The theory is derived from a coupled waves approach for LMGs operating in the single-order regime, where an incident plane wave can only excite a single diffraction order. The results from calculations based on these very simple analytic expressions are demonstrated to be in excellent agreement with those obtained using the rigorous coupled-waves approach. The conditions for maximum reflectivity and diffraction efficiency are deduced and discussed. A brief investigation into p-polarized radiation diffraction is also performed.

Properties of broadband depth-graded multilayer mirrors for EUV optical systems

The optical properties of a-periodic, depth-graded multilayer mirrors operating at 13.5 nm wavelength are investigated using different compositions and designs to provide a constant reflectivity over an essentially wider angular range than periodic multilayers. A reflectivity of up to about 60% is achieved in these calculation in the [0, 18 degrees] range of the angle of incidence for the structures without roughness. The effects of different physical and technological factors (interfacial roughness, natural interlayers, number of bi-layers, minimum layer thickness, inaccuracy of optical constants, and thickness errors) are discussed. The results from an experiment on the fabrication of a depth-graded Mo/Si multilayer mirror with a wide angular bandpass in the [0, 16 degrees] range are presented and analyzed.

Specification of x-ray mirrors in terms of system performance: new twist to an old plot

Abstract. In the early 1990s, Church and Takacs pointed out that the specification of surface figure and finish of x-ray mirrors must be based on their performance in the beamline optical system. We demonstrate the limitations of specification, characterization, and performance evaluation based on conventional statistical approaches, including root-mean-square roughness and residual slope variation, evaluated over spatial frequency bandwidths that are system specific, and a more refined description of the surface morphology based on the power spectral density distribution. We show that these limitations are fatal, especially in the case of highly collimated coherent x-ray beams, like beams from x-ray free electron lasers (XFELs). The limitations arise due to the deterministic character of the surface profile data for a definite mirror, while the specific correlation properties of the surface are essential for the performance of the entire x-ray optical system. As a possible way to overcome the problem, we treat a method, suggested by Yashchuk and Yashchuk in 2012, based on an autoregressive moving average modeling of the slope measurements with a limited number of parameters. The effectiveness of the approach is demonstrated with an example specific to the x-ray optical systems under design at the European XFEL.

Unified analytical theory of single-order soft x-ray multilayer gratings

A universal analytical theory of soft x-ray multilayer gratings operating in the single-order regime is developed here. The single-order regime, in which an incident wave excites only the diffracted wave, is characterized by the maximum possible diffraction efficiency tending to the reflectivity of a conventional multilayer mirror. The theory is applied to analysis of different multilayer gratings, including lamella multilayer gratings, sliced multilayer gratings, blazed multilayer gratings, and blazed lamella multilayer gratings. A simple analytical formula that describes the diffraction efficiency of an arbitrary multilayer grating as a function of the wavelength and the incidence angle is deduced. Expressions for the peak value of the diffraction efficiency and the generalized Bragg condition corresponding to the maximum efficiency are obtained. The high accuracy of the deduced analytical expressions is justified by comparison with rigorous numerical calculations. Comparative analysis of different types of gratings is performed. The advantages and disadvantages of different gratings in practical applications are discussed.

Improved resolution for soft X-ray monochromatization using lamellar multilayer gratings

Lamellar Multilayer Gratings (LMG) offer improved resolution for soft-x-ray (SXR) monochromatization, while maintaining a high reflection efficiency in comparison to conventional multilayer mirrors (MM). We previously used a Coupled-Waves Approach (CWA) to calculate SXR diffraction by LMGs and identified a single-order regime in which the incident wave only excites a single diffraction order. We showed that in this regime the angular width of the zeroth-order diffraction peak simply scales linearly with Γ (lamel-to-period ratio) without loss of peak reflectivity. However, the number of bi-layers must then be increased by a factor of 1/Γ. Optimal LMG resolution and reflectivity is obtained in this single-order regime, requiring grating periods of only a few hundred nm, lamel widths < 100nm and lamel heights > 1μm [1]. For the fabrication of LMGs with these dimensions, we use a novel process based on UV-NanoImprint Lithography (UV-NIL) and Bosch-type Deep Reactive Ion Etching (DRIE). Successful fabrication of LMGs with periods down to 200nm, line widths of 60nm and multilayer stack heights of 1μm is demonstrated. SXR reflectivity measurements were performed on these LMGs at the PTB beamline at the BESSYII synchrotron facility. The measurements demonstrate an improvement in resolution by a factor 3,5 compared to conventional MMs. Further analysis of the SXR reflectivity measurements is currently being performed.

Exact solution of the phase problem in in situ x-ray reflectometry of a growing layered film

The recent development of an exact solution of the phase retrieval problem is applied to the case of in situ x-ray reflectometry measurements performed during the growth of a tungsten film. The measurement of the phase variation during deposition provides information about the depth distribution of the material density, even though the grazing angle of the probe beam is fixed. A comparison of two different approaches for reconstructing the material density profile is presented. The effect of roughness on the phase retrieval is analyzed.

Enhancement of soft X-ray reflectivity and interface stability in nitridated Pd/Y multilayer mirrors

Pd/Y multilayer mirrors operating in the soft X-ray region are characterized by a high theoretical reflectance, reaching 65% at normal incidence in the 8-12 nm wavelength range. However, a severe intermixing of neighboring Pd and Y layers results in an almost total disappearance of the interfaces inside the multilayer structures fabricated by direct current magnetron sputtering and thus a dramatic reflectivity decrease. Based on grazing incidence X-ray reflectometry and X-ray photoelectron spectroscopy, we demonstrate that the stability of the interfaces in Pd/Y multilayer structures can be essentially improved by adding a small amount of nitrogen (4-8%) to the working gas (Ar). High resolution transmission electron microscopy shows that the interlayer width is only 0.9 nm and 0.6 nm for Y(N)-on-Pd(N) and Pd(N)-on-Y(N) interfaces, respectively. A well-defined crystalline texture of YN (200) is observed on the electron diffraction pattern. As a result, the measured reflectance of the Pd(N)/Y(N) multilayer achieves 30% at λ = 9.3 nm. The peak reflectivity value is limited by the remaining interlayers and the formation of the YN compound inside the yttrium layers, resulting in an increased absorption.

Comparative study of the X-ray reflectivity and in-depth profile of a-C, B4C and Ni coatings at 0.1–2 keV

The use of soft X-rays near the carbon edge of absorption (270-300 eV) greatly enhances studies in various branches of science. However, the choice of reflecting coatings for mirrors operating in free-electron and X-ray free-electron laser (FEL and XFEL) beamlines in this spectral range is not so evident and experimental justifications of the mirror efficiency are rather limited. In the present paper it is demonstrated experimentally that the reflectivity of B4C- and Ni-coated grazing-incidence mirrors is high enough for their operation in FEL or XFEL beamlines near the carbon K-edge of absorption. The minimal reflectivity of both mirrors proves to exceed 80% near the carbon absorption edge at a grazing angle of 0.6°. An in-depth profile of the chemical elements composing the reflecting coatings is reconstructed based on analysis of a set of reflectivity curves measured versus the grazing angle at different photon energies in the soft X-ray spectral region. This allows us to predict correctly the mirror reflectivity at any X-ray energy and any grazing angle.

Exact determination of the phase in time-resolved X-ray reflectometry.

An exact solution of the phase retrieval problem is described as applied to in-situ X-ray reflectometry of a growing layered film. The following statement is proved: if the reflectivity R and the derivative dR/dt are known at the time t, then the real and the imaginary parts of the amplitude reflectivity r(t) are found uniquely at this point t.