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One of the goals for growing low dimensional structures is to explore their electronic structure variation with size due to confinement. Recent experiments in Pb adsorption on Pb islands of stable and unstable height at low temperatures have shown a spectacular variation in the nucleated island density (∼60 times) as a function of height. With Monte Carlo simulations we can faithfully reproduce the observed morphologies with a single assumption that i c is different on stable and unstable islands. This shows that confinement can result in large oscillations of nucleation rates and adsorption.

A novel growth low temperature morphology is observed in the growth of Pb/Si(1 1 1) related to the kinetics of Quantum Size effects. This morphology is globally observed over mesoscopic distances. Bilayer height rings nucleate first at the island perimeter which spread out towards the center. With Monte Carlo simulations the morphology is reproduced with highly anisotropic diffusion (i.e., radial diffusion out of a ring of one lattice constant is slower than azimuthal diffusion by at least 10−5 at 180 K). This shows that both kinetics and energetics are responsible for the uniform height island formation and the similar temperature “window” ∼180 K independent of the initial Si interface.

We use Monte Carlo simulations to study the mobility and collective diffusion of mutually interacting adparticles on stepped surfaces. We consider the case of nearest–neighbor repulsive interactions together with different binding and activation energies at the step edges in the disordered phase. To complement previous work that focused on diffusion across steps, here we concentrate on diffusion along the steps in the case of strong step binding. We find that the collective diffusion behavior is dictated by a complex interplay between enhanced or suppressed diffusion along the lower step edge positions, binding at step edges, and interactions between adparticles. Diffusion along the lower step edge positions plays a particularly important role at low coverages, while at high coverages diffusion is governed mainly by adparticle interactions.

Pb diffusion on the Si(1 1 1)-7 × 7 surface was studied with 16 different energy barriers. As a part of general problem of diffusion in the unit cell, some characteristics of diffusion (as frequency factor, effective energy barrier or differences in binding energy) was found analytically as a steady state solution of the master equation. The probability distribution of the occupation of particular sites was compared with the result of the Monte Carlo simulation and the STM experiment. Starting from the values obtained with the semi-empirical extended Huckel approximation, the diffusion barriers were adjusted to obtain a reasonable coherence with the experiment. The results of MC simulation and the analytical solution agree quite well and reproduce the dynamics of a Pb atom in the 7 × 7 unit cell.

We study non-equilibrium effects in spreading and collective diffusion of adatoms on stepped surfaces through Monte Carlo simulations of a lattice-gas model. The spreading density profiles are analyzed by the Boltzmann–Matano method to determine the temporal behavior of the effective collective diffusion coefficients. We find that the presence of steps induces considerable non-equilibrium effects in diffusion. For spreading along the steps, we find that these deviations can be explained by the slow approach of the different adparticle concentrations on terraces and at step edges towards equilibrium. For spreading across the steps, however, we find no such dependence, indicating the breakdown of the linear response theory at early times.

Surface diffusion is studied in a two barrier system, i.e. a system with two different activation energies. The dynamic and thermodynamic properties of the system of interacting ad-atoms on an fcc(1 1 1) surface are studied using Monte-Carlo simulations, the Bortz–Kalos–Lebowitz algorithm and the Metropolis algorithm. The results are compared with our previous analytical calculations in the same system. Numerical results fit well to the analytical results for high temperatures. At low temperatures, contrary to previous analytical calculation (based on quasi-chemical approximation), we observe a sharp local minimum at a coverage Θ =0.5 in the case with repulsive interaction and a large difference between activation energies. The Monte-Carlo simulations result in a higher occupation of deep sites, formation of an ordered phase and in lower diffusion coefficient in comparison with the analytical results.

The collective diffusion coefficient is studied for a system of particles adsorbed on a surface with two non-equivalent adsorption sites. The non-equilibrium conditions are characterized by the non-equilibrium distribution of atoms between adsorption sites with different energy of adsorption. The determination of the diffusion coefficient is based on the general theory published in [J. Phys. Condens. Matter. 12 (2000) 6343] and links to the former studies of the diffusion coefficient and phase diagrams of the same systems in equilibrium. Our analysis shows that non-equilibrium conditions strongly influence the step-like dependence of diffusion coefficient on coverage, as determined in equilibrium conditions for non-interactive adparticles, and that the diffusion coefficient can even have an opposite behavior. Far from equilibrium the appearance of a local maximum is observed. These deviations reflect the influence of the state of the adparticle system on their collective behavior.

We investigated phase diagram of a system of particles adsorbed on a lattice with two non-equivalent sites, the number of which in the elementary cell and adsorption energy is different. The repulsive lateral interaction between particles in the nearest neighbour non-equivalent sites is considered. The existence of phase transition was found, depending on the parameters of the system (the difference in adsorption energies and interaction energy) and on surface geometry. The phase diagram for repulsive interaction differs considerably from the phase diagram of an ordinary lattice gas with equivalent sites and shows non-monotonic dependence of the critical temperature T c on adparticle surface coverage θ .

The interrelation between the surface symmetry and diffusion of adsorbed atoms is studied theoretically on a model face-centred cubic (fcc) (111) surface within the lattice-gas approximation. Diffusion proceeds through two non-equivalent sites on the fcc(111) surface. Short-range repulsive interaction between particles in the nearest-neighbour non-equivalent sites is considered. This repulsion leads to a modification of the occupation numbers of both kinds of site and to changes in the energy barrier height for diffusion. The chemical surface diffusion coefficient, D, has been found to be strongly dependent on coverage, Θ, the interaction strength between adatoms, and the difference between the activation energies, ΔE. In the case of a small ΔE value, the diffusion coefficient D increases with Θ, as was expected for repulsive interaction. In our model the increase of D at Θ=0.5 is reduced for higher values of ΔE and a local maximum of D(Θ) is observed.

