Chemistry Reference
In-Depth Information
Fig. 5.8
(
a
) Optical photograph of a sample containing a 3
m slot, created by pho-
tolithography, thermal evaporation, and liftoff. (
b
) Schematic of the circular field around a single
wire and a cartoon of a rectangular metal line being modeled as bundle of infinitesimally thin
wires. (
c
) Contour plot of the curvature of the vertical component of the magnetic field from a wire
of rectangular cross section, modeled as shown in (
a
). (
d
) Line scan from the contour plot in (
c
),
taken 100 nm above the wire top surface
μ
m
×
40
μ
procedure and relatively low ion current (
∼
30 pA) were chosen to provide better
control of slit shape.
5.3.2.1 Demonstrating MFM Current Detection
For the purposes of intuitively understanding the MFM phase images, we may per-
form a simple analytical calculation of the expected vertical field curvature, where
the metal lines are modeled as bundles of infinitely long, infinitesimally thin wires,
as shown in the schematic of Fig.
5.8
b. Such systems possess two-dimensional sym-
metry and may be easily integrated. For simple systems where the current flows
along lengths that are long compared to characteristic tip dimensions, this model is
quite accurate. We may therefore solve for the magnetic field around the conduc-
tor, by integrating the magnetic field contributions of infinitesimally thin, infinitely
long wires over the cross-sectional area of the conductor. The expected MFM phase
signal can then be calculated by taking the second vertical spatial derivative of the
magnetic field. The resulting magnetic field lines must curve around the current
lines, and the vertical component of the magnetic field thus varies greatly across the
width of the wire, from zero along the middle of the line to a maximum at the edges,
