Electromigration Characteristics of Cu and Al Interconnections

1994 ◽  
Vol 338 ◽  
Author(s):  
S. Shingubara ◽  
K. Fujiki ◽  
A. Sano ◽  
H. Sakaue ◽  
Y. Horiike
Keyword(s):  
Grain Boundary ◽  
Activation Energies ◽  
Dislocation Dynamics ◽  
Small Resistance ◽  
Non Local ◽  
Rapid Transport ◽  
The One

ABSTRACTElectromigration activation energies (Ea) of Al and Cu interconnections are strongly dependent on the grain boundary morphology, and it is pointed out that Ea of bamboo-like Al interconnection is not less than Ea of small grain Cu interconnections. Small resistance oscillatory changes caused by electromigration, which are classified into three categories; oscillation, downward spikes, and upward spikes, are investigated in detail. It seems most likely that oscillations correspond to annihilation and formation of the one void. It is also pointed out that downward spikes are local, while upward spikes are non-local. Dislocation dynamics such as generation, rapid transport and subsequent annihilation are considered to be origins of spikes.

Grain boundary segregation in metals

1992 ◽  
Vol 50 (2) ◽  
pp. 1204-1205
Author(s):  
C.L. Briant
Keyword(s):  
Fracture Surface ◽  
Grain Boundary ◽  
Grain Boundaries ◽  
Material Properties ◽  
Electron Spectroscopy ◽  
High Vacuum ◽  
Boundary Segregation ◽  
Grain Boundary Segregation ◽  
Local Concentration ◽  
The One

Grain boundary segregation is the process by which solute elements in a material diffuse to the grain boundaries, become trapped there, and increase their local concentration at the boundary over that in the bulk. As a result of this process this local concentration of the segregant at the grain boundary can be many orders of magnitude greater than the bulk concentration of the segregant. The importance of this problem lies in the fact that grain boundary segregation can affect many material properties such as fracture, corrosion, and grain growth.One of the best ways to study grain boundary segregation is with Auger electron spectroscopy. This spectroscopy is an extremely surface sensitive technique. When it is used to study grain boundary segregation the sample must first be fractured intergranularly in the high vacuum spectrometer. This fracture surface is then the one that is analyzed. The development of scanning Auger spectrometers have allowed researchers to first image the fracture surface that is created and then to perform analyses on individual grain boundaries.

Atomistic and Continuum Studies of Diffusional Creep and Associated Dislocation Mechanisms in thin Films on Substrates

2003 ◽  
Vol 779 ◽  
Author(s):  
Markus J. Buehler ◽  
Alexander Hartmaier ◽  
Huajian Gao
Keyword(s):  
Thin Films ◽  
Stress Field ◽  
Grain Boundary ◽  
Large Scale ◽  
Strain Relaxation ◽  
Dislocation Dynamics ◽  
Biaxial Stress ◽  
Diffusional Creep ◽  
Material Transport ◽  
Dynamics Simulations

AbstractMotivated by recent theoretical and experimental progress, large-scale atomistic simulations are performed to study plastic deformation in sub-micron thin films. The studies reveal that stresses are relaxed by material transport from the surface into the grain boundary. This leads to the formation of a novel defect identified as diffusion wedge. Eventually, a crack-like stress field develops because the tractions along the grain boundary relax, but the adhesion of the film to the substrate prohibits strain relaxation close to the interface. This causes nucleation of unexpected parallel glide dislocations at the grain boundary-substrate interface, for which no driving force exists in the overall biaxial stress field. The observation of parallel glide dislocations in molecular dynamics studies closes the theory-experiment-simulation linkage. In this study, we also compare the nucleation of dislocations from a diffusion wedge with nucleation from a crack. Further, we present preliminary results of modeling constrained diffusional creep using discrete dislocation dynamics simulations.

