Dislocation Junctions

To have any hope of honestly addressing the dislocation-level processes that take place in plastic deformation, we must consider fully three-dimensional geometries. Though we earlier made disparaging remarks about the replacement of understanding by simulation, the evaluation of problems with full three-dimensional complexity almost always demands a recourse to numerics. Just as the use of analytic techniques culminated in a compendium of solutions to a variety of two-dimensional problems, numerical analysis now makes possible the development of catalogs of three-dimensional problems. In this section, we consider several very important examples of three-dimensional problems involving dislocations, namely, the operation of dislocation sources and dislocation junctions. 

Linear Elastic Models of Junction Formation. Yet another scheme for addressing the structure and energetics of dislocation junctions is using the machinery of full three-dimensional elasticity. Calculations of this type are especially provocative since it is not clear a priori to what extent elastic models of junction formation will be hampered by their inability to handle the details of the shortest range part... 

Line Tension Model for Dislocation Junctions Reproduce the arguments culminating in eqn (8.119). 

Rodney D. and Phillips R., Structure and Strength of Dislocation Junctions An Atomic Level Analysis, Phys. Rev. Lett. 82, 1704 (1999). 

Formation and Strength of Dislocation Junctions in FCC Metals A Study by Dislocation Dynamics and Atomistic Simulations. 

Many phenomena such as dislocations, electronic structures of polyacetylenes and other solids, Josephson junctions, spin dynamics and charge density waves in low-dimensional solids, fast ion conduction and phase transitions are being explained by invoking the concept of solitons. Solitons are exact analytical solutions of non-linear wave equations corresponding to bell-shaped or step-like changes in the variable (Ogurtani, 1983). They can move through a material with constant amplitude and velocity or remain stationary when two of them collide they are unmodified. The soliton concept has been employed in solid state chemistry to explain diverse phenomena. 

Fig. 5. A donor impurity is diffused into the silicon from a gaseous phase, (a) A shallow n region lias been created, (b) Continued diffusion, longer times, or higher temperatures increase the extent of the n region, (c) Surface diffusion has caused spreading of the n region along the SiCVsilicon interface, (d) A crystal defect, such as a dislocation, has provided a path for anomalously high diffusion and led to penetration of the junction to unanticipated distance from the surface. (See Fig. I for legend)...

FIGURE 1 shows a typical SIMS profile of Mg in GaN. The Mg concentration was uniformly distributed at a growth temperature of 750°C [8], The concentration of the Mg is 2 - 3 x 101 cm" near the surface and is the same at a depth of 0.4 pm towards the substrate. At the junction between the GaN Mg and undoped GaN buffer, the Mg concentration increases to 1 x 1019 cm 3 and is seen to diffuse into the buffer layer. This Mg peak is probably caused by enhanced diffusion of Mg, associated with defects and dislocations generated at the layer/substrate interface, towards the substrate. A wide chemical doping range in GaN Mg of 1 x 1017to 1 x 1019 cm 3 was obtained. 

Comparative studies of diffusion of Zn into heteroepitaxial GaN layers on sapphire and bulk pressure grown crystals showed that dislocations play a very important role in the diffusion process in heteroepitaxial GaN layers [29], The penetration of Zn into bulk crystal is a few orders of magnitude slower than into the heteroepitaxial layer. A similar effect of reduced diffusion due to the reduced density of dislocations can be expected for homoepitaxial GaN layers. Consequently this can improve the quality of GaN p-n junctions. 

Many different etchants have been developed for the evaluation of different types of crystal defects such as flow-pattern defects [115], stacking faults [74, 192, 193], dislocations [69, 72-74, 194], dislocation network [72, 193, 195], oxide precipitates [196], swirl patterns [74, 75, 148], striations [74, 197], hillock defects [198], epitaxial defects [192], epitaxial alignment [199], grain boundary [69, 72, 200], twin band [69], diamond saw damage [201], pn junction [202-204], metallic precipitates [205], and damaged layer of mechanically polished surface [206],... 

The state-of-the-art analysis methods for the evaluation of structural, chemical and electrical properties of thin layers in processed Si substrates are discussed. The properties of inclanted p-n junctions, Si-SiO interface, Ge inplant amorphization of Si aid misfit dislocation interface in epitaxial Si are exenplified to illustrate the features and limitations of the techniques. 

From the standpoint of the phenomenology of plastic deformation, one of the most important classes of three-dimensional configuration is that associated with dislocation intersections and junctions. As will become more evident in our... 

Fig. 8.43. Two different competing geometries (courtesy of D. Rodney) (a) Two dislocations with Burgers vectors bi and b2 and (b) junction case in which the junction segment has Burgers vector bi +b2.

Fig. 8.44. Schematic of the behavior of the arms of a dislocation before and after junction formation.

Fig. 8.47. Lomer-Cottrell junction as computed using three-dimensional elasticity representation of dislocation dynamics (adapted from Shenoy et al. (2000)).

Fig. 11.36. Schematic of the forest hardening process. Dislocation gliding in the primary slip plane forms junctions as a result of encounters with dislocations piercing that plane.

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