Thermal Adatoms on Si(001)

Tromp, R. M.; Mankos, M.

doi:10.1103/physrevlett.81.1050

Cited by 78 publications

(37 citation statements)

References 23 publications

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“…Dimers have also been shown to be mobile on the surface at the substrate temperatures in this experiment, 13 and a dimer diffusion energy has been determined. 14 This discrepancy between the experimental system and the classical model does not disqualify the model from use.…”

Section: Resultsmentioning

confidence: 98%

“…Experiments indicate that the supersaturation of the ad-dimer density is small. 13 Once islands nucleate, the ad-dimer density decreases because the chemical potential of the islands is lower than that of the wetting layer. Our results indicate that the ad-dimer density is supersaturated with respect to the 3D islands (the islands are growing), but not with respect to the wetting layer.…”

Section: Resultsmentioning

confidence: 99%

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Mechanisms determining three-dimensional SiGe lsland density on Si(001)

Sullivan

Evans

Savage

et al. 1999

Journal of Elec Materi

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Thin, coherently strained, films of SiGe were deposited on Si(001) in the Stranski-Krastanow (SK) growth mode to form small, faceted, dislocation-freethree-dimensional (3D) islands. The number density of these islands was determined as functions of SiGe alloy composition, growth rate, and substrate temperature during growth. From these experiments, the classical model of 3D island nucleation and growth yields an approximate activation energy for diffusion of Ge dimers on a Ge covered Si(001) surface of 0.70 eV. The dependence of the 3D-island number density on growth rate cannot be understood without modifying the classical model to account for the wetting layer present in SK systems. Heteroepitaxial strain is not included in the classical model of island nucleation and growth. A simple linear elastic model that fits the data is developed that predicts the island number density is proportional to the inverse square of the Ge mole fraction in the alloy plus a constant.

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Section: Resultsmentioning

confidence: 98%

Section: Resultsmentioning

confidence: 99%

Mechanisms determining three-dimensional SiGe lsland density on Si(001)

Sullivan

Evans

Savage

et al. 1999

Journal of Elec Materi

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“…Most of the sublimation energy, L = 4.63±0.04 eV/atom, is gained by formation of surface dimers, and very little extra energy remains to be gained when these dimers are incorporated into the growing crystal. These ad-dimers have low formation energy, E f2 , measured for Si/Si (001) as 0.35±0.05 eV [3,11]. These energies show that, although the Si and Ge(001) growth systems may be close to 2D equilibrium, they are very far from equilibrium with their (3D) vapor at normal growth temperatures, 450-650 0 C. This has encouraged a 'classical' W2.1.5 treatment of nucleation and growth in terms of edge energies for 2D nuclei; critical nucleus sizes up to i = 650 have been deduced in some cases; this approach has been reviewed recently [12].…”

Section: Comparison Of Ge/si(001) With Cu/cu(111)mentioning

confidence: 99%

Time-Dependent Capture Numbers with Repulsive Pair Interactions: Cu/Cu(111) and Ge/Si(001)

