Lattice Steps Research Articles

Atomic events at lattice steps and clusters: a direct view of crystal growth processes

The ability of the field ion microscope to depict individual metal atoms adsorbed on metal surfaces has made it feasible to directly examine the atomic events participating in crystal growth. Of special interest are phenomena occurring at lattice steps, where atoms are incorporated into the crystal. Work to define these phenomena on the atomic level has revealed a variety of processes much larger than anticipated from classical theories of growth. Such studies are briefly surveyed, with special emphasis on the diffusion of adatoms toward steps, their subsequent incorporation, atomic motion along steps, and condensation of atoms from the vapor, both on clusters and on crystal terraces.

New Charge Density Modulations in Confined Regions of Reconstructed Pt(100) Surface

In the narrow regions confined by lattice steps or domain boundaries of the reconstructed Pt(100) surface, new periodic structures have been observed with the scanning tunneling microscopy. These structures correlate well, or are commensurate, with the atomic structure of the original reconstructed surface. They can also be shown to arise from a redistribution of the electronic density of states. Thus, these charge density waves are produced by strongly coupled electrons and phonons, but are enhanced by the quantum confinement effect of the barriers. Such structures can also be induced near a domain boundary due to the strain of artificially created nanometer-size holes. Therefore we believe that coupling originates from the strain relief effect of the system reducing its strain and electronic energy.

Observation of new two-dimensional periodic structures in the confined regions of the reconstructed Pt(100) surface

New 2D periodic structures have been observed by STM in the regions of the reconstructed Pt(100) surface which are confined by domain boundaries or lattice steps. These structures can be seen only in a very narrow energy window near the Fermi level, and they are strongly correlated to the original atomic arrangements of the surface. These structures arise most probably from a modification in the distribution of the electronic density of states which is strongly coupled to the ion cores of the surface to produce a periodic shift in the atomic rearrangements in order to minimize the strain and free energy of the surface.

An FIM and STM study of the dynamical behavior of solid surfaces

Atoms at the surface are by no means static. When the temperature of a solid is increased gradually, surface atoms may start to dissociate from their lattice sites and diffuse on the surface around or slightly above the room temperature. This diffusion involves with single adatoms on terraces and ledge atoms along lattice steps. It may involve with small atomic clusters or even large islands. At a higher temperature, collective effects may become important and step as well as surface roughening, structure phase transitions and collective movements of surface atoms may start to occur. A similar behavior can occur for atoms condensed on the surface. This dynamical behavior of the solid surface can be described by the occurence of a series of elementary atomic processes or steps which are common to different surface phenomena involving the transport and movement of surface atoms. These phenomena include epitaxial growth of thin films, crystal growth, changes of the shape of crystals and surface layers, surface atomic reconstructions, and surface enhanced chemical reactions, etc. We have been studying in atomic details both the mechanisms and energetics of various surface atomic processes using the field ion microscope. Recently we have also started to use the scanning tunneling microscope and molecular dynamics to study the same problem. Our very recent works include finding a new atomic-exchange-displacement mechanism in adatom diffusion on the Ir(001) and the formation as well as two diffusion modes of and Ir-Re dimer-vacancy complex on the Ir(001). We have also measured the dissociation energies of step edge atoms at the Ir(001), binding energies of Ir atoms in kink sites and adsorption sites of the Ir(001) surface, and the formation energies of single- and di-vacancies at the Si(111) (7 × 7) surface etc. Details of these studies can be found in the papers listed in the references below and some of our upcoming papers. These works were done in collaboration with Chonglin Chen, Jiang Liu, C.S. Chang, R.L. Lo and others

Field ion microscope studies of single-atom surface diffusion and cluster nucleation on metal surfaces

After nearly 30 years of research, investigations of surface diffusion and cluster nucleation phenomena with the field ion microscope (FIM) continue to provide new insights into the fundamental aspects of atomic interactions on solid surfaces. In this article I review the experimental procedures used in FIM surface diffusion studies and discuss the results in relation to the atomistics of crystal and epitaxial growth processes. Diffusion parameters for over 20 metal-metal combinations are tabulated and chemical trends associated with the measured values are examined. Experiments and theories leading to the discovery of novel diffusion modes and unexpected cluster configurations are described in detail. The influence of surface defects, such as lattice steps and substitutional impurity atoms, as well as external perturbations, such as chemisorbed atoms and applied electric fields, on the surface diffusion rate and transport mechanism is discussed. Methods to extract quantitative information on a variety of atom-surface, atom-defect, and atom-atom interactions are also described. The article is concluded with a section describing the contributions of various theoretical models to the interpretation of FIM experimental results.

