JOURNAL OF APPLIED PHYSICS
VOLUME 93, NUMBER 4
15 FEBRUARY 2003
Elastic, mechanical, and thermal properties of nanocrystalline
diamond films
J. Philip and P. Hessa)
Institute of Physical Chemistry, University of Heidelberg, D-69120 Heidelberg, Germany
T. Feygelson
GeoCenters Inc., Fort Washington, Maryland 20639
J. E. Butler
Code 6174, Naval Research Laboratory, Washington, DC 20375
S. Chattopadhyay, K. H. Chen, and L. C. Chen
Center for Condensed Matter Sciences, National Taiwan University, Taipei, Taiwan 106, Republic of China
共Received 2 October 2002; accepted 20 November 2002兲
Nanocrystalline columnar-structured diamond films with column diameters less than 100 nm and
thicknesses in the range of 1–5 ␮m were grown on silicon substrates by chemical vapor deposition
共CVD兲 in a microwave plasma reactor with purified methane and hydrogen used as the reactants.
Uniform conformal nucleation densities in excess of 1012 cm⫺2 were accomplished prior to growth
by seeding with explosively formed nanodiamonds, which resulted in good optical quality films.
The film thickness was measured in situ by the laser reflectometry method. The grain size and
optical quality of the films were characterized by scanning electron microscopy and Raman
measurements. Broadband surface acoustic wave pulses were used to measure the anomalous
dispersion in the layered systems. The experimental dispersion curves were fitted by theory,
assuming the diamond film as an isotropic layer on an anisotropic silicon substrate, to determine
mean values of the density and Young’s modulus of the diamond films. The density was close to the
density of single crystal diamond or polycrystalline diamond plates grown by the CVD technique,
whereas the Young’s modulus varied strongly with the nucleation density between 517 and 1120
GPa. Young’s moduli close to the single crystal values were obtained for films grown with a
nucleation density ⭓1012 cm⫺2 . The thermal diffusivity in these films was measured by the
traveling wave technique. The value for ⬃3.5-␮m-thick nanocrystalline diamond films with
nucleation densities ⭓1012 cm⫺2 was ⬃7.2 cm2 /s, whereas those with lower nucleation densities
showed a value of ⬃5.5 cm2 /s. © 2003 American Institute of Physics. 关DOI: 10.1063/1.1537465兴
I. INTRODUCTION
dependent mechanical properties that may significantly differ
from those of their coarser–grained counterparts.
The changes in the mechanical properties due to reduction in grain sizes are due to the fact that a larger percentage
of the atoms are expected to be in grain boundary environments with broken bonds, hydrogen termination, amorphous
regions, and/or sp 2 bonded carbon.1 In addition, the mechanical properties will be affected by other features such as
flaws, strains, impurities, etc., that result from synthesis and
processing. Similarly the phonon scattering processes in diamond that determine its thermal conductivity are also dependent on the local bonding environment in the crystal as well
as in the grain boundaries. Most of the defects and bonding
nature, sp 2 or sp 3 , that could affect the mechanical properties would affect the lattice thermal conductivity also. Therefore, it is very important to understand the mechanical and
elastic properties before designing and fabricating complex
mechanical structures. At present only limited information is
available in the literature on the elastic properties, density,
and thermal conductivity/diffusivity of nanocrystalline films.
In the case of nanocrystalline cubic boron nitride films it has
been found recently that the elastic properties may differ
substantially from those of single-crystal c-BN.2 Even
Diamond is the material of choice for many scientific
and technological applications because of its exceptional mechanical, electrical, thermal, and optical properties. In particular, the high hardness and stiffness of diamond make it
desirable for many mechanical applications. For this reason
there is great interest in the preparation of thin diamond
films, which can be used as hard and wear-resistant coatings
in a variety of applications, the preparation of diamond cantilevers for scanning force microscopy, or fabrication of
high-Q and high-frequency micromechanical resonators. The
extreme thermal conductivity in diamond has also propelled
the material for heat spreader applications. While microcrystalline diamond films with thickness in the range of several
micrometers have been successfully prepared and characterized, the interest in synthesizing diamond films with grain
sizes in the nanometer scale 共⭐100 nm兲 is increasing. One
reason is to reduce the intrinsic roughness of the diamond
surface. However, such nanophase materials have grain size
a兲
Electronic mail: [email protected]
0021-8979/2003/93(4)/2164/8/$20.00
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© 2003 American Institute of Physics
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Philip et al.
