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Compositional control over vapor–liquid–solid III–V ternary nanowires based on group V intermix (VLS IIIVxV1−x NWs) is complicated by the presence of a catalyst droplet with extremely low and hence undetectable concentrations of group V atoms. The liquid–solid and vapor–solid distributions of IIIVxV1−x NWs at a given temperature are influenced by the kinetic parameters (supersaturation and diffusion coefficients in liquid, V/III flux ratio in vapor), temperature and thermodynamic constants. We analyze the interplay of the kinetic and thermodynamic factors influencing the compositions of VLS IIIVxV1−x NWs and derive a new vapor–solid distribution that contains only one parameter of liquid, the ratio of the diffusion coefficients of dissimilar group V atoms. The unknown concentrations of group V atoms in liquid have no influence on the NW composition at high enough levels of supersaturation in liquid. The simple analytic shape of this vapor–solid distribution is regulated by the total V/III flux ratio in vapor. Calculating the temperature-dependent desorption rates, we show that the purely kinetic regime of the liquid–solid growth occurs for VLS IIIVxV1−x NWs in a wide range of conditions. The model fits the data well on the vapor–solid distributions of VLS InPxAs1−x and GaPxAs1−x NWs and can be used for understanding and controlling the compositions of any VLS IIIVxV1−x NWs, as well as modeling the compositional profiles across NW heterostructures in different material systems.

Due to the very efficient relaxation of elastic stress on strain-free sidewalls, III–V nanowires offer almost unlimited possibilities for bandgap engineering in nanowire heterostructures by using material combinations that are attainable in epilayers. However, axial nanowire heterostructures grown using the vapor–liquid–solid method often suffer from the reservoir effect in a catalyst droplet. Control over the interfacial abruptness in nanowire heterostructures based on the group V interchange is more difficult than for group-III-based materials, because the low concentrations of highly volatile group V atoms cannot be measured after or during growth. Here, we develop a self-consistent model for calculations of the coordinate-dependent compositional profiles in the solid and liquid phases during the vapor–liquid–solid growth of the axial nanowire heterostructure Ax0B1−x0C/Ax1B1−x1C with any stationary compositions x0 and x1. The only assumption of the model is that the growth rates of both binaries AC and BC are proportional to the concentrations of group V atoms A and B in a catalyst droplet, requiring high enough supersaturations in liquid phase. The model contains a minimum number of parameters and fits quite well the data on the interfacial abruptness across double heterostructures in GaP/GaAsxP1−x/GaP nanowires. It can be used for any axial III–V nanowire heterostructures obtained through the vapor–liquid–solid method. It forms a basis for further developments in modeling the complex growth process and suppression of the interfacial broadening caused by the reservoir effect.

Control over the composition of III–V ternary nanowires grown by the vapor–liquid–solid (VLS) method is essential for bandgap engineering in such nanomaterials and for the fabrication of functional nanowire heterostructures for a variety of applications. From the fundamental viewpoint, III–V ternary nanowires based on group V intermix (InSbxAs1−x, InPxAs1−x, GaPxAs1−x and many others) present the most difficult case, because the concentrations of highly volatile group V atoms in a catalyst droplet are beyond the detection limit of any characterization technique and therefore principally unknown. Here, we present a model for the vapor–solid distribution of such nanowires, which fully circumvents the uncertainties that remained in the theory so far, and we link the nanowire composition to the well-controlled parameters of vapor. The unknown concentrations of group V atoms in the droplet do not enter the distribution, despite the fact that a growing solid is surrounded by the liquid phase. The model fits satisfactorily the available data on the vapor–solid distributions of VLS InSbxAs1−x, InPxAs1−x and GaPxAs1−x nanowires grown using different catalysts. Even more importantly, it provides a basis for the compositional control of III–V ternary nanowires based on group V intermix, and it can be extended over other material systems where two highly volatile elements enter a ternary solid alloy through a liquid phase.

