Accuracy in x-ray reflectivity analysis

Jouni Tiilikainen, Juha-Matti Tilli, Vesa Bosund, Marco Mattila, Teppo Hakkarainen, Jaakko Sormunen, Harri Lipsanen

    Research output: Contribution to journalArticleScientificpeer-review

    6 Citations (Scopus)

    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.
    Original languageEnglish
    Pages (from-to)7497-7501
    Number of pages5
    JournalJournal of Physics D: Applied Physics
    Volume40
    Issue number23
    DOIs
    Publication statusPublished - 16 Nov 2007
    MoE publication typeA1 Journal article-refereed

    Keywords

    • atomic layer deposition
    • confidence limits
    • curve fitting
    • x-ray relectivity

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