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Journal ArticleDOI

Diamond-like amorphous carbon

24 May 2002-Materials Science & Engineering R-reports (Elsevier)-Vol. 37, Iss: 4, pp 129-281
TL;DR: In this paper, the authors describe the deposition methods, deposition mechanisms, characterisation methods, electronic structure, gap states, defects, doping, luminescence, field emission, mechanical properties and some applications of diamond-like carbon.
Abstract: Diamond-like carbon (DLC) is a metastable form of amorphous carbon with significant sp3 bonding. DLC is a semiconductor with a high mechanical hardness, chemical inertness, and optical transparency. This review will describe the deposition methods, deposition mechanisms, characterisation methods, electronic structure, gap states, defects, doping, luminescence, field emission, mechanical properties and some applications of DLCs. The films have widespread applications as protective coatings in areas, such as magnetic storage disks, optical windows and micro-electromechanical devices (MEMs).

Summary (2 min read)

Introduction

  • There is great current interest in hard ceramics prepared by vapour-deposited such as diamond, diamond-like carbon (DLC), cubic BN, boron carbides and TiN.
  • While the technology of diamond deposition develops, interest turned to related materials such as DLC [1, .
  • DLC is a dense, metastable form of amorphous carbon (a-C) or hydrogenated amorphous carbon (a-C:H) containing a significant sp3 bonding.
  • The sp3 bonding confers valuable 'diamond-like' properties such as mechanical hardness, low friction, optical transparency and chemical inertness.
  • Fe or plastic substrates and superior surface smoothness.

Deposition

  • Diamond itself can be deposited by various chemical vapour deposition (CVD) methods such as hot filament, microwave plasma, etc [1, 2] .
  • Hydrocarbon source gases are used and the role of the power source is to create an excess of atomic hydrogen which alters the thermodynamic stability of the depositing surface.
  • This links DLC to the wider field of ion-beam modification of materials [lo] .
  • The major growth species are radicals such as CH,'.
  • H is grown on room temperature substrates from pure hydrocarbons such as acetylene, methane or benzene, under conditions of low pressure (3 Pa), moderate RF power, low pressure (3 Pa) and negative substrate bias to maximise the positive ion flux at the substrate [4], also known as Diamond-like a-C.

Properties of DLC

  • The nature of the DLC depends on the deposition process used.
  • Ion-assisted sputtering onto well-cooled substrates can produce a highly sp' bonded a-C [8] .
  • H (open symbols in Fig. 1 ) still has sizeable H and sp2 content which limits its diamond-like character, also known as Note that PD a-C.
  • The electrode configurations allow the powered electrode and plasma to acquire a negative self-bias and a plasma beam exits through a grid into the substrate chamber [21] .
  • H also depend strongly on ion energy, with the density and sp3 fraction reaching a peak at 200 eV per ion (Fig. 6 ), also known as The properties of ta-C.

Deposition Mechanism

  • The process creating the metastable, densified phase DLC is called ion subplantation [14,22-241.
  • An optimum ion energy occurs where the surface penetration is maximised but relaxation is minimised.
  • The sharpness of the density dependence in Fig. 6 is the key reason why a monochromatic, single species ion beam is needed to give ta-C:H.
  • The transition from graphite to diamond occurs when the Gibbs free energy of graphite G(P,T) rises above that of diamond.
  • In the case of a-C, the fully sp' bonded a-C is expected to form when the compressive stress exceeds the necessary threshold.

Energy

  • The authors now consider the atomic structure and electronic structure of a-C and a-C:H.
  • The well known examples of amorphous semiconductors and glasses such as a-Si and a-SiO, are random, a-bonded covalent networks.
  • Their chemical bonding is generally the same as in the crystal, with the same coordination number and bond length.
  • Disorder is primarily topological, giving 5and 7-membered rings in a-Si in addition to the 6membered rings, 'chairs', of crystalline Si.
  • Thus, the electronic density of states (DOS) resembles a smoothed version of the crystalline DOS.

graphite --c

  • This situation is complex (a) because sp" and sp3 sites have similar energies and (b) because a bonding allows more possibilities such as resonance and longer range bonding.
  • The a bonds of sp' and sp' sites again form the network's skeleton, and their energetics depend on only their bond lengths and bond angles.
  • The problem is that the disorder potential in interesting forms of a-C and a-C:H is quite large, and in particular it is larger than the ordering energies of sp' sites.
  • It is therefore possible to account for the observed optical gaps in terms of distorted, single sp2 ring structures.

