Intersecting Glide Planes Research Articles

Finite-deformation phase-field microelasticity with application to dislocation core and reaction modeling in fcc crystals

The purpose of the current work is the formulation of finite-deformation phase-field microelasticity (FDPFM) and its application to the modeling of (i) the dislocation core and (ii) dislocation interaction/reaction on intersecting glide planes in fcc crystals. The corresponding model formulation is carried out in the context of continuum thermodynamics; for simplicity, isothermal, quasi-static conditions are assumed. The resulting model rests in particular on generalized Ginzburg–Landau relations for dislocation slip-line phase field evolution depending on the Peach-Koehler (PK) force. Restricting attention to (periodic) bulk single crystal behavior, the algorithmic formulation and numerical implementation of FDPFM employs Green function, spectral, and Fourier methods generalized to geometric non-linearity. More specifically, algorithms for control of either the mean deformation gradient, or the mean Cauchy stress (i.e., PK force control) are developed. As in ”standard” linear PFM, the free energy model in FDPFM is based on elastic, crystal and gradient contributions. In order to model dislocation interaction and reactions on multiple intersecting glide planes, the ”standard” 2D stacking-fault-energy-based PFM crystal energy is generalized here to 3D crystallographic form for dissociation, partial fcc dislocations and stacking fault formation. Comparison of FDPFM and atomistic (MS) simulation results for higher-order local continuous and discrete deformation measures (e.g., dislocation tensor) in the core of a dissociated edge dislocation in Au show generally good agreement. In addition, results from FDPFM and MS are compared for dislocation reactions in Al on two intersecting glide planes. In the case of collinear reaction, for example, good qualitative agreement with MS results is obtained only when the dislocation slip on multiple glide planes is energetically coupled in the crystal energy.

Mechanism and Dynamics of Fracture of the Stressed Granite Surface by a Shock Wave

The dynamics of emission of positively charged ions from the granite surfaces containing different concentrations of quartz and feldspar under the action of a shock wave is investigated with a time resolution of 2 ns. The ions are assumed to be emitted at the instants of emergence of dislocations moving in intersecting glide planes at the sample surface. Defects in the form of extended “grooves” are formed in the region of emergence of dislocations. A compressive load suppresses the defect formation.

Surface effects on the mechanical behavior of silicon nanowires: Consequence on the brittle to ductile transition at low scale and low temperature

Understanding the origin of the brittle to ductile transition at low scale in Si requires the characterization of the elementary mechanisms governing crack formation or dislocation nucleation. By molecular dynamics simulations, we have investigated the role of three surface states of silicon nanowires (NWs), fresh cut, reconstructed by annealing at 300 K and amorphized, for the activation of plastic mechanisms under tensile and compressive strains. We show that the onset of crack formation identified as wedge-shaped defect on the surface was only observed in fresh-cut NWs in tension. These NWs present high yield strain due to the high symmetry of the surface and the absence of surface defects favoring dislocation nucleation as for the other surface states. This result seems to confirm that the crack formation in nanostructures could be linked to dislocations interactions on intersecting glide planes as experimentally observed rather than direct crack opening.

Dislocation interactions in thin FCC metal films

High strength, high hardening rates, and strong Bauschinger-like effects in thin films have been attributed to constraints on dislocation motion and dislocation interactions. To understand these phenomena, dislocation interactions in (1 1 1) and (0 0 1) oriented single crystal FCC films were studied using dislocation dynamics simulations. Interactions on intersecting glide planes resulted in junction formation, annihilation, or attractive non-junction-forming configurations, while dislocations on parallel glide planes formed dipoles. The configurations adopted by interacting dislocations, and thus the strengths of the interactions, were found to be sensitive to the applied strain, film thickness, crystallographic orientation, and boundary conditions. Different interactions thus dominate film behavior in different ranges of film thickness and applied strain. Interactions are stronger on unloading than on loading. Interactions involving three or more dislocations are found to be different from pairwise interactions. The results suggest that simple analytical calculations are unlikely to describe film phenomena but that full 3-D simulations can be used to understand many features of thin film mechanical behavior.

Formation of misfit dislocations in thin film heterostructures

We have studied characteristics of 60° and 90° dislocations in GaAs/Si(100) thin-film heterostructures grown by metal-organic chemical-vapor deposition at 650 °C. The misfit dislocation network consists of approximately 60% of 90° dislocations, and 40% of the closely spaced pairs of 60° dislocations with intersecting glide planes. This ratio has remained essentially constant after rapid thermal annealing at 800 °C for 90 sec. It is envisaged that these 60° dislocation pairs have parallel screw components and as a result they cannot combine to form a 90° dislocation. Upon annealing, some of the 60° dislocation pairs split to form stacking faults in agreement with our earlier model. Based upon these observations, we propose a model where a first set of 60° dislocations is generated from the undulated surface above a critical thickness. The second set of 60° dislocations is nucleated at a larger thickness and at the smoother surface. The Burgers vectors of these dislocations are controlled by the dislocations from the first set, and only low-energy dislocation pairs are formed through glide towards the interface and later through short glide and climb along the interface plane. We have used a numerical analysis based on elasticity theory to evaluate the changes in the nucleation barrier for the 60° dislocations caused by the interaction with the existing misfit dislocations.

