The length distribution function of semiconductor filamentary nanocrystals

The length distribution function of semiconductor filamentary nanocrystals is analyzed based on the adsorption–diffusion growth model. It is demonstrated that the asymptotic distribution has a Gaussian shape. If the diffusion flux to the apex comes from the entire lateral surface, the average length increases exponentially with time, and the mean-square deviation is proportional to the average length (exponential growth regime). If the diffusion collection of adatoms is limited to the top of the crystal, the average length increases linearly and the mean-square deviation equals the square root of average length (linear Poisson growth regime). In real-world systems, transition from exponential to Poisson growth occurs at lengths of the order of the diffusion length of adatoms. The dispersion of the distribution is actually defined at the exponential stage. The general classification of length distributions of various crystals is given. It is demonstrated that self-induced GaN- and Ga-catalytic III–V filamentary nanocrystals should be more homogeneous than Au-catalytic ones.     

Synthesis of single-crystalline Zn metal nanowires utilizing cold-wall physical vapor deposition

Zinc metal nanowires (NWs) of two different morphologies have been synthesized in a cold-wall physical vapor deposition (CWPVD) chamber at high vacuum conditions and growth temperatures of 150 degrees C. Substrates initially seeded by gold or platinum crystals show NWs of wool-like and/or unidirectional morphologies. Transmission electron microscopy (TEM) studies revealed that the rodlike NWs consist of single-crystalline Zn covered with a thin native oxide. NWs of wool-like morphology are suppressed using platinum as the seed metal. NW growth proceeds via vapor-solid (VS) kinetics without any catalyst particles on the wire tips. The highest observed growth rates exceed the Zn deposition rate by factors up to 860, indicating the dominant role of surface diffusion of Zn adatoms, also along the NWs. The surface diffusion length of Zn adatoms on the NW side facet is determined to be 39 mum. Direct impingement of precursor atoms on the NW tip is not significant for the growth process.     

The initial stage of autocatalytic growth of GaAs filamentary nanocrystals

The initial stage of growth of autocatalytic GaAs filamentary nanocrystals by the vapor–liquid–crystal mechanism from a Ga droplet with diffusion collection of gallium adatoms from the entire crystal length is investigated. The dependence of the crystal radius on its length at various ratios of fluxes of elements of groups III and V is analyzed theoretically. Various growth regimes (specifically, the regime of radius selffocusing and droplet disappearance) are examined. The calculations for crystals of a small radius are performed with the Gibbs–Thomson effect taken into account.     

Homoepitaxial growth kinetics in the presence of a Schwoebel barrier

Nowadays it is well-recognized that the additional barrier to downhill adatom diffusion at the step edge plays an important role in the epitaxial growth. Very recently we have developed a simple model for homoepitaxial layer growth kinetics which allows to take into account the Schwoebel barrier impact on adatoms interlayer diffusion by using the concept of a feeding zone, as we have proposed earlier. This paper is devoted to further refinement and extension of the model to the cases of an arbitrary nucleus size and coalescence behaviour of growing islands. The model consists of an infinite set of coupled non-linear rate equations for adatom and 2D island surface densities and coverage in each successive growing layer. These equations in combination with an integral condition determining the new layer formation onset fully describe homoepitaxial growth kinetics at predetermined five model parameters, characterizing adatoms diffusion rate, critical nucleus size and stability, Schwoebel barrier effect, and coalescence. The growth mechanisms and kinetics in a wide range of parameter values are studied and growth mechanism phase diagrams in various parameter spaces are constructed and discussed.     

Periodically twinned nanowires and polytypic nanobelts of ZnS: The role of mass diffusion in vapor-liquid-solid growth

There are two mass diffusion processes regarding the vapor-liquid-solid (VLS) growth of nanostructures: one is inside the catalyst droplet toward the liquid-solid interface; the other is along the side surface planes of the growing nanostructures. In this letter, microscale, modulated mass diffusion scenarios are exhibited through the synthesis of two types of ZnS nanostructures in an Au-catalyzed VLS process: periodically twinned nanowires originated from periodical fluctuation between diffusion rate inside the catalytic droplet and the growth rate on the liquid-solid interface; the formation of asymmetrically polytypic nanobelts is related to one certain side surface bounded by high surface-energy plane, which serves as a preferential diffusion direction of reactant adatoms. The results may have important impact on the understanding of the physical and chemical process of the VLS mechanism. These longitudinally and latitudinally tunable crystalline structures enrich the family of one-dimensional nano-building blocks, and may find potential applications in nanotechnology.     

