Accuracy in x-ray reflectivity analysis

Abstract

The influence of Poisson noise on the accuracy of x-ray reflectivity analysis is studied with an aluminium oxide (AlO) layer on silicon. A null hypothesis which argues that other than the exact solution gives the best fitness is examined with a statistical p-value test using a significance level of α = 0.01. Simulations are performed for a fit instead of a measurement since the exact error caused by noise cannot be determined from the measurement. The p-value is studied by comparing trial curves to 1000 'measurements', each of them including synthetic Poisson noise. Confidence limits for the parameters of Parratt's formalism and the Nevot–Croce approximation are determined in (mass density, surface roughness), (thickness, surface roughness) and (thickness, mass density) planes. The most significant result is that the thickness determination accuracy of AlO is approximately ±0.09 nm but the accuracy is better for materials having higher mass density. It is also shown that the accuracy of mass density determination can be significantly improved using a suitably designed fitness measure. Although the power of the presented method is demonstrated only in one case, it can be used in any parameter region for a plethora of single layer systems to find the lower limit of the error made in x-ray reflectivity analysis.