Statistical analysis of electromigration lifetimes and void evolution

Abstract

Electromigration failure statistics and the origin of the log-normal standard deviation for copper interconnects were investigated by analyzing the statistics of electromigration lifetime and void size distributions at various stages during testing. Experiments were performed on 0.18 m wide Cu interconnects with tests terminated after certain amounts of resistance increase, or after a specified test time. The lifetime and void size distributions were found to follow log-normal distribution functions. The sigma values of these distributions decrease with increasing test time. The statistics of resistance-based void size distributions can be simulated by considering geometrical variations of the void shape. In contrast, the characteristics of time-based void size distributions require consideration of kinetic aspects of the electromigration process. The sigma values of lifetime distributions can be adequately simulated by combining the statistics of both types of void size distributions. Thus, a statistical correlation between electromigration lifetimes and void evolution was established. Using simulation to fit the experimental data, the parameters influencing the electromigration lifetime statistics were identified as variations in void sizes, geometrical and experimental factors of the electromigration experiment, and kinetic aspects of the mass transport process, such as differences in interface diffusivity between the lines. The latter is the result of variations in the copper microstructure at the cathode ends of the interconnects.

Atomic flux divergence-based AC electromigration model for signal line reliability assessment

“…It has been observed experimentally that the void caused by EM first reaches its critical size horizontally limited by the grain boundary before it begins to span the interconnect trench [14] [15]. With such a void growth, the step-up resistance of some signal lines (Eg: clockline and bit-line of SRAM) may not exceed the failure threshold typically defined as 10% resistance increase even when the void spans the whole trench.…”

“…Thus, to model the time constant of a signal line, we need to model its EM resistance curve. According to previous research, the resistance evolution curve of the metal line consists of 3 portions [7][8] [14] [15], shown in Fig. 4.…”

“…The void growth rate of stage 1 is proportional to the maximum average AFD of stage 1, as shown in (14), in which Vatom denotes the volume of copper atom and VAFD,cube denotes the unit cubic volume we define when the 3D RC model is built.…”

Physically based models of electromigration: From Black’s equation to modern TCAD models

“…voids that trigger the line failure is the ultimate cause for the electromigration induced interconnect failure [67,68]. The failure criterion is typically set as a maximum resistance increase that is tolerated for the corresponding interconnect line.…”

Analysis of multistate models for electromigration failure

“…Since, in the case of a Ta, the electrical resistivity of the liner is around 20-70 times larger 11,15 than that of Cu, and the cross-section of the liner is around 10%-40% ͑Ref. 11͒ of the line cross-section, Cu A liner / liner A will be small ͑around 0.25/ 50= 0.005 say͒, and will only contribute to Eq.…”