Surface and Coatings Technology 177 – 178 (2004) 812–817
Structural properties of amorphous carbon films by molecular dynamics
simulation
Seung-Hyeob Lee, Churl-Seung Lee, Seung-Cheol Lee, Kyu-Hwan Lee, Kwang-Ryeol Lee*
Future Technology Research Division, Korea Institute of Science and Technology, P.O. Box, 131, Cheongryang, Seoul, South Korea
Abstract
Structure and properties of amorphous carbon film was investigated by molecular dynamics simulation using a Tersoff potential
for carbon–carbon interaction. Quantitative determination of coordination numbers, atomic density, and pair correlation function
was adapted to investigate the relationship between incident energies and structural properties. The structural properties of the
amorphous carbon film made by the simulations were compared with those of the films deposited by filtered vacuum arc (FVA)
process. As in the experimental result, the structural properties of the modeled film have their maximum values when the incident
energy of deposited atoms is between 50 and 75 eV. At the optimum kinetic energy condition, we could observe in pair correlation
˚ By melting and
functions that significant amount of carbon atoms were placed at a meta-stable site of atomic distance of 2.1 A.
quenching simulation of diamond lattice, it could be shown that the population of the meta-stable site is proportional to the
quenching rate. These results suggest that the hard and dense diamond-like film could be obtained when the localized thermal
spike due to the collision of the high-energy carbon ion can be effectively dissipated to the lattice.
䊚 2003 Elsevier B.V. All rights reserved.
Keywords: Amorphous carbon films; Molecular dynamics simulation; Tersoff potential
1. Introduction
Amorphous carbon thin films are one of the widely
used materials for industrial applications due to their
superior optical, physical, and chemical properties. Especially, tetrahedral amorphous carbon (ta-C) films, a kind
of amorphous carbon films, have attracted much attention because they have a high sp3 fraction, high hardness
(60–90 GPa), and good optical transparency, which are
comparable to those of the crystalline diamond. Moreover, ta-C films are expected to satisfy current industrial
requirements of ultra-thin films less than 10 nm in
thickness with excellent mechanical properties. For successful application of the ta-C film, however, some
technical limitations should be overcome. One of the
most significant problems is the high residual compressive stress of the ta-C film ranging from 6 to 20 GPa,
which can deteriorate the adhesion between the film and
the substrate w1,2x. Therefore, a vast effort has been
devoted to reducing residual stress as well as improving
*Corresponding author. Tel.: q82-2-958-5494; fax: q82-2-95855093.
E-mail address: [email protected] (K.-R. Lee).
the mechanical and physical properties of ta-C film w3–
6 x.
From the viewpoint of atomic scale, these materials
are interesting since they are complex and largely varied
mainly due to the interplay between sp2 and sp3 hybrid
bonds. It is most important to understand how the
fraction of sp2 and sp3 bonding in amorphous carbon
film affects its mechanical properties and the residual
stresses. Although a number of mechanism has been
proposed to explain the structural evolution and the
origin of the residual stress w7–9x, its relationship to the
structural features is not fully understood yet. Atomic
level simulation is valuable in investigating the evolution
of the film and their structural characteristics w10x,
especially in the case of ultra-thin films. We employed
molecular dynamics to simulate the growth of amorphous carbon films on diamond (100) substrates. Many
previous works of the molecular dynamic simulation
reported the relationship between incident energy of
carbon and structural properties such as residual stress,
density, bonding structure and pair correlation functions
w8,11–14x. However, mechanism of the structural evolution is yet to be clarified. In the present work, we
compared the pair correlation functions between the
0257-8972/04/$ - see front matter 䊚 2003 Elsevier B.V. All rights reserved.
doi:10.1016/j.surfcoat.2003.06.014
S.-H. Lee et al. / Surface and Coatings Technology 177 – 178 (2004) 812–817
813
amorphous carbon film simulated by energetic carbon
bombardment and that by rapid quenching of liquid
carbon. We could show that the structure of high sp3
hybridized bond fraction can be obtained where thermal
spike due to energetic carbon bombardment is rapidly
quenched by the surrounding lattice.
