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

An Overview of Modeling Approaches for Compositional Control in III-V Ternary Nanowires

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.

Theory of MOCVD Growth of III-V Nanowires on Patterned Substrates

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.

Modeling the Radial Growth of Self-Catalyzed III-V Nanowires

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.

Cathodoluminescence mapping of electron concentration in MBE-grown GaAs:Te nanowires

Cathodoluminescence mapping is used as a contactless method to probe the electron concentration gradient of Te-doped GaAs nanowires. The room temperature and low temperature (10 K) cathodoluminescence analysis method previously developed for GaAs:Si is first validated on five GaAs:Te thin film samples, before extending it to the two GaAs:Te NW samples. We evidence an electron concentration gradient ranging from below 1 × 10¹⁸cm^-3to 3.3 ×10¹⁸cm^-3along the axis of a GaAs:Te nanowire grown at 640 °C, and a homogeneous electron concentration of around 6-8 × 10¹⁷cm^-3along the axis of a GaAs:Te nanowire grown at 620 °C. The differences in the electron concentration levels and gradients between the two nanowires is attributed to different Te incorporation efficiencies by vapor-solid and vapor-liquid-solid processes.

Interfacial profile of axial nanowire heterostructures in the nucleation limited regime

We report thermodynamic modeling of the formation of axial III–V nanowire heterostructures grown by the self-catalyzed and Au-catalyzed vapor–liquid–solid methods.

Low growth rate synthesis of GaAs nanowires with uniform size

The growth of nanowires (NWs) with uniform sizes is crucial for future NW-based electronics. In this work, an efficient one-step process is introduced for the growth of uniform gallium arsenide NWs on the native oxide surface of Si, which could be even considered as an alternative for expensive and sophisticated patterning approaches. The proposed strategy considers a Ga pre-deposition step leading to the formation of droplets with homogeneous sizes. That is followed by controlled nucleation of gallium arsenide from those droplets only. Our key to controlling the nucleation of gallium arsenide is to perform the NW growth at temperatures above 580 ± 10 °C and low Ga fluxes. By this method, the statistical distribution of the length and diameter of the vertically grown NWs decreased to about 3%–6% of their averaged values. Moreover, 100% epitaxial growth was realized. Besides, the growth of undesired parasitic islands is addressed and accordingly suppressed. Our study focuses on NW low growth rates, which is so far not investigated in the literature and, could be of great interest e.g. for in situ growth studies.

Broadband optical spin dependent reflection in self-assembled GaAs-based nanowires asymmetrically hybridized with Au

Hybridization of semiconductor nanostructures with asymmetric metallic layers offers new paths to circular polarization control and chiral properties. Here we study, both experimentally and numerically, chiral properties of GaAs-based nanowires (NWs) which have two out of six sidewalls covered by Au. Sparse ensembles of vertical, free-standing NWs were fabricated by means of lithography-free self-assembled technique on Si substrates and subsequently covered by Au using tilted evaporation. We report on optical spin-dependent specular reflection in the 680–1000 nm spectral range when the orientation of the golden layers follows the rule of extrinsic chirality. The analysis shows reflection peaks of the chiral medium whose intensity is dependent on the light handedness. We further propose a novel, time-efficient numerical method that enables a better insight into the far-field intensity and distribution of the scattered light from a sparse NW ensembles. The measurements done on three different samples in various orientations show good agreement with theoretical predictions over a broad wavelength range.

Kinetic broadening of size distribution in terms of natural versus invariant variables

We study theoretically the size distributions of nanoparticles (islands, droplets, nanowires) whose time evolution obeys the kinetic rate equations with size-dependent condensation and evaporation rates. Different effects are studied which contribute to the size distribution broadening, including kinetic fluctuations, evaporation, nucleation delay, and size-dependent growth rates. Under rather general assumptions, an analytic form of the size distribution is obtained in terms of the natural variable s which equals the number of monomers in the nanoparticle. Green's function of the continuum rate equation is shown to be Gaussian, with the size-dependent variance. We consider particular examples of the size distributions in either linear growth systems (at a constant supersaturation) or classical nucleation theory with pumping (at a time-dependent supersaturation) and compare the spectrum broadening in terms of s versus the invariant variable ρ for which the regular growth rate is size independent. For the growth rate scaling with s as s^{α} (with the growth index α between 0 and 1), the size distribution broadens for larger α in terms of s, while it narrows with α if presented in terms of ρ. We establish the conditions for obtaining a time-invariant size distribution over a given variable for different growth laws. This result applies for a wide range of systems and shows how the growth method can be optimized to narrow the size distribution over a required variable, for example, the volume, surface area, radius or length of a nanoparticle. An analysis of some concrete growth systems is presented from the viewpoint of the obtained results.

