Christian Ratsch

Equilibrium theory of the Stranski-Krastanov epitaxial morphology

Abstract We present a theory of the equilibrium morphology adopted by N atoms of one material when they crystallize epitaxially onto the surface of a dissimilar material. The discussion is limited to the case of the so-called Stranski-Krastanov morphology where a strongly bound but elastically strained wetting layer coats the substrate. The arrangement of atoms atop this layer is determined by minimizing an approximate total energy expression derived for a set of vertically coupled Frenkel-Kontorova chains of finite yet variable length. In this way, both elastic and plastic strain accommodation are treated with a common formalism. Our semi-analytic treatment permits us to compare very rapidly the energy of essentially all configurations of N atoms (up to about N = 5000) including uniform films, coherent islands and dislocated islands. The results are presented in the form of a morphological phase diagram as a function of misfit, surface energy and total particle number for the case of diamond structure materials. Coherent islands are found to be stable in a non-negligible portion of the phase diagram and the relevant phase boundaries are well predicted by simple analytic expressions. A kinetic interpretation of the results is possible when the variable N is redefined appropriately.

Nucleation theory and the early stages of thin film growth

A review is given of nucleation and growth models as applied to the earliest stages of thin film growth. Rate equations, kinetic Monte Carlo, and level set simulations are described in some detail, with discussion of remaining uncertainties, in particular the functional form of the so-called capture numbers in rate equations. Recent examples are given of sub-monolayer nucleation at surface defects, attachment-limited capture, and Ostwald ripening. The experimental literature is cited, and experiment–theory comparisons are made where possible. Emphasis is given to fast computational models that can span a large range of length and time scales, which might be further developed in the direction of on-line process control.

Strain dependence of surface diffusion: Ag on Ag(111) and Pt(111)

Using density-functional theory with the local-density approximation and the generalized gradient approximation we compute the energy barriers for surface diffusion for Ag on Pt(111), Ag on one monolayer of Ag on Pt(111), and Ag on Ag(111). The diffusion barrier for Ag on Ag(111) is found to increase linearly with increasing lattice constant. We also discuss the reconstruction that has been found experimentally when two Ag layers are deposited on Pt(111). Our calculations explain why this strain driven reconstruction occurs only after two Ag layers have been deposited.

ISLAND DYNAMICS AND THE LEVEL SET METHOD FOR EPITAXIAL GROWTH

Abstract We adapt the level set method to simulate the growth of thin films described by the motion of island boundaries. This island dynamics model involves a continuum in the lateral directions, but retains atomic scale discreteness in the growth direction. Several choices for the island boundary velocity are discussed, and computations of the island dynamics model using the level set method are presented.

Submonolayer epitaxy without a critical nucleus

Abstract The nucleation and growth of two-dimensional islands is studied with Monte Carlo simulations of a pair-bond solid-on-solid model of epitaxial growth. The conventional description of this problem in terms of a well-defined critical island size fails because no islands are absolutely stable against single atom detachment by thermal bond breaking. When two-bond scission is negligible, we find that the ratio of the dimer dissociation rate to the rate of adatom capture by dimers uniquely indexes both the island size distribution scaling function and the dependence of the island density on the flux and the substrate temperature. Effective pair-bond model parameters are found that yield excellent quantitative agreement with scaling functions measured for Fe Fe (001) .

Structure determination of small vanadium clusters by density-functional theory in comparison with experimental far-infrared spectra

The far-infrared vibrational spectra for charged vanadium clusters with sizes of 3-15 atoms have been measured using infrared multiple photon dissociation of Vn+Ar-->Vn(+)+Ar. Using density-functional theory calculations, we calculated the ground state energy and vibrational spectra for a large number of stable and metastable geometries of such clusters. Comparison of the calculated vibrational spectra with those obtained in the experiment allows us to deduce the cluster size specific atomic structures. In several cases, a unique atomic structure can be identified, while in other cases our calculations suggest the presence of multiple isomers.

The far-infrared spectra of neutral and cationic niobium clusters: Nb50∕+ to Nb90∕+

Far-infrared absorption spectra of small neutral and cationic niobium clusters containing five to nine Nb atoms have been obtained by multiple photon dissociation spectroscopy of their argon complexes. The experimental far-IR spectra are recorded in the 85–600cm−1 region and cover the range of the structure-specific vibrational fundamentals, i.e., the finger-print range, for these metal clusters. The experiments are accompanied by quantum chemical calculations employing the density-functional theory. A comparison of the experimental and calculated far-IR spectra allows to identify the cluster structures. Although the experimental spectra for clusters containing five, six, eight, and nine Nb atoms are very different for cationic and neutral clusters, the comparison with theory reveals that, nevertheless, the overall geometries for cations and neutrals are very similar, except for Nb60∕+.

Efficient symmetric discretization for the Poisson, heat and Stefan-type problems with Robin boundary conditions

We present a novel and efficient method for solving the Poisson equation, the heat equation, and Stefan-type problems with Robin boundary conditions over potentially moving, arbitrarily-shaped domains. The method utilizes a level set framework, thus it has all of the benefits of a sharp, implicitly-represented interface such as the ease of handling complex topological changes. This method is straightforward to implement and leads to a linear system that is symmetric and positive definite, which can be inverted efficiently with standard iterative methods. This approach is second-order accurate for both the Poisson and heat equations, and first-order accurate for the Stefan problem. We demonstrate the accuracy in the L^1 and L^~ norms.

Scaling of heteroepitaxial island sizes

Monte Carlo simulations of an atomistic solid-on-solid model are used to study the effect of lattice misfit on the distribution of two-dimensional islands sizes as a function of coverage θ in the submonolayer aggregation regime of epitaxial growth. Misfit promotes the detachment of atoms from the perimeter of large pseudomorphic islands and thus favors their dissolution into smaller islands that relieve strain more efficiently. The number density of islands composed of s atoms exhibits scaling in the form Ns(θ) ~ θ/〈s〉2g(s/〈s〉) where 〈s〉 is the average island size. Unlike the case of homoepitaxy, a rate equation theory based on this observation leads to qualitatively different behavior than observed in the simulations.

Density-functional theory calculations of hopping rates of surface diffusion

Using density-functional theory we compute the energy barriers and attempt frequencies for surface diffusion of Ag on Ag(111) with different lattice constants, and on an Ag adsorbate monolayer on Pt(111). We find that the attempt frequency is of the order of 1 THz for all the systems studied. This is in contrast to the so-called compensation effect, and to recent experimental studies. Our analysis suggests that the applicability of simple (commonly used) scaling laws for the determination of diffusion and growth parameters is often not valid.