One-point turbulence structure tensors

2001 ◽  
Vol 428 ◽  
pp. 213-248 ◽  
Author(s):  
S. C. KASSINOS ◽  
W. C. REYNOLDS ◽  
M. M. ROGERS
Keyword(s):  
Turbulence Structure ◽  
Turbulence Statistics ◽  
Local Effects ◽  
Statistical Measures ◽  
Non Local ◽  
The One ◽  
Rate Correlation ◽  
Systematic Framework ◽  
Structure Tensors

The dynamics of the evolution of turbulence statistics depend on the structure of the turbulence. For example, wavenumber anisotropy in homogeneous turbulence is known to affect both the interaction between large and small scales (Kida & Hunt 1989), and the non-local effects of the pressure–strain-rate correlation in the one-point Reynolds stress equations (Reynolds 1989; Cambon et al. 1992). Good quantitative measures of turbulence structure are easy to construct using two-point or spectral data, but one-point measures are needed for the Reynolds-averaged modelling of engineering flows. Here we introduce a systematic framework for exploring the role of turbulence structure in the evolution of one-point turbulence statistics. Five one-point statistical measures of the energy-containing turbulence structure are introduced and used with direct numerical simulations to analyse the role of turbulence structure in several cases of homogeneous and inhomogeneous turbulence undergoing diverse modes of mean deformation. The one-point structure tensors are found to be useful descriptors of turbulence structure, and lead to a deeper understanding of some rather surprising observations from DNS and experiments.

The Effect of Insulated Cracks on Heat Transfer of Thermoelectric Plates Using Peridynamics

2020 ◽  
Vol 10 (4) ◽  
pp. 25-39
Author(s):  
Migbar Assefa Zeleke ◽  
Lai Xin ◽  
Liu Lisheng
Keyword(s):  
Electric Fields ◽  
Crack Surface ◽  
Temperature Fields ◽  
Two Dimensional ◽  
Electrical Potentials ◽  
Non Local ◽  
The One ◽  
Growing Cracks ◽  
Good Agreement ◽  
The Continuum

In this article, peridynamic (PD) theory is applied to analyze two-dimensional heat conduction of thermoelectric plate with discontinuities. It is a well-known fact that heat flux is undefined at the crack tip and causes the temperature field across the crack surface discontinuous. Hence, numerical procedures like finite element method (FEM) became unsuccessful to capture details of moving discontinuities like growing cracks. Therefore, this article proposes a PD theory that is appropriate in resolving moving discontinuities in thermal and electric fields. The PD equations were constructed by writing the continuum-based electrical potentials and temperature fields in the form of their respective non-local integrals that are remarkably powerful in solving continuum problems whether the authors have moving discontinuities or not. To elucidate the trustworthiness of the PD theory, the results in the case of stationary cracks are compared with the one from FEM and witnessed that they were in good agreement.

scholarly journals Uniqueness of one-dimensional Néel wall profiles

2016 ◽  
Vol 472 (2187) ◽  
pp. 20150762 ◽  
Author(s):  
Cyrill B. Muratov ◽  
Xiaodong Yan
Keyword(s):  
Domain Wall ◽  
Energy Functional ◽  
Wall Structure ◽  
One Dimensional ◽  
Uniform Estimates ◽  
Limiting Behaviour ◽  
Non Local ◽  
The One ◽  
Wall Profile ◽  
Domain Wall Structure

We study the domain wall structure in thin uniaxial ferromagnetic films in the presence of an in-plane applied external field in the direction normal to the easy axis. Using the reduced one-dimensional thin-film micromagnetic model, we analyse the critical points of the obtained non-local variational problem. We prove that the minimizer of the one-dimensional energy functional in the form of the Néel wall is the unique (up to translations) critical point of the energy among all monotone profiles with the same limiting behaviour at infinity. Thus, we establish uniqueness of the one-dimensional monotone Néel wall profile in the considered setting. We also obtain some uniform estimates for general one-dimensional domain wall profiles.

Dislocation dynamics described by non-local Hamilton–Jacobi equations

2005 ◽  
Vol 400-401 ◽  
pp. 162-165 ◽  
Author(s):  
O. Alvarez ◽  
E. Carlini ◽  
P. Hoch ◽  
Y. Le Bouar ◽  
R. Monneau
Keyword(s):  
Dislocation Dynamics ◽  
Non Local ◽  
Jacobi Equations
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