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Ultimate High Conductivity of Multilayer Graphene Examined byMultiprobe Scanning Tunneling Potentiometry on Artiﬁcially Grown
High-Quality Graphite Thin Film
Hiroyuki Mogi,† Takafumi Bamba,† Mutsuaki Murakami,‡ Yuki Kawashima,‡ Masamichi Yoshimura,§
Atsushi Taninaka,† Shoji Yoshida,† Osamu Takeuchi,† Haruhiro Oigawa,† and Hidemi Shigekawa*,††

Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305-8573, Japan
Materials Solutions New Research Engine, KANEKA Corporation, Osaka 566-0072, Japan§
Graduate School of Engineering, Toyota Technological Institute, Nagoya 466-8511, Japan

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‡

S Supporting Information*

ABSTRACT: With the discovery of graphene, the excellent characteristics of graphite (multilayer graphene), such as high thermal and electric
conductivities, heat resistance, and chemical stability, have also been
attracting considerable attention again. However, the production of alarge-area (>0.1 × 0.1 m2) graphite thin ﬁlm with uniformly high electric
conductivity, which will be indispensable in industrial applications, hasbeen diﬃcult because of its breakage occurring during the growth process.
Recently, we have succeeded, for the ﬁrst time, in growing large-area highquality graphite ﬁlms with thicknesses from ∼0.5 to ∼3 μm by anindustrial method, providing a fundamental platform for examining andutilizing the intrinsic and ultimate characteristics of such a material. Here,as a step toward realizing such eﬀorts, we performed microscopic
measurements of electric conductivity by the method of multiprobe
scanning tunneling potentiometry we have developed. Using the resistivity
along the c-axis, ρc = 1.72 ± 0.04 mΩ·m, which was directly measured for the ﬁrst time, we determined the resistivity in the abplane, ρab, to be 0.30 ± 0.01 μΩ·m, indicating that the conductance of the graphite thin ﬁlm we grew is about 1.3 times theprevious highest reported value for the highest grade single-crystal natural graphite with an ideal structure without grainboundaries or wrinkles (0.38 μΩ·m). Both the advantage of multilayer graphene, which is considered to reduce the eﬀect ofgrain boundaries on conductance, and the decrease in conductance as an eﬀect of wrinkles were directly evaluated.
KEYWORDS: multilayer graphene, artiﬁcially grown graphite, high conductivity, multi probe, scanning tunneling potentiometry■

INTRODUCTION

advance these applications, it is highly desirable to develop amethod of industrially obtaining high-quality thin-ﬁlm graphitewith a large area.
Kish graphite and highly oriented pyrolytic graphite(HOPG) are well-known artiﬁcial graphite materials, which
are produced from the liquid phase (molten metal) and the gas
phase, respectively.14−16 Although the obtained materials are ofgood quality, it is diﬃcult to produce large-area (on the orderof 0.1 × 0.1 m2) thin ﬁlms. As a possible means of overcoming
this limitation, a polymer pyrolysis (PP) method for producing
a graphite ﬁlm from the solid phase by heating a polymer ﬁlm
at a high temperature has been extensively studied.17−19 The
PP method was developed in 1986, and many studies havesince been reported on the production of large-area graphite
ﬁlms and large graphite blocks.17,19 However, the thickness ofGraphite is a material that has been used for a long time
because of its excellent properties such as high electric andthermal conductivities, chemical stability, heat resistance, andlow speciﬁc gravity. For example, the carrier mobility in the abplane of graphite is much larger than that of metals (forexample: Cu, 16 cm2/(V·s); graphite basal plane, ∼10000
cm2/(V·s)). Thereby, the electric conductivity of graphite in
the ab-plane, ∼25000 S/cm, is extremely high for anonmetallic material. With the discovery of graphene,1 further
applications of graphite that utilize its outstanding properties
as multilayer graphene, for example, as fabricable electrodematerials for solar cells,2 light-emitting diodes,3 ﬂat panel
displays,4 smart windows,5 touch panels,6 and Li-ion batteries,7in supercapacitors,8,9 and as a superconductor,10−12 have been
actively studied. For a ﬁeld-eﬀect transistor (FET) channel
formed by several layers of MoS2 with a multilayer graphene
electrode prepared by peeling layers from a bulk graphite, ahigh mobility exceeding 104 cm2/(V·s) was achieved.13 To© 2019 American Chemical Society

