5.3.2 Current Crowding

The first step of this analysis is to investigate the impact of current crowding on electromigration degradation. Current crowding is the effect of peaks in the current density due to regions of elevated electrical field strength. Corners are typical areas where current crowding occurs. Right angles in interconnect structures are sites where current density can become very high. The exact solution of the Laplace equation (3.3) of the electro-thermal model presented in Section 3.1 produces for these sites a singularity in the current density. The approximate solution obtained by FEM analysis cannot produce singularities, but instead produces high finite values for the current density in this area. By monitoring the distribution of the current density in the L-shaped geometry, the peak values are observed close to the corner of the right angled line, as depicted in (5.17(a)). Interconnect technology can never produce a perfect, sharp right angle. In (5.16), the L-shaped line is shown with varying angle sharpness, which depends on the radius ra of the arc that is created, tangent between the two straight lines. The current density distribution close to the corner of the L-shaped structure for different arc radii is illustrated in (5.17). As soon as the arc radius ra increases, the current density divergences become less prominent around the corner of the angled line (5.17(b)). However, even if one defines an angle with a small circular fillet, the peak in current density increases very quicky with a smaller arc radius , as presented in (5.17). Since the vacancy flux induced by electromigration increases due to the higher value of current density according to

\[\begin{equation} |\vec J_\text{v}| \sim \cfrac{eZ^*}{k_\text{b}T}|\vec j|, \end{equation}\] (5.4)

it is plausible to expect that electromigration degradation is significantly intensified in the presence of right angles in the interconnect.

Figure 5.17: Current density dependence on arc radius ra. Cross section views of the current density distribution are shown for two different arc radii ra: a) 0μm and b) 0.25μm. Current crowding decreases as soon as the arc radius increases.

In the experimental study of Croes et al. [39], the development of electromigration failure has been investigated in both straight and angled interconnects under identical test conditions. It was natural to expect that current crowding produced in the right angle interconnect corner would intensify electromigration and lead to a shorter lifetime of the studied structure. However, in the lognormal probability plots of the failure times obtained on both the standard linear and angled structure no difference in failure times is observed [39]. This indicates that the current crowding and current density gradient induced in the angled structure have no effect on electromigration lifetime estimation, also not in the lower percentile. Furthermore, the determination of the location of void nucleation was performed by using top-down scanning electron microscopy (SEM) after removing the top passivation layers. No voiding has been observed directly in the interconnect corner of the L-shaped structure. Voids seem to appear randomly along the interconnect line [39]. Other factors, such as grain boundaries and material interfaces, have a significant influence on the electromigration failure in the given case study.

M. Rovitto: Electromigration Reliability Issue in Interconnects for Three-Dimensional Integration Technologies