J. Appl. Phys., Vol. 93, No. 4, 15 February 2003
though the elastic and thermal properties of microcrystalline
diamond films with a thickness in the range of a few micrometers have been investigated by the surfaces acoustic
wave 共SAW兲 method,3 and the traveling wave technique
共TWT兲,4 respectively, no such work has been reported on
nanocrystalline diamond films.
The ‘‘nanocrystalline’’ diamond films studied here are
similar in their column structure to the thicker micro- or
polycrystalline diamond films and plates studied
previously,3,5 but very different from the ‘‘ultrananocrystalline’’ diamond films reported by Gruen et al.6,7 The present
nanocrystalline films are grown on substrates coated with
explosively prepared diamond,8 which promotes nucleation
densities from 1010 to greater than 1012 nuclei/cm2 . Subsequent growth to a thickness of 100–5000 nm results in grain
coarsening, polycrystalline texture development, and columnar growth yielding an anisotropic material whose local
grain size depends on the distance from the nucleation layer
and the growth conditions. The ultrananocrystalline films, on
the other hand, have much less grain coarsening, significantly higher s p 2 carbon fraction 共in fact the evidence for
crystalline carbon is barely detectable with conventional
techniques兲 and much higher optical absorption than the columnar nanocrystalline diamond films reported here.7,9
The current techniques used to investigate elastic properties of thin film samples are Brillouin scattering, ultrasonic
interferometry, nanoindentation, and the SAW method. Of
these, the dispersion of SAWs10 is a very suitable technique
to measure the elastic properties of superhard films. Thermal
conductivity/diffusivity
measurements
in
micro/
polycrystalline diamond were in general carried out by photothermal techniques11,12 which in some cases can probe
within a grain.11 The TWT measurements could distinguish
between the thermal diffusivity in the growth and nucleation
zones of free-standing polycrystalline diamond plates and
correlate it to the full width at half maxima of the 1332 cm⫺1
line in the Raman spectra.4
Raman and photoluminescence spectra were recorded to
evaluate the phase purity of the films and scanning electron
microscopy 共SEM兲 to gain insight into the structure and morphology. These measurements indicate that the column diameters were in range of 10–100 nm.
II. EXPERIMENT
A. Sample preparation
The nanocrystalline diamond films studied in this work
were fabricated by establishing a nucleation layer on 3 in.
diameter, 3-mm-thick silicon substrates by: 共1兲 first pretreating the substrate to the diamond growth plasma conditions for a brief period of time 共800 W microwave power,
720 °C substrate temperature, 900 sccm hydrogen flow rate,
and 4 sccm methane flow rate兲, typically 10–30 min; then
共2兲, putting the treated substrate into an ultrasonic bath of
nanocrystalline diamond powder in methanol or ethanol for
10– 60 min; followed by 共3兲, immediate rinsing and washing
with ethanol and nitrogen blow dry. This is an implementation of the nucleation process reported by Rotter.13 For film
growth, the seeded substrate is returned to the growth reactor
2165
and diamond is grown to the desired thickness at the conditions given earlier. The growth rate and film thickness were
monitored in situ by diode laser reflectometry at 677 nm.
Uniform and conformal nucleation densities in excess of 1012
cm⫺2 were observed on Si and SiO2 . The growth reactor
was a commercial microwave plasma reactor 共model PDS17, Astex Inc., Woburn, MA兲 operating at 2.45 GHz with a
maximum power of 1.5 kW.
Purified hydrogen and methane 共99.999%兲 were used as
reactants. The substrate was placed on an inductively heated
susceptor and the pressure of the flowing gases was maintained at 15 Torr. This reactor had been used previously for
growth of boron doped diamond films using diborane as a
reactant. Analysis of films similar to the ones studied in this
work has indicated residual boron doping levels of 1019 –1020
boron atoms per cubic centimeter.14
B. Raman and SEM measurements
Micro-Raman and photoluminescence spectra were measured using Ar-ion laser excitation at 488 nm and a commercial confocal micro-Raman spectrometer 共Renishaw S1000兲
using a 50⫻ microscope objective. The approximate laser
spot size on the sample was 1 ␮ m in diameter and the laser
power was less than 2 mW.
