Analysis of X-ray reflectivity curves of non-Gaussian surfaces

Abstract

Surfaces of symmetric diblock copolymers thin films exhibiting non-Gaussian distribution of height are studied by X-ray reflectivity and atomic force microscopy (AFM). When deposited on a silicon substrate, the surface is essentially flat and its roughness may be described by a Gaussian distribution of height. Upon annealing, films operate a two-dimensional phase transformation and form islands at the free surface having height and size that evolve as a function of annealing time. The height probability function cannot be represented by a Gaussian distribution anymore, and the question that arises is how to take into account the morphology of such surfaces in the reflectivity calculations. In a first approach, we show that the height distribution function derived from AFM measurements is directly transferable to analyze X-ray reflectivity curves according to a formalism that we present. In a second part, we determine the height distribution function from a fit to the observed reflectivity.