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.

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.

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.

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.

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.

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.