Thermal Roughening Research Articles

Thermal roughening of Cu(115): An energy-resolved helium-atom-beam scattering study.

The structure of the Cu(115) surface has been investigated in the temperature range between 160 and 700 K with energy-resolved helium-atom-beam scattering. The ``power-law'' diffraction profiles found in previous helium-scattering experiments without energy analysis are shown to be the result of inelastic (phonon) scattering. In our energy-resolved measurements, the line shapes of the elastically scattered intensity can be described by a two-dimensional Lorentzian. This asserts that on this surface a possible crossover of the height difference correlation function to the expected logarithmic behavior might only occur for distances larger than about 100 \AA{} (perpendicular to the average step direction).

Experimental investigation of criteria for thermal roughening

The morphology of single domain Si(001)2 × 1 surfaces has been investigated with scanning tunneling microscopy (STM). Using the model of Villain, Grempel and Lapujoulade, which is based on the microscopic properties of the surface, this vicinal surface is found to be thermally rough. On macroscopic scale, however, we did not observe any indication for the expected characteristic logarithmic divergence of the surface height-height correlation function. Possible causes for this discrepancy are discussed briefly.

Monte carlo simulation of transitions related to growth on (001) faces of Si and Ge

Abstract Based on Monte Carlo simulations for molecular beam epitaxy, three types of growth related transitions on the Si(001) and Ge(001) surfaces have been studied. In the thermal roughening simulations on a Ge(001) surface, a different type of transition from the Kosterlitz and Thouless type is obtained. The simulated result is consistent with the experimental x-ray diffraction data, at least qualitatively. In the growth simulations, a transition in the shape of growing islands is shown at the very initial stage of the homoepitaxial growth on a Si(001)-2x1 flat surface. During the transition, the step density variations as a function time show different behaviors at various temperatures. In the homoepitaxial growth on Si(001)-2x1 vicinal surfaces, the growth mode transition from two-dimensional island formation to the step-flow mode is reproduced by increasing the system temperature, which agrees qualitatively with the observed results. At the intermediate temperature, a transient growth mode is obtain...

Thermal and kinetic surface roughening studied by scanning tunneling microscopy and atomic force microscopy

Abstract Recent studies of thermal roughening on Si surfaces and kinetic roughening of some growing films, copper and tungsten, by using scanning tunneling microscopy and atomic force microscopy are reviewed. A logarithmic divergence of the surface height fluctuations of Si(111) vicinal surfaces is confirmed, in agreement with the theoretical prediction of rough surface in thermal equilibrium. For the kinetically formed rough surfaces, power law dependences of the interface width on the system size are clearly observed. Furthermore, the tungsten films show a short-range scaling regime and a long-range “smooth” regime. The roughness exponents α are compared with theoretical predictions: for the typical Cu electrode position condition (α=1/2), the exponent appears to be close to that found for local growth models, and for tungsten films (0.7∼0.8), it is consistent with recent predictions for growth where surface diffusion is predominant.

Properties and structure of crystal-solution interfaces of normal alkane crystals: Influence of solvents

The step energy of the {110} faces of n-paraffin crystals grown from various solutions is measured in thermal roughening experiments, and the values are compared with those calculated using a self-consistent field (SCF) lattice model calculation technique. The results turn out to be in good agreement. The interfacial fluid structure of n-paraffin crystals in various solutions is further examined on a molecular scale by means of SCF calculations. It is found that the interfacial structure of the solid–fluid interface of n-alkane crystals changed substantially, depending on the molecular structure and properties of the solvent. Subsequently, a ternary system, i.e., the n-C25H52–butanol-n-hexane solution, is analyzed. It follows that when the segmental density of the solute is kept constant, mixing a small amount of one solvent with another may lead to an increase in the step energy. Finally, the solvent-dependent critical behavior of the roughening transition for n-alkane crystals grown from various solutions is also discussed.

Roughening transition of tetragonal metals: an initial growth shape study

The thermal roughening of In and Sn microcrystals prepared in an UHV scanning electron microscope is studied in situ by initial growth shape measurements from 300 K to about 10 K below the melting point. On Sn crystals 11 faces could be identified, on In crystals 7 faces. The sequence of the roughening temperatures determined can be correlated with the packing densities of the faces and their surface energies. At present theory is only in partial agreement with experiment.