Coalescence of nanowires and other three-dimensional structures into continuous film is desirable for growing low-dislocation-density III-nitride and III-V materials on lattice-mismatched substrates; this is also interesting from a fundamental viewpoint. Here, we develop a growth model for vertical nanowires which, under rather general assumptions on the solid-like coalescence process within the Kolmogorov crystallization theory, results in a morphological diagram for the asymptotic coverage of a substrate surface. The coverage is presented as a function of two variables: the material collection efficiency on the top nanowire facet a and the normalized surface diffusion flux of adatoms from the NW sidewalls b. The full coalescence of nanowires is possible only when a=1, regardless of b. At a>1, which often holds for vapor–liquid–solid growth with a catalyst droplet, nanowires can only partly merge but never coalesce into continuous film. In vapor phase epitaxy techniques, the NWs can partly merge but never fully coalesce, while in the directional molecular beam epitaxy the NWs can fully coalesce for small enough contact angles of their droplets corresponding to a=1. The growth kinetics of nanowires and evolution of the coverage in the pre-coalescence stage is also considered. These results can be used for predicting and controlling the degree of surface coverage by nanowires and three-dimensional islands by tuning the surface density, droplet size, adatoms diffusivity, and geometry of the initial structures in the vapor–liquid–solid, selective area, or self-induced growth by different epitaxy techniques.

Compositional control in III–V ternary nanowires grown by the vapor–liquid–solid method is essential for bandgap engineering and the design of functional nanowire nano-heterostructures. Herein, we present rather general theoretical considerations and derive explicit forms of the stationary vapor–solid and liquid–solid distributions of vapor–liquid–solid III–V ternary nanowires based on group-III intermix. It is shown that the vapor–solid distribution of such nanowires is kinetically controlled, while the liquid–solid distribution is in equilibrium or nucleation-limited. For a more technologically important vapor-solid distribution connecting nanowire composition with vapor composition, the kinetic suppression of miscibility gaps at a growth temperature is possible, while miscibility gaps (and generally strong non-linearity of the compositional curves) always remain in the equilibrium liquid–solid distribution. We analyze the available experimental data on the compositions of the vapor–liquid–solid AlxGa1−xAs, InxGa1−xAs, InxGa1−xP, and InxGa1−xN nanowires, which are very well described within the model. Overall, the developed approach circumvents uncertainty in choosing the relevant compositional model (close-to-equilibrium or kinetic), eliminates unknown parameters in the vapor–solid distribution of vapor–liquid–solid nanowires based on group-III intermix, and should be useful for the precise compositional tuning of such nanowires.

GaN nanowires grown on metal substrates have attracted increasing interest for a wide range of applications. Herein, we report GaN nanowires grown by plasma-assisted molecular beam epitaxy on thin polycrystalline ZrN buffer layers, sputtered onto Si(111) substrates. The nanowire orientation was studied by X-ray diffraction and scanning electron microscopy, and then described within a model as a function of the Ga beam angle, nanowire tilt angle, and substrate rotation. We show that vertically aligned nanowires grow faster than inclined nanowires, which leads to an interesting effect of geometrical selection of the nanowire orientation in the directional molecular beam epitaxy technique. After a given growth time, this effect depends on the nanowire surface density. At low density, the nanowires continue to grow with random orientations as nucleated. At high density, the effect of preferential growth induced by the unidirectional supply of the material in MBE starts to dominate. Faster growing nanowires with smaller tilt angles shadow more inclined nanowires that grow slower. This helps to obtain more regular ensembles of vertically oriented GaN nanowires despite their random position induced by the metallic grains at nucleation. The obtained dense ensembles of vertically aligned GaN nanowires on ZrN/Si(111) surfaces are highly relevant for device applications. Importantly, our results are not specific for GaN nanowires on ZrN buffers, and should be relevant for any nanowires that are epitaxially linked to the randomly oriented surface grains in the directional molecular beam epitaxy.

Modeling of the growth process is required for the synthesis of III–V ternary nanowires with controllable composition. Consequently, new theoretical approaches for the description of epitaxial growth and the related chemical composition of III–V ternary nanowires based on group III or group V intermix were recently developed. In this review, we present and discuss existing modeling strategies for the stationary compositions of III–V ternary nanowires and try to systematize and link them in a general perspective. In particular, we divide the existing approaches into models that focus on the liquid–solid incorporation mechanisms in vapor–liquid–solid nanowires (equilibrium, nucleation-limited, and kinetic models treating the growth of solid from liquid) and models that provide the vapor–solid distributions (empirical, transport-limited, reaction-limited, and kinetic models treating the growth of solid from vapor). We describe the basic ideas underlying the existing models and analyze the similarities and differences between them, as well as the limitations and key factors influencing the stationary compositions of III–V nanowires versus the growth method. Overall, this review provides a basis for choosing a modeling approach that is most appropriate for a particular material system and epitaxy technique and that underlines the achieved level of the compositional modeling of III–V ternary nanowires and the remaining gaps that require further studies.

