Possible origin for the experimental scarcity of KPZ scaling in non-conserved surface growth

8 pages, 1 figure.-- PACS nrs.: 68.35.Ct; 64.60.Ht; 81.15.Gh; 81.15.Pq.-- MSC2000 codes: 82D20, 35Q53.Dedicated to H.E. Stanley on the occasion of his 60th birthday.Zbl#: Zbl 1001.82109The Kardar–Parisi–Zhang (KPZ) equation is generically expected to describe the scaling properties of rough surfaces growing in the absence of conservation laws. However, very few experimental realizations are known of this universality class. Here we focus on the role of instabilities, whether of diffusional origin or other, as physical mechanisms hindering the observation of KPZ scaling. Examples are drawn from various growth processes, such as electrochemical deposition (ECD), chemical vapor deposition (CVD), and erosion by ion-beam sputtering. We moreover consider an interface equation which, starting from the corresponding constitutive equations, can be derived to describe growth by either ECD or CVD depending on the interpretation of the quantities appearing. This approach makes contact with phenomenological parameters, and suggests that a more generic description of non-conserved growth may be provided by the Kuramoto–Sivashinsky equation and generalizations thereof. In this case, the experimental scarcity of KPZ scaling would be due to exceedingly long transients determined by the instabilities that occur.Work partially supported by DGES (Spain) Grant No. BFM2000-0006.Publicad

Comment on "Kinetic roughening of ion-sputtered Pd(001) surface: beyond the Kuramoto-Sivashinsky model"

1 page, no figures.-- PACS nrs.: 68.55.–a, 05.45.–a, 64.60.Cn, 79.20.Rf.A comment on the Letter by T. C. Kim et al., Phys. Rev. Lett. 92, 246104 (2004), http://dx.doi.org/10.1103/PhysRevLett.92.246104. The authors of the Letter offer a reply.This work has been partially supported by MECD (Spain) Grants No. BFM2003-07749-C05, No. -05 (M. C.), and No. -01 (R. C.).Publicad

Transients due to instabilities hinder Kardar-Parisi-Zhang scaling: a unified derivation for surface growth by electrochemical and chemical vapor deposition

4 pages, no figures.-- PACS nrs.: 68.35.Ct, 64.60.Ht, 81.15.Gh, 81.15.Pq.We propose a unified moving boundary problem for surface growth by electrochemical and chemical vapor deposition, which is derived from constitutive equations into which stochastic forces are incorporated. We compute the coefficients in the interface equation of motion as functions of phenomenological parameters. The equation features the Kardar-Parisi-Zhang (KPZ) nonlinearity and instabilities which, depending on surface kinetics, can hinder the asymptotic KPZ scaling. Our results account for the universality and the experimental scarcity of KPZ scaling in the growth processes considered.This work has been supported by DGES (Spain) Grant No. BFM2000-0006.Publicad

Aspectos metodológicos para la evaluación de sistemas de tomografía por emisión de positrones empleando técnicas Montecarlo, protocolos estandarizados y diferentes trazadores

