scholarly journals Relaxation of Thermal Stress by Dislocation Motion in Passivated Metal Interconnects

2004 ◽  
Vol 19 (4) ◽  
pp. 1216-1226 ◽  
Author(s):  
Lucia Nicola ◽  
Erik Van der Giessen ◽  
Alan Needleman
Keyword(s):  
Dislocation Motion ◽  
Slip Systems ◽  
Stress Evolution ◽  
Discrete Dislocation ◽  
Passivation Layers ◽  
Strain Formulation ◽  
On Line ◽  
Pitch Length ◽  
Metal Interconnects ◽  
Edge Dislocations

The development and relaxation of stress in metal interconnects strained by their surroundings (substrate and passivation layers) is predicted by a discrete dislocation analysis. The model is based on a two-dimensional plane strain formulation, with deformation fully constrained in the line direction. Plastic deformation occurs by glide of edge dislocations on three slip systems in the single-crystal line. The substrate and passivation layers are treated as elastic materials and therefore impenetrable for the dislocations. Results of the simulations show the dependence of the stress evolution and of the effectiveness of plastic relaxation on the geometry of the line. The dependence of stress development on line aspect ratio, line size, slip plane orientation, pitch length, and passivation layer thickness are explored.

Plasticity in Polycrystalline Thin Films: a 2D Dislocation Dynamics Approach

2003 ◽  
Vol 779 ◽  
Author(s):  
Lucia Nicola ◽  
Erik Van der Giessen ◽  
Alan Needleman
Keyword(s):  
Thin Films ◽  
Dislocation Dynamics ◽  
Stress Evolution ◽  
Polycrystalline Thin Films ◽  
Discrete Dislocation ◽  
Dislocation Plasticity ◽  
Strain Formulation ◽  
The Difference ◽  
Film Substrate ◽  
Edge Dislocations

AbstractThermal stress evolution in polycrystalline thin films is analyzed using discrete dislocation plasticity. Stress develops in the film during cooling from a stress-free configuration due to the difference in thermal expansion coefficient between the film and its substrate. A plane strain formulation with only edge dislocations is used and each grain of the polycrystal has a specified set of slip systems. The film–substrate interface and the grain boundaries are impenetrable for the dislocations. Results are presented for two film thicknesses, with higher hardening seen for the thinner films.

Simulations of Dislocation Dynamics in Aluminum Interconnects

2002 ◽  
Vol 731 ◽  
Author(s):  
Lucia Nicola ◽  
Erik Van der Giessen ◽  
Alan Needleman
Keyword(s):  
Thermal Stress ◽  
Cross Section ◽  
Dislocation Dynamics ◽  
Local Concentration ◽  
Small Cross Section ◽  
Discrete Dislocation ◽  
Thermal Stress Field ◽  
Strain Formulation ◽  
Edge Dislocations ◽  
Aluminum Interconnects

AbstractA discrete dislocation simulation of plastic deformation in metallic interconnects caused by thermal stress is carried out. The calculations are carried out using a two dimensional plane strain formulation with only edge dislocations. A boundary value problem is formulated and solved for the evolution of the thermal stress field and the evolution of the dislocation structure in the cross-section of the line as cooling proceeds. For lines with a small cross section (height or width less than 1 μm), the local concentration of stresses due to dislocation patterning strongly affects the overall stress build up and relaxation. The results show a clear dependence of the transverse stress development on the line aspect ratio.

Quantitative Infrared Photoelasticity of Silicon Photovoltaic Wafers Using a Discrete Dislocation Model

2015 ◽  
Vol 82 (1) ◽  
Author(s):  
T.-W. Lin ◽  
G. P. Horn ◽  
H. T. Johnson
Keyword(s):  
Residual Stress ◽  
Numerical Modeling ◽  
Strain Energy ◽  
Dislocation Model ◽  
Slip Systems ◽  
Inspection Method ◽  
Crystalline Defects ◽  
Discrete Dislocation ◽  
Stress Mapping ◽  
And Performance

