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THE EVOLUTION OF METAL GRAIN SIZE DISTRIBUTIONS

机译:金属晶粒尺寸分布的演变

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We use simulations to investigate the evolution of metal grain size distributions, employing the parallel levelset environment for nanoscale topography evolution (PLENTE) [Bloomfield et al.] and a simple grain boundary migration model. We compare computed trends to those experimentally observed in high temperature annealing and low temperature "self-annealing" of copper [Zielinski et al.]. We assume that for grain boundary motion the adatom concentration along a grain's boundary is a linear function of the local mean curvature, with high (convex) curvatures corresponding to high concentrations and low (concave) curvatures corresponding to low concentrations of adatoms. In this model, resistance to mass transfer across grain boundaries is assumed to depend on a fundamental sampling rate of adatoms across the grain boundary, activated by temperature. The mass fluxes of material parallel to grain boundaries and along the metal-barrier interface are considered to be small compared to motion transverse to the grain boundaries. The initial films, formed by isotropic deposition simulations, exhibit approximately log-normal distributions of grain sizes. During the annealing simulations, the structures begin to coarsen, with larger grains swallowing smaller grains, and the log-normal grain-size distributions become bimodal, similar to what has been observed in annealing of copper [Zielinski et al.]. The timescales of the simulated annealing processes compare qualitatively with experimental timescales, using representative physical parameters from the literature.
机译:我们使用模拟来研究金属晶粒尺寸分布的演变,采用平行水平集环境进行纳米尺度形貌演化(PLENTE)[Bloomfield等人]和简单的晶界迁移模型。我们将计算出的趋势与在铜的高温退火和低温“自退火”中实验观察到的趋势进行比较[Zielinski等]。我们假设对于晶界运动,沿晶界的原子浓度是局部平均曲率的线性函数,高(凸)曲率对应于高浓度,低(凹)曲率对应于低原子浓度。在该模型中,假设对跨晶界传质的阻力取决于温度激活的跨晶界的原子基本采样速率。与横向于晶界的运动相比,平行于晶界并沿着金属-阻挡层界面的材料的质量通量被认为较小。通过各向同性沉积模拟形成的初始薄膜呈现出近似的对数正态分布的晶粒尺寸。在退火模拟过程中,结构开始粗化,较大的晶粒吞噬了较小的晶粒,对数正态晶粒尺寸分布变为双峰态,类似于在铜的退火过程中观察到的[Zielinski等]。使用文献中的代表性物理参数,模拟退火过程的时间尺度与实验时间尺度进行定性比较。

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