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Quantitative analysis of anisotropic edge retraction by solid-state dewetting of thin single crystal films
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Image of FIG. 1.
FIG. 1.

Retraction of macroscopic edges via capillarity-driven surface self-diffusion. There is a flux of material flux from the high curvature edge to the flat surface, resulting in motion of the triple line. The decrease of the local curvature ahead of the retracting edge leads to accumulation of material and formation of a thickening rim.

Image of FIG. 2.
FIG. 2.

Macroscopic edges in Ni(100) films after retracting during a 3-h anneal at 890 °C under a reducing gas flow rate of 2310 sccm. In (a), the original edge was straight and was aligned at a 35° rotation away from the in-plane [001] orientation. In this case the edge breaks up into kinetically stable in-plane facets. The edge aligned along the [001] direction in (b) is kinetically stable. The in-plane facets in (a) lie along [001] and [110] orientations, both of which are kinetically stable during retraction. Scale bars are 10 μm long.

Image of FIG. 3.
FIG. 3.

Retraction rates of kinetically stable edges for Ni(100) and Ni(110) films. The samples were annealed at 890 °C under a 2310 sccm reducing gas (5% H2 95% N2) flow. The exponents for power law fits are also given. Appropriate equilibrium Winterbottom shapes were obtained using Wulffmaker, a program for equilibrium shape generation. 40

Image of FIG. 4.
FIG. 4.

SEM images of the cross-sections of retracting edges in (a) and (b) Ni (100) films, and (c) and (d) Ni(110) films after a 21-h anneal. Retraction directions and facet planes are indicated. The imaging was carried out at an angle between the electron beam and the cross section of 52°. These images have been modified to reflect viewing from a direction normal to the cross section and the plane of the film. Equilibrium facets found in the Wulff shape of Ni appear, but some nonequilibrium facets also appear during retraction.

Image of FIG. 5.
FIG. 5.

Evolution of rim height and width. Rim heights are defined as the distance between the highest point of the retracting rim and the undewetted flat film, and rim widths are defined as the distance between the retracting edge front and the point ahead of the rim where the thickness equals that of the undewetted flat film. As in the case of edge retraction distances, the data can be well fit through variations in the input diffusivities within the range of error with which they have been determined.

Image of FIG. 6.
FIG. 6.

(a) Example of a free-standing 2-dimensional structure originally dealt by Carter et al. 22 (b) Wulff-Herring construction 27 for a two-dimensional solid and (c) Winterbottom construction for a two-dimensional solid with 4-fold symmetry, after Winterbottom 26 γPV refers to the particle (film)-vapor interfacial energy, γPS the substrate-particle interfacial energy, and γSV the substrate-vapor interfacial energy. In the direction normal to the particle-substrate interface, the magnitude of the energy is equal to the adhesion energy of the interface. The envelope of lines drawn normal to all orientation vectors whose magnitude is the interfacial energy in each orientation is the equilibrium shape of the particle. (d) Example of a thin-film structure used in the model.

Image of FIG. 7.
FIG. 7.

2D simulation of the morphological evolution of retracting edges in a cross-section of a Ni(100) strip, with edge retraction in the [011] in-plane direction. The strip is initially 40 μm wide and 130 nm thick. The retracting edges locally thicken and merge in the later stage to form an island/line with the 2D equilibrium Winterbottom shape.

Image of FIG. 8.
FIG. 8.

Experimental results and the model fitted through adjustment of diffusivities within the ranges of the experimental error of their determination. D(111) was decreased by 74%, D(100) was decreased by 46%, D(110)[001] was decreased by 19%, and D(110)[ ] was increased by 89%.

Image of FIG. 9.
FIG. 9.

AFM scans of retracting edges after a 21-h anneal. All edges retract from the left to the right. (a) Edge retracting in the [010] direction in a Ni(100) film. (b) Edge retracting in the [011] direction in a Ni(100) film. No deepening valleys behind the retracting edges were observed for Ni(100) films. (c) Edge retracting in the [ ] direction in a Ni(110) film. (d) Edge retracting in the [001] direction in a Ni(110) film. Ni(110) films develop valleys for both edges.


Generic image for table
Table I.

Surface self-diffusivities of Ni, D, for different facets, 30,31 where . The diffusivity is isotropic in the (100) and (111) facets.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Quantitative analysis of anisotropic edge retraction by solid-state dewetting of thin single crystal films