In this section we present the simulation of the influence of electromigration promoting factors on the electromigration behavior for the case of a complex interconnect structure produced with advanced process simulation tools.
The results of the transient electro-thermal simulation (Section 4.3.2) are used to setup a thermo-mechanical (Section 4.3.2) and material transport simulation. The model applied is similiar to that presented in Section 4.4.5 but without taking into account the connection between the local vacancy dynamic and overall mechanical stress distribution.
An effective vacancy diffusivity is chosen assuming the copper/TiN barrier interface as the dominant diffusion path [55].
An interconnect structure with 6 metal (copper) lines crossing 4 other lines at a
lower level and connected with vias/contacts was generated using a typical
damascene process flow.
This was performed by using a combination of DEP3D [93] (only for deposition of TiN barrier
layer and copper deposition for the second metal layer and for dielectric deposition
of the topmost layer) with DEVISE [94] (used for emulating the other deposition,
etching and polishing steps).
The barrier layer is 0.02 
m thick; each metal line in the first layer is 3 m long with a width of 0.25 m and aspect ratio of 1.2.
For the second layer, each metal line is 2.2 m long with a width 0.3 m and aspect ratio 1.5.
The contacts/vias have a width of 0.2 m with an aspect ratio of 2.5.
The dielectric medium surrounding the metal lines is silicon-dioxide.
The contacts for electrical characterization were defined using DEVISE.
The simulation of the electro-thermal problem was carried out with the SAP [91] tool and the simulation of mechanical stress and electromigration problem with FEDOS tool. The simulation results are presented in the Figure 4.18 - Figure 4.20. We can see in Figure 4.18 electrical potential distribution. The gradient of the electrical potential determines direction and intensity of the electromigration driving force.
The corresponding temperature distribution is presented in Figure 4.19. The temperature has twofold influence on the electromigraton. First, temperature changes diffusion coefficeints on all diffusion paths according to Arrhenius' law. Secondly, for the case that due to specific interconnect layout and operating conditions a substantial gradients in the temperature distribution are available, these gradients represents additional driving force which can promote or opose electromigration (4.32). Additionally, thermal mismatch between copper, barrier and silicon-dioxide passivation layer causes a build-up of thermo-mechanical stress.
The peak values of the vacancy concentration indicate the spots where serious material transport discontinuity takes place. These hot spots are the locations where the void nucleation can be expected (Figure 4.20). Analysis of the experimental results [55,95,77] shows that the material transport discontunity can be intialised by the geometrical properties of layout itself, like in the cases where the segments of the copper interconnects are divided by barrier layer, and promoted due to electromigration unbalanced by other driving fources. A significant part plays also the grain boundary structure of the copper acting as a network of fast diffusivity paths.
During the operating of an interconnect generally the redistribution of vacancies under the influence of the promoting factors takes place. Starting from the uniformly distributed vacancies, during the operating of the interconnect local peaks of the vacancy concentration are built (Figure 4.20).
If the balance of promoting factors and temperature gradients which characterize operating conditions of the interconnect is reached, the vacancy concentration will remain at some
value independent of the simulation duration: the interconnect structure is virtually
immortal.
However, if the electrical field is so high that electromigration overrides the material reaction presented through concentration and mechanical stress gradients, the vacancy concentration will increase steadily and at some point (e.g. vacancy concentration reaches unrealistic high values) the applied model is no more valid.
If the vacancy concentration is higher than the lattice sites concentration throughout some volume of the macroscopic dimensions (for example 
of the interconnect width), we can assume that void is already nucleated and for further simulation void evolution models should be applied (Sections 4.6.1 and 4.6.2).
The interconnect layout and operating conditions choosen in our simulation example produce a situation where the vacancy concentration remains stable at
cm
and under the lattice sites concentration (
cm).
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