Lattice Langevin equations are derived from the rules of lattice growth models. These provide an exact mathematical description that is suitable for direct analysis, such as the passage to the continuum limit, as well as a computational alternative to kinetic Monte Carlo simulations. This approach is applied to ballistic deposition and a model for conditional deposition, both of which yield the Kardar–Parisi– Zhang equation in the continuum limit, and a model of strain relaxation during heteroepitaxy.

We study the epitaxial growth mechanisms of the zinc-blende CrAs on the GaAs substrates theoretically, from the first principles using the pseudopotential method. We assume some model structures containing various numbers of Cr adatoms or CrAs films on the GaAs (001) substrates, and compare the structural stabilities of them. We found that Cr adatoms may make some interstitial defects in the GaAs substrate in low coverage, but they can create a complete Cr layer in high coverage.

Kinetic Monte Carlo (KMC) simulation of atomistic models reveals the failure of mean-field treatments of the island size distribution (ISD) for islands formed by homogeneous nucleation during submonolayer deposition on perfect surfaces. KMC also facilitates analysis of scaling properties of the ISD, although here some misperceptions persist which we attempt to clarify. However, KMC becomes inefficient for highly reversible island formation (e.g., for large values of a critical size, i, above which islands are stable) due to the high density of diffusing adatoms on the surface. This reduced efficiency is quantified here with results for CPU time versus i. This feature has motivated development of alternative beyond-mean-field coarse-grained approaches which should be more efficient for large i. We provide results for the ISD for a range of i = 1, 2, 3, and 6 using one such approach, a stochastic geometry-based simulation (GBS) strategy.

Exposure of a vicinal Si(100) surface to oxygen at around 550 C produces etching-mediated step recession. In addition, some oxide islands are formed which locally pin receding steps. We develop an atomistic lattice-gas model for this process which accounts for the interplay between oxygen surface chemistry (adsorption, diffusion, oxide formation, and etching via SiO desorption) and the silicon surface and step dynamics (anisotropic diffusion and aggregation of di-vacancies formed by etching, and ad-dimer attachment-detachment dynamics at steps incorporating anisotropic energetics). Kinetic Monte Carlo simulation of this model produces step morphologies retaining some qualitative but not quantitative features of their equilibrium structure (alternating rough SB steps and smooth SA steps), except for pinning which produces protruding “fingers”. These features are seen in Scanning Tunneling Microscopy studies.

The strain driven self-assembly of faceted Ge nanocrystals during epitaxy on Si(001) to form quantum dots (QDs) is by now well known. We have also recently provided an understanding of the thermodynamic driving force for directed assembly of QDs on bulk Si (extendable to other QD systems) based on local chemical potential and curvature of the surface. Silicon-on-insulator (SOI) produces unique new phenomena. The essential thermodynamic instability of the very thin crystalline layer (called the template layer) resting on an oxide can cause this layer, under appropriate conditions, to dewet, agglomerate, and self-organize into an array of Si nanocrystals. Using low-energy electron microscopy (LEEM), we observe this process and, with the help of first-principles total-energy calculations, we provide a quantitative understanding of this pattern formation. The Si nanocrystal pattern formation can be controlled by lithographic patterning of the SOI prior to the dewetting process. The resulting patterns of electrically isolated Si nanocrystals can in turn be used as a template for growth of nanostructures, such as carbon nanotubes (CNTs). Finally we show that this growth may be controlled by the flow dynamics of the feed gas across the substrate.

The Low Pressure Chemical Vapor Deposition of Si from SiH4 is an industrial process that can be used to deposit epitaxial Si at relatively low surface temperatures. Multiscale models are necessary in order to tune the operating conditions to optimize the quality of the deposited materials. In this work we present a multiscale approach meant to describe the film morphological evolution at different time and length scales. The reactor fluid dynamics and overall mass and temperature balances are solved with the finite element method. The morphological evolution of the film is investigated with 3D kinetic Monte Carlo. We have systematically investigated the dependence of the growth morphology from temperature, pressure and gas phase composition (SiH4/H2 ratio) with the aim of determining the operating parameters window that can lead to the best film morphology. We found that the presence of a significant amount of hydrogen on the surface can significantly influence the surface morphology. In particular hydrogen can be considered as the principal responsible of the transition from an order terrace step flow growth regime, which prevails at high temperatures, to a disordered 3 dimensional growth regime. It is also worth noting that our KMC simulations show that the hydrogen surface chemistry active at low temperatures is probably richer than expected, since the formation of a significant number of island on the surface dramatically increases the concentration of steps, and thus the variety of configurations by which two adsorbed H atoms can interact.