Assembling your nanowire: an overview of composition tuning in ternary III-V nanowires

The ability to grow defect-free nanowires in lattice-mismatched material systems and to design their properties has made them ideal candidates for applications in fields as diverse as nanophotonics, nanoelectronics and medicine. After studying nanostructures consisting of elemental and binary compound semiconductors, scientists turned their attention to more complex systems-ternary nanowires. Composition control is key in these nanostructures since it enables bandgap engineering. The use of different combinations of compounds and different growth methods has resulted in numerous investigations. The aim of this review is to present a survey of the material systems studied to date, and to give a brief overview of the issues tackled and the progress achieved in nanowire composition tuning. We focus on ternary III _x III_1-x V nanowires (AlGaAs, AlGaP, AlInP, InGaAs, GaInP and InGaSb) and IIIV _x V_1-x nanowires (InAsP, InAsSb, InPSb, GaAsP, GaAsSb and GaSbP).

Modeling the dynamics of interface morphology and crystal phase change in self-catalyzed GaAs nanowires

The droplet contact angle and morphology of the growth interface (vertical, tapered or truncated facets) are known to affect the zincblende (ZB) or wurtzite (WZ) crystal phase of III-V nanowires (NWs) grown by the vapor-liquid-solid method. Here, we present a model which describes the dynamics of the morphological evolution in self-catalyzed III-V NWs in terms of the time-dependent (or length-dependent) contact angle or top nanowire radius under varying material fluxes. The model fits quite well the contact angle dynamics obtained by in situ growth monitoring of self-catalyzed GaAs NWs in a transmission electron microscope. These results can be used for modeling the interface dynamics and the related crystal phase switching and for obtaining ZB-WZ heterostructures in III-V.

The role of As species in self-catalyzed growth of GaAs and GaAsSb nanowires

Precise control and broad tunability of the growth parameters are essential in engineering the optical and electrical properties of semiconductor nanowires (NWs) to make them suitable for practical applications. To this end, we report the effect of As species, namely As₂ and As₄, on the growth of self-catalyzed GaAs based NWs. The role of As species is further studied in the presence of Te as n-type dopant in GaAs NWs and Sb as an additional group V element to form GaAsSb NWs. Using As₄ enhances the growth of NWs in the axial direction over a wide range of growth parameters and diminishes the tendency of Te and Sb to reduce the NW aspect ratio. By extending the axial growth parameter window, As₄ allows growth of GaAsSb NWs with up to 47% in Sb composition. On the other hand, As₂ favors sidewall growth which enhances the growth in the radial direction. Thus, the selection of As species is critical for tuning not only the NW dimensions, but also the incorporation mechanisms of dopants and ternary elements. Moreover, the commonly observed dependence of twinning on Te and Sb remains unaffected by the As species. By exploiting the extended growth window associated with the use of As_4, enhanced Sb incorporation and optical emission up to 1400 nm wavelength range is demonstrated. This wavelength corresponds to the telecom E-band, which opens new prospects for this NW material system in future telecom applications while simultaneously enabling their integration to the silicon photonics platform.

Kotlyar K, O. Gridchin V, V. Ubyivovk E, V. Federov V, I. Khrebtov A, S. Shevchuk D, E. Cirlin G. Low-Temperature In-Induced Holes Formation in Native-SiOx/Si(111) Substrates for Self-Catalyzed MBE Growth of GaAs Nanowires

The reduction of substrate temperature is important in view of the integration of III-V materials with a Si platform. Here, we show the way to significantly decrease substrate temperature by introducing a procedure to create nanoscale holes in the native-SiOx layer on Si(111) substrate via In-induced drilling. Using the fabricated template, we successfully grew self-catalyzed GaAs nanowires by molecular-beam epitaxy. Energy-dispersive X-ray analysis reveals no indium atoms inside the nanowires. This unambiguously manifests that the procedure proposed can be used for the growth of ultra-pure GaAs nanowires.

Template-free electrochemical synthesis of Cd/CdTe core/shell nanowires and CdTe nanotubes

Template-free electrodeposition was utilized to prepare Cd/CdTe nanowires and CdTe nanotubes for the first time, where the formation of one-dimensional structures was due to the highly anisotropic crystal structure and the Kirkendall effect.

Does desorption affect the length distributions of nanowires?

