Computer Simulation of Grain Growth in Thin-film Interconnect Lines

1991 ◽  
Vol 225 ◽  
Author(s):  
D. T. Walton ◽  
H. J. Frost ◽  
C. V. Thompson
Keyword(s):  
Thin Film ◽  
Grain Boundary ◽  
Grain Growth ◽  
Integrated Circuit ◽  
Strip Width ◽  
Grain Structure ◽  
Time To Failure ◽  
Interconnect Reliability ◽  
Bamboo Structure ◽  
Individual Grains

ABSTRACTMicrostructural evolution in thin-film strips is of interest due to the direct effect of grain structure on integrated circuit interconnect reliability and resistance to electromigration-induced failure. We have explored the evolution of interconnect grain structure via a two-dimensional grain growth simulation. We focus on the strip's transformation to the bamboo structure, in which individual grains traverse the width of the strip. We find that the approach to a fully bamboo structure is exponential, and that the rate of transformation is inversely proportional to the square of the strip width. When the simulation is extended to model grain boundary pinning due to grooving at grain boundary – free surface intersections, we find that there exists a maximum strip width to thickness ratio beyond which the transformation to the bamboo structure does not proceed to completion. By using our simulation results in conjunction with a “failure unit” model for electromigration-induced failure [4] we are able to reproduce the experimentally observed abrupt increase in time-to-failure below a critical strip width, and also model the reliability as a function of annealing conditions.

The Effect of Variability Among Grain Boundary Energies on Grain Growth in Thin Film Strips

1994 ◽  
Vol 338 ◽  
Author(s):  
H.J. Frost ◽  
Y. Hayashi ◽  
C.V. Thompson ◽  
D.T. Walton
Keyword(s):  
Thin Film ◽  
Grain Boundary ◽  
Grain Growth ◽  
Boundary Energy ◽  
Strip Width ◽  
Grain Boundary Energy ◽  
Triple Junctions ◽  
Interconnect Reliability ◽  
Bamboo Structure ◽  
Grain Boundary Pinning

ABSTRACTGrain growth in thin-film strips is important to interconnect reliability because grain boundary structures strongly effect the rate and mechanism of electromigration-induced failure. Previous simulations of this process have indicated that the transformation to the fully bamboo structure proceeds at a rate which decreases exponentially with time, and which is inversely proportional to the square of the strip width. We have also reported that grain boundary pinning due to surface grooving implies that there exists a maximum strip width to thickness ratio beyond which the transformation to the bamboo structure does not proceed to completion. In this work we have extended our simulation of grain growth in thin films and thin film strips to consider the effects of variations in grain boundary energy. Boundary energy is taken to depend on the misorientation between the two neighboring grain and the resulting variations in grain boundary energy mean that dihedral angles at triple junctions deviate from 120°. The proportionality between boundary velocities and local curvatures, and the critical curvature for boundary pinning due to surface grooving also both depend on boundary energy. In the case of thin-film strips, the effect of boundary energy variability is to impede the transformation to the bamboo structure, and reduce the width above which the complete bamboo structure is never reached. Those boundaries which do remain upon stagnation tend to be of low energy (low misorientation angle) and are therefore probably of low diffusivity, so that their impact on reliability is probably reduced.

Modeling of Grain Structure Evolution and its Impact on the Reliability of Al(Cu) Thin Film Interconnects

1997 ◽  
Vol 490 ◽  
Author(s):  
S. P. Riege ◽  
V. Andleigh ◽  
C. V. Thompson ◽  
H. J. Frost
Keyword(s):  
Grain Growth ◽  
Volume Fraction ◽  
Grain Structure ◽  
Structure Evolution ◽  
2D Simulation ◽  
Grain Structures ◽  
Average Grain Size ◽  
Interconnect Reliability ◽  
Bamboo Structure ◽  
Cu Thin Film

ABSTRACTWe have extended a 2D simulation of grain growth to treat the effects of precipitates on the evolution of interconnect grain structures during post-patterning processing. It is known from experiments that different annealing histories result in different precipitate sizes and locations. Precipitates capture and effectively pin grain boundaries and inhibit grain growth and evolution toward bamboo structures. We find that even a small volume fraction of precipitates prevent an interconnect strip from reaching the fully bamboo structure by retarding grain growth and lowering the average grain size. At a late stage of evolution, cluster regions are pinned by precipitates on both sides, preventing further transformation to the by far more reliable bamboo structure. The results from grain growth simulations have been used with our electromigration simulator MTT/EmSim to investigate the dependence of interconnect reliability on linewidth and precipitate distribution. We find that in lines with precipitates the bamboo structure is not reached during post-pattern annealing even if the line width is smaller than the average grain diameter. Furthermore, it is found that while Cu in solid solution improves interconnect reliability, Al2Cu precipitates can inhibit post-patterning grain structure evolution to more reliable bamboo or near-bamboo structures so much that similar lines made of pure Al would be more reliable. Linked grain structure evolution and electromigration simulations allow process optimization for maximum interconnect reliability.