We investigate the formation of (In, Ga) As self assembled quantum structures grown on different orientations of a GaAs substrate along one side of the stereographic triangle between (100) and (111)A surfaces. The samples were grown by Molecular Beam Epitaxy, monitored by Reflection High-Energy Electron Diffraction during the growth and characterized by in-situ Scanning Tunneling Microscopy and Atomic Force Microscopy. A systematic transition from zero dimensional (In, Ga) As quantum dots to one dimensional quantum wires was observed as the substrate was varied along the side of the triangle within 25° miscut from the (100) toward (111)A, which includes several high index surfaces. We propose an explanation for the role of the substrate in determining the type of the nanostructure that is formed.

In models of nucleation and growth on surfaces, it is usually assumed that the energy surface of the substrate is flat, that diffusion is isotropic, and that capture numbers can be calculated in the diffusion-controlled limit. We lift these restrictions analytically, and introduce a hybrid discrete FFT method of solving for the 2D time-dependent diffusion field of adparticles on general non-uniform substrates. The method, with periodic boundary conditions, is appropriate, for example, following nucleation on a regular (rectangular) array of defects. The programs, which have been realized in Matlab®6.5, are instructive for visualizing potential and diffusion fields, and for producing illustrative movies of crystal growth under various conditions. Here we demonstrate the time-dependence of capture numbers in the initial stages of annealing at high adparticle concentration in the presence of repulsive adparticle-cluster interactions; however it is clear that the method works in general for deposition, growth and annealing at all times.

The Kinetic Monte Carlo (KMC) method has become an important tool for examination of phenomena like surface diffusion and thin film growth because of its ability to carry out simulations for time scales that are relevant to experiments. But the method generally has limited predictive power because of its reliance on predetermined atomic events and their energetics as input. We present a novel method, within the lattice gas model in which we combine standard KMC with automatic generation of a table of microscopic events, facilitated by a pattern recognition scheme. Each time the system encounters a new configuration, the algorithm initiates a procedure for saddle point search around a given energy minimum. Nontrivial paths are thus selected and the fully characterized transition path is permanently recorded in a database for future usage. The system thus automatically builds up all possible single and multiple atom processes that it needs for a sustained simulation. Application of the method to the examination of the diffusion of 2-dimensional adatom clusters on Cu(111) displays the key role played by specific diffusion processes and also reveals the presence of a number of multiple atom processes, whose importance is found to decrease with increasing cluster size and decreasing surface temperature. Similarly, the rate limiting steps in the coalescence of adatom islands are determined. Results are compared with those from experiments where available and with those from KMC simulations based on a fixed catalogue of diffusion processes.

The characteristics of nucleation and island growth in oblique angle deposition with substrate rotation have recently attracted interest due to the formation of novel 3D nanostructures by a physical self-assembly process. In this study, we present the results of a solid-on-solid growth simulation by a kinetic Monte Carlo algorithm that explores the layer coverage evolution of thin films during oblique angle deposition. The simulations accounted for oblique incidence flux, shadowing effect, surface diffusion, and substrate rotation. The layer coverage, the ratio of average island volume to average island size, and root-mean-square (RMS) roughness values are reported for the initial stages of island growth from submonolayer thicknesses up to a few monolayers. RMS roughness was also investigated for later stages of the growth. Our results show that, for small deposition angles and with limited or no surface diffusion included, the average growth rate of islands is faster in lateral directions that results in enhanced layer coverages and smoother films. This is due to that the sides of the islands can be exposed to the incident flux more effectively at small deposition angles. On the other hand, normal incidence and high oblique angle depositions give poorer layer coverages and much rougher films due to the slower growth rates in lateral directions.