A fundamental role in the electromigration (EM)da mage of interconnects in electronic devices is represented by the granular structure of the materials employed, Al, Cu, Al alloys, etc. In fact, it is well known that the atomic transport through the grain boundaries (transport channels) far exceeds that through the bulk of the grains. Therefore, it is a good approximation to neglect mass transport everywhere except within these channels and to describe the film as an interconnected grain boundary network. On the basis of the above considerations, we have developed a stochastic model which allows a good description of EM phenomena in metallic lines. The model, which describes a thin metallic film as a two-dimensional random resistor network, accounts for the competition between the voids formation, driven by the external current, and the voids healing, induced by the growth of mechanical stress. A biased percolation mechanism is used to relate the voids formation to the strength of local currents. Furthermore, the presence of compositional disorder is also considered. Monte Carlo simulations enable us to investigate the EM damage of Al-0.5%Cu lines of different geometry and under different external conditions (stress current and temperature). In this manner, we are able to investigate within a unified theoretical framework a variety of relevant aspects of electromigration as: damage patterns, distribution of the times to failure, early stage resistance change due to compositional effects, Black’s law, geometrical effects, resistance noise spectra, etc. In particular, a direct comparison with EM failure tests performed in Al-0.5%Cu lines shows that the model reproduce very well the resistance evolutions and the distribution of the times to failure. Furthermore, the Gaussianity of resistance fluctuations is investigated and an interesting nonGaussian behavior is found in the pre-failure region. The features of this nonGaussianity are discussed.
Simulation of Electromigration Phenomena and Associated Resistance Noise in Al-Cu Metallic lines
SCORZONI, Andrea
2003
Abstract
A fundamental role in the electromigration (EM)da mage of interconnects in electronic devices is represented by the granular structure of the materials employed, Al, Cu, Al alloys, etc. In fact, it is well known that the atomic transport through the grain boundaries (transport channels) far exceeds that through the bulk of the grains. Therefore, it is a good approximation to neglect mass transport everywhere except within these channels and to describe the film as an interconnected grain boundary network. On the basis of the above considerations, we have developed a stochastic model which allows a good description of EM phenomena in metallic lines. The model, which describes a thin metallic film as a two-dimensional random resistor network, accounts for the competition between the voids formation, driven by the external current, and the voids healing, induced by the growth of mechanical stress. A biased percolation mechanism is used to relate the voids formation to the strength of local currents. Furthermore, the presence of compositional disorder is also considered. Monte Carlo simulations enable us to investigate the EM damage of Al-0.5%Cu lines of different geometry and under different external conditions (stress current and temperature). In this manner, we are able to investigate within a unified theoretical framework a variety of relevant aspects of electromigration as: damage patterns, distribution of the times to failure, early stage resistance change due to compositional effects, Black’s law, geometrical effects, resistance noise spectra, etc. In particular, a direct comparison with EM failure tests performed in Al-0.5%Cu lines shows that the model reproduce very well the resistance evolutions and the distribution of the times to failure. Furthermore, the Gaussianity of resistance fluctuations is investigated and an interesting nonGaussian behavior is found in the pre-failure region. The features of this nonGaussianity are discussed.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