Rules for Forest Interactions between Dislocations

The dynamical interactions of dislocations existing on intersecting glide planes have been investigated using numerical simulations based on isotropic linear elastic theory. It is found that such dislocations either repel, attract and form growing junctions, or attract and form bound crossed states. Which of these occurs can be predicted from a surprisingly simple analysis of the initial configurations. The outcome is determined primarily by the angles which the dislocations initially make with the glide-plane intersection edge, and is largely independent of the initial distance between the dislocations, their initial curvature, or ambient applied stresses. The results provide a rule for dealing with forest interactions within the context of large multiple-dislocation computations.

Dislocation dynamics near film edges and corners in silicon

The effect of film edge and corner stress fields on the behavior of dislocations in silicon is investigated. Stresses arising from a silicon–nitride film pad on a silicon substrate are calculated using the finite element method, and the resulting spatially varying stress–tensor components are utilized to drive numerical simulations of dislocation behavior. The dislocation dynamics code involves a full three-dimensional implementation of the Peach–Koehler force formalism. By studying the motion of dislocations on various slip systems in various locations relative to the nitride pad, we are able to determine the stationary dislocation configurations which can be achieved in this geometry. The zero resolved-stress contours near the silicon surface are shown to be a useful tool for understanding both the nature of the dislocation propagation as well as the final dislocation configurations. We examine the nucleation of dislocations qualitatively from the critical-radius point of view, and identify the “hot spots” for nucleation near the nitride film edge. Thicker nitride films are found to have a greater number of possible nucleation sites, and a greater variety of possible stable configurations, as experimentally observed. The simulations are extended to study the effect of changing the pad edge orientation relative to the silicon lattice. Finally, we demonstrate the usefulness and power of these techniques in handling more complex situations by illustrating the types of behavior resulting from cross-slip, reconnection between dislocations nucleated on intersecting glide planes, Frank–Read spiral sources, and traveling dislocations interacting with nitride edges.

Simulation of dislocations on the mesoscopic scale. I. Methods and examples

Peach–Koehler theory is implemented to simulate the motion of arbitrarily configured interacting dislocations, located on arbitrary glide planes and having any allowed Burgers vector. The self-interaction is regularized by a modified Brown procedure, which remains stable and loses accuracy in a well-controlled manner as atomic dimensions are approached. The method is illustrated by applying it to several examples of single and interacting dislocations in an fcc slip system. The critical strain for the propagation of a dislocation in a capped layer is calculated and found to be in excellent agreement with theory. Dislocations in a layer with a free surface are studied to test simplified methods for modeling the dislocation–surface interaction. Frank–Read sources are simulated in an infinite medium and in a strained layer. The latter are seen to give rise to the characteristic pileup structures often observed experimentally. The interaction between two initially straight dislocations on intersecting glide planes is studied as a function of relative angle and initial separation. It is found that an attractive instability occurs for a well-defined range of relative angles, and that this range depends only weakly on the initial separation. While this suggests that the detailed calculation of such interactions could be replaced by a simple set of interaction rules specifying their outcome, a variety of factors limiting the usefulness of such rules can be identified. It is further determined that, when an attractive instability occurs, the configuration assumed by the dislocations as they near each other bears little resemblance to any simple starting configuration. This suggests that calculations of the type presented here could provide a useful starting point for atomistic calculations of interacting dislocations.

Simulation of dislocations on the mesoscopic scale. II. Application to strained-layer relaxation

Numerical simulations are used to study various dislocation interactions expected to occur when a strained epitaxial layer relaxes. Frank–Read sources located on parallel glide planes are shown to produce elaborate network patterns of dislocations in the unstrained substrate of the layer. These are strikingly similar to experimentally observed patterns in high-quality relaxed SiGe layers grown by low-temperature ultrahigh vacuum chemical vapor deposition. Frank–Read sources on intersecting glide planes, on the other hand, produce characteristic corner-pileup structures which have previously been attributed to a “modified” Frank–Read source mechanism. The blocking of threading arms by misfit dislocations is found to occur only very near the critical strain. A much more important mechanism preventing ideal layer relaxation appears to be the formation of immobile pairs of threading dislocations on parallel glide planes.

