Diffusion–influenced nucleation: a case study of oxygen precipitation in silicon

Kelton, K. F.

doi:10.1098/rsta.2002.1138

Cited by 18 publications

(9 citation statements)

References 42 publications

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“…Such a biphasic behavior is experimentally observed for some crystallization systems. 40,41 As the x eth increases, the distribution becomes wider such that two distinct peaks disappear, indicating that the number of events where molecules experience an undersaturated local environment has decreased. In Figure 4a, the case of x eth = 0.5 has the widest distribution.…”

Section: Resultsmentioning

confidence: 99%

Emulsification of Supersaturated Solutions Amplifies Induction Time Variation in Crystallization

Dighe

Podupu

Singh

2023

Crystal Growth & Design

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The induction time for the onset of nucleation is known to decrease with increasing solution supersaturation. A large variation in induction time is experimentally observed for various organic crystals, whose origin is often associated with the stochastic nature of the nucleation process. Although several empirical models for induction time and nucleation rate have been developed, they remained highly unreliable, with model predictions differing by orders of magnitude from experimental measurements. A satisfactory explanation for the induction time variation has not been developed yet. We report here that the variations in induction times can be attributed to a previously unrecognized consequence of the phase separation or emulsification of supersaturated solution, in addition to the effect of stochastic nucleation. A large-scale Brownian dynamics simulation of antisolvent crystallization of histidine in a water–ethanol mixture is performed to demonstrate the mechanism of microphase/emulsion formation in supersaturated solutions and its consequence on induction time variation. Furthermore, we show that the average induction time depends on supersaturation, and the supersaturation-dependent diffusion of histidine molecules governs the stochastic nature of the induction time. Moreover, at varying supersaturations, the likelihood of forming stable and metastable polymorphs of histidine was estimated. This approach provides valuable insights into the crystallization behavior of histidine, and predicted induction time reasonably matches the experimentally observed induction time.

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Section: Resultsmentioning

confidence: 99%

Emulsification of Supersaturated Solutions Amplifies Induction Time Variation in Crystallization

Dighe

Podupu

Singh

2023

Crystal Growth & Design

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“…Furthemore, Takeno et al [ 36 ] have calculated the effective oxygen diffusivities in the range of 2–4 × 10 −14 cm 2 s −1 between 400 and 700 °C based on the extended nucleation theory. [ 37 ] Based on the enhanced oxygen diffusivities, Kelton [ 38 ] has demonstrated enhanced OP nucleation, and Takeno et al [ 36 ] have presented enhanced growth rates of OPs below 700 °C. Therefore, we have considered the effective diffusivity of oxygen to be 3 × 10 14 cm 2 s −1 at 450 °C.…”

Section: Discussion Of Resultsmentioning

confidence: 99%

Ring‐Like Defect Formation in N‐Type Czochralski‐Grown Silicon Wafers during Thermal Donor Formation

Basnet

Sio

Siriwardhana

et al. 2020

Physica Status Solidi (a)

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This article presents experimental and simulation studies on the formation of recombination‐active ring‐like defects during thermal donor (TD) formation at 450 °C in n‐type Czochralski‐grown silicon wafers. With increasing anneal duration from 1 to 24 h, the resistivity and interstitial oxygen concentration of samples decrease, consistent with the formation of TDs. However, after a subsequent TD annihilation treatment, the resistivity recovers completely, while the interstitial oxygen concentration recovers only partially. Furthermore, the wafers exhibit ring‐like defects in photoluminescence images after the TD generation and remain persistent even after annihilation treatment. By applying a tabula rasa (TR) treatment prior to TD generation anneals, the net loss of interstitial oxygen is reduced, and the incubation time of the ring‐like defects is extended in comparison to as‐grown wafers. Finally, to investigate the possibility of low‐temperature precipitation, simulation of oxygen precipitation (OP) kinetics during the 450 °C annealing steps is performed using an enhanced effective diffusivity of oxygen. These simulations demonstrate that OP can occur simultaneously during TD formation, resulting in recombination‐active ring‐like defects.

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“…This core-shell structure * iwamatsu@ph.ns.tcu.ac.jp also appears in various problems such as semiconductor nano-crystals [15], polymer crystallizations [16], and nano-clusters of alloys [17]. It is also used as a model of linked-flux nucleation or partitioning transformation when the interface-limited growth and diffusion of material is coupled [18][19][20][21]. In this model, a core of the final stable phase is surrounded by a shell of the dense pre-nucleus environment [18].…”

Section: Introductionmentioning

confidence: 99%

Nucleation pathway of core-shell composite nucleus in size and composition space and in component space

Iwamatsu

2012

Phys. Rev. E

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The kinetics of nucleation of a core-shell composite nucleus that consists of a core of stable final phase surrounded by a wetting layer of intermediate metastable phase is studied using the kinetic theory of binary nucleation not only in the size and composition space but also in the component space. The steady-state solution of the Fokker-Planck equation is considered. Various formulas for the critical nucleus at the saddle point as well as for the postcritical nucleus are derived. The kinetics of nucleation at the saddle point is more appropriately characterized in the size and composition space, while the kinetics of the postcritical nucleus is more appropriately described in the component space. Although both the free-energy landscape and the reaction rates play decisive role to determine the kinetics of nucleation at the saddle point, the details of the free-energy landscape are irrelevant to the kinetics of the postcritical nucleus.

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Diffusion–influenced nucleation: a case study of oxygen precipitation in silicon

Cited by 18 publications

References 42 publications

Emulsification of Supersaturated Solutions Amplifies Induction Time Variation in Crystallization

Emulsification of Supersaturated Solutions Amplifies Induction Time Variation in Crystallization

Ring‐Like Defect Formation in N‐Type Czochralski‐Grown Silicon Wafers during Thermal Donor Formation

Nucleation pathway of core-shell composite nucleus in size and composition space and in component space

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