Kinetic modeling of interfacial abruptness in axial nanowire heterostructures

Kinetic modeling of the formation of axial III-V nanowire heterostructures grown by the Au-catalyzed vapor-liquid-solid method is presented. The method is based on a combination of kinetic growth theory for different binaries at the liquid-solid interface and thermodynamics of ternary liquid and solid alloys. Non-stationary treatment of the compositional change obtained by swapping material fluxes allows us to compute the interfacial abruptness across nanowire heterostructures and leads to the following results. At high enough supersaturation in liquid, there is no segregation of dissimilar binaries in solid even for materials with strong interactions between III and V pairs, such as InGaAs. This leads to the suppression of the miscibility gaps by kinetic factors. Increasing the Au concentration widens the heterointerface at low Au content and narrows it at high Au content in a catalyst droplet. The model fits quite well the data on the compositional profiles across nanowire heterostructures based on both group III and group V interchange. Very sharp heterointerfaces in double of InAs/InP/InAs nanowire heterostructures is explained by a reduced reservoir effect due to low solubility of group V elements in liquid.

Formation of wurtzite sections in self-catalyzed GaP nanowires by droplet consumption

Wurtzite GaP nanowires are interesting for the direct bandgap engineering and can be used as templates for further growth of hexagonal Si shells. Most wurtzite GaP nanowires have previously been obtained with Au catalysts. Here, we show that long (∼500 nm) wurtzite sections are formed in the top parts of self-catalyzed GaP nanowires grown by molecular beam epitaxy on Si(111) substrates in the droplet consumption stage, which is achieved by abruptly increasing the atomic V/III flux ratio from 2 to 3. We investigate the temperature dependence of the length of wurtzite sections and show that the longest sections are obtained at 610 °C. A supporting model explains the observed trends using a phase diagram of GaP nanowires, where the wurtzite phase is formed within a certain range of the droplet contact angles. The optimal growth temperature for growing wurtzite nanowires corresponds to the largest diffusion length of Ga adatoms, which helps to maintain the required contact angle for the longest time.

Improving the yield of GaAs nanowires on silicon by Ga pre-deposition

GaAs nanowire (NW) arrays were grown by molecular beam epitaxy using the self-assisted vapor-liquid-solid method with Ga droplets as seed particles. A Ga pre-deposition step is examined to control NW yield and diameter. The NW yield can be increased with suitable duration of a Ga pre-deposition step but is highly dependent on oxide hole diameter and surface conditions. The NW diameter was determined by vapor-solid growth on the NW sidewalls, rather than Ga pre-deposition. The maximum NW yield with a Ga pre-deposition step was very close to 100%, established at shorter Ga deposition durations and for larger holes. This trend was explained within a model where maximum yield is obtained when the Ga droplet volume approximately equals the hole volume.

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.

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.

Modeling selective-area growth of InAsSb nanowires

An analytical growth model is presented to explain the influence of antimony fractional flux on the morphology evolution of catalyst-free InAs_1-x Sb _x semiconductor nanowires grown by the selective-area vapor-solid mechanism on a Si (111) substrate by molecular beam epitaxy. Increasing Sb fractional flux promoted radial growth and suppressed axial growth, resulting in 'nano-disks'. This behavior is explained by a model of indium adatom diffusion along nanowire facets.

Quasi One-Dimensional Metal-Semiconductor Heterostructures

The band offsets occurring at the abrupt heterointerfaces of suitable material combinations offer a powerful design tool for high performance or even new kinds of devices. Because of a large variety of applications for metal-semiconductor heterostructures and the promise of low-dimensional systems to present exceptional device characteristics, nanowire heterostructures gained particular interest over the past decade. However, compared to those achieved by mature two-dimensional processing techniques, quasi one-dimensional (1D) heterostructures often suffer from low interface and crystalline quality. For the GaAs-Au system, we demonstrate exemplarily a new approach to generate epitaxial and single crystalline metal-semiconductor nanowire heterostructures with atomically sharp interfaces using standard semiconductor processing techniques. Spatially resolved Raman measurements exclude any significant strain at the lattice mismatched metal-semiconductor heterojunction. On the basis of experimental results and simulation work, a novel self-assembled mechanism is demonstrated which yields one-step reconfiguration of a semiconductor-metal core-shell nanowire to a quasi 1D axially stacked heterostructure via flash lamp annealing. Transmission electron microscopy imaging and electrical characterization confirm the high interface quality resulting in the lowest Schottky barrier for the GaAs-Au system reported to date. Without limiting the generality, this novel approach will open up new opportunities in the syntheses of other metal-semiconductor nanowire heterostructures and thus facilitate the research of high-quality interfaces in metal-semiconductor nanocontacts.

