Free Fermionic Elliptic Reflection Matrices and Quantum Group Invariance

Elliptic diagonal solutions for the reflection matrices associated to the elliptic $R$ matrix of the eight vertex free fermion model are presented. They lead through the second derivative of the open chain transfer matrix to an XY hamiltonian in a magnetic field which is invariant under a quantum deformed Clifford--Hopf algebra.Comment: 9 pages, Late

Solid flow drives surface nanopatterning by ion-beam irradiation

Ion Beam Sputtering (IBS) is known to produce surface nanopatterns over macroscopic areas on a wide range of materials. However, in spite of the technological potential of this route to nanostructuring, the physical process by which these surfaces self-organize remains poorly under- stood. We have performed detailed experiments of IBS on Si substrates that validate dynamical and morphological predictions from a hydrodynamic description of the phenomenon. Our results elucidate flow of a nanoscopically thin and highly viscous surface layer, driven by the stress created by the ion-beam, as a description of the system. This type of slow relaxation is akin to flow of macroscopic solids like glaciers or lead pipes, that is driven by defect dynamics.Comment: 12 pages, 4 figure

Noisy Kuramoto-Sivashinsky equation for an erosion model

We derive the continuum equation for a discrete model for ion sputtering. We follow an approach based on the master equation, and discuss how it can be truncated to a Fokker-Planck equation and mapped to a discrete Langevin equation. By taking the continuum limit, we arrive at the Kuramoto-Sivashinsky equation with a stochastic noise term.Comment: latex (w/ multicol.sty), 4 pages; to appear in Physical Review E (Oct 1996

Roughening of ion-eroded surfaces

Recent experimental studies focusing on the morphological properties of surfaces eroded by ion-bombardment report the observation of self-affine fractal surfaces, while others provide evidence about the development of a periodic ripple structure. To explain these discrepancies we derive a stochastic growth equation that describes the evolution of surfaces eroded by ion bombardment. The coefficients appearing in the equation can be calculated explicitly in terms of the physical parameters characterizing the sputtering process. Exploring the connection between the ion-sputtering problem and the Kardar-Parisi-Zhang and Kuramoto-Sivashinsky equations, we find that morphological transitions may take place when experimental parameters, such as the angle of incidence of the incoming ions or their average penetration depth, are varied. Furthermore, the discussed methods allow us to calculate analytically the ion-induced surface diffusion coefficient, that can be compared with experiments. Finally, we use numerical simulations of a one dimensional sputtering model to investigate certain aspects of the ripple formation and roughening.Comment: 20 pages, LaTeX, 5 ps figures, contribution to the 4th CTP Workshop on Statistical Physics "Dynamics of Fluctuating Interfaces and Related Phenomena", Seoul National University, Seoul, Korea, January 27-31, 199

Coupling of morphology to surface transport in ion-beam irradiated surfaces. I. Oblique incidence

We propose and study a continuum model for the dynamics of amorphizable surfaces undergoing ion-beam sputtering (IBS) at intermediate energies and oblique incidence. After considering the current limitations of more standard descriptions in which a single evolution equation is posed for the surface height, we overcome (some of) them by explicitly formulating the dynamics of the species that transport along the surface, and by coupling it to that of the surface height proper. In this we follow recent proposals inspired by ``hydrodynamic'' descriptions of pattern formation in aeolian sand dunes and ion-sputtered systems. From this enlarged model, and by exploiting the time-scale separation among various dynamical processes in the system, we derive a single height equation in which coefficients can be related to experimental parameters. This equation generalizes those obtained by previous continuum models and is able to account for many experimental features of pattern formation by IBS at oblique incidence, such as the evolution of the irradiation-induced amorphous layer, transverse ripple motion with non-uniform velocity, ripple coarsening, onset of kinetic roughening and other. Additionally, the dynamics of the full two-field model is compared with that of the effective interface equation.Comment: 23 pages, 14 figures. Movies of figures 6, 7, and 8 available at http://gisc.uc3m.es/~javier/Movies

Dynamical Renormalization Group Study for a Class of Non-local Interface Equations

