2,430 research outputs found
The ReaxFF reactive force-field : development, applications and future directions
The reactive force-field (ReaxFF) interatomic potential is a powerful computational tool for exploring, developing and optimizing material properties. Methods based on the principles of quantum mechanics (QM), while offering valuable theoretical guidance at the electronic level, are often too computationally intense for simulations that consider the full dynamic evolution of a system. Alternatively, empirical interatomic potentials that are based on classical principles require significantly fewer computational resources, which enables simulations to better describe dynamic processes over longer timeframes and on larger scales. Such methods, however, typically require a predefined connectivity between atoms, precluding simulations that involve reactive events. The ReaxFF method was developed to help bridge this gap. Approaching the gap from the classical side, ReaxFF casts the empirical interatomic potential within a bond-order formalism, thus implicitly describing chemical bonding without expensive QM calculations. This article provides an overview of the development, application, and future directions of the ReaxFF method
Study of Strain and Temperature Dependence of Metal Epitaxy
Metallic films are important in catalysis, magneto-optic storage media, and
interconnects in microelectronics, and it is crucial to predict and control
their morphologies. The evolution of a growing crystal is determined by the
behavior of each individual atom, but technologically relevant structures have
to be described on a time scale of the order of (at least) tenths of a second
and on a length scale of nanometers. An adequate theory of growth should
describe the atomistic level on very short time scales (femtoseconds), the
formation of small islands (microseconds), as well as the evolution of
mesoscopic and macroscopic structures (tenths of seconds).
The development of efficient algorithms combined with the availability of
cheaper and faster computers has turned density functional theory (DFT) into a
reliable and feasible tool to study the microscopic aspects of growth phenomena
(and many other complex processes in materials science, condensed matter
physics, and chemistry). In this paper some DFT results for diffusion
properties on metallic surfaces are presented. Particularly, we will discuss
the current understanding of the influences of strain on the diffusion (energy
barrier and prefactor) of a single adatom on a substrate.
A DFT total energy calculation by its nature is primarily a static
calculation. An accurate way to describe the spatial and temporal development
of a growing crystal is given by kinetic Monte Carlo (KMC). We will describe
the method and its combination with microscopic parameters obtained from ab
initio calculations. It is shown that realistic ab initio kinetic Monte Carlo
simulations are able to predict an evolving mesoscopic structure on the basis
of microscopic details.Comment: 25 pages, 6 figures, In: ``Morphological Organisation during
Epitaxial Growth and Removal'', Eds. Z. Zhang, M. Lagally. World Scientific,
Singapore 1998. other related publications can be found at
http://www.rz-berlin.mpg.de/th/paper.htm
Ab initio atomistic thermodynamics and statistical mechanics of surface properties and functions
Previous and present "academic" research aiming at atomic scale understanding
is mainly concerned with the study of individual molecular processes possibly
underlying materials science applications. Appealing properties of an
individual process are then frequently discussed in terms of their direct
importance for the envisioned material function, or reciprocally, the function
of materials is somehow believed to be understandable by essentially one
prominent elementary process only. What is often overlooked in this approach is
that in macroscopic systems of technological relevance typically a large number
of distinct atomic scale processes take place. Which of them are decisive for
observable system properties and functions is then not only determined by the
detailed individual properties of each process alone, but in many, if not most
cases also the interplay of all processes, i.e. how they act together, plays a
crucial role. For a "predictive materials science modeling with microscopic
understanding", a description that treats the statistical interplay of a large
number of microscopically well-described elementary processes must therefore be
applied. Modern electronic structure theory methods such as DFT have become a
standard tool for the accurate description of individual molecular processes.
Here, we discuss the present status of emerging methodologies which attempt to
achieve a (hopefully seamless) match of DFT with concepts from statistical
mechanics or thermodynamics, in order to also address the interplay of the
various molecular processes. The new quality of, and the novel insights that
can be gained by, such techniques is illustrated by how they allow the
description of crystal surfaces in contact with realistic gas-phase
environments.Comment: 24 pages including 17 figures, related publications can be found at
http://www.fhi-berlin.mpg.de/th/paper.htm
Modeling of metal nanocluster growth on patterned substrates and surface pattern formation under ion bombardment
This thesis addresses the metal nanocluster growth process on prepatterned substrates, the development of atomistic simulation method with respect to an acceleration of the atomistic transition states, and the continuum model of the ion-beam inducing semiconductor surface pattern formation mechanism.
Experimentally, highly ordered Ag nanocluster structures have been grown on pre-patterned amorphous SiO^2 surfaces by oblique angle physical vapor deposition at room temperature. Despite the small undulation of the rippled surface, the stripe-like Ag nanoclusters are very pronounced, reproducible and well-separated. The first topic is the investigation of this growth process with a continuum theoretical approach to the surface gas condensation as well as an atomistic cluster growth model. The atomistic simulation model is a lattice-based kinetic Monte-Carlo (KMC) method using a combination of a simplified inter-atomic potential and experimental transition barriers taken from the literature.
