Detection of nano scale thin films with polarized neutron reflectometry at the presence of smooth and rough interfaces

By knowing the phase and modules of the reflection coefficient in neutron reflectometry problems, a unique result for the scattering length density (SLD) of a thin film can be determined which will lead to the exact determination of type and thickness of the film. In the past decade, several methods have been worked out to resolve the phase problem such as dwell time method, reference layer method and variation of surroundings, among which the reference method and variation of surroundings by using a magnetic substrate and polarized neutrons is of the most applicability. All of these methods are based on the solution of Schrodinger equation for a discontinuous and step-like potential at each interface. As in a real sample there is some smearing and roughness at the boundaries, and consideration of smoothness and roughness of interfaces would affect the final output result. In this paper, we have investigated the effects of the smoothness of interfaces on the determination of the phase of reflection as well as the retrieval process of the SLD, by using a smooth varying function (Eckart potential). The effects of the roughness of interfaces on the same parameters have also been investigated by random variation of the interface around its mean position.