Scanning electron micrographs were obtained in a commercial field emission SEM 共Leo-1550兲 with no coatings applied to the samples. The nucleation surface was prepared for
SEM examination by etching the silicon substrate with a
combination of hydrofluoric, acetic, and nitric acids.
C. Surface acoustic wave dispersion measurements
In this technique the surface of the sample is irradiated
with nanosecond laser pulses to generate broadband SAW
pulses.10 These pulses propagate over a known distance and
are detected with a suitable broadband transducer. The presence of the film on the substrate surface introduces a length
scale, and thus generates the dispersion effect, which contains the information on the elastic and mechanical properties of the film and substrate system. If the substrate properties are known, one or more film properties can be extracted
from a theoretical fit of the nonlinear dispersion curve.15–17
We report here on measurements performed on three
separate nanodiamond films with varying thickness 共see
Table I兲. Samples D1 and D2 were the initial batch prepared.
Sample D5 was prepared several months later after a problem with the solution used to seed the nucleation layer was
discovered and corrected. All films were deposited on 3 in.
diameter Si共100兲 substrates with 3 mm thickness. The thickness of the films varied between 0.6 and 4.1 ␮m and was
determined by in situ laser interferometry at 677 nm during
growth near the center of the film, and at other points displaced from the center, by counting the number of interference fringes 共Newton’s rings兲 under 546 nm light. These
measurements were confirmed by Fourier-transform infrared
共FTIR兲 transmission and reflection measurements using the
refractive indexes: n VIS⫽2.41 and n IR⫽2.378 and SAW
measurements performed at different locations of the wafers
to realize different film thicknesses. In order to ensure that
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Philip et al.
J. Appl. Phys., Vol. 93, No. 4, 15 February 2003
TABLE I. Growth conditions for each sample are presented, along with the results of the film thickness at the center of the wafer by various techniques, fitting
of the SAW measurements, and thermal diffusivity/conductivity values. A constant substrate temperature of 720 °C and deposition pressure of 15 Torr was
maintained. ␳: film density; ␴: Poisson’s ratio; Y: Young’s modulus; ␣: thermal diffusivity; ␬: thermal conductivity.
Film thickness
Growth conditions
Sample name
共Est. error兲
D1
D2
D5
CVD plate
Time
共min兲
% CH4
in H2
Laser interferometry
during growth
共␮m兲
905
905
1605
0.33
0.88
0.33
1.61
3.45
3.61
SAW measurements
Reflection
FTIR 共␮m兲
SAW
共␮m兲
␳
(g/cm3 )
␴
1.41
2.98
共⫾0.2兲
2.0
3.4
3.6
共⫾0.15兲
3.5
3.51
3.44
3.52
共⫾0.04兲
0.12
0.12
0.12
0.09
the film thickness did not vary significantly over the propagation distance of the SAW pulse, the direction of SAW
propagation was selected to be parallel to the 具110典 direction
of silicon and tangential to the circular interference fringes.
Since the Rayleigh wave velocity in diamond is significantly higher than in silicon, the phase velocity strongly increases with frequency in the layered system 共anomalous dispersion兲. Frequency components up to about 250 MHz could
be detected. A good signal-to-noise ratio was achieved up to
100 MHz for the thicker films and up to 170 MHz for the
thinner films. The same experimental conditions were maintained for the measurements performed at different thickness
values.
D. TWT for the determination of thermal diffusivity
The diamond films on silicon were systematically studied for the thermal diffusivity by the TWT. The method of
determining the thermal diffusivity from the phase lag between a temperature forcing function and the traveling thermal wave in the material was described by Kosky.18 The
present technique uses a probe laser to compare the phase
instead of a IR microscope to determine the actual temperature in the material. A sine wave 共2 Hz兲 modulated GaAs
共SDL-3490-S兲 diode laser (␭⫽812 nm兲 was used to generate
a sinusoidal thermal wave in the thin film by irradiating the
edge of the sample with the laser. By monitoring the phase
difference 共⌬␪兲, from the deflection of a He–Ne probe laser
beam 共15 mW, Melles Griot兲, as a function of the distance
共d兲 along the sample, the thermal diffusivity 共␣兲 is determined. The relation between the phase difference 共⌬␪兲 at a
particular point on the sample as detected by the probe laser
and the distance 共d兲 of that point from the IR source is given
by
⌬␪⫽
冉 冊冑
␲
180
⫹
4
␲
f␲
•d,
␣
where f ⫽2 Hz is the frequency of the modulating sine wave.