Mechanical Properties

  • The valuable mechanical properties of diamond and DLC such as high Youngs modulus and hardness arise from its strong, directional sp3 bonds.
  • In contrast, the u bonds of graphitic bonding or the C-H bonds of hydrocarbon polymers contribute little to the modulus because they do not form a three dimensional net- Equations (5) and (6) were found to give a good description of the modulus and hardness of a-C and a-C:H in terms of the underlying bonding where this is known [47,48].

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Content maybe subject to copyright    Report

Pure
&
Appl.
Chem.,
Vol.
66,
No.
9,
pp.
1789-1796, 1994.
Printed in Great Britain.
(6
1994
IUPAC
Diamond-like
carbon
J
Robertson
Engineering Dept, Cambridge University, Cambridge CB2 lPZ,
UK
Abstract: Diamond-like carbon (DLC) is a dense, partially sp3 bonded form of
amorphous carbon prepared by ion beam or plasma deposition and frequently
used
as
a hard coating material. Its sp3 bonding arises from C+ ions penetrating surface layers
and giving a quenched-in density increase. The formation of DLC can be viewed as
a phase transition to a denser metastable phase. The atomic structure of DLC consists
of a network of sp3 and sp2 sites. The
?r
states of sp2 sites control the electronic
properties and the connectivity of sp’ sites controls the mechanical properties.
Introduction
There is great current interest in hard ceramics prepared by vapour-deposited such as diamond, diamond-like
carbon (DLC), cubic BN, boron carbides and TiN. Diamond’s unique properties make it an excellent
coating material and a potentially important high temperature semiconductor [1,2]. While the technology
of diamond deposition develops, interest turned to related materials such as DLC [1,3-51. DLC is a dense,
metastable form of amorphous carbon (a-C) or hydrogenated amorphous carbon (a-C:H) containing a
significant sp3 bonding. The sp3 bonding confers valuable ’diamond-like’ properties such as mechanical
hardness, low friction, optical transparency and chemical inertness. Although DLC films have poorer
properties than diamond films, they have some advantages, notably deposition at room temperature,
deposition onto Fe or plastic substrates and superior surface smoothness.
Deposition
Diamond itself can be deposited by various chemical vapour deposition (CVD) methods such as hot
filament, microwave plasma, etc [1,2]. Hydrocarbon source gases are used and the role of the power source
is to create an excess of atomic hydrogen which alters
the
thermodynamic stability of the depositing surface.
DLC was originally prepared by ion beam deposition [6] and is now prepared by many methods such as
magnetron sputtering [7], ion sputtering [8], laser plasma deposition [9], plasma deposition [4]
and
ion
plating [5]. The common factor in these process is deposition from a beam containing medium energy (10-
500
eV) ions
[l].
This links DLC to the wider field of ion-beam modification of materials
[lo].
Plasma deposition
can
be
used
to prepare CVD diamond, a-C:H and the important semiconductor a-Si:H
so
it is of interest to compare the preferred conditions for each case. Diamond is typically grown on
substrates held at 700-900°C from a
99:
1 H,/methane gas mixture under moderate pressures
(250
Pa) in
microwave plasmas, to maximise the atomic hydrogen flux and minimise the ion bombardment
of
the film.
The major growth species are radicals such as CH,’. Diamond-like a-C:H is grown on room temperature
substrates from pure hydrocarbons such as acetylene, methane or benzene, under conditions of low pressure
(3
Pa), moderate
RF
power, low pressure
(3
Pa) and negative substrate bias to maximise the positive ion
flux at the substrate [4]. High quality a-Si:H is grown from pure silane at low
RF
or microwave power and
medium pressure onto substrates held at 250°C [ll]. These conditions give a growth species of SiH,’
radicals, moderate surface mobility, and minimum ion bombardment of the sample.
1789

