ABSTRACT
As we saw in the last chapter, fitting the intensity of the specular x-ray scatter to a model layer structure enables the x-ray metrologist to measure the interface widths, in simple cases to better than 0.5 nm precision. However, the effects on the specular scatter of a compositionally graded interface and a topologically rough interface are identical. There is no information in the specular scatter about the structure in the plane of the surface or interface. If we model the variations for the averaged electron density across both these types of interface as error functions, we can add in quadrature the root mean squared (rms) roughness
σ
and the grading width
Σ
to give the total interface width
σ
. Explicitly this is
(9.1)
The compositionally graded interface remains parallel to the surface and everywhere perpendicular to the scattering vector. All changes in the specular scatter due to the composition variation therefore must arise from coherent effects. On the contrary, the topologically rough interface is locally oriented in different directions and the reduction in specular scatter arises through diffuse scatter out of the specular direction. Measurement of this diffuse scatter and its variation in angular space provides a powerful method, complementary to scanning probe techniques, for the measurement of surface roughness and a unique method for the measurement of topological roughness of buried interfaces. By combination of specular and diffuse scatter measurement, we can distinguish between the three parameters in Equation 9.1, as the specular scatter measures
σ
and the diffuse scatter arises only from
σ
.
