Applied Physics Express 5 (2012) 016602
DOI: 10.1143/APEX.5.016602

Microwave Atomic Force Microscopy: Quantitative Measurement
and Characterization of Electrical Properties on the Nanometer Scale
Lan Zhang, Yang Ju, Atsushi Hosoi, and Akifumi Fujimoto
Department of Mechanical Science and Engineering, Nagoya University, Nagoya 464-8603, Japan
Received September 22, 2011; accepted December 1, 2011; published online December 21, 2011
In this paper, we report a noncontact and quantitative method of evaluating and characterizing electrical properties with a nanometer-scale spatial
resolution. Microwave atomic force microscopy (M-AFM) can be used to obtain the topography and microwave image of materials in one scanning
process simultaneously. Under the frequency modulation (FM) AFM mode, we successfully applied M-AFM to create a microwave image of a Au
nanowire with a spatial resolution of 170 nm. Moreover, based on the analytical and explicit expressions proposed, M-AFM can implement thequantitative evaluation and characterization of the local conductivity of materials on the nanometer scale.
# 2012 The Japan Society of Applied Physics

tomic force microscopy (AFM)1,2) has played an
important role in nanoscale science and technology.
Recently, several attempts based on atomic force
microscopy have been made to characterize the electricalinformation of materials on the nanometer scale, such as
conducting atomic force microscopy (C-AFM),3) scanning
capacitance microscopy (SCM),4) and electrostatic force
microscopy (EFM).5) Although C-AFM can be used for thenanoscale electrical characterization of thin ﬁlms, it is only
suitable for measuring conducting materials, and the contact
between the scanning AFM tip and the sample surface may
cause scratch damage to the sample. SCM can be used tocharacterize electrical properties by measuring the capacitance between the tip of the probe and the sample. However,it suﬀers from a limited spatial resolution and is sensitive
to the thickness of the specimen. EFM, including Kelvinprobe force microscopy (KFM),6) scanning surface potential
microscopy (SSPM),7) and scanning Maxwell-stress microscopy (SMM),8) can be used to measure the surface
electrical potential of materials by detecting the electrostaticforce between the probe tip and the sample. However, theresults are aﬀected by the sample surface chemistry andatmospheric conditions, since the van der Waals forces andchemical bonding forces cannot be excluded during themeasurement.
On the other hand, microwave measurements have been of
great interest to many researchers because microwaves canpropagate easily in air, and the sample response is directly
related to the electrical properties of the material.9) A varietyof microwave methods with well-calibrated instruments
have been developed to obtain the microscopic electricalinformation.10–16) However, to evaluate the electrical properties of materials using microwaves, it is necessary to keep
the standoﬀ distance between the microwave probe and thesample constant because microwave signals in the near-ﬁeld
are extremely sensitive to this distance.
Recently, we proposed a novel microwave atomic force
microscopy (M-AFM).17–21) By combining the advantagesof AFM with microwave-based measurement, M-AFM has
the ability to sense the topography and microwave image
simultaneously with a high spatial resolution. Although thepossibility of evaluating the conductivities of metallic materials has been quantitatively demonstrated,21) the measurement of the distribution of the conductivities and the quan-AE-mail address: ju@mech.nagoya-u.ac.jp

titative evaluation of the conductivities from microwave
images have not been realized yet. Thus, in this work, thequantitative measurement of the local conductivity ofsamples is realized by applying a newly proposed analyticaland explicit evaluation equation.
An undoped GaAs wafer was used as the substrate of the
M-AFM probe to restrict the attenuation of microwaves in it.
To obtain the desired structure, wet etching was used to fabricate the M-AFM probe.18) To make the microwave signals
propagate well in the probe, two Au ﬁlms were deposited on
the top and bottom surfaces of the probe by electron beam(EB) evaporation to form a parallel-plate waveguide. Bothplane surfaces of the probe, which are evaporated Au ﬁlms,
are connected at the end of the probe cantilever. However,there is no Au ﬁlm on the sides of the M-AFM probe.
Finally, a nanoslit at the tip of the probe was fabricated by afocused ion beam (FIB) process, from which the microwave
emits.
Figure 1(a) shows schematically the integrated measurement system of M-AFM. In our M-AFM system, the initial
microwave signals working at a frequency of 16.66 GHz are
generated with a microwave generator. Then, the frequencyof the microwave signal is extended by a six-time frequency
multiplier, resulting in a stable operational frequency of
94 GHz. The microwave signal transmits through an isolator
and a circulator and propagates into the M-AFM probe. The
M-AFM probe consists of a homogeneous parallel plate and ananoslit that cuts across the tip apex. These special structures
allow microwave signals to propagate through the probe andemit from the tip of the M-AFM probe. When the M-AFM
probe is located above a sample surface, the nanoslit on the
tip acts as a transmitter of microwave signals emitted onto
the surface of the sample and as a receiver of the microwave signals reﬂected from the measured sample. Finally, adetector connected to the circulator measures the microwave
signals received by the tip of the probe and indicates thevoltage converted from the reﬂected microwave signals.
The measured signals are synchronized with the position
information obtained from the AFM scanner to create themicrowave image. Figure 1(b) shows the measured widthand height of a single Au nanowire on a glass substrate to be
480 and 210 nm, respectively, as obtained with M-AFM. The
Au nanowires were formed by partially etching the Au ﬁlm
using FIB with a width of 500 nm and a space of 400 nm,
where the Au ﬁlm was coated on a glass-wafer substrate of
200 nm thickness by EB evaporation. Figure 1(c) shows the016602-1# 2012 The Japan Society of Applied Physics