1790
J.
ROBERTSON
. .
.-
LL
-_A-
0
ta-C:H
SP3
A
nn
films
Fig. 1. Ternary diagram showing sp', sp' and H
content of a-C, PD a-C:H [12] and ta-C:H [20].
Fig.
2.
sp3 fraction vs. ion energy for ta-C
deposited from filtered ion beam [16].
Properties
of
DLC
The nature of the DLC depends on the deposition process used. The sp' and H content is most conveniently
displayed on a ternary phase diagram [12] as in Fig. 1. The three comers correspond to diamond, graphite
and the hydrocarbons, respectively. There is an excluded region at high H contents, where molecular solids
cannot form. The familiar forms of non-crystalline carbon such as glassy carbon and evaporated a-C lie in
the sp' corner, Sputtering methods produce hard but predominantly sp' bonded a-C
[T.
Ion-assisted
sputtering onto well-cooled substrates can produce a highly sp' bonded a-C [8]. Laser plasma methods can
produce rather highly sp3 bonded a-C films [9].
A
particularly useful form of ion beam deposition is filtered ion
beam
deposition in which a magnetic filter
removes neutrals, particulates and other ions and allows deposition from a monochromatic, single species
ion beam [13-161. The resulting a-C attains
an
sp3 content
of
up to 85% and is called highly tetrahedral a-C
or 'ta-C' [15]. Diffraction data suggest that its atomic structure is truly amorphous and resembles the 4-fold
coordinated random network of a-Si, except for the finite content of 3-fold sites [17]. The properties of ta-C
depend strongly on the energy of the ion beam. The sp' content, density
and
hardness each pass through
a maximum at an optimum ion energy of order 140 eV [16](Fig.
2).
Ta-C films also possess a very high
intrinsic compressive stress arising from
the
deposition process which turns out to be a key signature of
DLC [15].
A
linear correlation is found between sp3 fraction and density (Fig.
3)
and
the
stress (Fig.
4).
Plasma deposition (PD) is
the
most popular means of producing a-C:H [4]. The substrate is attached to the
RF
powered electrode which acquires a negative DC self-bias,
so
the substrate attracts positive ions from
the plasma. The proportion of ions in the total deposition flux is relatively low, typically 10% [18]. The
2.8
I
I:,'
a-C
Fig.
3.
Density vs.
sp3
content for ta-C [16] and
0
aC, Fallon
rn
a-C, McKenzie
A
a-C:H, Tamor
0
,,'
0
6
8
10
12
01.j
"
'
"
'I
'
"
I
"
"
"
"
"
'
"
'
024
Stress,
GPa
Fig.
4.
Compressive stress vs. sp3 fraction for
I
ta-C:H-[20].
ta-C [15,16], PD a-C:H [19] and ta-C:H [20].

