Chemistry Reference
In-Depth Information
Fig. 5.14
Rectangular defects of variable width. (
a
) The sample topography includes notches 2-
μ
m. (
b
) Corresponding MFM image. (
c
) Inverted current
density, calculated from the MFM measurement in (
a
). From
left
to
right
, the panels correspond
to 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 1.3, the darkest to 0 (in units of current density that have been normalized to the
reference current density far from the defects); the scale for the horizontal component
J
perp
m wide, with lengths of 1, 0.5, and 2
μ
=
J
x
is such that the brightest (darkest) color corresponds to 0.1 (
−
0
.
1)
m
2
, and (1
m
2
μ
m-wide lines are shown in
Fig.
5.14
a, b. The corresponding inverted current density of this sample is shown
in Fig.
5.14
c, with respective maximum (normalized) current density of 1.10, 1.29,
and 1.29. The value of 1.1 is less than expected, which is likely due to incomplete
deconvolution. The current density for both the 1 and 0
×
2)
μ
rectangular notches of 12-
μ
.
5
μ
m notches is clearly
higher than that of the 2
m notch, as expected. For the two shorter notches, the
dipole-like appearance of the perpendicular component of the current density also
appears to be sharper than the longer notch, which indicates that the change in cur-
rent path is more abrupt. The inverted current density of the shortest 0
μ
.
5
μ
m notch
μ
is equivalent to that of the larger 1
m notch. The similarity of the current density
around the two defects occurs because their crowding behaviors are dominated by
the defect edges.
5.3.5.4 Effect of Feature Sharpness
As noted above, the lack of abrupt boundaries in physical structures may account
for reduced current crowding in physical structures as compared with calculations
for perfectly sharp boundaries. To address such effects, a set of (6
m
2
notches
with corners of varying radii of curvature was fabricated in a current line. The notch
corners were fabricated with radii of curvature
R
×
2)
μ
m, as shown
in Fig.
5.15
. The inverted current density of the sample containing the notches
with radii of curvature of
R
=
1
.
0 and 0
.
05
μ
=
.
=
.
μ
m yields respective maximum
normalized current densities of 1.94 and 1.97. The current density at the rounded
corner is not distinguishable from that at the sharp corner, above the random noise
intrinsic to the measurement, and the systematic error introduced by the analy-
sis techniques. Since any focused ion beam damage corresponding to the dosage
1
0 and
R
0
05
