J. M. Pimbley

Atomic correlations of stepped surfaces and interfaces

We have developed a scheme to evaluate the atomic pair correlation function exactly for stepped surfaces and interfaces. This pair correlation function is particularly useful in calculating the diffracted beam width and shape from an arbitrary distribution of steps using low‐energy electron diffraction, reflection high‐energy electron diffraction, and grazing x‐ray diffraction. We have made model calculations for several realistic terrace width distributions. By comparing the calculated and measured diffracted beam widths and shapes, one can extract valuable, quantitative structural information on surfaces, interfaces, and epitaxially grown films.

Exact one‐dimensional pair correlation functions of a monolayer/substrate system

We have derived an exact expression for the one‐dimensional atomic pair correlation function of the combined overlayer and substrate system in the very first stages of epitaxy. The overlayer can have an arbitrary island size distribution. This pair correlation function is then used to evaluate the widths and shapes of low‐energy (or high‐energy) electron diffraction intensity profiles. Several model calculations have been computed and the diffraction profiles resemble the recent molecular beam epitaxy measurements of Si/Si(111) and W/W(110) systems reported by Henzler and co‐workers.

Atomic correlations during the first stages of epitaxy

We have developed a new scheme to evaluate the atomic pair correlation function analytically and exactly for the combined overlayer and substrate system during the first stages of epitaxy. This function describes the morphology of growth on the atomic scale. The overlayer atoms can be a random lattice gas or islands with an arbitrary distribution of sizes. The atomic pair correlation function is particularly useful in calculating the widths and shapes of the intensity diffracted from epitaxially grown films using low energy or high energy electron diffraction (LEED or RHEED). We have carried out several realistic model calculations involving metal–metal and semiconductor–semiconductor epitaxy. The results are compared to the recent molecular beam epitaxy measurements of W/W(110) and Si/Si(111) reported by Henzler and co‐workers.

Integral representation of the diffracted intensity from one‐dimensional stepped surfaces and epitaxial layers

An integral representation of the diffracted intensity from one‐dimensional stepped surfaces and overlayers is obtained based on the single‐scattering (kinematic) theory. We find exact solutions for an arbitrary terrace or island size distribution on stepped surfaces or epitaxial layers in an extremely simple manner. This theory greatly expands the utility of the kinematic analysis of electron, atom, or grazing x‐ray diffraction data. A particularly useful area of application is the quantitative study of the nucleation kinetics during the epitaxial growth of thin films. Several surface ordering models are discussed in terms of this simplified approach.

A two-dimensional random growth model in layer-by-layer epitaxy

Abstract We present an epitaxial growth model in which a random occupation of substrate lattice sites is assumed before the completion of each layer in layer-by-layer growth. The atomic pair correlation function of the combined adsorbate and substrate system is evaluated. Based on this correlation function we have calculated in closed-form the backscattered electron diffraction beam profile as a function of coverage in the kinematic approximation. We show that the diffracted beams do not broaden but the intensity oscillates as a function of the layer thickness. Realistic applications of this model are discussed.

Two‐dimensional atomic correlations of epitaxial layers

We have evaluated the two‐dimensional atomic pair correlation function for surfaces containing finite layers of adsorbed atoms and having a random distribution of steps. The step probabilities for the two lateral directions are mutually dependent. We employ a third‐rank tensor formalism to describe the two‐dimensional array of occupation probability vectors from which we derive the pair correlation function. The two‐dimensional electron diffraction angular profile is obtained from this pair correlation function. We have made detailed calculations with the two‐layer system as an example and found that the diffraction characteristics describe qualitatively a recent molecular beam epitaxy experiment of Si on Si(111) surface.

Weakly coupled two‐dimensional correlations in finite‐level epitaxy and chemisorption

We formulate a two‐dimensional ordering model for a finite‐level system of adatoms on a crystalline surface. The placement of steps in the two surface directions obeys Markovian disorder. Steps in the two directions are weakly correlated due to the restriction that the system occupies only a finite number of levels in the vertical dimension. In particular, we derive the surface atom pair correlation function and the diffracted intensity for the two‐level system and obtain a closed‐form solution. We discuss the effect of the weak correlation of the two surface directions. This is perhaps the simplest two‐dimensional model that can describe the molecular‐beam epitaxy measurements of Si/Si(111) reported by Gronwald and Henzler [Surf. Sci. 117, 180 (1982)]. The results of our calculation are also compared to our previous one‐dimensional and fully correlated two‐dimensional model calculations.

Characterization of surface defect structure by low energy electron diffraction

Low energy electron diffraction is a surface sensitive tool which is most widely used for the determination of surface symmetries and equilibrium atomic positions. Experimental and theoretical advances made in the past five years make it possible now to use LEED also for the characterization of a wide variety of surface defect structures. In this paper a variety of experimental results involving analysis of diffracted electron beam shapes as a function of primary electron beam energy, adsorbate coverage, crystal temperature and ordering time are presented. These experimental results coupled with kinematic theory, allow the determination of step density, size and shape of reconstruction domains and overlayer islands, island size distribution in an overlayer during growth, and the mode of growth. 27 references, 4 figures.

Island coalescence in a chemisorbed overlayer

We have constructed and solved an overlayer island growth model in which the distribution of the islands obeys an ‘‘extended geometric distribution function.’’ This model describes quantitatively the growth of oxygen p(2×1) islands on a W(112) surface as the coverage is increased from 0 to 1. The average size of the islands is seen to increase sharply as the coverage approaches 1/2 monolayer, which is an indication of the coalescence of the overlayer islands.

Distribution of domain sizes during overlayer growth

Abstract The distribution of antiphase boundaries created in an overlayer after quenching from a two-dimensional lattice gas phase is described by Markovian disorder. We show that many types of antiphase boundaries with different widths are possible. This one-dimensional distribution is used to describe the growth of oxygen p(2×1) antiphase domains along the doubly-spaced direction on a W(112) surface after quenching from a disordered, lattice gas state.