State-of-the art models for statistical properties within the nanowire ensembles consider influx of precursors, reflection and surface diffusion of adatoms. These models predict a delay in the nanowire growth start and the evolution toward an asymmetric length distribution. We demonstrate here the effect of desorption of the nanowire material, which has not been considered so far in studies of the nanowire length distributions. We show that at the very beginning of growth the length distribution should be asymmetric due to the slow nucleation of nanowires. At longer times, the length distribution acquires a symmetric Gaussian shape due to the increased weight of desorption. The width of this distribution is larger than Poissonian and increases for higher ratio of desorption over deposition rate. Our model is consistent with the length evolution of organized self-catalyzed GaAs nanowires. We outline that desorption of the nanowire material should be minimized to achieve arrays of highly identical nanowires. These results are relevant for a wide variety of material systems.

Impact of the Ga flux incidence angle on the growth kinetics of self-assisted GaAs nanowires on Si(111)

In this work we show that the incidence angle of group-III element fluxes plays a significant role in the diffusion-controlled growth of III-V nanowires (NWs) by molecular beam epitaxy (MBE). We present a thorough experimental study on the self-assisted growth of GaAs NWs by using a MBE reactor equipped with two Ga cells located at different incidence angles with respect to the surface normal of the substrate, so as to ascertain the impact of such a parameter on the NW growth kinetics. The as-obtained results show a dramatic influence of the Ga flux incidence angle on the NW length and diameter, as well as on the shape and size of the Ga droplets acting as catalysts. In order to interpret the results we developed a semi-empirical analytical model inspired by those already developed for MBE-grown Au-catalyzed GaAs NWs. Numerical simulations performed with the model allow us to reproduce thoroughly the experimental results (in terms of NW length and diameter and of droplet size and wetting angle), putting in evidence that under formally the same experimental conditions the incidence angle of the Ga flux is a key parameter which can drastically affect the growth kinetics of the NWs grown by MBE.

Gradients of Be-dopant concentration in self-catalyzed GaAs nanowires

Effective and controllable doping is instrumental for enabling the use of III-V semiconductor nanowires (NWs) in practical electronics and optoelectronics applications. To this end, dopants are incorporated during self-catalyzed growth via vapor-liquid-solid mechanism through the catalyst droplet or by vapor-solid mechanism of the sidewall growth. The interplay of these mechanisms together with the competition between axial elongation and radial growth of NWs can result in dopant concentration gradients along the NW axis. Here, we report an investigation of Be-doped p-type GaAs NWs grown by the self-catalyzed method on lithography-free Si/SiO _x templates. The influence of dopant incorporation on the structural properties of the NWs is analyzed by scanning and transmission electron microscopy. By combining spatially resolved Raman spectroscopy and transport characterization, we are able to estimate the carrier concentration, mobility and resistivity on single-NW level. We show that Be dopants are incorporated predominantly by vapor-solid mechanism for low Be flux, while the relative contribution of vapor-liquid-solid incorporation is increased for higher Be flux, resulting in axial dopant gradients that depend on the nominal doping level.

Evolution of the Length and Radius of Catalyst-Free III-V Nanowires Grown by Selective Area Epitaxy

We present a new model for the length and radius evolution of catalyst-free III-V nanowires grown by selective area epitaxy. We consider simultaneous axial and radial growth of nanowires, which is more typical for this technique compared to the vapor-liquid-solid growth of nanowires. Analytic expressions for the time evolution of the nanowire length and radius are derived, showing the following properties. As long as the nanowire length is shorter than the collection length of group III atoms on the sidewalls, the length evolves superlinearly and the radius evolves linearly with time. For longer nanowires, both the length and radius increase sublinearly with time. The scaling growth laws are controlled by a single parameter that depends on group V flux. The model fits well the data on the selective area growth of InAs and GaAs nanowires by different techniques. Overall, these results can be used for controlling the catalyst-free growth of III-V nanowires and their morphology, including ternary III-V material systems.

Vapor Phase Growth of Semiconductor Nanowires: Key Developments and Open Questions

Nanowires are filamentary crystals with a tailored diameter that can be obtained using a plethora of different synthesis techniques. In this review, we focus on the vapor phase, highlighting the most influential achievements along with a historical perspective. Starting with the discovery of VLS, we feature the variety of structures and materials that can be synthesized in the nanowire form. We then move on to establish distinct features such as the three-dimensional heterostructure/doping design and polytypism. We summarize the status quo of the growth mechanisms, recently confirmed by in situ electron microscopy experiments and defining common ground between the different synthesis techniques. We then propose a selection of remaining defects, starting from what we know and going toward what is still to be learned. We believe this review will serve as a reference for neophytes but also as an insight for experts in an effort to bring open questions under a new light.