ATOMIC LEVEL STUDIES OF THE DYNAMICS AND DYNAMICAL BEHAVIOR OF SOLID SURFACES

Some of our recent results on the dynamics and dynamical behavior of atoms at metal surfaces are presented. Long range charge density oscillations due to chemisorbed impurities have been observed with the FIM. Two adatoms can interact with each other through mutual perturbation of the surface. This interaction is very weak, and exhibits a small but long range oscillatory tail. Surface self diffusion of adatoms can occur at about 1/10 to 1/5 the melting point of metals. This diffusion occurs by either atomic hopping or by atomic replacement-displacement. Diffusion of ledge atoms along a lattice step can occur at a similar temperature. At about 1/5 the melting point of a metal, dissociation of step edge atoms to terraces can occur and lattice steps can also start to roughen. Energetics of the atomic processes involved can be studied from their temperature dependences of their rates of occurrence and also from the densities of surface defects created. Recent progress in theoretical calculations makes it possible to compare them directly with experimental result, thus gaining insights into the dynamics in the dynamical behavior of metal surfaces.

Diffusion on stepped square surfaces: A Monte Carlo approach.

Adatom diffusion on stepped square lattices has been studied by means of Monte Carlo modeling. Steps consisting of two adjacent rows running in the x direction have been separated by two terrace rows and it has been assumed that one of the step rows is located on the up side and the other on the down side of a lattice step. In order to account for differences between up and down sides of steps, an extra adsorption energy ${\mathit{cphi}}_{\mathrm{st}}$ has been added or subtracted for adatoms on down-side or up-side step rows. Pairwise interaction energies between nearest neighbors ${\mathit{cphi}}_{\mathrm{NN}}$ have also been taken into account. It has been assumed that these couplings are not effective between adatoms on up-side and down-side step sites. At low surface coverages \ensuremath{\theta} and temperatures T, most of the adatoms are trapped by down-side step sites. Both parallel and perpendicular diffusion require detachment from such step sites, and therefore diffusion is almost isotropic. As coverage increases the down-side step sites become highly populated and then act as barriers for perpendicular diffusion. The up-side step sites constitute channels for fast parallel diffusion so that anisotropy increases. In the case of nearest-neighbor repulsion ${\mathit{cphi}}_{\mathrm{NN}}$0 the activation energies for surface diffusion are generally smaller. At low temperatures T\ensuremath{\le}${\mathit{T}}_{\mathit{c}}$c(2\ifmmode\times\else\texttimes\fi{}2) ordered lattice gas domains are observed for \ensuremath{\theta}\ensuremath{\approxeq}0.5 with disordered regions nucleating at step rows in between. The effect of ordering on surface diffusion is described.

Wire-like incorporation of dopant atoms during MBE growth on vicinal GaAs(001) surfaces

The ordered incorporation of dopant atoms by combining lattice step growth on vicinal GaAs(001) surfaces and Si delta(δ)-doping has been studied by real-time reflection high-energy electron diffraction (RHEED) measurements. For Si deposition on 2° toward the (111)Ga plane misoriented surfaces and 0.4° toward the (1 1 1)As plane misoriented surfaces it is shown that the Si atoms arrange themselves preferentially along the step edges in a (3 × 2) structure consisting of an ordered array of Si dimers. For Si concentrations not exceeding substantially the amount expected to be attached at the step edges the GaAs growth can be continued at reduced substrate temperature without adverse effects on the growth front. By pulsed δ-doping an unusual high concentration of Si atoms can be incorporated as donors on Ga sites.

