Extension of the one-dimensional Stoney algorithm to a two-dimensional case

• Autorzy: Gniazdowski Zenon

Identyfikatory

DOI

10.26348/znwwsi.20.41

• Języki publikacji: EN

Abstrakty

EN

This article presents the extension of the one-dimensional Stoney algorithm to a two-dimensional case. The proposed extension consists in modifying the method of curvature estimation. The surface profile of the wafer before deposition of the thin film and after its deposition was locally approximated by the quadric. From this quadric, a quadratic form and the first degree surface were separated. An eigenproblem was solved for the matrix of this quadratic form. From eigenvectors a new coordinate system was created in which a new formula of the quadric was found. In this new coordinate system, the two-dimensional problem of estimating thecurvaturetensorhasbeensolvedbysolvingtwoindependentone-dimensional problems of curvature estimation. Returning to the primary coordinate system, in this primary system, a solution to the two-dimensional problem was obtained. The article proposes five versions of the two-dimensional Stoney algorithm, with diverse complexity and accuracy. The recommendation for the version of the algorithm that could be practically used was also presented.

Słowa kluczowe

EN

Stoney formula; Stoney equation; 2D Stoney algorithm; tensor of curvature; stress in a thin film; anisotropy; quadric; quadratic form

• Wydawca: Warszawska Wyższa Szkoła Informatyki
• Czasopismo: Zeszyty Naukowe Warszawskiej Wyższej Szkoły Informatyki
• Rocznik: 2019
• Tom: nr 20
• Strony: 41--66
• Opis fizyczny: Bibliogr. 9 poz., tab., wykr.

Twórcy

autor

Gniazdowski Zenon

• Warsaw School of Computer Science

Bibliografia

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• [5] J. F. Nye, Physical properties of crystals. Oxford: Clarendon Press, 1957.
• [6] B. Groshong, G. Bilbro,and W. Snyder, “Fittinga Quadratic Surface toThree Dimensional Data,” Center for Communications and Signal Processing, Electrical and Computer Engineering Department North Carolina State University, Tech. Rep., 1989, Access: July 12, 2019. [Online]. Available: https://repository.lib.ncsu.edu/bitstream/handle/1840.4/ 1311/CCSP 1989 17.pdf
• [7] I. N. Bronsztejn, K. A. Siemiendiajew, G. Musiol, and H. Mühlig, Modern compendium of mathematics. Warszawa: PWN, 2004.
• [8] K. Manczak, Metody identyfikacji wielowymiarowych obiektów sterowania. Warszawa: WNT, 1971.
• [9] Z. Gniazdowski, “New interpretation of principal components analysis,” Zeszyty Naukowe WWSI, vol. 11, no. 16, pp. 43-65, 2017.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).