Length distributions of nanowires: Effects of surface diffusion versus nucleation delay

Dubrovskiı̆, V. G.

doi:10.1016/j.jcrysgro.2017.02.014

Cited by 12 publications

(12 citation statements)

References 30 publications

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“…While the diameter distributions of self-catalyzed III–V can be made remarkably narrow under the appropriate growth conditions (as shown theoretically in refs and and confirmed experimentally for Ga-catalyzed GaAs NWs in ref ), the measured LDs of Au-catalyzed , and In-catalyzed InAs NWs and Ga-catalyzed GaAs NWs appear disappointingly broad, in fact, much broader than Poissonian in most cases. There are five main reasons for that: (i) nucleation randomness of NWs emerging from the substrate (meaning that different NWs start at different times and the initial length dispersion becomes larger for longer nucleation step − ), (ii) fluctuation-induced broadening due to random character of growth, − (iii) diffusion-induced contributions into the NW elongation rate in the case of Au-catalyzed growth, , (iv) nucleation of secondary group III droplets in the self-catalyzed approach, , and (v) possible collective effects in the NW ensemble such as shadowing in directional molecular beam epitaxy (MBE) growth.…”

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“…In order to quantify the statistical properties of the LDs shown in Figure , we use the rate equations for the normalized (∑ s ≥0 f s = 1) probabilities f s ( t ) to observe a NW with the length of s = L / h monolayers at time t , given by ,,,, For the growth rates p s , we use the model of the form Here, v = V / h gives the length-independent average axial growth rate in MLs per min. The second term stands for the shadow effect in the linear approximation, with shorter NWs (with s < ⟨ s ⟩) growing slower and longer NWs (with s < ⟨ s ⟩) growing faster than the NWs having the mean length ⟨ s ⟩ = ⟨ L ⟩/ h .…”

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

et al. 2017

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“…A large variation of the NW diameter implies that the diameters of the original Ga droplets exhibit a broad distribution. Also, the simplest explanation for a pronounced inhomogeneity of the NW length is that NWs nucleate at different times [35,36], leading to broader length distributions for longer incubation times. Conversely, NWs that are very homogeneous in length and diameter, as found below 620 °C, must have nucleated from similar droplets and almost simultaneously.…”

Section: Resultsmentioning

confidence: 99%

“…A theoretical analysis of the initial Ga droplet size was based on the assumption that an incubation time is needed to reach a critical As concentration in the droplets [34]. Further studies showed how the incubation time affects the length distribution of the final NW ensembles [35,36]. Faster nucleation always yields more uniform length over the ensemble, while longer nucleation delay results in broader length distributions with a pronounced asymmetry toward smaller lengths (corresponding to nanowires that have emerged later).…”

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Analysis of incubation time preceding the Ga-assisted nucleation and growth of GaAs nanowires on Si(111)

Bastiman

Küpers

Somaschini

et al. 2019

Phys. Rev. Materials

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The incubation time preceding nucleation and growth of surface nanostructures is interesting from a fundamental viewpoint but also of practical relevance as it determines statistical properties of nanostructure ensembles such as size homogeneity. Using in situ reflection high-energy electron diffraction, we accurately deduce the incubation times for Ga-2 assisted GaAs nanowires grown on unpatterned Si(111) substrates by molecular beam epitaxy under different conditions. We develop a nucleation model that explains and fits very well the data. We find that, for a given temperature and Ga flux, the incubation time always increases with decreasing As flux and becomes infinite at a certain minimum flux, which is larger for higher temperature. For given As and Ga fluxes, the incubation time always increases with temperature and rapidly tends to infinity above 640 °C under typical conditions. The strong temperature dependence of the incubation time is reflected in a similar variation of the nanowire number density with temperature. Our analysis provides understanding and guidance for choosing appropriate growth conditions that avoid unnecessary material consumption, long nucleation delays, and highly inhomogeneous ensembles of nanowires. On a more general ground, the existence of a minimum flux and maximum temperature for growing surface nanostructures should be a general phenomenon pertaining for a wide range of material-substrate combinations.

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“…The uptake of substrate atoms by nanoparticles deposited on the substrate at elevated temperatures has been observed for A c c e p t e d M a n u s c r i p t different nanoparticle/substrate systems [12][13][14][15][16][17] and, in nanowire growth experiments, claimed responsible for changing growth directions [18] or optical properties of nanowires [19][20] (due to incorporation of substrate atoms into the nanowire). Another important consequence of the substrate dissolution into the catalyst is a delayed nanowire growth, which is suspected to cause broad nanowire length distributions [21], thus making such nanowire arrays unsuitable for device fabrication.…”

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confidence: 99%

Catalyst–substrate interaction and growth delay in vapor–liquid–solid nanowire growth

et al. 2018

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Understanding of the initial stage of nanowire growth on a bulk substrate is crucial for the rational design of nanowire building blocks in future electronic and optoelectronic devices. Here, we provide in situ scanning electron microscopy and Auger microscopy analysis of the initial stage of Au-catalyzed Ge nanowire growth on different substrates. Real-time microscopy imaging and elementally resolved spectroscopy clearly show that the catalyst dissolves the underlying substrate if held above a certain temperature. If the substrate dissolution is blocked (or in the case of heteroepitaxy) the catalyst needs to be filled with nanowire material from the external supply, which significantly increases the initial growth delay. The experiments presented here reveal the important role of the substrate in metal-catalyzed nanowire growth and pave the way for different growth delay mitigation strategies.

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Length distributions of nanowires: Effects of surface diffusion versus nucleation delay

Cited by 12 publications

References 30 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

Analysis of incubation time preceding the Ga-assisted nucleation and growth of GaAs nanowires on Si(111)

Catalyst–substrate interaction and growth delay in vapor–liquid–solid nanowire growth

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