High Layer Uniformity of Two-Dimensional Materials Demonstrated Surprisingly from Broad Features in Surface Electron Diffraction.

Paradoxically, a very broad diffraction background, named the bell-shaped-component (BSC), has been established as a feature of graphene growth. Recent diffraction studies as a function of electron energy have shown that the BSC is not related to scattering interference. Here, additional experiments are carried out as a function of temperature over the range in which single-layer graphene (SLG) grows. Quantitative fitting of the profiles shows that the BSC follows the increase of the Gr(10) spot, proving directly that the BSC indicates high-quality graphene. Additional metal deposition experiments provide more information about the BSC. The BSC is insensitive to metal deposition, and it increases with metal intercalation, because a more uniform interface forms between graphene and SiC. These experiments support the conclusion that the BSC originates from electron confinement within SLG, and surprisingly, it is an excellent measure of graphene uniformity.

Correlations between In Situ Conductivity and Uniform-Height Epitaxial Morphology in Pb/Si(111)-(7×7).

The growth of Pb on Si(111)-(7×7) at temperatures from 72 to 201 K has been investigated using in situ electrical resistivity measurements and scanning tunneling microscopy. For temperatures T>140 K the specific resistivity ρ(θ) versus coverage θ shows an unusual "hump," instead of the expected monotonic decrease with θ. This novel result correlates well with the formation of uniform height eight-layer Pb islands and the superdiffusive motion of the wetting layer, despite the low temperatures. A model of the film resistivity as two resistors in series, the amorphous wetting layer and the crystalline islands, explains quantitatively the resistivity dependence on θ.

Nonclassical "explosive" nucleation in Pb/Si(111) at low temperatures.

Classically, the onset of nucleation is defined in terms of a critical cluster of the condensed phase, which forms from the gradual aggregation of randomly diffusing adatoms. Experiments in Pb/Si(111) at low temperature have discovered a dramatically different type of nucleation, with perfect crystalline islands emerging "explosively" out of the compressed wetting layer after a critical coverage Θ_{c}=1.22 ML is reached. The unexpectedly high island growth rates, the directional correlations in the growth of neighboring islands and the persistence in time of where mass is added in individual islands, suggest that nucleation is a result of the highly coherent motion of the wetting layer, over mesoscopic distances.

Structural transformations in Pb/Si(111) phases induced by C60 adsorption.

Structural transformations at the Pb/Si(111) surface occurring upon C60 adsorption onto Pb/Si(111)1 × 1 phase at room temperature and Pb/Si(111)[Formula: see text] at low temperatures between 30 and 210 K, have been studied using scanning tunneling microscopy and low-energy electron diffraction observations. Typically, C60 fullerenes agglomerate into random molecular islands nucleated at the surface defects. C60 island formation is accompanied by expelling Pb atoms to the surrounding surface area where more dense Pb/Si(111) phases form. Productivity of C60-induced expelling of Pb atoms is controlled by surface defects and is suppressed dramatically when regular ('crystalline') C60 islands self-assemble at the defect-free Pb/Si(111) surface. When Pb atoms are ejected by the random C60 islands, extended structural transformations involving reordering of numerous Pb atoms are fully completed at the surface within the shortest possible time (a few dozen seconds) to reapproach and image the surface after C60 deposition. Estimations show that the observed transformations cannot be controlled by random walk diffusion of Pb adatoms, which implies a highly correlated motion of the Pb atom displacements within the layer.

Nucleation on a stepped surface with an Ehrlich-Schwöbel barrier.

During deposition on a stepped surface the growth mode depends on the conditions such as temperature T, deposition rate F and width of the terraces w. In this work we studied the influence of all the above mentioned characteristics using the kinetic Monte Carlo (kMC) technique. We concentrated on the conditions on the terrace at the moment of the first nucleation. The critical density of monomers for nucleation ηm decreases with the width of the terrace and the nucleation starts at surprisingly low densities of monomers. We tested several definitions of the critical width for nucleation wc used in various articles in the past and we compared our results with results of the analytical steady-state mean-field model (Ranguelov and Altman 2007 Phys. Rev. B 75 245419). To check how the simplified assumption about the steady-state regime during deposition influences the resulting dependence of wc =/~ (D/F)(κ), we set and also solved a time-dependent analytical model. This analytical model as well as kMC predict that wc =/~ (D/F)(1/5). kMC simulation also shows that the Ehrlich-Schwöbel barrier has only limited influence on the nucleation on the stepped surface at conditions close to the nucleation regime. For all widths of terraces there is a critical value of the Ehrlich-Schwöbel barrier ΔE(c)(ES)/k(B)T ~ 7.3 (ΔE(c)(ES) ~0.11 eV at T = 175 K), and only below this critical value does the Ehrlich-Schwöbel barrier affect the final value of the density of nuclei. The results of the kMC are summarized in a semi-empirical analytical formula which describes the dependence of the step-flow growth and nucleation on the terrace width w, diffusion coefficient D and deposition rate F. In our simulations we tested two models of the stepped surface with different thicknesses of the step, both with an Ehrlich-Schwöbel barrier on the edge of the terrace.

