5.6.2 Simulation Approach

In Figure 5.36 a schema of the simulation procedure used to determine the distribution of electromigration lifetimes is presented. First, several interconnects are generated, each one having a different microstructure which is produced by the microstructure generator (see Section 5.6.1). The structures are simulated and the electromigration lifetimes are determined. The lifetimes are then used for statistical analysis, from where the corresponding distribution, specified by the mean time to failure and standard deviation, is obtained.

Three standard deviations for the distribution of grain sizes are considered, namely 0.1, 0.3 and 0.6. For each of them 20 dual-damascene interconnect structures are created. As the interconnect line is assumed to present a bamboo-like structure, the median grain size is equal to the line width, 0.10 $\mu$m. The barrier, capping and interlayer dielectric layers are Ta, SiN, and SiO$_2$, respectively. The applied current density is 1.5 MA/cm$^2$, and the test temperature is 300 $^\circ$C. A stress threshold value as failure criterion is used, which means that the electromigration time to failure represents the time for a void nucleation to occur. Thus, the time to failure is determined by the time for the stress to reach a given threshold value at some intersection between a grain boundary and the capping layer.

It should be pointed out that the model parameters are equal for all simulated structures. Grain boundaries, and generally, every interface of the structure have to be supplied with an appropriately fine mesh. Therefore, the mesh refinement procedure described in Section 4.3.5 is used. This is necessary in order to provide sufficient resolution for the results along the grain boundaries and other interfaces.

Figure 5.36: Schematic simulation procedure.