This book (Practical Electron Microscopy and Database) is a reference for TEM and SEM students, operators, engineers, technicians, managers, and researchers.
 

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In the grain boundary diffusion mechanism of electromigration, the electromigration process is retarded if the grain sizes are too small. For instance, the increased time to failure of Al-4 wt. % Cu alloy over pure Al in electromigration [1] can be explained by the difference of grain growth rates. In Al-4 wt. % Cu alloy, the grains are initially small and thus the ions remain essentially immobile to migration, resulting in enhanced component life.

The failure distribution function for the lines, G_sp(t), can be given by [2],

         ---------------------- [2894a]
where,
         N_p -- The number (=w/d) of parallel units,
         N_s -- The number of units which is approximately equal to the line length divided by the grain size, l/d.
         ---------------------- [2894b]

f(z) is described and given on page 2887.

When the grain size is less than the linewidth, multiple failure units across the width of the line can occur at a failure site because w/d > 1.

Figure 2894 shows the calculated MTTF as a function of the ratio of the line width and the grain size.  As the ratio of the linewidth to the grain size decreases, MTTF decreases to a minimum and then increases exponentially.

Figure 2894. The calculated MTTF as a function of the ratio of the line width and the grain size. Adapted from [2]

[1] William C. Mcbee, and John A. Mccomb, Grain Growth in Thin Aluminum-4% Copper Alloy Films, Thin Solid Films, 30 (1975) 137-143.
[2] Cho, J. and Thompson, C. V., Grain size dependence of electromigration-induced failures in narrow interconnects, 54(25), 2577 (1989).