The thermal roughening of liquid surfaces and its effect on gas–liquid collisions

Collisions of inert gases with a perfluorinated liquid over an 85 K range reveal how gas–liquid energy transfer depends on the temperature of the liquid. At higher temperatures, thermal accommodation of impinging Ne, Ar, and Xe atoms grows at the expense of prompt inelastic scattering. The experiments suggest that hotter liquids possess rougher surfaces, which promote multiple collisions that dissipate the atom’s incident energy and which may momentarily trap gases in gaps created by incommensurate packing of the surface molecules. The fraction of energy transferred during a high energy impulsive collision remains almost unaltered by changes in the liquid’s temperature, implying that impulsive encounters within the scattering plane are dominated by single collision events.

Surface roughening and surface diffusion in kinetic thin-film deposition.

We have studied the correlation between surface roughening and surface diffusion in kinetic thin-film deposition by Monte Carlo simulation. Through a variation of simulation parameters, we have obtained an optimal deposition window for layer-by-layer growth in the parameter space of temperature and impingement rate. We have found that an atomically smooth surface can only be obtained at a regime of intermediate temperatures and low impingement rate, beyond which the growing surface is either kinetically rough (at low temperatures) or thermally rough (at high temperatures). The kinetic roughening can be avoided by choosing a lower deposition rate, but the thermal roughening cannot be compensated by any choice of particle impingement. We have shown that surface diffusion is closely correlated with surface roughening. Only when the surface diffusion length is long can a surface be grown in a layer-by-layer mode.

The relation between rough and flat growth of crystal faces: an effective approach to volume transport resistances

In this paper, a simple approach has been presented to describe and estimate the resistance against volume transport during crystal growth. Following from a simple model, it is obtained that using the relation between the kinetics of rough growth and that of flat growth, the resistances against volume diffusion can be estimated. Within the framework of this approach, a so-called auxiliary straight line method is developed to extract the fractions of the total driving force remaining at the surface from available experimental results. As applications and experimental verifications, the kinetic data of different n-paraffin and naphthalene crystal-solution systems are analyzed by the aforementioned method. For the n-paraffin systems, the data obtained from kinetic roughening experiments are compared with those obtained from thermal roughening experiments. The results turn out to be in excellent agreement with eaxh other.

High-temperature crystalline effects in Auger electron spectroscopy: the possibility of observation of the surface roughening transition on the Ni(110) face

The Auger signal of the M 2,3VV (62 eV) transition is measured as a function of the primary beam incidence angle for the (001) and (110) nickel faces with the samples maintained at temperatures of 300–1500 K. From those measurements the contrast C = 2(I max − I min ) (I max + I min) is calculated for the direction normal to the surface and the dependence of In C on the sample temperature is presented. For the Ni(001) face two linear parts of this dependence are found in the whole temperature range used (with the smaller and larger slope below and above 740 K, respectively) while for the Ni(110) face ln C drops appreciably faster than linearly for T > 1300 K. The increased slope above 740 K observed for both samples is ascribed to the anharmonic effects, while the fast drop of ln C observed for the Ni(110) face for T > 1300 K is interpreted as a result of thermal roughening of this face. Thus, crystalline effects in AES can give information on the thermal roughening.

Kinetics of faceting of crystals in growth, etching, and equilibrium.

The faceting of crystals in equilibrium with the gas phase and also during crystal growth and etching conditions is studied using the Monte Carlo method. The dynamics of the transformation of unstable crystallographic orientations into hill and valley structures and the spatial patterns that develop are examined as functions of surface temperature, crystallographic orientation, and strength of interatomic potential for two transport processes: adsorption-desorption and surface diffusion. The results are compared with the continuum theory for facet formation. Thermodynamically unstable orientations break into hill and valley structures, and faceting exhibits three time regimes: disordering, facet nucleation, and coarsening of small facets to large facets. Faceting is accelerated as temperature increases, but thermal roughening can occur at high temperatures. Surface diffusion is the dominant mechanism at short times and small facets but adsorption-desorption becomes important at long times and large facets. Growth and etching promote faceting for conditions close to equilibrium but induce kinetic roughening for conditions far from equilibrium. Simultaneous irreversible growth and etching conditions with fast surface diffusion result in enhanced faceting.

