6 Atomic Scale Kinetics of TSV Protrusion
153
6.8 Future Work
As discussed above, the PFC model can provide abundant microstructural information complementary to experimental results and can be considered as a useful
microstructural modeling tool for the 3D TSV-based integration. However, future
work on the following aspects can be considered.
Grain boundary engineering (GBE) [30] is the first direction worthy of further
studies. GBE has been applied to improve the bulk properties and performance of
polycrystalline materials. As an example, Lu et al. proposed to optimize strength
and ductility of Cu by identifying the structural characteristics for GBs, i.e., generating coherent boundaries through control of pulsed electrodeposition processing
parameters [31, 32]. Motivated by the experimental studies of nano-Cu by Lu et al.
[32], including coherent GBs, e.g., twin boundaries, in the PFC model can control
the mechanical properties of Cu filler in TSV. Through this approach, an optimized
structure may be found to alleviate the dilemma of TSV protrusion.
Secondly, more detailed and rigorous analysis on the PFC simulation results
are needed, in particular, quantitative descriptions of the microstructural evolution.
Quantitative rather than qualitative descriptions are desirable, including GB mobility, diffusion-controlled creep, grain growth mechanisms and triple junction motion
as discussed by Gottstein [33]. Quantitative and in-depth analysis on the result of the
atomic scale simulations can help to further clarify the origin of the TSV protrusion.
Thirdly, the complex-amplitude expansion of PFC models (APFC) developed by
Goldenfeld et al. can be used to simulate materials processing and behavior at larger
scales [34, 35]. The method is based on a renormalization group theory to express the
atomic density function, i.e., order parameter in the PFC models, providing coarse
graining in both time and space in a single framework. APFC model focuses on the
amplitudes of the atomic probability density which vary on a larger length scale than
the atomic spacing, which makes the using of adaptive meshes possible. It is reported
that the largest system of the APFC model can deal with ∼ 8 × 10
6 atoms, with a
mean volume of ∼ (45 nm)
3 for Cu [36]. In addition, the coarse-grain APFC model
are shown to govern the elastic and plastic deformation of crystal by the introduction
of a deformation field in the complex amplitude [37, 38]. This may be another way
to introduce loading besides the “penalty term" approach used in this chapter.
Finally, using the so-called structural PFC (XPFC) model can deal with multicomponents and multi-phases systems. For example, Greenwood et al. used XPFC
model to study the solute segregation in a two-component alloy with structurally
different phases, including 2D triangle lattice and square lattice [39]. In TSV applications, interfaces, e.g., Cu/TiN, Cu/Ta, Cu/TaN, and Cu/SiO 2 , are important for
mechanical reliability. On the other hand, controlling the additives in electrode position Cu in TSV can mitigate the protrusion behavior [40] and this effect can be
studied using the XPFC model as well.
Acknowledgements The authors acknowledge financial support from the National Natural Science
Foundation of China (NSFC) under grant 51832002 and the Guangdong Natural Science Foundation
153
6.8 Future Work
As discussed above, the PFC model can provide abundant microstructural information complementary to experimental results and can be considered as a useful
microstructural modeling tool for the 3D TSV-based integration. However, future
work on the following aspects can be considered.
Grain boundary engineering (GBE) [30] is the first direction worthy of further
studies. GBE has been applied to improve the bulk properties and performance of
polycrystalline materials. As an example, Lu et al. proposed to optimize strength
and ductility of Cu by identifying the structural characteristics for GBs, i.e., generating coherent boundaries through control of pulsed electrodeposition processing
parameters [31, 32]. Motivated by the experimental studies of nano-Cu by Lu et al.
[32], including coherent GBs, e.g., twin boundaries, in the PFC model can control
the mechanical properties of Cu filler in TSV. Through this approach, an optimized
structure may be found to alleviate the dilemma of TSV protrusion.
Secondly, more detailed and rigorous analysis on the PFC simulation results
are needed, in particular, quantitative descriptions of the microstructural evolution.
Quantitative rather than qualitative descriptions are desirable, including GB mobility, diffusion-controlled creep, grain growth mechanisms and triple junction motion
as discussed by Gottstein [33]. Quantitative and in-depth analysis on the result of the
atomic scale simulations can help to further clarify the origin of the TSV protrusion.
Thirdly, the complex-amplitude expansion of PFC models (APFC) developed by
Goldenfeld et al. can be used to simulate materials processing and behavior at larger
scales [34, 35]. The method is based on a renormalization group theory to express the
atomic density function, i.e., order parameter in the PFC models, providing coarse
graining in both time and space in a single framework. APFC model focuses on the
amplitudes of the atomic probability density which vary on a larger length scale than
the atomic spacing, which makes the using of adaptive meshes possible. It is reported
that the largest system of the APFC model can deal with ∼ 8 × 10
6 atoms, with a
mean volume of ∼ (45 nm)
3 for Cu [36]. In addition, the coarse-grain APFC model
are shown to govern the elastic and plastic deformation of crystal by the introduction
of a deformation field in the complex amplitude [37, 38]. This may be another way
to introduce loading besides the “penalty term" approach used in this chapter.
Finally, using the so-called structural PFC (XPFC) model can deal with multicomponents and multi-phases systems. For example, Greenwood et al. used XPFC
model to study the solute segregation in a two-component alloy with structurally
different phases, including 2D triangle lattice and square lattice [39]. In TSV applications, interfaces, e.g., Cu/TiN, Cu/Ta, Cu/TaN, and Cu/SiO 2 , are important for
mechanical reliability. On the other hand, controlling the additives in electrode position Cu in TSV can mitigate the protrusion behavior [40] and this effect can be
studied using the XPFC model as well.
Acknowledgements The authors acknowledge financial support from the National Natural Science
Foundation of China (NSFC) under grant 51832002 and the Guangdong Natural Science Foundation