R. Kariotis

Determination of roughness correlations in multilayer films for x-ray mirrors

Interfacial roughness in multilayer films may be random or correlated, i.e., replicated from layer to layer. It is shown that these can be separated and quantified using x‐ray diffraction rocking curves and a straightforward analysis. The lateral correlation length along the interfaces can additionally be determined. A quantitative evaluation for W/C multilayers shows that correlated roughness contributes significantly to the total roughness, even at length scales that are surprisingly short, of the order 2–6 nm.

Scanning tunneling microscopy study of diffusion, growth, and coarsening of Si on Si(001)

The growth, diffusion, and coarsening of Si on Si(001) have been investigated with scanning tunneling microscopy (STM). A diffusion coefficient for Si has been determined. Anisotropy in the island shapes during epitaxy is shown to be principally a growth structure due to an anisotropic accommodation coefficient. Diffusional anisotropy is small. An ordered ‘‘diluted‐dimer’’ structure is observed at low coverages and temperatures.

Surface step configurations under strain: kinetics and step-step interactions

Abstract Strain is an important ingredient in the physics of surfaces as has been shown in experiments with thin films and alloys. It is desirable to have strain as an externally applied and continuous variable. We have studied the effect of strain by loading a cantilevered bar and observing the effects on the surface with both LEED and the STM. On the Si(100) surface, strain produces a reversible asymmetry in the relative population of the 2 × 1 and 1 × 2 domains. This requires the motion of monatomic steps which are the domain boundaries. The effect is driven by the relaxation of the energy associated with a long-range strain field extending into the bulk due to the anisotropy of the intrinsic stress tensor of the two reconstructed domains. It is similar to magnetic domain structures reducing the magnetic field energy. These long-range strain fields have important consequences for a number of surface phenomena. Here we first report experiments on the terrace width distributions which gives information about the effective step-step interactions. Then we report experiments on the kinetics of the step migration which gives information about surface diffusion.

Rate equation modelling of epitaxial growth

Abstract A rate equation model describing molecular beam epitaxy (MBE) is presented. This formulation of the problem consists of a set of equations that govern the population of islands of varying sizes and heights above the substrate. There is one equation for the time rate of change of the number of islands of each possible size at the j th level above the substrate. Use of this information is made in combination with some simple arguments from statistical mechanics to obtain a qualitatively detailed pair correlation function, and from this the scattered intensity as a function of time. The rate equation approach allows for a compact and fast method of simulation of film growth, complementing the more complete but time consuming Monte Carlo (MC) and molecular dynamics (MD) methods. By varying the different energy parameters in the equations it is possible to model situations in which the interface grows approximately in the layer-by-layer, or in the completely rough, mode. As a particular application we discuss the problem of the interface width growth (IWG) as a function of temperature, deposition rate, and binding energies. This width is essentially the number of incomplete layers (coverage different from either 0 or 1) at any given instant, and is a useful measure of the extent to which the system has made the transition from the bounded to unbounded IWG mode.

Ordering kinetics at surfaces

Abstract Aspects of the kinetics of ordering at surfaces are briefly reviewed, including discussions of the growth law and diffusion in a nonequilibrium environment both for phase coexistence and for single stable phases. Examples of two-dimensional ordering are given, including a low-energy electron diffraction study of O / W (110) and a scanning tunneling microscopy (STM) study of the initial stages of growth of Si on Si (001). Ordering kinetics involving the third dimension are illustrated, with an STM study of step bunching on vicinal Si (111) and model calculations using rate equations for A-on-A epitaxial growth.

X‐ray diffraction measurement of partially correlated interfacial roughness in multilayers

The existence of partially correlated roughness in multilayer thin films is demonstrated using x‐ray diffraction diffuse‐intensity distribution measurements. The method is generally applicable and produces, in addition to values of magnitudes of interfacial roughness and its lateral correlation length, a measure of the cross correlation between interfaces separated by intermediate ones. A simple phenomenological model can describe roughness in W/C multilayers prepared under standard conditions. A cumulative roughness function is used to show that the wavelength range in which the interfacial roughness predominates in these layers lies between 50 A and 2000 A and that the long‐wavelength roughness replicates better than the short‐wavelength roughness.

Diffraction from multilayer films with partially correlated interfacial roughness

The interfacial roughness in multilayer films is described by a model in which the parameters are directly related to those of microscopic growth processes. The height‐height correlation function is extracted from this model. Stationary and nonstationary roughness are discussed. The diffuse intensity in diffraction from multilayer films that have various degrees of correlation in roughness between interfaces is calculated. The presence of perfect or partial interfacial roughness correlation can be distinguished unambiguously in the diffusely scattered intensity.

Temperature dependence of the step structure of vicinal Si(001) surfaces

Abstract Si(001) surfaces miscut slightly towards the [110] direction consist of alternating domains of (1 × 2) and (2 × 1) reconstruction, separated by inequivalent, single-atomic-height steps; at higher miscut angles, the surface is mainly monodomain, with terraces separated by double-atomic-height steps. High-resolution low-energy electron diffraction has been used to determine the step structure of vicinal Si(001) as a function of both temperature and miscut angle. The concentration of double-atomic-height steps continuously increases with miscut angle and, for vicinalities greater than ~ 2°, decreases with increasing temperature. From a comparison of the experimental results with the predictions of a one-dimensional model treating the problem in terms of chemical equilibrium in a two-component system we obtain information on the energetics of the structure transformation.

Maximum entropy calculation of the island‐size distribution for a simple diffraction profile

In this article we derive several results concerning diffraction from random surface configurations. First, we describe a practical method for inverting diffraction data in order to obtain an explicit expression for the size distribution of diffracting islands on a substrate. The principle of maximum entropy is used to fix the distribution in the form P=exp[−F(A)], where F(A) is a polynomial in the island area A. Then we show that the most general use of the maximum entropy principle requires that F for the exact size distribution be a simple, linear function of the geometry of the scatterers. While this result is of considerable practical use, of greater importance is the fact that it puts distinct and well‐defined limits on the possible functional form that P(A) may exhibit. An example calculation is made using our diffraction data for indium on gallium arsenide.

Calculation of terrace-edge structure distributions for vicinal surfaces

Abstract Systematic calculations of the distributions that describe terrace-edge properties on vicinal surfaces are presented. These calculations provide a complete framework for the quantitative analysis of STM images. Using a simple one-dimensional model of vicinal terrace-edge structures, we calculate: the correlation length along the terrace edge; the distribution of kink lengths and kink separations at the edge; the distribution of zero-crossing separations; the distribution of edge displacements; the pinned-edge distribution.