An effective transition event classification method is introduced which allows a boost factor of several thousand compared to a traditional KMC approach, thus allowing experimental time scales to be modeled. The simulation predicts a low sticking probability for the arriving atoms, millisecond order lifetimes for single Ag monomers and ≈1 nm square surface migration ranges of Ag monomers. The simulations give excellent reproduction of the experimentally observed nanocluster growth patterns.
The second topic specifies the acceleration scheme utilized in the metallic cluster growth model. Concerning the atomistic movements, a classical harmonic transition state theory is considered and applied in discrete lattice cells with hierarchical transition levels. The model results in an effective reduction of KMC simulation steps by utilizing a classification scheme of transition levels for thermally activated atomistic diffusion processes. Thermally activated atomistic movements are considered as local transition events constrained in potential energy wells over certain local time periods. These processes are represented by Markov chains of multi-dimensional Boolean valued functions in three dimensional lattice space. The events inhibited by the barriers under a certain level are regarded as thermal fluctuations of the canonical ensemble and accepted freely. Consequently, the fluctuating system evolution process is implemented as a Markov chain of equivalence class objects. It is shown that the process can be characterized by the acceptance of metastable local transitions. The method is applied to a problem of Au and Ag cluster growth on a rippled surface. The simulation predicts the existence of a morphology dependent transition time limit from a local metastable to stable state for subsequent cluster growth by accretion.
The third topic is the formation of ripple structures on ion bombarded semiconductor surfaces treated in the first topic as the prepatterned substrate of the metallic deposition. This intriguing phenomenon has been known since the 1960\'s and various theoretical approaches have been explored. These previous models are discussed and a new non-linear model is formulated, based on the local atomic flow and associated density change in the near surface region. Within this framework ripple structures are shown to form without the necessity to invoke surface diffusion or large sputtering as important mechanisms. The model can also be extended to the case where sputtering is important and it is shown that in this case, certain \\lq magic\' angles can occur at which the ripple patterns are most clearly defined. The results including some analytic solutions of the nonlinear equation of motions are in very good agreement with experimental observation
Modeling of metal nanocluster growth on patterned substrates and surface pattern formation under ion bombardment
This thesis addresses the metal nanocluster growth process on prepatterned substrates, the development of atomistic simulation method with respect to an acceleration of the atomistic transition states, and the continuum model of the ion-beam inducing semiconductor surface pattern formation mechanism.
Experimentally, highly ordered Ag nanocluster structures have been grown on pre-patterned amorphous SiO2 surfaces by oblique angle physical vapor deposition at room temperature. Despite the small undulation of the rippled surface, the stripe-like Ag nanoclusters are very pronounced, reproducible and well-separated.
The first topic is the investigation of this growth process with a continuum theoretical approach to the surface gas condensation as well as an atomistic cluster growth model. The atomistic simulation model is a lattice-based kinetic Monte-Carlo (KMC) method using a combination of a simplified inter-atomic potential and experimental transition barriers taken from the literature. An effective transition event classification method is introduced which allows a boost factor of several thousand compared to a traditional KMC approach, thus allowing experimental time scales to be modeled. The simulation predicts a low sticking probability for the arriving atoms, millisecond order lifetimes for single Ag monomers and about 1 nm square surface migration ranges of Ag monomers. The simulations give excellent reproduction of the experimentally observed nanocluster growth patterns.
The second topic specifies the acceleration scheme utilized in the metallic cluster growth model. Concerning the atomistic movements, a classical harmonic transition state theory is considered and applied in discrete lattice cells with hierarchical transition levels. The model results in an effective reduction of KMC simulation steps by utilizing a classification scheme of transition levels for thermally activated atomistic diffusion processes. Thermally activated atomistic movements are considered as local transition events constrained in potential energy wells over certain local time periods. These processes are represented by Markov chains of multi-dimensional Boolean valued functions in three dimensional lattice space. The events inhibited by the barriers under a certain level are regarded as thermal fluctuations of the canonical ensemble and accepted freely. Consequently, the fluctuating system evolution process is implemented as a Markov chain of equivalence class objects. It is shown that the process can be characterized by the acceptance of metastable local transitions. The method is applied to a problem of Au and Ag cluster growth on a rippled surface. The simulation predicts the existence of a morphology dependent transition time limit from a local metastable to stable state for subsequent cluster growth by accretion.
The third topic is the formation of ripple structures on ion bombarded semiconductor surfaces treated in the first topic as the prepatterned substrate of the metallic deposition.
This intriguing phenomenon has been known since the 1960s and various theoretical approaches have been explored. These previous models are discussed and a new non-linear model is formulated, based on the local atomic flow and associated density change in the near surface region. Within this framework ripple structures are shown to form without the necessity to invoke surface diffusion or large sputtering as important mechanisms. The model can also be extended to the case where sputtering is important and it is shown that in this case, certain "magic" angles can occur at which the ripple patterns are most clearly defined. The results including some analytic solutions of the nonlinear equation of motions are in very good agreement with experimental observation.:1 Introduction: Atomistic Models 1
1.1 Density Functional Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 Schroedinger equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.2 Density functional theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Molecular Dynamics Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.1 Lagrangian mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2.2 MD algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3 Lattice Monte Carlo simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3.1 Thermodynamic variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.3.2 Metropolis Algorithm and limit theorem . . . . . . . . . . . . . . . . . . . . . 15
1.3.3 Kinetic Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.3.4 Imaginary time reaction diffusion . . . . . . . . . . . . . . . . . . . . . . . . . 24
2 Cluster Growth on Pre-patterned Surfaces 29
2.1 Nanocluster growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.1.1 Classical nucleation theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.1.2 Cluster growth on substrates . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.1.3 Experimental motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.2 Local flux and surface ad-monomer diffusion . . . . . . . . . . . . . . . . . . . . . . 35
2.2.1 Surface topography and local flux . . . . . . . . . . . . . . . . . . . . . . . . 35
2.2.2 Surface gas diffusion under inhomogeneous flux . . . . . . . . . . . . . . . . . 37
2.2.3 Surface migration of ad-monomers . . . . . . . . . . . . . . . . . . . . . . . . 40
2.2.4 Simulation vs. experimental gauge . . . . . . . . . . . . . . . . . . . . . . . . 45
2.3 Nucleation models: Surface gas condensation . . . . . . . . . . . . . . . . . . . . . . 46
2.3.1 Simulation setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.3.2 Simulation parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.3.3 Evolution of sticking probability . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.3.4 Evolution of Ag cluster growth . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.3.5 Simulation time and system evolution . . . . . . . . . . . . . . . . . . . . . . 57
2.4 Extended cluster growth model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.4.1 Modified setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.4.2 Simulation result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.4.3 Comparison with experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3 A Markov chain model of transition states 63
3.1 Acceleration of thin film growth simulation . . . . . . . . . . . . . . . . . . . . . . . 63
3.2 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.3 Transition states of Markov chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.3.1 Local transition events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.3.2 The Monte-Carlo method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.4 Effective transitions of objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.4.1 Convergence of the local fluctuation . . . . . . . . . . . . . . . . . . . . . . . 67
3.4.2 The importance of individual local transitions . . . . . . . . . . . . . . . . . . 68
3.4.3 The modified algorithm for effective transition states . . . . . . . . . . . . . . 69
3.5 Cluster growth simulation models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.5.1 The configuration energy and migration barriers . . . . . . . . . . . . . . . . 72
3.5.2 Transition events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.5.3 Comparison with Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.5.4 Cluster growth stability evaluation . . . . . . . . . . . . . . . . . . . . . . . . 78
3.6 Stability of modified convergence limit . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.6.1 Acceleration of convergence to Gibbs field . . . . . . . . . . . . . . . . . . . . 80
3.6.2 Relative convergence speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.6.3 1D Ag models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.6.4 Stability theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4 Ion beam inducing surface pattern formation 89
4.1 Ion-inducing pattern formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.1.1 Bradley-Harper equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.1.2 Nonlinear continuum models . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.1.3 Other approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.2 Simulation of surface defects induced by ion beams . . . . . . . . . . . . . . . . . . . 94
4.2.1 MD simulation of single ion impact . . . . . . . . . . . . . . . . . . . . . . . . 94
4.2.2 Monte-Carlo simulations of surface modification . . . . . . . . . . . . . . . . 96
4.2.3 Curvature dependent surface diffusion . . . . . . . . . . . . . . . . . . . . . . 102
4.3 Continuum model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.3.1 Equation of motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.3.2 A travelling wave solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4.3.3 Lyapunov stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.3.4 Comparison with experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.3.5 Approximate solutions for other angles . . . . . . . . . . . . . . . . . . . . . . 110
4.4 Contribution of other effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.4.1 Surface diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.4.2 Surface Sputtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
5 Summary 119
Appendix 123
A The discrete reaction diffusion equation . . . . . . . . . . . . . . . . . . . . . . . . . 123
B The derivation of the solution (2.20) . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
C Contribution of overlapping migration area . . . . . . . . . . . . . . . . . . . . . . . 125
D The RGL potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
E Stability of the traveling wave solution . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Density Functional Theory of Epitaxial Growth of Metals
This chapter starts with a summary of the atomistic processes that occur
during epitaxy. We then introduce density functional theory (DFT) and describe
its implementation into state-of-the-art computations of complex processes in
condensed matter physics and materials science. In particular we discuss how
DFT can be used to calculate parameters of microscopic processes such as
adsorption and surface diffusion, and how they can be used to study the
macroscopic time and length scales of realistic growth conditions. This meso-
and macroscopic regime is described by the ab initio kinetic Monte Carlo
approach. We discuss several specific theoretical studies that highlight the
importance of the different diffusion mechanisms at step edges, the role of
surfactants, and the influence of surface stress. The presented results are for
specific materials (namely silver and aluminum), but they are explained in
simple physical pictures suggesting that they also hold for other systems.Comment: 55 pages, 20 figures, to be published "Growth of Ultrathin Epitaxial
Layers", The Chemical Physics of Soild Surfaces, Vol. 8, Eds D. A. King and
D. P. Woodruff (Elsevier Science, Amsterdam, 1997
Modelling zinc oxide thin-film growth
Photovoltaics have a significant role in the solution of energy supply and energy security. Research on photovoltaic devices and their production processes has been carried out for decades. The transparent conducting oxide layer, in the photovoltaic solar cell, composed of aluminium doped zinc oxide, is produced through deposition techniques. By modelling these depositions using classical molecular dynamics, a better understanding on the short term kinetics occurring on the growing surface has been achieved. Compared to the molecular dynamics, the employment of the adaptive kinetic Monte Carlo method enabled such surface growth dynamics simulation to reach much longer time scale. Parallelised transition searching was carried out in an on-the-fly manner without lattice approximation or predefined events table. The simulation techniques allowed deposition conditions to be easily changed, such as deposition energy, deposition rate, substrate temperature, plasma pressure, etc. Therefore, in this project three main deposition techniques were modelled including evaporation (thermal and assisted electron beam), reactive magnetron sputtering and pulsed laser depositions.
ZnO as a covalent compound with many uses in semiconductors was investigated in its most energy favourable wurtzite configuration. The O-terminated surface was used as the substrate for the growth simulation. Evaporation deposition at room temperature (300 K) with a stoichiometric distribution of deposition species produced incomplete new layers. Holes were observed existing for long times in each layer. Also, stacking faults were formed during the low-energy (1 eV) growth through evaporation. The reactive sputtering depositions were more capable of getting rid of these holes structures and diminished these stacking faults through high energy bombardments but could also break these desirable crystalline structure during the growth. However, single deposition results with high energies showed that the ZnO lattice presented good capacity of self-healing after energetic impacts. Additionally, such self-healing effects were seen for substrate surface during thin film growth by the sputtering depositions. These facts shed some light on that the sputtering technique is the method of choice for ZnO thin film depositions during industrial production. Simulation results of pulsed laser deposition with separated Zn and O species showed the thin films were grown in porous structures as the O-terminated surface could be severely damaged by Zn atoms during the very short pulse window (10 microseconds). An important growth mechanism with ZnO dimer deposited on the O-terminated polar surface was the coupling of these single ZnO dimers, forming highly mobile strings along the surface and thus quenching its dipole moments, whilst the isolated single ZnO dimers were hardly of this mobility. Such strings were the building blocks for the fabrication occurring on the surface resulting in new layers. Last but not least, a reactive force field for modelling Al doped ZnO was fitted. DFT calculations showed that the Al atoms on the surface were likely to replace Zn atoms in their lattice sites for more energy favourable structures. Al on the ZnO surfaces, structures with Al in the bulk as well as configurations with Al interstitials were used to train the force field to reproduce favourable surface binding sites, cohesive energies and lattice dimensions.
The combination scheme of MD and the AKMC allowed simulation work to reach over experimentally realistic time scale. Therefore, crucial mechanisms occurring during the growth could be precisely understood and investigated on an atomistic level. It has been shown from the simulation results that certain types of deposition play significant roles in the quality of resultant thin films and surface morphology, thus providing insight to the optimal deposition conditions for growing complete crystalline ZnO layers
Atomistic studies of thin film growth
We present here a summary of some recent techniques used for atomistic
studies of thin film growth and morphological evolution. Specific attention is
given to a new kinetic Monte Carlo technique in which the usage of unique
labeling schemes of the environment of the diffusing entity allows the
development of a closed data base of 49 single atom diffusion processes for
periphery motion. The activation energy barriers and diffusion paths are
calculated using reliable manybody interatomic potentials. The application of
the technique to the diffusion of 2-dimensional Cu clusters on Cu(111) shows
interesting trends in the diffusion rate and in the frequencies of the
microscopic mechanisms which are responsible for the motion of the clusters, as
a function of cluster size and temperature. The results are compared with those
obtained from yet another novel kinetic Monte Carlo technique in which an open
data base of the energetics and diffusion paths of microscopic processes is
continuously updated as needed. Comparisons are made with experimental data
where available
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