Accuracy in x-ray reflectivity analysis

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Accuracy in x-ray reflectivity analysis. / Tiilikainen, Jouni; Tilli, Juha-Matti; Bosund, Vesa; Mattila, Marco; Hakkarainen, Teppo; Sormunen, Jaakko; Lipsanen, Harri.

In: Journal of Physics D: Applied Physics, Vol. 40, No. 23, 16.11.2007, p. 7497-7501.

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Tiilikainen, Jouni ; Tilli, Juha-Matti ; Bosund, Vesa ; Mattila, Marco ; Hakkarainen, Teppo ; Sormunen, Jaakko ; Lipsanen, Harri. / Accuracy in x-ray reflectivity analysis. In: Journal of Physics D: Applied Physics. 2007 ; Vol. 40, No. 23. pp. 7497-7501.

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@article{407a202e21604d43bbd5ae74a2927300,
title = "Accuracy in x-ray reflectivity analysis",
abstract = "The influence of Poisson noise on the accuracy of x-ray reflectivity analysisis studied with an aluminium oxide (AlO) layer on silicon. A nullhypothesis which argues that other than the exact solution gives the bestfitness is examined with a statistical p-value test using a significance level ofα = 0.01. Simulations are performed for a fit instead of a measurementsince the exact error caused by noise cannot be determined from themeasurement. 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 theNevot–Croce approximation are determined in (mass density, surfaceroughness), (thickness, surface roughness) and (thickness, mass density)planes. The most significant result is that the thickness determinationaccuracy of AlO is approximately ±0.09 nm but the accuracy is better formaterials having higher mass density. It is also shown that the accuracy ofmass density determination can be significantly improved using a suitablydesigned fitness measure. Although the power of the presented method isdemonstrated only in one case, it can be used in any parameter region for aplethora of single layer systems to find the lower limit of the error made inx-ray reflectivity analysis.",
keywords = "atomic layer deposition, confidence limits, curve fitting, x-ray relectivity, atomic layer deposition, confidence limits, curve fitting, x-ray relectivity, atomic layer deposition, confidence limits, curve fitting, x-ray relectivity",
author = "Jouni Tiilikainen and Juha-Matti Tilli and Vesa Bosund and Marco Mattila and Teppo Hakkarainen and Jaakko Sormunen and Harri Lipsanen",
year = "2007",
month = "11",
day = "16",
doi = "10.1088/0022-3727/40/23/037",
language = "English",
volume = "40",
pages = "7497--7501",
journal = "Journal of Physics D - Applied Physics",
issn = "0022-3727",
number = "23",

}

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TY - JOUR

T1 - Accuracy in x-ray reflectivity analysis

AU - Tiilikainen, Jouni

AU - Tilli, Juha-Matti

AU - Bosund, Vesa

AU - Mattila, Marco

AU - Hakkarainen, Teppo

AU - Sormunen, Jaakko

AU - Lipsanen, Harri

PY - 2007/11/16

Y1 - 2007/11/16

N2 - The influence of Poisson noise on the accuracy of x-ray reflectivity analysisis studied with an aluminium oxide (AlO) layer on silicon. A nullhypothesis which argues that other than the exact solution gives the bestfitness is examined with a statistical p-value test using a significance level ofα = 0.01. Simulations are performed for a fit instead of a measurementsince the exact error caused by noise cannot be determined from themeasurement. 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 theNevot–Croce approximation are determined in (mass density, surfaceroughness), (thickness, surface roughness) and (thickness, mass density)planes. The most significant result is that the thickness determinationaccuracy of AlO is approximately ±0.09 nm but the accuracy is better formaterials having higher mass density. It is also shown that the accuracy ofmass density determination can be significantly improved using a suitablydesigned fitness measure. Although the power of the presented method isdemonstrated only in one case, it can be used in any parameter region for aplethora of single layer systems to find the lower limit of the error made inx-ray reflectivity analysis.

AB - The influence of Poisson noise on the accuracy of x-ray reflectivity analysisis studied with an aluminium oxide (AlO) layer on silicon. A nullhypothesis which argues that other than the exact solution gives the bestfitness is examined with a statistical p-value test using a significance level ofα = 0.01. Simulations are performed for a fit instead of a measurementsince the exact error caused by noise cannot be determined from themeasurement. 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 theNevot–Croce approximation are determined in (mass density, surfaceroughness), (thickness, surface roughness) and (thickness, mass density)planes. The most significant result is that the thickness determinationaccuracy of AlO is approximately ±0.09 nm but the accuracy is better formaterials having higher mass density. It is also shown that the accuracy ofmass density determination can be significantly improved using a suitablydesigned fitness measure. Although the power of the presented method isdemonstrated only in one case, it can be used in any parameter region for aplethora of single layer systems to find the lower limit of the error made inx-ray reflectivity analysis.

KW - atomic layer deposition

KW - confidence limits

KW - curve fitting

KW - x-ray relectivity

KW - atomic layer deposition

KW - confidence limits

KW - curve fitting

KW - x-ray relectivity

KW - atomic layer deposition

KW - confidence limits

KW - curve fitting

KW - x-ray relectivity

UR - http://dx.doi.org/doi:10.1088/0022-3727/40/23/037

U2 - 10.1088/0022-3727/40/23/037

DO - 10.1088/0022-3727/40/23/037

M3 - Article

VL - 40

SP - 7497

EP - 7501

JO - Journal of Physics D - Applied Physics

JF - Journal of Physics D - Applied Physics

SN - 0022-3727

IS - 23

ER -

ID: 3355310