Equilibrium shape of Si

Eaglesham, D. J.; White, Alice E.; Feldman, L. C.; Moriya, N.; Jacobson, D. C.

doi:10.1103/physrevlett.70.1643

Cited by 493 publications

(256 citation statements)

References 22 publications

Supporting

Mentioning

231

Contrasting

Unclassified

Order By: Relevance

“…This implies that these QDs are voids in the Si matrix that are only partially filled. This is consistent with the equilibrium shape of a void in Si, which has been shown to be the same tetrakaidecahedron 10 shape shown in Figs. 1͑b͒ and 2͑a͒.…”

supporting

confidence: 77%

Void-mediated formation of Sn quantum dots in a Si matrix

Lei

Möck

Topuria

et al. 2003

Applied Physics Letters

View full text Add to dashboard Cite

Atomic scale analysis of Sn quantum dots ͑QDs͒ formed during the molecular beam-epitaxy ͑MBE͒ growth of Sn x Si 1Ϫx (0.05рxр0.1) multilayers in a Si matrix revealed a void-mediated formation mechanism. Voids below the Si surface are induced by the lattice mismatch strain between Sn x Si 1Ϫx layers and Si, taking on their equilibrium tetrakaidecahedron shape. The diffusion of Sn atoms into these voids leads to an initial rapid coarsening of quantum dots during annealing. Since this formation process is not restricted to Sn, a method to grow QDs may be developed by controlling the formation of voids and the diffusion of materials into these voids during MBE growth.

show abstract

supporting

confidence: 77%

Void-mediated formation of Sn quantum dots in a Si matrix

Lei

Möck

Topuria

et al. 2003

Applied Physics Letters

View full text Add to dashboard Cite

show abstract

“…Voids have been observed directly by TEM to organize into octahedral structures aligned almost exclusively along the (111) crystallographic planes of the silicon lattice 25 . This phenomenon has been explained by the low energy of the Si (111) surface relative to other orientations 26 , and an important goal of this work is to make a detailed connection between the thermodynamics of small vacancy clusters and large octahedral voids.…”

Section: Vacancy Aggregation In Crystalline Siliconmentioning

confidence: 99%

Internally consistent approach for modeling solid-state aggregation. I. Atomistic calculations of vacancy clustering in silicon

Prasad

Sinno

2003

Phys. Rev. B

View full text Add to dashboard Cite

A computational framework is presented for describing the nucleation and growth of vacancy clusters in crystalline silicon. The overall approach is based on a parametrically consistent comparison between two representations of the process in order to provide a systematic method for probing the details of atomic mechanisms responsible for aggregation. In this paper, the atomistic component of the overall framework is presented. First, a detailed set of targeted atomistic simulations are described that characterize fully the thermodynamic and transport properties of vacancy clusters over a wide range of sizes. It is shown that cluster diffusion is surprisingly favorable because of the availability of multiple, almost degenerate, configurations. A single large-scale parallel molecular dynamics simulation is then used to compute directly the evolution of the vacancy cluster size distribution in a supersaturated system initially containing 1000 uniformly distributed vacancies in a host lattice of 216,000 Si atoms at 1600 K. The results of this simulation are interpreted in the context of mean-field scaling theory based on the observed power-law evolution of the size distribution moments. It is shown that the molecular dynamics results for aggregation of vacancy clusters, particularly the evolution of the average cluster size, can be very well represented by a highly simplified mean-field model. A direct comparison to a detailed continuum model is made in a subsequent article. ABSTRACT A computational framework is presented for describing the nucleation and growth of vacancy clusters in crystalline silicon. The overall approach is based on a parametrically consistent comparison between two representations of the process in order to provide a systematic method for probing the details of atomic mechanisms responsible for aggregation. In this paper, the atomistic component of the overall framework is presented. First, a detailed set of targeted atomistic simulations are described that characterize fully the thermodynamic and transport properties of vacancy clusters over a wide range of sizes. It is shown that cluster diffusion is surprisingly favorable because of the availability of multiple, almost degenerate, configurations. A single large-scale parallel molecular dynamics simulation is then used to compute directly the evolution of the vacancy cluster size distribution in a supersaturated system initially containing 1000 uniformly distributed vacancies in a host lattice of 216,000 Si atoms at 1600 K. The results of this simulation are interpreted in the context of mean-field scaling theory based on the observed power-law evolution of the size distribution moments. It is shown that the molecular dynamics results for aggregation of vacancy clusters, particularly the evolution of the average cluster size, can be very well represented by a highly simplified mean-field model. A direct comparison to a detailed continuum model is made in a subsequent article.

show abstract

“…As mentioned above, the equilibrium shape of a void in Si is a tetrakaidecahedron, Fig. 1b, [13]. The applications of Neumann's and Curie's symmetry principles [15] to the determination of the shape of small α-Sn and Sn y Si 1-y precipitates in a Si matrix shows that this can be a tetrakaidecahedron as well [10,16].…”

Section: Resultsmentioning

confidence: 99%

“…Finally, we would like to remark that the equilibrium shape of a void in Si has been determined experimentally [13] to be a tetrakaidecahedron, Fig. 1b.…”

Section: Introductionmentioning

confidence: 99%

Endotaxial Growth Mechanisms of Sn Quantum Dots in Si Matrix

et al. 2003

View full text Add to dashboard Cite

Two distinct mechanisms for the endotaxial growth of quantum dots in the Sn/Si system were observed by means of analytical transmission electron microcopy. Both mechanisms operate simultaneously during temperature and growth rate modulated molecular beam epitaxy combined with ex situ thermal treatments. One of the mechanisms involves the creation of voids in Si, which are subsequently filled by Sn, resulting in quantum dots that consist of pure α-Sn. The other mechanism involves phase separation and leads to substitutional solid solution quantum dots with a higher Sn content than the predecessor quantum well structures possess. In both cases, the resultant quantum dots possess the diamond structure and the shape of a tetrakaidecahedron. (Sn,Si) precipitates that are several times larger than the typical (Sn,Si) quantum dot possess an essentially octahedral shape.

show abstract

Equilibrium shape of Si

Cited by 493 publications

References 22 publications

Void-mediated formation of Sn quantum dots in a Si matrix

Void-mediated formation of Sn quantum dots in a Si matrix

Internally consistent approach for modeling solid-state aggregation. I. Atomistic calculations of vacancy clustering in silicon

Endotaxial Growth Mechanisms of Sn Quantum Dots in Si Matrix

Contact Info

Product

Resources

About