Diamond-like carbon
1791
3.2
3
E
2.8
Y
g2.6
-
0
2.4
m
C
O!
0"
2.2
2
100 200
300
400
SdO
l.aO
'
'
'
'
'
'
'
'
Fig.
5.
sp3 fraction, H content, density,
band gap of PD a-C:H, after [4,19].
properties of PD a-C:H depend primarily on bias volt-
age
vb
and source gas.
vb
is a measure of the mean ion
energy and at typical operating pressures (3 Pa)
Ei
r:
0.4Vb. Overall, H content and sp3 fraction decline
steadily with Vb (Fig.
5)
so
that a-C:H has polymeric
character at low
vb,
has a maximum density and dia-
mond-like character at intermediate V, and has disorde-
red
sp2
bonded character at high
vb
[4,19]. The overall
density variation is reminiscent of ta-C, except that
the
energy scale now depends on source gas. Note that PD
a-C:H (open symbols in Fig. 1) still has sizeable H and
sp2 content which limits its diamond-like character.
Recently, a highly tetrahedral form of a-C:H, 'ta-C:H', was deposited from acetylene using a novel plasma
beam source [20]. The electrode configurations allow the powered electrode and plasma to acquire a
negative self-bias and a plasma beam exits through a grid into the substrate chamber [21].
The
properties
of ta-C:H also depend strongly on ion energy, with the density and sp3 fraction reaching a
peak
at 200 eV
per ion (Fig.
6).
The high sp3 fraction
(75%
of total C) attained by ta-C:H sets it well above other forms
of
a-C:H
in
Fig. 1. The ta-C:H also has a high intrinsic compressive stress, and its stress and density each
vary linearly with sp3 fraction (Figs. 3,4). The high sp3 fraction of this ta-C:H arises from three factors:
the high ionisation of
the
plasma beam,
the
mono-energetic character of the ions and the predominance of
one ion, C2Hx+, due to the use of acetylene as a source gas with its simple ionisation pattern.
Deposition Mechanism
The process creating the metastable, densified phase DLC is called ion subplantation [14,22-241. At the
moderate ion energies of interest, ions they loose their energy mainly by elastic collisions with target nuclei
(nuclear stopping) and their range is only a few monolayers.
In
subplantation, incident ions of sufficient
energy penetrate the surface of the growing film, enter interstitial subsurface positions and increase the local
density. Penetration occurs by direct
entry
or knock-on displacement of a surface atom (Fig.
7).
Lower
energy ions have insufficient energy to penetrate the surface and just stick to
the
surface to form
sp?
a-C.
Higher energy ions penetrate further into the film and increase the density in deeper layers. However, ions
need only exceed a certain threshold energy (just less than
the
displacement threshold) to penetrate the
surface, any excess energy rapidly dissipates in a 'thermal spike' [25] during which
the
excess density can
relax by thermally activated diffusion (Fig. 7c). An optimum ion energy occurs where the surface
penetration is maximised but relaxation is minimised. Under the energetic conditions of ion bombardment,
the local bonding hybridisation adjusts to the local density, becoming more sp3 at high density and more
sp2 density at a lower density. The fractional increase in density
ApIp,,
for a film growing from an incident
beam containing a fraction
4
of ions of energy
Ei
is given by

1792
J.
ROBERTSON
ion subplantation
direct
1000
entry
1:::
knock-on
relaxation during
thermal spike
0
100
ion energy (ev)
Fig.
7.
Two stages of subplantation; ion Fig.
8.
Schematic penetration probability
(f)
and
penetration and density relaxation. ion energy distribution (IED) for filtered ion
beam, plasma, and sputter deposition.
ApIpO
=
f/[(
l/d)-f
+
0.0
1 ~P(E~/E#~]
(1)
where
E,,
is the activation energy of relaxation,
f
is the penetration fraction and p is a constant of order 1.
The subplantation mechanism describes well the density variation
of
ta-C films, as
seen
in Fig. 2,
with
&=3.1 eV, p0=2.2 gm.~m-~, p =0.1 and
f
represented empirically by [23] (Fig.
8)
with
the penetration threshold
Ep
=25
eV and a spread factor
E2=57
eV [16].
When the depositing species is a molecular ion such as C2H2+, the ion fragments on impact at the surface.
Its energy partitions, by momentum conservation, roughly equally between two daughter C+ ions
[HI,
which then undergo separate subplantations (Fig.
8).
The penetration
of
the daughter ions is characterised
by their energy, which is 46% of the parent ion energy for C2H2+. The thermal spikes of each daughter ion
overlap (Fig. Sb),
so
the relaxation is characterised by the total energy
-
the energy of the parent ion. With
these adjustments, the subplantation model can also describe the density variation of ta-C:H [20], as shown
in Fig. 6. The penetration threshold rises markedly to
55
eV, as it now includes the energy needed to break
the C-C bond of C2H2+ on impact. The sharpness of the density dependence in Fig. 6 is the key reason
why
a monochromatic, single species ion beam is needed to give ta-C:H.
The deposition process is essentially the same
in
conventional
PD
a-C:H [22,23]. The lower ionisation of
the incident beam, the presence of a number of different ions and the broad ion energy spectrum (due to
collisions in the plasma sheath, Fig. 9b) convert the sharp density
peak
of
ta-C:H (Fig. 6) into the wider,
shallower density
peaks
seen in Fig.
5.
Note that the density of a-C:H prepared from methane, acetylene
and benzene reaches a
peak
at ion energies approximately in the ratio of 1:2:6 (Fig.
5),
that is the same
energy per daugther C atom after energy partition [22]. The ion
flux
also causes dehydrogenation. The
incident species have a H/C ratio
of
a least 1. Ions cause hydrogen loss by preferential sputtering, creating
H2
molecules which effuse out of the
film.
The sputtering cross-section increases with ion energy, causing
the H content to decrease with bias.
The deposition mechanism of sputtered and laser-deposited a-C may also involve subplantation, although
further proof is desirable. Sputtering can involve a range
of
ion energies, the
mean
is of order 10
eV
[8],
lower
than
in ion beam deposition, and lower than the penetration threshold of C,
25
eV. The penetration

