6 Atomic Scale Kinetics of TSV Protrusion
151
1. Prediction criteria for the effect of loading on TSV protrusion profile are summarized:
• Protrusion can be observed when the TSVs are subjected to a compressive
strain ε x , γ xy and ε y . TSVs under pure shear strain γ yx exhibit no protrusion.
• Under a compressive strain ε x , the protrusion profile generally bumps up near
both edges and remains almost flat in the middle of the top surface. The
application of a tensile strain ε y results in bumping up in the middle of the top
surface.
• A larger strain applied near the top end of TSV, a larger protrusion is resulted.
• A symmetric mechanical loading leads to a larger protrusion.
2. Under the same applied loading that produces protrusion, i.e. θ = 150
◦ , the
copper grain microstructure in a TSV controls the protrusion behavior:
• The grains in the top end contribute more to protrusion than the grains below.
• A smaller grain size along the y-direction leads to a higher level of protrusion.
• Under the mechanical loading of ε x , γ xy , a larger grain size along the xdirection results in a higher protrusion.
• With the application of ε y , a larger grain size along the x-direction produces
a lower level of protrusion.
3. A higher temperature results in a larger TSV protrusion.
4. TSVs with smaller sidewall roughness R a and wavelength λ a exhibit larger
protrusions.
6.7.3 A Viewpoint from Plastic Flow
A different viewpoint from plastic flow [29] can provide a visual guide to understand
the protrusion behavior. By connecting the initial and final positions of the atoms,
the flow field can be plotted as shown in Figs. 6.20b, e. With the loading θ = 150
◦ ,
the flow field can be considered as two components: one component moves the
atoms upwards/downwards and leads to protrusion/intrusion, and the other component rotates the atoms and results in local deformation. The magnitude of “disordered" in the flow field can be characterized by vorticity, i.e., curl of the velocity
∇ × u. Figure 6.20c, f plot the magnitude of vorticity |∇ × u|. Larger “disordered"
region with substantial vorticity is found in Fig. 6.20f. Heterogeneous local deformation occurs in the “disordered" region by means of GB migration or dislocation
motion. Larger local deformation produced in the TSV meant that fewer atoms moved
upwards and results in a lower protrusion, as shown in Fig. 6.20a, d.
151
1. Prediction criteria for the effect of loading on TSV protrusion profile are summarized:
• Protrusion can be observed when the TSVs are subjected to a compressive
strain ε x , γ xy and ε y . TSVs under pure shear strain γ yx exhibit no protrusion.
• Under a compressive strain ε x , the protrusion profile generally bumps up near
both edges and remains almost flat in the middle of the top surface. The
application of a tensile strain ε y results in bumping up in the middle of the top
surface.
• A larger strain applied near the top end of TSV, a larger protrusion is resulted.
• A symmetric mechanical loading leads to a larger protrusion.
2. Under the same applied loading that produces protrusion, i.e. θ = 150
◦ , the
copper grain microstructure in a TSV controls the protrusion behavior:
• The grains in the top end contribute more to protrusion than the grains below.
• A smaller grain size along the y-direction leads to a higher level of protrusion.
• Under the mechanical loading of ε x , γ xy , a larger grain size along the xdirection results in a higher protrusion.
• With the application of ε y , a larger grain size along the x-direction produces
a lower level of protrusion.
3. A higher temperature results in a larger TSV protrusion.
4. TSVs with smaller sidewall roughness R a and wavelength λ a exhibit larger
protrusions.
6.7.3 A Viewpoint from Plastic Flow
A different viewpoint from plastic flow [29] can provide a visual guide to understand
the protrusion behavior. By connecting the initial and final positions of the atoms,
the flow field can be plotted as shown in Figs. 6.20b, e. With the loading θ = 150
◦ ,
the flow field can be considered as two components: one component moves the
atoms upwards/downwards and leads to protrusion/intrusion, and the other component rotates the atoms and results in local deformation. The magnitude of “disordered" in the flow field can be characterized by vorticity, i.e., curl of the velocity
∇ × u. Figure 6.20c, f plot the magnitude of vorticity |∇ × u|. Larger “disordered"
region with substantial vorticity is found in Fig. 6.20f. Heterogeneous local deformation occurs in the “disordered" region by means of GB migration or dislocation
motion. Larger local deformation produced in the TSV meant that fewer atoms moved
upwards and results in a lower protrusion, as shown in Fig. 6.20a, d.