Denise C. George

Modeling microstructure evolution in three dimensions with Grain3D and LaGriT

This paper will describe modeling microstructure evolution using a combination of our gradient-weighted moving finite elements code, Grain3D and our 3-D unstructured grid generation and optimization code, LaGriT. Grain boundaries evolve by mean curvature motion, and Grain3D allows for the incorporation of grain boundary orientation dependence modeled as anisotropic mobility and energy. We also describe the process of generating an initial computational grid from images obtained from electron backscatter diffraction. We present the grid optimization operations developed to respond to changes in the physical topology such as the collapse of grains and to maintain uniform computational grid quality. For 3-D columnar microstructures, validation of the method is demonstrated by comparison with experiments. For large systems of fully 3-D microstructures, simulations compare favorably to the parabolic law of normal grain growth.

Linking Experimental Characterization and Computational Modeling of Grain Growth in Al-Foil

Experimental results on grain boundary properties and grain growth obtained using the Electron Backscattered Diffraction (EBSD) technique are compared with the Finite Element simulation results of an Al-foil with a columnar grain structure. The starting microstructure and grain boundary properties are implemented as an input for the three-dimensional grain growth simulation. In the computational model, minimization of the interface energy is the driving force for the grain boundary motion. The computed evolved microstructure is compared with the final experimental microstructure, after annealing at 550°C. Good agreement is observed between the experimentally obtained microstructure and the simulated microstructure. The constitutive description of the grain boundary properties was based on a 1-parameter characterization of the variation in mobility with misorientation angle.

Moving Adaptive Unstructured 3-D Meshes in Semiconductor Process Modeling Applications

The next generation of semiconductor process and device modeling codes will require 3-D mesh capabilities including moving volume and surface grids, adaptive mesh refinement and adaptive mesh smoothing. To illustrate the value of these techniques, a time dependent process simulation model was constructed using analytic functions to return time dependent dopant concentration and time dependent SiO2 volume and surface velocities. Adaptive mesh refinement and adaptive mesh smoothing techniques were used to resolve the moving boron dopant diffusion front in the Si substrate. The adaptive mesh smoothing technique involves minimizing the L2 norm of the gradient of the error between the true dopant concentration and the piecewise linear approximation over the tetrahedral mesh thus assuring that the mesh is optimal for representing evolving solution gradients. Also implemented is constrained boundary smoothing, wherein the moving SiO2/Si interface is represented by moving nodes that correctly track the interface motion, and which use their remaining degrees of freedom to minimize the aforementioned error norm. Thus, optimal tetrahedral shape and alignment is obtained even in the neighborhood of a moving boundary. If desired, a topological “reconnection” step maintains a Delaunay mesh at all times. The combination of adaptive refinement, adaptive smoothing, and mesh reconnection gives excellent front tracking, feature resolution, and grid quality for finite volume/finite element computation.

Effect of anisotropic interfacial energy on grain boundary distributions during grain growth

Through simulations with the moving finite element program GRAIN3D, we have studied the effect of anisotropic grain boundary energy on the distribution of boundary types in a polycrystal during normal grain growth. An energy function similar to that hypothesized for magnesia was used, and the simulated grain boundary distributions were found to agree well with measured distributions. The simulated results suggest that initially random microstructures develop nearly steady state grain boundary distributions that have local maxima and minima corresponding to local minima and maxima, respectively, of the energy function.

Comparison of Experimental and Computational Aspects of Grain Growth in Al-Foil

Grain boundary and crystallographic orientation information of an Al-foil with a columnar grain structure is characterized by Electron Backscattered Diffraction (EBSD) technique. The starting microstructure and grain boundary properties are implemented as an input for the three- dimensional grain growth simulation. In the computational model, minimization of the interface energy is the driving force for the grain boundary motion. The computed evolved microstructure is compared with the final experimental microstructure, after annealing at 550 °C. Good agreement is observed between the experimentally obtained microstructure and the simulated microstructure. The constitutive description of the grain boundary properties was based on a 1- parameter characterization of the variation in mobility with misorientation angle.

X3D Moving Grid Methods for Semiconductor Applications

The Los Alamos 3D grid toolbox handles grid maintenance chores and provides access to a sophisticated set of optimization algorithms for unstructured grids. The application of these tools to semiconductor problems is illustrated in three examples: grain growth, topographic deposition and electrostatics. These examples demonstrate adaptive smoothing, front tracking, and automatic, adaptive refinement/derefinement.