Atomistic Calculation of Stability and Metastability of Coherently Strained Silicon-Like Structures

1986 ◽  
Vol 77 ◽  
Author(s):  
Brian W. Dodson ◽  
Paul A. Taylor
Keyword(s):  
Lattice Mismatch ◽  
Continuum Theory ◽  
Stability Limit ◽  
Test System ◽  
Misfit Dislocations ◽  
Strained Layers ◽  
Empirical Potentials ◽  
The Stability ◽  
Three Body ◽  
Microscopic Techniques

ABSTRACTMonte Carlo based microscopic techniques were used to study the stability and metastability of thin coherently strained layers of mismatched siliconlike semiconductor material grown on the (111) silicon surface. The structural energy was calculated using three-body empirical potentials. For layers greater than about 20 Å thickness, the critical layer thickness associated with thermodynamic stability agrees quantitatively with continuum theory. For thinner layers, however, considerable variations from the continuum theory are found. For a strained layer six monolayers thick, the test system is found to be metastable against the nucleation of misfit dislocations to a lattice mismatch of about 11%, compared to the 4% equilibrium stability limit.

The Roles of Stress, Geometry and Orientation on Misfit Dislocations Kinetics and Energetics in Epitaxial Strained Layers.

1991 ◽  
Vol 239 ◽  
Author(s):  
R. Hull ◽  
J. C. Bean ◽  
F. Ross ◽  
D. Bahnck ◽  
L. J. Pencolas
Keyword(s):  
Misfit Dislocation ◽  
Lattice Mismatch ◽  
Strain Relaxation ◽  
Misfit Dislocations ◽  
Slip Systems ◽  
Strained Layers ◽  
Burgers Vector ◽  
Partial Dislocations ◽  
Strain Stress ◽  
Kinetics Of

ABSTRACTThe geometries, microstructures, energetics and kinetics of misfit dislocations as functions of surface orientation and the magnitude of strain/stress are investigated experimentally and theoretically. Examples are drawn from (100), (110) and (111) surfaces and from the GexSi1–x/Si and InxGa1–x/GaAs systems. It is shown that the misfit dislocation geometries and microstructures at lattice mismatch stresses < - 1GPa may in general be predicted by operation of the minimum magnitude Burgers vector slipping on the widest spaced planes. At stresses of the order several GPa, however, new dislocation systems may become operative with either modified Burgers vectors or slip systems. Dissociation of totál misfit dislocations into partial dislocations is found to play a crucial role in strain relaxation, on surfaces other than (100) under compressive stress.

Morphological Stability of Semicoherent Solid-Solid Interfaces: a Simple Model

1991 ◽  
Vol 229 ◽  
Author(s):  
Craig Rottman
Keyword(s):  
Simple Model ◽  
Lattice Mismatch ◽  
Misfit Dislocations ◽  
Morphological Stability ◽  
Small Lattice Mismatch ◽  
Wide Range ◽  
Small Lattice ◽  
Interface Orientation ◽  
The Stability

AbstractThe stability of semicoherent interfaces between two solids with small lattice mismatch is examined. I consider the cases in which the rotation θ between the two solids is both zero and small. The interface orientation, characterized by a single angle φ, is arbitrary. The interfaces are composed of regularly spaced misfit dislocations, steps, and lattice dislocations. For a wide range of φ, many flat interfaces are unstable with respect to breaking up into two interfaces of distinct orientations, one of which contains only one of the two types of dislocations possible.

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.

Structural properties of GaAs/InGaAs/GaAs (001) and InGaAs/GaAs (001) heterostructures and correlation with electronic properties

1990 ◽  
Vol 48 (4) ◽  
pp. 602-603
Author(s):  
J.M. Bonar ◽  
R. Hull ◽  
R. Malik ◽  
R. Ryan ◽  
J.F. Walker
Keyword(s):  
Band Gap ◽  
Electronic Properties ◽  
Gaas Substrate ◽  
Critical Thickness ◽  
Lattice Mismatch ◽  
Band Offset ◽  
Misfit Dislocations ◽  
Gaas Substrates ◽  
Gaas Structure ◽  
Low X