Residual stress and crystalline defects in silicon wafers can affect solar cell reliability and performance. Infrared photoelastic measurements are performed for stress mapping in monocrystalline silicon photovoltaic (PV) wafers and compared to photoluminescence (PL) measurements. The wafer stresses are then quantified using a discrete dislocation-based numerical modeling approach, which leads to simulated photoelastic images. The model accounts for wafer stress relaxation due to dislocation structures. The wafer strain energy is then analyzed with respect to the orientation of the dislocation structures. The simulation shows that particular locations on the wafer have only limited slip systems that reduce the wafer strain energy. Experimentally observed dislocation structures are consistent with these observations from the analysis, forming the basis for a more quantitative infrared photoelasticity-based inspection method.

scholarly journals 2 Dimensional Dislocation Dynamics – A New Technique for the Simulation of Deformation Microtextures

1997 ◽  
Vol 28 (3-4) ◽  
pp. 167-179
Author(s):  
F. Roters ◽  
D. Raabe
Keyword(s):  
Cold Deformation ◽  
Dislocation Motion ◽  
Dislocation Dynamics ◽  
New Technique ◽  
Linear Elastic ◽  
Straight Line ◽  
Simulation Step ◽  
Local Stresses ◽  
A New Technique ◽  
Edge Dislocations

A new technique for the simulation of microtexture evolution during cold deformation which is based on 2 dimensional (2D) dislocation dynamics is presented. In the simulation all involved dislocations are regarded as infinite straight line detects which are embedded in an otherwise isotropic linear elastic medium. As the model is 2D only edge dislocations are considered.In the first simulation step the net local stresses are derived and used to calculate the resulting dislocation motion. Dislocation multiplication, annihilation and reactions are taken into account. Thermal activation is included. In the second step the local misorientations arising from the dislocation distribution are calculated.This method shows in microscopic detail how misorientations are generated and distributed within grains during plastic deformation.

In-Situ Tem Investigation During Thermal Cycling of thin Copper Films

1996 ◽  
Vol 436 ◽  
Author(s):  
R.-M. Keller ◽  
W. Sigle ◽  
S. P. Baker ◽  
O. Kraft ◽  
E. Arzt
Keyword(s):  
Grain Growth ◽  
Room Temperature ◽  
Dislocation Motion ◽  
In Situ Tem ◽  
Copper Films ◽  
Stress Evolution ◽  
Cu Films ◽  
Transmission Electron ◽  
Insight Into

AbstractIn-situ transmission electron microscopy (TEM) was performed to study grain growth and dislocation motion during temperature cycles of Cu films with and without a cap layer. In addition, the substrate curvature method was employed to determine the corresponding stresstemperature curves from room temperature up to 600°C. The results of the in-situ TEM investigations provide insight into the microstructural evolution which occurs during the stress measurements. Grain growth occurred continuously throughout the first heating cycle in both cases. The evolution of dislocation structure observed in TEM supports an explanation of the stress evolution in both capped and uncapped films in terms of dislocation effects.

A Discrete Dislocation Plasticity Analysis of Plane-Strain Indentation of a Single-Crystal Half-Space by a Smooth and a Rough Rigid Asperity

2010 ◽  
Author(s):  
X. Yin ◽  
K. Komvopoulos
Keyword(s):  
Single Crystal ◽  
Plane Strain ◽  
Half Space ◽  
Crystal Surface ◽  
Normal Load ◽  
Surface Profile ◽  
Dislocation Source ◽  
Discrete Dislocation ◽  
Dislocation Plasticity ◽  
Edge Dislocations

A discrete dislocation plasticity analysis of plane-strain indentation of a single-crystal half-space by a smooth or rough (fractal) rigid asperity is presented. The emission, movement, and annihilation of edge dislocations are incorporated in the analysis through a set of constitutive rules [1,2]. It is shown that the initiation of the first dislocation is controlled by the subsurface Hertzian stress field and occurs in the ±45° direction with respect to the normal of the crystal surface, in agreement with the macroscopic yielding behavior of the indented halfspace. For fixed slip-plane direction, the dislocation density increases with the applied normal load and dislocation source density. The dislocation multiplication behavior at a given load is compared with that generated by a rough indenter with a fractal surface profile. The results of the analysis provide insight into yielding and plastic deformation phenomena in indented single-crystal materials.

