College Park, MD 20742
3
Department of Physics, University of Maryland, Baltimore Country, MD 20742
ABSTRACT
We demonstrate Magnetic Force Microscopy (MFM) imaging, at room temperature in
air, of a 0.25mA DC current path in a 140nm-wide gold nanowire. The nanowire was created by
focused ion beam milling of a 12
µm wide Cr/Au line of 20nm/110nm Cr/Au thickness. Iterative
fitting of the MFM data to an idealized model of the structure yielded a nanowire resistivity a
factor of 3.5 higher than that of a control Cr/Au region which was unaffected by the ion beam
processing. MFM imaging of an ion-implant patterned line shows current deflection around the
implant region.
INTRODUCTION
We have previously demonstrated the ability of Magnetic Force Microscopy (MFM) to
perform relative quantification [1,2] and observe current behaviors in conducting lines [3].
Additionally, a fully rigorous analysis involving both image deconvolution and inversion has
been achieved and will be presented in future work [4,5]. Although our analysis has previously
been limited to micron-scale current line widths, extension of these techniques to nanoscale
devices and structures with spatial variations in resistivity is highly desirable. The key issues in
making this extension are the conflicting demands of the sensitivity and spatial resolution needed
to resolve nanoscale current paths.
Nanoscale resolution of MFM has been demonstrated for magnetic films [6-9]. However,
the fields around nanoscale conducting lines containing nondestructive DC current densities are
weak (typically <<mT) and thus require a relatively large magnetic tip volume to achieve
sufficient signal to noise. Furthermore, the MFM response for standard vertical tip
magnetization consists of sharp peaks of opposite polarity at the edges of the line, which result in
mutual attenuation when the line width is less than the instrumental broadening due to the tip
size. For example, with typical commercial MFM tips, such as the Digital Instruments MESP-
HM tip, the magnetic film coats the entire tip pyramid (of about 8
µm height and 8µm base)
resulting in a large magnetic volume but limited spatial resolution. Given the long-range nature
of the weak magnetic interaction between the MFM tip and current-carrying line, it will clearly
push the limits of the present instrumental capability to resolve current paths at the nanoscale.
We will here demonstrate measurements at the scale of 100 nm width wires, using a commercial
MFM operated in air. The limits determined here may be improved with higher resolution tips,
with more selectively placed magnetic coatings [6-9], although gains in spatial resolution are
likely to be offset by smaller signal sensitivity. The loss of sensitivity could be compensated, at
least in part, by performing the measurement in vacuum and/or at low temperature to increase the
sensitivity to the magnetic interaction [10]. However, such instruments have not yet been
demonstrated for current-carrying devices, which are subject to the difficulties discussed above,
as well as generating heat due to power dissipation.
G5.6.1
Mat. Res. Soc. Symp. Proc. Vol. 738 © 2003 Materials Research Society EXPERIMENTAL DETAILS
Experiments were performed using a Digital Instruments Multimode, operated in tapping
(intermittent non-contact) mode with standard MFM phase detection. The signal detected is
proportional to the curvature of the magnetic field component perpendicular to the sample plane,
integrated over the magnetic tip volume. The magnetic tips used are commercially available
Co/Cr coated Digital Instruments MESP-HM tips, magnetized along the tip axis, perpendicular
to the sample surface. All magnetic phase data is interpreted relative to a known reference
standard, thereby avoiding the need for exact knowledge of the tip magnetization.
The nanowire sample, shown in Fig. 1, was fabricated using a combination of standard
photolithography, liftoff, and focused-ion beam (FIB) milling techniques. The Cr/Au metal line,
chosen for chemical and physical stability, was 12
µm wide, as defined by lift-off. The thickness
of the Cr was 20nm, and the Au was 110nm. Additional structures, such as the (2x6)
µm
2
rectangular defects were fabricated by FIB milling [11]. The lower rectangular defect was
milled to leave a 140nm conducting line width on the left edge of the line. Ion milling was
performed with 50 kV Ga
+
ions using a Micrion 2500 FIB machine with a 5 nm beam column. A
serpentine beam scanning procedure and relatively low (~30 pA) ion current were chosen to
provide a better defect shape.
