Vacancy-type microdefect formation in Czochralski silicon

Voronkov, V. V.; Falster, R.

doi:10.1016/s0022-0248(98)00550-8

Cited by 204 publications

(161 citation statements)

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“…with the experimentally observed range of 1320-1370 K during crystal growth 48 . The appearance of larger clusters that would be detectable experimentally would occur at slightly lower temperatures, typically only a few degrees because aggregation is very rapid 49 .…”

Section: ∑ ∑mentioning

confidence: 99%

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

Prasad

Sinno

2003

Phys. Rev. B

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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.

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Section: ∑ ∑mentioning

confidence: 99%

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

Prasad

Sinno

2003

Phys. Rev. B

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“…The standard approach to suppress void formation is by hot zone design in order to obtain the critical value of the ratio of the pulling rate over the thermal gradient predicted by the Voronkov theory [1], leading to an intrinsic point defect lean crystal so that no intrinsic point defect clustering occurs during crystal cooling, see e.g. [2] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Germanium doping for improved silicon substrates and devices

Vanhellemont

Chen

Lauwaert

et al. 2011

Journal of Crystal Growth

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During the last decade, the 300 mm silicon wafer has been optimized and one is studying the move to 450 mm crystals and wafers. The ever increasing silicon crystal diameter leads to two important trends with respect to substrate characteristics: the interstitial oxygen concentration decreases while the size of grown in voids (COP's) in vacancy-rich crystals is increasing.The first effect is due to the large melt in which movements have to be controlled and partly suppressed by the use of magnetic fields. This magnetic confinement leads to a more uniform dopant incorporation but at the same time to a more limited transport of oxygen from the quartz crucible to the melt and the growing crystal. The reduced interstitial oxygen concentration and the lower thermal budget of modern device processing leads to strongly reduced oxygen precipitation and thus internal gettering capacity.The increasing COP size (accompanied by a decreasing density) is caused by the decreasing pulling rate and thermal gradient that have to be used in order to avoid dislocation formation. The slower cooling of the crystal leads to a decreased void nucleation rate and at the same time to an increased thermal budget for void growth as well as a larger number of vacancies available per void. Journal of Crystal Growth November 9, 2010 In the present paper the effect of germanium doping in the range between 10 16 cm −3 and 10 19 cm −3 on COP formation and oxygen precipitation is discussed and illustrated. Also the beneficial effect of germanium doping with respect to wafer breakage during processing, with respect to the suppression of thermal donor formation and with respect to improving device radiation hardness is addressed. Preprint submitted to

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“…Vanhellemont 3 on the other hand, adopted the incorrect expression (3) of Tan and Goesele in his starting Eq. (1), instead of the correct-and conventional-expression (2). Accordingly, all his subsequent analysis of defect transport is meaningless.…”

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confidence: 99%

“…1,2 During crystal growth, after mutual annihilation upon lowering the temperature, only one of the defects, either V or I, becomes dominant in the crystal bulk (in other words-becomes incorporated into the crystal). These point defects give rise to aggregates known as "grown-in microdefects" which are of crucial importance for the quality of silicon materials.…”

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confidence: 99%

“…These point defects give rise to aggregates known as "grown-in microdefects" which are of crucial importance for the quality of silicon materials. The type of the dominant incorporated defect was shown 1,2 to be determined by the ratio of the growth rate V and the axial temperature gradient G defined in the vicinity of the crystal-melt interface. If V/G exceeds a certain critical value (V/G) cr , then the incorporated defects are vacancies and they give rise to voids.…”

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confidence: 99%

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