Appl. Phys. Express 5 (2012) 016602

L. Zhang et al.

The two undetermined constants k0 and b0 can becalibrated with two samples whose conductivities are known.
For good conductors, which are used in this experiment,
the surface reﬂection coeﬃcient23) js j can be written as24)

pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 
 1  =j!"0 
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ;ð2Þ
js j ¼ 
1 þ =j!"0 
where "0 and  represent the permittivity of free space andthe conductivity of the measured material, respectively, and! is the angular frequency of the microwave. For semiconductor or isolating materials, similar equations can also
be constructed.9,24) Then, the conductivity can be determinedfrom eq. (2) as
Microwave atomic force microscopy setup and typical surface
topography and microwave image of a nanowire sample: (a) schematic
graph of the AFM compact microwave instrument setup and schematic
diagram of the Au nanowires scanned using the M-AFM probe;(b) topography image of measured sample; (c) microwave image of the
nanowire created from the voltage of the measured microwave signals;(d) crossing proﬁle corresponding to the arrow in the topography image;(e) crossing proﬁle of the selected area in the microwave image.
Fig. 1.

microwave image of the Au nanowire, where the voltage wasmeasured from the reﬂected microwave signal without
calibration. The M-AFM worked in frequency modulation(FM) mode (noncontact mode). The measurements were
performed in air ambient, with a working environment
temperature of 26.0  C and a relative humidity of 50%. The
scanning area and scanning speed were 1:5  1:5 m2 and
500 nm/s, respectively. In Fig. 1(e), it is noted that thediﬀerence in the measured voltages of the Au and glass
substrate is approximately 16 mV, and the spatial resolution
is 170 nm. This result illustrates that M-AFM is capable ofsensing the microwave image of a nanostructure. In contrast
to the traditional four-point method, which requires some
nanowires to be in suitable positions for conductivity
measurements by dispersing the nanowires onto an insulated
substrate with electrode arrays, M-AFM can spot thenanostructures directly and measure the microwave image
and topography simultaneously.
For quantitative measurement, the operating frequencyof M-AFM is set at 94 GHz. The high-frequency microwaves are easy to propagate in the waveguide and emit fromthe nanoslit on the probe tip. Since the width of the nanoslit isaround 100 nm, the ﬁeld of microwave interacting with themeasured materials can be considered to be in the 100 nm
order. Thus, if the thickness of the measured materials islarger than 100 nm, the reﬂection from the bottom surface ofthe sample can be neglected. Therefore, only the reﬂection
from the top surface needs to be considered. Moreover, thediode detector works in a small signal range, where it isconsidered to be a square-law detector.22) Therefore, while
keeping the standoﬀ distance between the tip of the M-AFM
probe and samples constant, the output reﬂected voltage V ,which varies only with the conductivity of the sample, has arelationship with the squared absolute value of the top surface
reﬂection coeﬃcient js j2 as
V ¼ k0 js j2 þ b0 :

ð1Þ ¼ !"04js j2  ðjs j2 þ 1Þ2
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ:
ðjs j2 þ 1Þ 4js j2  ðjs j2  1Þ2  4js j2

