Molecular dynamics simulation of void electromigration under a high‐density electric current stress in an aluminum interconnection

Abstract

Three‐dimensional molecular dynamics simulation of behaviors of a void in an Al interconnection under high current stress has been accomplished employing empirical two‐body potential and the Huntington‐Grone ballistic model for an electron wind force. Stability of a void under a uniform strain field was first investigated; it was shown that a void was stable under a tensile strain, while it was unstable under a compressive strain. Then, a void movement into cathode direction was clearly demonstrated in the single‐crystalline Al interconnection at the high current density of 1 × 1010 A/cm2. The activation energy of the drift velocity of the void was 0.76 eV. Next, behaviors of a void in [111] bicrystal grains with a periodic boundary condition which resembled a bamboo structure interconnection was investigated. A void was stabilized at the grain boundary at low current density conditions; however, it could go across the grain boundary and move further to the cathode direction when the current density was high enough. It was shown that when a void comes close to the grain boundary, it suddenly annihilates into vacancies and rapid movement of vacancies into the grain boundary occur. A void was formed again at the grain boundary. This model will explain the void annihilation phenomena, reported by the in situ scanning electron microscope (SEM) observations. After stopping the current, a backflow of a void was observed as a consequence of the strain energy relaxation when the current density was high. These obtained results explained well the experimental observations qualitatively; furthermore, new predictions were obtained with quantitative analysis based on total potential energy analysis.

Exact results with the J-integral applied to free-boundary flows

“…During the drift, it remains a fixed parameter in a steady or non-steady process according to (4.1). This seems to be found in experiments and it is confirmed by molecular dynamic simulations (Singubara, Utsunomiya & Fuji 1995;Ohkubo, Hirotsu & Nikawa 1996). When travelling steadily along the x-axis, in the absence of capillarity, the bubble has the symmetry x → −x and y → −y.…”

Crystal Alignment of Titanium under Simultaneous Imposition of Electric Current and Magnetic Field

“…Until now, these phenomena have been investigated mainly from the viewpoint of the reliability of integrated circuits, because the electric current density in LSI (large-scale integrated circuit) and ULSI (ultra-large scale integrated circuit) has drastically increased of late. For example, simulations and computer models, 1) temperature dependence of electromigration, 2) and transformation behavior of solder alloys, 3) have been performed. In these studies, copper, aluminum, and solider alloys have been treated as the test materials usually used in integrated circuits.…”