Growth of fcc(111) Dy multi-height islands on 6H-SiC(0001) graphene.

Graphene based spintronic devices require an understanding of the growth of magnetic metals. Rare earth metals have large bulk magnetic moments so they are good candidates for such applications, and it is important to identify their growth mode. Dysprosium was deposited on epitaxial graphene, prepared by thermally annealing 6H-SiC(0001). The majority of the grown islands have triangular instead of hexagonal shapes. This is observed both for single layer islands nucleating at the top of incomplete islands and for fully completed multi-height islands. We analyze the island shape distribution and stacking sequence of successively grown islands to deduce that the Dy islands have fcc(111) structure, and that the triangular shapes result from asymmetric barriers to corner crossing.

Superdiffusive motion of the Pb wetting layer on the Si(111) surface.

Mass transport in the Pb wetting layer on the Si(111) surface is investigated by observing nonequilibrium coverage profile evolution with low energy electron microscopy and microlow energy electron diffraction. Equilibration of an initial coverage step profile occurs by the exchange of mass between oppositely directed steep coverage gradients that each move with unperturbed shape. The bifurcation of the initial profile, the shape of the profile between the two moving edges, and the time dependence of equilibration are all at odds with expectations for classical diffusion behavior. These observations signal a very unusual coverage dependence of diffusion or may even reveal an exceptional collective superdiffusive mechanism.

High island densities and long range repulsive interactions: Fe on epitaxial graphene.

The understanding of metal nucleation on graphene is essential for promising future applications, especially of magnetic metals which can be used in spintronics or computer storage media. A common method to study the grown morphology is to measure the nucleated island density n as a function of growth parameters. Surprisingly, the growth of Fe on graphene is found to be unusual because it does not follow classical nucleation: n is unexpectedtly high, it increases continuously with the deposited amount θ and shows no temperature dependence. These unusual results indicate the presence of long range repulsive interactions. Kinetic Monte Carlo simulations and density functional theory calculations support this conclusion. In addition to answering an outstanding question in epitaxial growth, i.e., to find systems where long range interactions are present, the high density of magnetic islands, tunable with θ, is of interest for nanomagnetism applications.

Femtosecond population inversion and stimulated emission of dense Dirac fermions in graphene.

We show that strongly photoexcited graphene monolayers with 35 fs pulses quasi-instantaneously build up a broadband, inverted Dirac fermion population. Optical gain emerges and directly manifests itself via a negative conductivity at the near-infrared region for the first 200 fs, where stimulated emission completely compensates absorption loss in the graphene layer. Our experiment-theory comparison with two distinct electron and hole chemical potentials reproduce absorption saturation and gain at 40 fs, revealing, particularly, the evolution of the transient state from a hot classical gas to a dense quantum fluid with increasing the photoexcitation.

Metals on graphene: correlation between adatom adsorption behavior and growth morphology.

We present a systematic study of metal adatom adsorption on graphene by ab initio calculations. The calculations cover alkali metals, sp-simple metals, 3d and group 10 transition metals, noble metals, as well as rare earth metals. The correlation between the adatom adsorption properties and the growth morphology of the metals on graphene is also investigated. We show that the growth morphology is related to the ratio of the metal adsorption energy to its bulk cohesive energy (E(a)/E(c)) and the diffusion barrier (ΔE) of the metal adatom on graphene. Charge transfer, electric dipole and magnetic moments, and graphene lattice distortion induced by metal adsorption would also affect the growth morphologies of the metal islands. We also show that most of the metal nanostructures on graphene would be thermally stable against coarsening.

Lead growth on Si(111) surfaces reconstructed by indium.