Esta tesis analiza los elementos que afectan a la evaluación del rendimiento dentro de la técnica de radiodiagnóstico mediante tomografía por emisión de positrones (PET), centrándose en escáneres preclínicos. Se exploran las posibilidades de los protocolos estándar de evaluación sobre los siguientes aspectos: su uso como herramienta para validar programas de simulación Montecarlo, como método para la comparación de escáneres y su validez en el estudio del efecto sobre la calidad de imagen al utilizar radioisótopos alternativos. Inicialmente se estudian los métodos de evaluación orientados a la validación de simulaciones PET, para ello se presenta el programa GAMOS como entorno de simulación y se muestran los resultados de su validación basada en el estándar NEMA NU 4-2008 para escáneres preclínicos. Esta validación se ha realizado mediante la comparación de los resultados simulados frente a adquisiciones reales en el equipo ClearPET, describiendo la metodología de evaluación y selección de los parámetros NEMA. En este apartado también se mencionan las aportaciones desarrolladas en GAMOS para aplicaciones PET, como la inclusión de herramientas para la reconstrucción de imágenes. Por otro lado, la evaluación NEMA del ClearPET es utilizada para comparar su rendimiento frente a otro escáner preclínico: el sistema rPET-1. Esto supone la primera caracterización NEMA NU 4 completa de ambos equipos; al mismo tiempo que se analiza cómo afectan las importantes diferencias de diseño entre ellos, especialmente el tamaño axial del campo de visión y la configuración de los detectores. El 68Ga es uno de los radioisótopos no convencionales en imagen PET que está experimentando un mayor desarrollo, sin embargo, presenta la desventaja del amplio rango o distancia recorrida por el positrón emitido. Además del rango del positrón, otra propiedad física característica de los radioisótopos PET que puede afectar a la imagen es la emisión de fotones gamma adicionales, tal como le ocurre al isótopo 48V. En esta tesis se evalúan dichos efectos mediante estudios de resolución espacial y calidad de imagen NEMA. Finalmente, se analiza el alcance del protocolo NEMA NU 4-2008 cuando se utiliza para este propósito, adaptándolo a tal fin y proponiendo posibles modificaciones. Abstract This thesis analyzes the factors affecting the performance evaluation in positron emission tomography (PET) imaging, focusing on preclinical scanners. It explores the possibilities of standard protocols of assessment on the following aspects: their use as tools to validate Monte Carlo simulation programs, their usefulness as a method for comparing scanners and their validity in the study of the effect of alternative radioisotopes on image quality. Initially we study the methods of performance evaluation oriented to validate PET simulations. For this we present the GAMOS program as a simulation framework and show the results of its validation based on the standard NEMA NU 4-2008 for preclinical PET scanners. This has been accomplished by comparing simulated results against experimental acquisitions in the ClearPET scanner, describing the methodology for the evaluation and selection of NEMA parameters. This section also mentions the contributions developed in GAMOS for PET applications, such as the inclusion of tools for image reconstruction. Furthermore, the evaluation of the ClearPET scanner is used to compare its performance against another preclinical scanner, specifically the rPET-1 system. This is the first complete NEMA NU 4 based characterization study of both systems. At the same time we analyze how do the significant design differences of these two systems, especially the size of the axial field of view and the detectors configuration affect their performance characteristics. 68Ga is one of the unconventional radioisotopes in PET imaging the use of which is currently significantly increasing; however, it presents the disadvantage of the long positron range (distance traveled by the emitted positron before annihilating with an electron). Besides the positron range, additional gamma photon emission is another physical property characteristic of PET radioisotopes that can affect the reconstructed image quality, as it happens to the isotope 48V. In this thesis we assess these effects through studies of spatial resolution and image quality. Finally, we analyze the scope of the NEMA NU 4-2008 to carry out such studies, adapting it and proposing possible modifications

Unstable nonlocal interface dynamics

4 pages, 2 figures.-- PACS nrs.: 68.35.Ct, 05.45.−a, 47.54.−r.Nonlocal effects occur in many nonequilibrium interfaces, due to diverse physical mechanisms like diffusive, ballistic, or anomalous transport, with examples from flame fronts to thin films. While dimensional analysis describes stable nonlocal interfaces, we show the morphologically unstable condition to be nontrivial. This is the case for a family of stochastic equations of experimental relevance, paradigmatically including the Michelson-Sivashinsky system. For a whole parameter range, the asymptotic dynamics is scale invariant with dimension-independent exponents reflecting a hidden Galilean symmetry. The usual Kardar-Parisi-Zhang nonlinearity, albeit irrelevant in that parameter range, plays a key role in this behavior.This work has been partially supported through Grants No. FIS2006-12253-C06-01 and No. FIS2006-12253-C06-06 (MEC, Spain) and No. S-0505/ESP-0158 (CAM, Spain). M. N. acknowledges support by Fundación Carlos III (Spain) and by Fondazione Angelo Della Riccia (Italy).Publicad

Unified moving-boundary model with fluctuations for unstable diffusive growth

17 pages, 9 figures.-- PACS nrs.: 81.10.-h, 68.35.Ct, 64.60.Ht, 81.15.Gh.-- MSC2000 code: 82C24.-- ArXiv pre-print available at: http://arxiv.org/abs/0812.4160MR#: MR2496824 (2010c:82073)Final publisher version available Open Access at: http://gisc.uc3m.es/~cuerno/publ_list.htmlWe study a moving-boundary model of nonconserved interface growth that implements the interplay between diffusive matter transport and aggregation kinetics at the interface. Conspicuous examples are found in thin-film production by chemical vapor deposition and electrochemical deposition. The model also incorporates noise terms that account for fluctuations in the diffusive and attachment processes. A small-slope approximation allows us to derive effective interface evolution equations (IEEs) in which parameters are related to those of the full moving-boundary problem. In particular, the form of the linear dispersion relation of the IEE changes drastically for slow or for instantaneous attachment kinetics. In the former case the IEE takes the form of the well-known (noisy) Kuramoto-Sivashinsky equation, showing a morphological instability at short times that evolves into kinetic roughening of the Kardar-Parisi-Zhang (KPZ) class. In the instantaneous kinetics limit, the IEE combines the Mullins-Sekerka linear dispersion relation with a KPZ nonlinearity, and we provide a numerical study of the ensuing dynamics. In all cases, the long preasymptotic transients can account for the experimental difficulties in observing KPZ scaling. We also compare our results with relevant data from experiments and discrete models.This work has been partially supported by UC3M/CAM (Spain) Grant No. UC3M-FI-05-007, CAM (Spain) Grant No. S-0505/ESP-0158, and by MEC (Spain), through Grants No. FIS2006-12253-C06-01, No. FIS2006-12253-C06-06, and the FPU program (M. N.).Publicad