2. Computational method
To simulate the depositions and structure evolutions
of amorphous carbon films, we used the three body
empirical potential of carbon suggested by Tersoff w15x.
The amorphous carbon films were produced on a diamond (001) surface by the bombardment of 500 neutral
carbon atoms of various kinetic energies. The incident
kinetic energy of carbon atoms was varied from 1 to
300 eV. A 4.75a0=4a0=4a0 (here, a0 is equilibrium
lattice constant of bulk diamond) diamond crystal slab
composed of 608 carbon atoms was used as the substrate. All substrates were equilibrated at 300 K for 1
ps. Deposited atoms were bombarded on the substrate
at normal incidence. Horizontal position of the incident
atom was randomly selected at the distance of 5.35 nm
from the substrate surface. The time interval between
two consecutive atoms hitting the substrate was fixed at
1 ps, resulting in the ion flux of approximately
1=1030 ym2s. Temperature of the substrate was rescaled
to 300 K after the atomic rearrangement caused by the
bombardment of carbon was finished. The carbon flux
in this simulation was unrealistically high by reducing
the interval between the bombarding events that are
very rare in real deposition condition. However, the
temperature rescaling method could prevent the substrate
heating. The time interval was selected to be larger than
the sum of the time required to relax the atomic structure
and that for rescaling the temperature. We applied
periodic boundary conditions parallel to the diamond
(001) surface. The atomic position of bottom one layer
was fixed to simulate the bulk substrate. All other atoms
in the substrate were allowed to move freely. The time
steps were exponentially decreased from 0.5 to 0.155 fs
while increasing the kinetic energy of incident carbon
atom from 1 to 300 eV.
Fig. 1 shows the changes in potential and kinetic
energy of the system when four carbon atoms of the
kinetic energy 50 eV bombarded the substrate. The total
energy equilibrates within 1 ps after bombardment.
When a new carbon atom is introduced in the vacuum
region with its initial kinetic energy (indicated by an
arrow 1), the kinetic energy of the system is increased
by the amount of the initial kinetic energy. The potential
energy of the system also increases, since the incident
atom is located far from its equilibrium position. At the
moment of impact (indicated by an arrow 2), the kinetic
energy decreased with the dissipation of the kinetic
energy to the substrate atoms. At this moment, the
Fig. 1. The changes in the potential and the kinetic energy of the
system during the simulation, when carbon atoms of kinetic energy
of 50 eV were bombard to the substrate.
potential energy is suddenly increased as indicated by
an arrow 3. This sudden increase in potential energy is
associated with the atomic agitation in the surface due
to the bombardment of deposited atom. The sudden
increase in potential energy was observed only when
the kinetic energy of the incident atom was larger than
50 eV. In the range of the initial kinetic energy up to
300 eV, the perturbation of the substrate atom was fully
stabilized within 300 fs after the impact. Therefore, if
the time interval of the bombardment is set to be larger
than 300 fs, it would be possible to treat the deposition
behavior as quasi-steady state. If atoms are recoiled
from the substrate, the kinetic energy of the system can
be higher after the bombardment as indicated by an
arrow 4.
3. Results and discussion
Fig. 2 shows the morphologies of the amorphous
carbon films deposited with 500 carbon atoms of various
initial kinetic energies. The dotted line indicates the
initial position of the surface. White balls are the
deposited atoms and black balls the substrate atoms. In
the case of 1 eV of initial kinetic energy (Fig. 2a), the
film exhibits a sparse amorphous structure and the
substrate surface is not affected by the bombardment.
Since the mobility of the carbon atom is very low at
the simulation temperature (300 K), it is assumed the
film morphology does not change with time after the
deposition. Increasing the kinetic energy to 10 eV
resulted in the denser carbon film as shown in Fig. 2b,
whereas the interface morphology between the film and
the substrate was essentially same as that of 1 eV. As
814
S.-H. Lee et al. / Surface and Coatings Technology 177 – 178 (2004) 812–817
Fig. 2. The snapshots of amorphous carbon structure after 500 carbon atoms were deposited with the kinetic energy of (a) 1 eV, (b) 10 eV, (c)
50 eV, (d) 100 eV, (e) 150 eV, (f) 300 eV.
