Fourier Reconstruction of Density Profiles of Thin Films Using Anomalous X-Ray Reflectivity

Abstract

The use of X-ray and neutron reflectivity measurements to determine the density profile across and interface or across thin films has become increasingly popular over the last few years. However, in general convenient model-independent methods of inverting the reflectivity profiles to obtain the density profile have been missing. We present here one such approach using the method of anomalous reflectivity from the substrate and demonstrate its applicability in the case of an organic thin film.

Anomalous x-ray scattering study of the growth of inverted quantum hut structures in a Si-Ge superlattice emitting strong photoluminescence

“…In our study we have carried out measurements at the Ge K edge (11 103 eV) and away from it (11 043 eV) to determine shape, composition, and strain of Ge IQH structures embedded in a Si-Ge superlattice [19][20][21]. X-ray measurements were performed both at beamline [22] P08 of the synchrotron radiation source PETRA III, DESY, Germany and at the Indian beamline [23] BL-18B, Photon Factory, KEK, Japan.…”

“…2(a) at two energies around (800). At the Ge K edge, the contribution of the Ge atomic scattering factor in the diffracted x rays is much less [19][20][21] as compared to this contribution when the x-ray measurement is done away from the Ge K edge. The reduction in Ge scattering at the x-ray edge leads to the reduction in the intensity of the diffraction peak as can be seen in radial scans of Fig.…”

Ion distributions at charged aqueous surfaces: Synchrotron X-ray scattering studies

“…However, anomalous X-ray reflectivity technique, by collecting reflectivity data at different energies (at and away from the resonance of a specific ion), can yield the spatial distributions of the probed ion. This was successfully applied to extract the ion distribution from an organic thin film [45], a metal oxide thin film [46], and a charged LM surface [47]. Energy scans at fixed momentum transfer (dubbed resonant anomalous X-ray reflectivity in some literature) is a technique with an ability to yield specific ion distribution, as well as the dispersion corrections at the interface [48].…”

“…by a sum of error functions as follows: 45) where N is the number of discrete boxes between the air and the liquid subphase, …”

Optical Response Near the Soft X-Ray Absorption Edges and Structural Studies of Low Optical Contrast System Using Soft X-Ray Resonant Reflectivity

“…In the hard X-ray region, resonant X-ray scattering/reflectivity is utilized as tool in many different fields, for examples to study ion distribution at biomembranes [23], spectroscopic structures of ion adsorbed at oxide-water interfaces [24], chemical depth profile of passive oxide [25], magnetic material [26], and monolayaer of bromostearic acid at the air/water interface [27], charged aqueous surfaces/interfaces [28], metal oxides thin films [29]. Sanyal et al have proposed a model-independent method to obtain density profile by inverting reflectivity profile using anomalous XRR [30]. They have demonstrated this on organic thin films by tuning photon energies close to, and away from, absorption edge of substrate (germanium).…”