Catalyst-free growth of III-V and III-nitride nanowires (NWs) by the self-induced nucleation mechanism or selective area growth (SAG) on different substrates, including Si, show great promise for monolithic integration of III-V optoelectronics with Si electronic platform. The morphological design of NW ensembles requires advanced growth modeling, which is much less developed for catalyst-free NWs compared to vapor–liquid–solid (VLS) NWs of the same materials. Herein, we present an empirical approach for modeling simultaneous axial and radial growths of untapered catalyst-free III-V NWs and compare it to the rigorous approach based on the stationary diffusion equations for different populations of group III adatoms. We study in detail the step flow occurring simultaneously on the NW sidewalls and top and derive the general laws governing the evolution of NW length and radius versus the growth parameters. The rigorous approach is reduced to the empirical equations in particular cases. A good correlation of the model with the data on the growth kinetics of SAG GaAs NWs and self-induced GaN NWs obtained by different epitaxy techniques is demonstrated. Overall, the developed theory provides a basis for the growth modeling of catalyst-free NWs and can be further extended to more complex NW morphologies.

Controlling the morphology and composition of semiconductor nano- and micro-structures is crucial for fundamental studies and applications. Here, Si-Ge semiconductor nanostructures were fabricated using photolithographically defined micro-crucibles on Si substrates. Interestingly, the nanostructure morphology and composition of these structures are strongly dependent on the size of the liquid–vapour interface (i.e., the opening of the micro-crucible) in the CVD deposition step of Ge. In particular, Ge crystallites nucleate in micro-crucibles with larger opening sizes (3.74–4.73 μm2), while no such crystallites are found in micro-crucibles with smaller openings of 1.15 μm2. This interface area tuning also results in the formation of unique semiconductor nanostructures: lateral nano-trees (for smaller openings) and nano-rods (for larger openings). Further TEM imaging reveals that these nanostructures have an epitaxial relationship with the underlying Si substrate. This geometrical dependence on the micro-scale vapour–liquid–solid (VLS) nucleation and growth is explained within a dedicated model, where the incubation time for the VLS Ge nucleation is inversely proportional to the opening size. The geometric effect on the VLS nucleation can be used for the fine tuning of the morphology and composition of different lateral nano- and micro-structures by simply changing the area of the liquid–vapour interface.

A model for the nucleation of vertical or planar III-V nanowires (NWs) in selective area growth (SAG) on masked substrates with regular arrays of openings is developed. The optimal SAG zone, with NW nucleation within the openings and the absence of parasitic III-V crystallites or group III droplets on the mask, is established, taking into account the minimum chemical potential of the III-V pairs required for nucleation on different surfaces, and the surface diffusion of the group III adatoms. The SAG maps are plotted in terms of the material fluxes versus the temperature. The non-trivial behavior of the SAG window, with the opening size and pitch, is analyzed, depending on the direction of the diffusion flux of the group III adatoms into or from the openings. A good correlation of the model with the data on the SAG of vertical GaN NWs and planar GaAs and InAs NWs by molecular beam epitaxy (MBE) is demonstrated.

GaN nanowires were grown using selective area plasma-assisted molecular beam epitaxy on SiOx/Si(111) substrates patterned with microsphere lithography. For the first time, the temperature–Ga/N2 flux ratio map was established for selective area epitaxy of GaN nanowires. It is shown that the growth selectivity for GaN nanowires without any parasitic growth on a silica mask can be obtained in a relatively narrow range of substrate temperatures and Ga/N2 flux ratios. A model was developed that explains the selective growth range, which appeared to be highly sensitive to the growth temperature and Ga flux, as well as to the radius and pitch of the patterned pinholes. High crystal quality in the GaN nanowires was confirmed through low-temperature photoluminescence measurements.

