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Dislocation Dynamics

Numerical Simulation of Dislocation Dynamics on the Mesoscopic Scale

The interaction and propagation of dislocations over mesoscopic distances is fundamental to many phenomena in crystalline materials, ranging from the work hardening and fracture of bulk solids to strain relaxation processes in semiconductor heterostructures. Because both the dynamics and the interactions of dislocations are complicated, little is known about the effects that individual dislocations have on each other when they come into close proximity, and, more generally, about the evolution of collections of strongly interacting dislocations.

The power of modern supercomputers allows one to address these issues by direct numerical simulation. A highly parallelized and adaptive code (PARANOID) has been developed to allow the realistic simulation of dislocation behavior in a wide variety of situations. The code is based on elastic theory in the continuum limit, and should thus be applicable to situations in which the dislocation cores are more than a few nanometers apart. The stress tensor which moves the dislocations is calculated at every point by evaluating the full Peach-Koehler expression over all of the dislocations present. The self-interaction of the dislocations is regularized by the Brown method of splitting the dislocation in half, moving the two halves outward by some core parameter, and averaging the result. The code allows one to study the interactions between arbitrarily configured dislocations, located on any allowed glide plane, passing from one glide plane to another, and having any allowed Burgers vector.

The simulation approach has proved successful both in unveiling qualitatively new dislocation mechanisms, and in providing quantitative comparisons between experiment and theory. Specifically, PARANOID has:

Modeled strain relaxation in thin heteroepitaxial films (SiGe), successfully predicting the complicated dislocation networks that were previously observed, and demonstrating that the pairing of threading dislocations on parallel glide planes is by far the strongest mechanism for immobilizing such dislocations in a thin film.
Discovered an entirely new dislocation-blocking mechanism in thin films, providing a quantitative interpretation of recent experiments on dislocation motion in thin films.
Simulated dislocation nucleation and patterning in the edge fields of a nitride pad on silicon. This system represents a simple prototype of one kind of dislocation problem arising during the manufacture of semiconductor devices.
Discovered rules for predicting the outcome of strong dislocation-dislocation interactions in fcc and bcc systems. This is an essential first step in modeling work-hardening, dislocation patterning, metal fatigue, and related issues in metallurgy. Large scale simulations to explore these problems are currently being carried out in collaboration with Lawrence Livermore National Laboratory.
Successfully explained the dislocation networks which are observed in relaxed quantum-dot structures. The cone or pyramid-like island structures grow epitaxially on semiconductor surface and, because of their very high strain fields, become dislocated above a certain size. The picture at right shows dislocation patterns observed in a CoSi2 island growing on a (111) silicon surface, compared to the numerical simulations. The agreement between the observations and the predictions obtained using PARANOID illustrates the ability of the code to produce realistic results even at very small scales.