Modeling and Simulation of Heteroepitaxial Growth.

Mathematical Modeling;Heteroepitaxy;Kinetic Monte Carlo;Quantum Dot Self-assembly;Mathematics;Science;Applied and Interdisciplinary Mathematics

Baskaran, ArvindMirecki-Millunchick, Joanna ;

University of Michigan

关键词: Mathematical Modeling;    Heteroepitaxy;    Kinetic Monte Carlo;    Quantum Dot Self-assembly;    Mathematics;    Science;    Applied and Interdisciplinary Mathematics;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/63846/baskaran_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

The objective of this work is to construct a model for simulation and study of strainedHeteroepitaxial growth and use the same to study the nature of the surface instabilityin the system. This is done with the intent of studying the intermixing andits effects, on the surface instability and the critical thickness of island formation. Asolid on solid kinetic Monte Carlo approach is adopted in order to model the discretestochastic effects. The model uses simple surface atom hops to capture surface diffusioneffectively. The hopping rates are modeled based on the energetics of the system.The energetics of the system are in turn modeled by bond counting (surface energy)and a ball and spring network (elastic energy). An efficient numerical method forthe elastic computations is constructed. This approach involves the local estimationof the change in elastic energies using the Expanding Box method and upon failurethe global evaluation using the Multigrid Fourier method. An efficient algorithm forevolution of the system based on a reduced rejection kinetic Monte Carlo is presented.In this method the hopping rates are replaced by computationally inexpensive upperbounds with a rejection step to compensate for the overestimate.The continuumlimit of this model is shown to be equivalent to a classical phenomenological continuum model. Using this relation the existence of the Asaro-Tiller-Grinfeld instabilityin the model is discussed. The limitations of the continuum theory and the needfor the discrete stochastic approach is addressed. Finally the kinetic Monte Carlomodel is used to study the role of intermixing in the surface instability. Significantintermixing of the film with the substrate due to kinetic roughening of the film andhence the dilution of the film, is observed. This dilution is found to have a stabilizingrole in the surface instability, leading to a retarded onset of island formation. Thedependence of critical thickness on the composition of the film and the temperatureis found to be consistent with experiments. The effect of surface segregation on thecritical thickness is also discussed.