Climb-Enabled Discrete Dislocation Plasticity Analysis of the Deformation of a Particle Reinforced Composite

2015 ◽  
Vol 82 (7) ◽  
Author(s):  
C. Ayas ◽  
L. C. P. Dautzenberg ◽  
M. G. D. Geers ◽  
V. S. Deshpande
Keyword(s):  
Particle Size ◽  
Size Effect ◽  
Strain Hardening ◽  
Volume Fraction ◽  
Dislocation Motion ◽  
Dislocation Climb ◽  
Discrete Dislocation ◽  
Dislocation Plasticity ◽  
Wall Structures ◽  
The Matrix

The shear deformation of a composite comprising elastic particles in a single crystal elastic–plastic matrix is analyzed using a discrete dislocation plasticity (DDP) framework wherein dislocation motion occurs via climb-assisted glide. The topology of the reinforcement is such that dislocations cannot continuously transverse the matrix by glide-only without encountering the particles that are impenetrable to dislocations. When dislocation motion is via glide-only, the shear stress versus strain response is strongly strain hardening with the hardening rate increasing with decreasing particle size for a fixed volume fraction of particles. This is due to the formation of dislocation pile-ups at the particle/matrix interfaces. The back stresses associated with these pile-ups result in a size effect and a strong Bauschinger effect. By contrast, when dislocation climb is permitted, the dislocation pile-ups break up by forming lower energy dislocation wall structures at the particle/matrix interfaces. This results in a significantly reduced size effect and reduced strain hardening. In fact, with increasing climb mobility an “inverse size” effect is also predicted where the strength decreases with decreasing particle size. Mass transport along the matrix/particle interface by dislocation climb causes this change in the response and also results in a reduction in the lattice rotations and density of geometrically necessary dislocations (GNDs) compared to the case where dislocation motion is by glide-only.

Discrete dislocation sim ulation of thin film plasticit y

2001 ◽  
Vol 673 ◽  
Author(s):  
B. von Blanckenhagen ◽  
P. Gumbsch ◽  
E. Arzt
Keyword(s):  
Thin Film ◽  
Dislocation Motion ◽  
Source Size ◽  
Dislocation Dynamics ◽  
Polycrystalline Thin Film ◽  
Confined Geometry ◽  
Free Standing ◽  
Capping Layer ◽  
Discrete Dislocation Dynamics ◽  
Discrete Dislocation

ABSTRACTA discrete dislocation dynamics sim ulation is used to investigate dislocation motion in the confined geometry of a polycrystalline thin film. The repeated activ ation of a Frank-Read source is sim ulated. The stress to activate the sources and to initiate plastic fiow is significantly higher than predicted by models where the dislocations extend o ver the entire film thic kness. An efiective source size, which scales with the grain dimensions, yields fiow stresses in reasonable agreemen t with experimen ts. The infiuence of dislocations deposited at interfaces is investigated by comparing calculations for a film sandwic hed between a substrate and a capping layer with those for a free standing film.

Anisotropy in the hardness of single crystals

1971 ◽  
Vol 322 (1548) ◽  
pp. 73-88 ◽  
Keyword(s):  
Crystal Structure ◽  
Shear Stress ◽  
Single Crystals ◽  
Dislocation Motion ◽  
Slip Systems ◽  
Maximum Hardness ◽  
Indentation Process ◽  
Wide Range ◽  
Knoop Indentation ◽  
Active Slip

The results of this work, and those published by other researchers who have used Knoop indentation measurements, confirm that the nature of anisotropy in hardness is essentially determined by the crystal structure and the primary slip systems which accommodate dislocation motion during indentation. Materials belonging to the same class of crystal structure and having common slip systems possess similar anisotropic properties. The varying extent of work-hardening or fracture, associated with indentations, does not appear to influence the anisotropy— although twinning on the basal planes of hexagonal closepacked metals may have a significant effect. An analysis of the indentation process is presented which establishes a clear relationship between the ‘effective resolved shear stress’ (t 0 '), in the bulk of the crystal beneath the indenter, and the observed hardness. Directions which correspond to the minimum values of t' e , on specific crystallographic surfaces, are those of maximum hardness and conversely. The analysis is shown to be equally applicable to a wide range of crystalline solids including nonmetallic materials, of various crystal structure, and typical f.c.c., b.c.c. and c.p.h. metals. Finally, anisotropy in hardness can be used to identify active slip systems in those crystals where it is possible for dislocations to move on more than one system.

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