Andrea K. Myers-Beaghton

Growth of III-V compounds on vicinal planes by molecular beam epitaxy

The dynamics of growth of III-V compounds by molecular beam epitaxy can be evaluated experimentally using the temporal variation of the intensity of reflection high-energy electron diffraction patterns. The use of substrate surfaces which are slightly misoriented from an exact low-index plane (vicinal planes) enables direct measurements to be made of cation migration parameters, but a correct analysis requires both step anisotropy and nucleation on the terraces to be taken into account. The experimental results are strongly supported by Monte Carlo simulations of growth, especially with regard to growth mode changes and the anisotropy of cation incorporation at steps. The direct growth of quantum wires (structures giving quantum confinement of carriers in two dimensions) on vicinal planes has been achieved experimentally and it is shown here how the wire quality, as determined by its compositional integrity, can be obtained by the simulation technique. The effects of flux, temperature, misorientation direction and interruptions of growth on quality are demonstrated.

Nonequilibrium lattice models of epitaxial growth

Abstract We illustrate the use of the Chapman-Kolmogorov and Master equations as a frame-work for solving models of epitaxial growth. Within this probabilistic approach, we specify rules governing the incorporation and migration of individual atoms, which then determine the transition rates between surface configurations. The Chapman-Kolmogorov and Master equations are then solved for either the full probability distribution of surface configurations, or for a reduced distribution function. Several idealized models for epitaxial growth are formulated and solved based upon rules for adatom incorporation into the growth front. Atoms are immobile once attached to the surface. The models studied are: (i) the random deposition model, wherein incident atoms attach to the point of initial contact with the surface; (ii) the perfect layer growth model, in which incident atoms are incorporated into the highest unfilled layer; (iii) the local perfect layer growth model, where incident atoms are incorporated into the highest unfilled layer within subsections of an adjustable size; and (iv) the local island model, which takes into account the tendency of an adsorbing atom to select sites with nearest-neighbor atoms. Inclusion of this modification results in the growth of square or rectangular islands whose size increases with the size of a subsection. These models are exactly solvable using the Chapman-Kolmogorov equation, yet some exhibit complex behavior, including decaying oscillations in the diffracted intensity and non-trivial spatial correlations within the surface. The mechanism for the damping of the oscillations is shown to be phase incoherence between growth occurring in different subsections, which is also manifested by an increasing surface roughness as measured by the root-mean-square distribution of occupied layers. Examining the relationship between the evolutions of the step density and kinematic reflection high-energy electron-diffraction (RHEED) intensities in these models underscores the role of surface correlations in determining the profile of measured RHEED intensities.

Nonlinear diffusion equation for epitaxial growth and recovery on vicinal surfaces

Abstract Recently, we derived a theoretical model for molecular-beam epitaxy (MBE) on vicinal surfaces that includes both adatom diffusion and a nonlinear term for diatomic island formation. The model was shown to reproduce and explain both the transient behavior of reflection high-energy electron-diffraction measurements of MBE on stepped surfaces and their dependence on the growth conditions. Here, we refine the model to include the formation of higher-atomic islands (with up to ten atoms) as well as their decay, and incorporate a simple model for atom attachment and detachment kinetics at the step edges. We show that incorporation of island break-up is necessary for a realistic model of recovery.

Growth Kinetics on Vicinal (001) Surfaces: The Solid-on-Solid Model of Molecular-Beam Epitaxy

Growth kinetics during molecular-beam epitaxy (MBE) on vicinal surfaces are simulated with a kinetic solid-on-solid model. Comparison is made between the simulated step-density and the specular intensity of reflection high-energy electron-diffraction (RHEED) measurements. In addition to identifying the kinetic mechanisms giving rise to observed phenomena, this similarity provides considerable insight into the sensitivity of specular RHEED to specific features of morphological sensitivity involving two-point surface correlations. Applications of the model encompass both III-V and group-IV semiconductors. Examples for GaAs(001) MBE include: (i) a discussion of growth modes on vicinal surfaces as a function of substrate temperature, with (ii) a direct determination of model parameters from a comparison of step-density and RHEED evolutions; and (iii) the fabrication of quantum wires. For growth on Si(001) surfaces, we discuss (iv) the role of monatomic and biatomic steps and the dimer reconstruction in determining the mode of growth, and (v) the coverage of 2 × 1 and 1 × 2 domains during growth and after recovery.