Control of lateral dimension in metal-catalyzed germanium nanowire growth: usage of carbon sheath

We report on the catalytic growth of thin carbon sheathed single crystal germanium nanowires (GeNWs), which can solve the obstacles that have disturbed a wide range of applications of GeNWs. Single crystal Ge NW core and amorphous carbon sheath are simultaneously grown via vapor-liquid-solid (VLS) process. The carbon sheath completely blocks unintentional vapor deposition on NW surface, thus ensuring highly uniform diameter, dopant distribution, and electrical conductivity along the entire NW length. Furthermore, the sheath not only inhibits metal diffusion but also improves the chemical stability of GeNWs at even high temperatures.     

Control of the crystal structure of InAs nanowires by tuning contributions of adatom diffusion

The dependence of crystal structure on contributions of adatom diffusion (ADD) and precursor direct impingement (DIM) was investigated for vapor-liquid-solid growth of InAs nanowires (NWs). The ADD contributions from the sidewalls and substrate surface can be changed by using GaAs NWs of different length as the basis for growing InAs NWs. We found that pure zinc-blende structure is favored when DIM contributions dominate. Moreover, without changing the NW diameter or growth parameters (such as temperature or V/III ratio), a transition from zinc-blende to wurtzite structure can be realized by increasing the ADD contributions. A nucleation model is proposed in which ADD and DIM contributions play different roles in determining the location and phase of the nucleus.     

Temperature profile along a nanowhisker growing in high vacuum

A theoretical model describing the temperature profile along a nanowhisker (NW) growing in high vacuum is proposed. Under such conditions, the growing crystal is cooled due to thermal radiation from the surface. Knowledge of the temperature field is necessary for simulation of the NW growth process and determination of the properties of NWs obtained using molecular beam epitaxy and magnetron sputtering methods. Theoretical predictions are in good agreement with experimental data for a model system. For GaAs nanowhiskers with a length of 15 μm and a diameter of 30 nm, the difference between the temperature of the crystal apex and that of the substrate can be about 30 K. Original Russian Text ? N.V. Sibirev, I.P. Soshnikov, V.G. Dubrovskii, E. Arshansky, 2006, published in Pis’ma v Zhurnal Tekhnicheskoĭ Fiziki, 2006, Vol. 32, No. 7, pp. 28–35.     

Molecular dynamics simulation of microcrystalline Si deposition processes by silane plasmas

Molecular dynamics (MD) simulations have been performed to examine enhanced surface diffusion of Si adatoms during silane(SiH₄)-based plasma enhanced chemical vapor deposition (PECVD) processes. Such high surface diffusion, if it actually takes place, has been known to account for the growth of microcrystalline silicon(μc-Si) in the PECVD process. Focused in the present study is the motion of a silicon (Si) adatom on a hydrogenated Si surface and the surface diffusion coefficient of Si adatoms on the fully hydrogenated (111) Si surface at 600 K was evaluated from MD simulations. The obtained diffusion coefficient is much larger than those of typical clean Si surfaces known in the literature. The interatomic potential functions for Si-H systems used for the simulations, which we have developed for this study based on ab initio calculations of the interatomic energies, are also presented.     

Physical consequences of the equivalence of conditions for the steady-state growth of nanowires and the nucleation on triple phase line

A new theoretical model describing the steady-state growth and crystalline structure of semiconductor nanowires (NWs) is proposed and its physical consequences are considered. It is demonstrated that the Nebol’sin-Shchetinin condition (nonwetting of the NW side surface by the liquid drop) necessary for the steady-state growth of NWs according to the vapor-liquid-solid (VLS) mechanism is equivalent to the Glas condition of nucleation on the triple phase line for the monocentric NW growth. An energy criterion for the steady-state growth of NWs is formulated in the general case of faceted NW side surface. Effective surface energies are found that determine the activation barrier for nucleation at the NW top. Based on the proposed model, the issue of determining the III–V semiconductor NW crystal structure (cubic zinc blende type versus hexagonal wurtzite type) is considered. In particular, it is shown that a decrease in the surface energy of a catalyst must lead to the predominant formation of a cubic phase, which is confirmed by experimental data on the growth of GaAs nanowires according to the VLS mechanism with Au and Ga catalysts.     

