122
J. Liu et al.
(a)
(b)
(c)
(d)
Fig. 5.7 An example of magnetic field induced phase transition: (a) t = 0, (b) t = 100,000, (c)
t = 103,000, and (d) t = 200,000 [33]. An external field H is applied after t = 100,000
∂n
∂t
= ∇
2 δF
δn
= ∇
2 δ(F + F EM )
δn
∇ · (σ 0 ∇V ) = 0
(5.37)
where σ 0 is conductivity and the electric field evolution is assumed to follow the
electrostatic condition because the electromigration-driven atom migration is a rather
slow process.
Figure 5.8 shows an atomic-scale void nucleation near a triple junction in an
electromigration process that occur during interconnect failure [35].
J. Liu et al.
(a)
(b)
(c)
(d)
Fig. 5.7 An example of magnetic field induced phase transition: (a) t = 0, (b) t = 100,000, (c)
t = 103,000, and (d) t = 200,000 [33]. An external field H is applied after t = 100,000
∂n
∂t
= ∇
2 δF
δn
= ∇
2 δ(F + F EM )
δn
∇ · (σ 0 ∇V ) = 0
(5.37)
where σ 0 is conductivity and the electric field evolution is assumed to follow the
electrostatic condition because the electromigration-driven atom migration is a rather
slow process.
Figure 5.8 shows an atomic-scale void nucleation near a triple junction in an
electromigration process that occur during interconnect failure [35].