Mean-field theory of nucleation and growth on strained surfaces

Grima, Ramon; Degraffenreid, James; Venables, J. A.

doi:10.1103/physrevb.76.233405

Cited by 8 publications

(8 citation statements)

References 16 publications

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“…[19][20][21] Moreover, the activation energies for the surface diffusion have been theoretically shown to strongly depend on the local strain field experienced by the diffusing atoms on the substrate surface along their diffusion pathway. [41][42][43][44][45] We show here that a first-order expansion of the activation energy E A = E A 0 + E A 1 ͑ − 0 ͒ as a function of the C coverage, ͑defined as the ratio between the thickness of the carbon layer as determined by the discrete layer model and the thickness of one monolayer in the C diamond crystalline structure͒, is enough to reproduce the gross features of the experimental dependence. The coverage threshold 0 = 0.16Ϯ 0.06 ML comes from the tendency of carbon to intermix with Si into the shallow layers of the substrate rather than stay at the surface.…”

Section: B Continuous Surface Diffusion On a C Covered Si(100) Surfacementioning

confidence: 91%

Quantitative investigation of the influence of carbon surfactant on Ge surface diffusion and island nucleation on Si(100)

et al. 2010

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We investigated the surface diffusion and island nucleation of Ge on Si(100) in presence of a submonolayer coverage of carbon as surfactant by using scanning Auger microscopy and atomic force microscopy. Ge stripes have been deposited and lithographically etched on a Si substrate and used as sources for the surface diffusion of Ge promoted by annealing at 600, 650, and 700 °C. The diffusion coefficient has been determined by fitting the postannealing coverage profiles measured by Auger microscopy with a one-dimensional continuous model. The carbon coverage has been spatially modulated on a single sample, allowing the measurement of the diffusion coefficient as a function of the C thickness at 600 °C. We show that the reduction in the diffusion coefficient while increasing the surfactant coverage is described by a linear dependence of the diffusion activation energy on the C coverage. This dependence is discussed in terms of the chemical interactions among Si, C, and Ge, of the surface roughness and the local strain field induced by the C surfactant. Spontaneous nucleation of SiGe islands coexists with the continuous surface diffusion of Ge. The transition of the island nucleation as a function of the carbon coverage is observed to be continuous from the Stranski-Krastanov mode to the Volmer-Weber regime. We propose a consistent scenario correlating diffusion and nucleation parameters within a diffusion limited growth regime and show the existence of a threshold for C coverage below which no effect is observed

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Section: B Continuous Surface Diffusion On a C Covered Si(100) Surfacementioning

confidence: 91%

Quantitative investigation of the influence of carbon surfactant on Ge surface diffusion and island nucleation on Si(100)

et al. 2010

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“…Moreover, this estimate does not account for the adatom repulsion from islands which favor smaller and denser islands because adatoms drift away from islands due to the elastic chemical potential gradient. 19 In the irreversible case, the island density was found to increase with elasticity because the adatom repulsion effect is alone at stake. 17,18 We note also here that the reversible study of the 2D/3D transition of Ref.…”

Section: ͑4͒mentioning

confidence: 99%

“…One may first expect that the weak long-range elastic repulsions favor adatoms to drift away from other adatoms 17,18 and existing islands. 19 They should also favor atom detachment from islands. 20 Most studies of these effects focused on the irreversible growth, 17,18,21 but little is known about the statistical properties of submonolayer strained islands during reversible growth.…”

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confidence: 99%

Elastic interactions and kinetics during reversible submonolayer growth: Monte Carlo simulations

Aqua

Frisch

2008

Phys. Rev. B

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The reversible submonolayer heteroepitaxial growth is studied by means of kinetic Monte Carlo simulations of a simple model with short-and long-range interactions. The Green function of a film on a deformable substrate allows a fast computation of elastic energy barriers and the investigation of the islands statistical properties as functions of strain and the diffusion to deposition flux ratio. We find an unexpected decrease of the island density due to elastic interactions which can be understood as a decrease of the effective adatom binding energy coupled to kinetic effects. The island size distribution satisfies the usual scaling and does not significantly depend on elasticity.Aggregation phenomena are ubiquitous in physics, chemistry, or biology. A paradigm arising in surface science deals with island formation during molecular beam epitaxy, which involves adatom deposition and diffusion, island nucleation, growth, and coalescence. In heteroepitaxial systems, elasticity is an extra crucial effect which can lead to a transition between two-͑2D͒ and three-͑3D͒ dimensional islands and quantum dot formation. 1 The progress in experimental techniques for surface scanning, together with application for electronic devices fabrication has shed some new light on this field. 2-4 The understanding of the density, mean size, and size dispersion of submonolayer strained islands is then of significant importance as they are templates for the subsequent surface evolution. Moreover, beyond aggregation mechanisms, the submonolayer regime may be used to measure adatom diffusion coefficients otherwise hard to measure. 5,6 To tackle this far-from-equilibrium many-body problem, different approaches are available without elasticity in the irreversible case where adatoms never detach from islands. 7,8 Scaling analysis 9,10 first predict that the number N s of islands with s atoms is merelygiven by the scaling function f and the only characteristic island size ͗s͘. They depend solely on the ratio of the adatom diffusion constant D to the deposition flux F, and ͗s͘ = ⌰ z ͑D / F͒ , where ⌰ is the deposited coverage ⌰ = Ft, and z and -two scaling exponents. More detailed information are then found from rate equations which treat the system in a mean-field way 11-14 and compare favorably with kinetic Monte Carlo ͑KMC͒ simulations. However, even if the irreversible hypothesis is well suited for metallic materials at low temperatures, it fails for semiconductors or at high temperatures when E N , the atom binding energy to islands, is no longer large compared to the thermal energy k B T. A simple solid-on-solid ͑SOS͒ model accounting for reversible aggregation 15 reveals that the system depends both on D / F and E N , and exhibits a different regime where the island density saturates before coalescence occurs. In another de-scription, islands with more than the critical nucleus i atoms do not loose matter and are characterized by both i and D / F ͑see Ref. 13 and 16͒. For strained systems with a misfit between the film and substrate, the...

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“…Elastic interaction between islands 46 was recently shown to correct islands sizes and size distribution. In irreversible growth, the long-range repulsive elastic interactions subsequently favor adatoms to drift away from other adatoms 47,48 and existing islands 49 . In addition, SiGe quantum dots involve more complex phenomena with the presence of a wetting layer 50 , reversible aggregation, shape transition and anomalous coarsening 33 .…”

Section: Introductionmentioning

confidence: 99%