Formation mechanism for nanodefects on surfaces of loaded metals

Tunneling profilometry is used to investigate the shape and orientation of defects that form at the surfaces of Cu, Au, Mo and Pd under loading. The defects have the shape of an indented prism. The value of the angles at the tip of the defects coincide with the angles between glide planes, while the orientation of the walls coincide with the orientation of these planes. At the edges of the defects there exist “swellings” caused by expulsion of material at the surface. Based on these results, the creation of these defects is explained by the exit of dislocations as they burst through barriers formed at intersecting glide planes.

Simulation of Dislocation Dynamics in the Continuum Limit

AbstractPeach-Koehler theory is implemented to simulate the motion of three-dimensionally interacting dislocations, located on various glide planes and having any allowed Burgers vector. The self-interaction is regularized by a modified Brown procedure, which remains stable and loses accuracy in a well-controlled manner as atomic dimensions are approached. The method is illustrated by applying it to several problems involving interacting dislocations in an fcc slip system. The strong interaction of two dislocations on intersecting glide planes is investigated with a view towards developing a set of rules to describe the outcome of such interactions. The effect of Frank-Read sources in relaxing a strained layer are illustrated, both for sources on parallel and on intersecting glide planes.

Interaction of Dislocations on Crossed Glide Planes in a Strained Epitaxial Layer

The full three-dimensional Peach-Koehler formalism is implemented numerically and used to investigate encounters between threading and misfit dislocations in a strained epitaxial layer. The possible outcomes of such interactions are found to include blocking, binding, repulsive passage, and attractive instabilities. We show that blocking is a weak effect, and that the peculiar substrate pileup structures previously attributed to a ``modified Frank-Read mechanism'' are actually a natural consequence of having sources operating on intersecting glide planes.

Formation of Interfacial Dislocations in Hetero-Epitaxial Layers Grown in Two-Dimensional Mode

ABSTRACTHigh-resolution transmission electron microscopy has been used to study formation of interfacial defects related to misfit strain accommodation in Ge/Si heterostructures (mismatch 4%) grown in the two-dimensional mode. Special emphasis is placed on the conditions leading to a two-dimensional (layer-by-layer) growth mode. We discuss general features of a dislocation tangle resulted from glide-limited plastic relaxation, typical for highly mismatched (001)-diamond and zinc-blende heterostructures. The evolution of the dislocation network as a function of film thickness and thermal annealing is controlled by growth instabilities and dislocation interactions. The observed correlation in distribution of parallel misfit dislocations including pairing (at <2 nm) of misfit segments from intersecting glide planes and rearrangements in a nonequilibrium dislocation network driven by elastic interaction between 60° dislocation segments in the almost relaxed heterostructures are discussed in detail. Pairing of the 60° glide dislocations results either in their combination to form pure edge 90° dislocations or in the dissociation into partials. We propose and experimentally verify a model for the latter process involving the formation of extrinsic stacking faults in the heterolayers under compressive strain.

Diffusion-Induced Dislocations in Silicon

ABSTRACTThe stresses in a silicon wafer which has undergone diffusion by a high concentration of boron are partially relaxed by the generation of dislocations in the boron-diffused regions of Si. It is found that these dislocations nucleate at the Si surface as dissociated half-loops lying on {111} planes inclined to the surface. Expansion of the half-loops to the diffused/virgin Si interface produce segments of misfit dislocations which are of the dissociated 60º type. These misfit dislocations move deeper into the crystal as the diffusion front moves further in the wafer and often intersect other misfit dislocations on intersecting glide planes. In this paper, the misfit dislocations and the reactions between them are characterized and discussed.

The Role of an Interface Misfit Dislocation in Blocking the Glide of a Threading Dislocation in a Strained Epitaxial Layer

AbstractThe glide of a threading dislocation in a strained layer may be impeded as it encounters interface misfit dislocations on intersecting glide planes. An estimate of the change in driving force on the threading dislocation during this interaction is discussed within the framework of elastic dislocation theory.

Complex Potential Analysis of Screw Dislocation Arrays

Complex potential theory is utilized to analyze the mechanics of screw dislocations on arbitrary glide planes. An analogy with airfoil theory is shown to be useful. General procedures are given for calculating stress fields and distribution functions with the aid of conformal mapping. The theory is applied to several specific problems, including dislocations on a circular glide plane, on perpendicular intersecting glide planes, and on a glide plane within a thin film. Applications to dislocation pile-ups on neighboring glide planes are also given.

Interactions between dislocations with burgers vectors at 120° in crystals of silver bromide

Abstract A detailed analysis is given of examples of the combination, in crystals of silver bromide.of two dislocations on intersecting glide planes with Burgers vectors at 120°.The observations provide direct evidence for the occurrence of pencil glide in which slip can occur on any plane containing a <110> lattice vector.