Received: May 13, 2019
Accepted: August 9, 2019
Published: August 9, 2019
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Figure 1. Sample conditions and schematic illustrations of measurements. (a) Cross-sectional TEM image of a graphite sample. (b) Secondary
electron microscopy (SEM) image. (c) Raman spectra obtained before and after exfoliation. The D peak corresponds to defects. The G peak, whichcorresponds to other factors such as strain and the dopant used, is shown for comparison with the D peak in intensity. (d) FIB−SEM system used
to produce a cross section of graphite ﬁlm and a SEM image of the obtained sample. (e) Setup of the MP-STP measurement. (f) Measurement
sequence.

the graphite thin ﬁlms produced by the PP method has been
limited to the range of 10−50 μm, and their electric andthermal conductivities were lower than those of Kish graphiteand HOPG.20 With decreasing ﬁlm thickness, the shrinkage
and expansion of the graphite thin ﬁlms during the growth
process caused their breakage during the heating process.21
Therefore, the development of new techniques is highly
desirable to produce thinner ﬁlms.
Recently, the industrial growth of large-area high-quality
graphite ﬁlms with thicknesses from ∼0.5 to ∼3 μm has beensuccessfully realized by devising a handling technique formaterials during the growth process,22 which provides afundamental platform for examining and utilizing the intrinsic
and ultimate characteristics of such materials. However, since
the grain size of high-quality graphite ﬁlms prepared by the PP

method is on the order of micrometers, it is necessary to
perform resistivity measurement on a similar scale, which has
not yet been achieved. In general, the resistivity of graphite in
the ab-plane has been measured using the conventional fourterminal method.14,23 When measurement is performed by
reducing the distance of electrodes, methods such as ion beametching and lithography are used to form a one-dimensional(1D) device structure.24,25 Therefore, it is diﬃcult to clarify theeﬀects of such physical and chemical processes on thecharacteristics of graphite. In addition, since graphite haslarge anisotropy between the resistivities in the ab-plane, ρab,and along the c-axis, ρc (ρc/ρab = 2500−550026 for pyrolytic
graphite), the resistivity along the c-axis is an important factor.
However, the resistivity in the c-axis direction has beenmeasured by forming wiring on the surface of the graphite ab1763

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plane,26,27 and its direct measurement has not yet been realized
because it is very diﬃcult to prepare electrodes on the crosssection of thin-ﬁlm graphite by conventional methods such aslithography.
The four-probe method scanning tunneling microscopy(STM) was developed to measure the local electric
conductivity of a sample.28 In this method, four probes arebrought into contact with the sample. Current is allowed to
ﬂow between the two outer probes, and the voltage ismeasured by the two inner probes, similarly to the conventional four-terminal method. It is possible to perform local
measurements without the complicated pretreatment of thesample. However, in general, the four probes come in contact
with the sample.
On the other hand, scanning tunneling potentiometry (STP)
is a method of measuring the local potential below a probe tipthat does not come in contact with the sample.29,30 Current isallowed to ﬂow between the two outer probes, andpotentiometry is performed by using the inner STM probe.
More accurate measurement becomes possible by adding aprobe as a reference electrode (multiprobe STP: MP-STP).
STM observation may also be performed simultaneously withthe potentiometry measurement. However, when MP-STP is
performed on a thin ﬁlm such as graphite, the tip coming incontact with the ﬁlm causes damage. In addition, the current
path becomes three-dimensional (3D), and the direct
measurement of the conductivity in the c-axis direction isrequired, which has not yet been achieved.
Here, we present the results obtained by MP-STP
measurement in combination with the technique of atomic
force microscopy (AFM). Local conductivity measurement was
successfully performed on a 2.7 μm thick graphite ﬁlm grownby the PP method. The resistivity along the c-axis was directly
obtained for the ﬁrst time by MP-STP measurement over across section. The highest conductivity in the ab-plane, whichis ∼1.3 times that of single-crystal natural graphite (SCNG)
and is considered to be an intrinsic and ultimate characteristics
of multilayer graphite, was conﬁrmed for the ﬁrst time.