MFM measurements were made with typical currents in the individual lines of 30mA,
corresponding to current densities on the order of 2-5
×10
6
A/cm
2
. To exclude topographical
artifacts, the MFM phase measurements were performed in Digital Instruments Interleave Linear
Lift Mode, using a lift height of 200nm (which corresponds to a separation of 110nm between
the tip and the top surface of the Cr/Au line). To exclude phase response due to electrostatic
forces, the potential between the tip and sample was nulled by an external voltage divider, as
discussed in previous work [1,2].
DISCUSSION
The nanowire can be seen in the lower left of the topographic image of Figure 1a. The
effect of the nanowire is not immediately apparent in the MFM image to the left of Fig. 1b,
which shows the expected MFM contrast at the line edges where the magnetic field must curve
into or out of the sample plane. There is significantly higher contrast at the inner edge of the
rectangular defects than at the line edge on the side opposite the defect, due to a nonuniform,
localized increase in current density, discussed in previous work [3]. Figure 1b presents a close-
up of the 140nm line. Halfway through the image scan, the current in the line was reversed and
the expected reversal in MFM signal polarity was observed. A separate image of the
topography, taken with a non-magnetic, topography-specific OTESP tip, has yielded a nanowire
width of 140nm and a remainder (region not milled away) line width of 6
µm. Given the known
total current of 40mA flowing through the structure and the relative line widths of the nanowire
and the wire, we may estimate that 2.3% of the total current, or 0.9mA is flowing through the
line. This value is likely to be an upper estimate, since the nanowire suffered damage during the
ion milling and is probably more resistive than the rest of the line. At a current of 1mA and a
tip-sample separation of about 100nm, this nanowire would produce a field of 0.5mT, a field
gradient of 4900 T/m, and a field curvature of 7x10
10
T/m
2
. Although the nanowire line width is
140nm, the peak centers of the MFM signal shown are separated by approximately 180nm,
G5.6.2 Figure 1: 140nm nanowire created by focused ion beam milling
a) The 12
µm wide, 130nm thick Cr/Au line contains (2x6) µm
2
notches where the corners
have varying radii of curvature. In the bottom notch, the milling left a 140nm conducting
line width. The total current in the 12
µm line is 40 mA.
b) The polarity in the MFM signal of the close-up of the nanowire changes as the current is
reversed, confirming that the signal is due to current flowing through the nanowire. The
apparent physical line width is larger than the actual 140nm width due to tip convolution
effects.
demonstrating limits in magnetic spatial resolution resulting from the large tip size and tip-
sample separation.
The relative MFM signal strength at the 140 nm line and in the defect-free part of the
12
µm line can be used to determine the relative current levels in the two lines. This in turn may
be used to deduce the relative resistivity change due to processing techniques such as the focused
ion beam milling performed on this sample. Given a simple sample configuration and barring
the need to extract a full two-dimensional map of the current distribution, the unprocessed MFM
data may be interpreted by iterative fitting to a simple model.
The model consists of a 140nm wide line parallel to a 6
µm wide line and separated by
6
µm, assumed to be infinitely long with uniform current density and thus analytically calculable.
The nanowire is sufficiently far from the 6
µm line that it is negligibly affected by the
inhomogeneous current density in the larger line. To deduce the current running in the wire, the
calculation was convolved with an estimated two-dimensional instrumental response function.
G5.6.3 Using an average of 15 line scans, corresponding to a 1.2
µm line segment length, yields the
signal shown as the thick gray line in Fig. 2a. The nanowire signal appears as a small feature
near 15
µm and the signal from the 6µm wide remainder segment of the line is located between
20
µm and 30 µm. A portion of the line sufficiently far from the nanowire region is used as a
reference for signal normalization. The experimental ratio of MFM peak heights is
MFM
nano
=0.062MFM
ref.
To evaluate the amount of current flowing through the nanowire, the
current density in the nanowire is adjusted until the shape and relative amplitude of the forward
convolution is as consistent as possible with the actual data. Using a resistivity 3 times that of
the remaining line (e.g. assuming a current density three times smaller than the value of 0.9 mA
deduced from geometrical consideration), we obtain the forward convolution of Fig. 2a, where
the data is the thick gray line and the forward convolution is the thin black line; the theoretical
ratio for this scenario is MFM
nano
=0.072MFM
ref
. Using a resistivity of 4 yields curves of similar
shape and magnitude, with a ratio of MFM
na