We provide a detailed Dynamic Renormalization Group study for a class of stochastic equations that describe non-conserved interface growth mediated by non-local interactions. We consider explicitly both the morphologically stable case, and the less studied case in which pattern formation occurs, for which flat surfaces are linearly unstable to periodic perturbations. We show that the latter leads to non-trivial scaling behavior in an appropriate parameter range when combined with the Kardar-Parisi-Zhang (KPZ) non-linearity, that nevertheless does not correspond to the KPZ universality class. This novel asymptotic behavior is characterized by two scaling laws that fix the critical exponents to dimension-independent values, that agree with previous reports from numerical simulations and experimental systems. We show that the precise form of the linear stabilizing terms does not modify the hydrodynamic behavior of these equations. One of the scaling laws, usually associated with Galilean invariance, is shown to derive from a vertex cancellation that occurs (at least to one loop order) for any choice of linear terms in the equation of motion and is independent on the morphological stability of the surface, hence generalizing this well-known property of the KPZ equation. Moreover, the argument carries over to other systems like the Lai-Das Sarma-Villain equation, in which vertex cancellation is known {\em not to} imply an associated symmetry of the equation.Comment: 34 pages, 9 figures. Journal of Statistical Mechanics: Theory and Experiments (in press

Dynamic Scaling of Non-Euclidean Interfaces

The dynamic scaling of curved interfaces presents features that are strikingly different from those of the planar ones. Spherical surfaces above one dimension are flat because the noise is irrelevant in such cases. Kinetic roughening is thus a one-dimensional phenomenon characterized by a marginal logarithmic amplitude of the fluctuations. Models characterized by a planar dynamical exponent $z>1$, which include the most common stochastic growth equations, suffer a loss of correlation along the interface, and their dynamics reduce to that of the radial random deposition model in the long time limit. The consequences in several applications are discussed, and we conclude that it is necessary to reexamine some experimental results in which standard scaling analysis was applied

Strong anisotropy in surface kinetic roughening: analysis and experiments

We report an experimental assessment of surface kinetic roughening properties that are anisotropic in space. Working for two specific instances of silicon surfaces irradiated by ion-beam sputtering under diverse conditions (with and without concurrent metallic impurity codeposition), we verify the predictions and consistency of a recently proposed scaling Ansatz for surface observables like the two-dimensional (2D) height Power Spectral Density (PSD). In contrast with other formulations, this Ansatz is naturally tailored to the study of two-dimensional surfaces, and allows to readily explore the implications of anisotropic scaling for other observables, such as real-space correlation functions and PSD functions for 1D profiles of the surface. Our results confirm that there are indeed actual experimental systems whose kinetic roughening is strongly anisotropic, as consistently described by this scaling analysis. In the light of our work, some types of experimental measurements are seen to be more affected by issues like finite space resolution effects, etc. that may hinder a clear-cut assessment of strongly anisotropic scaling in the present and other practical contexts

Growth dynamics of reactive-sputtering-deposited AlN films

8 pages, 7 figures.-- PACS nrs.: 81.05.Ea, 68.47.Fg, 81.15.Cd, 68.55.Ac, 68.55.Jk, 68.35.Bs.-- Issue title: "Structural, mechanical, thermodynamical and optical properties of condensed matter".We have studied the surface kinetic roughening of AlN films grown on Si(100) substrates by dc reactive sputtering within the framework of the dynamic scaling theory. Films deposited under the same experimental conditions for different growth times were analyzed by atomic force microscopy and x-ray diffraction. The AlN films display a (002) preferred orientation. We have found two growth regimes with a crossover time of 36 min. In the first regime, the growth dynamics is unstable and the films present two types of textured domains, well textured and randomly oriented, respectively. In contrast, in the second regime the films are homogeneous and well textured, leading to a relative stabilization of the surface roughness characterized by a growth exponent β=0.37±0.03. In this regime a superrough scaling behavior is found with the following exponents: (i) Global exponents: roughness exponent α=1.2±0.2 and β=0.37±0.03 and coarsening exponent 1/z=0.32±0.05; (ii) local exponents: α(loc)=1, β(loc)=0.32±0.01. The differences between the growth modes are found to be related to the different main growth mechanisms dominating their growth dynamics: sticking anisotropy and shadowing, respectively.Financial support from Spanish MCyT: Projects No. MAT 2002-04037-C03-03 and BFM 2003-07749-C05-01, BFM 2003-07749-C05-02, and BFM 2003-07749-C05-05, European Community: Project No. G5RD-CT-2000-00333, Slovak governmental Project No. 2003-SO 51/03R0600/01, and Slovak Grant Agency for Science VEGA, Project No. 2/3149/23, are acknowledged.Publicad