The slope of the ⌬␪ vs d plot yields the value of the thermal
diffusivity. The details of the thermal diffusivity measure19
ment setup are given elsewhere.
12
Graebner et al. reported anisotropy in the thermal conductivity of chemical vapor deposition 共CVD兲 diamond measured by a laser flash technique and fast infrared detection.
TWT measurements
Y
共GPa兲
共⫾30兲
517
553
1120
1120
␣
(cm2 /s兲
␬
共W/cm K兲
共⫾0.3兲
2.8
5.5
7.2
5.3
10.4
13.7
Ono et al.20 reported the thermal conductivity values of microwave CVD diamond films by making use of radiation
heat transfer and radiation thermometry. Irrespective of the
method used, the measurement and the interpretation of the
results become complicated for a thin film on a particular
substrate, as in this case, where the heat is conducted both by
the film and the substrate.
III. RESULTS
Table I presents a summary of the growth conditions, the
film thicknesses, the results of the SAW dispersion analysis,
and thermal diffusivity measurements for the diamond films
investigated. Photographs of the films D1 and D2 are shown
in Figs. 1共a兲 and 1共b兲, respectively, where the samples are
illuminated with monochromatic light 共546.1 nm兲. Interference fringes, Newton’s rings, are observed as a result of the
variation in film thickness with position on the wafer. A scanning electron micrograph 共SEM兲 of a portion of the growth
surface of films D2 and D5 are shown in Figs. 2共a兲 and 2共b兲,
respectively, while SEMs of portions of the initial nucleation
surfaces of the films D2 and D5 are shown in Figs. 3共a兲 and
3共b兲, respectively. Figure 4共a兲 presents the micro-Raman
spectra and Fig. 4共b兲 presents the photoluminescence spectra
of samples D2 and D5, excited by 488 nm Ar-ion laser radiation, including the Raman scattering portion of the spectra. Figures 5共a兲 and 5共b兲 display the micro-Raman spectra
recorded at different distances from the center of the wafer
共thickness values兲 for the films D2 and D5.
Figure 6 shows two SAW pulses measured for a 2-␮mthick nanodiamond film. Pulses 共a兲 and 共b兲 in the figure were
detected at distances of 6.2 and 14.2 mm from the excitation
line, respectively. Figure 7 presents the dispersion curve resulting from the Fourier transformation of these two SAW
pulses. As can be seen, the phase velocity increases with
frequency, as expected for the stiffer diamond film 共anomalous dispersion兲. Due to the large acoustic contrast between
the silicon substrate and the diamond film the dispersion
curve is strongly nonlinear. The best theoretical fit to the
experimental dispersion curve is also shown in Fig. 7, and
was used to extract the values of the Young’s modulus, thickness, and film density.
The value of the Poisson’s ratio was fixed to 0.12⫾0.04,
the value reported in the literature for microcrystalline diamond. It should be noted that the values of the Young’s
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J. Appl. Phys., Vol. 93, No. 4, 15 February 2003
Philip et al.
2167
FIG. 1. Optical photographs of samples 共a兲 D1 and 共b兲 D2 under monochromatic 共546 nm兲 illumination. The variation of film thickness with position
gives rise to the observed interference rings.
FIG. 2. SEM of a portion of the growth surfaces of the film 共a兲 D2 and 共b兲
D5.
modulus and density determined by the SAW method do not
depend sensitively on the Poisson’s ratio. For example, a
variation in the Poisson’s ratio by 33% changes the Young’s
modulus and density only by a few percent.
The best theoretical fits of the experimental dispersion
curves yielded densities in the range of 3.47⫾0.15 g/cm3 ,
irrespective of the thickness of the film. This value is to be
compared with 3.515 g/cm3 reported for single crystal
diamond3 and indicates a surprisingly high density of all
three films. The relatively large error in the density values
seems to be mainly due to a coupling of the Young’s modulus and density in the SAW analysis applied.
