Simulation of oxygen precipitation in Czochralski grown silicon

Schrems, M.; Brabec, Thomas; Budil, M.; Pötzl, H.; Guerrero, E.; Huber, D.; Pongratz, P.

doi:10.1016/0921-5107(89)90277-8

Cited by 16 publications

(12 citation statements)

References 10 publications

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“…More explicit models consider the concentrations of each species (cluster size) using a sequence of coupled Master and FokkerPlanck equations [14,[21][22][23]. Sinno and Brown [24] addressed the fully coupled problem of point defect recombination and aggregation with diffusive transport in a one-dimensional quasisteady state simulation.…”

Section: Experimental and Theoretical Characterization Of Void Formatmentioning

confidence: 99%

A microscopically accurate continuum model for void formation during semiconductor silicon processing

Frewen

Kapur

Haeckl

et al. 2005

Journal of Crystal Growth

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Section: Experimental and Theoretical Characterization Of Void Formatmentioning

confidence: 99%

A microscopically accurate continuum model for void formation during semiconductor silicon processing

Frewen

Kapur

Haeckl

et al. 2005

Journal of Crystal Growth

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“…As discussed in Paper 1, many previous efforts [1,2,3,29,31,32] aimed at predicting the distribution of vacancy (and self-interstitial) aggregates during the growth and processing of Si crystals and wafers have neglected the effect of cluster diffusion. Figure 14 demonstrates the effect on the nucleation rate if this mechanism is omitted.…”

Section: B Cluster Diffusionmentioning

confidence: 99%

Internally consistent approach for modeling solid-state aggregation. II. Mean-field representation of atomistic processes

Prasad

Sinno

2003

Phys. Rev. B

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A detailed continuum (mean-field) model is presented that captures quantitatively the evolution of a vacancy cluster size distribution in crystalline silicon simulated directly by large-scale parallel molecular dynamics. The continuum model is parameterized entirely using the results of atomistic simulations based on the same empirical potential used to perform the atomistic aggregation simulation, leading to an internally consistent comparison across the two scales. It is found that an excellent representation of all measured components of the cluster size distribution can be obtained with consistent parameters only if the assumed physical mechanisms are captured correctly. In particular, the inclusion of vacancy cluster diffusion and a model to capture the dynamic nature of cluster morphology at high temperature are necessary to reproduce the results of the large-scale atomistic simulation. Dynamic clusters with large capture volumes at high temperature, which are the result of rapid cluster shape fluctuations, are shown to be larger than would be expected from static analyses, leading to substantial enhancement of the nucleation rate. Based on these results, it is shown that a parametrically consistent atomistic-continuum comparison can be used as a sensitive framework for formulating accurate continuum models of complex phenomena such as defect aggregation in solids. ABSTRACT A detailed continuum (mean-field) model is presented that captures quantitatively the evolution of a vacancy cluster size distribution in crystalline silicon simulated directly by large-scale parallel molecular dynamics. The continuum model is parameterized entirely using the results of atomistic simulations based on the same empirical potential used to perform the atomistic aggregation simulation, leading to an internally consistent comparison across the two scales. It is found that an excellent representation of all measured components of the cluster size distribution can be obtained with consistent parameters only if the assumed physical mechanisms are captured correctly. In particular, the inclusion of vacancy cluster diffusion and a model to capture the dynamic nature of cluster morphology at high temperature are necessary to reproduce the results of the large-scale atomistic simulation. Dynamic clusters with large capture volumes at high temperature, which are the result of rapid cluster shape fluctuations, are shown to be larger than would be expected from static analyses, leading to substantial enhancement of the nucleation rate. Based on these results, it is shown that a parametrically consistent atomistic-continuum comparison can be used as a sensitive framework for formulating accurate continuum models of complex phenomena such as defect aggregation in solids.

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“…Кроме того, в рамках этой модели нельзя описывать процесс образования зародышей и собственно преципитации, при этом модель описывает только рост преципитатов, но не учитывают процесс растворения. Перечисленные недостатки можно преодолеть, если использовать уравнение Фоккера-Планка [68][69][70][71][72] (см. также [67,73]).…”

Section: современные представления об эволюции микродефектов в кремнииunclassified

Kinetics of Formation and Growth of Microdefects in Crystals

2006

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Simulation of oxygen precipitation in Czochralski grown silicon

Cited by 16 publications

References 10 publications

A microscopically accurate continuum model for void formation during semiconductor silicon processing

A microscopically accurate continuum model for void formation during semiconductor silicon processing

Internally consistent approach for modeling solid-state aggregation. II. Mean-field representation of atomistic processes

Kinetics of Formation and Growth of Microdefects in Crystals

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