Theoretical analysis of texture effects on the surface morphological stability of metallic thin films

Tomar, V S; Gungor, M. Rauf; Maroudas, Dimitrios

doi:10.1063/1.2912037

Cited by 19 publications

(12 citation statements)

References 14 publications

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“…Otherwise one may have extreme instabilities induced by the electromigration forces on the surface morphology rather than healing effects. This healing phenomenon has been first reported very recently by Tomar et al 25,26 who also produced very interesting linear instability analysis, in conjunction with the dynamical simulation studies, which reveals improved surface morphological stability over a range of misorientation angles between the electric field and easy direction of surface drift diffusion. This healing effect of electromigration on the grain boundary grooving was first noticed by Averbuch et al 31 as slowing down in the displacement kinetics in their rather early terminated numerical experiments.…”

Section: Introductionmentioning

confidence: 75%

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The orientation dependent electromigration induced healing on the surface cracks and roughness caused by the uniaxial compressive stresses in single crystal metallic thin films

Oǧurtani

2009

Journal of Applied Physics

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The first order unified linear instability analysis (ULISA) of the governing equation for evolutions of surfaces and interfaces under the capillary, electromigration, and elastostatic forces including the thermomigration (Soret effect) is developed very recently by the author. In the present application of the theory, the concurrent effects of uniaxial applied stresses and the electrostatic field on the sidewall morphological evolution of a single crystal thin metallic film are explored by dynamic computer simulations by taking the surface drift diffusion anisotropy fully into account. These computer experiments, which are supported by ULISA, clearly show that only the applied elastic compressive stresses are primary agents responsible for the morphological instability of the surface undulations through the elastic dipole tensor interactions but not the uniaxial tension loading in thin solid films. It is also demonstrated that these morphological instabilities manifested themselves as formations of the surface cracks and thus one may fully control the roughness. To do that, one needs to select crystal orientations properly with respect to the applied field so that a counteraction of the applied electrostatic fields (healing effect) is created above well defined threshold levels of electromigration. On the contrary to the healing effects, the improper selection of crystal orientations may drastically enhance the instability and eventually may cause catastrophic interconnect failure. At large normalized surface undulation amplitudes (a¯≥0.20), the drastic reductions in the decay rate constants (i.e., the strain relaxation rate) are detected in the nonlinear uniaxial tension regime compared to the ULISA theory regardless of the intensity of the normalized stress by analyzing the data obtained from the computer simulations. This situation is contrary to the results deduced from the low to moderate normalized amplitude (a¯≤0.10) measurements, where one finds that the decay rate constant closely obeys the prediction of the ULISA theory even for very high stress intensities.

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Section: Introductionmentioning

confidence: 75%

“…In their very recent paper, Tomar et al 26 presented a very elegant instability analysis by defining a new parameter ͓k 4 − k 3 ͔ : ͉⌶ ͉, which measures the instability bandwidth of the wave number. This parameter should be the explicit functions of ͓m , ͔ for a given set of input and system parameters.…”

Section: Physical and Mathematical Modelingmentioning

confidence: 99%

The orientation dependent electromigration induced healing on the surface cracks and roughness caused by the uniaxial compressive stresses in single crystal metallic thin films

Oǧurtani

2009

Journal of Applied Physics

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“…For instance, the action of electric fields has been shown to have significant effects on the surface morphological stability of solids, including the current-induced stabilization of stressed solid surfaces. 9,10 In this letter we aim to illuminate the dynamic shape evolution process of conductive nanostructures under electric field.…”