An analytic model for III-V nanowire growth by metal organic chemical vapor deposition (MOCVD) in regular arrays on patterned substrates is presented. The model accounts for some new features that, to the author’s knowledge, have not yet been considered. It is shown that MOCVD growth is influenced by an additional current into the nanowires originating from group III atoms reflected from an inert substrate and the upper limit for the group III current per nanowire given by the total group III flow and the array pitch. The model fits the data on the growth kinetics of Au-catalyzed and catalyst-free III-V nanowires quite well and should be useful for understanding and controlling the MOCVD nanowire growth in general.

A new model for the radial growth of self-catalyzed III-V nanowires on different substrates is presented, which describes the nanowire morphological evolution without any free parameters. The model takes into account the re-emission of group III atoms from a mask surface and the shadowing effect in directional deposition techniques such as molecular beam epitaxy. It is shown that radial growth is faster for larger pitches of regular nanowire arrays or lower surface density, and can be suppressed by increasing the V/III flux ratio or decreasing re-emission. The model describes quite well the data on the morphological evolution of Ga-catalyzed GaP and GaAs nanowires on different substrates, where the nanowire length increases linearly and the radius enlarges sub-linearly with time. The obtained analytical expressions and numerical data should be useful for morphological control over different III-V nanowires in a wide range of growth conditions.

A new model for nanowire growth by molecular beam epitaxy is proposed which extends the earlier approaches treating an isolated nanowire to the case of ensembles of nanowires. I consider an adsorbing substrate on which the arriving growth species (group III adatoms for III-V nanowires) may diffuse to the nanowire base and subsequently to the top without desorption. Analytical solution for the nanowire length evolution at a constant radius shows that the shadowing of the substrate surface is efficient and affects the growth kinetics from the very beginning of growth in dense enough ensembles of nanowires. The model fits quite well the kinetic data on different Au-catalyzed and self-catalyzed III-V nanowires. This approach should work equally well for vapor-liquid-solid and catalyst-free nanowires grown by molecular beam epitaxy and related deposition techniques on unpatterned or masked substrates.

InSb nanoflags are grown by chemical beam epitaxy in regular arrays on top of Au-catalyzed InP nanowires synthesized on patterned SiO2/InP(111)B substrates. Two-dimensional geometry of the nanoflags is achieved by stopping the substrate rotation in the step of the InSb growth. Evolution of the nanoflag length, thickness and width with the growth time is studied for different pitches (distances in one of the two directions of the substrate plane). A model is presented which explains the observed non-linear time dependence of the nanoflag length, saturation of their thickness and gradual increase in the width by the shadowing effect for re-emitted Sb flux. These results might be useful for morphological control of InSb and other III-V nanoflags grown in regular arrays.

Selective area growth (SAG) of III-V nanowires (NWs) by molecular beam epitaxy (MBE) and related epitaxy techniques offer several advantages over growth on unpatterned substrates. Here, an analytic model for the total flux of group III atoms impinging NWs is presented, which accounts for specular re-emission from the mask surface and the shadowing effect in the absence of surface diffusion from the substrate. An expression is given for the shadowing length of NWs corresponding to the full shadowing of the mask. Axial and radial NW growths are considered in different stages, including the stage of purely axial growth, intermediate stage with radial growth, and asymptotic stage, where the NWs receive the maximum flux determined by the array pitch. The model provides good fits with the data obtained for different vapor–liquid–solid and catalyst-free III-V NWs.

We present a growth model that describes the nanowire length and radius versus time in the absence of evaporation or scattering of semiconductor atoms (group III atoms in the case of III-V NWs) from the substrate, nanowire sidewalls or catalyst nanoparticle. The model applies equally well to low-temperature metal-catalyzed or selective area growth of elemental or III-V nanowires on patterned substrates. Surface diffusion transport and radial growth on the nanowire sidewalls are carefully considered under the constraint of the total material balance, yielding some new effects. The nanowire growth process is shown to proceed in two steps. In the first step, the nanowire length increases linearly with time and is inversely proportional to the nanowire radius squared and the nanowire surface density, without radial growth. In the second step, the nanowire length obeys the Chini equation, resulting in a non-linear increase in length with time and radial growth. The nanowire radii converge to a stationary value in the large time limit, showing a kind of size-narrowing effect. The model fits the data on the growth kinetics of a single self-catalyzed GaAs nanowire on a Si substrate well.

