Kossel Effect in Periodic Multilayers

Abstract

The Kossel effect is the diffraction by a periodically structured medium, of the characteristic X-ray radiation emitted by the atoms of the medium. We show that multilayers designed for X-ray optics applications are convenient periodic systems to use in order to produce the Kossel effect, modulating the intensity emitted by the sample in a narrow angular range defined by the Bragg angle. We also show that excitation can be done by using photons (X-rays), electrons or protons (or charged particles), under near normal or grazing incident geometries, which makes the method relatively easy to implement. The main constraint comes from the angular resolution necessary for the detection of the emitted radiation. This leads to small solid angles of detection and long acquisition times to collect data with sufficient statistical significance. Provided this difficulty is overcome, the comparison or fit of the experimental Kossel curves, i.e., the angular distributions of the intensity of an emitted radiation of one of the element of the periodic stack, with the simulated curves enables getting information on the depth distribution of the elements throughout the multilayer. Thus the same kind of information obtained from the more widespread method of X-ray standing wave induced fluorescence used to characterize stacks of nanometer period, can be obtained using the Kossel effect.

Spectral purity systems applied for laser-produced plasma extreme ultraviolet lithography sources: a review

“…According to the Bragg’s law, when the optical path difference of the reflected light at two adjacent interfaces is half a wavelength, the reflected light at the interface will incur constructive interference and get a strong reflection [ 42 ] . The formula formation of Bragg’s law in the case of periodic multilayers [ 43 , 44 ] is as follows: where is the multilayer period, is the incident angle, is diffraction order and is the incident wavelength. The reflectivity is determined by the number of layers and the refractive index difference between materials.…”

Grazing-emission X-ray fluorescence as a multiprobe tool for thin-film metrology

“…Another distinction is that here the excitation beam is not necessarily monochromatic or even necessarily an X-ray beam. Anything that excites characteristic radiation can be used, for example an implementation with a 'pink' X-ray beam (Gog et al, 1994) (non-monochromatic radiation with a spectrum inversely proportional to the photon energy), with positive ions (Roberto et al, 1975), or with electrons and protons (Le Guen et al, 2019). There are also exotic realizations of angle-resolved XRF where both the incident and emission angles are shallow.…”

Kossel interferences of proton-induced X-ray emission lines to study thin film waveguides

“…The ionization source can be energetic electrons [5][6][7], X-ray photons [8,9], charged particles including protons or ions [10,11]. Kossel diffraction associated to X-rays is related to the grazing exit X-ray fluorescence (GEXRF) technique [2,12].…”

“…In our previous works [12,20,21], we develop a methodology, that is particle-induced X-ray emission (PIXE) combined with Kossel diffraction, to study the structure of nano-scale Cr/Sc and Pd/Y periodic multilayers. PIXE analysis possesses a good sensitivity to measure the radiations emitted by electron state changes and distinguishes the elements of the sample in a wide range of atomic numbers, without destruction of the sample [11,22].…”

“…In Ref. [12,20,21], the generated X-ray emission is recorded in Kossel geometry to obtain the so-called Kossel curve, which is the intensity of characteristic X-ray emission as a function of the detection angle. Kossel curves are convenient to study the interfacial environment in multilayers made of a periodic alternation of nanometer-thick films.…”