Atomic Level Modelling of Structure and Growth of Materials

The research of our group 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.

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 HUT Computing Centre 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 structure and mechanical properties of surfaces and various nanostructures - e.g. thin films, quantum dots and carbon nanotubes. In addition to crystalline materials properties of silicon nanocrystals in amorphous silicon dioxide have been studied by computational methods. As regards to metals, the focus has been on detailed microscopic 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 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.

Dislocation Nucleation in Mismatched Heterostructures

Researchers: Marco Patriarca, Antti Kuronen, Kimmo Kaski

We study the conditions for nucleation of dislocations in lattice-mismatched heterostructures, which have recently risen a great interest due to their technological importance. To this aim we use programs Boundary3D Boundary2D developed in our laboratory and consisting of a graphical user interface coupled to a molecular dynamics code. We consider different values of the misfit parameter, temperature, layer thickness, and boundary conditions. Examples of simulation results are shown in Figs. 17 and 18.

Figure 17a Figure 17b

Figure 17: Left: Typical geometry used for the numerical simulations. Colours signify atom type. Right: The same system with colours signifying potential energy. Steps on the top and irregularities on the lateral surface are due to stacking faults formed beyond the critical misfit.

Figure 18a Figure 18b

Figure 18: Results from dislocation nucleation barrier calculation of a 2D Lennard-Jones system. Left: Atomic configurations of a nucleation event in the case of -2.5% misfit. Right: The system potential energy along the reaction path for different values of the misfit. Letters a-d on the left correspond to positions marked a-d on the reaction path on the right hand side of the picture.

Minimum Energy Paths in 2D Systems

Researchers: Antti Kuronen, Tapio Nieminen

The 2D simulation code Boundary has been further developed by implementing the nudged elastic band (NEB) method to calculate the minimum energy path between two atomic configuration.

Figure 19a Figure 19b

Figure 19: The main window of Boundary simulation program.

Phase Separation in Amorphous Semiconductors

Researchers: Sebastian von Alfthan, Antti Kuronen and Kimmo Kaski

We have developed computational methods to study phase separation in amorphous solids on an atomistic level. We are using these methods to study the formation of silicon nanocrystals in SiO. This problem has practical applications since one possibility for creating active light emitting devices made of silicon is based on small clusters of crystalline silicon embedded in amorphous SiO2. Recently, a promising method for creating these nanocrystals with greater control of their density and size distribution has been presented. This method consists of annealing SiO/SiO2 superlattices which results in phase separation and thermal crystallization of small silicon nanocrystals in the SiO layer.

The computational method we are using is a variant of a Monte Carlo (MC) method called the Wooten Wiener and Weaire (WWW) method. In the WWW method the structure of the material is described by the topology of the bonds connecting the atoms. The system is allowed to evolve by doing trial moves that change the bonding topology. Using this method we are able to directly model the development of the structure of the material. This enables us to study the phase separation and the crystallization. This would be impossible with normal molecular dynamics or Monte Carlo methods because of the timescales involved.

We have also using openDx ( developed a visualization program called atomicDx that can be used to visualize atomic systems. The program has been developed for analyzing the structural properties of semiconductors but it can also be used for other cases.

Figure 20a Figure 20b Figure 20c

Figure 20: Pictures created using atomicDx of a phase separated SiO system. left: Red atoms depict silicon atoms while blue atoms depict oxygen atoms. middle: The color of the bonds corresponds to their length. right: Blue corresponds to atoms in pure silicon while red corresponds to atoms in silica.

Static and Dynamic Properties of Dislocations in FCC Metals

Researchers: Péter Szelestey, Marco Patriarca, and Kimmo Kaski

Dislocations are topological defects that have major influence on the plastic nature of crystals. We are using Molecular Dynamics simulations to determine properties of the most common type of dislocations in face-centered-cubic metals. These dislocation generally split into partials and may extend over several lattice constants laterally. Primarily we concentrate on nickel as a model material. Most of our simulation tools have already been developed in the previous years including the inter-atomic potential.

In our recent work we calculated the properties of both edge and screw type of dislocations and carried out a detailed comparison of both type of dislocations with theoretical results and each other. The separation distance of partials have been calculated and we found that there exists several meta-stable separation distances. The profile of dislocation distribution function was compared with the Peierls-Nabarro model and possible reasons of the discrepancies were explained.

Dislocation motion is basic mechanism responsible for plastic behaviour of materials. Dislocation motion is affected by the external stress and the underlying lattice, which results in a small periodic potential for the dislocation. We measured the minimum stress required to move a dislocation, the so-called Peierls barrier and found reasonable agreement with the Peierls-Nabarro model. In addition our results show that dislocations may change their structure during the motion reflected from the change in the separation distance. Although theoretically this has been prediced for a long time, we could observe this effect by means of simulations.

