JOURNAL OF APPLIED PHYSICS 102, 113706 共2007兲
Electrical conduction in undoped ultrananocrystalline diamond
thin films and its dependence on chemical composition
and crystalline structure
Eric J. Correa and Yan Wu
Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign,
1206 West Green Street, Urbana, Illinois 61801, USA
Jian-Guo Wen
Center for Microanalysis of Materials, Frederick Seitz Materials Research Laboratory, University of Illinois
at Urbana-Champaign, 104 South Goodwin Avenue, Urbana, Illinois 61801, USA
Ramesh Chandrasekharan and Mark A. Shannona兲
Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign,
1206 West Green Street, Urbana, Illinois 61801, USA
共Received 17 July 2007; accepted 23 September 2007; published online 6 December 2007兲
The electrical conduction behavior of undoped ultrananocrystalline diamond 共UNCD兲 and its
dependence on deposition temperature and chemical structure are presented. UNCD films were
grown using a microwave plasma-enhanced chemical vapor deposition technique at deposition
temperatures of 400 ° C and 800 ° C. The chemical structure of the UNCD films is characterized
with several tools including: Elastic recoil detection analysis, Fourier transform infrared
spectroscopy, electron energy loss spectroscopy, Raman spectroscopy, and environmental scanning
electron microscope. The results show a higher content of sp2-bonded carbon for the 800 ° C
deposition samples 共⬃65%兲 in comparison with the 400 ° C samples 共⬃38%兲. In both kinds of
films, the hydrocarbon bonds have the saturated sp3 structures, while there is lower hydrogen
content in the 800 ° C samples 共⬃8%兲 than in the 400 ° C samples 共⬃10%兲. For conduction
properties, experiments are conducted using a probe station and conductive-atomic force
microscopy. Experimental data show that the samples deposited at 800 ° C are several orders of
magnitude more conductive than the 400 ° C samples. The conduction occurs primarily along the
grain boundary for both types of samples. The conductivity of both types of films also shows field
dependent nonlinear behavior. Both the Poole–Frenkel models and single and overlapping
Coulombic potential models show that the conduction is directly correlated with the sp2 bond
carbon density, and the role of the hydrocarbon bonds in the conduction path is formed by the
network of the sp2 bonded carbon. © 2007 American Institute of Physics.
关DOI: 10.1063/1.2816214兴
I. INTRODUCTION
The ultrananocrystalline diamond 共UNCD兲 is a thin film
form of diamond developed by the Argonne National Laboratory researchers. The UNCD film is grown through a patented microwave plasma-enhanced chemical vapor deposition 共MPCVD兲 technique1 using a mixture of CH4 共⬃1%兲
with inert gases 共e.g., Ar, Kr, or Xe兲. In contrast to conventional CVD microcrystalline diamond films prepared by
atomic hydrogen-rich microwave plasma, the UNCD films
are grown with less than 5% molecular hydrogen in gas mixtures and consist of equiaxial nanograins of less than 10 nm
diameter and elongated twinned dendritic grains around 100
nm in length.2
The high surface smoothness offered by the nanometer
scale grain sizes, the diamondlike mechanical and tribological properties, the thermal stability, and the chemical inertness make the UNCD an attractive material for microscale
microelectromechanical systems 共MEMS兲 devices and
a兲
Electronic mail: mshannon@uiuc.edu
0021-8979/2007/102共11兲/113706/10/$23.00
applications.3 It is known that the electrical properties of the
UNCD can be conducting or insulating by controlling the
nitrogen content 共doping兲 during the deposition process. In
particular, we are interested in undoped UNCD as a dielectric in the MEMS applications. A better understanding of the
electrical conduction behavior of the UNCD as a function of
chemical bonding and nanostructure will provide a basis for
the use of the UNCD in the MEMS and other devices in need
of a low-surface energy hard tribological material.
Experimental work has also shown that the deposition
temperature has an impact on the hydrogen content in the
UNCD film as well as the grain size of the CVD diamond
and the sp2 / sp3-bonded carbon ratio.4,5 The hydrogen abstraction is lower for lower deposition temperatures, leading
to lower secondary nucleation density and larger grains.4
Three parameters, the sp2 / sp3-bonded carbon ratio, the hydrogen content, and the grain size, are not only each dependent on the film growing process, together they also determine the many physical properties of the CVD diamond
films,6 such as density and hardness. With respect to electrical properties, sp2-bonded carbon within the CVD diamond
102, 113706-1
© 2007 American Institute of Physics
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Correa et al.
films can be thought of as a conduction promoter, particularly if the sp2 forms interconnected networks of bonds
along which electrons are free to move. Most of the sp2
structure has been detected in the grain boundaries in the
UNCD.7 Hydrogen is also thought to be located at the grain
boundaries since atomic hydrogen can easily react with carbon atoms having dangling bonds in the grain boundaries
during the film growing process, which can then saturate
these dangling bonds. However, the role of hydrogen in the
conduction path is not clear.