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.

scholarly journals The Influence of Mg-Based Inclusions on the Grain Boundary Mobility of Austenite in SS400 Steel

Metals ◽  
2019 ◽  
Vol 9 (3) ◽  
pp. 370
Author(s):  
Chih-Ting Lai ◽  
Hsuan-Hao Lai ◽  
Yen-Hao Su ◽  
Fei-Ya Huang ◽  
Chi-Kang Lin ◽  
...  
Keyword(s):  
Grain Boundary ◽  
Grain Growth ◽  
High Temperatures ◽  
Growth Curves ◽  
Solute Drag ◽  
Grain Structure ◽  
Growth Equation ◽  
Boundary Mobility ◽  
Grain Boundary Mobility ◽  
Boundary Velocity

In this study, the effects of the addition of Mg to the grain growth of austenite and the magnesium-based inclusions to mobility were investigated in SS400 steel at high temperatures. A high-temperature confocal scanning laser microscope (HT-CSLM) was employed to directly observe, in situ, the grain structure of austenite under 25 torr Ar at high temperatures. The grain size distribution of austenite showed the log-normal distribution. The results of the grain growth curves using 3D surface fitting showed that the n and Q values of the growth equation parameters ranged from 0.2 to 0.26 and from 405 kJ/mole to 752 kJ/mole, respectively, when adding 5.6–22 ppm of Mg. Increasing the temperature from 1150 to 1250 °C for 20 min and increasing the addition of Mg by 5.6, 11, and 22 ppm resulted in increases in the grain boundary velocity. The effects of solute drag and Zener pinning on grain boundary mobility were also calculated in this study.

Comparison of Experimental and Computational Aspects of Grain Growth in Al-Foil

2000 ◽  
Vol 652 ◽  
Author(s):  
Melik C. Demirel ◽  
Andrew P. Kuprat ◽  
Denise C. George ◽  
Bassem S. El-Dasher ◽  
Neil N. Carlson ◽  
...  
Keyword(s):  
Grain Boundary ◽  
Grain Growth ◽  
Three Dimensional ◽  
Interface Energy ◽  
Grain Structure ◽  
Electron Backscattered Diffraction ◽  
Boundary Properties ◽  
Ebsd Technique ◽  
Columnar Grain ◽  
Grain Boundary Motion

ABSTRACTGrain boundary and crystallographic orientation information of an Al-foil with a columnar grain structure is characterized by Electron Backscattered Diffraction (EBSD) technique. The starting microstructure and grain boundary properties are implemented as an input for the three- dimensional grain growth simulation. In the computational model, minimization of the interface energy is the driving force for the grain boundary motion. The computed evolved microstructure is compared with the final experimental microstructure, after annealing at 550 °C. Good agreement is observed between the experimentally obtained microstructure and the simulated microstructure. The constitutive description of the grain boundary properties was based on a 1- parameter characterization of the variation in mobility with misorientation angle.

scholarly journals Grain Boundary Properties and Grain Growth: Al Foils, Al Films

2004 ◽  
Vol 819 ◽  
Author(s):  
Katayun Barmak ◽  
Wayne E. Archibald ◽  
Anthony D. Rollett ◽  
Shlomo Ta'asan ◽  
David Kinderlehrer
Keyword(s):  
Grain Size ◽  
Grain Boundary ◽  
Grain Growth ◽  
Misorientation Angle ◽  
Driving Forces ◽  
Boundary Energy ◽  
Orientation Imaging Microscopy ◽  
Solute Drag ◽  
Grain Structure ◽  
Two Dimensional