Cone- and wedge-gated field emitter diode and microtriode modeling

Two kinds of vertical-type gated field emission diodes (GFED) and field emission microtriodes (FEMT) are modeled and their performances compared, one based on cone emitters (CE) and the other based on wedge emitters (WE). The emitters have parabolic shape. The CE and WE structure basal areas are chosen to be the same, allowing extension of the results to GFED and FEMT arrays. The planar Fowler-Nordheim (FN) current density-electric field J( E) relationship is assumed to be valid. The current I is obtained by integration of J over the emitter's surface. No “field enhancement” and “area” factors are used. The two-dimensional Laplace equation for the electric potential is solved numerically using a Gauss-Seidel iterative procedure, having as special features: appropriate coordinate systems; a unique lattice for both CE and WE modeling; lattice steps in both directions in geometrical progression; emitters described by lattice points lying on it. The GFED model parameters are: emitter curvature radius R, height h and work function φ, together with the gated anode circular aperture radius r, height H and gate voltage V g. Besides these parameters, the FEMT model includes also as parameters the anode height D and the anode voltage V a. GFED- and FEMT-obtained simulation results refer to the effect of model parameters on the emission current. FEMT modeling results also include transconductance, base resistance, gain, capacitance and cut-off frequency. Several device design suggestions are drawn.

Atom condensation at lattice steps and clusters.

The deposition of individual Ir atoms on an Ir(111) surface with a central iridium cluster on it has been observed in the field ion microscope. Around Ir clusters of both 12 and 59 atoms at [ital T]=20 K there is an empty zone, [similar to]2 nearest-neighbor spacings wide, in which condensed atoms are not found. From quantitative measurements of the distribution of adatoms over the surface it appears that atoms from the vapor striking this region skitter over the surface, even at [ital T][similar to]20 K, and are collected at cluster edges. Atoms from the vapor striking the cluster condense without damage to the cluster.

Energetics of surface atomic processes

The energetics of surface atomic processes such as the binding energy of surface atoms with the substrate, the energy barrier for a surface atom to overcome to displace to a neighbor site and the interaction between two adsorbed atoms or between an adsorbed atom and a lattice step or an impurity atom in the surface layer, etc, can be studied by field ion microscope and time-of-flight atom-probe experiments. We will briefly describe methods of measuring these energies and how some of them are related. In general, the binding energy of an atom with the substrate is of the order of the cohesive energy of the solid, or a few eV. The height of the diffusion barrier for single adsorbed atoms is of the order of several tenths of an eV, or about one tenth the binding energy of the adatom with the substrate. The interaction energy between two adsorbed atoms or between an adatom and a substitutional impurity atom is of the order of a few tens of meV, and is thus another order of magnitude smaller than the diffusion barrier height.

Determination of the surface vibrational amplitude with LEIS

LEIS is used to determine the surface Debye temperature of a Cu(110) single crystal and to estimate the nearest neighbor correlation coefficient from polar angular ion spectra measured at room temperature. It is shown that under well chosen conditions these spectra can be described very well with a three-particle model. In addition, an estimate of the number of lattice defects and steps is obtained.

Determination of the surface debye temperature with LEIS

LEIS is used to determine the surface Debye temperature from room temperature polar angular ion spectra. It is shown that under the right conditions these spectra can be described very well with a three particle model. Furthermore an estimate of the number of lattice defects and steps is given.

Lattice-gas automata: A model for the simulation of dispersion phenomena

The dispersion of a tracer in two-dimensional (2-D) parallel flow between two parallel plates has been studied numerically using a lattice-gas model with two different species of particles. After a stepwise change of concentration at one end of the model, the tracer distribution in the flow evolves theoretically, as predicted, toward a Gaussian profile in a time lapse in agreement with the predictions of the Taylor model. The mean square width of the front increases linearly with time after the stabilization period, as required for a diffusive spreading process. The longitudinal dispersion coefficient D∥ has been determined in a range of Peclet number values Pe between 4.3 and 35.4. It varies as the square of the velocity, in agreement with the Taylor–Aris model; the molecular diffusion coefficient value (Dm=0.62 in lattice and simulation step units) obtained from the proportionality coefficient is in good agreement with the values obtained by other independent methods.

Generating function methods for macromolecules at surfaces. II. One molecule between two planes

The configuration statistics for a macromolecule that is sandwiched between and either repelled or adsorbed by a pair of plane parallel surfaces are developed by means of a generating function technique. The theory is based on our previous work [J. Chem. Phys. 85, 5299 (1986)] on the problem of a single plane; it has the advantages of simplicity and flexibility. The generating functions that are constructed are used to evaluate expectation values for the lengths of loops, bridges, and tails as well as the number of bound segments. The canonical partition function for a molecule of n lattice steps is extracted from the generating function by use of numerical integration.