The values of the Young’s moduli obtained in the thickest region of the D1 and D2 films were in the range of 517–
553⫾30 GPa, whereas for the film D5 we measured a value
of 1120⫾30 GPa. A plot showing the variation of the
Young’s modulus with film thickness is presented in Fig. 8.
The stiffness slightly decreases in the direction of decreasing
film thickness at the edge of the wafers but this effect is in
the range of the experimental error. The measured moduli
should be compared with 1080⫾20 GPa reported previously
for a micrometer thick microcrystalline diamond film3 and
1143 GPa estimated theoretically for ideal polycrystalline
diamond, where it is assumed that the grain boundaries do
not influence the elastic properties.21
Note the substantial difference between the results for
the first batch of samples D1 and D2 and sample D5. The
first two samples were grown using a nucleation solution of
nanodiamonds, step 2 in the nucleation procedure described
earlier, which had gradually become depleted of seeds, resulting in incomplete coverage and lower nucleation density
with regions of amorphous carbon between nuclei, as can be
seen in Fig. 3共a兲. A comparison of Figs. 3共a兲 and 3共b兲 shows
a remarkable difference in the nucleation densities, ⬃1010
nuclei/cm2 for film D2 关Fig. 3共a兲兴, versus over 5⫻1011 to
greater than 1012 for film D5 关Fig. 3共b兲兴. SEM images of the
nucleation layer for film D1 are consistent with that shown
for film D2, while the SEM for film D5 is consistent with
other samples grown from a more concentrated solution of
seeds. Attempts at optimizing and quantifying the particle
size distribution and concentration in the solution are in
progress.
In order to compare the Young’s modulus of the nanocrystalline diamond films with that of a thicker polycrystalline diamond plate, a plate of thickness 400 ␮m was grown
by CVD on a polished tungsten plate in a similar 5 kW
microwave plasma reactor. The plate was polished down to a
thickness of 320 ␮m. The Rayleigh velocity of surface
acoustic waves on the plate was measured by laser excitation
of SAWs and detection after propagation over a known distance with the piezoelectric foil detector. The longitudinal
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Philip et al.
J. Appl. Phys., Vol. 93, No. 4, 15 February 2003
FIG. 3. SEM of a portion of the initial nucleation surfaces of the films 共a兲
D2 and 共b兲 D5. The much higher nucleation density of film D5 is evident
from these figures.
acoustic bulk wave velocity in the plate was determined by a
transmission technique, employing laser excitation on one
and detection on the opposite side of the plate. Assuming the
polycrystalline plate as isotropic, the mean value of the
Young’s modulus was evaluated following well-known
equations.22 The experimental results could be described
with a density of the plate of 3.52 g/cm3 , a Rayleigh velocity
of 10750⫾80 m/s, a longitudinal acoustic bulk velocity of
17980⫾100 m/s, a Poisson’s ratio of 0.089⫾0.03, and a
Young’s modulus of 1120⫾30 GPa. This indicates that the
mean stiffness of this thick plate was comparable to that of
sample D5 demonstrating the high quality of this diamond
sample.
Thermal diffusivity measured on samples D1, D2, and
D5 are tabulated in Table I. A considerable thickness effect
on the thermal diffusivity was observed for these films.
Sample D5 was found to have substantially higher 共⬎25%兲
thermal diffusivity value than sample D2, which is of a similar thickness as sample D5. Assuming the density and specific heat values of single crystal diamond for the nanocrystalline samples, the thermal conductivity of these
nanocrystalline diamond samples could be arrived at, which
are also shown in Table I. Thermal conductivity values were
in the range of 5–14 W/cm K, whereas for natural diamonds
this value can go up to 25 W/cm K. Figure 9 shows a comparison of the thickness dependence of the thermal diffusivity in sample D5, prepared under high nucleation densities,
and another sample prepared under low nucleation densities.
FIG. 4. Micro-Raman spectra 共a兲 and photoluminescence spectra 共b兲 of
samples D2 and D5 excited by 488 nm Ar-ion laser radiation. The latter
curves include the Raman scattering portion of the spectra.
Both samples show a strong thickness dependence, which
was not as pronounced in the SAW measurements, but
clearly sample D5 was the superior one having a higher
range of thermal diffusivities.
