Interplay of quantum size effect, anisotropy and surface stress shapes the instability of thin metal films

Khenner, Mikhail

doi:10.1007/s10665-016-9874-6

Cited by 3 publications

(14 citation statements)

References 35 publications

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“…We choose g 1 by requiring that when cos ω 1 h cos ω 2 h = 1, all heights larger than (the wetting layer thickness of Pb and Ag films) are linearly unstable. This gives [24]. Thus as far as the surface linear stability is concerned, the g 1 term with g 1 ≤ g 1c does not differentiate between various heights.…”

Section: Model Of the Morphological Evolution Of Pb And Ag Quantumentioning

confidence: 99%

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Morphologies, metastability, and coarsening of quantum nanoislands on the surfaces of the annealed Ag(110) and Pb(111) thin films

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Henner

Khenner

2018

Journal of Applied Physics

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Morphological evolution of heteroepitaxial nanoislands toward equilibrium (coarsening) is computed using the detailed continuum model that incorporates the quantum size effect. Results reveal the metastability of the "magic" heights, show the morphological transitions and the surface diffusion routes by which a quantum island reaches its stable height, and provide the coarsening laws for the island density and area, thus clarifying the kinetic morphology pathways in the growth of an ultrathin metal films.

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Section: Model Of the Morphological Evolution Of Pb And Ag Quantumentioning

confidence: 99%

“…Thus α = 1.95 × 10 −8 cm/8.9 × 10 −7 cm= 0.022 1 and, as in Refs. [23,24,38,41,42], we expand the adimensionalized form of Eq. (1) in α and then retain the dominant contributions.…”

Section: Appendixmentioning

confidence: 99%

Morphologies, metastability, and coarsening of quantum nanoislands on the surfaces of the annealed Ag(110) and Pb(111) thin films

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Henner

Khenner

2018

Journal of Applied Physics

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“…Also we provide the summary of key results of the linear stability analysis (LSA) for the trivial equilibrium (the planar film surface); for more details, see Ref. [13].…”

Section: The Model For Surface Morphology Evolutionmentioning

confidence: 99%

“…Following the seminal paper by Hamilton & Wolfer [41], in Ref. [13] we derived the closed-form analytical expression for the surface stress energy. The dimensionless form of this expression is…”

Section: The Model For Surface Morphology Evolutionmentioning

confidence: 99%

“…In order to enable the studies of the morphology evolution of a metal film surface without the above-mentioned constraints, the author recently introduced a new model [13] that may be seen as partially complementary to Ref. [9,10] The new model is a specification to material systems with strong QSE of the classical surface diffusion model that was very successfully used to study the morphology evolution in a semiconductor-on-semiconductor systems [14][15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

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Height transitions, shape evolution and coarsening of equilibrating quantum nanoislands

Khenner¹

2017

Modelling Simul. Mater. Sci. Eng.

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Morphology evolution and coarsening of metal nanoislands is computed within the framework of a surface diffusion-type model that includes the effects of the electron energy confinement within the film, the charge spillage at the film/substrate interface, the energy anisotropy of the film surface and the surface stress. The conditions that result in large islands with flat tops, steep edges, and strongly preferred heights are determined. A strong influence of the film height on the coarsening dynamics and final morphologies is found; the conditions leading to interrupted coarsening are highlighted. The dependence of the geometric parameters of the equilibrium island on the film height and on the island initial volume is computed.

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Even–Odd Layer Oscillatory Behavior of Electronic and Phononic Specific Heat in an Ultra-Thin Metal Film

Chong,

Shen

2024

Materials

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Both electronic and phononic statistical and thermal properties, modulated by the quantum size effect, are suggested in a thin metal film. In order to show the quantum size effect of specific heat, the densities of the electron and phonon states of an ultra-thin film are treated within the framework of quantum statistics. It was found that strong and weak “even–odd layer oscillatory behavior” was exhibited by the ultra-thin metal film in electronic and lattice specific heat, respectively. Such a behavior, which depends on film thickness, results from the quantum confinement of electrons and phonons in the vertical (thickness) direction of the film, where both electrons and phonons form their respective quantum well standing wave modes. If, for example, the thickness of the ultra-thin metal film is exactly an integer multiple of a half wavelength of the standing wave of electrons in the thickness direction, the corresponding density of states would become maximized, and the electronic specific heat would take its maximum. In the literature, less attention has been paid to the size-dependent electron Fermi wavelength for quantum size effects, i.e., the Fermi wavelength in ultra-thin metal films has always been identified as a constant. We shall show how the Fermi wavelength varies with the size of a nanofilm, including an explicit analytic formulation for the thickness dependence of the electron Fermi wavelength. Size-dependent resonantly oscillatory behavior, depending on the ultra-thin or nanoscale film thickness, would have possible significance for researching some fundamental physical characteristics (e.g., low-dimensional quantum statistics) and may find potential applications in new thermodynamic device design.

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Interplay of quantum size effect, anisotropy and surface stress shapes the instability of thin metal films

Cited by 3 publications

References 35 publications

Morphologies, metastability, and coarsening of quantum nanoislands on the surfaces of the annealed Ag(110) and Pb(111) thin films

Morphologies, metastability, and coarsening of quantum nanoislands on the surfaces of the annealed Ag(110) and Pb(111) thin films

Height transitions, shape evolution and coarsening of equilibrating quantum nanoislands

Even–Odd Layer Oscillatory Behavior of Electronic and Phononic Specific Heat in an Ultra-Thin Metal Film

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