Formation and evolution of grain structures in thin films

Bloomfield, Max O.; Cale, Timothy S.

doi:10.1016/j.mee.2004.07.054

Cited by 21 publications

(18 citation statements)

References 31 publications

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“…Grain growth and evolution can be modelled by means of phase-field approaches [22], level set methods [23,24], curvature-driven grain growth [25], and others. However, these approaches may not directly generate a geometrical model, e.g.…”

Section: Introductionmentioning

confidence: 99%

A duality‐based method for generating geometric representations of polycrystals

Rimoli

Ortiz

2010

Numerical Meth Engineering

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SUMMARYWe present a method, which we have termed Relaxed Dual Complex (RDC), for generating geometric representations and computational models of polycrystals of arbitrary shape. The RDC method combines a first topological step, which defines an initial unrelaxed polycrystal geometry as the barycentric dual of an input triangulation of the solid, and a second relaxation step, in which the grain boundaries are relaxed by means of a gradient flow driven by grain boundary energy. The RDC method applies to arbitrary solids defined by means of a triangulation and, in this manner, it couples seamlessly to standard solid modelling engines. An additional appealing feature of the RDC method is that it generates a conforming tetrahedral mesh of the polycrystal that can be used as a basis for subsequent simulations. The RDC method also affords some control over the statistical properties of the polycrystal, including grain size, which provides a convenient device for matching experimental statistical data. The range, versatility, and performance of the RDC method have been demonstrated by means of selected examples.

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Section: Introductionmentioning

confidence: 99%

A duality‐based method for generating geometric representations of polycrystals

Rimoli

Ortiz

2010

Numerical Meth Engineering

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“…CDGBM is highly dependent on the local shape of the GBs. As grains relax under CDGBM, high curvature areas from the as-deposited structure will tend to smooth out and the peak in the distribution will shift to the left [2]. Further, although the driving energy for CDGBM is stored in the structure, the driving energy for SDGBM is induced in the structure by the work done upon changing its temperature, or in other cases, by work done by an imposed load.…”

Section: Resultsmentioning

confidence: 99%

“…To produce a starting grain structure, PLENTE [1][2][3] is used to model the deposition of Cu grains in a 1.5 m diameter, 23.6 m tall cylindrical via. With a nominal nucleation density of 0.7 m -2 along the via sidewalls, Cu nuclei are allowed to grow as if they were produced by a kinetically limited electrochemical or electroless plating process [16] until the via is filled.…”

Section: Methodsmentioning

confidence: 99%

“…Multiplying this pressure by the mobility of Cu GBs, (1.3x10 -16 m 4 /J s at 425 K [13,17]) we arrive at a normal speeds for each triangle on the Cu GBs, in the GC section of the structure. Gibb-Thompson-like relation [2], the product of the mean curvature and the surface energy density is identified as a driving pressure, and normal speeds are determined using the same mobility as for SDGBM.…”

Section: Methodsmentioning

confidence: 99%

“…We have used grain-focused simulations to study microstructure formation and evolution in Cu interconnects [1][2][3], because of their impacts on IC performance and reliability characteristics, including electromigration resistance [6,7], resistivity [8], and yield strength [9]. This paper reports on our on-going grain-focused modeling effort to understand microstructure evolution in polycrystalline Cu vias as they might be used in 3D-ICs [10].…”

Section: Introductionmentioning

confidence: 99%

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Strain Energy Driven and Curvature Driven Grain Boundary Migration in 3D-IC Cu Vias

Awo-Affouda

Bloomfield

Cale

Simulation of Semiconductor Processes and Devices 2007

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We use grain-focused models to study grain boundary (GB) migration (GBM) in polycrystalline Cu vias that interconnect MLM layers in 3D ICs. Curvature-driven GB velocities are calculated by PLENTE [1-3] using the local mean curvature of the GBs, as described in Ref. 2. We use Comsol Multiphysics [4] to calculate GB velocities due to thermally induced strain energy jumps across GBs [5]. The thermo-mechanical calculations needed for this are made using model structures that combine continuum models and grain-continuum (GC) models (see [1-3, 5]); we call these 'hybrid' graincontinuum (HGC) models. Curvature driven GB dominates in this work; however, there are uncertainties in the absolute stress values used and how the relative magnitudes of these phenomena will change as the structure evolves.

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Stress-Induced Grain Boundary Migration in Polycrystalline Copper

Bloomfield

Bentz

Cale

2007

Journal of Elec Materi

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We use three-dimensional (3D) grain-continuum models to study grain boundary migration, treating each grain with anisotropic elastic properties. Grain boundary speeds are computed using a finite element method to calculate differences in strain energy density across grain boundaries. Bodyfitted finite element meshes are used. An interface tracking program, PLENTE, is used to develop starting structures and move the grain boundaries based on these speeds. We demonstrate this procedure on textured films consisting of h100i and h111i fiber textured film. We also apply the model to a short section of a Cu line embedded in oxide. We conclude with a discussion on the relative impact of different driving forces for grain boundary motion.

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Formation and evolution of grain structures in thin films

Cited by 21 publications

References 31 publications

A duality‐based method for generating geometric representations of polycrystals

A duality‐based method for generating geometric representations of polycrystals

Strain Energy Driven and Curvature Driven Grain Boundary Migration in 3D-IC Cu Vias

Stress-Induced Grain Boundary Migration in Polycrystalline Copper

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