Figure 1a shows a transmission electron microscopy (TEM)
image of the sample. It can be seen that the layered structure ofgraphite is well formed. Figure 1b shows a scanning electron
microscopy (SEM) image of the sample. The average grain size
estimated by the channeling contrast method32,33 was 7.48 μm.
Figure 1c shows Raman spectra obtained before and after
exfoliation. The D peak, which corresponds to defects,
disappeared after exfoliation, indicating the high quality ofthe sample at the level of Raman evaluation. No millimeterorder wrinkles, which are formed during the growth by the PP
method,22 were detected as D signals in the Raman spectra.
In MP-STP measurements, unlike macroscale sheet
resistance measurements, current is applied from the uppersurface of the sample via an almost ideal point contact.
Therefore, since the current path is an essential factor in theanalysis, it is important to accurately measure the thickness ofthe sample. The graphite ﬁlm was ﬁxed onto a mica substrateby using an epoxy insulating adhesive. After the resistivity ofthe sample in the ab-plane was measured by MP-STP, which
will be explained later, the sample was transferred to thechamber of a focused-ion-beam (FIB) SEM system (Helios
NanoLab 600i, FEI Inc.) schematically shown in Figure 1d.
Then, to expose a clean cross section, the part of the sample
used for the ab-plane measurement was sputtered to a depth of∼3 μm perpendicular to the ab-plane by irradiating the surface
with a focused 30 kV Ga+ ion beam in a vacuum chamber of∼10−5 Pa. A SEM image of the obtained cross section is shownin Figure 1d. Because the contrast in the graphite cross section
and the epoxy part in the secondary electron image was clearly
diﬀerent, as shown in the SEM image in Figure 1d, thethickness of the graphite ﬁlm was successfully determined to be∼2.1 μm. The ρab of this sample which is cut to a 0.01 × 0.01
m2 square measured by the VDP method was 0.427 μΩ·m, thelowest resistivity within the 0.5−3 μm thick ﬁlms fabricated by
the PP method.22
MP-STP Measurement over the ab-Plane. Figure 1eshows the experimental setup of MP-STP. Because layeredmaterials such as graphite are very fragile, it is necessary for theprobe to come in contact with the sample without damaging its
surface when measuring the intrinsic electric conductivity.
Therefore, three conductive AFM (c-AFM) cantilevers (PtIr5coated, spring constant of 0.2 N/m, NANOSENSORS) wereused as the contact probes. The contact between the
cantilevers and the sample was conﬁrmed by measuring the
rapid increase in current. A constant current (Isample) wasapplied from probe 1 to probe 4, and the reference potential
was measured by using probe 3. Because a soft contact by acantilever tends to cause contact resistance ﬂuctuations, aconstant-current source was used instead of a constant-voltage
source when applying a current to the sample. For STM and
STP measurements, a probe made of electropolished tungsten(W) was used (probe 2). All the electric conduction
measurements were performed in a UHV chamber (∼10−7Pa) at room temperature, and the location of the tip apex on
the surface was determined by optical microscopy (working
distance, 25 mm; spatial resolution, ∼1 μm; Keyence Co.,
Ltd.) through the upper-side view port.
For the STM and STP measurements, a laboratory-built
preampliﬁer was used to switch the circuit between thetransimpedance ampliﬁer mode (current measurement mode)and the potentiometer circuit mode (potentiometry mode)through a mechanical relay. Figure 1f shows a schematic of the
STP measurement sequence. First, the preampliﬁer was set to■

RESULTS AND DISCUSSION
Sample Preparation. Cracks and wrinkles forming ingraphite ﬁlms because of their shrinkage and expansion during
the heating process have long been a technical problem.
Generally, when the conventional industrial production
method used for ﬁlms thicker than 10 μm is applied to thefabrication of ﬁlms with thicknesses of <3 μm, the ﬁlms breakand large-area ﬁlms cannot be produced. Recently, we have
improved the method of handling the polyimide (PI)membrane during the heating process, which is called themultipoint-support method and has enabled fabrication ofhigh-quality large-area graphite thin ﬁlms. Square graphite
ﬁlms with one side being 0.1 m and thicknesses from ∼0.5 to∼3 μm were successfully grown (see the Methods section andref 22 for details). As described in refs 17 and 22, although thequality of the sample deteriorates for a ﬁlm with a thickness ofabout 10 μm because of the insuﬃcient graphitization inside
the ﬁlm, graphitization occurs throughout the entire ﬁlm with athickness of about 3 μm or less. Therefore, in this experiment,
measurement was performed by cleaving a sample of ∼2.7 μm
thickness (reduced to ∼2.1 μm by cleaving) whose
conductivity was highest in the ab-plane direction as conﬁrmedby the macroscopic van der Pauw (VDP)31 method.
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Figure 2. Results of MP-STM measurement in the ab-plane. (a) Optical microscopy image of the four probes during the measurement. (b)Topography image on which the grid measurement method was performed (1.5 × 1.5 μm2, tip bias Vt = 20 mV, and set-point current It = 30 pA).
(c) 2D map of ΔΦ/Isample obtained over the surface in (b). The black arrow indicates the line corresponding to the green line in (b). (d) ΔΦ−Isample plot acquired in the black rectangles in (c). (e) Line proﬁle of ΔΦ/Isample along the green line in (b). (f) Line proﬁle of the topographic image
along the green line in (b).

