David A. Reed

Surface diffusion, atomic jump rates and thermodynamics☆

Abstract The connection is established between the surface diffusivity D (θ) and Γ(θ), the rate of atom jumps in an adsorbed gas at a coverage θ. For a Langmuir layer, the two quantities are related at all coverages by D (θ) = Γ(0) λ 2 , where λ. is the jump distance, For interacting adatoms, however, the diffusivity also depends upon the chemical potential μ of the adatoms through D (θ) = Γ(θ) λ 2 [∂(μ/ kT )/∂ In θ] T . Techniques are presented for evaluating the thermodynamic factor [∂(μ/ kT )/∂ In θ] T in the diffusivity from adsorption isotherms as well as from fluctuation studies. The extent to which this factor affects the interpretation of diffusion measurements is tested in several ways: diffusion of a nearest neighbor lattice gas is formulated in the quasi-chemical approximation, the behavior of adatoms with interactions of longer range is examined by Monte Carlo simulations, and the available experimental measurements are analyzed. Both the jump rate and the thermodynamic factor are found to be affected by interactions between adatoms; the formation of superlatttices results in anomalies in both. These studies suggest that for layers of interacting adatoms, knowledge of the thermodynamics of the adsorbed layer is essential in any attempt to derive quantitative information about atomic jump rates.

Surface diffusivity and the time correlation of concentration fluctuations

Abstract Time correlation studies of concentration fluctuations have provided most of the recent data on the surface diffusivity of adsorbed gases. We examine the formalism which relates experimentally measured values of the time autocorrelation function, describing the number of particles in a small area element, to the diffusivity. It is shown that an exact expression can be obtained subject to only one important restriction: the decay of concentration fluctuations is characterized by a constant diffusion coefficient. In adsorbed layers, interactions between adatoms are likely to be strong, and the diffusivity is therefore expected to vary with surface coverage. The extent to which the same formalism can be utilized to obtain an effective diffusivity D C for interacting adatoms is examined using Monte Carlo simulations of two-dimensional lattice gases. The validity of the diffusion coefficient D C so derived is tested by comparing it with diffusivities D K obtained from a kinetic model or with values D M derived from a Boltzmann-Matano analysis. For a lattice gas with nearest neighbor interactions amounting to kT ∗ , where T ∗ is the temperature of the simulations, agreement between D C and the ordinary diffusivity is good even though the latter varies strongly with concentration. For interactions of longer range, comparisons of D C and D M again reveal good agreement. Only under conditions leading to the formation of a highly ordered superlattice on the surface do we find that the correlation methods fail to yield a diffusivity in agreement with values from the Matano analysis. With this proviso it appears that the present formalism for interpreting autocorrelation studies of diffusion is generally adequate to handle layers of interacting adatoms.

Vibrational excitation and surface reactivity: An examination of the ν3 and 2ν3 modes of CH4

The effect of vibrational excitation upon the chemisorption of methane on thin films of rhodium has been investigated. Vibrational modes of the gas are selectively excited by infrared radiation. The rate of reaction is measured by following the pressure decrease in a closed system containing CH4 in contact with the metal surface. Neither irradiation with a He–Ne laser at 3.39 μ to excite the ν3 mode, nor using an arc source with wavelengths in the range overlapping 2ν3, produces any detectable changes in the rate. From these experiments we estimate that the reaction probability of CH4 is <1×10−4 in the first excited state of ν3, and <7×10−2 in 2ν3. Other excitations must be involved in overcoming the barrier of ?7 kcal/mole which has previously been found for the chemisorption of CH4 on rhodium.

Chemical specificity in the surface diffusion of clusters: Ir on W(211)

Abstract Although the diffusion of tungsten and rhenium clusters over the (211) plane of tungsten has recently been found to be quite similar, a significant chemical specificity should be expected for cluster migration. Such specificity has now been established in quantitative measurements on iridium doublets diffusing on W(211). With tungsten and rhenium, dimers have a lower activation energy for diffusion than do single atoms. For iridium dimers, the situation is reversed: single atoms diffuse over a barrier of 51 ± 5 kJ mol−1, compared to a barrier of 65 ± 6 kJ mol−1 for dimers. This, and differences in the diffusion dynamics, are shown to be a consequence of interactions specific to iridium adatoms.