Kinetically coordinated difference schemes for modelling flows of a viscous heat-conducting gas

The connection between the solutions obtained using kinetically-coordinated difference schemes (KCDS) and the solution of the Navier-Stokes equation for flows of a compressible viscous gas is analysed. It is shown that the KCDS model viscous flows and correspond to the Navier-Stokes equations with a Reynolds number that depends upon the spatial lattice step in the boundary layer. KCDS are constructed with a correction, and these model viscous flows with a real Reynolds number. The results of modelling a number of problems, in which viscous and inviscid parts of the current have a significant interaction are briefly presented.

Lattice model of microemulsions

A lattice model of microemulsions is proposed. It proves to be equivalent to a spin-1/2 Ising model in a magnetic field, with ferromagnetic nearest-neighbor, antiferromagnetic next-nearest-neighbor (next-nearest defined as two lattice steps, regardless of the metrical distance), and three-spin interactions. The respective interaction constants H, J, M, and L in the Ising model are related to the ratios zBB/zAA and zAB/(zAAzBB)1/2 of the activities of the oil (AA), water (BB), and surfactant (AB), to the surfactant-film-curvature energy (surfactant–surfactant interaction energy) K, and to the curvature-bias parameter (Bancroft parameter) λ, in the microemulsion model. A table of translations is given. In mean-field approximation the symmetrical version of the model, in which H=L=0 (or zBB/zAA =1 and λ=0 in microemulsion language), is equivalent also to the ANNNI (anisotropic, or axial, next-nearest-neighbor Ising) model. The analog of the three-phase (Winsor III) equilibrium of surfactant solutions is identified in the ANNNI model’s phase diagram. States of vanishing tension of the microscopic surfactant film are identified in the symmetrical model. They prove to be the same as those in which the tension of the interface between (metastable) bulk oil and water phases (the ferromagnetic phases in the Ising model) vanishes. Those states are reflected in the phase diagram, and also in the ultralow tensions of the interfaces between stable phases in their neighborhood.

Lattice steps and adatom binding on W(211)

The role of a lattice step in affecting the binding of adatoms in its vicinity has been explored for tungsten as well as rhenium adatoms on the (211) plane of tungsten. On this plane adatoms are confined to sites in a one-dimensional channel along [1̄11]. From the equilibrium distribution of an adatom over all sites in a channel it is possible to derive the relative free energy of binding at the different sites. Such measurements have been made using a field ion microscope supported by an automated data handling system. Contrary to expectations based on potential calculations using standard pair interactions, atom binding is found to be stronger close to the plane edges rather than in the center, where the number of distant neighbors around the adatom is larger. These edge effects have a surprisingly long range, extending at least over three sites, and are strongly dependent upon the chemical identity of the adatom.

Lattice steps and adatom binding on W(211)

Lattice steps and adatom binding on W(211)

Field induced and surface catalyzed formation of novel ions : A pulsed-laser time-of-flight atom-probe study

High electric field induced formation of novel ions such as H+3, AuH+2, RhHe2+, and PtHe2+2 on metal surfaces has been studied in the pulsed-laser time-of-flight atom-probe field ion microscope. From the fractional abundances, and the high resolution mass spectra and energy distributions measured for these ions, several conclusions can be drawn. Field desorption of hydrogen below the evaporation field of the substrate often results in formation of H+3 ions. This formation depends not only on the applied field strength, but surprisingly also on the material and the atomic structure of the substrate. Plenty of H+3 ions can be found from the high index planes and the lattice steps of Mo, W, and Au surfaces in the field range of 2 to 3 V/Å. Few are found from Ir and Ni surfaces, and none are found from the densely packed W(110) plane. Formation of H+3 can therefore be considered a surface catalyzed and field induced chemical reaction. Using H2–D2 mixed gases, we find little correlation between the ionic species obseved in field desorption and the chemisorption states of the gases. The field desorbed ions are formed directly from the field adsorbed state. Field adsorption occurs mostly in the diatomic molecular form. On highly protruded atomic sites of some materials, field adsorption occurs also partly in the triatomic molecular form. Field evaporation of metals in hydrogen or helium often results in the formation of metal hydride and metal helide ions. These ions are formed right at the metal surface by a polarization binding. A fraction of them dissociates in the high field region near the surface. The ‘‘dissociation zone’’ is found to be only several Å in width. From this width, the average lifetime of these complex ions in a field of 3 to 4.4 V/Å is estimated to be on the order of 5×10−13 s.