Stress distribution and mass transport along grain boundaries during steady-state electromigration

1995 ◽  
Vol 43 (9) ◽  
pp. 3525-3538 ◽  
Author(s):  
M. Scherge ◽  
C.L. Bauer ◽  
W.W. Mullins
Keyword(s):  
Steady State ◽  
Stress Distribution ◽  
Mass Transport ◽  
Grain Boundaries

Stress Distribution and Mass Transport along Grain Boundaries during Electromigration

1996 ◽  
Vol 207-209 ◽  
pp. 457-460
Author(s):  
X. Chu ◽  
M. Scherge ◽  
C.L. Bauer ◽  
W.W. Mullins
Keyword(s):  
Stress Distribution ◽  
Mass Transport ◽  
Grain Boundaries

Stress Distribution and Mass Transport Along Grain Boundaries During Steady-State Electromigration

1994 ◽  
Vol 338 ◽  
Author(s):  
M. Scherge ◽  
C. L. Bauer ◽  
W. W. Mullins
Keyword(s):  
Steady State ◽  
Stress Distribution ◽  
Grain Boundary ◽  
Boundary Conditions ◽  
Grain Boundaries ◽  
Driving Forces ◽  
Bottom Surface ◽  
Triple Junctions ◽  
Flux Divergence ◽  
Transient Time

ABSTRACTStress distribution and mass flux in the plane of each grain boundary within a polycrystalline thin-film conductor have been calculated during electromigration for zero flux divergence (steady state) and various boundary conditions. Steady state, representing a balance between the (applied) electric and (induced) stress driving forces, is assumed to develop after a short transient time. Boundary conditions at the intersection of grain boundaries with the top and bottom conductor surfaces (surface junctions) and with the conductor edges (edge junctions) are assumed to be of two types: open (flux passes freely) and closed (zero flux). Flux is assumed to pass freely at the intersection of grain boundaries with each other (triple Junctions). Several grain boundary configurations are considered, including individual boundaries, single triple junctions, and combinations thereof, assuming that bottom surface junctions (conductor/ substrate interface) are closed and that top surface junctions are either open (bare conductor) or closed (passivation layer). Results clearly show the formation of incipient holes and hillocks near the intersection of triple junctions and/or closed (blocked) edge junctions with open surface junctions.

Effect of mass transport along interfaces and grain boundaries on copper interconnect degradation

2004 ◽  
Vol 812 ◽  
Author(s):  
Ehrenfried Zschech ◽  
Moritz A. Meyer ◽  
Eckhard Langer
Keyword(s):  
Mass Transport ◽  
Grain Boundaries ◽  
Void Formation ◽  
Degradation Process ◽  
Copper Interconnects ◽  
Second Phase ◽  
Copper Interconnect ◽  
Void Evolution ◽  
Two Phases

AbstractIn-situ SEM electromigration studies were performed at fully embedded via/line interconnect structures to visualize the time-dependent void evolution in inlaid copper interconnects. Void formation, growth and movement, and consequently interconnect degradation, depend on both interface bonding and copper microstructure. Two phases are distinguished for the electromigration-induced interconnect degradation process: In the first phase, agglomerations of vacancies and voids are formed at interfaces and grain boundaries, and voids move along weak interfaces. In the second phase of the degradation process, they merge into a larger void which subsequently grows into the via and eventually causes the interconnect failure. Void movement along the copper line and void growth in the via are discontinuous processes, whereas their step-like behavior is caused by the copper microstructure. Directed mass transport along inner surfaces depends strongly on the crystallographic orientation of the copper grains. Electromigration lifetime can be drastically increased by changing the copper/capping layer interface. Both an additional CoWP coating and a local copper alloying with aluminum increase the bonding strength of the top interface of the copper interconnect line, and consequently, electromigration-induced mass transport and degradation processes are reduced significantly.