obtained.34 By performing this process at each lattice pointin the image during the STM scan, we obtained a 2D image ofΔΦ/Isample. Hereinafter, this measurement is called gridmeasurement.
The four-point probe method has been used for conductivity
measurement in the past, and the validity of the analysis model
has been conﬁrmed by many measurements.35 In thisexperiment, the AFM technique was used to minimize thecontact force between the tip and the sample to suppress thedamage to the sample, but the mechanism is the same as thatof the previous method. Therefore, analysis can be performed
using the same model.
For a sample with isotropic conductivity, the resistivity ρ canbe represented as

the current measurement mode for STM imaging. Then, thescan was stopped at the measurement point in the image, andthe tunnel resistance was decreased to about 10 MΩ orders byincreasing the set-point current. Thereafter, the preampliﬁer
was switched to the potentiometry mode, and the potential
diﬀerence ΔΦ between the area immediately below the STM
tip and probe 3 was measured.
When the applied current Isample is swept linearly, ΔΦ alsochanges linearly when the sample is metallic. Measurement
errors, the ﬂuctuation of the oﬀset voltage due to such as thethermal electromotive force, can be eliminated by extracting
the slope of ΔΦ/Isample. In addition, nonlinearity wassometimes observed in the current−voltage characteristics
between probe 1 and probe 4 because of the eﬀect of adheredmaterials at the AFM cantilever−sample contact point. This isconsidered to have caused the resistance at the contact point tochange at certain applied voltages. However, the nonlinearchange in resistance at the contact points of probes 1 and 4 canbe eliminated by carrying out potentiometry to measure thepotential diﬀerence ΔΦ between probes 2 and 3 with the fourtip probe method, while the position of probe 2 is changed.
Namely, we can obtain the intrinsic resistivity of the sample bymeasuring ΔΦ generated by the applied constant current
Isample, which is not aﬀected by the nonlinear characteristics ofthe contact points. In fact, a linear ΔΦ−Isample curve, which
reﬂects the metallic characteristics of the sample, wasρ = 2πΔϕIsample1(

1siso,1 − 2− s1
iso,2 − 4

)−(

1
1
− s
siso,1 − 3
iso,3 − 4)(1)

where siso,n−m is the distance between probe n and probe m (n,m: 1, 2, 3, 4) in the isotropic conduction model. To estimate
the resistivity in the ab-plane, it is necessary to obtain ananalytical formula by considering the conduction model (2D
or 3D). The large anisotropy between the resistivity in the abplane and that along the c-axis was converted into the modelwith an isotropic resistivity using the scaling law36,37 in
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Figure 3. Results of cross-sectional MP-STM measurement. (a) Setup of the MP-STP measurement over the cross section. (b) Optical microscopy
image of the upper side of the structure shown in (a). (c) Tapping AFM topographic image of the surface shown in (b). (d) Amplitude image(diﬀerential image) of the topographic image shown in (c). (e) Line proﬁle along the blue line shown in the topography image in (c). (f) 2D
distribution of ΔΦ/Isample obtained by the grid measurement over a scanning range of 800 × 800 nm2. (g) Line proﬁle of ΔΦ/Isample along the xdirection, in which ΔΦ/Isample was averaged in the y-direction.