the incident energy increased to 50 eV, intermixing
occurred between film and substrate. Fig. 2c shows the
morphology of the film deposited at 50 eV. As the
energy of the incident atom is much higher than the
cohesive energy of diamond (7.4–7.7 eVyatom) w16,17x,
the incident atom could penetrate into the film. The
substrate surface was amorphized due to the significant
agitation of the substrate atoms. Since the amorphous
structure generated by the bombardment cannot return
to their equilibrium phase at this temperature, a highly
stressed and dense surface layer was formed on the
substrate surface. In the case of a 100 eV incident
energy, the intermixing of atoms at the interface is
substantially increased. It should be noted that the
substrate atom was found at the surface of the deposited
film. As can be seen from Fig. 2a,b,c and d, the thickness
of the intermixing layer increased with increasing incident energy. Atomic intermixing in covalent bonded
materials would require the breaking of the existing
bond before any reconfiguration occurs. By considering
the cohesive energy in diamond, it can be understood
that the intermixing occurred only when the incident
energy was larger than 10 eV. These results is in good
agreement with the calculation of Pailthorpe et al. w18x.
The densities of the film normalized to that of pure
diamond were summarized in Fig. 3. The films deposited
with 1 eV incident energy have a density approximately
64% of that of pure diamond. However, the films of
S.-H. Lee et al. / Surface and Coatings Technology 177 – 178 (2004) 812–817
Fig. 3. Dependence of the film density on the incident energy of
deposited carbon atoms. The density was normalized to that of crystalline diamond. Broken line in the figure is included only to guide
the eyes.
80% normalized density can be obtained when the
kinetic energy of the incident atom is between 50 and
75 eV. When the incident energy is larger than 100 eV,
significant decrease in the density was observed. Fig.
4a,b show the dependence of residual stress and sp3
bond fraction on the kinetic energy of the incident
atoms, respectively. When the kinetic energy of the atom
815
was 1 eV, the film has residual tensile stress. The
residual stress became compressive as the incident energy increased. The maximum residual compressive stress
could be obtained at an incident energy between 50 and
75 eV. This behavior coincides with the sp3 fraction in
the film shown in Fig. 4b. The maximum value of sp3
fraction was also obtained at the incident energy between
50 and 75 eV. The results of Figs. 3 and 4 exhibit an
intimate relationship between the density, residual stress
and sp3 fraction in the film. Since the sp3 bond in an
amorphous carbon film without hydrogen increases
three-dimensional interlinks between carbon atoms, the
hardness and the density of the films is proportional to
the sp3 fraction. However, increasing the three-dimensional interlinks in the amorphous covalent materials
would result in the distortion of both the bond angle
and the bond length, which can increase the stress level
of the film. Hence, the residual stress and the hardness
of diamond-like carbon film show almost identical
dependence on an experimental parameter, because they
are dependent on the common structural factor of threedimensional interlinks.
Shin et al. w19x investigated the dependence of the
residual stress of ta-C film on the negative bias voltage
applied to the substrate during the deposition. More than
90% of carbon atoms produced by the vacuum arc is
ionized in filtered vacuum arc process. Hence, the
experimental deposition environment is similar to the
present simulation condition. They reported that the
maximum residual stress of approximately 7 GPa was
observed when the bias voltage of the substrate is in the
Fig. 4. (a) Residual stress and (b) sp3 hybridized bond fraction of the film for various values of the incident energy of deposited carbon atoms.
Broken line in the figure is included only to guide the eyes.
816
S.-H. Lee et al. / Surface and Coatings Technology 177 – 178 (2004) 812–817
Fig. 5. Pair correlation functions of the deposited films for various
values of the incident energy of deposited carbon atoms.
range from y50 to y100 V. The ion energy in this
optimum condition is estimated to be between y70 and
y150 eV, because the carbon ion generated on the
surface of graphite cathode is also accelerated by the
voltage bump formed near the anode of approximately
20 to 50 V w20x. This experimental result qualitatively
agrees with the calculations of Fig. 4a,b. However, the
quantitative values of the residual stress or the sp3
fraction are considerably different from the experimental
results. For example, the calculated maximum value of
sp3 fraction is 48%, which is much smaller than experimental determination of sp3 fraction w13x. Although
experimental measurement of sp3 fraction is not well
established, a limit of Tersoff potential that p bonding
is not considered in the force field calculation should
be also considered. In addition, one should note that the
time scale of the simulation is not sufficient to allow
relaxation of the atomic configuration after the highenergy bombardment.
