X-ray phase determination in multilayers

Abstract

A procedure is described for the determination of the phases of waves scattered by a multilayer structure using interference between surface reflections and structure diffraction. The applicability of the method to Langmuir-Blodgett and metallic sputtered multilayers is discussed.

Polyimide multilayer thin films prepared via spin coating from poly(amic acid) and poly(amic acid) ammonium salt

“…A broad oscillation was observed after 0.3 o in each XRR curve of the multilayer thin films, which is considered to be a Kiessig fringe. [16][17][18][19] The film thickness can be obtained from the Kiessig fringe using the reflectance angle θ as a unit of measure. The ΔQ z value was derived from the equation, Q z (Å -1 )=4π sin θ/λ, where λ (1.541 Å) is the wavelength of Cu-K α radiation used in the XRR experiment.…”

Localized destructive interference in X-ray specular reflectivity

“…The advantage of the kinematical equation is its transparency: the ®rst term is a background due to the Fresnel surface re¯ectivity, the second term corresponds to a Laue factor due to the whole stack with main maxima at 9 = n% (n is an integer), and the third term is an interference between the ®rst two contributions. The in¯uence of this term has already been discussed with respect to its use in structure and phase determination in multilayers (Rieutord et al, 1987(Rieutord et al, , 1989. The lth order peaks of the Laue condition (superlattice Bragg peak) are obtained for`(9) = l%, and the re¯ectivity is simply written as² The term r 0 /r 1 N must be larger than 1 to have a negative interference effect at the superlattice Bragg peak.…”

Fitting of x-ray or neutron specular reflectivity of multilayers by Fourier analysis

“…If the reflectivity is low enough, the relation between the reflectance and the scattering density becomes a mere Fourier transform in the BA, 1,[13][14][15] R͑q ͒ϭ 4b…”

“…Since d/dz is zero outside the layers, i.e., in the substrate and in the vacuum, it is possible to apply the box refinement technique to get the phases of the scattered waves and, in turn, to get the scattering density profile. [13][14][15][16] This technique assumes a scattering density profile for the sample under examination and makes a Fourier transform of its derivative d/dz ͑i.e., the trial function͒ to get the phases for each point of the reflectivity curve. These phases are combined with the modulus ͉R͉ of the reflectance of the multilayer and are then Fourier transformed to give a d/dz.…”

“…12 Existing methods based on BA have the advantage that they model the interface in a realistic way and are less difficult to apply. [12][13][14][15][16][17] It has been pointed out that the number of possible phase solutions is limited when the spatial extent of the structure is known. 16 The box refinement technique needs fewer constraints to obtain a physically realistic scattering density profile than the leastsquares-fitting method does.…”