Step dynamics on vicinal Si(001) during epitaxial growth

Adatom migration and attachment kinetics of vicinal Si(001) surfaces are described within a nonlinear continuum framework for epitaxial growth. The transient and steady‐state terrace widths during growth are evaluated as a function of the growth conditions. Island formation is shown to be crucial in balancing the different capture rates of the two types of step edges to allow for a steady state of monatomic steps. We also find a greater tendency to form biatomic steps with increasing substrate temperature, decreasing beam flux, and increasing misorientation, in qualitative agreement with experimental measurements.

Two-dimensional kinematic diffraction patterns from simulations of epitaxial growth

Abstract In this paper, a procedure is described for the calculation of two-dimensional diffraction patterns from surface atom arrangements produced from computer simulations of epitaxial growth. The advantages of calculating diffraction patterns numerically from simulated atomic configurations over existing analytical work are: (i) since two-dimensionality is built into the simulation, it is possible to calculate the entire diffuse pattern in reciprocal space without any restricting assumptions about separability of the surface morphology into one-dimensional surface correlations; and (ii) it is possible to model intricate atom arrangements and diffraction patterns resulting from epitaxial growth, since complex kinetics such as migration and island formation can be easily incorporated into a simulation. The treatment is developed for simple cubic lattices within the kinematic approximation. The two-dimensional correlation function of the surface is calculated numerically and Fourier transformation yields the two-dimensional diffraction pattern. Very large surfaces (200 × 200 lattice sites) are used in order to include long-range correlations in the atomic arrangement, and averaging over several independent simulations limits the noise in the diffraction pattern. Two sample surfaces, one with elongated islands on a flat substrate and the other a vicinal surface with rough step edges, exhibit complex, anisotropic surface correlations and diffraction patterns.

Nonlinear theory for epitaxial growth of semiconductor alloys on vicinal surfaces

A set of coupled nonlinear diffusion equations is derived for describing the epitaxial growth of semiconductor alloys on vicinal surfaces. The equations include diffusion and a quadratic interaction term to account for incipient island formation. A criterion is obtained for determining the temperature Tc at which growth becomes dominated by step advancement as a function of alloy composition, substrate temperature, and growth rate. The sensitivity of Tc to variations in the interaction parameters is briefly discussed.

Nonlinear diffusion equation for crystal growth on stepped surfaces

An equation that includes both adatom diffusion and diatomic island formation is derived for describing growth on stepped surfaces. The equation is integrated numerically to obtain adatom and island concentration profiles along the terraces. Comparison of this solution with experimental measurements on vicinal GaAs(001) for a variety of Ga and As2 fluxes and with Monte Carlo simulations shows that inclusion of island formation in the growth equation is crucial in determining the temperature beyond which growth becomes dominated by step propagation.

The dynamic variations of terrace length during growth on stepped surfaces

A recently derived theoretical method for modelling molecular beam epitaxy on stepped surfaces, which includes a nonlinear term for nucleation, has been extended so that large deviations from periodic step structure can be examined. The method is used in conjunction with Monte Carlo simulations to monitor the growth dynamics of a stepped surface with unequal terrace lengths and identify the stable configuration. The authors show that the equidistant step configuration is favoured even in growth regimes where nucleation on the terraces competes with atom incorporation at steps. Furthermore, they found a remarkable qualitative correspondence of the results obtained from the nonlinear diffusion equations and the simulations.

Growth kinetics and electronic characteristics of quantum wires

Abstract The fabrication and characterization of narrow quantum wires is studied with a combination of theoretical techniques. Using the compositional integrity as a measure of quality, our earlier work has shown that quantum wires generated by a Monte Carlo simulations of crystal growth attain the highest quality within a narrow range of substrate temperatures that depends upon the beam flux and terrace width. We examine the factors that influence the electronic density of states of such quantum wires within a tight-binding framework and discuss the compositional integrity of the structures in relation to the quantum mechanical integrity. The effects of migrating species with different mobility parameters are then considered by appealing to recent work describing growth on vicinal surfaces with an effective nonlinear diffusion equation.