Pair correlation functions for various incident energies
are shown in Fig. 5. Regardless of the incident ion
˚ and
energy, the first nearest neighbor appears at 1.5 A
˚
the second nearest neighbor at 2.6 A. The positions of
these peaks correspond to those of the crystalline diamond, respectively. In addition to the mains peaks, a
˚ (as indicated by an
small peak was observed at 2.1 A
arrow in Fig. 5). Because this peak cannot be observed
in crystalline diamond, it might be considered as a metastable site in the amorphous carbon structure. The
number of carbons placed in this site reaches a maximum at 50 eV. This is the same behavior as those of
the density, sp3 fraction and the mechanical properties
of the film. This meta-stable peak was also observed in
the previous simulation works of amorphous carbon
structure w11x. Systematic analysis of its intensity enables us to find a close relationship between the formation
of dense carbon film and the quenching rate of thermal
spike due to the bombardment of energetic carbon atoms.
The meta-stable site could be also found in the
amorphous structures generated by rapid quenching of
liquid carbon. Fig. 6 shows the pair correlation functions
of the amorphous carbon film when the liquid carbon
was quenched from 10 000 K to 0 K at various quench˚ was proportional
ing rates. The peak intensity at 2.1 A
to the quenching rate. The intensity of the peak, i.e.
population of carbon atom at this site can be reduced
only by thermal annealing at higher temperature, following Ahrrenius type kinetics with barrier energy of
approximately 0.03 eV per atom w21x. This result shows
˚ are in a meta-stable state
that the carbon atoms at 2.1 A
and require activation energy to return to more stable
states. Since the population of carbon atom in the metastable state is proportional to the quenching rate (Fig.
6) and the maximum population was observed when the
kinetic energy of deposited atom was 50 eV (Fig. 5), it
can be concluded that the quenching rate of the localized
high temperature spike due to the bombardment is
maximum under the optimized deposition condition. Our
calculation result is thus consonant with the thermal
spike model on the synthesis of diamond-like carbon
films: the bombardment of energetic carbon atom makes
a localized thermal spike region, which is rapidly
quenched as the thermal energy is dissipated to adjacent
Fig. 6. Pair correlation functions of the amorphous carbon modeled
by rapid quenching from the liquid phase of carbon at 10 000 K.
S.-H. Lee et al. / Surface and Coatings Technology 177 – 178 (2004) 812–817
substrate atoms w8,22–24x. In the case of the present
simulation condition, the effect of the rapid quenching
seems to be maximized when the incident energy is 50
eV. In this condition where the agitated carbon atom is
rapidly quenched to prevent the rearrangement of the
atom to the equilibrium state, the film of maximum sp3
fraction, density and residual stress could be obtained.
If the incident energy were higher than the optimum
value, decreased cooling rate would result in the rearrangement of the carbon atoms to an equilibrium position. Graphitization of the film occurs as the atoms at
the meta-stable state move to the stable state such as in
sp2 bonding structure.
4. Conclusions
Atomic bond structure and properties of amorphous
carbon film were investigated by molecular dynamic
simulation using the Tersoff potential as the force field
between carbon atoms. The simulated film has high
density, sp3 fraction, and residual stress at the optimum
kinetic energy ranging from 50 to 75 eV, which were
consistent with experimental observations of ta-C films.
In the present work, we observed that the population of
the carbon atom placed at a meta-stable site of distance
˚ was maximum at the optimum kinetic energy of
2.1 A
the deposited carbon. By comparing the intensity with
that of the amorphous carbon modelled by rapid quenching from a liquid carbon, it can be concluded that hard
and dense amorphous carbon film was obtained when
the localized thermal spike due to the collision of
energetic carbon can be effectively dissipated to the
lattice.
Acknowledgments
The authors gratefully acknowledge the financial support from Korean Ministry of Science and Technology
817
through the Center for Nano-structured Materials and
Technology.
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