iiso = iρiρ

direction x of probe 1 was adjusted to be along the directionof Isample. The position of each probe was determined from theoptical microscopy image considering the conﬁguration of thecantilever, and the distances between the probes were
estimated to be s1−2 = ∼9 μm, s2−4 = ∼27 μm, s1−3 = ∼16
μm, and s2−4 = ∼9 μm.
Figure 2b shows a topography image obtained over the area
where the grid measurement was performed (1.5 × 1.5 μm2,
tip bias Vt = 20 mV, and set-point current It = 30 pA), and thevalues of ΔΦ/Isample are shown in Figure 2c in a color scale.
Although measurements at some points are missing in Figure
2c because we could not obtain the linear I−V curves at thosepoints probably because of the ﬂuctuations in the tunnel
junction, atomic layer steps and grain boundaries wereobserved as indicated by the blue and black arrows,
respectively.40 As shown in Figure 2c, ΔΦ/Isample increased
from left to right. The line indicated by the black arrow in
Figure 2c shows the results obtained along the green line in
Figure 2b, and the ΔΦ−Isample plot acquired in the black
rectangles (1 to 3) is shown in Figure 2d. Each curve shows alinear characteristic, indicating that the sample is metallic, andthe slopes of the curves are clearly diﬀerent. The distribution ofΔΦ/Isample will later be discussed in comparison with thecalculated results.
The line proﬁles of ΔΦ/Isample and the topographic image
along the green line in Figure 2b are shown in Figures 2e and2f, respectively. The ΔΦ/Isample plot is not sensitive to thesurface structures; namely, there is no correspondence between
the ΔΦ/Isample plot shown in Figure 2e and the structures of
the atomic layer step and the grain boundary indicated by theblue and black triangles in Figures 2b and 2f. Namely, no
voltage drop was observed at the grain boundaries.
Cross-Sectional STP Experiment and Analysis. To
experimentally obtain ρc, we performed MP-STP measurement
over a cross section, as schematically shown in Figure 3a (seethe Methods section for details). Figure 3b shows an optical
microscopy image of the upper side of the structure shown in
Figure 3a. While applying a constant current through the Cu
plates, the STM probe was made to approach the graphite(i = x , y , z )ρ = 3 ρab 2 ρc(2)where (x, y, z) and (xiso, yiso, ziso) represent the axes in thematerial with an anisotropic resistance and those in theconverted space with an isotropic resistance, respectively. The
x- and y-axes are in the ab-plane, and the z-axis corresponds tothe c-axis direction. For a typical ratio of the electric
conductivity of graphite (ρc/ρab = ∼500026), when the length
in the ab-plane and that along the c-axis are multiplied by 0.24
and 17, respectively, the model can be transformed into a
rectangular model with an isotropic conductivity. Whether the
conduction model is 2D or 3D is determined by the ratio of
L′1−4 (distance between probe 1 and probe 4 after scaling) to t′(the thickness of graphite after scaling); the model becomes
3D when t′/L′1−4 > 0.75.38,39 In this experiment, by use of L1−4
= 23 μm and t = 2.1 μm, the ratio is t′/L′1−4 = 8.82 (L′1−4 = 5
μm, t′ = 44.1 μm), and a 3D model was employed. Finally, theanalytic equation of the 3D conduction model considering theelectric conductivity anisotropy between ρab and ρc is expressed
as
ij
jj
Δϕ
j
ρab = jjjj2π
jj Isample
j
k

yz
zz
zz 1
zz
zz ρ
zz c
{
2

1

(

1
s1 − 2

− s

1
2−4

)−(

1
1
− s
s1 − 33−4)(3)where sn−m is the actual distance between probe n and probe m(n, m: 1, 2, 3, 4). By applying the coordinate transformation ofeq 2 to the interprobe distance siso,n−m in eq 1, and substituting
ρ of eq 2 into eq 1, we obtain eq 3, which represents a modelof the sample with anisotropic conductivity. Experiments were
performed to obtain ρab by measuring ρc and the otherparameters.
Figure 2a shows an optical microscopy image of the four
probes during the measurement. As the current Isample ﬂows
from probe 1 to probe 4, ΔΦ between probe 2 and probe 3
was determined by a grid measurement. The scanning
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Figure 4. Experimental and calculated results ρab. (a) Histogram of ρab calculated using ΔΦ/Isample obtained at each grid point in Figure 2c. (b)Scaling model from the original structure with high anisotropic resistivity (left) to the structure with isotropic resistivity. (c) 2D distribution ofΔΦ/Isample shown in Figure 2c. (d) ΔΦ/Isample obtained by calculation.

cross section under observation with an optical microscope,and ΔΦ between the STM probe and the cantilever located in
the Ag epoxy part was measured by STP.
Figure 3c shows a topographic image of the surface shown in
Figure 3b obtained before the STP measurement by tapping
AFM in the constant-amplitude mode. Figure 3d shows theamplitude image (diﬀerential image) of the topographic image,in which each edge region is clearly determined. The deep
groove between the graphite and the silver epoxy on the left
side is clearly observed. Figure 3e shows the line proﬁle along
the blue line shown in the topography image in Figure 3c. It
was conﬁrmed that the graphite part had a very ﬂat crosssection with a roughness of <3 nm. The slope observed on
both sides is considered to have been formed during the
cutting process.
Figure 3f shows the 2D distribution of ΔΦ/Isample obtainedby grid measurement over a scanning range of 800 × 800 nm2.
The scan direction x was parallel to the current direction. The
feedback conditions were Vt = −3 mV and It = 10 pA. The
topography image was acquired simultaneously with the STP
measurement, and the cross-sectional surface was conﬁrmed tobe very ﬂat (roughness p−p < 3 nm). ΔΦ/Isample was measured
on each grid point by measuring ΔΦ while changing Isample
stepwise between −9 and +9 mA. In this experiment, nononlinearity was observed in the current−voltage characteristics at the contact point because of the formation of a wide
contact area; therefore, ΔΦ was obtained from the diﬀerence
between the two points (−9 and +9 mA). ΔΦ/Isample increases
from left to right. The values averaged in the y-direction are
shown in Figure 3g. The linearity was conﬁrmed, from which
the slope of ΔΦ/(Isampled) was obtained to be 2.45 ± 0.05 V
A−1 m−1, where d is the length of the measured area along thex-direction. Therefore, ρc can be obtained from the simple 1D
conduction model as