ð3Þ

After k0 and b0 in eq. (1) are calibrated using two
reference samples with known conductivities, the conductivities of any sample can be calculated from the measured
voltage.
It should be noted that eqs. (2) and (3) are derived
under the plane wave condition, while the probe works innear-ﬁeld mode. Although near-ﬁeld analysis may further
improve the precision of evaluation results, it requires morereference samples, which will increase the complexity ofthe measurement. Since the tested material was very close
to the open end of the probe tip (the standoﬀ distance ofseveral nanometers was extremely small as compared withthe waveguide width (100 nm) and the wavelength), thisproblem can be equivalent to the case that the material
surface is terminated at the end of the waveguide, which
can be represented by the plane wave model. Therefore, theplane wave approximation is used in this work.
Five diﬀerent metallic ﬁlms (Cu, Pb, Al, Co, and Zn) wereprepared by EB evaporation method for the quantitative
measurement. The tested electrical conductivities by thefour point probe van der Pauw method were obtained as thestandard values for calibration and evaluation of M-AFM
results. The tested electrical conductivities of these metalﬁlms are in the range of 4:46  106 to 5:68  107 S/m. The
scanning area was 2  2 m2 , and the scanning speed was
1 m/s. Before scanning, we set the original voltage to be zero
while maintaining a constant distance of 2.6 m between theprobe tip and the sample. During the scanning process, thestandoﬀ distance between the probe tip and samples was ﬁxed
at several nanometers using the atomic force, and the voltage corresponding to the inspected sample was measured.
Figures 2(a)–2(e) show the topographies and microwave
images of the ﬁve samples. The variations of the measured
voltages for the ﬁve samples are less than 0:46 mV, which
is much smaller than the dynamic range of the M-AFM.
The signal-to-noise ratio of the M-AFM measurements wasevaluated to be 20.14 dB on average. The Fig. 2(f ) shows thevariation margins of measured local voltages for samples with
diﬀerent conductivities. Using the measured voltages of two
samples obtained from Figs. 2(a) and 2(b) (4.89 mV for Cu
and 18.01 mV for Pb on average) and their tested conductivities (5:68  107 S/m for Cu and 4:46  106 S/m for Pb) for
calibration, the two undetermined constants in eq. (1) were
calculated to be k0 ¼ 5:9632 and b0 ¼ 5:9629. Then, theconductivities of Al, Co, and Zn samples were evaluated with

016602-2# 2012 The Japan Society of Applied Physics

Appl. Phys. Express 5 (2012) 016602

L. Zhang et al.

Fig. 3. Evaluated conductivities of the samples in comparison with tested
conductivities of them.

Fig. 2. (a)–(e) Clockwise from the top-left corner, topographies and
M-AFM images of Cu, Pb, Al, Co, and Zn samples; (f ) variation margins ofmeasured local voltages for samples with diﬀerent conductivities.

eqs. (1) and (3) by using the measured voltages obtained from
Figs. 2(c)–2(e). Figure 3 shows the evaluated results versus
the tested values of Al, Co, and Zn samples.
It is noted from Figs. 2(a)–2(e) that no correlation can beobserved between the microwave images and their corresponding geometry images. In other words, the variations of
the measured local voltages are not caused by the surface
morphology. The main causes of error bars of the evaluatedconductivities are as follows. Firstly, the ﬁlm samples
prepared by EB evaporation were not homogenous in the
microscopic view, and the distribution of conductivity
was location dependent (local conductivity). It is believedthat the variation margins of measured local voltages [seeFig. 2(f )] by M-AFM caused the error bars of the evaluatedconductivities. Secondly, the microwave signal for conductivity measurement was very small, which might beaﬀected by the measurement environment. Therefore, theuncertainty of the microwave measurement may contributeto the error bars. It is also noted from Fig. 3 that thedeviation of evaluated conductivities from the values testedby the van der Pauw method is 2.03, 7.24, and 11.6% for
the Zn, Co, and Al, respectively. One of the causes ofthis deviation is that the standoﬀ distance variation between
diﬀerent materials may aﬀect the measured voltage, thereby
inducing deviation of evaluated conductivity, especially forhigh-conductivity materials such as Al. Another cause of thedeviation may be the evaluation equation which was derived
under the plane wave approximation rather than the much
more complicated near ﬁeld analysis. The quantitativeevaluation was performed three times, and similar results
as shown in Fig. 3 were obtained.
By maintaining a constant standoﬀ distance between theprobe tip and sample surface and measuring the microwave
signal interaction with the sample, both the topography andelectrical properties of the sample were imaged by M-AFM

simultaneously. A microwave image of a Au nanowire was
successfully created with a resolution on nanometer order.
We also demonstrated a novel evaluation equation andcalibration technique for the quantitative measurement of thelocal conductivity. Our results demonstrate that M-AFM canbe used to quantitatively measure, in situ, the distribution ofelectrical properties on the nanometer scale.

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