Diamond-like carbon
1793
threshold equals the displacement threshold minus the cohesive energy
[23].
In practice, the surface
of
a-C
may be described by a distribution of penetration thresholds, with local low density regions having low
thresholds, as shown schematically in Fig.
9(c).
The penetration probability,
fin
(l), would then arise from
the convolution
of
the low energy
tail
of the penetration distribution and the high energy
tail
of
the ion
energy distribution. This would give the relatively low sp’ fractions (but disordered structures) found
in
sputtered a-C
[7,3].
A
generalisation of such a model could describe many ion beam modification processes,
currently given more qualitative descriptions
[10,27].
00
h
penetration
-
ions separate
relaxation
-
si’ngle spike
I
Fig.
9.
Subplantation by a molecular ion, with
impact fragmentation, separate penetration
and
a common thermal spike. phases.
Fig. 10. Energy vs. volume and P-T curves for
transitions between a-C phases.
The creation of DLC can also be viewed as a phase transition to a denser phase. The transition from graph-
ite to diamond occurs when the Gibbs free energy of graphite G(P,T) rises above that of diamond. The tem-
perature dependence of the transition pressure between graphite and diamond is known as the Berman-Simon
line. McKenzie [15,
271
recognised that phases present in deposited thin films could also be described by
equilibrium thermodynamics and free energy differences, despite the irreversible nature of the deposition
process. The key observation is that most deposition processes create an intrinsic stress, which can be
compressive or tensile
[28],
although it is rarely as large as in DLC. This stress
u
is biaxial and is equi-
valent to a hydrostatic pressure of
2u/3
plus a shear of
d3.
The hydrostatic component a compressive stress
can therefore stabilise a denser metastable phase. McKenzie et al
[29]
applied these ideas to the deposition
of cubic BN (c-BN). BN, like carbon, has a low density sp’ bonded phase hexagonal BN (h-BN) and a
denser but less stable sp3 phase, c-BN. It differs from
C
in that its amorphous phases are less prevalent.
McKenzie et al
[29]
found that c-BN was formed when the measured compressive stress exceeded the criti-
cal value expected from the known
AG
of c-BN.
In the case of a-C, the fully sp’ bonded a-C is expected to form when the compressive stress exceeds the
necessary threshold. Experimentally, the sp’ content of ta-C and ta-C:H varies linearly with stress, and does
not display a threshold value (Fig.
4).
This suggests that a-C shows a continuous phase transition of
increasing sp’ content as shown in Fig.
lo@).
This is possible because the random network can accommo-
date a variable sp3 content, each with its own
AG
versus
V
curves (Fig. lOa), whereas a sharp transition
must occur between the crystalline phases h-BN and c-BN. The difference
AG
between sp2 and sp’ a-C can
be estimated as
1
PAV from the difference in density of each form (from Fig.
3)
and the hydrostatic
pressure equivalent to the total stress of
13
GPa
needed
to form fully sp’ a-C (Fig.
4)
to give
AG
=
0.10
eV
(3)
This value is larger
than
that
0.03
eV between graphite
and
diamond at
O’K,
presumably due to the large
distortion energy of the very stiff sp’ bonded random network.

