Step Height Oscillations during Layer-by-Layer Growth of Pb on Ge(001)

Crottini, A.; Cvetko, D.; Floreano, Luca; Gotter, R.; Morgante, A.; Tommasini, F.

doi:10.1103/physrevlett.79.1527

Cited by 61 publications

(51 citation statements)

References 20 publications

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“…The helium atom scattering [13][14][15] and scanning tunneling microscopy 12 data have shown extremely large relaxations up to −30% for ⌬͑d 12 ͒ and +15% for ⌬͑d 23 ͒ around the bulk equilibrium spacing.…”

Section: Discussionmentioning

confidence: 99%

Surface relaxations in quantum-confined Pb

et al. 2005

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The relationship between electronic and atomic structure of quantum confined objects is a key issue in nanoscience. We performed low-energy electron diffraction to determine the surface relaxations of ultrathin Pb films on Si͑111͒7 ϫ 7 with thicknesses ranging from four to nine atomic layers. The results indicate a contraction of the first interlayer spacing d 12 for all films. The d 12 contraction exhibits a small bilayer modulation as a function of thickness, indicative of a quantum size effect. The oscillatory relaxations furthermore suggest an interesting correlation with the work function oscillations predicted from density functional theory ͓Wei and Chou, Phys. Rev. B 66, 233408 ͑2002͔͒ and can be understood qualitatively on the basis of the jellium model.

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Section: Discussionmentioning

confidence: 99%

Surface relaxations in quantum-confined Pb

et al. 2005

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Section: -6mentioning

confidence: 99%

“…The observed oscillations of film thickness and interlayer spacing had the same QSE period. 3,6,[15][16][17] So far the calculated and observed QSE periods can be simply understood from a nesting vector of the bulk band structure along the direction perpendicular to the film, which projects to the center of the film Brillouin zone ͑FBZ͒.In this Brief Report we show from a density-functional theory ͑DFT͒ study of thin Pb͑100͒ films that the symmetry of the stacking geometry of a thin film can have a profound influence on the QSE through QW states at the FBZ boundary. In particular, the film energy, relaxations, and work functions exhibit a bilayer periodicity that cannot be understood in terms of nesting vectors of the Fermi surface along the ⌫X direction in the bulk BZ.…”

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confidence: 99%

Quantum size effect in Pb(100) films: Role of symmetry and implications for film growth

Scheffler

Persson

2006

Phys. Rev. B

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We show from density-functional calculations that Pb͑100͒ thin films exhibit quantum size effect with a bilayer periodicity in film energies, film relaxations, and work functions, which originate from different symmetry of the stacking geometry of odd and even layer films. This symmetry-driven quantum size effect on the film energy could allow for growth of "magically" thick even-layer Pb͑100͒ films on an appropriate substrate. Furthermore, it is found that the quantum well states in a simple metal film can be classified into -bonded and -bonded states, which quantize independently. The so-called "electronic growth" model of metallic thin film on a semiconductor substrate has attracted much scientific and technological interest. 1 This model provides conditions for the growth of atomically flat thin films or nanostructures, which are of significant technological interest. The underlying physical mechanism behind "electronic growth" is the quantum size effect ͑QSE͒ on the film energy introduced by quantum well ͑QW͒ states in the film. In addition to the film energy, the energy gain associated by the charge transfer occurring at the film semiconductor interface needs also to be considered to determine the film stability. The total energy of the system may then result in "critical" thicknesses in which the film is stable when the number of atomic layers is above or below a critical number and "magical" film thicknesses in which the film has a pronounced stability for a certain number of atomic layers. The "electronic growth" model has been very successful in understanding observed "critical" thicknesses of alkali metal and noble metal overlayers grown on a GaAs surface, 1 and the observed "magical" thicknesses of Pb͑111͒ films or islands on various substrates. 2-6The nature of observed QW states and the associated QSE in metal film have so far been well-understood from simple models based on bulk band structure and Fermi surface nesting. [7][8][9][10] In general, QW states are formed by the quantization of the valence electrons confined in the perpendicular direction of the thin film, as described by the phase accumulation model. The energies of the QW states are then obtained from the energies of the valence bulk bands at the quantized wave vectors. This simple model has been widely used in analysis of photoemission measurements of QW states. [8][9][10] The QSE on the film energy and other physical properties arises from the consecutive occupation of QW states with increasing film thickness. An enhanced density of states at the Fermi surface by QW states is then obtained from extremal spanning ͑nesting͒ vectors q of the Fermi surface that are perpendicular to the film, resulting in a QSE period QSE =2 / q for the film energy. For a free-electron model of the bulk bands, corresponding to a spherical Fermi surface, q =2k F where k F is the Fermi wave vector and QSE = / k F . This simple model for QSE has been supported by firstprinciples, electronic structure calculations for various systems. Schulte 11 found that t...

