The extended Self Learning Kinetic Monte Carlo Method: now lurking into 3D*

Talat Rahman
University of Central Florida

Together with accurate techniques for calculations of diffusion parameters, the kinetic Monte Carlo (KMC) method is an important tool for simulation of temporal and spatial evolution of surface phenomena such as epitaxial growth, adatom-island diffusion, coarsening, and morphological transformations. To enhance its predictive capacity, we have developed a self-learning method (SLKMC) [1,2], in which standard KMC is combined 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. Nontrivial paths are thus selected and the fully characterized transition path is permanently recorded in a database for future usage. Once the data base of all possible single and multiple atom processes is built, the system evolves automatically and efficiently by picking diffusion processes of its choice. I will present application of the method to the diffusion and coalescence of 2-dimensional Cu and Ag adatom and vacancy clusters on the (111) surface of these metals. Of interest are multiple atom processes revealed in the simulation whose presence may have been ignored otherwise. For adatom clusters varying in size from 2 to 100, I will discuss the dependence of the diffusion coefficient, effective energy barriers, and dominant mechanism (periphery atom or concerted-cluster motion), on cluster size. I will highlight the role played by specific diffusion processes and show that a crossover from collective island motion to periphery diffusion takes place at critical sizes which are specific to the metallic system in question. I will discuss recent developments in the technique [3,4] which facilitate simulations in three dimensions, thereby allowing realistic modeling of thin-film growth processes. I will also comment on efforts to calculate diffusion prefactors and scenarios in which the prefactor may be quite different from the “normal” one.
*Work done in collaboration with O. Trushin, A. Kara, A. Karim, G. Nandipati and S. I. Shah.
1. O. Trushin, A. Karim, A. Kara , and T. S. Rahman, Phys. Rev. B 72, 115401 (2005).
2. A. Karim, O. Trushin, A. Al-Rawi, A. Kara, T. Ala Nissila, and T. S. Rahman, Phys. Rev. B 73, 165411 (2006).
3. S. I. Shah, G. Nandipati, A. Kara, and T. S. Rahman, J. Phys. Condens. Matt. 24, 354004 (2012).
4. G. Nandipati, A. Kara, S. I. Shah, T. S. Rahman, J. Comp. Phys. 231, 3548 (2012).

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