Chemistry Reference
In-Depth Information
rounded line/defect edges are not accurately described by the present calculation,
which assumes perfectly sharp edges; there is also a 50-100 nm skin of ion beam-
damaged, higher resistance material surrounding the defect which should physically
reduce the sharpness of the crowding.
Various structural characteristics of the slit defect contribute to its influence on
local current. To better understand the current crowding effect, we may qualitatively
decouple the structure's effects into a current direction changing component and a
geometric component, which are discussed in the following sections.
5.3.5.2 Effect of Change of Current Direction
Conductive structures which induce large changes in current direction, such as inter-
connect vias and bends, are likely to exhibit significant current crowding, even
though they are not defects per se. This effect is particularly important for indus-
trial applications because all integrated circuits incorporate many bends and vias to
increase the device density on chips. To illustrate this crowding effect, topography
and MFM measurements were performed on a metallic line with a 90
◦
bend, as
shown in Fig.
5.12
a, b. Once again, there is clear evidence of spatial variation in
the current density, specifically strong variations in the MFM signal near the cor-
ners of the structure. These data were deconvolved and inverted using the methods
described above, to obtain a quantitative image of the current density variations, as
shown in Fig.
5.12
c. From left to right, the panels correspond to the current density
y
-component, the current density
x
-component, and the total current density.
Fig. 5.12
90
◦
bend in metallic line. (
a
) Topography of the 90
◦
corner. (
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 1.74, the darkest to 0 (in units of current density that
have been normalized to the reference current density far from the corner); the scale for
J
y
(where
the line is oriented at
45
◦
with respect to the
y
-axis) is similar; the scale for
J
x
is such that the
brightest (darkest) color corresponds to
J
max
sin 45
◦
(
±
J
max
sin 45
◦
). The inversion is composed
of relative values (that can be scaled by the known current density in the reference region, if so
desired)
−