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confidence: 99%

Control morphology of nanostructures with electric field

Park

Lü

2009

Applied Physics Letters

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We showed that the morphology of nanostructures on a dielectric substrate may be tuned by electric field. The collective action of surface energy, interface energy between nanostructures and the substrate, and electrostatic energy defines a thermodynamic force that drives surface diffusion. The evolution is characterized by a quick adjustment of the dihedral angle at the triple junction, followed by an extrusion of a thin layer from the edges, and subsequent significant overall morphology change through long range mass transport. A high voltage can induce instability of the extrusion, causing the formation of a pattern of tiny islands.The ability of designing and constructing useful devices with engineered properties and features at the nanometer length scale promises to have a dramatic impact on the future. Controlled surface morphology of nanostructure is critical for the applications. Electric field is an excellent driving force to control structures on length scales difficult to manipulate in other manner. It is easy to apply and the electrostatic interactions are strong and long range. Electric field has been used to move, separate and assemble micro/nanoparticles, 1,2 trap nanospheres, 3 and align nanowires. 4 It has also been used on continuum fluidic media to change the morphology such as inducing surface features in polymer melts. 5 Recent studies showed that the wetting angles of liquid droplets on a dielectric substrate can be tuned by an applied electric field. This electrowetting approach has become a promising mechanism for many applications, such as next generation optical systems with camera lens of variable focal lengths achieved by applying designed electric fields. 6 While these systems have demonstrated morphological changes of continuum liquids, we expect electric field can also be used to control the morphology of solids like stress field. 7,8 The effect may be negligible in larger scale bodies, but is important in nanostructures due to high mobility and small dimension comparable to the diffusion length. For instance, the action of electric fields has been shown to have significant effects on the surface morphological stability of solids, including the current-induced stabilization of stressed solid surfaces. 9,10 In this letter we aim to illuminate the dynamic shape evolution process of conductive nanostructures under electric field.Several features distinguish the morphological evolution of solid nanostructures from the typical electrowetting phenomenon. The latter involves putting a liquid droplet on the surface of a thin dielectric substrate with a conductive plate beneath it. Electric field is applied to the conductive droplet and the substrate. Equilibrium configuration is of major interest in electrowetting process due to the fluidic media and kinetics of viscous flow. However, the evolution process through surface diffusion and various transitional morphologies are important in solid structures. The droplet size for electrowetting applications ranges from a few millimeters to hundre...

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“…orientation. [6][7][8][9] For ⌶ = 0, i.e., for finite stress ϱ in the absence of electric field, ͑k͒ is positive for all k Ͻ k c , i.e., the planar surface is unstable for all perturbations with wavelength ˜Ͼ ˜c ϵ 2 / k c ; ˜ϵ / l. For a given parameter set, A, m, and , R͑⌶͒ decreases as ⌶ increases from 0 to ⌶ c , i.e., as E ϱ is increased from zero to some critical value. For ⌶ Ͼ⌶ c , R vanishes, i.e., ͑k͒ Ͻ 0 for all k; therefore, a stronger-than-critical E ϱ stabilizes fully the morphological response of a stressed solid at given ϱ .…”

mentioning

confidence: 99%

“…8 We consider a semi-infinite, single crystalline, conducting solid bounded by a planar surface ͑y =0͒ under a uniform uniaxial stress and an electric field of magnitudes ϱ and E ϱ , respectively, both along the x-direction in a Cartesian frame of reference. 6,7 We parameterize the surface morphology according to the height function y = h͑x , t͒. An important element of our model is the anisotropy of surface diffusivity through the inhomogeneity …”

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confidence: 99%

Rippling instability on surfaces of stressed crystalline conductors

Tomar

Gungor

Maroudas

2009

Applied Physics Letters

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We report a surface morphological stability analysis for stressed, conducting crystalline solids without and with the simultaneous application of an electric field based on self-consistent dynamical simulations according to a fully nonlinear model. The analysis reveals that in addition to a cracklike surface instability, a very-long-wavelength instability may be triggered that leads to the formation of secondary ripples on the surface morphology. We demonstrate that the number of ripples formed scales linearly with the wavelength of the initial perturbation from the planar surface morphology and that a sufficiently strong electric field inhibits both the cracklike and the rippling instability.

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Theoretical analysis of texture effects on the surface morphological stability of metallic thin films

Cited by 19 publications

References 14 publications

The orientation dependent electromigration induced healing on the surface cracks and roughness caused by the uniaxial compressive stresses in single crystal metallic thin films

The orientation dependent electromigration induced healing on the surface cracks and roughness caused by the uniaxial compressive stresses in single crystal metallic thin films

Control morphology of nanostructures with electric field

Rippling instability on surfaces of stressed crystalline conductors

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