Reflections Function Method In the X-Ray Reflectometry

TL;DR

This paper introduces a reflection function method (RFM) for analyzing specular X-ray reflectivity from rough interfaces, transforming the wave equation into a Riccati equation and providing a series solution that improves interface characterization.

Contribution

The paper develops a novel RFM approach that simplifies the wave equation to a Riccati form and includes phase corrections, enhancing interface asymmetry analysis in X-ray reflectometry.

Findings

The RFM reproduces the Nevot-Croce approximation.

The second term provides phase correction for larger angles.

Application to Fe/Cr superlattice demonstrates the method.

Abstract

The theory of specular X-ray reflectivity from a rough interface based upon the reflection function method (RFM) is proposed. The RFM transforms the second order differential equation for the wave amplitude into the non-linear first order differential equation of Riccati type for the reflection function. This equation is solved in the approximation of the abruptly changing potential, which is justified for the typical angles of X-ray reflectometry. The reflectivity is represented as a series. The first term of this series reproduces the Nevot-Croce approximation and second one gives the phase correction for greater angles. It is shown that the phase correction can be used to obtain the degree of interface asymmetry. The X-ray reflectometry model profiles for Fe/Cr superlattice are used to illustrate the method.