Observations on the Mechanics of Strained Epitaxial Island Growth

1995 ◽  
Vol 399 ◽  
Author(s):  
L. B. Freund ◽  
H. T. Johnson ◽  
R. V. Kukta
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Energy ◽  
Aspect Ratio ◽  
Misfit Dislocation ◽  
Strain Distribution ◽  
Strain Relaxation ◽  
Lattice Parameter ◽  
Island Growth ◽  
Numerical Finite Element

ABSTRACTAn epitaxial material island which has a lattice parameter differing by a small amount for that of its substrate is considered within the framework of continuum mechanics. The strain distribution in the island is determined for a range of aspect ratio, taking into account the compliance of the substrate. It is demonstrated that the total free energy of a strained island is minimum for some value of aspect ratio, and that this value depends on the volume of the island. To consider strain relaxation, the nucleation of a dislocation at the edge of a strained island is examined and the equilibrium aspect ratio of a dislocated island is computed. In particular, it is shown that an island can reduce its free energy by reducing its aspect ratio and, simultaneously, forming an interface misfit dislocation. The simulations are based on the numerical finite element method.

Finite element method for epitaxial island growth

2004 ◽  
Vol 266 (1-3) ◽  
pp. 381-387 ◽  
Author(s):  
Frank Haußer ◽  
Axel Voigt
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Island Growth ◽  
Element Method

Mechanical Behavior of SiC Fiber Reinforced Al Matrix Composites: A Study Based on Finite Element Method

2011 ◽  
Vol 239-242 ◽  
pp. 2785-2789
Author(s):  
Chao Sun ◽  
Min Song ◽  
Ru Juan Shen ◽  
Yong Du
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Aspect Ratio ◽  
Plastic Region ◽  
Matrix Composites ◽  
Fiber Reinforced ◽  
Sic Fiber ◽  
Al Matrix Composites ◽  
Al Matrix ◽  
Element Method

The effects of SiC fiber shape, aspect ratio and loading direction on the deformation behavior of SiC fiber reinforced Al matrix composites were studied by finite element method using axisymmetric unit cell model. The results showed that the addition of reinforcements will cause constraint on the plastic flow of ductile matrix, and thus result in no-uniform stress distribution. The reinforcement shape has a pronounced effect on the overall plastic deformation of the metal matrix composites. The loading condition will cause different failure mechanisms of composites. Under tensile loading, the stress-bearing ability in the plastic region is increased with the fiber aspect ratio due to the increase in the interface between the reinforcement and matrix and the decrease in the inter-particle space.

Analytic Calculation About the Strain Distribution of Any-Shaped Self-Organized Quantum Dot

2007 ◽  
Author(s):  
Yumin Liu ◽  
Zhongyuan Yu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Quantum Dot ◽  
Function Approximation ◽  
Strain Distribution ◽  
Function Technique ◽  
Plane Wave Expansion ◽  
The Finite Element Method ◽  
Self Organized ◽  
Element Method

The strain distribution of quantum dots is analytically calculated using the Green’s function technique; the general expressions for any shaped quantum dot are derived. As examples, this method is applied to cube, pyramid column, and taper-shaped quantum dot. Our expressions are correct comparing with the calculated results by finite element method and finite difference. This approach is very powerful and can be applied to any-shaped quantum dot, especially this method can directly used in the calculation of electronic structure of quantum dot by the envelop function approximation or plane wave expansion methods, because the analytic expression can exactly calculate the strain at any position. In the paper, we give the strain distribution of four types of shaped quantum dot, and some comparisons are given with the results calculated by the finite element method.

The Computation of Elastic Constants of Double Wall Carbon Nanotubes Based on the Finite Element Method Considering Van Der Waals' Force

2012 ◽  
Vol 562-564 ◽  
pp. 334-338 ◽  
Author(s):  
Li Jie Chen ◽  
Lin Bo Li ◽  
Qi Zhao
Keyword(s):  
Finite Element Method ◽  
Carbon Nanotubes ◽  
Finite Element ◽  
Aspect Ratio ◽  
Elastic Constants ◽  
Van Der Waals ◽  
Van Der Waals Force ◽  
Internal Layer ◽  
The Finite Element Method ◽  
Double Wall

Based on the finite element method (FEM), we study the elastic constants of double-wall carbon nanotubes (DWCNTs). In the models, the Lennard-Jones potential function is used to consider the Van der Waals' force between non-bond atoms from different layers. The variations of the elastic constants with the diameter and the aspect ratio of the internal layer nanotube are investigated systematically. The computational results indicate that for both the armchair and the zigzag DWCNTs, the elastic moduli are generally lower than those of the single-wall carbon nanotubes with the same chirality as the internal and external layers. With the increase of the diameter and the aspect ratio of the internal layer carbon nanotubes, the elastic constant of DWCNTs will fall to a stable value.

