82
P. Kumar et al.
Fig. 4.9 Cross sections of Cu-filled TSVs in: (a) the as- received state, showing a zone of large
grains in the center surrounded by smaller grains; and (b) after annealing, showing an expanded
central zone with large grains [29]
the drawbacks of this kind of model is clear. First, although the mechanical analysis
is conducted directly on copper microstructure, the microstructure is assumed to
remain unchanged during the mechanical loading process. Second, the plastic deformation mechanisms at the atomic scale, e.g. the motion of dislocations, have not been
considered. However, the dislocation involved processes such as recovery, recrystallization and grain growth have been reported to occur in electrodeposited copper
and can significantly influence its mechanical properties [48]. Recrystallization has
also been suspected to account for the copper-pumping phenomenon [15, 36, 49].
Considering the limitation of the current modeling techniques, more robust simulation methodologies that take into account the polycrystalline nature of Cu TSVs
and their complex deformation and stress relaxation mechanisms are needed [36].
Section 4.4 will introduce atomistically-informed modeling techniques to address
this limitation.
4.3.1.3 Metal Pumping: Extrusion or Intrusion of TSVs
During service and consequent thermal cycling, the CTE mismatch between Cu
and Si results in residual stresses in each material (σ Cu , σ Si ), as well as significant
interfacial shear stresses (T i ) near the extremities of the via. The induced stresses,
if high enough, may cause plastic deformation of the filler [39, 47, 50, 51] with the
differential straining between Cu and Si sometimes accommodated by interfacial
sliding [52–54]. This results in extrusion (and sometimes, intrusion) of Cu relative
to the Si. Generally, the extrusion of the Cu occurs due to plastic deformation of the
metal near the via-ends (typically, towards the top or mouth of the via), and can be
enhanced by creep and grain boundary sliding. Two examples of this phenomenon
are illustrated in Fig. 4.12.
P. Kumar et al.
Fig. 4.9 Cross sections of Cu-filled TSVs in: (a) the as- received state, showing a zone of large
grains in the center surrounded by smaller grains; and (b) after annealing, showing an expanded
central zone with large grains [29]
the drawbacks of this kind of model is clear. First, although the mechanical analysis
is conducted directly on copper microstructure, the microstructure is assumed to
remain unchanged during the mechanical loading process. Second, the plastic deformation mechanisms at the atomic scale, e.g. the motion of dislocations, have not been
considered. However, the dislocation involved processes such as recovery, recrystallization and grain growth have been reported to occur in electrodeposited copper
and can significantly influence its mechanical properties [48]. Recrystallization has
also been suspected to account for the copper-pumping phenomenon [15, 36, 49].
Considering the limitation of the current modeling techniques, more robust simulation methodologies that take into account the polycrystalline nature of Cu TSVs
and their complex deformation and stress relaxation mechanisms are needed [36].
Section 4.4 will introduce atomistically-informed modeling techniques to address
this limitation.
4.3.1.3 Metal Pumping: Extrusion or Intrusion of TSVs
During service and consequent thermal cycling, the CTE mismatch between Cu
and Si results in residual stresses in each material (σ Cu , σ Si ), as well as significant
interfacial shear stresses (T i ) near the extremities of the via. The induced stresses,
if high enough, may cause plastic deformation of the filler [39, 47, 50, 51] with the
differential straining between Cu and Si sometimes accommodated by interfacial
sliding [52–54]. This results in extrusion (and sometimes, intrusion) of Cu relative
to the Si. Generally, the extrusion of the Cu occurs due to plastic deformation of the
metal near the via-ends (typically, towards the top or mouth of the via), and can be
enhanced by creep and grain boundary sliding. Two examples of this phenomenon
are illustrated in Fig. 4.12.