ρc =

SΔϕ
Isampled(4)

where S, the area over which the graphite sample was measured
by optical microscopy, was estimated to be 0.703 mm2. As
shown in Figure 3a, a constant current was applied between
the electrodes attached to both sides of the sample, and thevoltage drop between them was measured by the four-probe
method. Because the size of the ab-plane of the sample used is
1 mm × 0.7 mm, and the bulk part is very large compared withthe edge area, the current that ﬂowed on the bulk side isconsidered to be approximately equal to the applied constantcurrent Isample. As a result, ρc was determined to be 1.72 ± 0.04mΩ·m.
Next, ρab was estimated from the data obtained from eq 3
and the value of ρc. Figure 4a shows a histogram of ρab
calculated using the value of ΔΦ/Isample obtained at each grid
point in Figure 2c by measuring the relationship shown in
Figure 2d. From the peak value of the Gaussian ﬁtting and its
half-width at half-maximum, ρab was estimated to be 0.30 ±0.01 μΩ·m. From these results, ρc/ρab was found to be ∼5.7 ×103. With this value, as shown in Figure 4b, if the length in thex- and y-directions is compressed 0.23 times and the length
along the z-axis is stretched 18 times, transformation into an
isotropic resistivity structure is realized. The scaling law
applied to the isotropic conduction model was found to be t′/
L′1−4 = 7.09 (t′ = 37.5 μm, L′1−4 = ∼ 5.3 μm). Because t′/L′1−4> 0.75, it was conﬁrmed that the application of the 3D model
was reasonable.
Finally, the 2D distribution of ΔΦ/Isample was calculated
from the values of ρab and ρc. For comparison, the ΔΦ/Isample
map in Figure 2c is shown in Figure 4c. Figure 4d shows themap of ΔΦ/Isample obtained by calculation using eq 3.
Although the experimental values ﬂuctuate because of the
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Figure 5. Eﬀect of wrinkles on the resistance of ρab. (a) Optical image of the wrinkles of the sample. (b) Optical image of the measured area with awrinkle. (c) Optical image of the same area in (b) with a diﬀerent light angle to make the wrinkle more visible. (d) Measurement area including awrinkle. (e) Measurement area without wrinkle. (f) ΔΦ/Isample as a function of the position of tip 2. A and B correspond to those in (d). (g) ΔΦ/Isample as a function of the position of tip 2. C and D correspond to those in (e). Blue solid lines in (f) and (g) show the ﬁtting curves obtained byusing ρab as a parameter while retaining ρc constant.

7.48 μm, the number of grain boundaries contained in eachmeasurement area is roughly estimated to be ∼2 by MP-STP
and ∼1337 by VDP. From these results and the resistivity ρab,the 1D resistance of the entire sheet is estimated to be ∼0.15
Ω by MP-STP (= R1D,MPSTP) and ∼0.21 Ω by VDP (=R1D,VDP). Assuming that the diﬀerence of ∼0.06 Ω (0.21−0.15
Ω) was only due to the diﬀerence in the number of grainboundaries contained in the measurement area, the resistanceis ∼4.5 × 10−5 Ω (0.06/1335 Ω) per grain boundary. Using
the grain boundary width of 10 nm41 and the sample crosssectional size (0.01 m × 2 μm), we estimated the resistivity of agrain boundary to be 9.0 × 10−5 Ω·m, which is lower than thatin graphene reported previously (10−3−10−1 Ω·m).41,42 The
voltage drop at the grain boundaries is calculated to be ∼675
μV using the current density of ∼7.5 × 10−4 A/μm2 in the MPSTP measurement and the resistance of ∼4.5 × 10−5 Ω [7.5 ×
10−4 A/μm2 × (0.01 m × 2 μm) × (4.5 × 10−5 Ω)] per a grainboundary. However, as shown in Figure 2e, the cross section
microscopically obtained is almost linear, and the voltage drop
observed in this experiment is less than the resolution of thesystem (∼10 μV).
The observed reduction in resistivity may be attributed tothe eﬀects originated from multilayer graphene. The eﬀect of,for example, grain boundaries on the conductivity, which isvery high in graphene,41−44 is expected to be reduced in
multilayer graphene because more conductive paths are formed
in a multilayer structure because of the diﬀerent locations of
domains in the layers along the c-axis direction, parallel to thenoise and the instability of the probe state, as shown in thehistogram in Figure 4a, it was conﬁrmed that the observed
characteristics are consistent with the calculated values.
The ρab measured by the MP-STM method was estimated tobe 0.30 ± 0.01 μΩ·m, which was about 30% lower than that
(0.427 μΩ·m) obtained by the macroscale VDP method. Thisdiﬀerence may be due to the fact that the measurement by the
VDP method being performed in a region including grainboundaries. We made a simple estimation of their eﬀects on
the conductance.
In the case of a metallic material, the resistivity is expressedby Matthiesen’s rule asρ = ρT + ρdef + ρimp(5)

