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.

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.

Grain Growth in Thin Films With Variable Grain Boundary Energy

1993 ◽  
Vol 317 ◽  
Author(s):  
H.J. Frost ◽  
Y. Hayashi ◽  
C.V. Thompson ◽  
D.T. Walton
Keyword(s):  
Thin Films ◽  
Grain Boundary ◽  
Grain Growth ◽  
Boundary Energy ◽  
High Energy ◽  
Grain Boundary Energy ◽  
Triple Junctions ◽  
Variable Boundary ◽  
Von Neumann ◽  
Grain Size Distributions

ABSTRACTIn simulations of grain growth in thin films we have considered the effect of variations in grain boundary energy. Boundary energy depends on both the misorientation between the two neighboring grains, and the angles which the boundary plane makes with the crystallographic axes of the two crystals. 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. One effect of variable boundary energies is that grains no longer gain or lose area at rates determined solely by their topology or number of sides. (They no longer obey the Von Neumann/Mullins law). Another effect is that as the grain structures evolve, the fraction of high-energy boundaries decreases. Also, the stagnant structures have broader grain size distributions.

Grain boundary energy changes during grain growth in nickel and 316L austenitic steel

1986 ◽  
Vol 2 (2) ◽  
pp. 106-109 ◽  
Author(s):  
W. Przetakiewicz ◽  
K. J. Kurzydłowski ◽  
M. W. Grabski
Keyword(s):  
Grain Boundary ◽  
Austenitic Steel ◽  
Grain Growth ◽  
Boundary Energy ◽  
Grain Boundary Energy

Monte-Carlo Simulation of Goss Abnormal Grain Growth in Fe-3%Si Steel by Sub-Boundary Enhanced Solid-State Wetting

2012 ◽  
Vol 715-716 ◽  
pp. 146-151
Author(s):  
K.J. Ko ◽  
A.D. Rollett ◽  
N.M. Hwang
Keyword(s):  
Monte Carlo ◽  
Solid State ◽  
Grain Boundary ◽  
Grain Growth ◽  
Boundary Energy ◽  
Three Dimensional ◽  
Abnormal Grain Growth ◽  
Grain Boundary Energy ◽  
Simulation Based ◽  
Mc Simulation

The selective abnormal grain growth (AGG) of Goss grains in Fe-3%Si steel was investigated using a parallel Monte-Carlo (MC) simulation based on the new concept of sub-boundary enhanced solid-state wetting. Goss grains with low angle sub-boundaries will induce solid-state wetting against matrix grains with a moderate variation in grain boundary energy. Three-dimensional MC simulations of microstructure evolution with textures and grain boundary distributions matched to experimental data is using in this study.

Phase Field Model of Grain Growth Using Quaternions

2012 ◽  
Vol 715-716 ◽  
pp. 776-781
Author(s):  
Santidan Biswas ◽  
Indradev Samajdar ◽  
Arunansu Haldar ◽  
Anirban Sain
Keyword(s):  
Grain Boundary ◽  
Grain Growth ◽  
Phase Field ◽  
Boundary Energy ◽  
Scaling Law ◽  
Phase Field Model ◽  
Polycrystalline Sample ◽  
Mechanical Processing ◽  
Grain Boundary Energy ◽  
Grain Orientations

The microstructure of a material determines its mechanical properties. Since microstructure can be tailored by thermo-mechanical processing of the metal, it is important to understand how the microstructure evolves under thermo-mechanical processing. We have constructed a phase field formalism to study recrystallization and grain growth in polycrystalline material. A unique feature of our model is that the Euler Angles (φ1,φ,φ2), obtained from Electron Back Scattered Diffraction (EBSD) data of a polycrystalline sample can be taken as an input to our model. In our model, the grain orientations at discrete grid points are represented by a non-conserved vector field, namely a quaternion. The free energy used for the evolution of the local orientations contains bulk energy for various preferred grain types and grain boundary energy. The grain orientations evolve in time following a Langevin dynamics. So far we have established that the rate of grain growth follows the usual L ~ t1/2scaling law when the grain boundary energy is independent of the misorientation angle between neighboring grains. Work on other aspects of this model is in progress.

Three-Dimensional Simulation of Coarsening and Grain Growth in Sintering

2007 ◽  
Vol 539-543 ◽  
pp. 2359-2364 ◽  
Author(s):  
Fumihiro Wakai
Keyword(s):  
Grain Boundary ◽  
Grain Growth ◽  
Boundary Energy ◽  
Three Dimensional ◽  
Grain Boundary Energy ◽  
Surface Evolver ◽  
Grain Boundary Mobility ◽  
Surface Mobility ◽  
Dimensional Simulation ◽  
Grain Boundary Motion

The interparticle mass transport causes the larger particles to grow at the expense of the smaller particles in the process of sintering. Coarsening during sintering results from surface motion, while grain growth results from grain boundary motion. The three-dimensional simulation was performed to study coarsening and grain growth during sintering by using the Surface Evolver program. The coarsening and grain growth were affected by the ratio of grain boundary energy to surface energy, the ratio of grain boundary mobility to surface mobility, the size of a particle, and its coordination number.

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