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将晶核析出的Avrami方程应用于描述超大规模集成电路中金属Al薄膜互连电迁移过程中电阻的演变.根据电子散射理论,晶界电阻主要起源于晶界处空位或者空洞对电子的散射.为了描述这些离子的特征,引入了自由体积的概念,将晶界处电子散射这个复杂的过程简化用自由体积的有效散射截面来描述,从而建立了自由体积与电阻变化的定量关系,统一描述了电迁移过程中不同阶段的电阻变化.数值模拟结果表明,在第一个空洞成核时刻电阻会发生急剧变化,这一结果已被实验所证实.
The Avrami equation developed by the nucleus is used to describe the evolution of resistance in the electromigration of metal Al interconnects in VLSI circuits. According to the theory of electron scattering, the grain boundary resistance mainly originates from the scattering of electrons by vacancies or voids in the grain boundaries. In order to describe the characteristics of these ions, the concept of free volume was introduced, and the complicated process of electron scattering at the grain boundary was simplified by the effective scattering cross section of free volume to describe the quantitative relationship between free volume and resistance change. The results show that the resistance changes sharply at the first nucleation time. This result has been verified experimentally.