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.

Three-fold Symmetric Doping Mechanism in GaAs Nanowires

A new dopant incorporation mechanism in Ga-assisted GaAs nanowires grown by molecular beam epitaxy is reported. Off-axis electron holography revealed that p-type Be dopants introduced in situ during molecular beam epitaxy growth of the nanowires were distributed inhomogeneously in the nanowire cross-section, perpendicular to the growth direction. The active dopants showed a remarkable azimuthal distribution along the (111)B flat top of the nanowires, which is attributed to preferred incorporation along 3-fold symmetric truncated facets under the Ga droplet. A diffusion model is presented to explain the unique radial and azimuthal variation of the active dopants in the GaAs nanowires.

Exactly solvable model for cluster-size distribution in a closed system

We obtain an exact solution for the cluster-size distributions in a closed system described by nonlinear rate equations for irreversible homogeneous growth with size-linear agglomeration rates of the form K_{s}=D(a+s-1) for all s≥1, where D is the diffusion coefficient, s is the size, and a is a positive constant. The size spectrum is given by the Pólya distribution times a factor that normalizes the first moment of the distribution to unity and zeroes out the monomer concentration at t→∞. We show that the a value sets a maximum mean size that equals e for large a and tends to infinity only when a→0. The size distributions are monotonically decreasing in the initial stage, converting to different monomodal shapes with a maximum at s=2 in the course of growth. The variance of the distribution is narrower than Poissonian at large a and broader than Poissonian at small a, with the threshold occurring at a≅1. In most cases, the sizes present in the distributions are small and hence can hardly be described by continuum equations.

Length distributions of Au-catalyzed and In-catalyzed InAs nanowires

We present experimental data on the length distributions of InAs nanowires grown by chemical beam epitaxy with Au catalyst nanoparticles obtained by thermal dewetting of Au film, Au colloidal nanoparticles and In droplets. Poissonian length distributions are observed in the first case. Au colloidal nanoparticles produce broader and asymmetric length distributions of InAs nanowires. However, the distributions can be strongly narrowed by removing the high temperature annealing step. The length distributions for the In-catalyzed growth are instead very broad. We develop a generic model that is capable of describing the observed behaviors by accounting for both the incubation time for nanowire growth and secondary nucleation of In droplets. These results allow us to formulate some general recipes for obtaining more uniform length distributions of III-V nanowires.

Conditions for high yield of selective-area epitaxy InAs nanowires on SiO x /Si(111) substrates

Experimental data and a model are presented which define the boundary values of V/III flux ratio and growth temperature for droplet-assisted nucleation of InAs semiconductor nanowires in selective-area epitaxy on SiO(x)/Si (111) substrates by molecular beam epitaxy. Within these boundaries, the substrate receives a balanced flux of group III and V materials allowing the growth of vertically oriented nanowires as compared to the formation of droplets or crystallites.

Understanding the growth and composition evolution of gold-seeded ternary InGaAs nanowires

InGaAs nanowires offer great promise in fundamental studies of ternary compound semiconductors with variable composition and opens up a wide range of applications due to their bandgap tunability and high carrier mobility. Here, we report a study on the growth of Au-seeded InGaAs nanowires by metal-organic vapour phase epitaxy and present a model to explain the mechanisms that govern the growth and composition evolution in ternary III-V nanowires. The model allows us to further understand the limitations on the growth rate and incorporation of the two group III species imposed by the deposition conditions and some intrinsic properties of the material transport and nucleation. Within the model, the evolution of InGaAs nanowire growth rate and composition with particle size, temperature and V/III ratio is described and correlates very well with experimental findings. The understanding gained in this study should be useful for the controlled fabrication of tunable ternary nanowires for various applications.