Demonstration of extrinsic chirality of photoluminescence with semiconductor-metal hybrid nanowires

Chiral optical response is an inherent property of molecules and nanostructures, which cannot be superimposed on their mirror images. In specific cases, optical chirality can be observed also for symmetric structures. This so-called extrinsic chirality requires that the mirror symmetry is broken by the geometry of the structure together with the incident or emission angle of light. From the fabrication point of view, the benefit of extrinsic chirality is that there is no need to induce structural chirality at nanoscale. This paper reports demonstration extrinsic chirality of photoluminescence emission from asymmetrically Au-coated GaAs-AlGaAs-GaAs core-shell nanowires fabricated on silicon by a completely lithography-free self-assembled method. In particular, the extrinsic chirality of PL emission is shown to originate from a strong symmetry breaking of fundamental HE₁₁ waveguide modes due to the presence of the asymmetric Au coating, causing preferential emission of left and right-handed emissions in different directions in the far field.

Analytic form of the size distribution in irreversible growth of nanoparticles

We study theoretically the size distributions of nanoparticles (surface islands, droplets, molecular chains, and semiconductor nanowires) which grow without decay and with arbitrary size and time-dependent growth rates. Using a special transformation of variables, the analytic Green's function is obtained in the form of a Gaussian the variance of which is determined by the size dependence of the growth rate k(s). In the case of the power-law growth rates k(s)=(a+s)^{α}, the explicit formulas for the expectation and variance are given that contain earlier results in the limiting regimes. In the case of heterogeneous nucleation in a closed system, by convoluting Green's function with the exponential nucleation rate, we find an analytic size distribution which takes into account a delay in forming the smallest dimer and shows how it affects the distribution shapes. The recently discovered sub-Poissonian narrowing of the size distribution by nucleation antibunching is also included in the treatment. We briefly consider the length distribution of vapor-liquid-solid nanowires in the context of the obtained results. Overall, simple analytic size distributions obtained here under rather general assumptions may be useful for understanding and modeling statistical properties of different growth systems.

Deterministic Switching of the Growth Direction of Self-Catalyzed GaAs Nanowires

The typical vapor-liquid-solid growth of nanowires is restricted to a vertical one-dimensional geometry, while there is a broad interest for more complex structures in the context of electronics and photonics applications. Controllable switching of the nanowire growth direction opens up new horizons in the bottom-up engineering of self-assembled nanostructures, for example, to fabricate interconnected nanowires used for quantum transport measurements. In this work, we demonstrate a robust and highly controllable method for deterministic switching of the growth direction of self-catalyzed GaAs nanowires. The method is based on the modification of the droplet-nanowire interface in the annealing stage without any fluxes and subsequent growth in the horizontal direction by a twin-mediated mechanism with indications of a novel type of interface oscillations. A 100% yield of switching the nanowire growth direction from vertical to horizontal is achieved by systematically optimizing the growth parameters. A kinetic model describing the competition of different interface structures is introduced to explain the switching mechanism and the related nanowire geometries. The model also predicts that the growth of similar structures is possible for all vapor-liquid-solid nanowires with commonly observed truncated facets at the growth interface.

A simple route to synchronized nucleation of self-catalyzed GaAs nanowires on silicon for sub-Poissonian length distributions

We demonstrate a simple route to grow ensembles of self-catalyzed GaAs nanowires with a remarkably narrow statistical distribution of lengths on natively oxidized Si(111) substrates. The fitting of the nanowire length distribution (LD) with a theoretical model reveals that the key requirements for narrow LDs are the synchronized nucleation of all nanowires on the substrate and the absence of beam shadowing from adjacent nanowires. Both requirements are fulfilled by controlling the size and number density of the openings in SiO _x , where the nanowires nucleate. This is achieved by using a pre-growth treatment of the substrate with Ga droplets and two annealing cycles. The narrowest nanowire LDs are markedly sub-Poissonian, which validates the theoretical predictions about temporally anti-correlated nucleation events in individual nanowires, the so-called nucleation antibunching. Finally, the reproducibility of sub-Poissonian LDs attests the reliability of our growth method.

Tuning the morphology of self-assisted GaP nanowires

Patterned arrays of self-assisted GaP nanowires (NWs) were grown on a Si substrate by gas source molecular beam epitaxy using various V/III flux ratios from 1-6, and various pitches from 360-1000 nm. As the V/III flux ratio was increased from 1-6, the NWs showed a change in morphology from outward tapering to straight, and eventually to inward tapering. The morphologies of the self-assisted GaP NWs are well described by a simple kinetic equation for the NW radius versus the position along the NW axis. The most important growth parameter that governs the NW morphology is the V/III flux ratio. Sharpened NWs with a stable radius equal to only 12 nm at a V/III flux of 6 were achieved, demonstrating their suitability for the insertion of quantum dots.