The Stability of a Dislocation Threading a Strained Layer on a Substrate

1987 ◽  
Vol 54 (3) ◽  
pp. 553-557 ◽  
Author(s):  
L. B. Freund
Keyword(s):  
Optical Properties ◽  
Critical Thickness ◽  
Continuum Theory ◽  
Threading Dislocation ◽  
Critical Layer Thickness ◽  
Strained Layer ◽  
Mismatch Strain ◽  
The Stability ◽  
Work Done ◽  
The Continuum

The continuum theory of elastic dislocations is applied to estimate the critical thickness of a strained layer bonded to a substrate for a given mismatch strain. The formation of strained epitaxial layers is of interest due to their special electronic or optical properties, and critical thickness is understood to be the smallest thickness at which interface dislocations con form “spontaneously.” The criterion invoked here is based on the work done by the layer stress in driving a threading dislocation to lay down a misfit dislocation along the layer-substrate interface, and it is applied in a way that leads to a result that is independent of the deflected shape of the threading dislocation. The general form of the dependence of critical layer thickness on mismatch strain is similar to that based on equilibrium dislocation analysis.

Dislocation Threading Through an Epitaxial Film: an Analysis Based on the Peierls-Nabarro Concept

1993 ◽  
Vol 308 ◽  
Author(s):  
G. E. Beltz ◽  
L. B. Freund
Keyword(s):  
Critical Thickness ◽  
Epitaxial Film ◽  
Continuum Theory ◽  
Dislocation Core ◽  
Critical Layer Thickness ◽  
Cutoff Parameter ◽  
Mismatch Strain ◽  
Realistic Description ◽  
Cutoff Radius ◽  
The Continuum

ABSTRACTThe Peierls-Nabarro theory of crystal dislocations is applied to estimate the critical thickness of a strained layer bonded to a substrate for a given mismatch strain. Previous analyses were based on the continuum theory of elastic dislocations, and hence depended on the artificial core cutoff parameter r0. The Peierls-Nabarro theory makes use of an interplanar shear law, which leads to a more realistic description of the stresses and displacements in the vicinity of a dislocation core, thus eliminating the need for the core cutoff parameter. The dependence of the critical layer thickness on the mismatch strain in films with a diamond cubic lattice is found to be similar to that predicted by the continuum elastic dislocation theory, provided that a core cutoff radius equal to about one-tenth the Burgers displacement is used.

Mechanics of Elastic Dislocations in Strained Layer Structures

1988 ◽  
Vol 130 ◽  
Author(s):  
L. B. Freund ◽  
A. Bower ◽  
J. C. Ramirez
Keyword(s):  
Critical Thickness ◽  
Strain Relaxation ◽  
Continuum Theory ◽  
Growth Surface ◽  
Threading Dislocation ◽  
Strained Layer ◽  
Periodic Arrays ◽  
Layer Structures ◽  
Surface Irregularities ◽  
Generalized Driving Force

AbstractApplication of the elastic continuum theory of dislocations to modeling of phenomena associated with elastic strain relaxation in strained layer epitaxial heterostructures is discussed. The concept of critical thickness for onset of strain relaxation in a strained epitaxial layer is first reviewed, and some extensions to periodic arrays of dislocations and to multiple layers are described. Then, two issues are addressed that arise when the assumptions underlying the critical thickness concept are not met. One issue concerns the nucleation of dislocations at the growth surface of an epitaxial film, particularly the influence of surface irregularities on the activation energy for surface nucleation. A second issue concerns the kinetics of glide of a threading dislocation as it lays down an interface misfit dislocation when the layer thickness exceeds the critical thickness. A generalized driving force for the glide process is defined, and a relationship between this force and the glide speed is proposed.

Critical Thickness for Strained Quantum Wires

1995 ◽  
Vol 379 ◽  
Author(s):  
T. J. Gosling ◽  
L. B. Freund
Keyword(s):  
Finite Element ◽  
Critical Thickness ◽  
Quantum Wires ◽  
Lattice Mismatch ◽  
Threading Dislocations ◽  
Element Analysis ◽  
Strained Layers ◽  
Strained Layer ◽  
The Finite Element Analysis ◽  
The Stability

ABSTRACTThe stability of strained quantum wires against the propagation of threading dislocations is considered, using a critical thickness criterion due to Matthews and Blakeslee that is extensively used for strained layers. Given first are results for the critical mismatch at which a buried wire of a given thickness becomes susceptible to degradation. It is found that a wire, once buried, is extremely stable, being able to support, without loss of coherency, around five times the lattice mismatch that can be supported by a buried strained layer of the same thickness. It is concluded that if a strained wire contains dislocations then those dislocations must have been introduced during its growth, when the top surface of the wire is exposed. To investigate this, the results of finite element calculations are presented that give the critical relationship between mismatch and thickness during the growth of a triangular quantum wire being deposited in a [110]-oriented V-groove in a patterned (001) substrate. The results may be approximately expressed through an expression of the same form as that derived by Matthews and Blakeslee for a strained layer, but with modified coefficients obtained via the finite element analysis. Contact is made with the limited experimental evidence available.