Steady-State stress distributions in circumferentially notched bars subjected to creep

1982 ◽  
Vol 17 (3) ◽  
pp. 123-132 ◽  
Author(s):  
K D Al-Faddagh ◽  
R T Fenner ◽  
G A Webster
Keyword(s):  
Steady State ◽  
Stress Distribution ◽  
Stress Index ◽  
Stress Distributions ◽  
Computer Solution ◽  
Time Intervals ◽  
Throat Region ◽  
Intermediate Time ◽  
State Stress ◽  
Good Agreement

The paper describes a procedure, based on a finite element method, for calculating directly the steady-state stress distribution in circumferentially notched bars subjected to creep without the need for obtaining solutions at intermediate time intervals. Good agreement is obtained with relevant approximate plasticity solutions and with numerical calculations which approach the steady-state over a period of time from the initial elastic stress distribution. Also, the procedure is equally applicable to primary, secondary, and tertiary creep, provided the variables of stress and time are separable in the creep law. Results obtained for a range of notch geometries and values of the stress index, n, are reported. It is found for each profile that a region of approximately constant effective stress, σ, independent of n, is obtained which can be used to characterise the overall behaviour of the notch throat region when a steady-state is reached sufficiently early in life. An approximate method for estimating the maximum equivalent steady-state stress across the notch throat is also presented which does not require a computer solution.

scholarly journals Geometry and Dynamics of a Surge-type Glacier

1977 ◽  
Vol 18 (79) ◽  
pp. 181-194 ◽  
Author(s):  
R. Bindschadler ◽  
W. D. Harrison ◽  
C. F. Raymond ◽  
R. Crosson
Keyword(s):  
Steady State ◽  
Stress Distribution ◽  
Internal Stress ◽  
Ice Thickness ◽  
Surface Slope ◽  
Local Surface ◽  
Order Of Magnitude ◽  
Internal Deformation ◽  
Longitudinal Profiles ◽  
Similar Depth

AbstractMeasurement of geometry, motion, and mass balance from Variegated Glacier, Alaska portray conditions in this surge-type glacier close to the mid-point of its 20 year surge cycle. Comparison of longitudinal profiles of ice depth, surface slope, and surface speed indicate that the motion occurs largely by internal deformation assuming the ice deforms according to the experimental law of Glen. Surface speed is not noticeably affected by local surface slope on the scale of the ice thickness or smaller, but correlates well with slope determined on a longitudinal averaging scale about one order of magnitude larger than the ice depth. The rate of motion on Variegated Glacier agrees well with rates on non-surge type temperate glaciers which have similar depth and slope. Although the (low regime at the time of the measurements is apparently typical of temperate glaciers, a large discrepancy between the balance flux needed for steady state and the actual flux is indicative of a rapidly changing surface elevation profile and internal stress distribution.

Migrating Interfaces in Sapphire Bicrystals and Tricrystals

2000 ◽  
Vol 6 (S2) ◽  
pp. 386-387
Author(s):  
N. Ravishankar ◽  
M.T. Johnson ◽  
C. Barry Carter
Keyword(s):  
Mass Transport ◽  
Liquid Film ◽  
Grain Boundaries ◽  
Ostwald Ripening ◽  
Chemical Potential ◽  
Driving Forces ◽  
Boundary Migration ◽  
Liquid Phase Sintering ◽  
Polycrystalline Materials ◽  
Second Phase

The migration of grain boundaries in polycrystalline materials can occur under a variety of driving forces. Grain growth in a single-phase material and Ostwald ripening of a second phase are two common processes involving boundary migration. The mass transport in each of these cases can be related to a chemical potential difference across the grains; due to curvature in the former case and due to a difference in the chemistry in the latter case. The mass transport across grains controls the densification process during sintering. In the case of liquid-phase sintering (LPS), a liquid film may be present at the grain boundaries which results in an enhanced mass transport between grains leading to faster densification. Hence, in LPS, it is important to understand mass transport across and along a boundary containing a liquid film. The use of bicrystals and tricrystals with glass layers in the boundary can provide a controlled geometry by which to study this phenomenon.

Reference Stress for Redistribution Time in Creep of Structures

1969 ◽  
Vol 11 (4) ◽  
pp. 429-431 ◽  
Author(s):  
I. M. Bill ◽  
A. C. Mackenzie
Keyword(s):  
Steady State ◽  
Stress Distribution ◽  
Initial Stress ◽  
Creep Test ◽  
Linear Elastic ◽  
Reference Stress ◽  
Creep Analysis

When creep occurs in a structure subject to a step load the stresses redistribute with time. It is shown that if the initial stress distribution is the linear elastic one, and the material obeys an n-power creep law, the time for a particular stress to reach its steady state value may be estimated from the results of a single creep test at a selected value of stress with-out the parameters of the creep law being known. This reference stress is identified from the results of an appropriate elastic-creep analysis.

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