6 Atomic Scale Kinetics of TSV Protrusion
147
Fig. 6.16 Plot of the mean
protrusion versus
temperature. The grain
structure and loading
condition are defined in
Fig. 6.5c
and a transition to Nabarro-Herring creep occurs as the temperature increases [20,
21]. Both the diffusional creep and dislocation creep contribute to the protrusion and
lead to a larger protrusion at temperatures higher than 320
◦ C.
6.6 Effect of Geometry
6.6.1 TSV Shape
In this section, the effects of TSV shape on defect motion are discussed. The TSV
shapes considered include a rectangle, a trapezoid, and an hourglass, as illustrated
in Fig. 6.17. Why such geometries exist are referred to [22]. Note that irrespective
of the geometry, all the models are set with the same initial condition, although
some of the grains may be truncated by the constraint from a specific geometry.
To investigate the effect of TSV geometry on defect motion, the number of mobile
defect atoms are recorded, which is referred to as DAs hereinafter. The larger the
number DAs is, the faster the defects diffuse. Figure 6.17 plots the number of DAs
versus time in the three kinds of TSVs. As time goes on, the mobile defects either
diffuse to the edges of the TSVs and become immobile, or are absorbed by the GBs.
Figure 6.17 clearly shows that DAs in the rectangle TSV is the largest among the
three geometries, which suggests that the defects diffuse with the fastest rate in the
rectangle TSV. A possible explanation is that the ratio of the perimeter over the area
of the TSV, is what influences the diffusion rate of the defects. It is calculated that
the ratio of perimeter to area is 0.008, 0.011, and 0.014 for rectangle, trapezoid,
and hourglass TSVs, respectively. The larger the ratio is, the higher the density of
defects are clustering at boundaries, where mobile defects become immobile. It can
147
Fig. 6.16 Plot of the mean
protrusion versus
temperature. The grain
structure and loading
condition are defined in
Fig. 6.5c
and a transition to Nabarro-Herring creep occurs as the temperature increases [20,
21]. Both the diffusional creep and dislocation creep contribute to the protrusion and
lead to a larger protrusion at temperatures higher than 320
◦ C.
6.6 Effect of Geometry
6.6.1 TSV Shape
In this section, the effects of TSV shape on defect motion are discussed. The TSV
shapes considered include a rectangle, a trapezoid, and an hourglass, as illustrated
in Fig. 6.17. Why such geometries exist are referred to [22]. Note that irrespective
of the geometry, all the models are set with the same initial condition, although
some of the grains may be truncated by the constraint from a specific geometry.
To investigate the effect of TSV geometry on defect motion, the number of mobile
defect atoms are recorded, which is referred to as DAs hereinafter. The larger the
number DAs is, the faster the defects diffuse. Figure 6.17 plots the number of DAs
versus time in the three kinds of TSVs. As time goes on, the mobile defects either
diffuse to the edges of the TSVs and become immobile, or are absorbed by the GBs.
Figure 6.17 clearly shows that DAs in the rectangle TSV is the largest among the
three geometries, which suggests that the defects diffuse with the fastest rate in the
rectangle TSV. A possible explanation is that the ratio of the perimeter over the area
of the TSV, is what influences the diffusion rate of the defects. It is calculated that
the ratio of perimeter to area is 0.008, 0.011, and 0.014 for rectangle, trapezoid,
and hourglass TSVs, respectively. The larger the ratio is, the higher the density of
defects are clustering at boundaries, where mobile defects become immobile. It can