6 Atomic Scale Kinetics of TSV Protrusion
135
6.3 Protrusion Under Different Mechanical Loading
Conditions
The stress and strain states in TSVs are complex and closely related to the random
structures of Cu grains [12, 13]. Meanwhile, experimentally characterization is facing
difficulties in the microscale TSVs considering all the loading conditions combining
all possible microstructural configurations. In this section, the protrusion behavior of
Cu-TSVs under different loading conditions is investigated. Note that the loading is
firstly assumed to be uniformly distributed along the edges of the TSV for simplicity
and inhomogeneous loading distribution will be discussed in Sect. 6.3.4. The effect
of grain structure will be discussed in the next section.
6.3.1 Shear Strain γ yx
When the TSV is under pure shear strain γ yx , no protrusion is observed. Following
the shear direction, the atoms diffuse in the x-direction and the dislocations move
to the left or right edges of the TSV. As an example, the coordinates of the trajectory of a dislocation under the shear strain is recorded in Fig. 6.4. The direction
of the shear loading is switched at t = 5000 and t = 10000 and this results in the
dislocation moving in the opposite x-direction. It is observed that the dislocation
does not immediately respond the direction switch of the shear loading, instead after
a lag in time, the dislocation then moves following the shear direction. Note that
the dislocation also moves along the positive y-direction, but the displacement along
y-direction is much smaller than that along x-direction during t = 0 − 5000. In addition, the TSV is of a high aspect ratio structure, which means that the dislocations are
likely to reach the left and right edges under the shear strain γ yx , instead of to the top
surface and resulting in the protrsuion. Furthermore, the atoms near the top end are
observed to move along the x-direction, motivated by the “penalty term" in Eq. 6.3.
Consequently, the pure shear strain γ yx does not contribute to the TSV protrusion
and will not be discussed further in the following sections.
6.3.2 Normal Strain ε x and Shear Strain γ x y
Various combinations of strains ε x and γ xy that could occur on the left and right edges
of TSV are studied by controlling the direction of loading θ , as shown in Fig. 6.5c.
As an example, the loading with θ = 180
◦ indicates a pure compressive strain ε x ,
while θ = 150
◦ represents a mixture of a compressive strain ε x and a shear strain
γ xy .
The relationship between the TSV protrusion and loading direction θ is plotted
in Fig. 6.6, wherein θ varies systematically from 0 to 360
◦ . The result shows that
135
6.3 Protrusion Under Different Mechanical Loading
Conditions
The stress and strain states in TSVs are complex and closely related to the random
structures of Cu grains [12, 13]. Meanwhile, experimentally characterization is facing
difficulties in the microscale TSVs considering all the loading conditions combining
all possible microstructural configurations. In this section, the protrusion behavior of
Cu-TSVs under different loading conditions is investigated. Note that the loading is
firstly assumed to be uniformly distributed along the edges of the TSV for simplicity
and inhomogeneous loading distribution will be discussed in Sect. 6.3.4. The effect
of grain structure will be discussed in the next section.
6.3.1 Shear Strain γ yx
When the TSV is under pure shear strain γ yx , no protrusion is observed. Following
the shear direction, the atoms diffuse in the x-direction and the dislocations move
to the left or right edges of the TSV. As an example, the coordinates of the trajectory of a dislocation under the shear strain is recorded in Fig. 6.4. The direction
of the shear loading is switched at t = 5000 and t = 10000 and this results in the
dislocation moving in the opposite x-direction. It is observed that the dislocation
does not immediately respond the direction switch of the shear loading, instead after
a lag in time, the dislocation then moves following the shear direction. Note that
the dislocation also moves along the positive y-direction, but the displacement along
y-direction is much smaller than that along x-direction during t = 0 − 5000. In addition, the TSV is of a high aspect ratio structure, which means that the dislocations are
likely to reach the left and right edges under the shear strain γ yx , instead of to the top
surface and resulting in the protrsuion. Furthermore, the atoms near the top end are
observed to move along the x-direction, motivated by the “penalty term" in Eq. 6.3.
Consequently, the pure shear strain γ yx does not contribute to the TSV protrusion
and will not be discussed further in the following sections.
6.3.2 Normal Strain ε x and Shear Strain γ x y
Various combinations of strains ε x and γ xy that could occur on the left and right edges
of TSV are studied by controlling the direction of loading θ , as shown in Fig. 6.5c.
As an example, the loading with θ = 180
◦ indicates a pure compressive strain ε x ,
while θ = 150
◦ represents a mixture of a compressive strain ε x and a shear strain
γ xy .
The relationship between the TSV protrusion and loading direction θ is plotted
in Fig. 6.6, wherein θ varies systematically from 0 to 360
◦ . The result shows that