Epitaxial Growth in Dislocation-Free Strained Alloy Films

2002 ◽  
Vol 715 ◽  
Author(s):  
Zhi-Feng Huang ◽  
Rashmi C. Desai
Keyword(s):  
Deposition Rate ◽  
Elastic Moduli ◽  
Composition Dependence ◽  
Critical Thickness ◽  
Lattice Misfit ◽  
Misfit Strain ◽  
Joint Stability ◽  
Alloy Films ◽  
The Stability ◽  
Stability Results

AbstractThe morphological and compositional instabilities in the heteroepitaxial strained alloy films have attracted intense interest from both experimentalists and theorists. To understand the mechanisms and properties for the generation of instabilities, we have developed a nonequilibrium, continuum model for the dislocation-free and coherent film systems. The early evolution processes of surface pro.les for both growing and postdeposition (non-growing) thin alloy films are studied through a linear stability analysis. We consider the coupling between top surface of the film and the underlying bulk, as well as the combination and interplay of different elastic effects. These e.ects are caused by filmsubstrate lattice misfit, composition dependence of film lattice constant (compositional stress), and composition dependence of both Young's and shear elastic moduli. The interplay of these factors as well as the growth temperature and deposition rate leads to rich and complicated stability results. For both the growing.lm and non-growing alloy free surface, we determine the stability conditions and diagrams for the system. These show the joint stability or instability for film morphology and compositional pro.les, as well as the asymmetry between tensile and compressive layers. The kinetic critical thickness for the onset of instability during.lm growth is also calculated, and its scaling behavior with respect to misfit strain and deposition rate determined. Our results have implications for real alloy growth systems such as SiGe and InGaAs, which agree with qualitative trends seen in recent experimental observations.

scholarly journals Transparent TiO2/Cu/TiO2 Multilayer for Electrothermal Application

Materials ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 1024
Author(s):  
Jingjing Peng ◽  
Changshan Hao ◽  
Hongyan Liu ◽  
Yue Yan
Keyword(s):  
Optical Properties ◽  
Heating Rate ◽  
Figure Of Merit ◽  
Annealing Temperature ◽  
Critical Thickness ◽  
Experimental Results ◽  
Tio2 Layer ◽  
Electrical And Optical Properties ◽  
Partial Crystallization

Highly transparent indium-free multilayers of TiO2/Cu/TiO2 were obtained by means of annealing. The effects of Cu thickness and annealing temperature on the electrical and optical properties were investigated. The critical thickness of Cu mid-layer with optimal electrical and optical properties was 10 nm, with the figure of merit reaching as high as 5 × 10−3 Ω−1. Partial crystallization of the TiO2 layer enhanced the electrical and optical properties upon annealing. Electrothermal experiments showed that temperatures of more than 100 °C can be reached at a heating rate of 2 °C/s without any damage to the multilayers. The experimental results indicate that reliable transparent TiO2/Cu/TiO2 multilayers can be used for electrothermal application.

scholarly journals The Wheel of Change Moves On: Assessing the Severity of Stalking Behavior

2021 ◽  
pp. 088626052110152
Author(s):  
Ewa B. Stefanska ◽  
Nicholas Longpré ◽  
Rekayla S. Harriman
Keyword(s):  
Social Issue ◽  
Item Response ◽  
Text Messages ◽  
Severity Scale ◽  
Communication Behaviors ◽  
Phone Calls ◽  
Ranking Order ◽  
Minimal Work ◽  
Work Done ◽  
The Continuum

Stalking is a significant social issue. The inconsistency as to what defines stalking has resulted in the creation of different methods to measure the crime. However, there has been minimal work done that assesses the severity of individual stalking behaviors. The aim of the present study was to assess the level of stalking behavior in terms of severity within a randomly selected sample of 924 cases from the database of the National Stalking Helpline. Item response theory analyses were used to assist in developing a scale that displays the ranking order of each stalking behavior. These analyses were also used to examine whether the stalking behavioral items created a single continuum of severity of stalking. Results indicated that 16 stalking behavioral items of the 28 items present in the National Stalking Helpline, best represented the severity of stalking. Unwanted communication behaviors such as text messages and phone calls were located at the lower end of the severity scale, whereas criminal damage and death threats were mapped on the higher end of the continuum. The findings also revealed that the 16 items categorized under 6 factors. The findings of the present study provide many implications for stalking agency professionals and criminal justice responses.

Confirming the continuum theory of dynamic brittle fracture for fast cracks

Nature ◽  
10.1038/16891 ◽  
1999 ◽  
Vol 397 (6717) ◽  
pp. 333-335 ◽  
Author(s):  
Eran Sharon ◽  
Jay Fineberg
Keyword(s):  
Brittle Fracture ◽  
Continuum Theory ◽  
Dynamic Brittle Fracture ◽  
The Continuum

scholarly journals Matrix integrals & finite holography

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Dionysios Anninos ◽  
Beatrix Mühlmann
Keyword(s):  
Critical Exponents ◽  
Continuum Theory ◽  
Point Of View ◽  
Leading Order ◽  
Minimal Models ◽  
Point Evaluation ◽  
Brst Cohomology ◽  
Matrix Integrals ◽  
The Matrix ◽  
The Continuum

Abstract We explore the conjectured duality between a class of large N matrix integrals, known as multicritical matrix integrals (MMI), and the series (2m − 1, 2) of non-unitary minimal models on a fluctuating background. We match the critical exponents of the leading order planar expansion of MMI, to those of the continuum theory on an S2 topology. From the MMI perspective this is done both through a multi-vertex diagrammatic expansion, thereby revealing novel combinatorial expressions, as well as through a systematic saddle point evaluation of the matrix integral as a function of its parameters. From the continuum point of view the corresponding critical exponents are obtained upon computing the partition function in the presence of a given conformal primary. Further to this, we elaborate on a Hilbert space of the continuum theory, and the putative finiteness thereof, on both an S2 and a T2 topology using BRST cohomology considerations. Matrix integrals support this finiteness.

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