Oleg Trushin

Self-learning kinetic Monte Carlo method: Application to Cu(111)

We present a method of performing kinetic Monte Carlo simulations that does not require an a priori list of diffusion processes and their associated energetics and reaction rates. Rather, at any time during the simulation, energetics for all possible single- or multiatom processes, within a specific interaction range, are either computed accurately using a saddle-point search procedure, or retrieved from a database in which previously encountered processes are stored. This self-learning procedure enhances the speed of the simulations along with a substantial gain in reliability because of the inclusion of many-particle processes. Accompanying results from the application of the method to the case of two-dimensional Cu adatom-cluster diffusion and coalescence on Cu111 with detailed statistics of involved atomistic processes and contributing diffusion coefficients attest to the suitability of the method for the purpose.

Minimum energy paths for dislocation nucleation in strained epitaxial layers

We study numerically the minimum energy path and energy barriers for dislocation nucleation in a two-dimensional atomistic model of strained epitaxial layers on a substrate with lattice misfit. Stress relaxation processesfrom coherent to incoherent states for different transition paths are determined using saddle point search based on a combination of repulsive potential minimization and the Nudged Elastic Band method. The minimum energy barrier leading to a final state with a single misfit dislocation nucleation is determined. A strong tensile-compressive asymmetry is observed. This asymmetry can be understood in terms of the qualitatively different transition paths for the tensile and compressive strains.

Global transition path search for dislocation formation in Ge on Si(001)

Abstract Global optimization of transition paths in complex atomic scale systems is addressed in the context of misfit dislocation formation in a strained Ge film on Si(001). Such paths contain multiple intermediate minima connected by minimum energy paths on the energy surface emerging from the atomic interactions in the system. The challenge is to find which intermediate states to include and to construct a path going through these intermediates in such a way that the overall activation energy for the transition is minimal. In the numerical approach presented here, intermediate minima are constructed by heredity transformations of known minimum energy structures and by identifying local minima in minimum energy paths calculated using a modified version of the nudged elastic band method. Several mechanisms for the formation of a 90° misfit dislocation at the Ge–Si interface are identified when this method is used to construct transition paths connecting a homogeneously strained Ge film and a film containing a misfit dislocation. One of these mechanisms which has not been reported in the literature is detailed. The activation energy for this path is calculated to be 26% smaller than the activation energy for half loop formation of a full, isolated 60° dislocation. An extension of the common neighbor analysis method involving characterization of the geometrical arrangement of second nearest neighbors is used to identify and visualize the dislocations and stacking faults.

Equilibrium shape and dislocation nucleation in strained epitaxial nanoislands.

We study numerically the equilibrium shapes, shape transitions, and dislocation nucleation of small strained epitaxial islands with a two-dimensional atomistic model, using simple interatomic pair potentials. We first map out the phase diagram for the equilibrium island shapes as a function of island size (up to

Strain relief in Cu-Pd heteroepitaxy.

N=105

Mechanisms of dislocation nucleation in strained epitaxial layers

atoms) and lattice misfit with the substrate, and show that nanoscopic islands have four generic equilibrium shapes, in contrast with predictions from the continuum theory of elasticity. For increasing substrate-adsorbate attraction, we find islands that form on top of a finite wetting layer as observed in Stranski-Krastanow growth. We also investigate energy barriers and transition paths for transitions between different shapes of the islands and for dislocation nucleation in initially coherent islands. In particular, we find that dislocations nucleate spontaneously at the edges of the adsorbate-substrate interface above a critical size or lattice misfit.

Minimum energy path for the nucleation of misfit dislocations in Ge/Si(0 0 1) heteroepitaxy

We present experimental and theoretical studies of Pd/Cu(100) and Cu/Pd(100) heterostructures in order to explore their structure and misfit strain relaxation. Ultrathin Pd and Cu films are grown by pulsed laser deposition at room temperature. For Pd/Cu, compressive strain is released by networks of misfit dislocations running in the [100] and [010] directions, which appear after a few monolayers (ML) already. In striking contrast, for Cu/Pd the tensile overlayer remains coherent up to about 9 ML, after which multilayer growth occurs. The strong asymmetry between tensile and compressive cases is in contradiction with continuum elasticity theory and is also evident in the structural parameters of the strained films. Molecular dynamics calculations based on classical many-body potentials confirm the pronounced tensile-compressive asymmetry and are in good agreement with the experimental data.

Cluster Diffusion and Coalescence on Metal Surfaces: applications of a Self-learning Kinetic Monte-Carlo method

Using molecular static simulations we have studied possible mechanisms of stress relaxation with misfit dislocation nucleation in strained heteroepitaxial layers. Two-dimensional models of atomic systems with Lennard-Jones type potential were considered. Combination of total energy minimization with spherical repulsion and nudged elastic band calculation allowed us to study possible transitions between an initial coherent interface state and a final state with a single dislocation. Different transition paths involving either successive relaxation of layers or concerted sliding along atomic rows have been identified as possible mechanisms with low activation energies. The role of these mechanisms in heteroepitaxial thin film growth and possible implementations in three dimensions are discussed.

Atomistic studies of strain relaxation in heteroepitaxial systems

A possible mechanism for the formation of a 90° misfit dislocation at the Ge/Si(0 0 1) interface through homogeneous nucleation is identified from atomic scale calculations where a minimum energy path connecting the coherent epitaxial state and a final state with a 90° misfit dislocation is found using the nudged elastic band method. The initial path is generated using a repulsive bias activation procedure in a model system including 75 000 atoms. The energy along the path exhibits two maxima in the energy. The first maximum occurs as a 60° dislocation nucleates. The intermediate minimum corresponds to an extended 60° dislocation. The subsequent energy maximum occurs as a second 60° dislocation nucleates in a complementary, mirror glide plane, simultaneously starting from the surface and from the first 60° dislocation. The activation energy of the nucleation of the second dislocation is 30% lower than that of the first one showing that the formation of the second 60° dislocation is aided by the presence of the first one. The simulations represent a step towards unraveling the formation mechanism of 90° dislocations, an important issue in the design of growth procedures for strain released Ge overlayers on Si(1 0 0) surfaces, and more generally illustrate an approach that can be used to gain insight into the mechanism of complex nucleation paths of extended defects in solids.

Equilibrium shape and size of supported heteroepitaxial nanoislands

The Kinetic Monte Carlo (KMC) method has become an important tool for examination of phenomena like surface diffusion and thin film growth because of its ability to carry out simulations for time scales that are relevant to experiments. But the method generally has limited predictive power because of its reliance on predetermined atomic events and their energetics as input. We present a novel method, within the lattice gas model in which we combine standard KMC with automatic generation of a table of microscopic events, facilitated by a pattern recognition scheme. Each time the system encounters a new configuration, the algorithm initiates a procedure for saddle point search around a given energy minimum. Nontrivial paths are thus selected and the fully characterized transition path is permanently recorded in a database for future usage. The system thus automatically builds up all possible single and multiple atom processes that it needs for a sustained simulation. Application of the method to the examination of the diffusion of 2-dimensional adatom clusters on Cu(111) displays the key role played by specific diffusion processes and also reveals the presence of a number of multiple atom processes, whose importance is found to decrease with increasing cluster size and decreasing surface temperature. Similarly, the rate limiting steps in the coalescence of adatom islands are determined. Results are compared with those from experiments where available and with those from KMC simulations based on a fixed catalogue of diffusion processes.