In this study we have examined a series of strained heteropeitaxial GaAs/InGaAs/GaAs and InGaAs/GaAs structures, both on (001) GaAs substrates. These heterostructures are potentially very interesting from a device standpoint because of improved band gap properties (InAs has a much smaller band gap than GaAs so there is a large band offset at the InGaAs/GaAs interface), and because of the much higher mobility of InAs. However, there is a 7.2% lattice mismatch between InAs and GaAs, so an InxGa1-xAs layer in a GaAs structure with even relatively low x will have a large amount of strain, and misfit dislocations are expected to form above some critical thickness. We attempt here to correlate the effect of misfit dislocations on the electronic properties of this material.The samples we examined consisted of 200Å InxGa1-xAs layered in a hetero-junction bipolar transistor (HBT) structure (InxGa1-xAs on top of a (001) GaAs buffer, followed by more GaAs, then a layer of AlGaAs and a GaAs cap), and a series consisting of a 200Å layer of InxGa1-xAs on a (001) GaAs substrate.

The Tangled Tale of Phase Space

2018 ◽  
Author(s):  
David D. Nolte
Keyword(s):  
Phase Space ◽  
Chaotic Behavior ◽  
Three Body Problem ◽  
Henri Poincaré ◽  
History Of ◽  
The Stability ◽  
Three Body ◽  
Space Phase ◽  
Central Paradigm ◽  
System Phase

This chapter presents the history of the development of the concept of phase space. Phase space is the central visualization tool used today to study complex systems. The chapter describes the origins of phase space with the work of Joseph Liouville and Carl Jacobi that was later refined by Ludwig Boltzmann and Rudolf Clausius in their attempts to define and explain the subtle concept of entropy. The turning point in the history of phase space was when Henri Poincaré used phase space to solve the three-body problem, uncovering chaotic behavior in his quest to answer questions on the stability of the solar system. Phase space was established as the central paradigm of statistical mechanics by JW Gibbs and Paul Ehrenfest.

Optimization of the Robust Stability Limit for Multi-Cutter Turning Processes

2015 ◽  
Author(s):  
Marta J. Reith ◽  
Daniel Bachrathy ◽  
Gabor Stepan
Keyword(s):  
Robust Stability ◽  
Optimal Parameter ◽  
Stability Limit ◽  
Boundary Function ◽  
Lower Envelope ◽  
Computation Method ◽  
Parameter Region ◽  
Dynamical Parameters ◽  
The Stability ◽  
Machining Parameter

Multi-cutter turning systems bear huge potential in increasing cutting performance. In this study we show that the stable parameter region can be extended by the optimal tuning of system parameters. The optimal parameter regions can be identified by means of stability charts. Since the stability boundaries are highly sensitive to the dynamical parameters of the machine tool, the reliable exploitation of the so-called stability pockets is limited. Still, the lower envelope of the stability lobes is an appropriate upper boundary function for optimization purposes with an objective function taken for maximal material removal rates. This lower envelope is computed by the Robust Stability Computation method presented in the paper. It is shown in this study, that according to theoretical results obtained for optimally tuned cutters, the safe stable machining parameter region can significantly be extended, which has also been validated by machining tests.

HIGH RESOLUTION ELECTRON MICROSCOPE STUDY OF CdTe-Cd0.6Mn0.4 Te SUPERLATTICES

1985 ◽  
Vol 56 ◽  
Author(s):  
C. CHOI ◽  
N. OTSUKA ◽  
L. A. KOLODZIEJSKI ◽  
R. L. GUNSHOR-a
Keyword(s):  
Electron Microscopy ◽  
High Resolution ◽  
Phase Contrast ◽  
Electron Microscope Study ◽  
Lattice Mismatch ◽  
Thick Layer ◽  
High Resolution Electron Microscopy ◽  
Misfit Dislocations ◽  
Resolution Electron ◽  
High Resolution Electron Microscope

AbstractStructures of CdTe-Cd0.6Mn0.4Te superlattices which are caused by the lattice mismatch between suterlattice layers have been studied by high resolution electron microscopy (HREM). In thin-layer superlattices, the crystal lattice in each layeris elastically distorted, resulting in the change of the crystal symmetry from cubic to rhombohedral. The presence of the small rhombohedral distrotion has been confirmed through a phase contrast effect in HREM images. In a thick-layer superlattice, the lattice mismatch is accommodated by dissociated misfit dislocations. Burgers vectors of partial misfit dislocations have been identified from the shift of lattice fringes in HREM images.