AbstractRelative grain boundary energy as a function of misorientation angle has been measured in cube-oriented, i.e., <100> fiber-textured, 120 [.proportional]m-thick Al foil using orientation imaging microscopy and a statistical multiscale method. The energies of low-angle boundaries increase with misorientation angle, in good agreement with the Read-Shockley model. The relative energies of high-angle boundaries exhibit little variation with misorientation. Examination of the grain structure of <111> fiber-textured, 100 nm-thick Al films annealed at 400°C for 0.5-10 h shows 5 and 6 sided grains to be the most frequent, and the fraction of four-sided grains to be significant. The mean number of sides is slightly lower than the expected value of 6 for two- dimensional structures. Of lognormal, gamma and Rayleigh distributions, gamma gives the best fit to the grain size data in the films; however, the difference between gamma and lognormal is small. Grain growth is not self-similar and stagnates after one hour of annealing. The evolution of the grain size distribution with time indicates that the growth stagnation in the films is neither consistent with boundary pinning by grooving nor with conventional treatments of solute drag. Surface, elastic-strain and plastic-strain energy driving forces do not play a significant role in the grain growth and the subsequent stagnation since the films are strongly textured even in the as- deposited state. The steady-state distributions of reduced grain area for two-dimensional, Monte Carlo and partial differential equation based simulations show excellent agreement with each other, even when anisotropic boundary energies are used. However, comparison with experimental distributions reveals a significantly higher population of small grains in the experiments.

Void Intergranual Motion Under the Action of Electromigration Forces in Thin Film Interconnects with Bamboo Structure

2001 ◽  
Vol 695 ◽  
Author(s):  
Ersin Emre Oren ◽  
Tarik Omer Ogurtani
Keyword(s):  
Thin Film ◽  
Grain Boundary ◽  
Entropy Production ◽  
Computer Simulations ◽  
Triple Junction ◽  
Tearing Mode ◽  
Virtual Displacement ◽  
Component Systems ◽  
Bamboo Structure ◽  
Metallic Interconnects

ABSTRACTThe rigorous formulation of the internal entropy production, and the generalized forces and conjugate fluxes associated with the virtual displacement of a triple junction are presented in multi-component systems. Extensive computer simulations are performed on the void configurational evolution during the intergranual motion; under the actions of capillary and electromigration forces in thin film metallic interconnects with bamboo structure having various grain textures. The texture studies in this work show clearly that there are two different and very distinct modes, namely: the grain boundary carving or tearing mode, and the interconnect edge cutting mode by the oblique slit formation (about 450) on the wind-side of the grain boundary.

Electromigration Failure in Thin Film Conductors Possessing a Near-Bamboo Structure

1994 ◽  
Vol 338 ◽  
Author(s):  
J.R. Lloyd
Keyword(s):  
Thin Film ◽  
Grain Boundary ◽  
Stress Gradient ◽  
Diffusion Path ◽  
Flux Divergence ◽  
Cluster A ◽  
Bamboo Structure

ABSTRACTElectromigration failure in a near bamboo structure is investigated theoretically. Assuming that the diffusion path is interfacial, a flux divergence can be predicted based on the stress gradient induced by grain boundary electromigration in a sub Blech Length grain cluster. A possible explanation for the recently observed “trans-granular” voids is proposed.

Further Investigations of the Microstructural Mechanism of Electromigration Failure in Al-Cu Lines with Quasi-Bamboo Microstructures

1996 ◽  
Vol 428 ◽  
Author(s):  
S. H. Kang ◽  
F. Y. Génin ◽  
C. Kim ◽  
J. W. Morris
Keyword(s):  
Thin Film ◽  
Silicon Nitride ◽  
Current Density ◽  
Segment Length ◽  
Time To Failure ◽  
Failure Distribution ◽  
Conventional Test ◽  
Bamboo Structure ◽  
Microstructural Mechanism

AbstractThin-film Al-2Cu conducting lines with “quasi-bamboo” microstructures were investigated to understand the microstructural mechanism of electromigration failure. Both conventional test structures and electron-transparent lines fabricated on silicon nitride windows were utilized to identify the “weakest” polygranular segments. Even when the current density was reduced to 0.75 MA/cm2 and the segment length was on the order of a few microns, failure occurs at the upstream termination of the longest polygranular segment in the line, at a time that decreases exponentially with the segment length. There is no apparent “Blech length” in quasi-bamboo Al- Cu lines; the longest segments are the failure sites, and their lifetime decreases with segment length in a regular way, even when the longest segments are only a few microns in length. It follows (and is observed) that the time-to-failure distribution of a group of lines is fixed by the distribution of the longest polygranular segments within them. This distribution can be effectively controlled by post-pattern annealing, which can refine the quasi-bamboo structure so that the longest polygranular segments are short and the distribution of longest polygranular segment lengths is narrow. Consequently, post pattern annealing is a very effective method for improving reliability by increasing the time to first failure.

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