Prediction of the Diffraction Order Dependence of the Integral Reflection Coefficient of Multilayer Structures using Atomic Force Microscope Measurements

Abstract

The evaluation and understanding of the x-ray diffraction properties of multilayer structures is critical in predicting the degree of success in their utilization in x-ray optics applications. A key material parameter affecting the diffracting efficiency of multilayer structures is the roughness of the interfaces between the deposited layers. This paper will use measured roughness to predict the integral reflection coefficient as a function of diffraction order for several multilayer structures.

We have made atomic force microscope (AFM) measurements of the detailed displacement distribution for me surface roughness of W/C and W/Si multilayer structures. This information has been introduced into a theoretical model to predict the reduction of the integral reflection coefficient induced by surface roughness. In a fashion analogous to the Debye-Waller factor, this reduction in diffracted intensity is predicted to be strongly dependent on the diffraction order. These predictions have been compared with experimental integral reflection coefficient data. The measured diffraction results indicate a greater reduction in reflection than is predicted by the AFM measurements. A possible explanation for this discrepancy is that the AFM measurements underestimate the roughness. Possible reasons for the differences between these methods will be discussed.