Diffusion on a fcc(111) surface will be studied theoretically. Diffusion proceeds through non-equivalent hcp and fcc sites with different adsorption energy. Repulsive interaction between particles in the first neighbour sites and change of saddle point energy due to interaction are included. In this model the repulsion to the next neighbour site results in the inadequately increased diffusion coefficient. The large difference of adsorption energy between hcp and fcc sites depresses diffusion at higher coverages and diffusion coefficient has maximum at Θ=1/2. Inclusion of the change of the saddle point energy reduces increase of D and results in a tame local minimum, emphasizing a local maximum.

The effective energy barrier for diffusion, E a , has been previously determined as a function of coverage and temperature within a two-barrier model of diffusion, assuming an Arrhenius form of chemical diffusion coefficient. To determine the diffusion coefficient at a given temperature and coverage, we used previously published results based on the lattice gas model of non-interacting adatoms. The presence of two non-equivalent sites for adsorption and diffusion of atoms on a surface (with energy barriers E 1 , E 2 ) results in substantial changes to E a within coverage Θ , with a step-like shape having a value close to Θ =1/3. The temperature dependence of E a shows a slight minimum, and the Arrhenius shape (with constant E a ) seems to be good approximation of the relatively small differences in energy barriers E 1 , E 2 . We obtain considerable deviation from such an Arrhenius behaviour of diffusion when there is a large difference in the energy barriers.

We calculated the surface diffusion coefficient D as a function of coverage in the quasi-chemical approximation of a system of particles on a square lattice with two non-equivalent binding sites characterized by different activation energies E1 and E2 for diffusion. A short-range repulsive interaction between particles in the nearest neighbour non-equivalent sites is considered, resulting in the modification of these energies by δE. The thermodynamic and kinetic parts of D have been calculated separately, in order to estimate their contribution to the diffusivity at different concentrations. It has been found that D exhibits a step-like increase at a critical coverage Θc which varies from Θc=0.33 for δE=0 to Θc=0.5 for E1=E2. The origin of the concentration dependence of D is discussed in terms of the repulsion strength between particles and their jump-rate through the sites existing on the surface.

The chemical surface diffusion coefficient D has been determined for a lattice-gas model where diffusion proceeds through two non-equivalent lattice sites with different activation energies, E1 and E2. By calculating the thermodynamic factor as well as jump diffusion rate we obtain the coverage dependence of D as a function of the energy difference E1 − E2. No lateral interactions are considered. Depending on the sign of E1 − E2, the diffusion coefficient shows either a maximum or a step-like increase at a particular coverage, both of which develop into discontinuities in the limits of either E1 − E2 → ± ∞. In the case of the step-like behaviour of D, the variation of D can be classified as being due to a kind of diffuse phase transition between a low and a high diffusivity state, which in the limits is shown to be of first order.

By calculating the jump diffusion rate (Г) and the thermodynamical factor (Kd) for a layer of non-interacting particles on a lattice with the non-equivalent bond sites we show that the diffusion coefficient D = ГK d exhibits specific features as a function of coverage, such as steps or maxima at critical coverages, which correspond to phase transformations in the adlayer. The chemical potential of the adlayer is derived analytically from the free energy. The difference of binding energy between the two kinds of sites is described by a parameter k and it is shown that the chemical potential (or the thermodynamic factor) at the critical coverage indicates the existence of a diffuse phase transition which develops for k → 0 into a first-order point phase transition.

The capability of the laser-induced thermal desorption technique (LITD) to detect the migration of adsorbed oxygen on a semiconductor surface is demonstrated. The surface diffusion coefficient of oxygen on Ge{100}(2 × 1) has been measured for a constant initial coverage in a wide temperature range (220–650 K). The experimental results show that after an initial stage of fast refilling of the depleted area the diffusion process strongly slows down. In the first stage the data can be fitted by the solution of Fick's second law. Within this approximation of a constant diffusion coefficient, an extremely low activation energy (∼ 0.04 eV) is obtained. The observations suggest that the second stage in the refilling process is connected with an irreversible chemical reaction between adsorbate and substrate.

An analytical expression for the surface diffusion coefficient is derived by summing the fluxes due to single jump events between adjacent sites on a simple square lattice. All microscopic configurations of a layer of interacting particles are included at particular coverages. In a quasi-chemical approach, the nearest-neighbour particle-particle interactions are introduced by adjusting the jump rate as well as by adapting the probability of occurrence of particular configurations consistent with the concentration. The diffusion coefficient is found to be dominated by the latter contribution at medium and high concentrations. A comparison with the results of Monte Carlo simulations shows that an improved approximation can be achieved if the interactions are accounted for not only by changes of the activation energy of diffusion but also by their effect on the equilibrium distribution of the particles.

A dynamical description of surface diffusion is presented for a surface containing two non-equivalent bonding sites with different binding energies. Diffusion proceeds via single hopping events between adjacent sites which can be of both kinds. Dynamical coupling is introduced by assuming that the hopping rates into and out of one type of site depend on whether the adjacent site of the other kind is occupied or empty. The derivation starts out from the microscopic difference equations accounting for the single jump events for all possible configurations. These are then transformed into differential equations with continuous functions and solved by the method of finite differences. The activation energies for individual jumps serve as adjustable parameters. It is shown that the widely observed dependence of the diffusion coefficient on coverage also follows naturally from this model, although direct particle-particle interactions in the usual sense are specifically excluded. The influence of the substrate-adsorbate interaction and of the surface geometry on the diffusion process is also discussed.