where ρT is the temperature-dependent term and the main
factor, which originates from the scattering by phonons. ρimp is
the term representing scattering due to impurities, which isconsidered to be independent of temperature. ρdef is the term
related to defects. At room temperature, ρT is expected to be
the dominant term, which is included in both MP-STP and
VDP measurements. Therefore, assuming that the impurity
level is low because of the controlled sample preparation
environment, and thus the term ρimp is negligible, thediﬀerence between the results of MP-STP and VDP measurements is considered to be due to ρdef.
We discuss this result by converting the measurement
conditions of a 0.01 × 0.01 m2 sheet of 2 μm thickness to asimple 1D resistance model. By use of an average grain size of
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ArticleACS Applied Electronic Materials

0.38 μΩ·m for SCNG.47 Although it is the result of fourterminal measurement at the conventional macroscopic(millimeters) scale, SCNG is the graphite with the highest
known conductivity because of its ideal structure without grainboundaries or wrinkles. In fact, the residual resistance of
SCNG, 0.1 μΩ·m or less, is in good agreement with 0.08 μΩ·m, which is the diﬀerence between the current measurement
result (0.30 μΩ·m) and that of SCNG (0.38 μΩ·m).
Therefore, the highest conductivity in the ab-plane, ∼1.3
times that of SCNG, may be the intrinsic and ultimatecharacteristic of multilayer graphite. The advantage ofmultilayer graphene, which reduces the eﬀect of grainboundaries on conductance, was successfully conﬁrmed.
Therefore, when the density of wrinkles is decreased by
improving the manufacturing conditions, it becomes possible
to industrially produce large-area highest-quality graphite,which has never been produced. This is a major progress
toward the realization of its future applications.

2D sheet. In such a case, the eﬀect of grain boundaries isreduced because current ﬂows avoid the boundaries.
Therefore, what causes the diﬀerence between the values
obtained by VDP and MP-STP methods? One possibility is theeﬀect of the wrinkles shown in Figure 5a, which formed on thesample during heat treatment. Here, the sample was
illuminated from right above, and the wrinkles in the directionof the shadow appeared widespread and black. Although it has
been considered that the wrinkles formed are smooth, asobserved in Figure 5b, and do not aﬀect the resistance, toclarify its eﬀect in more detail, the area including a wrinkle wasmeasured by the four-point probe method.
Figure 5c shows an image of the same area shown in Figure
5b, in which the irradiation angle of light was changed to makethe wrinkle appear. Figures 5f and 5g show the results ofmeasurement across a wrinkle as shown in Figure 5d and in thearea without wrinkles shown in Figure 5e, respectively. Fitting
was performed using eq 3, where ρc was assumed to beconstant and ρab was used as a ﬁtting parameter. In Figure 5f,
the obtained ρab (= 0.428 ± 0.01 μΩ·m) was almost the sameas that (0.427 μΩ·m) obtained by the VDP method,22 whereas
the ρab (= 0.31 ± 0.01 μΩ·m) obtained for the area shown in
Figure 5g was in good agreement with that obtained for thearea shown in Figure 2 (0.30 ± 0.01 μΩ·m). That is the value
obtained by VDP is aﬀected by the smooth wrinkles. The slightdeviation diﬀerence of the ﬁtting curve from the experimental
values between the left and right of the dotted line in Figure 5f
may be due to the fact that the change in resistance is localizednear the area surrounding the wrinkle.
SCNG is the graphite with the highest known conductivity,
and although it is the result of measurement at theconventional macroscopic (millimeters) scale, we have used
it because of its ideal structure without grain boundaries orwrinkles for comparison. However, the conductivity of SCNG
is considered to be determined by the impurities contained
during the crystal growth in addition to the eﬀect of phonon
vibration. In ref 47, the residual resistance (resistancecomponents other than thermal phonons) of SCNG isshown to be 0.1 μΩ·m or less. This value is in good agreementwith 0.08 μΩ·m, which is the diﬀerence between the current
measurement result (0.30 μΩ·m) and that of SCNG (0.38 μΩ·m).
A more detailed examination of the area with wrinkles
should be further studied, but the elimination of wrinkles is
expected to provide high conductivity comparable to that in
the ideal area. A method of eliminating wrinkles is currently
underway. In addition, when forming thinner ﬁlms by, forexample, the chemical etching of multilayer graphite, it
becomes increasingly diﬃcult to evaluate the characteristics
in the c-axis direction, and the method developed in this study
is expected to play a key role. Analysis of dynamics by timeresolved measurement may give important information.45,46■