IV. DISCUSSION
Usually the Young’s modulus or stiffness of a film correlates with its density. As is evident from the values presented in Table I, the Young’s modulus of the nanodiamond
films D1 and D2 is only about half the value found for the
high quality nanodiamond film D5 and the plate. On the
other hand, the corresponding density values vary only by a
few percent. Since the experimental error in the density is in
the same range as the differences measured for the three film
samples and the plate, it is not possible to extract from these
density values more detailed information on the reason for
the strong reduction of the stiffness in films D1 and D2.
The micro-Raman and photoluminescence spectra of the
films exhibit a broadened diamond zone center phonon mode
at 1332 cm⫺1 , Raman scattering between 1340 and 1600
cm⫺1 associated with resonance enhanced Raman scattering
from sp 2 -bonded carbon, and a broad background photolu-
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J. Appl. Phys., Vol. 93, No. 4, 15 February 2003
Philip et al.
2169
FIG. 7. Typical SAW dispersion curve and the best theoretical fit for a
nanodiamond film of thickness 2 ␮m.
FIG. 5. The micro-Raman spectra for samples 共a兲 D5 and 共b兲 D2 recorded at
different distances from the center.
FIG. 6. Typical SAW pulses on a nanocrystalline diamond film of thickness
2 ␮m after propagation over a distance of 共a兲 6.2 and 共b兲 14.2 mm from
excitation line on a Si共100兲 substrate in the 具110典 direction.
minescence from 500 to 800 nm. The broad photoluminescence is likely due to the presence of electronic states in the
band gap of diamond due to dislocations and extended defects within the grains. There is no evidence of photoluminescence from nitrogen vacancy centers with zero phonon
lines at 575 and 637 nm, which are frequently seen in CVD
diamond materials. The weak broad luminescence at 737 nm
is likely due to a trace of the Si–V center, also frequently
seen in CVD diamond.
The high density of these films, coupled with the faceted
grain structure observed in the SEM, and low sp 2 -bonded
carbon content, is consistent with a material comprised of
bulk crystalline diamond domains separated by incoherent
grain boundaries, probably containing many twin related
grains, stacking faults, and stress induced dislocations.
Transmission electron microscopy studies of thicker polycrystalline CVD diamond films have demonstrated this general structure beginning with growth of individual nuclei until they coalesce into a film, followed by rapid overgrowth of
most nuclei by a few preferentially oriented nuclei 共or
growth sectors兲. Then further grain coarsening or enlarge-
FIG. 8. Variation of the Young’s modulus with thickness for the nanodiamond films and plate.
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J. Appl. Phys., Vol. 93, No. 4, 15 February 2003
FIG. 9. Variation of thermal diffusivity with the thickness of nanodiamond
samples grown under nucleation densities 共䊏兲⭓1012/cm2 共sample D5兲 and
共䊐兲⭐1010/cm2 .
ment occurs as the film thickens.23 Dislocations were observed primarily near incoherent grain boundaries, or in
highly twinned regions.23
The slightly higher s p 2 -bonded carbon content of films
D1 and D2, as compared with film D5, which is likely located at grain boundaries and extended defects, suggests that
the bulk mechanical properties of these two films are
strongly influenced by these weakest links, namely the grain
boundaries and extended defects.
The drastic decrease in the values of Young’s modulus
for samples D1 and D2 from that of the D5 film and the plate
throws light on the role played by the nucleation density
during growth on the elastic properties of nanodiamond
films. The SEM pictures indicate nucleation transition layers
of 10–250 nm, which are expected to have a lower density
and Young’s modulus. The influence of these transition layers on the mean values of the elastic and mechanical constants increases with decreasing film thickness and may be
responsible for the systematically lower Young’s moduli
found for thinner samples but also in thinner regions of a
particular sample. A higher nucleation density during growth
leads to more rapid film coalescence and thus less volume of
voids, amorphous, or s p 2 -bonded carbon in the nucleation
layer and early stage of film growth 共⬃10–100 nm兲. This in
turn may impact the strength or degree of amorphous carbon
extending into some of the grain boundaries. As can be seen
in Figs. 4共a兲– 4共b兲 slightly more s p 2 共amorphous兲 carbon is
present in film D2 than film D5 while comparison of the
SEM images on the nucleation side indicates large dark
cracks or lines between the nuclei in film D2, Fig. 3共a兲, and
on the growth surface, Fig. 2共a兲. All this is suggestive that
the properties of the grain boundaries and film microstructure, whose evolution depends on the nucleation density, impact the mechanical properties in a dramatic way.