Catalyst-free growth of InAs nanowires on Si (111) by CBE

We investigate a growth mechanism which allows for the fabrication of catalyst-free InAs nanowires on Si (111) substrates by chemical beam epitaxy. Our growth protocol consists of successive low-temperature (LT) nucleation and high-temperature growth steps. This method produces non-tapered InAs nanowires with controllable length and diameter. We show that InAs nanowires evolve from the islands formed during the LT nucleation step and grow truly catalyst-free, without any indium droplets at the tip. The impact of different growth parameters on the nanowire morphology is presented. In particular, good control over nanowire aspect ratio is demonstrated. A better understanding of the growth process is obtained through the development of a theoretical model combining the diffusion-induced growth scenario with some specific features of the catalyst-free growth mechanism, along with the analysis of the V/III flow ratio influencing material incorporation. As a result, we perform a full mapping of the nanowire morphology versus growth parameters which provides useful general guidelines on the self-induced formation of III-V nanowires on silicon.

Self-Equilibration of the Diameter of Ga-Catalyzed GaAs Nanowires

Designing strategies to reach monodispersity in fabrication of semiconductor nanowire ensembles is essential for numerous applications. When Ga-catalyzed GaAs nanowire arrays are grown by molecular beam epitaxy with help of droplet-engineering, we observe a significant narrowing of the diameter distribution of the final nanowire array with respect to the size distribution of the initial Ga droplets. Considering that the droplet serves as a nonequilibrium reservoir of a group III metal, we develop a model that demonstrates a self-equilibration effect on the droplet size in self-catalyzed III-V nanowires. This effect leads to arrays of nanowires with a high degree of uniformity regardless of the initial conditions, while the stationary diameter can be further finely tuned by varying the spacing of the array pitch on patterned Si substrates.

Mono- and polynucleation, atomistic growth, and crystal phase of III-V nanowires under varying group V flow

We present a refined model for the vapor-liquid-solid growth and crystal structure of Au-catalyzed III-V nanowires, which revisits several assumptions used so far and is capable of describing the transition from mononuclear to polynuclear regime and ultimately to regular atomistic growth. We construct the crystal phase diagrams and calculate the wurtzite percentages, elongation rates, critical sizes, and polynucleation thresholds of Au-catalyzed GaAs nanowires depending on the As flow. We find a non-monotonic dependence of the crystal phase on the group V flow, with the zincblende structure being preferred at low and high group V flows and the wurtzite structure forming at intermediate group V flows. This correlates with most of the available experimental data. Finally, we discuss the atomistic growth picture which yields zincblende crystal structure and should be very advantageous for fabrication of ternary III-V nanowires with well-controlled composition and heterointerfaces.

Analytic scaling function for island-size distributions

We obtain an explicit solution for the island-size distribution described by the rate equations for irreversible growth with the simplified capture rates of the form σ(s)(Θ)∝Θ(p)(a+s-1) for all s≥1, where s is the size and Θ is the time-dependent coverage. The intrinsic property of this solution is its scaling form in the continuum limit. The analytic scaling function depends on the two parameters a and p and is capable of describing very dissimilar distribution shapes, both monomodal and monotonically decreasing. The obtained results suggest that the scaling features of the size distributions are closely related to the size linearity of the capture rates. A simple analytic scaling is obtained rigorously here and helps to gain a better theoretical understanding of possible origins of the scaling behavior of the island-size distributions.

Natural scaling of size distributions in homogeneous and heterogeneous rate equations with size-linear capture rates

We obtain exact solutions of the rate equations for homogeneous and heterogeneous irreversible growth models with linear size dependences of the capture rates. In the limit of high ratios of diffusion constant over deposition rate, both solutions yield simple analytical scaling functions with the correct normalizations. These are given by the cumulative distribution function and the probability density function of the gamma-distribution in homogeneous and heterogeneous cases, respectively. Our size distributions depend on the value of the capture rate a in the reaction of joining two mobile monomers A1 (A1 + A1 → A2) or the monomer attachment to the reactive defect B (A1 + B → AB). In homogeneous cases, the size distribution is monotonically decreasing regardless of a. In heterogeneous growth, the distribution is monotonically decreasing when a ≤ 1 and monomodal when a > 1. The obtained solutions describe fairly well the experimental data on the length distributions of Al, Ga, In, and Mn adatom chains on Si(100)-2 × 1 surfaces.

Control of morphology and crystal purity of InP nanowires by variation of phosphine flux during selective area MOMBE

We present experimental results showing how the growth rate, morphology and crystal structure of Au-catalyzed InP nanowires (NWs) fabricated by selective area metal organic molecular beam epitaxy can be tuned by the growth parameters: temperature and phosphine flux. The InP NWs with 20-65 nm diameters are grown at temperatures of 420 and 480 °C with the PH3 flow varying from 1 to 9 sccm. The NW tapering is suppressed at a higher temperature, while pure wurtzite crystal structure is preferred at higher phosphine flows. Therefore, by combining high temperature and high phosphine flux, we are able to fabricate non-tapered and stacking fault-free InP NWs with the quality that other methods rarely achieve. We also develop a model for NW growth and crystal structure which explains fairly well the observed experimental tendencies.