METHODS■ASSOCIATED CONTENT

Sample Synthesis. Sample graphite ﬁlms were prepared asfollows. Highly orientated PDMA/ODA (PDMA: 3,3′,4,4′-biphenyltetracarboxylic dianhydride; ODA: 4,4′-diaminodiphenyl ether) typePI ﬁlms were used as raw materials. First, carbonization was
performed by heating the ﬁlms at ∼1000 °C in a nitrogen ﬂow andthen hollowed by using a graphite heater with the temperature
increased to 3300 °C in an argon ﬂow (heating rate: 20 °C/min;retention time at 3300 °C: 5 min).21,22
Sample Preparation for Cross-Sectional STP. First, after thevapor deposition of 200 nm thick gold (Au) along the ab-plane on
both sides of a graphite sample, the sample was cut into a rectangularshape (∼0.5 × 1.5 mm2), and a 0.3 mm thick copper (Cu) plate of
approximately the same size was adhered to each 200 nm thick Au
layer, using a conductive silver (Ag) epoxy paste (resistivity ≤4 μΩ·m). At the same time, an insulating epoxy paste was applied to theedge of the graphite to prevent a short circuit between the Cu plates
on both sides and the graphite edges and to accurately maintain the
thickness of the graphite sample contributing to the measurement.
Subsequently, the sample was cut roughly with a diamond cutter, andthen a ﬂat cross-sectional surface was formed by Ar ion sputtering (6kV acceleration voltage, 10−5 Pa) by using a cross-sectional polisher(IM 4000 PLUS, Hitachi High-Technologies Corp.). A deep groove
was observed between the graphite and the silver epoxy on the left
side, as shown in Figure 3a−e, which was formed because of theshrinkage of the silver epoxy caused by the heat generated during the
sputtering with the Ar beam.
S Supporting Information*

The Supporting Information is available free of charge on the
ACS Publications website at DOI: 10.1021/acsaelm.9b00298.
Electron backscattered diﬀraction pattern (EBSD)
image, SEM image (PDF)■■

CONCLUSION
We performed measurements by MP-STP on a high-quality 2.7
μm thick graphite ﬁlm with a large area fabricated by the PP
method. In addition to the measurement of ρab over an abplane without wrinkles, MP-STP measurement over a crosssection perpendicular to the ab-plane to acquire ρc along the caxis was successfully achieved for the ﬁrst time. The ρab, which
was measured to be 0.427 μΩ·m by the VDP method, wasfound to be 0.30 ± 0.01 μΩ·m by MP-STP; that is, it was
extremely lower than the previously reported lowest value of

AUTHOR INFORMATION

Corresponding Author*E-mail: hidemi@ims.tsukuba.ac.jp.
ORCID

Hidemi Shigekawa: 0000-0001-9550-5148
Author Contributions

H.M., T.B., and A.T. performed the experiments. M.M. and
Y.K. developed the PP method to grow high quality graphite
sample ﬁlms. M.Y. evaluated the sample quality by Raman
spectroscopy and the EBSD method. S.Y. and O.T. provided
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technical advice. H.S. organized and supervised the project andedited the paper with H.M. and the other authors.
Notes

The authors declare no competing ﬁnancial interest.

■

ACKNOWLEDGMENTS
H.S. acknowledges the ﬁnancial support of a Grant-in-Aid for
Scientiﬁc Research (17H06088) from Japan Society for the
Promotion of Science. This work was supported in part by
University of Tsukuba Nanofabrication Platform and the AIST
Nano-Processing Facility in the “Nanotechnology Platform
Project” sponsored by the Ministry of Education, Culture,
Sports, Science and Technology (MEXT), Japan.

■

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