Kinetic roughening in relation to the roughening transition in odd-numbered alkane crystals

In this paper kinetic roughening and thermal roughening are compared with each other in a quantitative way. First a non-equilibrium condition recipe is introduced to describe the shape of a D nucleus. After defining a proper criterion for the occurrence of kinetic roughening, a relation between critical supersaturations σ c and the edge free energy γ kT is derived. In comparison with the data of the roughening transition obtained from some n-paraffin-n-hexane solution systems, it is found that the relation between σ c and the edge free energies γ x and γ y of a rectangular nucleus on surfaces is in very good agreement with experimental data.

Modification of surface structures and roughening phase transition in Pb(110) by impurities

Using high-resolution low-energy electron diffraction, we show that the thermal roughening transition of a clean unreconstructed Pb(110) surface can be altered by impurities in the surface. The flat surface becomes a two-level regular terrace structure (1D) along the close-packed direction above 350 K with terraces modeled by a cut-off geometric distribution. The original Kosterlitz-Thouless roughening transition at 415 K for the clean surface was delayed until 480 K and the transition was irreversible due to the change in the amount of impurities in the surface.

Modification of surface structures and roughening phase transition in Pb(110) by impurities

Using high-resolution low-energy electron diffraction, we show that the thermal roughening transition of a clean unreconstructed Pb(110) surface can be altered by impurities in the surface. The flat surface becomes a two-level regular terrace structure (1D) along the close-packed direction above 350 K with terraces modeled by a cut-off geometric distribution. The original Kosteriitz-Thouless roughening transition at 415 K for the clean surface was delayed until 480 K and the transition was irreversible due to the change in the amount of impurities in the surface.

Monte Carlo studies of the interdependence of crystal growth morphology, surface kinetics and bulk transport

The evolution of crystal growth morphologies was explored using a Monte Carlo model. The model combines diffusive transport in the nutrient with thermally activated and local configuration-dependent steps for attachment, surface diffusion and detachment. The solid pair interaction energy, ϕ, temperature, T, and chemical potential difference between nutrient and surface, Δµ, were used as input parameters. For a given set of simulation parameters, we found that, due to the competing effects of bulk diffusion and interface kinetics, there is a critical size beyond which a crystal cannot retain its macroscopically faceted shape. This critical size scales linearly with the mean free path in the nutrient, a. The stabilization of the growth shape by anisotropies in the kinetics is reduced through thermal and kinetic roughening. Thus, further increases either in T or Δµ, and/or decreases in ϕ, cause successive transitions from faceted to compact dendritic and side-branched dendritic morphologies. On interfaces with emerging screw dislocations the spiral growth mechanism dominates at low Δµ. When a is comparable to the lattice constant, the combination of bulk and surface diffusion reduces the terrace width near the centre of a growth spiral. At elevated T and Δµ, 2D nucleation-controlled growth can dominate in the more readily supplied corner and edge regions of a facet, while spiral growth prevails in its centre.

Thermal roughening of FEM-clean Pt{110} and its vicinal areas

Abstract After heat treatment at ∼1600 K and rapid quenching, thermal roughening through kink formation could be observed on “FEM-clean” Pt{110} and on all its vicinal areas (which are made up of {110} terraces). Noticeable exceptions were the areas between {771} and {331} (including {771}), which are located on the [110] zone. These areas may remain topographically unchanged, or, more likely, may form {111}-microfacets during heat treatment. Upon annealing, the high-temperature roughness on {110} started to decrease at 830 K (formation of an 1 × 2 structure) and reached a minimum at 960 ± 25 K (≡ transition temperature, Tc). Thereafter, it increased precipitously until 1030 K was reached (surface roughening/deconstruction). Surface roughening could be suppressed readily by gas phase and/or bulk impurities (surface segregation). Vapour deposited Si, P, SiO, TiO2, Al2O3 and C (graphite) prevented surface roughening on Pt{110}. All investigations were carried out by FEM.