Single-phase-field model of stepped surfaces

8 pages, 5 figures.-- PACS nrs.: 81.10.Aj, 68.35.Ct, 81.15.Hi, 81.15.Aa.We formulate a phase-field description of step dynamics on vicinal surfaces that makes use of a single dynamical field, at variance with previous analogous works in which two coupled fields are employed, namely, a phase-field proper plus the physical adatom concentration. Within an asymptotic sharp interface limit, our formulation is shown to retrieve the standard Burton-Cabrera-Frank model in the general case of asymmetric attachment coefficients (Ehrlich-Schwoebel effect). We confirm our analytical results by means of numerical simulations of our phase-field model. Our present formulation seems particularly well adapted to generalization when additional physical fields are required.The present work has been partially supported by MEC (Spain) Grants No. FIS2006-12253-C06-01, No. FIS2006-12253-C06-05, and No. FIS2006-12253-C06-06, UC3M/CAM (Spain) Grant No. UC3M-FI-05-007, and CAM (Spain) Grant No. S-0505/ESP-0158.Publicad

Energy dependence of the ripple wavelength for ion-beam sputtering of silicon: experiments and theory

This proceeding at: 22nd International Conference on the Application of Accelerators in Research and Industry (CAARI), took place 2012-Auguts, 05-10, in Fort Worth (Texas).In spite of the efforts devoted for the last 20 years to elucidating ion-beam sputtering (IBS) as an instance of surface self-organization, the classic view on the main mechanism inducing the morphological instability has been recently challenged. We report on the verification of a recent theoretical description of this nanopattern formation process for semiconducting targets, as driven by stress-induced, viscous flow of a thin amorphous layer that develops at the surface [M. Cuerno and R. Cuerno, Appl. Surf. Sci. 258, 4171 (2012)]. Through experiments on silicon as a representative case, we study the dependence of the ripple wavelength with the average ion energy, finding a linear dependence in the 0.3-1 keV range. This is explained within the viscous flow framework, taking into account the energy dependence of the number of displaced atoms generated by collision cascades in the amorphous layer, as predicted by previous models of ion-generated stress. For our analysis, we provide a systematic criterion to guarantee actual linear dynamics behavior, not affected by the onset of nonlinear effects that may influence the value of the ripple wavelength.Partial support has been provided by the Spanish MICINN Grants, Nos. FIS2009-12964-C05-01, -03, and -04, and MEC Grants, Nos. FIS2012-38866-C05-01 and -05, and FIS2012-32349.Publicad

Stress vs sputtering effects in the propagation of surface ripples produced by ion-beam sputtering

The proceeding at: 19th International Conference on Ion Beam Modification of Materials (IBMM 2014). Took place at 2014, September, 14-19, in Bruges (Belgium). The event Web Site in https://iks32.fys.kuleuven.be/indico/event/16/Under low energy ion irradiation, periodic features (ripples) can develop on the surfaces of semiconductor materials, with typical sizes in the nanometric range. Recently, a theory of pattern formation has been able to account for the variability with the ion/target combination of the critical angle value separating conditions on ion incidence that induce the presence or the absence of ripples. Such a theory is based in the accumulation of stress in the damaged irradiated layer and its relaxation via surface-confined viscous flow. Here we explore the role of stress, and its competition with purely erosive mechanisms, to deter-mine the sign of the velocity with which the ripple pattern moves across the target plane. Based on this theory, we discuss different situations and make specific testable predictions for the change of sign in that velocity.Our work has been funded through MINECO (Spain) grants FIS2012-38866-C05-01, FIS2012-32349, and FIS2013-47949-C2-2. A.M.-B. acknowledges support from MINECO, through FPI scholarship BES-2010-036179.Publicad

Universality of cauliflower-like fronts: from nanoscale thin films to macroscopic plants

Chemical vapor deposition (CVD) is a widely used technique to grow solid materials with accurate control of layer thickness and composition. Under mass-transport-limited conditions, the surface of thin films thus produced grows in an unstable fashion, developing a typical motif that resembles the familiar surface of a cauliflower plant. Through experiments on CVD production of amorphous hydrogenated carbon films leading to cauliflower-like fronts, we provide a quantitative assessment of a continuum description of CVD interface growth. As a result, we identify non-locality, non-conservation and randomness as the main general mechanisms controlling the formation of these ubiquitous shapes.We also show that the surfaces of actual cauliflower plants and combustion fronts obey the same scaling laws, proving the validity of the theory over seven orders of magnitude in length scales. Thus, a theoretical justification is provided, which had remained elusive so far, for the remarkable similarity between the textures of surfaces found for systems that differ widely in physical nature and typical scales.Publicad