Chemistry Reference
In-Depth Information
m
2
45
◦
-slanted slit defect. (
b
) Inverted current density,
calculated from the MFM measurement in (
a
). From
left
to
right
, the panels correspond to the
AFM topography of the sample, the parallel current density component, the perpendicular current
density component, and the total current density. In the image of
J
total
, the color scale was chosen
so that the brightest color corresponds to 3.9, the darkest to 0 (in units of current density that
have been normalized to the reference current density far from the slit); the scale for the vertical
component
J
y
Fig. 5.11
(
a
)MFMimageof(1
×
9)
μ
J
par
is similar (since to lowest order, the current flow is parallel to the line); the
scale for the horizontal component
J
perp
=
J
x
is such that the brightest (darkest) color corresponds
to 1.6 (
−
1
.
6). Since the raw MFM data is normalized to the signal from a uniform reference
region far from the defect, the inversion is composed of relative values (that can be scaled by the
known current density in the reference region, if so desired). (
c
) Topography of the slit defect.
(
d
) Finite-element calculation of the expected current density, based on the topography in (
c
). The
color scale of each panel is equivalent to that of the corresponding panel in the inversion of (
b
).
The maximum (normalized) calculated current density is 4.4
=
“true” signal would suggest that our results should be interpreted as a lower bound
of the extent of the current crowding behavior. Errors associated with imperfect
deconvolution will tend to make our results systematically low, but the
10% dis-
crepancy between the inversion and the calculation for the slanted slit is also due
to the physical issues associated with a real sample. In particular, the “softer,” more
−
