Mark R. Wilby

Theory of homoepitaxy on Si(001): I. Kinetics during growth

Abstract Growth kinetics during Si(001) homoepitaxy are studied with a Monte Carlo computer simulation of a solid-on-solid model. The effect of the surface reconstruction, driven by the formation of dimers, is taken into account through longer residence times of atoms attached to other atoms or clusters perpendicular to the dimer-bond axis on the same layer than for atoms attached in the parallel direction. Although local fluctuations can bypass these rules, this prescription is correct on the average and leads naturally to the stability of steps for which the dimer axis is normal to the step edge in comparison to steps where the dimer axis is perpendicular to the step edge. By calculating the angle-resolved density of surface steps on the growing substrate, qualitative comparisons can be made between the simulations and the specular intensity measured in situ by reflection high-energy electron-diffraction (RHEED). Furthermore, by calculating the fractional coverages of 1 × 2 and 2 × 1 domains during growth, comparisons can be made with the fractional-order RHEED beams. Specific aspects of Si(001) homoepitaxy that are addressed are: (i) the azimuthal dependence of RHEED intensity oscillations and the formation of elongated clusters, (ii) the dependence of the growth characteristics upon the domain structure of the initial substrate, i.e., sustained RHEED oscillations for surfaces with a single 2 × 1 domain but decaying oscillations for a substrate with coexistent 2 × 1 and 1× 2 domains, (iii) the observation of RHEED oscillations at temperatures too low (≈ 300°C) to promote the mobility of surface adatoms, as evidenced by the absence of recovery upon the termination of the incident molecular beam, and (iv) a temperature-induced monolayer-to-bilayer transition in the RHEED oscillations.

Morphological model of reflection high‐energy electron‐diffraction intensity oscillations during epitaxial growth on GaAs(001)

Reflection high‐energy electron diffraction (RHEED) measurements have been carried out on vicinal GaAs(001) surfaces which are misoriented by 2° and 3° toward the [010] direction. The misorientation‐angle dependence and the Ga‐flux dependence of the growth‐mode transitions for a fixed As/Ga ratio of approximately 2.5 have been reproduced by Monte Carlo simulations of a solid‐on‐solid model. The surface step‐density evolutions generated by the simulations are remarkably similar in profile to the measured RHEED oscillations, and show approximately the same relative change of amplitude with temperature for the chosen diffraction conditions.

Monolayer to bilayer transition in reflection high‐energy electron diffraction intensity oscillations during Si(001) molecular beam epitaxy

We report the observation of a thermally driven monolayer to bilayer transition in the period of reflection high‐energy electron diffraction oscillations during molecular beam epitaxy on Si(001). This behavior is reproduced in a Monte Carlo growth simulation, from which we infer the origin of the transition results from the competition between incorporation and diffusion kinetics.

Epitaxial growth kinetics on patterned substrates

The temperature dependence of the growth kinetics on V‐grooved substrates is studied by computer simulation, with attention focused upon the evolution of the morphology. We find a distribution of growth rates on GaAs(001) at high temperatures due to surface diffusion of adatoms from one facet to the other. However, at low temperatures, where surface migration processes are less important, growth on these substrates proceeds in a shape‐preserving manner. Comparison with scanning microprobe reflection high‐energy electron‐diffraction intensity oscillations on GaAs(001) near (111) surfaces shows that our results are in qualitative agreement with observed behavior.

Equations of motion for epitaxial growth

A set of discrete, stochastic equations of motion which describe the epitaxial growth of a single crystal are derived beginning with a master equation description of the dynamics of a solid-on-solid model. The final set of coupled Langevin equations takes explicit account of the elementary microscopic processes of deposition, surface diffusion and desorption. The first of these contributes shot noise to the system while the last two produce configuration-dependent noise correlations. Direct numerical integration of these equations provides a formal alternative to Monte Carlo simulation of the growth process. Other applications and extensions are outlined in brief.

Continuous-space Monte Carlo simulations of epitaxial growth

Abstract Although lattice models have been very successful in modelling many aspects of epitaxial growth, the confinement of atoms to sites on a regular lattice is a severe impediment to extending these simulation studies to the heteroepitaxial growth of materials with a lattice mismatch. In principle molecular dynamics overcomes this limitation, but the disparity between simulational and laboratory timescales limits this method to the submonolayer regime of growth. Following the early work of Faux et al. [Phys. Rev. B 42 (1990) 2914], we have developed a Monte Carlo simulation where a continuous range of atomic positions are allowed. By adopting hard sphere interactions and a simple form of site hopping, we have investigated the effects of mismatch on the growth mode and made comparisons with Lennard-Jones molecular dynamics simulations. We will discuss the strengths and limitations of this way of combining the Monte Carlo and molecular dynamics methods for modelling epitaxial growth.

Math professor turns classroom program into successful business

The application of a distributed memory MIMD (multiple‐instruction multiple‐data) computer architecture to simulate growth during molecular‐beam epitaxy is discussed. The stochastic nature of the problem and the spatial distribution of the lattice onto an array of processors leads to the development of some new ideas and constructs to ensure the system follows the correct dynamical evolution. Performance statistics for the parallel implementation and comparisons of morphological indicators with the sequential model are presented.

Growth kinetics of non-planar substrates

Abstract We examine the temperature dependence of the growth kinetics on patterned (V-grooved) substrates by means of a Monte Carlo simulation of a solid-on-solid model. We have extended our previous model of MBE to include second nearest-neighbour interactions to incorporate facetting during growth. At high temperatures, surface diffusion of adatoms from one facet to the other leads to a distribution of growth rates on GaAs(001). However at low temperatures, where surface migration process are rare, growth on such substrates proceeds in a shape preserving manner. This behaviour has been observed experimentally by scanning microprobe RHEED experiments on GaAs(001) near the (111) surface, where the growth rate is associated with the period of the specular intensity. Such variations of the growth rates on different facets may open avenues for optoelectronic devices, which exploits the higher mobility of Ga adatoms as compared to Al.

Adatom mobility on vicinal surfaces during epitaxial growth

We present a generalization of the Burton-Cabrera-Frank (BCF) model of step flow growth on a vicinal surface which takes exact account of island nucleation due to adatom interactions. Our basic result takes the form of a BCF-type equation where the adatom concentration is replaced by a quantity which involves the concentration of atoms in all possible bonding environments. Under conditions where islands larger than dimers can be neglected, we obtain a non-linear differential equation for the adatom concentration which has a simple analytic solution. In conjunction with Ficks law, the origin of reduced adatom mobility in the presence of island nucleation is demonstrated explicitly.

Growth kinetics on vicinal surfaces

Abstract The application of Monte Carlo simulations to the kinetics of growth on vicinal surfaces by molecular beam epitaxy (MBE) is reviewed. Comparison with the experiments of Neave et al. illustrates the role of kinetic factors in determining the mode of growth at a given substrate temperature. The importance of surface steps in homoepitaxy upon the Si(001) surface is highlighted by inclusion of anisotropic bonding in the model to account for dimer formation. Application to the fabrication of quantum-well wires by MBE reveals an optimum regime of growth conditions (substrate temperature and beam flux) for producing high-quality structures.