We study the Pb growth on both √3 × âˆš3-In and 4 × 1-In reconstructed Si(111) surfaces at room and low temperature (160 K). The study takes place with complementary techniques, to investigate the role of the substrate reconstruction and temperature in determining the growth mode of Pb. Specifically, we focus on the correlation between the growth morphology and the electronic structure of the Pb films. The information is obtained by using Auger electron spectroscopy, low energy electron diffraction, soft x-ray photoelectron spectroscopy, scanning tunneling microscopy and spot profile analysis-low energy electron diffraction. The results show that, at low temperature and coverage ≤12 ML on the Si(111)√3 × âˆš3-In surface, Pb does not alter the initial semiconducting character of the substrate and three-dimensional Pb islands with poor crystallinity are grown on a wetting layer. On the other hand, for the same coverage range, Pb growth on the Si(111)4 × 1-In surface results in metallic Pb(111) crystalline islands after the completion of a double incomplete wetting layer. In addition, the bond arrangement of the adatoms is studied, confirming that In adatoms interact more strongly with the silicon substrate than the Pb ones. This promotes a stronger Pb-Pb interaction and enhances metallization. The onset of the metallization is correlated with the amount of pre-deposited In on the Si(111) surface. The decoupling of the Pb film from the 4 × 1-In interface can also explain the unusual thermal stability of the uniform height islands observed on this interface. The formation of these Pb islands is driven by quantum size effects. Finally, the different results of Pb growth on the two reconstructed surfaces confirm the importance of the interface, and also that the growth morphology, as well as the electronic structure of the Pb film can be tuned with the initial substrate reconstruction.

Nucleation and growth of Ag islands on the (√3 × âˆš3)R30° phase of Ag on Si(111).

We use scanning tunneling microscopy to measure densities and characteristics of Ag islands that form on the (√3 × âˆš3)R30°-Ag phase on Si(111), as a function of deposition temperature. Nucleation theory predicts that the logarithm of island density varies linearly with inverse deposition temperature. The data show two linear regimes. At 50-125 K, islands are relatively small, and island density decreases only slightly with increasing temperature. At 180-250 K, islands are larger and polycrystalline, and island density decreases strongly with increasing temperature. At 300 K, Ag atoms can travel for distances of the order of 1 µm. Assuming that Ag diffusion occurs via thermally activated motion of single atoms between adjacent sites, the data can be explained as follows. At 50-125 K, the island density does not follow conventional Arrhenius scaling due to limited mobility and a consequent breakdown of the steady-state condition for the adatom density. At ∼ 115-125 K, a transition to conventional Arrhenius scaling with critical nucleus size (i = 1) begins, and at 180-250 K, i > 1 prevails. The transition points indicate a diffusion barrier of 0.20-0.23 eV and a pairwise Ag-Ag bond strength of 0.14 eV. These energy values lead to an estimate of i≈3-4 in the regime 180-250 K, where island density varies strongly with temperature.

2D nucleation limited by slow diffusion.

We extend a standard theory of second-layer nucleation in the regime of low temperature, where the diffusion is the limiting process. The theory takes into consideration the fluctuations of the adatoms and the distribution of stable clusters on a surface, and yields an expression for the nucleation rate and time evolution of the density of stable clusters. When diffusion is slow, the fluctuations of the monomer distribution play an important role and results differ qualitatively and quantitatively from those obtained using the standard rate-equation approach to nucleation. We argue that in this case the standard theory fails because slow diffusion delays nucleation and the nucleation rate depends on the fluctuations of interatomic distances. It is shown that the final density of stable clusters depends on the fluctuations of the monomer and stable clusters distribution and can be even independent of the deposition rate, as was experimentally observed at low temperatures.

Probing the buried Pb/Si(111) interface with SPA LEED and STM on Si(111)-Pbα√3×√3.

High resolution spot profile analysis low energy electron diffraction (SPA-LEED) and variable temperature scanning tunneling microscopy (STM) have been used to observe the growth of Pb on the Pb/Si(111)-α√3×√3 phase, which is driven by quantum size effects (QSE). A change in the rotation of the Pb grown islands with respect to the Si substrate has been observed with increasing coverage θ. At lower coverage, separated two-step islands are grown and are aligned with the [110] axis of the substrate. With increasing coverage above 1.5 ML, of the islands coalesce and form a bilayer, with additional islands grown on top. The preferred Pb island orientation changes to 5.6° with respect to the [110] direction. These changes at the metal/semiconductor buried interface are obtained both with SPA LEED and STM as changes to the period of the Moire pattern. The method of analysis of the corrugation period and rotation angle of the Moire pattern measured with diffraction and STM can be applied to obtain the structure of buried metal/substrate interfaces in other epitaxial systems.

Strong metal adatom-substrate interaction of Gd and Fe with graphene.

