Atomic Level Modelling of Structure and Growth of Materials

This research is concerned with the study of structural properties of and growth phenomena in solid materials. All studies rely on microscopic modeling, in which the inter-atomic interactions are described through pairwise and many-body model potentials. In generic studies we have used Lennard-Jones potentials, while in more specific cases the Tersoff, Stillinger- Weber and Valence Force Field potentials as regards to the study of semiconductors and Effective Medium and the Embedded Atom model potentials as regards to studies of metals have been used. Because these semiempirical potential models have their drawbacks and limitations when attempting to describe bonding in certain materials (especially carbon in tubular form) the more accurate tight-binding approach has been used as a complementary method to describe inter-atomic interactions.

The main topics of investigation in the case of semiconductor materials have been structure and mechanical properties of surfaces, interfaces and various nanostructures – e.g. thin films, quantum dots, clusters and carbon nanotubes. In addition to crystalline materials recrystallization of amorphous silicon has been studied by computational methods. As regards to metals, the focus has been on detailed microscopic structure and dynamics of dislocations.

Large scale Molecular Dynamics (MD) and Monte Carlo (MC) simulations have been the standard tools employed in all these studies and their execution have been done using mostly our in-house parallel cluster computers. This has entailed program development especially for parallel computing puposes. In connection with the MD simulations, development of the graphical user interface for the simulation programs has been continued. In addition interactive simulation programs have been developed and used to study dislocation dynamics and strain relaxation in two and three-dimensional heteroepitaxial systems and mechanical and structural properties of carbon nanotubes. A more general development of scientific visualization has also been done using the open-source program package OpenDX.


Hetero-structures

Researchers: Marco Patriarca, Antti Kuronen, and Kimmo Kaski

The study of nucleation and dynamics of dislocations in lattice-mismatched heterostructures has a special interest, due to its technological importance for potential applications. In this type of systems, dislocations may arise from instabilities appearing already during the formation of the hetero-strucure, e. g. during the growth of the overlayer, due to different origins. In the present work we analyze, in particular, thermodynamical instabilities – whose main characteristics are only related to the properties of the two materials.

We employ a numerical molecular dynamics approach to the problem, in order to fully take into account the atomic nature of the scale of the problem. To this aim the misfit m is then slowly modified, by changing some parameters of the interaction potential, starting from the initial value, m=0, until the critical misfit m = m*h , corresponding to the given heigth h, is reached and one or more dislocations are nucleated in the overlayer. The transformation is carried out slowly enough (adiabatically) and under some suitable controls, in order to be reversible and such that the system is always almost in thermal equilibrium at a given temperature . This procedure should be compared with (the simulation of) a real growth process, in which the misfit m is fixed, while it is the (average) heigth h which increases.

Fig. 15 shows a sample with sizes 15 x 20 x 100 lattice constants. A step was created around the over-layer in order to give it the structure of a dot. Atoms of type 1 in the lower part are supposed to represent a very large substrate, on which a dot of atoms of type 2 is present. When the misfit reached the critical threshold , one can observe a sudden release of kinetic energy, with visible oscillations and misfit dislocation nucleation.

For a review see M. Patriarca and A. Kuronen, Atomistic modeling of hetero-structures, to be published in Handbook of Theoretical and Computational Nanotechnology Michael Rieth and Wolfram Schommers Editors, ASP, in press.

Figure 15

Figure 15: Left: For a misfit close to the critical value m = -0.9 there are no dislocations yet, but a cut of the sample along the interface shows a zone with regularly shaped zones under high strain induced by the mismatch. Right: The dislocations have appeared and the stacking fault left by a nucleated misfit dislocation appears as a step on the surface of the system. Atoms are colored according to a potential energy mapping.

Interactive graphical tool for numerical experiment

Researchers: Marco Patriarca, Antti Kuronen, and Kimmo Kaski

Numerical simulations represent an invaluable contribution to the current description of the behavior of matter. They are particularly helpful in describing the processes in solid state systems in which employ many-body potential models are to be used. Interactive numerical simulations, based on the association of a visualization tool, such as a graphical user interface (GUI), with a numerical simulation code, present specific advantages. First of all the amount of memory storage required can be greatly reduced. Furthermore, the possibility of a real time variation of the simulation parameters, such as temperature and applied fields, and the analysis of the corresponding feedback made possible by the graphical environment offer the possibility to perform a fine tuning in the regions of parameter space for a better monitoring of the evolution of a process, similarly to what is done in a real experiment. This is best done with a program which can effectively visualize the system, e.g. by a selective visualization of only a part of the atoms, according to some criterion defined by parameters which can be changed in real time. For instance, one can choose those atoms with single-particle potential energy in a suitable energy window. Finally, numerical experiments allow one to vary parameters which are normally fixed, thus exploring the behavior of a system along dimensions not directly accessible to experiment, e. g. by varying the atomic interaction potential or the particles mass. This also allows a straightforward verification of the consistency of specific predictions of theoretical models, for which it would be difficult to set up a real experiment. The program developed at LCE can study N-particle systems, in which particles interact with each other either via a pair-wise or a many-body potential. While the MD code performs the standard computations and evolves the system in time, the GUI visualizes the system, at the same time allowing the user to modify the system parameters and chose an optimal visualization mode for the atoms. The program has been written in C and developed for an X11 Window System platform, all graphics being based on the MOTIF library, used by many UNIX workstations.

Figure 16

Figure 16: Left: Graphical user interface.

Modeling of thin semiconductor films

Researchers: Laura Juvonen, Francesca Tavazza*, David P. Landau*, Antti Kuronen, and Kimmo Kaski
*Center for Simulational Physics, The University of Georgia, Athens, GA, USA

Understanding the growth of thin semiconductor films is crucial for developing new types of nanoelectronic devices. We are studying the structure and properties of heteroepitaxial Ge/Si(001) systems which are estimated to be one of the most promising materials for novel electronic and optoelectronic components.

Semiconductor surfaces are often difficult to study because these systems are strongly in- fluenced by the strain-related effects and long-range elastic interactions which requires using large-scale simulation methods. Conventional algorithms can easily get trapped into metastable states, which prohibits the simulation from reaching the correct equilibrium structure.

In order to overcome these problems, we have developed advanced Monte Carlo algorithms which can be applied to problems where substantial configurational rearrangement is required. In the dimer-jump algorithm, trial MC moves consist of long displacements of atom pairs followed by a local relaxation using Molecular Dynamics.

Figure 17 shows a snapshot of a Si(001) surface on which small Si islands are forming. All surface atoms (shown red) are mobile.

Figure 17

Figure 17: Formation of small Si islands on Si(001) using the dimer-jump algorithm. All red atoms are mobile (atom pairs are moved as a unit). The color coding of the atoms in the underlying layers reflects their energy (green is higher and blue lower in energy).

Structure and energetics of grain boundaries in silicon

Researchers: Sebastian von Alfthan, Adrian Sutton, and Kimmo Kaski

Grain boundaries are formed when two crystalline slabs are put into contact with each other, so that the crystals are rotated with respect to each other. These are formed in polycrystalline silicon, which is used widely for solars cells and thin-film transistors. In pure twist grain boundaries the axis around which the crystals are rotated, is perpendicular to the interface. In Figure 1 one can see an example of how a twist grain boundary is formed. After the two crystals have been put into contact the atoms at the interface will self-organize into their minimum energy configuration. One cannot experimentally see the atomistic structure of twist grain boundaries, only the grain boundary energy can be measured. Therefore the atomistic structure of the interface is still considered controversial.

In this work we are using computational methods to study the atomistic structure of twist grain boundaries of different rotation angles. We are interested in knowing if the interface of all grain boundaries is comprised of a thin amorphous layer, or if there are certain angles for which the interface is crystalline. We are also interested in the grain boundary energy, since it can be compared to experimental results.

Using a combination of molecular dynamics and atomistic Monte Carlo methods we have found crystalline structures for many of the grain boundaries. These results are supported by experimental evidence since these grain boundaries have been measured to have a lower grain boundary energy. These are very important results since previous computational studies suggested that all grain boundaries are amorphous. These structures have never before to this authors knowledge been presented previously, and as such are of great interest.

Figure 18

Figure 18: A twist grain boundary has been formed after two crystalline slabs of silicon, which have been rotated with respect to each other, have been put into contact.