Due to the complicated morphology of the nanocrystalline diamond films, with a nucleation layer evolving from
lower diamond quality and composition into higher quality
grains separated by fewer grain boundaries with a columnar
structure, it is not possible to identify the weak bonding effects from the measured mean values of the mechanical
properties. We are led to conclude that the presence of
weaker three-dimensional bonding, e.g., by amorphous or
sp 2 -bonded carbon at the grain boundaries, which does not
have long-range order,24 causes the substantial reduction in
the Young’s modulus without significantly reducing the density.
Intergrain and intragrain phonon scattering are believed
to be the dominant factors in determining the mean thermal
diffusivity characteristic of the particular sample. Intergrain
scattering is mostly dominated by the sp 2 rich grain boundaries, whereas defects within a crystal dominate the intragrain scattering. For reasons mentioned earlier for the elastic
properties, here also sample D5 has a 25% higher thermal
diffusivity than sample D2 probably due to less intergrain
scattering. However, this was much less than the observed
difference in their Young’s modulus 共⬃100%兲. Physical
properties, such as density, that were found to have a considerable effect on the thermal diffusivity of a material,25 were
similar for these nanocrystalline diamonds. This may be one
of the reasons for not observing a drastic change in thermal
diffusivity in these samples. Generally one would have expected a change in mass density of the films when the grain
density is changing. Hence, in this case the change in the
thermal diffusivities in D2 and D5 should relate more to the
crystalline quality of the samples. The thickness dependence
of thermal diffusivity shown in Fig. 9 should be largely due
to the anisotropy across the thickness of the sample. The
quality of the grains and the defective grain boundaries are
all complex functions of growth time. Moreover, the interface between the film and the substrate will also produce
some interfacial thermal resistances that will change with
growth time and, hence, thickness of the film. The improving
quality of crystals and reducing interfacial thermal resistance
with the thickness of the film will translate into an increasing
thermal diffusivity. A detailed description of this thickness
dependence of thermal diffusivity in thin film on substrate
systems is given elsewhere.26 Interestingly, the thermal
diffusivity/conductivity values reported for polycrystalline
CVD diamond films are close to the values found for these
nanocrystalline diamonds.
V. CONCLUSION
The mean values of the Young’s modulus and density of
three nanocrystalline diamond films and a free-standing diamond plate were determined by analyzing the measured dispersion of broadband laser-generated SAW pulses. The thermal diffusivity of these nanocrystalline diamond materials
grown under high and low nucleation density conditions was
measured by the traveling wave technique. The morphology
of the films was determined by SEM and bonding information was extracted by micro-Raman. It was found that the
Young’s moduli of the nanocrystalline films grown with
lower nucleation densities (1010 cm⫺2 or lower兲 was roughly
half of those of a film and plate grown with much higher
nucleation density 共⭓1012 cm⫺2 ). For diamond grown with
high nucleation density, the Young’s modulus was close to
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Philip et al.
J. Appl. Phys., Vol. 93, No. 4, 15 February 2003
the corresponding values measured for high quality microcrystalline films or a polycrystalline diamond plates grown by
the CVD technique. On the other hand, the density of the
films was rather independent of the nucleation density and
agreed within a few percent with the value of single crystal
diamond. The thermal diffusivity value for the nanocrystalline film grown under high nucleation densities was found to
be 25% higher than of films grown under low nucleation
densities. A strong thickness dependence of the thermal diffusivity was observed in these nanocrystalline diamond films
that could be due to the crystalline quality and volume fraction, and interfacial thermal resistance in the layered structure, all of which are functions of growth time.
ACKNOWLEDGMENTS
One of the authors 共J.P.兲 thanks The Alexander von
Humboldt Foundation for providing support for a research
stay at Heidelberg. S. Chattopadhyay thanks the National
Science Council, Taiwan, for a postdoctoral fellowship. The
NRL portion of this work was supported in part by the Office
Naval Research and DARPA.