Figure 21

Figure 21: Snapshot of an extended screw dislocation looking from the direction of the dislocation line. Particles are denoted with different colors representing the magnitude of potential energy.

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

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.

The Ge/Si(001) system consists of a thin germanium layer on a silicon (001) surface. Despite its relatively simple composition, the system displays a wide variety of interesting phenomena related to relaxation of lattice-mismatch induced strain. Studying strain-related effects requires using large-scale simulation methods because these systems are strongly influenced by long-range elastic interactions. Accurate quantum-mechanical first-principles methods are currently limited to systems composed of a few hundred atoms at best. Tight-binding techniques can extend to a few thousand atoms, but in many cases empirical potentials are still the only practical choice.

We use empirical potentials in connection with advanced Monte Carlo techniques. This approach can be used to study phenomena where considerable atomic rearrangement takes place as well as temperature-dependent phenomena. Figure 22 shows the surface structure of a system which consists of two Ge layers deposited on a Si(001) substrate. Compressive strain in the Ge overlayer is relieved in part by formation of dimer vacancy lines and in part by Si/Ge intermixing.

Figure 22

Figure 22: Surface structure of 2ML of Ge on Si(001). Relaxation of strain is achieved by two mechanisms: (i) dimer vacancy lines allow for inward relaxation of the Ge overlayer and (ii) Si/Ge intermixing provides additional strain relief. The atomic interactions were modeled by the Stillinger-Weber potential. Si atoms are depicted as dark blue and Ge atoms are color coded according to their energies [from red (high energy), to green and light blue (lower energy)].

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. Fig. 23 shows nanotube buckling and bond reconstruction in the buckled region.

Figure 23

Figure 23: A (14,0)-nanotube first bent to an angle of 36 degrees and then annealed in a temperature of 3300 K for three periods of 130 ps. After each of the annealing sessions, the structure has been cooled down to 0 K. The enlarged protions at left and right show bond reconstructrion which relaxes the strain.

Studies on Microelectromechanical Systems

Researchers: Virpi Junttila, Jarmo Hietanen, Kimmo Kaski

This research is a project of "MIKSU technology program", which is partially funded by TEKES (National Technology Agency).

Studies on different problems arising in fabrication of MEM-systems were performed using various numerical methods. The possibility of contact of the membrane and the perforated Si-plate of a microphone fabricted on a SOI were studied. The affect of the pre-tension in the SiO2 layer between the plate and membrane was studied using Ansys. It revealed, that the displacement of the solid plates of varying thicknesses is small, 10-20% of the air layer thickness and 1.5-5.6% of the plate thickness. The homogenization of the holes would in stationary case affect only the Young's modulus; but even with half of the Young's modulus the displacement would be only 13-23% of the air layer thickness and 1.9-6.9% of the plate thickness. Thus it is very unlikely that the contact between the perforated plate and the membrane occur only due to the pretension.

The membrane displacement due to pressure difference was modelled using Elmer software. The modelling was performed in two levels: First the affect of an individual hole was modelled to an air layer thickness dependent acoustic impedance using linearized Navier-Stokes model. Second the membrane displacement was solved using time-dependent coupled homogenized Reynold's equation and Kirchhoff equation and linearly vanishing pressure difference. The membrane would contact the plate if the pressure difference vanishes slowly, in microseconds, even if the difference is small. The Acoustic impedance and the membrane displacement are shown in Fig. 24.

Also the breaking of the contact of the attachment lines of a wind sensor due to wind arisen pressure difference have been modelled. The force of the condensators of the sensor were solved using Femlab software and homogenized. The plate displacement was then solved using Kirchhoff equation. The membrane would unstick from the attachment area if the capasitive force was less than about twice the force arising from the wind. Two cases of a memrane displacement and plots of the maximum displacament as functions of force ratio are shown in Fig. 25.

Figure 24a Figure 24b

Figure 24: Left: Acoustic impedance of a hexagonal hole for compressible and incompressible fluids; curves fitted for data. Right: Minimum gas layer thickness as a function of time at pressure difference of 10%.

Figure 25a Figure 25b

Figure 25: Left: Membrane displacement for capasitive force being 1.32 times the force of pressure difference. On the left the free membrane, on the right a membrane glued to the sensor is in the middle. Right:Maximum and the corner displacement of the membrane of the wind sensor as a function of the ratio of the force of the condensator and force of the pressure difference. On top results for a free membrane, on the bottom results for a membrane glued to the condensator in the middle.