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36 SMT Magazine • February 2015
in some local regions, the further energy gain
can be achieved via the diameter increase (i.e.,
whiskers get thicker intermittently with the pe-
riods of faster length increase). A snapshot of
many such whisker lengths and diameters will
therefore show broad statistical distributions
that are mutually uncorrelated.
Figure 7 illustrates the process of whisker
growth in a 2D fashion where the color coding
is such that upward and downward local elec-
tric field directions are shown in respectively
red and blue. The sign fluctuations of the field
at large distances shown in Figure 5 do not
eliminate the polarization energy gain. Indeed,
consider a long metal whisker as a succession of
many small metal rods, each occupying a small
range of more or less constant field. They have
local dipole moments p=aE, and partial electro-
static energies pE=aE2 that are quadratic in field
and do not cancel each other. Taking into ac-
count the explanation in Figures 3 and 5, it is
intuitively clear that the maximum polarization
and electrostatic energy gain are achieved for
the "color-matched" whiskers (all in blue or all
in red). The corresponding pathways for whis-
ker growth can be kinked in order to collect as
many as possible color matched regions. This
explains how whiskers can be kinked. It should
be noted however that each kink entails certain
deformation energy loss, so the whisker geom-
etry will optimize between the gain in electro-
static energy and loss in deformation energy
due to kinking. (These subtle features remain
unaccounted quantitatively in the current elec-
trostatic whisker theory.) Furthermore, some
configurations of color-matched regions pres-
ent pathways parallel or partially parallel to the
surface; this explains the observed longitudinal
or circumferential striations shown in dash in
Figure 7.
6. In the course of growing at h>>L, whis-
kers encounter rare local regions of abnormally
low electric fields where its further growth is
blocked. The blockage is due to the fact that
further growth in these low field regions can-
not overweigh the energy loss due to increase in
surface area: the latter increase presents a signifi-
Figure 6: Sketch of the whisker growth rates vs.
time. Solid lines represent the two limiting cases
within the domains of their applicability (h<