Graphene is a unique 2D system of confined electrons with an unusual electronic structure of two inverted Dirac cones touching at a single point, with high electron mobility and promising microelectronics applications. The clean system has been studied extensively, but metal adsorption studies in controlled experiments have been limited; such experiments are important to grow uniform metallic films, metal contacts, carrier doping, etc. Two non-free-electron-like metals (rare earth Gd and transition metal Fe) were grown epitaxially on graphene as a function of temperature T and coverage θ. By measuring the nucleated island density and its variation with growth conditions, information about the metal-graphene interaction (terrace diffusion, detachment energy) is extracted. The nucleated island densities at room temperature (RT) are stable and do not coarsen, at least up to 400 °C, which shows an unusually strong metal-graphene bond; most likely it is a result of C atom rebonding from the pure graphene sp(2) C-C configuration to one of lower energy.

Surface diffusion experiments with STM: equilibrium correlations and non-equilibrium low temperature growth.

Measurements of surface diffusion depend on the state of the system whether the state is equilibrium versus non-equilibrium. Equilibrium experiments carried out in 2-d overlayers measure the collective diffusion coefficient D(c) and can test theoretical predictions in two-dimensional statistical mechanics. Growth experiments typically carried out at low temperatures and/or high flux rates probe systems under non-equilibrium conditions where novel diffusion mechanisms can potentially exist. The use of STM to study both types of measurements is discussed. D(c) can be measured from the autocorrelation of time-dependent tunneling current fluctuations generated by atom motion in and out of the tunneling area. Controlled experiments as function of temperature, coverage and tip-surface separation confirm that the signal is diffusive. For growth experiments the unusually uniform height island (for Pb/Si(111) In/Si(111)) has revealed a novel and intriguing type of diffusion at low temperatures that accounts for the high degree of the self organization. By monitoring the evolution of the stable islands out of a mixture of stable and unstable islands the unusual role of the wetting layer surrounding the growing islands is revealed.

Anomalous mass transport in the Pb wetting layer on the Si(111) surface.

The temporal evolution of nonequilibrium coverage profiles in the Pb wetting layer on the Si(111) surface is studied using low energy electron microscopy. The initial coverage step profile propagates rapidly at a constant velocity with an unperturbed shape. A model is proposed that attributes this nonclassical equilibration behavior to the diffusion of thermally generated adatoms on top of the wetting layer. This model can account for the observed convectionlike mass transport, as well as its dramatic dependence on Pb coverage. Such anomalous mass transport is believed to facilitate the remarkably efficient self-organization of uniform Pb quantum island height on the Si(111) surface that was observed previously.

Low-temperature ultrafast mobility in systems with long-range repulsive interactions: Pb/Si(111).

A realization of the numerous phases predicted in systems with long-range repulsive interactions was recently found in Pb/Si(111). Surprisingly, these numerous phases can be grown at low temperatures approximately 40 K over macroscopic distances. This unusual observation can be explained from theoretical calculations of the collective diffusion coefficient D(c) in systems with long-range repulsive interactions. Instead of a gradual dependence of D(c) on coverage, it was found that D(c) has sharp maxima at low temperatures for every stable phase (i.e., for every rational value of the coverage theta=p/q) in agreement with the experiment.

Quantum size effect on the diffusion barriers and growth morphology of Pb/Si(111).

An intriguing growth morphology of Pb islands on a Si(111) surface is observed in our STM experiments: the growth of a Pb layer on Pb islands with unstable heights starts from the periphery and moves towards the center, while the nucleation of the next layer on stable Pb islands starts away from the periphery. Using first-principles total energy calculations, we have studied the diffusion barriers of Pb adatoms on a freestanding Pb(111) film as a function of film thickness. The diffusion barriers are found to be very low (<60 meV), and a bi-layer oscillation due to the quantum size effect (QSE) is observed, with a lower barrier on the odd-layered, relatively unstable Pb films. The diffusion barrier difference between the odd- and even-layered film is as large as 40 meV. The observed unusual growth can be attributed to this big difference in the diffusion barriers due to QSE.

Influence of quantum size effects on island coarsening.

Surface x-ray scattering and scanning-tunneling microscopy experiments reveal novel coarsening behavior of Pb nanocrystals grown on Si(111)-(7 x 7). It is found that quantum size effects lead to the breakdown of the classical Gibbs-Thomson analysis. This is manifested by the lack of scaling of the island densities. In addition, island decay times tau are orders of magnitude faster than expected from the classical analysis and have an unusual dependence on the growth flux F (i.e., tau is approximately 1/F). As a result, a highly monodispersed 7-layer island height distribution is found after coarsening if the islands are grown at high rather than low flux rates. These results have important implications, especially at low temperatures, for the controlled growth and self-organization of nanostructures.