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Ultra-high frequency multilayer coated gratings which combine high dispersion and high diffraction efficiency are of eminent importance for high resolution EUV spectroscopy. Here we report on recent progress achieved in efficiency modelling of a high quality blazed grating which has been fabricated using electron beam lithography followed by wet anisotropic etching of Si. The 100-nm-period grating coated with an Al/Zr multilayer composed of 20 bi-layers demonstrated experimentally and theoretically an absolute efficiency of 13.3percent in the 1st diffraction order at 19.2 nm wavelength and 11 deg incidence angle. The groove profile of the grating was thoroughly characterized by AFM before and after the multilayer deposition. Investigation of the grating by TEM revealed a complex evolution of the groove profile from a triangular shape (bottom) to a sinusoidal one (top). The redundant metrology data were used for simulation of the grating efficiency with commercial PCGrate(R)-SX v.6.1 and v.6.4 codes. The grating boundary profile shapes and their horizontal shifts are the most difficult to determine parameters of the multilayer grating. The smoothing of boundary profiles is a crucial characteristic that dramatically affects on the grating efficiency. Yet, a good general agreement between theory and experiment was obtained for different wavelength and incident angles.

Diffraction gratings with high efficiency and high groove density are required for EUV and soft x-ray spectroscopy techniques (such as Resonant Inelastic X-ray Scattering, RIXS) designed for state-of-the-art spectral resolution and throughput. We report on recent progress achieved at the Advanced Light Source (ALS) in development of ultra-dense multilayer coated blazed (MCB) gratings. In order to fabricate a high quality MCB grating, one should address two main challenges. The first one is to fabricate nano-period saw-tooth substrates with perfect groove profile and atomically smooth surface of the blazed facets. The second challenge relates to uniformed deposition of a multilayer on a highly corrugated surface of the substrates. We show that the required saw-tooth substrates with groove density up to 10,000 lines/mm can be fabricated using high resolution interference and e-beam lithography techniques followed by wet anisotropic etching of silicon. Peculiarities of growth on the saw-tooth substrates of a variety of multilayers, optimized to provide high diffraction efficiency in EUV wavelength range, are also under throughout investigation. With cross-sectional TEM we reveal a transformation of the structure of the multilayer stack, consisting in smoothing of the groove profile of a coated grating. The multilayer profiles measured with the TEM are used for diffraction efficiency simulations and investigation of the impact of the smoothing on grating performance. Thus, we show that a strong smoothing of the grating grooves results in deterioration of the blazing ability of the gratings.

Multilayer coated blazed gratings with high groove density are the most promising candidate for high resolution EUV and soft x-ray spectroscopy. They combine the ability of blazed gratings to concentrate almost all diffraction energy in a desired high diffraction order with high reflectance of EUV and soft x-ray multilayers. The gratings however have to be of superior quality in order to realize their potential. Thus, the grating fabrication process should provide a perfect triangle groove profile and extremely smooth surface of the blazed facets. Here we report on recent progress in fabrication and characterization of the gratings designed for EUV applications. The gratings having groove density from 5000 to 10000 lines/mm were fabricated with scanning beam interference lithography or electron beam lithography followed by wet anisotropic etch of silicon wafers and multilayer deposition. The groove surface morphology was characterized with AFM and SEM, and evolution of the structure of the multilayer stack in the course of multilayer deposition onto the corrugated surface of the blazed grating was studied with TEM (Fig. 1). The grating diffraction efficiency measurements were performed at the ALS beam line 6.3.2. The grating coated with the Mo/Si multilayer composed of 30 bi-layers demonstrated diffraction efficiency more than 37percent in the 3rd diffraction order (Fig. 2). An impact of groove profile imperfections and perturbations of the multilayer stack was also investigated via efficiency simulations with PCGrate 6.1 code. The results of the study show good prospects to extend the technology towards soft x-rays.

The near-normal-incidence efficiencies of a 2400-groove/mm holographic master grating, a replica grating, and a multilayer grating are modeled in the soft-x-ray--extreme-ultraviolet (EUV) regions and are compared with efficiencies that are measured with synchrotron radiation. The efficiencies are calculated by the computer program PCGrate, which is based on a rigorous modified integral method. The theory of our integral method is described both for monolayer and multilayer gratings designated for the soft-x-ray--EUV-wavelength range. The calculations account for the groove profile as determined from atomic force microscopy with a depth scaling in the case of the multilayer grating and an average random microroughness (0.7 nm) for the short wavelengths. The refractive indices of the grating substrate and coatings have been taken from different sources because of the wide range of the wavelengths (4.5-50 nm). The measured peak absolute efficiency of 10.4% in the second diffraction order at a wavelength of 11.4 nm is achieved for the multilayer grating and is in good agreement with a computed value of ~11.5%. Rigorous modeling of the efficiencies of three similar gratings is in good overall agreement with the measured efficiency over a wide wavelength region. Additional calculations have indicated that relatively high normal incidence efficiency (of at least several percent) and large angular dispersion in the higher orders can be achieved in the 4.5-10.5-nm range by application of various multilayer coatings. OCIS codes: 050.1950, 050.1960, 260.7200, 310.6860, 340.7470.

