5 Phase-Field-Crystal Model: A Tool for Probing Atoms in TSV
123
(a)
(b)
(c)
(d)
Fig. 5.8 Nucleation of void near a triple junction in an electromigration process [35]
5.3 PFC Model for TSV
5.3.1 Triangle Lattice
In general, the one-mode PFC model can describe the BCC lattice, e.g., W, and 2D
triangle lattice. The first PFC model was put forward by Elder et al. [36, 37], and
this model was also called the original PFC model.
For a triangle lattice in 2D case, the order parameter n has the form:
n = n 0 + φ
1
2
cos
2qy
√
3
− cos(qx) cos
qy
√
3
(5.38)
where q =
√
3/2 minimizing the free energy. Then, the free energy functional F tri
can be written as:
123
(a)
(b)
(c)
(d)
Fig. 5.8 Nucleation of void near a triple junction in an electromigration process [35]
5.3 PFC Model for TSV
5.3.1 Triangle Lattice
In general, the one-mode PFC model can describe the BCC lattice, e.g., W, and 2D
triangle lattice. The first PFC model was put forward by Elder et al. [36, 37], and
this model was also called the original PFC model.
For a triangle lattice in 2D case, the order parameter n has the form:
n = n 0 + φ
1
2
cos
2qy
√
3
− cos(qx) cos
qy
√
3
(5.38)
where q =
√
3/2 minimizing the free energy. Then, the free energy functional F tri
can be written as: