6 Atomic Scale Kinetics of TSV Protrusion
143
Table 6.1 Loading distributions on the left and right edges
Model no.
Left edge
Right edge
MLA1
θ = 120 ◦
Zero stain
MLA2
θ = 120 ◦
θ = 135 ◦
MLA3
θ = 120 ◦
θ = 150 ◦
MLA4
θ = 120 ◦
θ = 120 ◦
MLA5
θ = 135 ◦
θ = 120 ◦
MLA6
θ = 150 ◦
θ = 120 ◦
MLA7
Zero strain
θ = 120 ◦
6.4 Effect of Grain Structures
This section focuses on the effect of grain structures and the corresponding loading
condition is referred to Fig. 6.1, i.e., a mixture of normal strain ε x and shear strain
γ xy , unless otherwise specified.
6.4.1 Grain Distribution
According to Messemaeker et al., the protrusion height shows a statistical correlation
to the grains near the TSV top end [2, 9]. It was reported that a greater number of
grains in the top end led to a higher protrusion, which contributed more to both
the protrusion profile and height than the grains below. In this subsection, the PFC
model simulations considering the effect of the grains in the top end will provide an
evidence supporting the experimental finding.
The protrusion behavior of twenty TSV samples with random initial grain structures are studied, among which ten contain the same two grains in the top layer, while
the rest contain three grains. The data of mean protrusion are calculated and plotted
by the solid circles in Fig. 6.13. It is observed that the protrusion height scatters
around the same level when the grains in the top layer remain the same, independent of the random grain structures below. The simulation result agrees well with
the experimental result of Messemaeker et al. [2, 9]: the protrusion behavior is more
closely related to the grains in the top end than other grains below. In addition, the
protrusion profiles exhibit similar characteristics as long as the grains in the top layer
remain unchanged.
143
Table 6.1 Loading distributions on the left and right edges
Model no.
Left edge
Right edge
MLA1
θ = 120 ◦
Zero stain
MLA2
θ = 120 ◦
θ = 135 ◦
MLA3
θ = 120 ◦
θ = 150 ◦
MLA4
θ = 120 ◦
θ = 120 ◦
MLA5
θ = 135 ◦
θ = 120 ◦
MLA6
θ = 150 ◦
θ = 120 ◦
MLA7
Zero strain
θ = 120 ◦
6.4 Effect of Grain Structures
This section focuses on the effect of grain structures and the corresponding loading
condition is referred to Fig. 6.1, i.e., a mixture of normal strain ε x and shear strain
γ xy , unless otherwise specified.
6.4.1 Grain Distribution
According to Messemaeker et al., the protrusion height shows a statistical correlation
to the grains near the TSV top end [2, 9]. It was reported that a greater number of
grains in the top end led to a higher protrusion, which contributed more to both
the protrusion profile and height than the grains below. In this subsection, the PFC
model simulations considering the effect of the grains in the top end will provide an
evidence supporting the experimental finding.
The protrusion behavior of twenty TSV samples with random initial grain structures are studied, among which ten contain the same two grains in the top layer, while
the rest contain three grains. The data of mean protrusion are calculated and plotted
by the solid circles in Fig. 6.13. It is observed that the protrusion height scatters
around the same level when the grains in the top layer remain the same, independent of the random grain structures below. The simulation result agrees well with
the experimental result of Messemaeker et al. [2, 9]: the protrusion behavior is more
closely related to the grains in the top end than other grains below. In addition, the
protrusion profiles exhibit similar characteristics as long as the grains in the top layer
remain unchanged.