Surface energy and modes of catalytic growth of semiconductor nanowhiskers

A thermodynamic theory of the growth of semiconductor nanowhisker (NW) crystals according to the vapor-liquid-solid (VLS) mechanism has been developed. An expression is proposed for the effective surface energy of the system, which is considered as a function of the NW radius and the contact angle of a liquid catalyst drop. Minimization of the surface energy leads to two possible modes of the VLS growth. In a standard mode that is realized when the Nebolsin-Shchetinin-Glas (NSC) condition is valid, the drop is not wetting the side surface of the NW. In the opposite case, the growth proceeds in a wetting mode, whereby the drop spreads about the NW top. It is shown for the first time that, even when the NSC condition is valid, the effective surface energy has two minima separated by a barrier and the minimum corresponding to the wetting mode is lower than that for the non-wetting mode. The results are applied to an analysis of the polytypism observed for GaAs nanowhiskers grown with Au and Ga catalysts.     

Step motion of the growth surface in the initial stage of semiconductor film epitaxy with ion sputtering

The development of relief inhomogeneity of the surrounding surface near (111)Si by thermal heating in an UHV oil pumped and gettered system has been studied. The essential features of the surface relief are discussed in connection with pre-epitaxial preparation of the substrate surface used for growing Si films by sputtering. The initial growth stage of layers 25, 65, 240 and 480 Å thick at a substrate temperature of 840°C is illustrated.It is shown that the formation of growth macrosteps is due to a complex system of sites for adatoms on the original Si surface because of the presence of etch micropits and silicon carbide particles. The conditions for formation of a crystallographic system of microsteps (with height of atomic order) on Si surfaces in the absence of etch pits and silicon carbide particles are analysed. The adsorption parameters and surface diffusion coefficient of adatoms are estimated.     

Modeling GaN nanowire growth on silicon

We have developed a kinetic theory of the growth of self-induced GaN nanowires (NWs) in the vertical and lateral directions on substrates with amorphous sublayers. A model is constructed that can describe temporal evolution of the NW length and radius. The results of model calculations are compared to experimental data on temporal dependences of the length and radius of GaN nanowires grown on amorphous Si _x N _y sublayers on Si substrates. The comparison shows good agreement between the proposed theory and experiment. Conditions, for which the NW length and radius are described by power functions of the time and the NW length exhibits scaling superlinear dependence on the radius, are determined.     

Ni-silicide growth kinetics in Si and Si/SiO2 core/shell nanowires

A systematic study of the kinetics of axial Ni silicidation of as-grown and oxidized Si nanowires (SiNWs) with different crystallographic orientations and core diameters ranging from ～ 10 to 100 nm is presented. For temperatures between 300 and 440?°C the length of the total axial silicide intrusion varies with the square root of time, which provides clear evidence that the rate limiting step is diffusion of Ni through the growing silicide phase(s). A retardation of Ni-silicide formation for oxidized SiNWs is found, indicative of a stress induced lowering of the diffusion coefficients. Extrapolated growth constants indicate that the Ni flux through the silicided NW is dominated by surface diffusion, which is consistent with an inverse square root dependence of the silicide length on the NW diameter as observed for (111) orientated SiNWs. In situ TEM silicidation experiments show that NiSi(2) is the first forming phase for as-grown and oxidized SiNWs. The silicide-SiNW interface is thereby atomically abrupt and typically planar. Ni-rich silicide phases subsequently nucleate close to the Ni reservoir, which for as-grown SiNWs can lead to a complete channel break-off for prolonged silicidation due to significant volume expansion and morphological changes.     