The vapor–liquid–solid growth of III-V nanowires proceeds via the mononuclear regime, where only one island nucleates in each nanowire monolayer. The expansion of the monolayer is governed by the surface energetics depending on the monolayer size. Here, we study theoretically the role of surface energy in determining the monolayer morphology at a given coverage. The optimal monolayer configuration is obtained by minimizing the surface energy at different coverages for a set of energetic constants relevant for GaAs nanowires. In contrast to what has been assumed so far in the growth modeling of III-V nanowires, we find that the monolayer expansion may not be a continuous process. Rather, some portions of the already formed monolayer may dissolve on one of its sides, with simultaneous growth proceeding on the other side. These results are important for fundamental understanding of vapor–liquid–solid growth at the atomic level and have potential impacts on the statistics within the nanowire ensembles, crystal phase, and doping properties of III-V nanowires.

The bottom-up assembly of nanowires facilitates the control of their dimensions, structure, orientation and physical properties. Surface-guided growth of planar nanowires has been shown to enable their assembly and alignment on substrates during growth, thus eliminating the need for additional post-growth processes. However, accurate control and understanding of the growth of the planar nanowires were achieved only recently, and only for ZnSe and ZnS nanowires. Here, we study the growth kinetics of surface-guided planar GaN nanowires on flat and faceted sapphire surfaces, based on the previous growth model. The data are fully consistent with the same model, presenting two limiting regimes—either the Gibbs–Thomson effect controlling the growth of the thinner nanowires or surface diffusion controlling the growth of thicker ones. The results are qualitatively compared with other semiconductors surface-guided planar nanowires materials, demonstrating the generality of the growth mechanism. The rational approach enabled by this general model provides better control of the nanowire (NW) dimensions and expands the range of materials systems and possible application of NW-based devices in nanotechnology.

Based on a thermodynamic model, we quantify the impact of adding silicon atoms to a catalyst droplet on the nucleation and growth of ternary III–V nanowires grown via the self-catalyzed vapor–liquid–solid process. Three technologically relevant ternaries are studied: InGaAs, AlGaAs and InGaN. For As-based alloys, it is shown that adding silicon atoms to the droplet increases the nanowire nucleation probability, which can increase by several orders magnitude depending on the initial chemical composition of the catalyst. Conversely, silicon atoms are found to suppress the nucleation rate of InGaN nanowires of different compositions. These results can be useful for understanding and controlling the vapor–liquid–solid growth of ternary III–V nanowires on silicon substrates as well as their intentional doping with Si.

III–V nanowires grown by the vapor–liquid–solid method often show self-regulated oscillations of group V concentration in a catalyst droplet over the monolayer growth cycle. We investigate theoretically how this effect influences the electron-to-hole ratio in Si-doped GaAs nanowires. Several factors influencing the As depletion in the vapor–liquid–solid nanowire growth are considered, including the time-scale separation between the steps of island growth and refill, the “stopping effect” at very low As concentrations, and the maximum As concentration at nucleation and desorption. It is shown that the As depletion effect is stronger for slower nanowire elongation rates and faster for island growth relative to refill. Larger concentration oscillations suppress the electron-to-hole ratio and substantially enhance the tendency for the p-type Si doping of GaAs nanowires, which is a typical picture in molecular beam epitaxy. The oscillations become weaker and may finally disappear in vapor deposition techniques such as hydride vapor phase epitaxy, where the n-type Si doping of GaAs nanowires is more easily achievable.

The growth mechanisms of self-catalyzed InAs/InSb axial nanowire heterostructures are thoroughly investigated as a function of the In and Sb line pressures and growth time. Some interesting phenomena are observed and analyzed. In particular, the presence of In droplet on top of InSb segment is shown to be essential for forming axial heterostructures in the self-catalyzed vapor-liquid-solid mode. Axial versus radial growth rates of InSb segment are investigated under different growth conditions and described within a dedicated model containing no free parameters. It is shown that widening of InSb segment with respect to InAs stem is controlled by the vapor-solid growth on the nanowire sidewalls rather than by the droplet swelling. The In droplet can even shrink smaller than the nanowire facet under Sb-rich conditions. These results shed more light on the growth mechanisms of self-catalyzed heterostructures and give clear route for engineering the morphology of InAs/InSb axial nanowire heterostructures for different applications.