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34 SMT Magazine • February 2015
dipoles with energy –pE in the driving them in
the region of stronger field E. It is important that
the energy gain due to formation of a polarized
metal needle does not depend on the field sign
as illustrated in Figure 3. The dipole vector p is
parallel to the field vector E, so the product –pE
is negative. Another wording would be to say
that like charges repel producing an outward
stress. It is relieved by expelling some of these
charges outward via creating a metal whisker
with the expelled charge sitting at its far end.
These nucleation events take place most easily
where the metal surface is locally weak.
eLeCTrOSTaTIC MeCHaNISM OF NuCLeaTION aNd GrOWTH OF MeTaL WHISKerS continues
Feature
It is worth mentioning that the existence of
strongly anisotropic stretched (needle-shaped)
metallic particles is due to their strong polariza-
tion gain in the external electric field. In turn,
that gain is a consequence of their large dipole
moments due to considerable dipole length. As
a result, long enough particles become ener-
getically favorable in the external field in spite
of the fact that their surfaces are much great-
er than that of an equivalent volume sphere.
The needle-shaped metallic particles dominate
when the field is greater than a certain critical
value as illustrated in Figure 4. This consider-
ation provides a physical mechanism of the very
existence of extremely high aspect ratio metal
whiskers not collapsing into spherical shapes of
equivalent volumes. Their energetically favor-
able shapes are dictated by the existing electric
fields. According to this understanding, whis-
kers would inevitably collapse into spherical-
like shapes in the absence of external electric
fields.
4. Following the nucleation is the growth
stage where whiskers increase their length by
accretion of material at their bases. The growth
kinetics are different for whisker lengths below
and above the characteristic charge patch di-
mension L. In particular, growth rates turn out
to be extremely low for short (h<