Atomic Level Modelling of Structure and Growth of Materials

The present line of research is concerned with the study of structural properties and growth phenomena of solids. 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 adopted as a complementary method to describe inter-atomic interactions.

Large scale Molecular Dynamics (MD) and Monte Carlo (MC) simulations have been the standard tools employed in all these studies. Cluster computer CLUX - installed at the CSC - Scientific Computing Ltd and partly owned by the laboratory - has been used to perform MC and MD simulations of systems containing up to 2 × 106 atoms. Execution of smaller scale parallel jobs and program development for parallel machines has been done using our in-house cluster computers.

The main topics of investigation in the case of semiconductor materials have been the growth on substrates, ideal or with imperfections, structure and mechanical properties of various nanostructures – e.g. thin films, quantum wells, quantum dots and carbon nanotubes. In addition to crystalline materials properties of amorphous silicon and silicon dioxide has been studied by computational methods.

As regards to metals, the focus has been on detailed microscopic structure of materials. Examples of these studies include modelling of brittle/ductile fracture, relaxation of grain boundaries, and structure and dynamics of dislocations.

In connection with the MD simulations, development of the graphical user interface for the simulation programs has been continued. The interactive simulation programs have been used to study dislocation dynamics and strain relaxation in two and three-dimensional heteroepitaxial systems and mechanical and structural properties of carbon nanotubes. Development of scientific visualization (on-line and off-line) has also been done using the open-source program package OpenDX.

In relation to all these simulation studies, parallel computation algorithms and methods are being developed, specifically targeted to computer cluster environments.

Modelling of Compound Semiconductors: Analytical Bond-order Potential for Ga, As and GaAs

Researchers: Karsten Albe*, Kai Nordlund1, Janne Nord1, and Antti Kuronen
*University of Illinois at Urbana-Champaign, IL, USA and Institut für Materialwissenschaften, TU Darmstadt, Germany
1University of Helsinki, Accelerator Laboratory

Various ab initio methods can be used to model materials at atomic level. However, due to the large demand for computational power their use is currently restricted to small systems containing up to 1000 atoms. Many phenomena like strain relaxation in heteroepitaxial systems or ion beam interaction with materials involve much larger amount of atoms. In these cases atomic level modelling has to be done using semiempirical potentials. For the III-IV compound materials there are very few potentials in the literature. We have assessed these potentials and found that their applicability for simulations in phenomena far from bulk equilibrium is poor.

Therefore we have developed a new analytical bond-order potential for GaAs, that allows to model a wide range of properties of the compound structures as well as the pure phases of gallium and arsenide including non-equilibrium configurations. The analytical form follows in principle the bond-order scheme as devised by Abell and Tersoff, but angular forces and mixed interactions are treated differently. A number of tests, that cover a wide range of structural geometries including the metallic phases of gallium and arsenide, point defect properties, elastic moduli, surface properties and melting behavior, have been performed in order to validate the accuracy and transferability of the potential model.

Figure 18

Figure 18: Structure of amorphous GaAs after melting at 1900 K at 0 pressure and subsequent cooling to 1500K predicted by the bond-order potential. Only the covalent bonds between atoms are shown. The low-density region on the upper left is a segregated As bubble which has formed during melting. On the lower left and lower right a recrystallized GaAs region has formed.

Nucleation and Dynamics of Dislocations in Mismatched Heterostructures

Researchers: Marco Patriarca, Antti Kuronen, Kimmo Kaski

Dislocations, as other kinds of crystal defects, are entities with striking dynamical characteristics as well as a physical individuality, despite they are usually defined statically in terms of deviations of the lattice geometry from that of a corresponding perfect lattice. For this reason Molecular Dynamics Simulations represent a valuable tool to study their properties. We study nucleation of dislocations and dislocation dynamics in lattice-mismatched heterostructures, which have recently risen a great interest due to the technological importance of such structures.

Figure 19

Figure 19: The Graphical User Interface "Boundary3D" used in the numerical simulations. In the upper graphical window a sample of the system under study is drawn, in which the colours signify the potential energy defined in the lower graphical window.

