Chemistry Reference
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factor of 30 increase in the force on kink site atoms at the island edge compared to
a free Ag atom. Using a quantum perspective rather than a classical perspective will
be important in fully quantifying the nature of such nanoscale defects [
2
,
60
-
62
].
5.3 Direct Observation of Current Distribution
As noted above, current crowding near defect structures is expected to play an
important role in determining the nature of electron scattering and the electromi-
gration force. At the nanoscale, the direct characterization of current distributions is
difficult. However, the classical electrostatic principles governing current flow are
independent of scale. Thus observations of current crowding at the micron scale can
be used to assess the classical limits of behavior at the nanoscale.
Here we demonstrate quantification of spatial distributions of current flow by
measurement of the magnetic fields above current-carrying structures using mag-
netic force microscopy (MFM). The effects of defect shape and size are character-
ized by systematically fabricating different structural defects using lithography and
focused ion beam milling. The structures were chosen to represent typical defects
observed in technological electromigration failures and to provide an evaluation of
the effects of defect aspect ratio, pitch, and rounding on the patterns of deflected
current.
5.3.1 Magnetic Force Measurements
In AFM [
63
,
64
] and all related techniques (MFM, EFM, LFM, etc.), properties of
the sample are deduced from the behavior of a small tip-cantilever system interact-
ing with the sample. A tip, typically some etched silicon or silicon nitride pyrami-
dal structure (see Fig.
5.7
a), is attached to a cantilever, typically between 50 and
200mm in length, that has a reflective coating on the top surface. The behavior of
this cantilever may be tracked by monitoring the position of a laser beam reflected
off the top reflective side of the cantilever, usually with some photodiode-based
detector.
The tapping (also known as “intermittent contact” or “non-contact”) AFM tech-
nique involves tracking the amplitude of the cantilever, driven in oscillation on (or
near) resonance, as its tip passes over the sample under study. As the cantilever is
brought near to a sample, its tip eventually begins to tap the surface, dissipating
energy and changing the vibrational amplitude of the tip. As the tip is scanned over
the sample surface, the feedback loop changes the height of the tip-cantilever to
keep this oscillation amplitude fixed. This tip height is recorded as a function of
position generating the topography of the sample. Tapping AFM is less damag-
ing and more sensitive than earlier contact AFM techniques, where a passive tip
is dragged across the surface and the deflection of the cantilever is the feedback
