Non-Gaussian Roughness of Interfaces: Cumulant Expansion in X-ray and Neutron Reflectivity

Within the Born approximation, a cumulant expansion is used for the formulation of X-ray or neutron reflectivity. Odd- (third-) order cumulants indicate asymmetric profiles; they may only be detected in layer systems via a Q_z dependence of the oscillation period of Kiessig fringes. Fourth-order cumulants are also visible in the larger Q_z regime for single interface systems. As an example of an asymmetric surface, a triangular height distribution function is discussed.