(a) Fast and slow grains generated randomly. Fast grains are indicated with a line through the middle. (b) Diffusivities values generated from a normal mixture (fast and slow) of diffusion activation energies.
Finite Element solution to the nonlinear and linear SEM equations. The nonlinear solution [solid curve, Eq. (15)] using the MATLAB routine ODE45 and the linear solution [dashed curve, Eq. (15) with Eq. (21)].
Comparison of FEM solutions to the linearized equation with a variety of mesh sizes ranging from around to .
Close up of one region of Fig. 3.
The nucleation time distribution (solid curve) for linear model (not lumped) compared to that obtained by a two-exponential lumped, MoM approximation (dashed-curve). and copper parameters as indicated in text. separate interconnects are simulated.
A lumped element model of the interconnect. Each mesh interval is approximated by a C–R–C -element. For most calculations here an element is of length of around .
Same as Fig. 5. The “true” nucleation time, solving the linear (not lumped) equation, Eq. (24), plotted against the two-exponential approximation Eq. (40).
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