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“…[5][6][7][8][9][10][11] The QSE also favors magic film thicknesses, corresponding to the electron energy minima at F / 2 intervals. [6][7][8]12,13 This drives metal thin films with unfavored thicknesses to stabilize by relaxing the interlayer spacing. However, if the resulting increase in strain energy cannot be compensated by the gain in electron energy, metal films with such thicknesses are unstable and do not form.…”

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confidence: 99%

“…[1][2][3][4] Perhaps, the best illustrated example of the QSE are Pb films on Si͑111͒, where various properties, such as the surface energy, the superconducting transition temperature, the interlayer spacing, and the film stability, oscillate with the film thickness. [5][6][7][8][9][10][11] The QSE also favors magic film thicknesses, corresponding to the electron energy minima at F / 2 intervals. [6][7][8]12,13 This drives metal thin films with unfavored thicknesses to stabilize by relaxing the interlayer spacing.…”

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confidence: 99%

Quantum size effect induced dilute atomic layers in ultrathin Al films

Jiang

Tang

et al. 2007

Phys. Rev. B

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We illustrate using scanning tunneling microscopy and low energy electron diffraction that thin Al films grown on Si͑111͒-ͱ 3 ϫ ͱ 3-Al substrates form layers having unusual thicknesses, not compatible with a normal fcc stacking of dense Al͑111͒-1 ϫ 1 layers ͑coverageϽ wetting layer+ 7 Å͒. This structure is shown to be based on inserted dilute 1.5ϫ 1.5 atomic layers. At a film thickness of the wetting layer+ 7 Å, the film undergoes a phase transformation and continues to grow in the normal stacking of Al͑111͒-1 ϫ 1 layers. The phenomenon is explained within the theory of the quantum size effects in a jellium metal combined with strain effects. We argue that the insertion of dilute atomic layers for small film thicknesses allows the Al film to reach thicknesses perfectly well adjusted to the minima of the oscillating electron energy, which arises from the spatial confinement of the free electrons in the thin film. In contrast, at larger thicknesses, where the electron energy differences diminish, a strain-driven phase transformation drives the system back to the classical close-packed Al͑111͒-1 ϫ 1 fcc stacking. The isotropic property of the metallic bonding drives metal ions to get as close as possible in order to maximize the overlap of the wave functions and to minimize the energy. Therefore, most metals form close-packed crystalline structures with high coordination numbers. Depending on the shape and extension of the wave functions involved, metals crystallize preferentially in the close-packed face-centered cubic or hexagonal structures or in the nearly close-packed body-centered cubic structure. In the conventional understanding, deviations from this principle should only occur if the bonds between the metal atoms become directional, i.e., exhibit covalent contributions. Here, we demonstrate, however, that a pure single element metal can also form a stack of dilute and dense close-packed atomic layers and thus deviate from the closed-packed principle in dimensionally reduced structures. The driving force is not a directional component of the metallic bond but rather a reduction of the electron energy governed by quantum size effects. Once the gain of electron energy vanishes with increasing film thickness, the whole system undergoes, however, a strain-driven phase transformation from alternating dilute and dense atomic layers to only close-packed layers.Quantum mechanics and thus also quantum size effects ͑QSEs͒ become relevant for spatially confined structures, such as thin metal films, whose thickness is comparable to the Fermi wavelength F . 1-4 Perhaps, the best illustrated example of the QSE are Pb films on Si͑111͒, where various properties, such as the surface energy, the superconducting transition temperature, the interlayer spacing, and the film stability, oscillate with the film thickness. [5][6][7][8][9][10][11] The QSE also favors magic film thicknesses, corresponding to the electron energy minima at F / 2 intervals. [6][7][8]12,13 This drives metal thin films with unfavored thicknesses to stabil...

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Step Height Oscillations during Layer-by-Layer Growth of Pb on Ge(001)

Cited by 61 publications

References 20 publications

Surface relaxations in quantum-confined Pb

Surface relaxations in quantum-confined Pb

Quantum size effect in Pb(100) films: Role of symmetry and implications for film growth

Quantum size effect induced dilute atomic layers in ultrathin Al films

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