One‐dimensional random walks of linear clusters

A stochastic formalism is developed for the one‐dimensional surface diffusion of atom clusters, with component atoms located in adjacent channels, by representing the diffusion as a random walk of the center of mass (c.m.). Relations between the mean square displacement of the center of mass and the rate constants characterizing c.m. motion are derived for dimers and trimers, starting from the Kolmogorov equation. For dimers in the limit of long diffusion intervals, c.m. rate constants and individual atomic jump rates can be deduced knowing the mean square displacement and the frequency of occurrence of different dimer configurations. This analysis is feasible for trimers only under special conditions; even then, separation into the individual atomic rate processes is not, in general, possible.

Monte Carlo analysis of experiments on individual adatoms

Abstract Quantitative studies of individual adatom motion using the field ion microscope are difficult in as much as the number of observations is limited. However, simulations by Monte Carlo techniques make it possible to maximize the information obtained from small statistical samples. Questions encountered in studying the diffusion and interaction of adatoms have therefore been examined by simulation, and results are presented for the following topics: (1) Corrections for the finite size of planes on which atomic diffusion is observed. (2) Statistical scatter in the estimation of diffusion parameters from the temperature dependence of the mean-square displacement. (3) Conditions for measuring rates of single- and double-length jumps in atomic diffusion. (4) Uncertainties in the estimation of interaction energies from pair distribution measurements.

Measurement of boron segregation at the SiO2/Si interface using SIMS

Quantification of SIMS to measure the segregation coefficient of boron at the SiO2/Si interface has been examined. Standard boron implants into SiO2, Si, and SiO2/Si have been used to derive calibration factors for the oxide, substrate, and interface regions, respectively. Differences between these factors can be minimized by ratioing the 11B+ and 30Si+ secondary ion counts and by using glancing incidence O+2 bombardment without oxygen backfill. A segregation coefficient of six is found for boron‐doped Si(100) oxidized at 900 °C in 10 atm steam.

Statistics of One-Dimensional Cluster Motion.

The statistics of clusters, made up of metal atoms in adjacent one‐dimensional diffusion channels, are developed quantitatively. Kolmogorov’s equation is used to find the mean square displacement for clusters capable of existing in energetically different configurations at the same position of the center of mass; this is done under steady state conditions, for which the probability of finding a specified configuration does not vary in time. Two systems are examined: (1) dimers capable of existing in an infinite number of states, a situation realized if dissociation is allowed, and (2) trimers diffusing on planes, such as W(211), on which nine distinct jump processes may contribute to the cluster motion. In dimer diffusion it is demonstrated that dissociation may be important even if the fraction dissociated is minor. For trimers, previous attempts to approximate the motion through the use of average transition rates are compared with the exact solutions and found wanting. Important statistical quantities ...

Abstract: Computer analysis of FIM diffusion studies

Field ion microscopy has made it possible to observe the diffusion of single atoms or atom clusters at a surface and to examine the interactions between individual atoms. There are two main problems associated with such studies: (1) Only a small number of adatom positions can be recorded per observation, so that statistical fluctuations have a profound effect on the data. (2) The available planes are no larger than 100 A in diameter, and the effects of the plane boundaries may be significant.We have performed computer simulations1 of the diffusion of one and two adatoms over a surface, both to determine the magnitude of the statistical errors in such experiments and to ascertain the optimal conditions for data collection. In the usual expression for the diffusion coefficient, D= D0 exp(−VD/kT), the activation energy VD can be obtained to ±8%, and the prefactor D0 to an order of magnitude, provided M, the number of diffusion intervals in the Arrhenius plot, amounts to 300. The statistical error in VD can b...

Use of ISS and doubly charged secondary ions to monitor surface composition during SIMS analyses

Abstract The use of doubly charged secondary ions and binary scattered primary Ar ions to monitor major constituents in a sample during analysis of impurity elements by secondary ion microscopy is demonstrated. Experiments were performed with an unmodified Cameca IMS-3f secondary ion microscope.