To this aim we developed a graphical user interface (Fig. 19) from a previous 2D version, also developed at LCE, which uses a mapping based on the effective potential energy to visualize and track dislocations and other types of crystal defects. With its help we have studied the nucleation of dislocation in lattice-mismatched heterostructures for different values of the misfit and temperature. While moving, such dislocations form a stacking fault crossing the sample, whose intersection with the outer surface of the sample is clearly visible as a region of higher potential energy.

Computational Study of Amorphous Silicon and Silica

Researchers: Sebastian von Alfthan, Antti Kuronen and Kimmo Kaski

Understanding of properties and structure of amorphous silica (SiO2) and silicon is an important subject for various technological reasons. The exact structure of these materials can not be obtained experimentally but by using computational methods one can create configurations which have the same characteristics as the real ones. By studying these configurations new insight can be obtained about them.

In this study models of amorphous silicon and silica have been created using two computational methods. These two methods simulate the way in which real amporphous samples are manufactured. They both start from a disordered state and by lowering the temperature of the system they reach an amorphous state. The first method is the Wooten, Winer and Weaire (WWW) method which by optimizing the bond-topology of the system using a Monte Carlo scheme quenches the system to an amorphous state. Another way of creating amorphous samples is by quenching the sample from a liquid state using a molecular-dynamics simulation, this is the 'quench-from-melt' (QFM) method.

The configurations obtained are analyzed using five different methods.(i) The radial distribution function is calculated and compared to experimentally obtained ones. This function shows how the distances between atoms are distributed. (ii) Distribution of angles between bonds is studied. (iii) Since amorphous silica may be porous, it is interesting to study properties of the pores. (iv) The distribution of the ring size is studied. Rings are closed paths along the bonds. (v) The vibrational density of states is studied by diagonalizing the dynamical matrix.

Figure 20

Figure 20: A small amorphous silica sample prepared using the WWW method.

Modeling of Thin Semiconductor Films

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

The structure of thin semiconductor films is not only of technological importance but also offers great challenges from a theoretical point of view. The heteroepitaxial system composed of a thin layer of germanium on a silicon (001)-surface is used as an example to study the properties of mixed semiconductor systems in which lattice mismatch induced strain plays a significant role. Currently it is impossible to use ab initio methods to study systems composed of thousands of atoms. Therefore, we are using empirical interatomic potentials, such as Stillinger-Weber and Tersoff forms, to perform large-scale Monte Carlo simulations of Si or Ge layers on a Si(001) substrate.

The Si(001) surface reconstructs to form parallel rows of dimerized atom pairs. The (2 × 1) reconstruction minimizes the surface energy by reducing the number of dangling bonds on the surface atoms. The empirical potentials were originally constructed with emphasis on the bulk properties of silicon. The structure of surfaces is generally much more complicated. We have therefore paid careful attention to the the ability of the different empirical potentials to model the Si(001) reconstruction. Specialized Monte Carlo techniques are developed to overcome the problem of getting trapped into metastable states associated with complicated energy landscapes. Figure 21 shows a snapshot of a simulation in which a Ge island has been deposited on a Si(001) substrate. The system is unable to reorganize into straight dimer rows, because breaking up a single dimer costs a large amount of energy. Thus the system is trapped in this metastable state.

Figure 21

Figure 21: Monte Carlo simulation of a Ge island on a Si(001) surface. The Tersoff potential T3 was used to model the atomic interactions. Ge atoms are depicted in red and Si atoms in yellow.

Static and Dynamic Properties of Dislocations in FCC Metals

Researchers: Péter Szelestey, Marco Patriarca, and Kimmo Kaski

Dislocations play a fundamental role in plastic deformation of materials. Studying the structure and mobility of dislocations is important in order to understand plasticity. We studied the most common edge dislocation in FCC structures, the dissociated 1/a211 Schockley partial dislocations which result from the dissociation of a perfect 1/a110 edge dislocation. We carried out 3D atomistic Molecular Dynamics simulations using the Embedded Atom potential with the parametrization that was developed in our laboratory for four different metals (Au, Cu, Ni, Al). These potentials incorporate elastic moduli up to third-order, give reasonable stacking-fault energy, and reproduces many other material properties well. We examined the separation distance of partials, which is crucial quantity for plastic behaviour, the structure of dislocation core, and the interaction of two dislocations. We also compared our numerical results with values predicted by continuum elasticity and the Peierls-Nabarro model.

