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

Apply

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

Journal Title: Zeszyty Naukowe Warszawskiej Wyższej Szkoły Informatyki - Year 2019, Vol 13, Issue 20

Abstract

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 the curvature tensor has been solved by solving two independent one-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.

Authors and Affiliations

Zenon Gniazdowski

Keywords

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

EP ID EP613781
DOI 10.26348/znwwsi.20.41
Views 97
Downloads 0