Multilayer roughness evaluated by X-ray reflectivity

Abstract

A crystal diffraction theory has been developed and compared with experimental measurements in order to model the integrated reflectivity of multilayer structures. This study shows that the most important defect reducing the integrated reflectivities of the multilayer structures studied was correlated roughness (root mean square value about 7 A). The theory describes correlated roughness as a probability distribution of the substrate surface displacement. A computer simulation and an analytical solution have been used to calculate the reflectivity of multilayer structures. The calculations using a rectangular distribution of correlated displacement result in a good first-order approximation of the experimental data. A Gaussian probability distribution for the substrate surface displacement results in calculations inconsistent with the measured reflectivities, although such a distribution has been assumed in other studies. Although other defects were studied, only roughness could explain the experimental data.

Reflection of X-Rays from Repeated Multilayer Structures

“…Brown, called XTALR.COM exists, ref. [3], which in its preliminary stages finds f in just the manner described abovei.e. by using Henke's numbers when available, and computing them according to Cromer when not.…”

“…[5], [61, [7] ). Rather, what is done here is the development of a formalism and a computer program conveniently applicable to a problem of continuing interest at the Naval Research Laboratory [3].…”

Comparison of measured and calculated values for the diffraction line profiles and integral reflection coefficients for multiple diffraction orders of multilayer structures

“…It has been shown that this equal probability or sawtooth-like distribution is a reasonable approximation for the roughness for some cases. 3 In particular, this strategy is expected to give good results for higher order diffraction. Calculations were performed for various thicknesses of the intermediate layer.…”