: Advances in Continuum Simulation Methods @ University of Virginia

To further isolate the roles of different mechanisms upon localization of nucleation, we have developed 2-D and 3-D continuum Cahn-Hilliard type (4th order nonlinear diffusion equation) phase field models of microstructural and surface evolution, through a collaboration of MRSEC researchers at UVa and UC-Irvine. New finite difference methods, fully implicit time discretizations, and nonlinear multigrid methods have been developed that efficiently solve the nonlinear discrete Cahn-Hilliard and phase field equations. These methods are 100-1000x faster than previous explicit methods and greatly accelerate solution of technologically-relevant 3-D problems. The simulations are robust enough to capture the essential physics of morphological evolution in GeSi/Si, incorporating: Heteroepitaxial misfit; extreme elastic heterogeneities of the system; strong elastic and surface anisotropies, chemical interaction of the film and substrate for modeling wetting dynamics; epilayer deposition; bulk and surface diffusion (via an atomic mobility function that is localized in the diffuse interface region); substrate topographical patterning; and complex thin film morphologies such as faceting of quantum dot (QD) structures (via a polynomial function for dependence of surface energy upon orientation that captures low energy facets), step structures and topological transitions. Figure 3 shows a snapshot of cluster evolution during deposition of an epitaxial thin film. Guided growth occurs via the strain fields associated with a buried inclusion below the film/substrate interface, directly below the largest pyramid. Other projects that explore the component effects of localization of cluster nucleation include: (i) Local/masked ion implantation to produce buried strain centers in Si (e.g., by formation of buried coherent metal silicide precipitates) with controlled magnitude and periodicity, to quantify the role of strain on Ge QD nucleation; (ii) Use of FIB tomographic reconstructions to explore 3-D correlations by propagation of strain fields in QD super-lattice structures, Figure 4, enabling us to track the size evolution of every QD through successive layers; (iii) Novel nanoscale electrochemical methods for creating complex 3-D surface topography, using both ultra-small machining electrodes and ultra-short charging pulses to localize the electrochemical reaction, and (iv) Development of new Ge-Ga and Si-Ga embedded atom potentials to enable atomistic modeling of adatom motion across Ga+ FIB- modified surfaces.