2002

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Recent experiments and calculations have shown that weak repulsive interactions between adsorbate atoms may shift nucleation kinetics from the well-known diffusion limit towards the attachment-limited case. The distinctions between diffusion-and attachment-limited kinetics are clarified, and the increased importance of the transient nucleation regime in the latter case is shown to be due to a combination of delayed nucleation and reduced capture. A time-dependent interpolation scheme between attachment-and diffusion-limited capture numbers is proposed, and tested against KMC simulations. Using this scheme to interpret recent STM results on Cu/Cu(111), bounds on the maximum adatom-adatom potential repulsive energy of 12±2 meV are deduced. Time-dependent effects also occur in the growth and ripening of strained Ge islands on Si(001), and the similarities and differences between these two systems are discussed. RATE EQUATIONS CONTAINING SELF-CONSISTENT CAPTURE NUMBERSRate equations have been used successfully to analyze data, notably of the nucleation density n x , as a function of experimental variables, usually the flux F (or equivalently deposition rate R) and the substrate temperature T [1-3]. The reaction rates in each equation, e.g. for the single adatom density n 1 , are of the form 2σ 1 D 1 n 1 2 (for the rate of adatoms forming pairs) or σ x D 1 n 1 n x (for the rate of adatoms joining stable clusters). In these terms σ 1 and σ x are capture numbers, and D 1 is the single-adatom diffusion coefficient. This paper discusses the determination of capture numbers, when there may be barriers for attachment of adatoms to other adatoms and to clusters. The full mathematical and computational details are given in a companion paper [4].Although the distinction between diffusion-limited and attachment-limited kinetics is generally well known, there have not been many explorations of such issues in connection with epitaxial crystal growth. But several recent Scanning Tunneling Microscopy (STM) experiments at low temperatures on smooth metal surfaces [5,6] and associated ab-initio calculations [7,8] have highlighted attachment-limited behavior, due to the presence of repulsive barriers between adatoms. In particular, we show that capture numbers exhibit these two limits, and indicate how the two limits can be combined to give generally applicable, including time-dependent, forms.Repulsive barriers modify the results of conventional (sometimes called classical) nucleation theory (CNT), by extending the transient nucleation regime to higher dose. New formulae are given for the capture numbers on the assumption of radial symmetry, and the expressions are tested against kinetic Monte Carlo (KMC) simulations. As a result, the maximum repulsive interaction energies can be reliably extracted from recent experiments on close-packed metal surfaces; here we concentrate on Cu/Cu(111). The methods may also be applied to other systems in future, and we compare our results qualitatively with Ge/Si(001).

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“…where A is (a␤ͱ /k B T) 2 , a 2 ϭ0.29 nm 2 is the squared lattice spacing for a diffusing adparticle, assumed here to be a dimer, 6,7,17,19 N is the number of dimers in a critical nucleus, ⌫ is the step mobility, which is related to the step attachment rate by 18 ϭ⌫/(a 4 c eq ), and ␤ is the step-free energy. Figure 11 shows how the total island number ⍀(t) varies with the deposition time for r D ϭ10 3/2 .…”

Section: Continuum Model Of the Formation Of Denuded Zonesmentioning

confidence: 99%

“…[7][8][9]13,17 We then solve the time-dependent diffusion equation to model how the adparticle concentration c(x,y,t) increases with time and then estimate the time-integrated island density (x,y,t) across the terrace using an expression for the island nucleation rate proposed by Theis and Tromp. 9 The solution is obtained up to the time n when the area-integrated total number of islands ⍀(t) is equal to the measured number of islands for that growth condition.…”

Section: Continuum Model Of the Formation Of Denuded Zonesmentioning

confidence: 99%

Simulations of denuded-zone formation during growth on surfaces with anisotropic diffusion

et al. 2003

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We have investigated the formation of denuded zones during epitaxial growth on surfaces exhibiting anisotropic diffusion of adparticles, such as Si(001)-2ϫ1, using Monte Carlo simulations and a continuum model. In both the simulations, which were mainly for low-temperature cases ͑small critical clusters͒, and the continuum model, appropriate for high-temperature cases ͑large critical clusters͒, it was found that the ratio of denuded-zone widths W f and W s in the fast-and slow-diffusion directions scales with the ratio D f /D s of the diffusion constants in the two directions with a power of 1/2, i.e., W f /W s Ϸ(D f /D s ) 1/2 , independent of various conditions including the degree of diffusion anisotropy. This supplies the foundation of a method for extracting the diffusion anisotropy from the denuded zone anisotropy which is experimentally measurable. Further, we find that unequal probabilities of a diffusing particle sticking to different types of step edges ͓e.g., S A and S B steps on Si͑001͔͒ does not affect the relation W f /W s Ϸ(D f /D s ) 1/2 seriously unless the smaller of the two sticking probabilities is less than about 0.1. Finally, we examined the relation between the number of steps and the number of sites visited in anisotropic random walks, finding it is better described by a crossover from one-dimensional to two-dimensional behavior than by scaling behavior with a single exponent. This result has bearing on scaling arguments relating denuded-zone widths to diffusion constants for anisotropic diffusion.

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Thermal Adatoms on Si(001)

Cited by 78 publications

References 23 publications

Mechanisms determining three-dimensional SiGe lsland density on Si(001)

Mechanisms determining three-dimensional SiGe lsland density on Si(001)

Time-Dependent Capture Numbers with Repulsive Pair Interactions: Cu/Cu(111) and Ge/Si(001)

Simulations of denuded-zone formation during growth on surfaces with anisotropic diffusion

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