Chemistry Reference
In-Depth Information
electromagnetism that govern the current flow are scale invariant, experimental
micron-scale observations can be used to illuminate nanoscale phenomena.
5.2 Direct Observation of Surface Electromigration
The nature of electron scattering at the internal surfaces of a conductor is illustrated
in Fig.
5.1
[
34
]. The specular scattering expected for perfectly flat surfaces will lead
to electromigration forces on any atoms that are free to diffuse on the surface. In
addition, the presence of defects, which have different scattering cross sections and
different local electric fields, can enhance scattering leading to an enhanced surface
resistivity. In the following we will describe the use of direct observations of diffu-
sion biased by an applied current to quantify the magnitude of the electromigration
force, and thus the underlying charge scattering characteristics of the defects.
Fig. 5.1
Schematic illustration of current flow adjacent to a surface with defects in the form of
steps. Enhanced scattering from step sites at the surface is suggested by the
arrows
that represent
the direction of motion of the charged carriers. The inset illustrates a lattice model of kinked
(thermally roughened) step edge segments of horizontal extent
L
o
=
13
a
, with six single and
one double height kinks [
34
]
5.2.1 Surface Electromigration and Surface Resistivity
The presence of the electromigration force introduces a small bias in the diffusion
of atoms on the surface, parallel to the current (and field). By convention, this bias
can be expressed as an energy difference between atoms diffusing parallel or anti-
parallel to the current
Z
∗
e
E
a
, where
E
is the electric field applied to the
U
=
sample,
Z
∗
is the effective valence of a diffusing atom, and
a
is the atomic lattice
