WAVELET ANALYSIS OF SURFACE MORPHOLOGIES OF MAGNETRON SPUTTERED Al-Cu THIN FILMS

A theory for multiresolution signal decomposition: the wavelet representation

Abstract: Multiresolution representations are effective for analyzing the information content of images. The properties of the operator which approximates a signal at a given resolution were studied. It is shown that the difference of information between the approximation of a signal at the resolutions 2/sup j+1/ and 2/sup j/ (where j is an integer) can be extracted by decomposing this signal on a wavelet orthonormal basis of L/sup 2/(R/sup n/), the vector space of measurable, square-integrable n-dimensional functions. In L/sup 2/(R), a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi (x). This decomposition defines an orthogonal multiresolution representation called a wavelet representation. It is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters. Wavelet representation lies between the spatial and Fourier domains. For images, the wavelet representation differentiates several spatial orientations. The application of this representation to data compression in image coding, texture discrimination and fractal analysis is discussed. >

Orthonormal bases of compactly supported wavelets

Abstract: We construct orthonormal bases of compactly supported wavelets, with arbitrarily high regularity. The order of regularity increases linearly with the support width. We start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction. The construction then follows from a synthesis of these different approaches.

Analysis of grain-boundary structure in Al–Cu interconnects

Abstract: The role of crystallographic texture in electromigration resistance of interconnect lines is well documented. The presence of a strong (111) fiber texture results in a more reliable interconnect structure. It is also generally accepted that grain-boundary diffusion is the primary mechanism by which electromigration failures occur. It has been difficult to this point, however, to obtain statistically reliable information of grain-boundary structure in these materials as transmission electron microscopy investigations are limited by tedious specimen preparation and small, nonrepresentative, imaging regions. The present work focuses upon characterization of texture and grain-boundary structure of interconnect lines using orientation imaging microscopy, and particularly, upon the linewidth dependence of these measures. Conventionally processed Al–1%Cu lines were investigated to determine the affects of a postpatterning anneal on boundary structure as a function of linewidth. It was observed that texture tende...

Structure and Hardness of the Sputtered Al-Cu Thin Films System

Abstract: The phase diagram of magnetron sputter-deposited Al-Cu thin films is simpler than the equilibrium diagram. Above 86.17 at.%Cu, the films are single ?Cu phase. Below, the microstructure consists of a mixture of the solid solution ?Al phase and an intermetallic compound phase, the previous ?(Al2Cu) phase for the 1.8 to 45.99 at.%Cu films and an unexpected (Cu3Al) phase for 49.07 to 66.64 at.%Cu films. We note the appearance of a phase separation (?Al + ?Cu + Cu3 Al) in 66.64 at.%Cu films. The microhardness and the young modulus of the sputtered films increase regularly with Cu concentration reaching a maximum (H ? 8000 MPa and E ? 200 GPa). This phenomenon of strengthening of aluminium by means of copper is essentially due to a combination of solid solution effects and grain size refinement.

Multiselective pyramidal decomposition of images: Wavelets with adaptive angular selectivity

Abstract: Many techniques have been devised these last ten years to add an appropriate directionality concept in decompositions of images from the specific transformations of a small set of atomic functions. Let us mention, for instance, works on directional wavelets, steerable filters, dual-tree wavelet transform, curvelets, wave atoms, ridgelet packets, etc. In general, features that are best represented are straight lines or smooth curves as those de. ning contours of objects ( e. g. in curvelets processing) or oriented textures ( e. g. wave atoms, ridgelet packets). However, real images present also a set of details less oriented and more isotropic, like corners, spots, texture components, etc. This paper develops an adaptive representation for all these image elements, ranging from highly directional ones to fully isotropic ones. This new tool can indeed be tuned relatively to these image features by decomposing them into a Littlewood-Paley frame of directional wavelets with variable angular selectivity. Within such a decomposition, 2D wavelets inherit some particularities of the biorthogonal circular multiresolution framework in their angular behavior. Our method can therefore be seen as an angular multiselectivity analysis of images. Two applications of the proposed method are given at the end of the paper, namely, in the fields of image denoising and N-term nonlinear approximation.