The purpose of this paper is to report the conduction
behavior of undoped UNCD films grown at 400 ° C and
800 ° C and its dependence in chemical composition and
crystalline structure. The deposition temperature affects the
ratio of sp2 and sp3 bonding, the hydrogen content, as well as
the crystalline structure. For macroscopic conduction properties, current-voltage 共I − V兲 curves for samples with electrical
contact pad sizes from 50 to 125 m2 are collected using an
electrical I − V probe station. For microscopic properties,
conductive-atomic force microscopy AFM 共C-AFM兲 measurements are performed within 1 m2 scans to study the
local conduction behavior of the UNCD film as a function of
surface morphology. Raman spectroscopy and electron energy loss spectroscopy 共EELS兲 are used to analyze the
chemical composition and bonding structure of the UNCD
films. The hydrogen content of the films is obtained by
through elastic recoil detection 共ERD兲. Fourier transform infrared spectroscopy 共FTIR兲 spectra are used to characterize
the bonding structure of the hydrocarbon bonds. Film thickness and grain size are characterized by using environmental
scanning electron microscopy 共ESEM兲 and transmission
electron microscopy 共TEM兲, respectively. The results show
that the I − V characteristics are consistent with changes observed in sp2 / sp3-bonded carbon ratios, hydrogen content,
and crystalline structures of the UNCD films. Similar to the
microcrystalline CVD diamond, the conductivity of both
types of UNCD films shows field dependent nonlinear behavior. Poole–Frenkel 共P-F兲 models with single and overlapping Coulombic potentials8–13 show that the conduction is
directly correlated with the sp2-bond carbon density and the
role of hydrocarbon bonds in the conduction path formed by
the sp2-bonded carbon, both of which act on the formation of
extended networks of bonds.
II. EXPERIMENTS
Thin films of tungsten 共10 nm thick兲 were deposited on
commercial n-type Si wafers 共using magnetron sputtering兲 in
order to enhance the nucleation and growth of the UNCD
film. The UNCD thin films were grown at Argonne National
Laboratory using the MPCVD at two deposition temperatures: 400 ° C. and 800 ° C. No nitrogen or hydrogen was
added during the deposition process. For electrical conduction property measurements, an Ohmic contact was created
on the back side of the sample by depositing chrome-gold
films and annealing the sample at 375 ° C in a furnace tube
with a nitrogen atmosphere. Chrome/gold thin films 共250 nm
thick兲 were deposited on the topside of the sample to form
electrical contacts of different sizes 共50− 125 m sq兲.
J. Appl. Phys. 102, 113706 共2007兲
The hydrogen content of the UNCD thin films was determined by elastic recoil detection analysis 共ERDA兲 using a
Van de Graaff accelerator. A 2 MeV He2+ ion beam was
incident on the UNCD film with an angle of 50° or 55° with
respect to the surface normal. The hydrogen atoms recoiled
by the ion beam are detected at 45° with respect to the incident beam direction by a Si surface barrier 共SSB兲 detector.
The detector was covered with a 1 m thick Mylar foil to
trap the recoiled carbon atoms from the films. High density
polyethylene 共关CH2兴n兲 was used as a standard to determine
the hydrogen concentration against the number of carbon
atoms. To characterize the bonding configuration of hydrocarbon in the UNCD film, a Nicolet IR-750 FTIR spectrometer was used to record the C–H stretching modes in the
2880– 3300 cm−1 range. All measurements were done using
the mercury–cadmium–telluride 共MCT兲 detector with a
2 cm−1 resolution.
Raman spectroscopy and EELS were used to analyze the
relative sp3 to sp2 bonding ratio of the UNCD films. For
Raman spectroscopy, the radiation of an Ar+ laser 共
= 488 nm兲 was used for excitation. The laser spot size was
50 m and the beam power used for the experiment was
100 mW. All the Raman spectra were collected by a SPEX
Triplemate spectrometer with a back-illuminated liquidnitrogen-cooled charge coupled device 共CCD兲 detector. Two
different samples were set and tested as standards; the first
one is natural diamond corresponding to 100% sp3-bonded
carbon, whereas highly ordered pyrolytic graphite 共HOPG兲
was used as a reference for graphite, which consists of 100%
sp2-bonded carbon.
Plan-view TEM samples were prepared by a mechanical
polishing down to about 30 m and then ion beam milling,
at a low ion incidence angle 共6 ° – 10°兲 at room temperature
with 5 kV argon ions, until reaching film perforation. The
final thickness of the film where the TEM images were taken
was less than 200 nm. The specimens were studied using a
JEOL-2010F scanning transmission electron microscope operated at 200 kV. The instrument was equipped with a Gatan
Image Filter to obtain EELS. As described by Wan and
Egerton,14 the sp2 / sp3 ratio in the diamond film can be obtained by using a graphite standard with 100% sp2. However,
edge intensity strongly depends on the orientation of a
single-crystal sample,6,14 so crystalline graphite cannot serve
as a standard. Thus, a lacey-carbon film 共100% sp2 amorphous carbon兲 supported by a 400 mesh copper grid was
placed on top of the sample to create the standard for the
EELS experiments. Figure 1 shows a TEM image of the
UNCD sample with the lacey carbon grid. EELS spectra
were measured over a 200 nm by 200 nm area randomly
selected on the UNCD film and the lacey carbon film. To
remove plural scattering, a zero-loss peak was recorded for
each EELS spectrum. Both Raman and EELS data were analyzed using OriginLab Scientific Graphing and Analysis
Software, in which multiple peak fitting routines are employed over the data through iterations to get the sp2 content
for each sample.
The cross-sectional area of the samples and its thickness
at randomly selected locations were imaged using an ESEM
共Philips XL30 ESEM-FEG兲. An ESEM was calibrated using
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113706-3
Correa et al.
FIG. 1. The TEM image of the UNCD sample with the lacey carbon grid
prepared for the EELS experiments.
a diffraction grating replica specimen from Ted Pella, Inc.
that consists of a grid with 2160 lines/mm. The calibration
was performed at different magnifications, beam voltages
共kV兲, and working distances 共WDs兲. An Alesi REL-2100
analytical probe station with a tungsten tip radius of 2.4 m
was used to perform the I − V measurements. A commercial
power supply 共Bertan, Series 225, Spellman High Voltage
Corporation, USA兲 was used as a power source with an operating range of 0–3 kV and 0–30 mA. Each sample was
randomly selected in terms of pad size and location. Both the
output current and the applied voltage were measured using
digital multimeters 共HP 3457A and HP 3478A, respectively兲.
To study the local electrical properties as a function of
surface morphology and position, conductive atomic force
microscopy 共C-AFM兲 measurements were performed using a
commercial AFM 共MFP-3D™, Asylum Research, USA兲 in a
setup shown in Fig. 2. In three scanning axes, the hysteresis
and creep of the piezoactuators were corrected by a closed
loop control system with a linear voltage differential transducer 共LVDT兲 as the feedback sensor. The AFM tip
J. Appl. Phys. 102, 113706 共2007兲
共AC240™ Electri-Lever, Olympus, Germany兲 was coated
with platinum iridium. When a dc bias was applied to the
sample, the conduction current was collected by the conductive AFM probe. The current signal was amplified by a transimpedance amplifier with a gain of 5 ⫻ 108 V / A and
sampled by a data acquisition system. The AFM can be operated in two modes: current imaging and the I − V spectrum.
In the current imaging mode, the tip is scanned in contact
with the sample surface, and a feedback loop maintains a
constant cantilever deflection signal to image the surface topography. At the same time, a constant bias voltage is applied to the sample, and the current at each pixel is measured
to generate the current image. In the I − V spectrum mode, the
AFM probe is moved to a specified location within an acquired image and brought into contact with the sample. The
sample bias voltage is ramped within a user specified range
and rate while the current is measured to generate the I − V
curve.
III. RESULTS AND DISCUSSION
A. Hydrogen content of the UNCD films and
hydrocarbon bonding configuration
The ERDA spectra of the two types of UNCD films are
shown in Fig. 3共a兲. The spectrum of each type of sample is
characterized by two height steps at 1148 and 544 eV. The
height of the first step is determined by the frequency that a
helium ion is forward scattered from a carbon atom at the top
UNCD surface layer. The second height is determined by the
frequency that a hydrogen atom at the top surface layer is
recoiled from a helium ion. The hydrogen content of the
films can be calculated from the ratio of the two height steps
in each spectrum.15,16 The spectra in Fig. 3共a兲 are rescaled so
that the two types of samples have the same height at 1148
eV. The slightly greater height at 544 eV for the 400 ° C
sample indicates a higher hydrogen content. Repeated measurements give an atomic percentage of hydrogen of
8.1% ± 1.2% and 10.0% ± 1.5% for the 800 ° C and 400 ° C
samples, respectively. Figure 3共b兲 shows the FTIR spectra of
the two types of UNCD films. For both of the films, the
primary dips are located at 2855 and 2920 cm−1, which are
identified to be saturated sp3 hydrocarbon bonds as in CH2
and CH, respectively.6 It is possible that there is also a small
amount of saturated sp3 hydrocarbon bonds as in CH3, which
shows up faintly at 2955 cm−1 within the broadband dip of
2920 cm−1.
B. Grain structure by TEM
FIG. 2. The conductive-AFM experimental setup for the microscopic experiments. When a dc bias is applied to the sample, the conduction current is
collected by the conductive AFM probe. The current signal is amplified by a
transimpedance amplifier with a gain of 5 ⫻ 108 V / A and is sampled by a
data acquisition system.
Figure 4 shows TEM microstructure photographs for undoped UNCD for samples grown at 400 ° C 关Figs. 4共a兲 and
4共b兲兴 and 800 ° C 关Figs. 4共c兲 and 4共d兲兴, respectively. From
the pictures, a variation in the grain shape for both samples
can be seen. Figure 4共a兲 shows that for samples grown at
400 ° C, the grain arrays are better oriented in one direction,
whereas Fig. 4共c兲 shows that for the samples grown at
800 ° C, the grains meet with each other more randomly. The
samples grown at 400 ° C also show elongated twined dendritic grains that are approximately 100 nm in length and less
than 5 nm in width, as depicted in Fig. 4共b兲. The UNCD
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J. Appl. Phys. 102, 113706 共2007兲
FIG. 4. The TEM images of UNCD films deposited at 共a兲, 共b兲 400 ° C and
共c兲, 共d兲 800 ° C. The 400 ° C films show elongated twined dendritic grains
around 100 nm in length and less that 5 nm in width as depicted in 共a兲. The
UNCD grown at 800 ° C exhibits different grain structure; the nanocrystalline grain arrays are more uniform or equiaxed with an average diameter of
4 nm.
FIG. 3. 共a兲 The ERD spectra of UNCD films grown at 400 ° C and 800 ° C.
The 400 ° C sample has a slightly higher step height at 544 eV indicating
higher hydrogen content than the 800 ° C sample. 共b兲 The FTIR spectra of
the UNCD films grown at 400 ° C and 800 ° C. The primary dips at 2855
and 2920 cm−1 are identified to be hydrocarbon bonds with saturated sp3
structure.
two features, a peak at 285 eV due to excitation to pⴱ states
of sp2- bonded carbon and a step at 290 eV due to excitation
to pⴱ states of sp3 and sp2 sites.6 Thus, pure 100% sp2
carbon phase such as the lacey-carbon reference possess well
resolved 285 and 290 eV peaks, whereas pure 100% sp3
carbon 共diamond兲 has no peak at 285 eV. The sp2 fraction of
the UNCD film is found by taking the ratio of the area of the
285 eV peak to the area of the 290 eV step within the energy
window from of 270–570 eV, and comparing it to the ratio of
the 100% sp2 lacey-carbon reference.14 As seen in Fig. 5, the
sp2 peak has greater intensity for the sample grown at
grown at 800 ° C shows a different grain structure; the nanocrystalline grain arrays are more uniform or equiaxial with
an average diameter of 4 nm 关Fig. 4共d兲兴. Both grain structures for the two deposition temperatures are comparable
with those in the UNCD literature.4,5 It is important to note
that all variables, save temperature, are kept constant during
the deposition of the films. Thus, the change in grain structure is primarily due to the difference in deposition temperature. The TEM pictures also show that the 800 ° C samples
exhibit a larger amount of grain boundaries per unit volume
than the 400 ° C samples.
C. sp2 vs sp3 ratio by EELS and Raman spectrum
analysis
The EELS spectra are shown in Fig. 5 for UNCD films
deposited at 400 ° C and 800 ° C. The spectrum consists of
FIG. 5. The EELS spectra for UNCD films deposited at 400 and 800 ° C.
The reference peak takes place near 285 eV corresponding to sp2-bonded
carbon. The higher intensity peak shows a higher concentration of
sp2-bonded carbon for the 800 than the 400 ° C samples.
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113706-5
Correa et al.
J. Appl. Phys. 102, 113706 共2007兲
TABLE I. The chemical composition and bonding structure of tested UNCD
films.
EELS & ERDA
Raman & ERDA
400
800
400
800
°C
°C
°C
°C
sp2 C%
sp2 C%
H%
39.6± 11.6
65.2± 13.2
36.9± 19.7
65.2± 4.4
50.4± 11.6
26.7± 13.2
53.1± 19.7
26.7± 4.4
10.0± 1.5
8.1± 1.2
10.0± 1.5
8.1± 1.2
800 ° C when compared to the 400 ° C sample, indicating a
higher sp2 content. Calculated results show the 800 ° C
sample has an average sp2 content of 65.2% ± 13.2% whereas
the 400 ° C sample showed a content of 39.6% ± 11.6% of
sp2 carbon, as listed in Table I.
Raman spectra are shown in Fig. 6 for the UNCD films
deposited at 400 ° C. and 800 ° C. A reference line for pure
diamond 共100% sp3兲 is also shown. Three modes 共peaks兲
can be identified at 1332, 1355, and 1550 cm−1. The sp3
mode is found to be near to 1332 cm−1, which agrees with
the reference line and the literature for natural diamond.17,18
The other two broadband modes are approximately at 1355
and 1550 cm−1. These modes represent disordered
sp2-bonded carbon within the UNCD films and are observed
for both deposition temperatures. The HOPG reference line
at 1580 cm−1 corresponding to single crystalline graphite is
also shown in Fig. 6.18 None of the samples showed a significant intensity near 1580 cm−1, but rather a shifted peak
closer to 1500 cm−1. This shift supports the assumption that
the sp2-bonded carbon within the UNCD is not the same as
in single crystalline graphite. Also, since Raman scattering in
the visible range is about 100 times more sensitive to
sp2-bonded carbon 共which is thought to reside almost exclu-
FIG. 7. Characteristic macroscopic I − V response curves for the UNCD. The
I − V curve for the 400 ° C sample exhibits a dielectric material behavior,
with a sharp transition from linear to exponential growth in conductivity
with applied electric field. The UNCD sample grown at 800 ° C shows a
semiconductorlike behavior. By inspection, the 800 ° C sample is more conductive by 1 to nearly 4 orders of magnitude than the 400 ° C sample.
sively in the grain boundary兲 than the sp3-bonded carbon, the
change in the sp2 peaks at 1355 and 1550 cm−1 shows that
the 800 ° C samples contain ⬃1.7 times more 共from Table I兲
sp2-bonded carbon in the grain boundaries than the 400 ° C
samples. Furthermore, the samples grown at 400 ° C show a
greater intensity at 1332 cm−1 in the Raman plot than the
800 ° C samples. The 1332 cm−1 peak is usually associated
with microcrystalline diamond grains and not nanocrystalline
diamond.5 Therefore, the 400 ° C sample has greater sp3
carbon-carbon bond content in the microcrystalline phase
than does the 800 ° C sample. Hence, there is a lower concentration of grain boundaries per unit volume in the 400 ° C
vs 800 ° C samples. Thus, the likelihood of extended interconnected networks of sp2-bonded carbon within the 800 ° C
grown samples is greater than the 400 ° C samples.
The sp3 vs sp2 ratio can be extracted from the Raman
plot by integrating the intensity of each mode with respect to
the wavelength18 and is listed in Table I. Since Raman scattering in the visible range does not see C–H bonds,6 the
results from the Raman spectrum analysis show the sp3
bonded carbon ratio in all types of carbon-to-carbon bonds.
The EELS results are consistent with the Raman results for
the 800 ° C and 400 ° C samples within 3% and 12%, respectively.
D. UNCD macroscopic and microscopic I − V curves
FIG. 6. The Raman spectra for UNCD at different growing temperatures.
Three modes can be identified from the plot: 1332, 1355, and 1550 cm−1.
They correspond to sp3 and sp2 carbon bonding. A natural diamond reference 共100% sp3兲 and a HOPG 共100% sp2兲 reference are also shown. The
sample grown at 400 ° C shows a greater intensity at 1332 cm−1 in the
Raman spectra than the 800 ° C, showing a higher sp3-bonded carbon content in the 400 ° C samples.
Figure 7 shows a characteristic I − V curve for UNCD as
a macroscopic property measurement for each deposition
temperature: 400 ° C and 800 ° C. Both samples have a
50 m pad size length and 1.50 m 共approximately兲 film
thickness as measured by the ESEM. The I − V curve for the
400 ° C sample shows two different behaviors: linear before
and exponential after a critical voltage is reached, which is
typical for a dielectric material. When the applied voltage is
under 60 V for the 400 ° C sample, a linear change in current
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Correa et al.
J. Appl. Phys. 102, 113706 共2007兲
FIG. 8. 共a兲 and 共b兲 1 m2 topography
scan, with 共c兲 and 共d兲 the corresponding current image, and 共e兲 and 共f兲
I − V response for the 400 ° C and
800 ° C grown UNCD samples, respectively. The specified locations of
where the I − V curves are taken are indicated in 共c兲 and 共d兲 for 400 ° C and
800 ° C samples, respectively. The
AFM topography pictures show that
the films prepared at 400 ° C and
800 ° C are both continuous and dense
with similar surface morphologies.
Calculated rms roughness for the
400 ° C film is 12.0 nm whereas the
800 ° C film is 8.4 nm.
is observed, and an exponential increase in current occurs
above 60 V as observed in Fig. 7. The critical voltage of 60
V corresponds to a critical electrical field of 40 MV/m.
The I − V curve for the 800 ° C data shows a different
behavior. No linear-exponential transition is observed for the
undoped UNCD sample grown at 800 ° C, but rather a semiconductorlike behavior is seen. In Fig. 7, the 800 ° C sample
starts to show an immediate exponential increase in conductivity. Notice that the samples grown at 400 ° C and 800 ° C
have the same pad size and thickness, so they are comparable. The I − V plot in Fig. 7 shows that the 800 ° C UNCD
is more conductive than the 400 ° C UNCD by a minimum
of an order of magnitude over the range tested and nearly 4
orders near 80 V.
Figures 8共a兲 and 8共b兲 show 1 m2 topography scans;
Figs. 8共c兲 and 8共d兲 the corresponding current images; and
Figs. 8共e兲 and 8共f兲 the I − V response for the UNCD 400 ° C
and 800 ° C samples, respectively. The current image for the
400 ° C sample is acquired at a bias of 50 V, and for the
800 ° C sample is acquired at a 40 V bias. The specified
locations of where the I − V curves are taken are indicated in
Figs. 8共c兲 and 8共d兲 for the 400 ° C and 800 ° C samples,
respectively. The AFM topography images in Figs. 8共a兲 and
8共b兲 show that the films prepared at 400 ° C and 800 ° C are
both continuous and dense with similar surface morphologies. The calculated root-mean-square 共rms兲 roughness for
the 400 ° C film is 12.0 nm, and for 800 ° C film it is 8.4 nm,
which is consistent with the difference in the nanometer
scale grain sizes as shown in the TEM images 共Fig. 5兲. Since
the lateral resolution of the topography image is limited by
the tip radius of the AFM probe 共15 nm in this case兲, the
grain structure shown in Figs. 8共a兲 and 8共b兲 is attributed to a
colony of nanocrystalline grains. The average thickness of
the UNCD film used in the AFM experiments is 0.51 m for
the 400 ° C films and 1.24 m for the 800 ° C films as measured by the ESEM. These values correspond to an averageapplied electrical field of 98 MV/m for the current images in
Fig. 8共c兲, and 32 MV/m in Fig. 8共d兲.
Figures 8共c兲 and 8共d兲 show that the 800 ° C sample is
more conductive since the average current is 120 pA at 32
MV/m of the applied field, whereas the 400 ° C sample
shows a smaller average current of 30 pA at a higher applied
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113706-7
Correa et al.
field of 98 MV/m. Comparing the current images with the
topography scans, no drastic change in conduction current is
observed that correlates to the surface features for either type
of sample, which implies that the conduction in these films is
not dominated by extrinsic structural defects, such as voids
or impurities in the films. The 800 ° C film does not behave
as having extended graphitic or amorphous carbon domains,
since the current response at every location behaves as a
semiconductor, not metallic as graphite does, even though
the sp2-bond fraction is high. On the other hand, most of the
higher conduction current sites coincide with the boundaries
of the colony of grains. The question arises as to whether the
higher conduction current is due to the higher electric field
for the same bias voltage at deeper surface valleys or comes
from an increased conductivity at the grain boundary. The
variation of the electrical field between surface valleys and
peaks for the given bias is calculated from the measured
roughness and thickness for each sample. Based on the
I − V response, the variation of the electrical field due to the
surface roughness leads to a maximum contrast of 14 pA for
the samples grown at a 400 ° C sample and 42 pA for the
samples grown at a 800 ° C sample. Both of these values are
less than the contrast of the current images in Figs. 8共c兲 and
8共d兲, which is 30 and 120 pA for the 400 ° C and 800 ° C
samples, respectively. We conclude that the higher conduction at the grain boundaries is indeed from an increased local
conductivity due to intrinsic conduction promoter such as
sp2-bonded carbon from the C-AFM measurements.
The I − V response at three specified locations are measured for both UNCD samples, and the results are shown in
Figs. 8共e兲 and 8共f兲. Although there is a slight difference
within the three I − V curves for each sample, all the I − V
curves in Fig. 8 show similar behavior as the macroscopic
measurements shown in Fig. 7. For the 400 ° C sample, there
is almost zero conduction below a critical voltage, and above
the critical voltage, the conduction current increases exponentially. For the 800 ° C sample, the microscopic I − V curve
again shows a semiconductorlike behavior. The critical field
for the 400 ° C sample in the microscopic I − V measurement
using the C-AFM is 71 MV/m, which is higher than the 40
MV/m critical field in the macroscopic I − V measurement
using the probe station. The difference between the critical
field measured by the C-AFM and the probe station indicates
there is some degradation in the dielectric property with increasing area coverage due to the extrinsic defects for the
samples grown at 400 ° C sample, which is consistent with a
slight dependence of conduction behavior on pad sizes for
the macroscopic I − V data, as shown in Fig. 9. The conduction behavior will be discussed in more detail in the next
section.
E. The dependence of conduction property on the
structure of UNCD samples
The CVD diamond thin films are often reported to have
a nonlinear conductivity as a function of the applied field due
to the presence of numerous defects and charge localization
sites, or ionizable sites, within the material, as well as nondiamond structured carbon within grain boundaries.8–13 The
UNCD samples we tested also exhibit nonlinear conductiv-
J. Appl. Phys. 102, 113706 共2007兲
FIG. 9. 共a兲 The P-F plot with single Coulombic potentials and 共b兲 the P-F
plot with overlapping Coulombic potentials for UNCD samples grown at
400 ° C and 800 ° C. The standard error 共SE兲 at the 95% Confidence Interval
共CI兲 of the fit for the P-F model with single Coulombic potential is found to
be 0.83 for the 400 ° C samples and 0.98 for the 800 ° C whereas the SE for
P-F with overlapping Coulombic potentials is found to be 0.63 and 0.80 for
400 ° C and 800 ° C, respectively. For clarity, the 95% CI limit lines are
omitted for the 800 ° C curves.
ity, as observed during the I − V experiments and shown in
Fig. 7. Raman, TEM, and EELS showed that UNCD, like the
other types of diamondlike films, has a high degree of grain
boundaries and fraction of sp2 to the total number of bonds.
Amorphous, graphitic, and extended networks of -bonded
carbon are well known to be highly conductive
共≫1000/ ⍀ cm兲. However, hydrogen remaining within the
structure after diamond growth can also play a strong role in
conductivity, potentially to increase or decrease conductivity
of the resulting structure. Hydrogen can act to interrupt sp3
diamond networks, creating unsaturated defects that could
act as charge localization sites, thereby increasing nonlinear
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113706-8
Correa et al.
J. Appl. Phys. 102, 113706 共2007兲
conductivity at high fields. Hydrogen can also act to terminate sp2-bonded carbon, thereby interrupting -bonded networks and reducing both linear 共Ohmic兲 and nonlinear conduction. Since the ERDA spectra show there is around 10%
hydrogen in both types of the tested UNCD films, hydrogen
could play a strong role in the conductivity of these films,
which needs further elucidation.
Non-Ohmic conductivity in dielectrics and semiconductors, such as that observed for these UNCD films, is most
often phenomenologically characterized with basic constitutive relationships that are based on low-dimensional conduction models. Nonlinear conductivity resulting from charge
hopping along the ionizable sites is often modeled for diamond films using a P-F type response model. Therefore, a
question arises as to whether the exponential increase in conductivity with applied field that is observed for these films
correlates with discrete ionizable sites, and if so, what are
these sites with respect to the films chemical composition
and crystalline structures.
P-F type responses, modeled as charges being excited
from Coulombic potential wells as detailed in Hill,20 differ
depending on the type of interactions of the ionizable sites.
Sparse ionization sites and single Coulombic wells leads to a
function of the form
冉
冊
− ⌽i + 冑E
,
Jsparse = AE exp
kT
共1兲
where A can be considered as a constant parameter, E is the
electrical field, ⌽i is the ionization energy of a localized site,
and  is the P-F coefficient
=
TABLE II. The fittings parameters, ln共a兲, b, ln共c兲, d, obtained from the data
in Fig. 9.
Statistical parameter
ln共a兲
400
800
400
800
400
800
400
800
b
ln共c兲
d
°C
°C
°C
°C
°C
°C
°C
°C
Mean
Standard deviation
Relative error
−30.35
−14.541
1.64⫻ 10−3
8.19⫻ 10−4
−3.896
5.384
8.05⫻ 10−8
6.83⫻ 10−8
1.040
0.2490
1.27⫻ 10−4
1.58⫻ 10−5
0.535
0.322
6.81⫻ 10−9
2.83⫻ 10−9
3.43⫻ 10−2
1.71⫻ 10−2
7.75⫻ 10−2
1.93⫻ 10−2
13.7⫻ 10−2
5.98⫻ 10−2
8.46⫻ 10−2
4.15⫻ 10−2
site. Therefore, after Hill20 and heeding the admonition of
Ongaro and Pillonnet,19 the use of two parameter fits of J to
E based on different types of charge motion and material
structure is proposed to relate gross material structure and
composition to the macroscopic conductivity properties observed, regardless of the attribution to global material properties such as permittivity, mobility, and activation energy.
Thus, Eqs. 共1兲 and 共2兲 take the simple form of
Jsparse = a E exp共b冑E兲,
共2兲
冑␥ o d ,
where e is the electronic charge, o is the permittivity of free
space, ␥ is a factor relating to geometry, and o is the local
dielectric function. For idealized one-dimensional wells
without additional barriers in the bulk, ␥ is unity, but in real
materials with complex aggregated three-dimensional 共3D兲
sites with interacting barriers, ␥ can vary by an order of
magnitude. Similarly, the local fields and dielectric function
also vary from the bulk values as Hill noted.20 Thus,  can
be expected to vary with material structure, composition, and
defect density.
In contrast to the case of sparse sites for charges to occupy, dense ionization sites with overlapping Coulombic potentials and interacting sites leads to a function of the form
冉
Jdense = C exp
冊
− ⌽i + 2/es + es E
,
kT
共3兲
where s is the ionization site spacing, which is thought to be
inversely proportional to N1/3
i , where Ni is the number density of ionization sites. Classic and semiclassic P-F models
utilize numerous simplifications that make it difficult to directly link structure of the material to a generalized conductivity property.19 The concern is that the conduction of
charge along defects and ionizable sites is fully 3D in terms
of material structure and Coulombic potentials, which in turn
affects the local susceptibility and fields at each interacting
共4兲
where a and b are fitting constants. Notice that b relates to 
as
b=

.
kT
共5兲
Similarly Eq. 共3兲 can be simplified in a simple expression
Jdense = c exp共d E兲,
e3/2
ln共Jsparse/E兲 = ln a + b冑E,
ln共Jdense兲 = ln c + d E,
共6兲
where c and d are fitting constants. Notice that d relates to s
as
d=
es
.
kT
共7兲
The constants a, b, c, and d can be obtained experimentally
from the I − V experiments by fitting the data to Eqs. 共4兲 and
共6兲, respectively.
Figures 9共a兲 and 9共b兲 show P-F plots with single 关Eq.
共4兲兴 and overlapping Coulombic potentials 关Eq. 共6兲兴, respectively. Table II shows the parameters, a, b, c, and d obtained
from the data in Fig. 9, along with the uncertainties. Both fits
show that the 800 ° C films are of orders of magnitude more
conductive than the 400 ° C films, which is consistent with
the I − V plots. A linear curve fit is also shown for a representative sample in both figures, along with confidence limits. In both Figs. 9共a兲 and 9共b兲 the films grown at 400 ° C
show a slight pad size dependence in the conduction behavior, whereas all the curves fall on one line for the films
grown at 800 ° C films. Lower conductivity films should be
more sensitive to extrinsic defects, such as submicron pinholes, and larger pads have a higher probability of being
affected by any increased conductivity due to the extrinsic
defects.
The TEM data from the UNCD samples grown at
400 ° C 关Figs. 4共a兲 and 4共b兲兴 showed a larger grain size with
higher alignment and orientation than the samples grown at
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113706-9
Correa et al.
J. Appl. Phys. 102, 113706 共2007兲
800 ° C 共Figs. 4共c兲 and 4共d兲兴. Thus, the 800 ° C UNCD has a
larger amount of grain boundaries, with grain boundary areas
1.4–1.8 times more than the 400 ° C films as estimated from
the TEM photographs, and thus presumably higher intrinsic
defect densities. From the C-AFM data in Fig. 8, the current
conduction is several times higher along the valleys and presumed grain boundaries than over the peaks, which are assumed to be associated with diamond crystallites. As some
researchers have suggested,7 the bulk of the sp2 bonds in
diamondlike films exist in the grain boundaries, which if
true, correlates with a fractional increase in sp2 versus total
carbon of 1.6 times for the 800 ° C vs 400 ° C films. However, the difference in the sp2-bonded carbon percentage
alone does not explain the orders of magnitude difference in
the conductivity between these two types of films as shown
in Table II. Hydrogen is also thought to be located at the
grain boundaries since atomic hydrogen can easily react with
carbon atoms having dangling bonds in the grain boundaries
during the film growing process. The FTIR spectra show that
in both types the UNCD films, hydrogen exists in the form of
saturated sp3 hydrocarbon as in CH3, CH2, and CH, and with
the remaining bonds to C. No unsaturated bond peaks, such
•
as 关−C-H兴, are observed in the spectra, suggesting that hy兩
drogen is not acting to increase the probability of charge
carriers in the films. It is well known that saturated sp3 hydrocarbon bonds are the building blocks of highly insulating
polymers, such as polyethylene 共关CH2兴n兲. Thus the role of
hydrocarbon at the grain boundary can be thought as conduction inhibitor. It has been shown previously in macroscale
composites, such as polyethylene/carbon black, that electrical conductivity is sensitive to small change in the ratio of
polyethylene/carbon black.21 Carbon black is essentially
sp2-bonded amorphous carbon.22 The conductivity of amorphous carbon separated by polyethylene can change 5 orders
of magnitude when the percolation limit is reached. Thus, the
proposed explanation of observed conductivity difference between the 400 ° Cand 800 ° C films lies in the ratio of hydrocarbon bonds over the sp2 carbon-carbon bonds at the grain
boundary, which are 0.253 and 0.123 for UNCD films deposited at 400 ° C and at 800 ° C, respectively.
The picture that emerges from these data is that the conductivity of these UNCD films is governed by networks of
-bonded and amorphous carbon6 resident in the grain
boundaries. As depicted in Fig. 10, one might think of the
grain boundaries as a 3D distribution of domains of
-bonded carbon that are bounded by hydrogen-saturated
carbon and/or diamond nano- or microcrystalliltes. Each domain can receive, carry, and inject electrons to and from
other domains. As such, these domains behave as ionizable
sites in the P-F model. As in Fig. 10共a兲, if the network of
these domains is sparse enough, the potential induced from
charges within each domain decay by either 1 / r2 for 3D or
1 / r for two-dimensional 共2D兲 structures. The effective field
will not sufficiently overlap an adjoining domain to superimpose fields. Conduction occurs when the transient local field
becomes high enough to either tunnel through 共low-field
conduction兲, or shift the intervening dielectric into the conduction band 共high-field conduction兲. Such conduction be-
FIG. 10. Depiction of -bonded carbon domains that provide a 3D conductive path for electrons through a dielectric matrix. The mode of conduction
depends on the spacing of the domains. With nonoverlapping potentials
shown in 共a兲 arising from a sparse network of domains shown in 共b兲, the
UNCD behaves as a dielectric, until the field is high enough for current to
increase exponentially, following a P-F response. With overlapping potentials shown in 共a兲 arising from a dense network of domains shown in 共b兲, the
UNCD behaves as a semiconductor.
havior is observed for the 400 ° C samples. As shown in Fig.
10共b兲, if the network is dense enough that the potential wells
overlap, fields superimpose to shift the intervening dielectric
into the conduction band at low fields, with conduction increasing exponentially with higher fields, which is described
by the Coulombic interacting-wells P-F model. The degree
of conduction depends on the applied field and conductivity,
giving rise to semiconductor behavior observed for the
800 ° C samples. Changing sp2 to hydrocarbon ratio by two
as measured for the 400 ° C and 800 ° C grown samples, if
shifted from nonoverlapping to overlapping fields can therefore exponentially change the conductivity as we observed.
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113706-10
Correa et al.
If the hydrogen to sp2 bond ratio drops further, it may be
possible to create complete interconnected domains. Thus, a
metallic conductive behavior may be possible in the UNCD
films, although we have not yet observed this behavior.
IV. CONCLUSION
The ERDA measurements show that the atomic percentage of hydrogen in the film is 10.0% ± 1.5% and 8.1% ± 1.2%
for the samples grown at 400 ° C and 800 ° C, respectively.
The average sp2-bonded carbon content for the samples
grown at 400 ° C according to the EELS and Raman spectra
is found to be 39.6 and 36.9%, respectively. For the 800 ° C
samples both Raman and EELS spectra gave an average sp2
content of approximately 65%. The TEM results showed
nanocrystal elongated twined dendritic grains around 100 nm
in length and less that 5 nm in width for the films grown at
400 ° C whereas the films grown at 800 ° C showed equiaxial nanograins with an average diameter of 4 nm. The I
− V data from both the C-AFM and probe station measurements showed a dielectric behavior for films grown at
400 ° C whereas the film grown at 800 ° C showed a semiconductorlike behavior, with 1–4 orders of magnitude higher
conductivity over 1 order of applied voltage. However, the
800 ° C film does not behave as having extended graphitic
domains even though the sp2-bond fraction is high. The
C-AFM measures show that the conduction in these films
共both deposition temperature兲 is not primarily governed by
extrinsic structural defects. The conductivity of both types of
films also shows field dependent nonlinear behavior similar
to microcrystalline CVD diamond. The P-F models with
single and overlapping Coulombic potentials are used to describe the conduction mechanism of the tested undoped
UNCD films. Both the P-F models showed that the conduction is directly correlated with the sp2 bond density and the
ratio of hydrocarbon bonds over sp2 bonded carbon in the
conduction path at the gain boundary.
ACKNOWLEDGMENTS
This work was supported by the NSF Nano-CEMMS
under Award No. DMI-0328162 and partially supported by
the WaterCAMPWS under CTS-0120978. Any opinions,
findings, and conclusions or recommendations expressed in
this publication are those of the authors and do not necessar-
J. Appl. Phys. 102, 113706 共2007兲
ily reflect the views of the NSF. The ERDA, TEM, AFM, and
Raman work is performed at the University of Illinois Center
for Microanalysis of Materials, partially supported by the
U.S. DOE under Grant No. DEFC02-91-ER45439. The authors would like to acknowledge Professor Ivan Petrov for
helpful discussions on the ERDA data and Dr. Changhui Lei
for the TEM sample preparation.
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