Framed carbon nanostructures: synthesis and applications in functional SPM tips

We present a synthesis method to fabricate framed carbon-based nanostructures having highly anisotropic shapes, in particular, the nanofork and nanoscalpel structures which are obtained systematically under optimized growth conditions. A theoretical model is developed to explain the formation of such nanostructures on Si cantilevers and W etched wires exposed to a focused electron beam. We then demonstrate the potentials of these nanostructures as functional tips for scanning probe microscopy. Owing to their anisotropic shapes, such tips can be very useful for nanolithography, nanosurgery of biological objects, and precise manipulation with surface particles. Overall, our method provides a simple and robust way to produce functional scanning probe microscopy tips with variable shapes and enhanced capabilities for different applications compared to standard cantilevers.

Rate equation approach to understanding the ion-catalyzed formation of peptides

The salt-induced peptide formation is important for assessing and approaching schemes of molecular evolution. Here, we present experimental data and an exactly solvable kinetic model describing the linear polymerization of L-glutamic amino acid in water solutions with different concentrations of KCl and NaCl. The length distributions of peptides are well fitted by the model. Strikingly, we find that KCl considerably enhances the peptide yield, while NaCl does not show any catalytic effect in most cases under our experimental conditions. The greater catalytic effect of potassium ions is entirely interpreted by one and single parameter, the polymerization rate constant that depends on the concentration of a given salt in the reaction mixture. We deduce numeric estimates for the rate constant at different concentrations of the ions and show that it is always larger for KCl. This leads to an exponential increase of the potassium- to sodium-catalyzed peptide concentration ratio with length. Our results show that the ion-catalyzed peptides have a higher probability to emerge in excess potassium rather than in sodium-rich water solutions.

The nucleation site selection of vapour-liquid-solid nanowires

Adopting twinning superlattice nanowires and III-V nanowires with [112¯] sidewalls, whose cross-sections are irregular hexagons, the precise catalyst droplet surface area variation for the calculation of the nuclei formation enthalpy are obtained for possible nucleation positions at the nanowire growth front. Regular nanowires with hexagonal cross-section are also calculated. The nucleation site selection rules are drawn from the fact that the favorable site corresponds to a smaller nucleation barrier, which is not deducible from the spherical-cap shaped droplet approximation. The influence of droplet volume and nanowire geometry on the nucleation site selection should also be taken into consideration when calculations of the nanowire nucleation properties are involved.

Narrowing the length distribution of Ge nanowires

Synthesis of nanostructures of uniform size is fundamental because the size distribution directly affects their physical properties. We present experimental data demonstrating a narrowing effect on the length distribution of Ge nanowires synthesized by the Au-catalyzed molecular beam epitaxy on Si substrates. A theoretical model is developed that is capable of describing this puzzling behavior. It is demonstrated that the direction of the diffusion flux of sidewall adatoms is size dependent and has a major effect on the growth rate of differently sized nanowires. We also show that there exists a fundamental limitation on the maximum nanowire length that can be achieved by molecular beam epitaxy where the direction of the beam is close to the growth axis.

Modeling of InAs-InSb nanowires grown by Au-assisted chemical beam epitaxy

Interesting phenomena during the Au-assisted chemical beam epitaxy of InAs-InSb nanowire heterostructures have been observed and interpreted within the framework of a theoretical model. An unusual, non-monotonous diameter dependence of the InSb nanowire growth rate is demonstrated experimentally within a range of deposition conditions. Such a behavior is explained by competition between the Gibbs-Thomson effect and different diffusion-induced material fluxes. Theoretical fits to the experimental data obtained at different flux pressures of In and Sb precursors allow us to deduce some important kinetic coefficients. Furthermore, we discuss why the InAs nanowire stem forms in the wurtzite phase while the upper InSb part has a pure zinc blende crystal structure. It is hypothesized that the 30° angular rotation of nanowire when passing from InAs to the InSb part is driven by the lowest surface energy of (1100) wurtzite and (110) zinc blende facets.

