Pavel Šmilauer

Submonolayer epitaxy without a critical nucleus

Abstract The nucleation and growth of two-dimensional islands is studied with Monte Carlo simulations of a pair-bond solid-on-solid model of epitaxial growth. The conventional description of this problem in terms of a well-defined critical island size fails because no islands are absolutely stable against single atom detachment by thermal bond breaking. When two-bond scission is negligible, we find that the ratio of the dimer dissociation rate to the rate of adatom capture by dimers uniquely indexes both the island size distribution scaling function and the dependence of the island density on the flux and the substrate temperature. Effective pair-bond model parameters are found that yield excellent quantitative agreement with scaling functions measured for Fe Fe (001) .

Step-edge barriers on GaAs(001)

We investigate the growth kinetics on vicinal GaAs(001) surfaces by making detailed comparisons between reflection high–energy electron–diffraction specular intensity measured near in–phase diffraction conditions and the surface step density obtained from simulations of a solid–on–solid model. Only by including a barrier to interlayer transport and a short–range incorporation process of freshly–deposited atoms can the simulations be brought into agreement with the measurements both during growth and during post–growth equilibration of the surface. 68.55.Jk, 61.14.Hg

Temperature-dependent unstable homoepitaxy on vicinal GaAs(110) surfaces

Abstract The surface morphology of GaAs thin films grown by molecular beam epitaxy on (110) substrates misoriented towards (111)A is studied using atomic force microscopy in a wide range of growth temperatures. Two regimes of unstable growth with distinct growth morphologies are identified. At substrate temperatures between 450 and 500°C, macrosteps are created with step edges oriented along [110] or [112]. Above 550°C, GaAs (110) vicinal surfaces become unstable towards transverse meandering, and a ripple pattern morphology with ridges running along the [001] direction is formed. We attribute the two types of growth instabilities observed to differences in attachment kinetics of adatoms to surface steps at different As surface coverages.

Reentrant layer-by-layer etching of GaAs(001).

We report the first observation of re-entrant layer-by-layer etching based on in situ reflection high-energy electron-diffraction measurements. With AsBr3 used to etch GaAs(001), sustained specular-beam intensity oscillations are seen at high substrate temperatures, a decaying intensity with no oscillations at intermediate temperatures, but oscillations reappearing at still lower temperatures. Simulations of an atomistic model for the etching kinetics reproduce the temperature ranges of these three regimes and support an interpretation of the origin of this phenomenon as the site-selectivity of the etching process combined with activation barriers to interlayer adatom migration.

Determination of step-edge barriers to interlayer transport from surface morphology during the initial stages of homoepitaxial growth

We use analytic formulas obtained from a simple model of crystal growth by molecular-beam epitaxy to determine step-edge barriers to interlayer transport. The method is based on information about the surface morphology at the onset of nucleation on top of first-layer islands in the submonolayer coverage regime of homoepitaxial growth. The formulas are tested using kinetic Monte Carlo simulations of a solid-on-solid model and applied to estimate step-edge barriers from scanning-tunneling microscopy data on initial stages of Fe(001), Pt(111), and Ag(111) homoepitaxy.

Analytical solution of generalized Burton-Cabrera-Frank equations for growth and post-growth equilibration on vicinal surfaces

We investigate growth on vicinal surfaces by molecular-beam epitaxy making use of a generalized Burton-Cabrera-Frank model. Our primary aim is to propose and implement an analytical program based on a perturbative solution of the nonlinear equations describing the coupled adatom and dimer kinetics. These equations are considered as originating from a fully microscopic description that allows the step boundary conditions to be directly formulated in terms of the sticking coefficients at each step. As an example, we study the importance of diffusion barriers for adatoms hopping down descending steps (Schwoebel effect) during growth and post-growth equilibration of the surface.

Morphology of singular and vicinal metal surfaces sputtered at different temperatures

Abstract The evolution of the morphology of sputtered metal surfaces is investigated using computer simulations of a solid-on-solid model. Our results correspond closely to available experimental data obtained using a scanning tunneling microscope. In particular, we observe the transition from pit formation to layer-by-layer removal regime and the formation of vacancy island free zone at the lower terrace near a pre-existing step when the sample temperature is increased. We have found that in order to obtain correct surface morphologies, it is necessary to consider step-edge barriers due to both descending and ascending steps.

Scale Invariance in Epitaxial Growth

We examine three manifestations of scale invariance during epitaxial growth from the standpoint of a single atomistic model. The first two manifestations are in the submonolayer regime of growth, where clusters are formed but have not yet begun to coalesce. Depending on the material deposited and the substrate, the clusters can exhibit either an effective fractal dimension or a Euclidean dimension. The cluster size distribution function in this regime also exhibits scaling as a function of time. Interestingly, this distribution function and its scaling properties can be accurately described in terms of rate equations that omit entirely the influence of any fluctuations. An altogether different picture emerges in the regime of long deposition times. To analyze the scaling properties of the growing surface in this limit, we use exact discrete Langevin equations that are obtained directly from the rules of our simulation model. A regularization procedure is then used to convert these discrete equations into (infinite-order) continuum partial differential equations. The truncation of these continuum equations is achieved by performing a renormalization-group analysis, which leads asymptotically to a fourth-order nonlinear stochastic differential equation that is identical to that proposed independently by Wolf and Villain and by Lai and Das Sarma. Large-scale Monte Carlo simulations in d = 1, 2, and 3 substrate dimensions show that for all spatial dimensions the observed exponents correspond to those obtained from our continuum equations. This shows that vapor deposition is an example of a driven, nonequilibrium process that evolves to a nontrivial scale-invariant structure under the influence of input noise.

Submonolayer Template Formation for Epitaxial Processes

Epitaxial growth in the submonolayer stage of deposition can exert a strong influence on the multilayer morphology. In the presence of barriers to interlayer atomic transport, the submonolayer island distribution can act as a template for the growth of three-dimensional islands. We investigate the form of the distribution of island sizes in the precoalescence regime as a function of growth conditions and in the presense of strain (for heteroepitaxial systems) and show how both growth conditions and material parameters affect the development of the surface morphology. We also consider the development of the surface morphology during chemical etching and show that similar considerations apply as for growth, with monovacancies and vacancy islands playing the roles of adatoms and adatom islands, respectively.