Chemistry Reference
In-Depth Information
Fig. 5.9
(
a
) Topography and MFM phase of line containing 1
μ
m
×
1
μ
m notch: 20
μ
m
×
20
μ
m
image of a 10
μ
mlinewitha1
μ
m
×
1
μ
m notch on one side. This line is carrying a 33mA current,
10
6
A/m
2
current density.
Left
: AFM topography (
z
-range: 350 nm).
Right
:
Corresponding MFM phase measured with 200 nm linear lift height (
z
-range: 1
corresponding to a 3
.
3
×
0
◦
). (
b
)MFM
.
phase line scans from line containing 1
m notch. The
bold gray line
is an MFM scan
measured perpendicular to the line and across the notch center, averaged over a 0
μ
m
×
1
μ
msegment
(12 out of 512 line scans), while the
thin dark line
is an MFM reference away from the notch.
(
c
) Model of current distribution in line containing 1
μ
m
×
1
μ
m notch.
Bottom inset bar graph
:
model current density profile along the conductor width, normalized to the base uniform current
in a normal, homogenous line; the 10
μ
m line width is divided into five segments, each a bundle
of infinitesimally thin, infinitely long wires.
Graphed curve
: calculated MFM signal at the notch
center, using the current density distribution shown in the inset. The calculated peak asymmetry is
about 1.5
.
5
μ
5.3.3 Deconvolution Procedure
Analysis of the MFM signals to determine the current distributions around defects
requires that the instrumental broadening effect due to the tip size is removed. Since
the tip is a real physical object, often in the form of an etched silicon pyramid
with a magnetic Co/Cr coating, the three-dimensional tip response function tends
to be narrow close to the tip apex and broadens higher up, toward the tip base. The
three-dimensional response function can be reduced to an effective two-dimensional
tip response. The measured MFM signal,
D
(
x, y, z
), obtained at tip height
z
is a
three-dimensional (3D) instrumental convolution