Growth of SiO(x) nanowires by laser ablation

Amorphous SiO(x) nanowires (NWs) were synthesized using laser ablation of silicon-containing targets. The influence of various parameters such as target composition, substrate type, substrate temperature and carrier gas on the growth process was studied. The NWs were characterized using high resolution scanning and transmission electron microscopes (HRSEM and HRTEM) with their attachments: electron dispersive spectroscopy (EDS) and energy electron loss spectroscopy (EELS). A metal catalyst was found essential for the NW growth. A growth temperature higher than 1000?°C was necessary for the NW formation using an Ar-based carrier gas at 500?Torr. The use of Ar-5%H(2) instead of pure Ar resulted in a higher yield and longer NWs. Application of a diffusion barrier on top of the Si substrate guaranteed the availability of metal catalyst droplets on the surface, essential for the NW growth. Ni was found to be a better catalyst than Au in terms of the NW yield and length. Two alternative sequences for the evolution of the amorphous SiO(x) NWs were considered: (a)?the formation of Si NWs first and their complete oxidation afterwards, which seems to be doubtful, (b)?the direct formation of SiO(x) NWs, which is more likely to occur. The direct formation mechanism was proposed to advance in three stages: preferential adsorption of SiO(x) clusters on the catalyst surface first, a successive surface diffusion to the catalyst droplet lower hemisphere, and finally the formation and growth of the NW between the catalyst and the substrate.     

Control of gold surface diffusion on si nanowires

Silicon nanowires (NW) were grown by the vapor-liquid-solid mechanism using gold as the catalyst and silane as the precursor. Gold from the catalyst particle can diffuse over the wire sidewalls, resulting in gold clusters decorating the wire sidewalls. The presence or absence of gold clusters was observed either by high angle annular darkfield scanning transmission electron microscopy images or by scanning electron microscopy. We find that the gold surface diffusion can be controlled by two growth parameters, the silane partial pressure and the growth temperature, and that the wire diameter also affects gold diffusion. Gold clusters are not present on the NW side walls for high silane partial pressure, low temperature, and small NW diameters. The absence or presence of gold on the NW sidewall has an effect on the sidewall morphology. Different models are qualitatively discussed. The main physical effect governing gold diffusion seems to be the adsorption of silane on the NW sidewalls.     

Void growth by grain-boundary diffusion in fine grained materials

Void growth by grain-boundary diffusion in fine grained materials is examined for the situation where the cavity spacing is greater than the grain size, which, in turn, is greater than the void radius. By solving the governing diffusional equations directly it is demonstrated that the volumetric growth rate of a void is much greater than that predicted by a linear viscous analysis, and by a procedure which ignores the full coupling between void growth and deformation.     

A model for whisker growth limited by a heterogeneous chemical reaction

A model has been proposed for whisker growth controlled by a heterogeneous chemical reaction on the surface of the liquid phase. The model considers a “feed” zone inside the boundary layer in the vapor phase, where the gas flow in the reactor has a negligible velocity. Since the feed zone is considerably larger than the crystal, the model possesses spherical symmetry. In the immediate vicinity of the surface of the liquid phase, there is a gas layer with constant reactant concentrations. The growth rate is determined by the reactant concentrations in this layer, which are controlled by the balance between the diffusion and chemical processes involved. Expressions are obtained for the concentrations of the components at the surface of the liquid phase and for the crystal growth rate as a function of crystal radius. The etching of a crystal through the liquid phase is considered.     

Catalyst and its diameter dependent growth kinetics of CVD grown GaN nanowires

GaN nanowires were grown using chemical vapor deposition with controlled aspect ratio. The catalyst and catalyst-diameter dependent growth kinetics is investigated in detail. We first discuss gold catalyst diameter dependent growth kinetics and subsequently compare with nickel and palladium catalyst. For different diameters of gold catalyst there was hardly any variation in the length of the nanowires but for other catalysts with different diameter a strong length variation of the nanowires was observed. We calculated the critical diameter dependence on adatoms pressure inside the reactor and inside the catalytic particle. This gives an increasing trend in critical diameter as per the order gold, nickel and palladium for the current set of experimental conditions. Based on the critical diameter, with gold and nickel catalyst the nanowire growth was understood to be governed by limited surface diffusion of adatoms and by Gibbs–Thomson effect for the palladium catalyst.