Modeling the nucleation statistics in vapor–liquid–solid nanowires

Sibirev, N. V.; Назаренко, М. В.; Zeze, Dagou A.; Dubrovskiı̆, V. G.

doi:10.1016/j.jcrysgro.2013.12.064

Cited by 12 publications

(9 citation statements)

References 29 publications

(71 reference statements)

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“…This discussion is limited to a simplified case of zero As evaporation from the catalyst. However, Sibirev and coauthors showed that a similar convergence of the LDs to a time-independent shape is observed when the evaporation is included. We will therefore proceed with the model without evaporation for further estimates, which is acceptable because the contribution into the saturated variance due to antibunching appears negligible anyway.…”

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confidence: 80%

Sub-Poissonian Narrowing of Length Distributions Realized in Ga-Catalyzed GaAs Nanowires

et al. 2017

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Herein, we present experimental data on the record length uniformity within the ensembles of semiconductor nanowires. The length distributions of Ga-catalyzed GaAs nanowires obtained by cost-effective lithography-free technique on silicon substrates systematically feature a pronounced sub-Poissonian character. For example, nanowires with the mean length ⟨L⟩ of 2480 nm show a length distribution variance of only 367 nm, which is more than twice smaller than the Poisson variance h⟨L⟩ of 808 nm for this mean length (with h = 0.326 nm as the height of GaAs monolayer). For 5125 nm mean length, the measured variance is 1200 nm against 1671 nm for Poisson distribution. A supporting model to explain the experimental findings is proposed. We speculate that the fluctuation-induced broadening of the length distribution is suppressed by nucleation antibunching, the effect which is commonly observed in individual vapor-liquid-solid nanowires but has never been seen for their ensembles. Without kinetic fluctuations, the two remaining effects contributing to the length distribution width are the nucleation randomness for nanowires emerging from the substrate and the shadowing effect on long enough nanowires. This explains an interesting time evolution of the variance that saturates after a short incubation stage but then starts increasing again due to shadowing, remaining, however, smaller than the Poisson value for a sufficiently long time.

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confidence: 80%

Sub-Poissonian Narrowing of Length Distributions Realized in Ga-Catalyzed GaAs Nanowires

et al. 2017

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“…In III-V NWs, forming even a single ML may then significantly deplete the droplet in group V atoms. We demonstrated experimentally and theoretically that this has a strong impact on the statistics of nucleation [2,20,21]: depletion makes a new nucleation less likely after a first one than before, so that the nucleation events are anti-correlated in time. This nucleation antibunching (which may also yield NW ensembles with very uniform lengths [22][23][24]) consists in the depletion induced by the fast growth of a ML affecting the formation of subsequent MLs.…”

Section: Introductionmentioning

confidence: 97%

Energetics and kinetics of monolayer formation in vapor-liquid-solid nanowire growth

Dubrovskiı̆

2020

Phys. Rev. Materials

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“…In the case of semiconductor nanowires (NWs) fabricated by the metalcatalyzed vapor-liquid-solid (VLS) method 10 , the ZNR is thought to determine the probability of 2D nucleation from a supersaturated liquid alloy of a metal catalyst with the growth constituencies 2 . In this way, the ZNR controls the vertical growth rate of NWs 2,11-13 , nucleation statistics in VLS NWs [14][15][16][17] , morphology of the growth interface 18,19 and even the preferred crystal structure of Au-catalyzed III-V NWs which can be either cubic zincblende (ZB) or hexagonal wurtzite (WZ) [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] . Since most NWs grow in the so-called mononuclear mode with only one island emerging in each NW monolayer (ML) 2 , we need to consider the chain of individual nucleation events.…”

Section: Introductionmentioning

confidence: 99%

“…This ZNR is widely used in modeling the size distribution of different “clusters” such as droplets and three-dimensional (3D) or two-dimensional (2D) surface islands. − In the case of semiconductor nanowires (NWs) fabricated by the metal-catalyzed vapor–liquid–solid (VLS) method, the ZNR is thought to determine the probability of 2D nucleation from a supersaturated liquid alloy of a metal catalyst with the growth constituencies . In this way, the ZNR controls the vertical growth rate of NWs, ,− nucleation statistics in VLS NWs, − morphology of the growth interface, , and even the preferred crystal structure of Au-catalyzed III–V NWs which can be either cubic zincblende (ZB) or hexagonal wurtzite (WZ). − Since most NWs grow in the so-called mononuclear mode with only one island emerging in each NW monolayer (ML), we need to consider the chain of individual nucleation events. This simplifies modeling due to the absence of any collective effects or ensembles of nuclei.…”

Section: Introductionmentioning

confidence: 99%

Zeldovich Nucleation Rate, Self-Consistency Renormalization, and Crystal Phase of Au-Catalyzed GaAs Nanowires

Dubrovskiı̆

Grecenkov

2014

Crystal Growth & Design

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We present a self-consistent model for the Zeldovich nucleation rate that determines the nucleation probabilities, growth rates and even the preferred crystal structure of Au-catalyzed III-V nanowires fabricated by the vapor-liquid-solid growth method. The obtained expression accounts for the nucleation kinetics in ternary Au-III-V alloys and shows that the nucleation rate in vapor-liquid-solid nanowires is proportional to the As concentration, As diffusion coefficient in the droplet and the activity of solid GaAs. The leading exponential term of the nucleation rate is modified due to the self-consistency renormalization. As a result, the behavior of the effective nucleation barrier versus Ga concentration is changed significantly with respect to the commonly used expression. This strongly affects the values of Ga concentrations during growth which are obtained within the self-consistent approach with the known nanowire elongation rates. In turn, the renormalized nucleation rates change the predictions regarding the zincblende-wurtzite phase transitions in III-V nanowires. In particular, our calculations show why the Aucatalyzed GaAs nanowires grown by molecular beam epitaxy at 550 o C are predominantly wurtzite, while the high temperature hydride vapor phase epitaxy at 715 o C yields pure zincblende crystal structure. We also obtain useful estimates for the As diffusion coefficients in ternary Au-Ga-As liquids at different conditions.

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Modeling the nucleation statistics in vapor–liquid–solid nanowires

Cited by 12 publications

References 29 publications

Sub-Poissonian Narrowing of Length Distributions Realized in Ga-Catalyzed GaAs Nanowires

Sub-Poissonian Narrowing of Length Distributions Realized in Ga-Catalyzed GaAs Nanowires

Energetics and kinetics of monolayer formation in vapor-liquid-solid nanowire growth

Zeldovich Nucleation Rate, Self-Consistency Renormalization, and Crystal Phase of Au-Catalyzed GaAs Nanowires

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