Ab initio study of surface stress response to charging

Umeno, Yoshitaka; Elsässer, Christian; Meyer, Bernd; Gumbsch, Peter; Nothacker, M.; Weißmüller, J.; Evers, Ferdinand

doi:10.1209/0295-5075/78/13001

Cited by 82 publications

(109 citation statements)

References 31 publications

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“…25 The electrocapillary coupling coefficient near the pzc is of interest because it may be discussed relative to computations of the same parameter by ab initio density functional theory. 41,42 The data of Fig. 5(a), when taken at face value, suggest distinctly different values of the coupling parameter at the pzc depending on the roughness.…”

Section: B Electrocapillary Coupling Coefficientmentioning

confidence: 94%

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Electrocapillary coupling at rough surfaces

Deng

Gosslar

Smetanin

et al. 2015

Phys. Chem. Chem. Phys.

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We investigate the impact of the surface roughness on the experimental value of the electrocapillary coupling coefficient, B. This quantity relates the response of electrode potential, E, to tangential elastic strain, e, and also measures the variation of the surface stress, f, with the superficial charge density, q. We combine experiments measuring the apparent coupling coefficient B eff for gold thin film electrodes in weakly adsorbing electrolyte with data for the surface roughness determined by atomic force microscopy and by the capacitance ratio method. We find that even moderate roughness has a strong impact on the value of B eff . Analyzing the mechanics of corrugated surfaces affords a correction scheme yielding values of B that are invariant with roughness and that agree with expectations for the true coupling coefficient on ideal, planar surfaces. The correction is simple and readily applied to experiments measuring B eff from surface stress changes in cantilever bending studies or from the potential variation in dynamic electrochemo-mechanical analysis.

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Section: B Electrocapillary Coupling Coefficientmentioning

confidence: 94%

“…The corrected coefficient value ofB in this study is yielded as À1.92 AE 0.04 V near the pzc, which is supported by the computation value of À1.86 V on Au(111) single crystal surface by the density functional theory calculation. 41 …”

Section: B Electrocapillary Coupling Coefficientmentioning

confidence: 99%

Electrocapillary coupling at rough surfaces

Deng

Gosslar

Smetanin

et al. 2015

Phys. Chem. Chem. Phys.

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“…The corresponding value of the local charge density is orders of magnitude larger than the values in the space-charge layers of semiconductor devices, such as field-effect transistors. Ab initio computation shows that the large local space-charge density at the metal-electrolyte interface will significantly affect the bonding between the metal atoms, [43][44][45] and mechanical equilibrium requires stress in the bulk for compensating the modified bond forces. [37,46] In a continuum description, the parameter that quantifies the mechanical interaction of the matter at the surface of a solid with the underlying bulk is the surface stress, s, the derivative of the surface tension with respect to the tangential strain.…”

Section: Description Of Actuation In a Continuum Picturementioning

confidence: 99%

Bulk Nanoporous Metal for Actuation

Jin¹,

Weißmüller²

2010

Adv Eng Mater

118

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Nanoporous metals prepared by controlled chemical or electrochemical corrosion of alloys can provide prototypical manifestations of bulk nanostructured material. Samples are readily prepared with dimensions at the millimeter or centimeter scale, while at the same time the microstructure is a homogeneous array of interpenetrating solid skeleton phase and pore channels with a characteristic size that can reach down to below 5 nm. The interest in nanoporous metals as functional materials derives from recent observations of unique materials behavior resulting from their extremely small structure size and their open porosity with large volume‐specific surface area. As an example, this article discusses the possible use of nanoporous metal for actuation.

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“…This value of the real component is consistent in both sign and magnitude with reported experimental stress-charge coefficient values for capacitive charging of Au 34,45,46 and Pt 35,47,48 in the double layer region, as well as from first principles electronicstructure calculations. 49,50 We now examine the stress-charge coefficient for Cu deposition, ς f . The time derivative of the stress-thickness response for Cu deposition can be expressed as…”

Section: 44mentioning

confidence: 99%

Dynamic Stress Analysis Applied to the Electrodeposition of Copper

Lafouresse

Bertocci

Stafford

2014

J. Electrochem. Soc.

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Stress development during the electrodeposition of copper from additive-free, acidic CuSO 4 electrolyte was analyzed by dynamic stress analysis, an in situ characterization technique that combines electrochemical impedance spectroscopy with cantilever curvature. Two sources of stress account for the dynamic stress behavior in the frequency range of 0.1 Hz to 25 Hz. The high frequency region is controlled by electrocapillarity (charge-induced stress). The stress is 180 • out of phase with the input potential, and its amplitude is relatively small. Low frequency is dominated by the growth stress of the Cu film, which under the conditions examined here is tensile. The amplitude of the stress response increases with decreasing frequency and its phase angle shifts from +180 • to +90 • . Both of these transitions are potential dependent and can be simulated from the electrochemical impedance, making use of separate stress-charge coefficients for double layer charging and Cu deposition. Since these stress-generating mechanisms have dramatically different frequency dependency, Cu deposition is a nice demonstration that highlights the attributes of DSA; i.e., using frequency to separate the various stress contributions. Electrodeposition is commonly used in electronic packaging, magnetic recording, copper interconnections in printed circuit boards and integrated circuits, and MEMS (micro-electromechanical systems) devices. These films tend to develop sizable residual stresses as a result of the nucleation and growth process that can adversely affect reliability and service life. Various mechanisms have been proposed to account for the stress evolution that has been observed experimentally in both electrodeposited films and those grown from the gas phase. These stress-generating processes sometimes occur sequentially as the film morphology develops. More often, stress development is a balance between competing mechanisms.Multiple studies appear in the literature that address stress evolution during Volmer-Weber or 3D island growth of polycrystalline films.1-4 Generally, films show three stages of stress evolution during growth. Compressive stress is often observed in the pre-coalescence regime where the deposit is comprised of discrete nuclei on the surface. This compressive stress has been attributed to Laplace pressure at the surface, 5,6 surface stress, 7 and the presence of adatoms and surface defects.8 When these nuclei coalesce into a continuous film, tensile stress rapidly develops. Several quantitative models have been suggested for the tensile stress generation during coalescence, but the basic premise of these models is the same.9-17 The surface energy of the islands is larger than the free energy of a grain boundary; therefore, the system energy can be reduced if the individual nuclei coalesce into a continuous film. The reduction of surface energy is balanced by an increase of elastic strain energy which gives rise to tensile stress in the film. As the coalesced film thickens, the stress reaches a steadystate ...

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Ab initio study of surface stress response to charging

Cited by 82 publications

References 31 publications

Electrocapillary coupling at rough surfaces

Electrocapillary coupling at rough surfaces

Bulk Nanoporous Metal for Actuation

Dynamic Stress Analysis Applied to the Electrodeposition of Copper

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