Phase sensitive reflectometry and the unambiguous determination of scattering length density profiles

Abstract

Exact methods for determining the complex neutron reflection amplitude for a thin film, which make use of multiple measurements of the specularly reflected intensities of composite systems, composed of the film adjacent to a reference layer and/or surrounding media, have been developed over the past several years. These techniques are valid even where the Born or distorted wave Born approximations break down. Thus, given both the modulus and phase of the specular reflection, a first-principles inversion can be performed which yields the scattering length density (SLD) depth profile of the film directly. Ideally, if the reflection amplitude is known for all wave vector transfers Q, the associated SLD profile is unique. Applying the aforementioned methods to a purely real SLD profile, which, effectively, is almost always that encountered in neutron reflection, at least two distinct reflectivity curves, corresponding to two different composite film systems, are required to determine the phase by direct algebraic computation, independently at each value of Q. Each of the composite systems consists of the common unknown part of the film plus a different reference layer segment and/or surrounding medium (e.g., the backing). Recently, investigations of certain classes of SLD profiles have been reported in the literature which examine whether a single X-ray reflectivity curve, given certain a priori knowledge about the system, i.e., about known parts of the film SLD and/or substrate, suffices to reconstruct the phase. Employing the exact formulation of phase sensitive reflectometry, we consider several illustrative and realistic cases in which a minimum of two reflectivity curves are required to distinguish the true SLD profile.