Eigenvector and eigenvalue analysis of thick plates resting on elastic foundation with first order finite element

2018 ◽  
Vol 4 (2) ◽  
pp. 61
Author(s):  
Yaprak Itır Özdemir
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Aspect Ratio ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Winkler Foundation ◽  
Thick Plates ◽  
First Order ◽  
Element Method

The purpose of this paper is to study free vibration analysis of thick plates resting on Winkler foundation using Mindlin’s theory with first order finite element, to determine the effects of the thickness/span ratio, the aspect ratio, subgrade reaction modulus and the boundary conditions on the frequency parameters of thick plates subjected to free vibration. In the analysis, finite element method is used for spatial integration. Finite element formulation of the equations of the thick plate theory is derived by using first order displacement shape functions. A computer program using finite element method is coded in C++ to analyze the plates free, clamped or simply supported along all four edges. In the analysis, 4-noded finite element is used. Graphs are presented that should help engineers in the design of thick plates subjected to earthquake excitations. It is concluded that 4-noded finite element can be effectively used in the free vibration analysis of thick plates. It is also concluded that, in general, the changes in the thickness/span ratio are more effective on the maximum responses considered in this study than the changes in the aspect ratio.

Effects of Aspect Ratio on the Stresses and Deformations of Radial Passenger Tires

1992 ◽  
Vol 20 (2) ◽  
pp. 74-82 ◽  
Author(s):  
G. Z. Wu ◽  
X. M. He
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Aspect Ratio ◽  
Testing Machine ◽  
Nonlinear Finite Element ◽  
Nonlinear Finite Element Method ◽  
Inflation Pressure ◽  
Rubber Composites ◽  
Universal Testing ◽  
Stiffness Properties

Abstract The effects of aspect ratio on the stresses and deformations of radial passenger tires under inflation pressure are analyzed with the nonlinear finite element method. The stiffness properties of the cord-rubber composites used in this paper were measured by a Shimadzu Universal Testing Machine DCS-500. The analysis shows that when the aspect ratio decreases from 80 to 70, while the properties of the materials and the inflation pressure of the tires remain the same, the stresses in the carcass decrease by 5%, and those in the belt increase by 10–15%. Illustrations are given for inflated shapes, cord loads, and lower sidewall displacements.

Nonlinear Transient Finite Element Analysis of the Relaxation Mechanisms in Strained Silicon Grown on SiGe Virtual Substrate

2005 ◽  
Vol 875 ◽  
Author(s):  
F. Sahtout Karoui ◽  
A. Karoui ◽  
G. Rozgonyi
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Strain Relaxation ◽  
Sige Layer ◽  
Lattice Parameter ◽  
Plastic Strain Rate ◽  
Strained Silicon ◽  
Threading Dislocation ◽  
Element Analysis ◽  
Strained Si

AbstractStrained-silicon (ε -Si) is essential for future nanoscale MOSFET devices. In this paper we report on the dynamics of strain relaxation in Si/SiGe heterostructures, investigated by transient nonlinear finite element analysis. The contribution to total misfit strain is found largely plastic in the graded SiGe layer and the top of the Si substrate, while it is mainly elastic in the strained Si layer and part of the SiGe constant layer. The calculated lattice parameter for the strained Si layer is about 5.47Å for Si0.8Ge0.2 and 5.52 Å for Si0.6Ge0.4. Calculated threading dislocation density was about 5.6x105 cm-2 for x=0.20 and 2.17x106cm-2 for x=0.40. A plastic strain rate of 8.4x10-3s-1 for Si0.8Ge0.2 and 4.1x10-2 s-1 for Si0.6Ge0.4 leading to a density of moving dislocations of ~2.2x109 cm-2 and ~ 1010cm-2, respectively, have been obtained. The elastic strain in the strained-Si layer appeared to increase with increasing the cooling rate, while plastic work was found to be independent of cooling rates.

Sign in / Sign up

Export Citation Format

Share Document