Regimes of Precursor-Mediated Epitaxial Growth

A discussion of epitaxial growth is presented for those situations (OMVPE, CBE, ALE, MOMBE, GSMBE, etc.) when the kinetics of surface processes associated with molecular precursors may be rate limiting. Emphasis is placed on the identification of various {\it characteristic length scales} associated with the surface processes. Study of the relative magnitudes of these lengths permits one to identify regimes of qualitatively different growth kinetics as a function of temperature and deposition flux. The approach is illustrated with a simple model which takes account of deposition, diffusion, desorption, dissociation, and step incorporation of a single precursor species, as well as the usual processes of atomic diffusion and step incorporation. Experimental implications are discussed in some detail.Comment: 10 pages, 2 figure

User's guide to Monte Carlo methods for evaluating path integrals

We give an introduction to the calculation of path integrals on a lattice, with the quantum harmonic oscillator as an example. In addition to providing an explicit computational setup and corresponding pseudocode, we pay particular attention to the existence of autocorrelations and the calculation of reliable errors. The over-relaxation technique is presented as a way to counter strong autocorrelations. The simulation methods can be extended to compute observables for path integrals in other settings

Noise-assisted Mound Coarsening in Epitaxial Growth

We propose deposition noise to be an important factor in unstable epitaxial growth of thin films. Our analysis yields a geometrical relation H=(RWL)^2 between the typical mound height W, mound size L, and the film thickness H. Simulations of realistic systems show that the parameter R is a characteristic of the growth conditions, and generally lies in the range 0.2-0.7. The constancy of R in late-stage coarsening yields a scaling relation between the coarsening exponent 1/z and the mound height exponent \beta which, in the case of saturated mound slope, gives \beta = 1/z = 1/4.Comment: 4 pages, RevTex Macros, 3 eps figure

X-ray absorption spectra at the Ca-L2,3_{2,3}-edge calculated within multi-channel multiple scattering theory

We report a new theoretical method for X-ray absorption spectroscopy (XAS) in condensed matter which is based on the multi-channel multiple scattering theory of Natoli et al. and the eigen-channel R-matrix method. While the highly flexible real-space multiple scattering (RSMS) method guarantees a precise description of the single-electron part of the problem, multiplet-like electron correlation effects between the photo-electron and localized electrons can be taken account for in a configuration interaction scheme. For the case where correlation effects are limited to the absorber atom, a technique for the solution of the equations is devised, which requires only little more computation time than the normal RSMS method for XAS. The new method is described and an application to XAS at the Ca $L_{2,3}$-edge in bulk Ca, CaO and CaF$_2$ is presented.Comment: 10 pages, 4 figures, submitted to Phys. Rev.

Cooperative Jahn-Teller phase transition of icosahedral molecular units

Non-linear molecules undergo distortions when the orbital degeneracy of the highest occupied level is lifted by the Jahn–Teller effect. If such molecules or clusters of atoms are coupled to one another, the system may experience a cooperative Jahn–Teller effect (CJTE). In this paper, we describe a model of how the CJTE leads to the crystallization of the disordered phase. The model Hamiltonian is based on a normal mode decomposition of the clusters in order to maintain the symmetry labels. We take account of the electron-strain and the electron-phonon couplings and, by displacing the coordinates of the oscillators, obtain a term that explicitly couples the Jahn–Teller centers, enabling us to perform a mean-field analysis. The calculation of the free energy then becomes straightforward, and obtaining phase diagrams in various regimes follows from the minimization of this free energy. The results show that the character of the phase transition may change from strong to weak first order and even to second-order, depending on the coupling to the vibrational modes. Taken together, these results may serve as a paradigm for crystallization near the transition temperature, where the atoms tend to form clusters of icosahedral symmetry