Very Thick Coherently Strained GexSi1−x Layers Grown in a Narrow Temperature Window

1991 ◽  
Vol 220 ◽  
Author(s):  
C. H. Chern ◽  
K. L. Wang ◽  
G. Bai ◽  
M. -A. Nicolet
Keyword(s):  
Growth Temperature ◽  
Strain Relaxation ◽  
Gas Pressure ◽  
High Density ◽  
Misfit Dislocations ◽  
High Quality ◽  
Strained Layers ◽  
Temperature Window ◽  
Residual Gas

ABSTRACTStrain relaxation of GexSi1−x layers is studied as a function of growth temperature. Extremely thick coherently strained layers whose thicknesses exceed more than fifty times of the critical thicknesses predicted by Matthews and Blakeslee's model were successfully grown by MBE. There exits a narrow temperature window from 310 °C to 350 °C for growing this kind of high quality thick strained layers. Below this temperature window, the layers are poor in quality as indicated from RHEED patterns. Above this window, the strain of the layers relaxes very fast accompanied with a high density of misfit dislocations as the growth temperature increases. Moreover, for samples grown in this temperature window, the strain relaxation shows a dependence of the residual gas pressure, which has never been reported before.

Some difficulties associated with the limit equilibrium method of slices

1983 ◽  
Vol 20 (4) ◽  
pp. 661-672 ◽  
Author(s):  
R. K. H. Ching ◽  
D. G. Fredlund
Keyword(s):  
Slope Stability ◽  
Factor Of Safety ◽  
Limit Equilibrium ◽  
Stability Limit ◽  
Limit Equilibrium Method ◽  
Soil Conditions ◽  
Side Force ◽  
Limit Equilibrium Methods ◽  
Equilibrium Method ◽  
The Stability

Several commonly encountered problems associated with the limit equilibrium methods of slices are discussed. These problems are primarily related to the assumptions used to render the inherently indeterminate analysis determinate. When these problems occur in the stability computations, unreasonable solutions are often obtained. It appears that problems occur mainly in situations where the assumption to render the analysis determinate seriously departs from realistic soil conditions. These problems should not, in general, discourage the use of the method of slices. Example problems are presented to illustrate these difficulties and suggestions are proposed to resolve these problems. Keywords: slope stability, limit equilibrium, method of slices, factor of safety, side force function.

Stress Relaxation in Uniquely Oriented SiGe/Si Epitaxial Layers

1999 ◽  
Vol 594 ◽  
Author(s):  
M. E. Ware ◽  
R. J. Nemanich
Keyword(s):  
Stress Relaxation ◽  
Surface Morphology ◽  
Strain Relaxation ◽  
Epitaxial Layers ◽  
Misfit Dislocations ◽  
Strained Layers ◽  
Force Microscopy ◽  
Si Substrates ◽  
Atomic Force ◽  
Deposited Films

AbstractThis study explores stress relaxation of epitaxial SiGe layers grown on Si substrates with unique orientations. The crystallographic orientations of the Si substrates used were off-axis from the (001) plane towards the (111) plane by angles, θ = 0, 10, and 22 degrees. We have grown 100nm thick Si(1−x) Ge(x) epitaxial layers with x=0.3 on the Si substrates to examine the relaxation process. The as-deposited films are metastable to the formation of strain relaxing misfit dislocations, and thermal annealing is used to obtain highly relaxed films for comparison. Raman spectroscopy has been used to measure the strain relaxation, and atomic force microscopy has been used to explore the development of surface morphology. The Raman scattering indicated that the strain in the as-deposited films is dependent on the substrate orientation with strained layers grown on Si with 0 and 22 degree orientations while highly relaxed films were grown on the 10 degree substrate. The surface morphology also differed for the substrate orientations. The 10 degree surface is relatively smooth with hut shaped structures oriented at predicted angles relative to the step edges.

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