Figure 19

Figure 19: The crystalline structure of a twist grain boundary, where the upper crystal has been rotated by 67.4 degrees.

Dislocations in FCC Metals: Interaction of Moving Dislocation with Defects

Researchers: Péter Szelestey, Marco Patriarca, and Kimmo Kaski

type of dislocations, the most common in face-centered-cubic materials, generally dissociate into two partials connected by a stacking-fault region. These dislocations have been the object of much research in recent years especially from their mobility point of view because of its importance in plasticity of materials. The interaction of the moving dislocation with defects is one mechanism obstructing dislocation motion, and the computational approach to study this problem has become an increasingly interesting topic in the past years. We used atomic level, Molecular Dynamics simulations, with the aid of the previously developed Embedded Atom potentials and visualization and tracking methods, in order to investigate the detailed interaction processes.

Our study concentrated on the interaction process of a screw dislocation with a perfect, vacancy-type stacking-fault tetrahedron (SFT). The detailed reaction turned out to depend on severals factors, such as the size and the orientation of the defect and the internal structure, the separation distance of partials, of the moving dislocation. When the glide plane of the moving dislocation is the same as one of the planes that bound the SFT the interaction process includes dislocation reactions, jog line formation and significant bending of the dislocation line. As an important quantity, the critical stress required to move the dislocation through the defect was measured.

Our study has importance in understanding the pinning process of a moving dislocation due to SFT, and the stability and destruction mechanisms of SFT. From the practical point of view our research has special relevance in nuclear materials, which are required to have exceptional mechanical properties while having a typically high concentration of SFTs induced by irradiation.

Figure 20

Figure 20: Snapshots of a stacking-fault tetrahedron (pyramid shaped object) intersected by a dissociated screw dislocation corresponding different defect orientations. The two partials can be identified by the blue lines. Only atoms in the dislocation core and the edges of SFT are shown.

Mechanical Properties of Carbon Nanotubes

Researchers: Maria Sammalkorpi, Kaisa Kautto, Antti Kuronen, and Kimmo Kaski

Carbon nanotubes are cylindrical all-carbon molecules composed of concentric graphitic shells with extremely strong covalent bonding of atoms within the shells but very weak van der Waals type interaction between them. Due to the unique atomic structure nanotubes have exceptional electronic and mechanical properties which imply a broad range of possible applications as constituents of nanometer-scale devices and novel composite materials.

The properties of a carbon nanotube depend on the local atomic configuration and defects. For composite and device development it is essential to understand how structural changes affect the properties and our work strives after shedding some more light on the occurring phenomena. Current projects concentrate on evaluating irradiation and irradiation induced defects as a means to improve carbon nanotube strength, load transfer and inter-shell friction. The tools employed are both classical molecular dynamics and dynamical tight binding methods. Fig. 21 shows an example of a defect typical to irradiation and how such defects can link tubes which efficiently prevents tube-tube slippage.

Figure 21

Figure 21: Left: A defect typical to irradiation, a vacancy. Right: Example of a nanotube bundle in which the nanotubes are linked together by the presence of vacancies.

Theoretical Particle Distributions on Curved Surfaces

Researchers: Kaisa Kautto, Maria Sammalkorpi, Adrian Sutton, and Kimmo Kaski

This work has been motivated by the general lack of knowledge concerning the analytic influence of surface curvature on the distribution of particles on the surface. This is relevant for understanding many optimal packing related problems of materials science, for example, biomolecular packings, changes in the vicinity of dislocations and, as in here, nanostructures of carbon. The long term aim of the work is to be able to model deformed carbon nanotubes. This involves understanding uniform distributions of points on curved surfaces and the connection between these distributions and atomic structures. The simplest curved surface is the sphere and therefore we started the analysis by considering the spherical fullerene C60. This carbon structure also known as the buckminsterfullerene corresponds to the uniform distribution of 32 points on a sphere. Studies have also been extended to ellipsoidal surfaces and to the analysis of uniform point distributions of other than 32 points.

Figure 22

Figure 22: A structure (on the left) that is closely related to the atomic configuration of the fullerene is obtained as the dual, or Voronoi diagram, of the uniform distribution of 32 points on a sphere (on the right).

 


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