Thin-film interference effects were observed in the normal-incidence efficiency of a 2400-groove/mm replica grating. The efficiency was measured in the 100-350-[Angstrom] wavelength range and had an oscillatory behavior that resulted from the presence of a thin Si[O.sub.2] coating. The thicknesses of the Si[O.sub.2] and the underlying oxidized aluminum layers were inferred from computer modeling of the zero-order efficiency. The efficiencies in the diffracted orders were calculated with the modified integral approach and accounting for the multilayer coating and the groove profile derived from atomic force microscopy. The calculated and measured efficiencies were in good agreement.

The paper presents a comprehensive numerical analysis of x-ray and neutron scattering from finite-conducting rough surfaces which is performed in the frame of the boundary integral equation method in a rigorous formulation for high ratios of characteristic dimension to wavelength. The single integral equation obtained involves boundary integrals of the single and double layer potentials. A more general treatment of the energy conservation law applicable to absorption gratings and rough mirrors is considered. In order to compute the scattering intensity of rough surfaces using the forward electromagnetic solver, Monte Carlo simulation is employed to average the deterministic diffraction grating efficiency due to individual surfaces over an ensemble of realizations. Some rules appropriate for numerical implementation of the theory at small wavelength-to-period ratios are presented. The difference between the rigorous approach and approximations can be clearly seen in specular reflectances of Au mirrors with different roughness parameters at wavelengths where grazing incidence occurs at close to or larger than the critical angle. This difference may give rise to wrong estimates of rms roughness and correlation length if they are obtained by comparing experimental data with calculations. Besides, the rigorous approach permits taking into account any known roughness statistics and allows exact computation of diffuse scattering. [ABSTRACT FROM AUTHOR]

It is shown from both a phenomenological study and exact modeling that the reason for the experimentally observed substantial (a few angstroms or nanometers) separation in wavelength between the maxima of the inside (negative numbered) and outside (positive numbered) diffraction orders of a multilayer-coated grating, operating at near normal incidence and close to the Bragg condition in the soft-x-ray and extreme-ultraviolet (EUV) regions, is related to the different angles of deviation of the orders. This wavelength separation is also a feature of uncoated diffraction gratings, although not clearly noticeable. The widely used approximate approach for calculating the absolute efficiency, the product of the relative grating efficiency and the reflectance of its multilayer coating, has until recently been considered accurate enough for the analysis of soft-x-ray and EUV near-normal-incidence multilayer-coated gratings. The inapplicability of this approximation for the analysis of the precise positions and shapes of the efficiency curves for the inside and outside orders, despite the small ratios of wavelength and groove depth to period and the small angles of incidence, is demonstrated using gratings with realistic groove profiles and operating in the EUV region. The rigorous modified integral method (MIM), which is a variant of boundary integral equation methods and is designed for the calculation of the efficiency of multilayer gratings with arbitrary layer thicknesses and boundary shapes (including microroughness) and over a wide wavelength range, is proposed in a general operator formalism. An analysis of a derived simple phenomenological expression and the exact numerical study indicates that the spectral separation between the inside and the outside orders grows with increasing either wavelength, angle of incidence, groove frequency, or diffraction order number |m|. The efficiency modeling carried out with the commercial program PCGRATE-SX, based on the MIM, gave not only the exact values of the spectral separation between the inside and outside orders of Mo4Ru6/Be, Mo/Si, and Mo/Y multilayer-coated gratings with various real groove profiles measured using atomic force microscopy (AFM) but also good agreement with synchrotron radiation measurements, including high orders as well. To determine the shapes and positions of efficiency curves in the soft-x-ray-EUV range of close to normal-incidence bulk and multilayer-coated gratings with real groove profiles (measured by AFM), one should use codes based on rigorous electromagnetic theory such as the MIM. The modeling is important for developing high efficiency and dispersion gratings for high-resolution spectroscopic studies of laboratory, solar, and astrophysical radiation sources. [ABSTRACT FROM AUTHOR]

We report time-resolved photoluminescence (TRPL) measurements performed at different temperatures for the Bragg structure containing 60 InAs monolayer-based quantum wells (QWs) periodically arranged in a GaAs matrix. TRPL data reveal an appearance of the additional superradiant (SR) mode originated from coherent collective interaction of QWs. The SR mode is not manifested in the case if a small number of QWs is excited, then only an exciton emission related to the InAs QWs dominates the PL spectrum. The SR mode demonstrates a superlinear dependence of the intensity and radiative decay rate on the excitation power and its intensity increases at elevated temperatures compared to the excitonic emission. The photoluminescence delay time is much shorter for the SR mode indicating that the relaxation of hot excitons can occur via stimulated scattering processes. The specific behavior of the SR emission can have a strong potential for different applications such as optical logic devices, superluminescent diodes, optical switches, and low-threshold lasers. Time-resolved photoluminescence image at low temperature for the Bragg structure consisting of InAs monolayer-based quantum wells (inset). [ABSTRACT FROM AUTHOR]