scholarly journals Million-Line Failure Distributions for Narrow Interconnects

1997 ◽  
Vol 505 ◽  
Author(s):  
M. C. Bartelt ◽  
J. J. Hoyt ◽  
N. C. Bartelt ◽  
J. J. Dike ◽  
W. G. Wolfer
Keyword(s):  
Failure Time ◽  
Void Formation ◽  
Stress Evolution ◽  
Computationally Efficient ◽  
Failure Times ◽  
Grain Sizes ◽  
Relaxation Of Stresses ◽  
Interconnect Reliability ◽  
Local Relaxation ◽  
Failure Time Distributions

ABSTRACTWe examine the distribution of failure times in a simple and computationally efficient, yet reasonably authentic, model of interconnect reliability that allows consideration of statistically significant samples. The model includes an approximate description of the distribution of grain sizes and texture in narrow interconnects, an effective treatment of stress evolution associated with mass transport along grain boundaries, and local relaxation of stresses due to void formation. Failure time distributions for populations of idealized structures are analyzed to aid in interpretation of model behavior.

Comparison of Line Stress Predictions with Measured Electromigration Failure Times

2005 ◽  
Vol 863 ◽  
Author(s):  
Rao R. Morusupalli ◽  
William D. Nix ◽  
Jamshed R. Patel ◽  
Arief S. Budiman
Keyword(s):  
Void Formation ◽  
Atomic Diffusion ◽  
Time To Failure ◽  
Stress Evolution ◽  
Failure Times ◽  
Induced Stress ◽  
Product Lifetime ◽  
Metal Interconnects ◽  
Interconnect Lines ◽  
Pure Cu

AbstractReliability of today's interconnect lines in microelectronic devices is critical to product lifetime. The metal interconnects are carriers of large current densities and mechanical stresses, which can cause void formation or metal extrusion into the passivation leading to failure. The modeling and simulation of stress evolution caused by electromigration in interconnect lines and vias can provide a means for predicting the time to failure of the device. A tool was developed using MathCAD for simulation of electromigration-induced stress in VLSI interconnect structures using a model of electromigration induced stress. This model solves the equations governing atomic diffusion and stress evolution in one dimension. A numerical solution scheme has been implemented to calculate the atomic fluxes and the evolution of mechanical stress in interconnects. The effects of line geometries and overhangs, material properties and electromigration stress conditions have been included in the simulation. The tool has been used to simulate electromigration-induced stress in pure Cu interconnects and a comparison of line stress predictions with measured electromigration failure times is studied. Two basic limiting cases were studied to place some bounds on the results. For a lower bound estimate of the stress it was assumed that the interface can be treated like a grain boundary in Cu. For an upper bound estimate it was assumed that the interface can be treated like a free surface of Cu. Existing data from experimental samples with known structure geometries and electromigration failure times were used to compare the electromigration failure times with predicted stress build-up in the interconnect lines.

The effect of intermittent exposure to risk on failure time distributions

1974 ◽  
Vol 11 (2) ◽  
pp. 310-319 ◽  
Author(s):  
Valerie Isham
Keyword(s):  
At Risk ◽  
Failure Time ◽  
Intermittent Exposure ◽  
Failure Time Distributions

The relation is investigated between the distributions of the total time until failure and the time of exposure to risk until failure, for individuals who are at risk only intermittently during their lifetimes. A specific example is considered in the case of computer failures.

The Microstructural Nature of Electromigration and Mechanical Stress Voids in Integratedcircuit Interconnect

1993 ◽  
Vol 309 ◽  
Author(s):  
Jamie H. Rose ◽  
Terry Spooner
Keyword(s):  
Grain Boundary ◽  
Integrated Circuit ◽  
Boundary Diffusion ◽  
Void Formation ◽  
Parallel Line ◽  
Relative Displacement ◽  
Test Conditions ◽  
Line Array ◽  
Interconnect Reliability ◽  
Diffusion Paths

AbstractIt is well known that stress and electromigration induced voiding is of major concern for integrated circuit interconnect reliability. However, there has been little systematiccharacterization of void morphology and crystallography in ever more technologically important narrow, “near-bamboo” conducting lines. Prior reports indicate thatvoids are typically wedge or slit shaped, with failure often associated with slit voids.Void face habit plane is most often reported to be {111}. Wedge and slit void morphology and crystallography have been studied in comb/serpentine and parallel line array test structures. In virtually all cases, void faces are {111} oriented. In contrast to earlier studies, intragranular wedge stress voids have been observed. All electromigration opens were due to slit voids; these were typically intragranular, in contradiction to current theories of void formation, and likely are mechanical fractures. Under accelerated test conditions, non-grain boundary diffusion paths appear to operate at distances of tens of micrometers. Relative displacement between wedge voids and attached grain boundaries occurs where a wedge face lies on a near common {111} plane for the two grains. It is suggested that slit voids are intragranular under both stress and electromigration conditions and likely associated with local interconnect depassivation. Based solely on appearance and crystallography, no void can uniquely be identified as due to stress alone or electromigration alone.

The effect of intermittent exposure to risk on failure time distributions

1974 ◽  
Vol 11 (02) ◽  
pp. 310-319
Author(s):  
Valerie Isham
Keyword(s):  
At Risk ◽  
Failure Time ◽  
Intermittent Exposure ◽  
Failure Time Distributions

The relation is investigated between the distributions of the total time until failure and the time of exposure to risk until failure, for individuals who are at risk only intermittently during their lifetimes. A specific example is considered in the case of computer failures.

On the limiting distribution of the failure time of fibrous materials

1983 ◽  
Vol 15 (02) ◽  
pp. 331-348
Author(s):  
Wagner De Souza Borges
Keyword(s):  
Materials Science ◽  
Failure Time ◽  
Large Deviation ◽  
Limiting Distribution ◽  
Statistical Characteristics ◽  
Fibrous Materials ◽  
Large Deviation Theorem ◽  
Science Area ◽  
The Individual ◽  
Failure Time Distributions

A large deviation theorem of the Cramér–Petrov type and a ranking limit theorem of Loève are used to derive an approximation for the statisticaldistribution of the failure time of fibrous materials. For that, fibrousmaterials are modeled as a series of independent and identical bundles of parallel filaments and the asymptotic distribution of their failure time is determined in terms of statistical characteristics of the individual filaments, as both the number of filaments in each bundle and the number of bundles in the chain grow large simultaneously. While keeping the numbernof filaments in each bundle fixed and increasing only the chain lengthkleads to a Weibull limiting distribution for the failure time, letting both increase in such a way that logk(n)= o(n), we show that the limit distribution isfor. Since fibrous materials which are both long and have many filaments prevail, the result is of importance in the materials science area since refined approximations to failure-time distributions can be achieved.

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