1
R. W. Siegel and G. E. Fougere, in Nanophase Materials, edited by G. C.
Hadjipanayis and R. W. Siegel 共Kluwer Academic, 1994兲, pp. 233–261.
G. Lehmann, P. Hess, S. Weissmantel, G. Reisse, P. Scheible, and A.
Lunk, Appl. Phys. A: Mater. Sci. Process. 74, 41 共2002兲.
3
R. Kuschnereit, P. Hess, D. Albert, and W. Kulisch, Thin Solid Films 312,
66 共1997兲.
4
S. Chattopadhyay S. C. Chien, L. C. Chen, K. H. Chen, and H. Y. Lee,
Diamond Relat. Mater. 11, 708 共2002兲.
5
G. Lehmann, M. Schreck, L. Hou, J. Lambers, and P. Hess, Diamond
Relat. Mater. 10, 686 共2001兲.
2
2171
6
S. Jiao, A. Sumant, M. A. Kirk, D. M. Gruen, A. R. Krauss, and O.
Auciello, J. Appl. Phys. 90, 118 共2001兲.
7
D. M. Gruen, Annu. Rev. Mater. Sci. 29, 211 共1999兲.
8
V. Y. Dolmatov, Russ. Chem. Rev. 70, 607 共2001兲.
9
D. Zhou, D. M. Gruen, L. C. Qin, T. G. McCauley, and A. R. Krauss, J.
Appl. Phys. 84, 1981 共1998兲.
10
A. Lomonosov, A. P. Mayer and P. Hess, in Modern Acoustical Techniques
for the Measurement of Mechanical Properties, edited by M. Levy, H. E.
Bass, and R. Stern 共Academic, Boston, 2001兲, Vol. 39, pp. 65–134.
11
J. Hartmann, P. Voigt, and M. Reichling, J. Appl. Phys. 81, 2966 共1997兲.
12
J. E. Graebner, S. Jin, G. W. Kammlott, B. Bacon, L. Seibles, and W.
Banholzer, J. Appl. Phys. 71, 5353 共1992兲.
13
S. Rotter, Proceedings of the Applied Diamond Conference/Frontier Carbon Technologies—ADC/FCT ’99, edited by M. Yoshikawa, Y. Koga, Y.
Tzeng, C.- P. Klages, and K. Miyoshi, 共MYU K.K., Tokyo, 1999兲, p. 25.
14
R. Kalish, C. Saguy, and J. E. Butler 共private communication兲.
15
A. Neubrand and P. Hess, J. Appl. Phys. 71, 277 共1991兲.
16
H. Coufal, R. Grygier, P. Hess, and A. Neubrand, J. Acoust. Soc. Am. 92,
2980 共1992兲.
17
G. W. Farnell and E. L. Adler, in Physical Acoustics IX, edited by W. P.
Mason and R. N. Thurston 共Academic, New York, 1972兲.
18
Philip G. Kosky, Rev. Sci. Instrum. 64, 1071 共1993兲.
19
D. M. Bhusari, C. W. Teng, K. H. Chen, S. L. Wei, and L. C. Chen, Rev.
Sci. Instrum. 68, 4180 共1997兲.
20
A. Ono, T. Baba, H. Funamoto, and A. Nishikawa, Jpn. J. Appl. Phys.,
Part 2 25, L808 共1986兲.
21
C. A. Klein and G. F. Cardinale, Diamond Relat. Mater. 2, 918 共1993兲.
22
I. A. Viktorov, in Rayleigh and Lamb Waves, edited by W. P. Mason
共Plenum, New York, 1967兲.
23
J. W. Steeds, A. E. Mora, J. E. Butler, and K. M. Bussman, Philos. Mag.
A 82, 1741 共2002兲.
24
T. Mura, N. Yamashita, T. Mishima, and Y. Hirose, Int. J. Eng. Sci. 27, 1
共1989兲.
25
S. Chattopadhyay, L. C. Chen, C. T. Wu, K. H. Chen, J. S. Wu, Y. F. Chen,
G. Lehmann, Appl. Phys. Lett. 79, 332 共2001兲.
26
S. Chattopadhyay, L. C. Chen, S. C. Chien, S. T. Lin, and F. Chen, J. Appl.
Phys. 92, 5150 共2002兲.
Downloaded 24 Feb 2003 to 147.142.186.53. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp