arXiv subjects

Alberto Pimpinelli

Publications and source records attributed to Alberto Pimpinelli.

18 recordsLinked to original sources

arXiv2024

Growth mechanisms of GaN/GaAs nanostructures by droplet epitaxy explained by complementary experiments and simulations

In this work, we present conception and study of gallium nitride (GaN) nanostructures on a gallium arsenide (GaAs) substrate with (111)A orientation. The nanostructures were designed by GaN droplet epitaxy and studied in-situ by X-ray photoelectron spectroscopy and ex-situ by atomic force microscopy, scanning electron microscopy and transmission electron microscopy. These studies were coupled with kinetic Monte Carlo simulations to precisely understand the phenomena occurring during the nitridation and to find the optimum conditions for complete nitridation of gallium droplets. The HRTEM observation showed a cubic (zinc blende) crystal structure of the GaN nanodots for a nitridation at 300{\deg}C. Ramping the temperature from 100{\deg}C to 350{\deg}C during droplet nitridation enabled to obtain a very high density (>1011cm-2) of GaN nanodots with the zinc blende crystallinity.

cond-mat.mtrl-sci↗

arXiv2022

Predicted universality class of step bunching found on DC-heated Si(111) surfaces

Concerted experimental and numerical studies of step bunching on vicinal crystal surfaces resulting from step-down electromigration of partially charged adatoms, confirmed the theoretical prediction of scaling dependence of the minimal bunch distance $l_{\rm min}$ on the bunch size $N$: $l_{\rm min} \sim N^{-\gamma}$, with $\gamma = 2/3$. The value of the so called size-scaling exponent $\gamma$ was observed in experiments on vicinal surfaces of semiconducting, metallic, and dielectric materials. Careful theoretical investigations and numerical calculations predict a second value of $\gamma = 1/2$. However, this value is still not been reported from experiments. And we report here experimental observation of step bunching in the universality class relative to $\gamma = 1/2$. This is achieved by monitoring step flow during sublimation of Si(111)-vicinals heated by a direct step-down current at ~1200$^\circ$C. In the experiment we also measure other characteristic for the bunching quantities, such as the mean total number of steps in the bunch $N$ and the mean bunch width $W$. We then compare our findings with published experimental and numerical data to arrive at a theoretically consistent framework in terms of universality classes. The ultimate benefit of our study is not only to advance fundamental knowledge but also to provide further guidance for bottom-up synthesis of vicinal nanotemplates.

cond-mat.mes-hall↗

arXiv2013

Exponent equality for capture-zone scaling in island nucleation: Theory and application to organic films

It is known in thin-film deposition that the density of nucleated clusters $N$ varies with the deposition rate $R$ as a power law, $N \sim R^α$. The exponent $α$ is a function of the critical nucleus size $i$ in a way that changes with the aggregation-limiting process active in a given system. We extend here to generic aggregation-limiting processes the derivation of the analytical capture-zone distribution function $P_β(s) = a_βs^β\exp(-b_βs^2)$ of Pimpinelli and Einstein [Phys. Rev. Lett. 99, 226102 (2007)]. We show that the exponent $β$ is generally related to the critical nucleus size $i$ and to the exponent $α$ by the equality $α(2β+ d_f - 2) = 2i$ where $d_f$ is the fractal dimensionality of the clusters. This remarkable results allows one to measure $i$ with no a priori knowledge of the actual aggregation mechanism. We apply this equality to measuring the critical nucleus size in pentacene deposition on mica.

cond-mat.mtrl-sci↗

arXiv2013

Dynamical Scaling Implications of Ferrari, Pr\"{a}hofer, and Spohn's Remarkable Spatial Scaling Results for Facet-Edge Fluctuations

Spurred by theoretical predictions from Spohn and coworkers [Phys. Rev. E {\bf 69}, 035102(R) (2004)], we rederived and extended their result heuristically as well as investigated the scaling properties of the associated Langevin equation in curved geometry with an asymmetric potential. With experimental colleagues we used STM line scans to corroborate their prediction that the fluctuations of the step bounding a facet exhibit scaling properties distinct from those of isolated steps or steps on vicinal surfaces. The correlation functions was shown to go as $t^{0.15(3)}$ decidedly different from the $t^{0.26(2)}$ behavior for fluctuations of isolated steps. From the exponents, we were able to categorize the universality, confirming the prediction that the non-linear term of the KPZ equation, long known to play a central role in non-equilibrium phenomena, can also arise from the curvature or potential-asymmetry contribution to the step free energy. We also considered, with modest Monte Carlo simulations, a toy model to show that confinement of a step by another nearby step can modify as predicted the scaling exponents of the step's fluctuations. This paper is an expansion of a celebratory talk at the 95$^{\rm th}$ Rutgers Statistical Mechanics Conference, May 2006.

cond-mat.stat-mech↗

arXiv2013

Analyzing Capture Zone Distributions (CZD) in Growth: Theory and Applications

We have argued that the capture-zone distribution (CZD) in submonolayer growth can be well described by the generalized Wigner distribution (GWD) $P(s)=a s^\beta \exp(-b s^2)$, where $s$ is the CZ area divided by its average value. This approach offers arguably the best method to find the critical nucleus size $i$, since $\beta \approx i + 2$. Various analytical and numerical investigations, which we discuss, show that the simple GWD expression is inadequate in the tails of the distribution, it does account well for the central regime $0.5 < s < 2$, where the data is sufficiently large to be reliably accessible experimentally. We summarize and catalog the many experiments in which this method has been applied.

cond-mat.mes-hall↗

arXiv2011

Mean-Field Approximation for Spacing Distribution Functions in Classical Systems

We propose a mean-field method to calculate approximately the spacing distribution functions $p^{(n)}(s)$ in 1D classical many-particle systems. We compare our method with two other commonly used methods, the independent interval approximation (IIA) and the extended Wigner surmise (EWS). In our mean-field approach, $p^{(n)}(s)$ is calculated from a set Langevin equations which are decoupled by using a mean-field approximation. We found that in spite of its simplicity, the mean-field approximation provides good results in several systems. We offer many examples in which the three methods mentioned previously give a reasonable description of the statistical behavior of the system. The physical interpretation of each method is also discussed.

cond-mat.stat-mech↗

arXiv2011

Spacing distribution functions for the one-dimensional point-island model with irreversible attachment

We study the configurational structure of the point-island model for epitaxial growth in one dimension. In particular, we calculate the island gap and capture zone distributions. Our model is based on an approximate description of nucleation inside the gaps. Nucleation is described by the joint probability density $p^{XY}_{n}(x,y)$, which represents the probability density to have nucleation at position $x$ within a gap of size $y$. Our proposed functional form for $p^{XY}_{n}(x,y)$ describes excellently the statistical behavior of the system. We compare our analytical model with extensive numerical simulations. Our model retains the most relevant physical properties of the system.

cond-mat.stat-mech↗

arXiv2009

Scaling and Universality in Models of Step Bunching: The "C+-C-" Model

We study further the recently introduced [Ranguelov et al., Comptes Rendus de l'Acad. Bulg. des Sci. 60, 4 (2007) 389] "C+-C-" model of step flow crystal growth over wide range of model parameters. The basic assumption of the model is that the reference ("equilibrium") densities used to compute the supersaturation might be different on either side of a step. We obtain the condition for linear stability of the whole step train in the form CL/CR>1 (L/R stands for left/right in a descending from left to right step train). Further we integrate numerically the equations of step motion to monitor the bunching process in the long times limit. Thus we obtain the exact size- and time- scaling of the step bunches including the numerical prefactors. We show that in a broad range of parameters the morphology is characterized with appearance of the minimal interstep distance in the bunch in the beginning of the bunches (at the trailing edge of the bunch) and may be described by a single universality class, different from those already generated by continuum theories [Krug et al., PRB 71, 045412].

cond-mat.stat-mech↗

arXiv2008

Relaxation of Terrace-width Distributions: Physical Information from Fokker-Planck Time

Recently some of us have constructed a Fokker-Planck formalism to describe the equilibration of the terrace-width distribution of a vicinal surface from an arbitrary initial configuration. However, the meaning of the associated relaxation time, related to the strength of the random noise in the underlying Langevin equation, was rather unclear. Here we present a set of careful kinetic Monte Carlo simulations that demonstrate convincingly that the time constant shows activated behavior with a barrier that has a physically plausible dependence on the energies of the governing microscopic model. Furthermore, the Fokker-Planck time at least semiquantitatively tracks the actual physical time.

cond-mat.mtrl-sci↗

arXiv2007

Capture-zone scaling in island nucleation: phenomenological theory of an example of universal fluctuation behavior

In studies of island nucleation and growth, the distribution of capture zones, essentially proximity cells, can give more insight than island-size distributions. In contrast to the complicated expressions, ad hoc or derived from rate equations, usually used, we find the capture-zone distribution can be described by a simple expression generalizing the Wigner surmise from random matrix theory that accounts for the distribution of spacings in a host of fluctuation phenomena. Furthermore, its single adjustable parameter can be simply related to the critical nucleus of growth models and the substrate dimensionality. We compare with extensive published kinetic Monte Carlo data and limited experimental data. A phenomenological theory sheds light on the result.

cond-mat.stat-mech↗

arXiv2007

New universality class for step bunching in the "C+ - C-" model

We formulate a new (1+1)D step model of potentially unstable vicinal growth that we call "C+ - C-" model and study the step bunching process in it. The basic assumption is that the equilibrium adatom concentrations on both sides of the step are different and this may cause destabilization of the regular step train. We deduce equations of step motion and numerically integrate them to obtain the step positions on a discrete time set. New dynamic phenomena are observed during the bunching process: 1. parts of the crystal surface undergo temporary evaporation in the course of coalescence of two bunches, the larger being the one that "goes back", 2. the minimal interstep distance appears in the beginning rather than in the middle of the bunch. We speculate that the latter may serve as a diagnostic criterion for a new universality class constructed from the time- and size-scaling exponents describing the bunching process in the diffusion-limited regime.

physics.chem-ph↗

arXiv2004

A facet is not an island: step-step interactions and the fluctuations of the boundary of a crystal facet

In a recent paper [Ferrari et al., Phys. Rev. E 69, 035102(R) (2004)], the scaling law of the fluctuations of the step limiting a crystal facet has been computed as a function of the facet size. Ferrari et al. use rigorous, but physically rather obscure, arguments. Approaching the problem from a different perspective, we rederive more transparently the scaling behavior of facet edge fluctuations as a function of time. Such behavior can be scrutinized with STM experiments and with numerical simulations.

cond-mat.stat-mech↗

arXiv2004

Scaling properties of step bunches induced by sublimation and related mechanisms: A unified perspective

This work provides a ground for a quantitative interpretation of experiments on step bunching during sublimation of crystals with a pronounced Ehrlich-Schwoebel (ES) barrier in the regime of weak desorption. A strong step bunching instability takes place when the kinetic length is larger than the average distance between the steps on the vicinal surface. In the opposite limit the instability is weak and step bunching can occur only when the magnitude of step-step repulsion is small. The central result are power law relations of the between the width, the height, and the minimum interstep distance of a bunch. These relations are obtained from a continuum evolution equation for the surface profile, which is derived from the discrete step dynamical equations for. The analysis of the continuum equation reveals the existence of two types of stationary bunch profiles with different scaling properties. Through a mathematical equivalence on the level of the discrete step equations as well as on the continuum level, our results carry over to the problems of step bunching induced by growth with a strong inverse ES effect, and by electromigration in the attachment/detachment limited regime. Thus our work provides support for the existence of universality classes of step bunching instabilities [A. Pimpinelli et al., Phys. Rev. Lett. 88, 206103 (2002)], but some aspects of the universality scenario need to be revised.

cond-mat.mtrl-sci↗

arXiv2000

Changing shapes in the nanoworld

What are the mechanisms leading to the shape relaxation of three dimensional crystallites ? Kinetic Monte Carlo simulations of fcc clusters show that the usual theories of equilibration, via atomic surface diffusion driven by curvature, are verified only at high temperatures. Below the roughening temperature, the relaxation is much slower, kinetics being governed by the nucleation of a critical germ on a facet. We show that the energy barrier for this step linearly increases with the size of the crystallite, leading to an exponential dependence of the relaxation time.

cond-mat.mtrl-sci↗

arXiv1999

Kinetics of shape equilibration for two-dimensional islands

We study the relaxation to equilibrium of two dimensional islands containing up to 20000 atoms by Kinetic Monte Carlo simulations. We find that the commonly assumed relaxation mechanism - curvature-driven relaxation via atom diffusion - cannot explain the results obtained at low temperatures, where the island edges consist in large facets. Specifically, our simulations show that the exponent characterizing the dependence of the equilibration time on the island size is different at high and low temperatures, in contradiction with the above cited assumptions. Instead, we propose that - at low temperatures - the relaxation is limited by the nucleation of new atomic rows on the large facets : this allows us to explain both the activation energy and the island size dependence of the equilibration time.

cond-mat.mtrl-sci↗

arXiv1997

On the morphological stability of two-dimensional epitaxial islands at high deposition rates

The morphological stability of two-dimensional islands nucleated on a substrate during vacuum or vapour-phase atom deposition is investigated. Using simple scaling arguments, it is shown that, contrary to expectation, dendritic islands may be converted into compact ones by increasing the deposition rate, provided that the size of the critical nucleus is large enough. Implications for recent observations of Pt deposition on Pt(111) are discussed.

cond-mat.stat-mech↗

arXiv1997

Growth of three-dimensional structures by atomic deposition on surfaces containing defects : simulations and theory

We perform a comprehensive study of the formation of three dimensional (pyramidal) structures in a large range of conditions, including the possible evaporation of adatoms from the surface and the presence of surface defects. We compare our computer simulations to theoretical calculations of the growth and find good agreement between them. This work clarifies precedent studies of three dimensional growth and predicts the island size distributions obtained in the different regimes. Finally, we show how our analysis can be used to interpret experimental data.

cond-mat.mtrl-sci↗

arXiv1996

The effect of monomer evaporation on a simple model of submonolayer growth

We present a model for thin film growth by particle deposition that takes into account the possible evaporation of the particles deposited on the surface. Our model focuses on the formation of two-dimensional structures. We find that the presence of evaporation can dramatically affect the growth kinetics of the film, and can give rise to regimes characterized by different ``growth'' exponents and island size distributions. Our results are obtained by extensive computer simulations as well as through a simple scaling approach and the analysis of rate equations describing the system. We carefully discuss the relationship of our model with previous studies by Venables and Stoyanov of the same physical situation, and we show that our analysis is more general.

cond-mat.mtrl-sci↗