Thermal roughening of FEM-clean Pt{110} and its vicinal areas

After heat treatment at ∼1600 K and rapid quenching, thermal roughening through kink formation could be observed on “FEM-clean” Pt{110} and on all its vicinal areas (which are made up of {110} terraces). Noticeable exceptions were the areas between {771} and {331} (including {771}), which are located on the [1̄10] zone. These areas may remain topographically unchanged, or, more likely, may form {111}-microfacets during heat treatment. Upon annealing, the high-temperature roughness on {110} started to decrease at 830 K (formation of an 1 × 2 structure) and reached a minimum at 960 ± 25 K (≡ transition temperature, T c ). Thereafter, it increased precipitously until 1030 K was reached (surface roughening/deconstruction). Surface roughening could be suppressed readily by gas phase and/or bulk impurities (surface segregation). Vapour deposited Si, P, SiO, TiO 2, Al 2O 3 and C (graphite) prevented surface roughening on Pt{110}. All investigations were carried out by FEM.

Growth of rough surfaces

The growth of objects with rough surfaces is a common phenomenon. We describe several models used in the study of the temporal evolution of fluctuating interfaces and then we explain the dynamical scaling in this class of growth models with self-affine surfaces. The recent progress in this field is reviewed. Much emphasis is put on roughness properties and in particular on a possible kinetic roughening transition — a nonequilibrium analog of the thermal roughening transition. Both analytical and numerical results for scaling exponents are summarized and indications of a phase transition in some models are discussed.

Kinetic surface roughening. II. Hypercube-stacking models.

The roughening behavior of moving surface under a deposition and evaporation dynamics is explored within the hypercube-stacking model. One limiting case of the model is an equilibrium surface, which exhibits thermal roughening for surface dimension d\ensuremath{\le}2. Another limiting case is nonequilibrium irreversible growth, where the model is shown to map exactly to zero-temperature directed polymers on a hypercubic lattice with a random energy distribution. Results of exact calculations for d=1 and of large-scale Monte Carlo simulations [N=${2}^{20}$, 11 ${520}^{2}$, and 2\ifmmode\times\else\texttimes\fi{}${192}^{3}$ surface sites for d=1, 2, and 3, respectively] are presented that establish the Kardar-Parisi-Zhang equation as the correct continuum description of the growth process. For pure deposition (i.e., irreversible growth), careful analysis of surface width data yields the exponents \ensuremath{\beta}(2)=0.240\ifmmode\pm\else\textpm\fi{}0.001 and \ensuremath{\beta}(3)=0.180\ifmmode\pm\else\textpm\fi{}0.005, which violate a number of recent conjectures. By allowing for evaporation, we observe a less rapid increase of the surface roughness as a function of time. This phenomenon is consistently explained by a crossover scenario for d=1 and 2 but a nonequilibrium roughening transition for d=3, as predicted by a perturbative renormalization-group analysis of the Kardar-Parisi-Zhang equation. Detailed predictions on crossover scaling from the renormalization-group analysis are also confirmed by simulation data. In the d=1 case, some of the continuum parameters characterizing the renormalization-group flow are obtained explicitly in terms of the lattice parameters via the exact calculation of steady-state properties of the model.

The work function of kinked areas on clean, thermally rounded Pt and Rh crystallites: its dependence on the structure of terraces and edges

Field emission studies on clean, thermally rounded Pt and Rh crystallites show that the work function of a kinked area is determined by the terrace structure, the kink atom density and the surface dipole moment of the kink atom. The dipole moment decreases with decreasing terrace interlayer spacing. The work function of kinked areas with given terrace and edge structure shows a linear dependence on the kink atom density if m ⩾ 3 atoms ( m ¬ terrace depth). Areas belonging to the face groups ( Pt, Rh) S-[ m{111} × {311}], ( Pt) S-[ m{110} × {100}] and of Pt{110} are thermally roughened. Thermal roughening could not observed on ( Pt, Rh) S-[ m{100} × {110}], ( Rh) S-[ m{110} × {100}] or on Rh{110}. Formulae were derived that permit calcula the work function of any face within the above listed non-roughened face groups.