Deformation of a crystal under stress is strongly dependent on the movement of dislocations. In particular dislocation velocity has direct implication on brittle and ductile behaviour. If a shear stress is applied along the gliding plane, the dislocation moves with a constant velocity which depends on the value of the shear stress and the material properties. A difficulty of this type of simulations is to make a model which represents an infinite system as well as possible. In our research we have studied the motion of Schockley partials, concentrating especially on the low shear stress regime. We have analyzed the shear stress vs. velocity relation and how the separation distance changes with increasing velocity.

Figure 22

Figure 22: Motion of two partials under shear stress (upper and lower curves with the same colour). Black lines: no external shear, red lines: with external stress, blue lines: with larger stress.

Influence of Many-body Interactions in Stress-velocity Relation of Single Dislocation in 2D Lattice

Researchers: Miguel Robles, Ville Mustonen and Kimmo Kaski

Mechanisms of deformation of a crystal under stress are strongly dependent on the movement of dislocations. So far, the dynamics of dislocations is not well understood due to the complexity and the difficulties in modelling the phenomena. Presently, due to large improvements in computing power, large scale simulations are making it possible to study the dynamics of dislocations in a consistent way. We have been studying the influence of many body interactions in the stress-velocity relation (see Fig. 23) of a single dislocation in a 2D lattice, using molecular dynamic software with graphical user interface previously done and reported. The physical model uses a hybrid interatomic model potential which couples Lennard-Jones(LJ) potential and the Embedded Atom Model (EAM) potential. Both parts are assembled by a parameter so that the potential can be changed to describe a pure radial interaction to a strong many body interaction in a continuous way. Setting up a constant-stress scenario, the movement of a single dislocation is tracked from zero velocity state, up to a terminal velocity state. Results have been analyzed using an augmented Peierls model to seek the connection between atomic scale, continuum variables and the limiting speed of dislocations.

Figure 23

Figure 23: External stress-velocity relation for different values of the potential coupling parameter, upmost curve corresponds to pure LJ potential and then in curves below the many body interactions are increased. The continuum lines are result after augmented Peierls model predictions are fitted with simulation results.

Structural Properties of Carbon Nanotubes and Nanotori

Researchers: Maria Huhtala, Kota Mogami, Antti Kuronen, and Kimmo Kaski

Carbon nanotubes are tubular all-carbon molecules with fascinating properties. Single walled nanotubes can be visualized as a graphite layer rolled seamlessly into a tubular form. Of the properties, the large aspect ratio and richness of achievable electronic properties have made carbon nanotubes the proposed material for diverse nanoelectronic and nanoelectromechanical devices whereas proposed mechanical applications rely on high elasticity combined with high yielding strength of the tubes.

The properties of a carbon nanotube depend on the local atomic configuration and in many of the proposed electromechanical applications this changes from one mode of function to another. The tube can be manipulated to bend, or buckle, or defects can be induced. For device development it is essential to understand these structural changes and our work strives after shedding some more light on the occurring phenomena. The tools employed are both classical molecular dynamics and dynamical tight binding methods. Figs. 24 and 25 show a sample of a bent nanotube and more detailed images of the bend.

Figure 24a Figure 24b Figure 24c Figure 24d

Figure 24: A series of images depicting an (8, 8)-nanotube behavior in the course of bending.

Figure 25a Figure 25b Figure 25c

Figure 25: An example of observed differences between the empirical molecular dynamics model with Tersoff-Brenner interaction and the dynamical tight binding model of Frauenheim et al.. The leftmost image corresponds to the first one in Fig. 24, the middle image to the next one, and the rightmost to the one after that in Fig. 24. The carbon framework is the relaxed configuration obtained by using the empirical Brenner model and the arrows indicate the displacement of atoms when relaxed with the tight binding model.