M. C. Bartelt

Nucleation and growth of square islands during deposition: Sizes, coalescence, separations and correlations

Abstract We analyze via simulation the irreversible nucleation, growth and coalescence of square islands during deposition and subsequent diffusion of adatoms. Our model mimics metal-on-fcc (100) metal epitaxy (at lower temperatures). We characterize the low-coverage scaling, and the effects of coalescence and percolation on the island density and full size distribution. Adatom-island, island-island separations, and also the pair correlations are analyzed. Depletion of the density of nearby islands manifested in these quantities is shown to produce a four-fold symmetric “Henzler ring” in the diffraction profile.

NUCLEATION AND GROWTH IN METAL-ON-METAL HOMOEPITAXY : RATE EQUATIONS, SIMULATIONS AND EXPERIMENTS

We illustrate the utility of the ‘‘mean‐field’’ rate equation treatment of nucleation and growth with critical size i≥1 for both isotropic and strongly anisotropic diffusion. Some comparison is made of rate equation predictions for mean densities and size distributions of stable islands with predictions from ‘‘exact’’ simulations for the low coverage precoalescence regime. We also consider island separation distributions, depletion effects, and associated splitting of kinematic diffraction profiles. We necessarily treat other issues via simulations. These include analysis of (i) transitions in island shape from compact to dendritic, as observed for Pt/Pt(111), and extraction of associated edge diffusion barriers; and (ii) adlayer percolation, which sometimes mediates the population of higher layers. We also briefly comment on nucleation and growth behavior in the specific systems M/M(100) with M=Fe, Pd, Au, Cu, Ni, and Ag.

Transitions in critical size for metal (100) homoepitaxy

Abstract For submonolayer nucleation and growth of islands during metal (100) homoepitaxy, we precisely characterize transitions, with increasing temperature, in the critical size, i , above which islands are effectively stable. For strong adatom bonding, we demonstrate universal crossover behavior from i = 1 directly to a well-defined “ i = 3” regime where tetramers are stable, but not, e.g., pentamers. A criterion is also presented for the ultimate breakdown of “ i = 3” due to double-bond scission. Various transition temperatures and key energies are thereby determined for Ag, Cu, Fe, Ni and Pd.

Dendritic islands in metal-on-metal epitaxy I. Shape transitions and diffusion at island edges

Abstract The development of dendritic island shape instabilities observed during metal-on-metal epitaxy is investigated via a lattice-gas model for the low coverage regime. The key assumption is that island structure is controlled by the competition between shape equilibration due to adatom edge diffusion, and Mullins-Sekerka-type shape instability due to diffusion-limited aggregation of adatoms with islands. From comparison with scanning tunneling microscopy data (for the island density and average width of dendritic arms), we advance estimates of the energy barrier for edge diffusion in several systems.

The initial stages of AgAg(1 0 0) homoepitaxy: scanning tunneling microscopy experiments and Monte Carlo simulations

Results are presented of a scanning tunneling microscopy study of AgAg(1 0 0) homoepitaxy. We examine both submonolayer nucleation and growth of two-dimensional islands, for temperatures between 295 and 370 K, and the initial stages of multilayer kinetic roughening at 295 K. Comparison with results of Monte Carlo simulations for an appropriate model for metal(1 0 0) homoepitaxy produces estimates of 330 ± 5 meV for the terrace diffusion barrier, and an effective value of 30 ± 5 meV for the additional step-edge barrier (assuming a common prefactor of 1012/s). We also assess adatom-adatom bonding by analyzing the transition from irreversible to reversible island formation.

Dendritic islands in metal-on-metal epitaxy. II: Coalescence and multilayer growth

Abstract Dendritic or fractal islands occur naturally during epitaxial growth in systems where island edge diffusion is restricted. Here we use a lattice-gas model to characterize the evolution of island structure in such systems, from the low coverage to the coalescence regime, and to consider the ramifications for multilayer growth. Island densification and slowing of radial growth prior to coalescence is observed in the simulations, as in Au/Ru(0001). We also elucidate the relationship of the real-space island structure to the width and shape of the corresponding kinematic diffraction profile. Our multilayer growth studies incorporate disruption of and downward funneling from island edges upon impact of depositing atoms, in the presence of a large Schwoebel barrier. Using the geometry and length scales appropriate for Pt/Pt(111), the calculated kinematic Bragg intensities for a two-layer model show that even limited disruption can produce the observed low-temperature “reentrant” oscillations.

Rate Equation Theory for Island Sizes and Capture Zone Areas in Submonolayer Deposition: Realistic Treatment of Spatial Aspects of Nucleation

Extensive information on the distribution of islands formed during submonolayer deposition is provided by the joint probability distribution (JPD) for island sizes, s, and capture zone areas, A. A key ingredient determining the form of the JPD is the impact of each nucleation event on existing capture zone areas. Combining a realistic characterization of such spatial aspects of nucleation with a factorization ansatz for the JPD, we provide a concise rate equation formulation for the variation with island size of both the capture zone area and the island density.

The car‐parking limit of random sequential adsorption: Expansions in one dimension

We consider the irreversible random sequential adsorption of particles taking k sites at a time, on a one‐dimensional lattice. We present an exact expansion for the coverage, θ(t,k)=A0(t)+A1(t)k−1+A2(t)k−2+..., for times, 0≤t≤O(k), and at saturation t=∞. The former is new and the latter extends Mackenzie’s results [J. Chem. Phys. 37, 723 (1962)]. For these expansions, we note that the coefficients Ai≥1(∞) are not obtained as large‐t limits of the Ai≥1(t). Finally, we comment on the Laurent expansions for general O(k)<t<∞, which reveal the occurrence of additional kn terms, with n≳0.