B. Pardo

Fourier transform and theory of fractal multilayer mirrors

Abstract A new type of non periodic interferential mirrors are proposed. These mirrors, built according to the pattern of a Cantor set, are autosimilar and are characterized by a fractional Hausdorff dimension. It is shown that such mirrors are able to reflect different radiations whose wavelengths are not harmonic.

Modulation of x-ray line intensity emitted by a periodic structure under electron excitation

We report on the intensity modulation of a characteristic x-ray line emitted by a periodic structure, as a function of the observation angle. This intensity variation takes place around the Bragg direction corresponding to the diffraction of the x-ray line by the emitting structure. An enhancement of the emitted radiation is observed and interpreted on the basis of the reciprocity theorem. The enhancement remains unchanged by varying the number of emitting periods. Following Yariv and Yeh [J. Opt. Soc. Am. 67, 438 (1977)], a possible application as x-ray resonator to achieve a distributed feedback soft x-ray laser is envisaged.

Application of the Fourier transform in a preliminary analysis of the reflectivity curve obtained by grazing x-ray reflectometry

Grazing X-ray reflectometry allows the analysis of thin layer stacks. The fitting of the reflectivity curve by a trial and error method can be used in order to determine the parameters of the films. In order to facilitate this trial and error method, the Fourier transforms of the Grazing X-ray reflectivity curves have been investigated. After the appropriate transformation of the original reflectivity curve in order to make the signal periodic, rough values of the thicknesses can be found. In first approximation, the Fourier transform leads to the auto correlation function of the derivative of the index profile of the stack. The spectrum can give also rough information about roughness by the widening of the peaks, and the height of the peaks are related to the contrast of the indices. The number of peaks in the spectrum is a function of the number of interfaces in the stack. It is shown how one can use the Fourier transform results to make a preliminary stack model before fitting the experimental data.

Bragg amplification of the Si Κα line emitted from a Mo/Si multilayer irradiated by an electron beam

We report on the intensity modulation of the Si Κα line emitted from a Mo/Si multilayer as a function of the exit angle of the photons. The observation takes place around the direction corresponding to the Bragg diffraction of Si Κα by the multilayer. The sample is irradiated by an electron beam whose the energy is varied between 2 and 6 keV. An important intensity variation is observed within the angular range corresponding to the diffraction pattern of the emitting structure. A 15 % enhancement of the emitted radiation is measured in the Bragg direction of the multilayer, whatever the incident electron energy. This amplification is interpreted on the basis of the reciprocity theorem. A possible application as x‐ray resonator is suggested.

Tunable and bright EUV sources using the interaction of medium–energy electron beams with periodic multilayer targets

We give the design of tunable and bright EUV sources based on the interaction of medium-energy electrons with periodic multilayer targets. The basic phenomon is the Bragg resonant transition radiation occurring when transition radiation is diffracted under the Bragg conditions within a periodic multilayer structure. To achieve the tunability, we propose to use laterally d-graded multilayer, and to obtain bright sources, we propose to associate multilayer targets deposited on thin semitransparent membranes. The typical performances of such sources are calculated by using a recently developed model.

High-performance neutron supermirrors deposited using an automatic accurate-thickness monitoring technique

High reflectivity neutron mirrors require perfectly smooth, sharp interfaces, uniform layer thicknesses and densities and high stack regularity. For this, the multilayers were deposited on water cooled glass substrates using a D-C low energy (300 - 700 V) triode sputtering unit equipped with an accurate thickness monitoring system. This last one is based on the dependence of the deposition rate on the target current. During deposition, the target current is sampled and converted to a digitalized voltage. This voltage value is then fed to a computer where a real-time numerical integration is made. The target current is integrated and the film thickness is given by the integration time. All sputtering parameters are regulated. A feed- back system between anode current and filament heating supply keeps the plasma current constant. The computer also automatically controls the setting and the timing of the runs. Thicknesses can be controlled to an accuracy of better than 1A. Reproducibility is better than 1%. Therefore, a high stack regularity can be achieved with sharp interfaces as will be shown by the characteristics of a 10[Ni-Ti] neutron monochromator. The experimental and theoretical reflection profiles are in perfect agreement indicating a high stack regularity. This technique is also efficient at producing high reflectivity aperiodic media: supermirrors. A 15[Ni-Ti] supermirror in Hayter-Mook configuration gives a neutron reflectivity of the order of 95% with an effective critical angel of 1.9(theta) cNi. The characteristics of the previous monochromator and supermirror have been measured also using secondary ion mass spectrometry, grazing angle x-rays reflectometry, and resistivity measurements.

Thermal stability of [Ni-Ti] multilayers

Diffusion in Ni-Ti multilayers with a period of 120 angstroms is studied in the temperature range of 293 - 743 K by using the grazing angle unpolarized neutron reflectometry. It was shown that Ni diffuses into Ti in this temperature range. The effective diffusion coefficient Deff of Ni into Ti and its corresponding activation energy Qa are determined by measuring the decay of the reflectivity of first Bragg peak arising from the nuclear scattering length density modulation, as a function of annealing temperature at constant time. Two diffusion regimes separated by a pseudo-transition temperature Tc approximately equals 543 K are observed in this Ni-Ti multilayer. The corresponding activation energy values are 0.21 eV and 0.43 eV respectively. The unpolarized neutron reflectivity measurements are completed by crystalline structure, chemical profiling, and magnetic studies.