New mode of vapor-liquid-solid nanowire growth

We report on the new mode of the vapor-liquid-solid nanowire growth with a droplet wetting the sidewalls and surrounding the nanowire rather than resting on its top. It is shown theoretically that such an unusual configuration happens when the growth is catalyzed by a lower surface energy metal. A model of a nonspherical elongated droplet shape in the wetting case is developed. Theoretical predictions are compared to the experimental data on the Ga-catalyzed growth of GaAs nanowires by molecular beam epitaxy. In particular, it is demonstrated that the experimentally observed droplet shape is indeed nonspherical. The new VLS mode has a major impact on the crystal structure of GaAs nanowires, helping to avoid the uncontrolled zinc blende-wurtzite polytylism under optimized growth conditions. Since the triple phase line nucleation is suppressed on surface energetic grounds, all nanowires acquire pure zinc blende phase along the entire length, as demonstrated by the structural studies of our GaAs nanowires.

Photoluminescence properties of InAs nanowires grown on GaAs and Si substrates

We report the first photoluminescence (PL) characterization of InAs nanowires (NWs). The InAs NWs were grown on GaAs(111) B and Si(111) substrates using the Au-assisted molecular beam epitaxy (MBE) growth technique or metal-organic chemical vapor deposition (MOCVD). We compared the PL response of four samples grown under different conditions using MBE or MOCVD. High-resolution transmission electron microscopy (HRTEM) and selected area electron diffraction (SAED) patterns were utilized to determine the crystal structure and growth directions of the NWs to relate PL features to NW structural parameters. We observed mainly three PL peaks which were below, near and above InAs bandgaps, respectively. Temperature and excitation intensity dependence PL measurements were also performed to help elucidate the origins of the PL peaks of NWs. Of particular interest was a band-edge emission peak that was blue-shifted due to quantization effects of the InAs NWs, as confirmed by our calculation.

Growth of Inclined GaAs Nanowires by Molecular Beam Epitaxy: Theory and Experiment

The growth of inclined GaAs nanowires (NWs) during molecular beam epitaxy (MBE) on the rotating substrates is studied. The growth model provides explicitly the NW length as a function of radius, supersaturations, diffusion lengths and the tilt angle. Growth experiments are carried out on the GaAs(211)A and GaAs(111)B substrates. It is found that 20° inclined NWs are two times longer in average, which is explained by a larger impingement rate on their sidewalls. We find that the effective diffusion length at 550°C amounts to 12 nm for the surface adatoms and is more than 5,000 nm for the sidewall adatoms. Supersaturations of surface and sidewall adatoms are also estimated. The obtained results show the importance of sidewall adatoms in the MBE growth of NWs, neglected in a number of earlier studies.

Shape modification of III-V nanowires: the role of nucleation on sidewalls

The effect of sidewall nucleation on nanowire morphology is studied theoretically. The model provides a semiquantitative description of nanowire radius as a function of its length and the distance from the surface. It is demonstrated that the wire shape critically depends on the diffusion flux of adatoms from the substrate and on the rate of direct impingement to the sidewalls. At high diffusion flux the wire shape is cylindrical. A decrease of diffusion from the surface leads to the onset of nucleation on the sidewalls resulting in the lateral extension and in the reduction of wire length. The wire shape changes from cylindrical to conical, because the supersaturation of adatoms driving the nucleation is higher at the wire foot than at the top. It is shown that the shape modification becomes pronounced at low growth temperatures. Theoretical results are used to model the experimentally observed shapes of GaAs and GaP wires, grown by Au-assisted molecular beam epitaxy at different temperatures.

Theoretical analysis of the vapor-liquid-solid mechanism of nanowire growth during molecular beam epitaxy

A theoretical model of nanowire formation by the vapor-liquid-solid mechanism during molecular beam epitaxy and related growth techniques is presented. The model unifies the conventional adsorption-induced model, the diffusion-induced model, and the model of nucleation-mediated growth on the liquid-solid interface. The concentration of deposit atoms in the liquid alloy, the nanowire diameter, and all other characteristics of the growth process are treated dynamically as functions of the growth time. The model provides theoretical length-diameter dependences of nanowires and the dependence of the nanowire length on the technologically controlled growth conditions, such as the surface temperature and the deposition thickness. In particular, it is shown that the length-diameter curves of nanowires might convert from decreasing to increasing at a certain critical diameter and that the nanowires taper when their length becomes comparable with the adatom diffusion length on the sidewalls. The theoretical dependence of the nanowire morphology on its lateral size and length and on the surface temperature are compared to the available experimental data obtained recently for Si and nanowires.