M. Zinke-Allmang

Clustering on surfaces

Abstract In this review we summarize the current theoretical and experimental understanding of clustering phenomena on surfaces, with an emphasis on dynamical properties. The basic theoretical concepts to predict evolving cluster size distributions are presented, with extensions to less restrictive assumptions, such as including the influence of non-zero deposition rates. The discussion of experimental results to test these concepts is preceded by a brief introduction of the experimental techniques used in morphological cluster studies. Finally, two important physical surface quantities, surface diffusion coefficients and adatom binding energies, are used to demonstrate the impact of clustering in their understanding.

Phase separation on solid surfaces: nucleation, coarsening and coalescence kinetics

Fundamental issues of the kinetics of phase separations on surfaces are reviewed with an emphasis on developments during the period from 1990 to present. Issues covered include: (i) the stability of thin films toward clustering, (ii) non-uniform film formation during deposition and (iii) non-uniform film evolution in the post-deposition phase.

Nitrogen content of oxynitride films on Si(100)

The absolute nitrogen concentration in SiOxNy/Si films grown by rapid thermal oxidation in N2O has been determined by nuclear reaction analysis. Compared with conventional surface analysis methods, i.e., Auger electron spectroscopy, x‐ray photoelectron spectroscopy, and secondary ion mass spectrometry, the nuclear reaction 14N(d,α)12C provides more accurate depth profiles of 14N due to the quantitative nature of the technique and its high sensitivity, ∼6.0×1013 atoms cm2. Silicon oxynitride films prepared under various conditions, specifically different growing temperatures and times, were analyzed. Nitrogen is observed to accumulate in a narrow region in the oxynitride (within ≲2.5 nm) close to the interface; the total amount of nitrogen increases with increasing temperature and growth time.

Rate equation approach to the late stages of cluster ripening

Off-critical phase separation processes are frequently described in literature on the basis of a set of rate equations describing the change rate of number of clusters of given size. This approach works very well for nucleation, but computational limitations and the complexity of processes impede its applicability in the early stages of cluster growth. Late stage clustering in mass conserved systems, which starts much later during the evolution of the morphology of the system, is well understood on the basis of the Lifshitz–Slyozov–Wagner (LSW) theory. In this paper both concepts are connected analytically, showing that identical predictions resulted for the same (simplified) assumptions. Significance of the equivalency of both models has been further explored, particularly in bridging the early stage of clustering, which is not well understood.

Fundamental problems concerning three dimensional clustering on surfaces

By extending the two dimensional theory of islanding by Marqusee to the case of three dimensional clustering on surfaces, we investigate the power law behaviour of average cluster radius as a function of time. We find that the average cluster radius asymptotically approaches the t1/4 behaviour predicted in previous models which have been based on physically unreasonable assumptions. We discuss the effect of reshaping during cluster formation on surfaces on the expected cluster size distribution. A nonequilibrium cluster shape may explain the positive skewness and the widening of the size distribution which have been observed experimentally.

Backscattering analysis of Si1−yCy layers using the 12C(4He,4He) 12C resonance at 4.265 MeV

Abstract Resonant backscattering of 4 He ions using the 12 C( 4 He, 4 He) 12 C resonance at 4.265 MeV has been used to analyze C in MBE grown Si 1− y C y layers and in ion implanted Si with C concentrations of the order of one at.%. With ion channeling the ratio of substitutional to interstitial C sites in the Si 1− y C y layers was determined and the obtained values for the tetragonal distortion are compared with results from X-ray diffraction measurements. The measured C amount of an ion implanted sample used for calibration was in good agreement with the nominal amount, while the range distribution was about 15% shallower than predicted by TRIM calculations. Strong deviations from the Rutherford scattering cross section are observed for scattering from Si and the influence due to background from nuclear reactions with Si on the C analysis is discussed.

Areal fraction effects during late-stage clustering on surfaces

Abstract Late stage cluster growth on surfaces is studied as a function of the areal coverage of the cluster phase for the system Sn on Si(111). Variations in the cluster size distributions were measured with increased precision based on relative measurements on the same sample using ultra-high vacuum deposition with the partial retraction of a mask. In addition, a variation of cluster growth rate on areal coverage was measured. The results show that the cluster growth rate increases by a factor of two with an increase in the areal coverage between 0.1% and 2%. This effect is larger than the increase predicted for three-dimensional systems (precipitate growth in a surrounding solution). Similarly, relative cluster distribution widths increase by 20% at 0.1% areal coverage and 30%–40% at 2% areal coverage. These effects are again larger than the predicted values for two- and three-dimensional systems.

Late stage cluster growth: spatial correlations and ordering on surfaces

Abstract The widely accepted models for late stage clustering, the Lifshitz-Slyozov-Wagner theory for Ostwald ripening and the self-similar Monte Carlo simulations by Family and Meakin for coalescence growth, are consistent with random spatial distributions of the clustered phase. Several detailed investigations have revealed that cluster-cluster interactions have to be further considered. Only one of these studies lead to predictions of spatial ordering when long-range repulsive forces were included. In this paper we investigate nearest neighbor cluster distance distributions for both late stage growth processes (coalescence for Ga on GaAs(0 0 1) and Ostwald ripening for Sn and In on Si(1 1 1)) and correlate the results with experimental and theoretical results for the cluster-cluster interaction in these systems. Non-random spatial distributions are found for ripening even at rather low areal cluster densities, indicating that (i) cluster-cluster interactions play a major role in the morphological evolution of ripening structures at much smaller areal fractions than previously assumed and (ii) the Gibbs-Thomson effect, in combination with a diffusion controlled exchange of matter between clusters, is sufficient as a driving force to obtain partially ordered structures.

Screening effects during late stage phase separation

Late stage phase separation is an important non-equilibrium thermodynamics process with a range of implications for applied systems such as thin film growth. A number of studies describe quantitatively Ostwald ripening, the dominant process under mass conservation. In these models the concept of a screening length occurs in different context, for three-dimensional systems to accommodate finite volume fractions of the minority phase, and for two-dimensional systems to circumvent the diverging steady state solution to the diffusion equation. We present a comprehensive review of this concept and show that the screening length in two- and three-dimensional systems has the same form if the average cluster radius and the average cluster cluster distance are used as parameters. In the experimental section, examples for two- and three-dimensional systems are given, showing that the screening length shields the interaction between clustering systems across a concentration step. This leads to sharper than expected interfaces between neighbouring ripening systems on a surface, and explains the resistance of sub-surface silicide clusters to dissolve into a uniform, buried film during annealing.

Thin film growth dynamics analyzed by ion scattering

The growth of new solid structures created by controlled, ultrathin film deposition has become the driving force for much of current-day solid state science. A typical example is the growth of strained-layer superlattices where new materials properties are sought based on both the strain and the composition modulation. However, for lattice mismatched systems a uniform film is never the equilibrium state, rather cluster formation is predicted (Volmer-Weber and Stranski-Krastanov growth models) and experimentally observed. In this paper experimental techniques to characterize clustering phenomena are reviewed with a main emphasis on ion scattering methods. We show how equilibrium structures as well as dominant cluster growth processes can be distinguished. As a result, the first determination of an activation energy for surface diffusion on a Stranski-Krastanov layer is presented.