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  • ...e lowest K ~ 0.1–0.3 W/mK, hydrogenated ta-C:H has K~1 W/mK, and ta-C has the highest K, which can go up to ~10 W/mK at RT [41]. Among amorphous solids, ta-C is likely the material with the highest K [35, 36]. If the sp3 phase orders, even in small grains such as in nanocrystalline diamond, a strong K increase occurs for a given density , Young’s modulus E, and sp3 content. Progress in CVD polycrystallin...

    [...]

  • ...y the intrinsic lattice dynamics. An important representative of this class of materials is diamond-like carbon (DLC), which is a metastable form of a-C containing a significant fraction of sp3 bonds [35]. DLC films are widely used as protective coatings with optical windows for magnetic storage disks and in biomedical applications. DLC consists not only of a-C but also of the hydrogenated alloys, a-C...

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Abstract: Recent years witnessed a rapid growth of interest of scientific and engineering communities to thermal properties of materials. Carbon allotropes and derivatives occupy a unique place in terms of their ability to conduct heat. The room-temperature thermal conductivity of carbon materials span an extraordinary large range – of over five orders of magnitude – from the lowest in amorphous carbons to the highest in graphene and carbon nanotubes. I review thermal and thermoelectric properties of carbon materials focusing on recent results for graphene, carbon nanotubes and nanostructured carbon materials with different degrees of disorder. A special attention is given to the unusual size dependence of heat conduction in two-dimensional crystals and, specifically, in graphene. I also describe prospects of applications of graphene and carbon materials for thermal management of electronics.

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  • ...The great versatility of carbon materials arises from the strong dependence of their physical properties on the ratio of sp2 (graphite-like) to sp3 (diamond-like) bonds (Robertson 2002)....

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References
More filters
Journal ArticleDOI
TL;DR: In this paper, a model and theoretical understanding of the Raman spectra in disordered and amorphous carbon is given, and the nature of the G and D vibration modes in graphite is analyzed in terms of the resonant excitation of \ensuremath{\pi} states and the long-range polarizability of the long range bonding.
Abstract: The model and theoretical understanding of the Raman spectra in disordered and amorphous carbon are given. The nature of the G and D vibration modes in graphite is analyzed in terms of the resonant excitation of \ensuremath{\pi} states and the long-range polarizability of \ensuremath{\pi} bonding. Visible Raman data on disordered, amorphous, and diamondlike carbon are classified in a three-stage model to show the factors that control the position, intensity, and widths of the G and D peaks. It is shown that the visible Raman spectra depend formally on the configuration of the ${\mathrm{sp}}^{2}$ sites in ${\mathrm{sp}}^{2}$-bonded clusters. In cases where the ${\mathrm{sp}}^{2}$ clustering is controlled by the ${\mathrm{sp}}^{3}$ fraction, such as in as-deposited tetrahedral amorphous carbon (ta-C) or hydrogenated amorphous carbon (a-C:H) films, the visible Raman parameters can be used to derive the ${\mathrm{sp}}^{3}$ fraction.

12,593 citations

Journal ArticleDOI
TL;DR: Raman spectra are reported from single crystals of graphite and other graphite materials as mentioned in this paper, and the Raman intensity of this band is inversely proportional to the crystallite size and is caused by a breakdown of the k-selection rule.
Abstract: Raman spectra are reported from single crystals of graphite and other graphite materials. Single crystals of graphite show one single line at 1575 cm−1. For the other materials like stress‐annealed pyrolitic graphite, commercial graphites, activated charcoal, lampblack, and vitreous carbon another line is detected at 1355 cm−1. The Raman intensity of this band is inversely proportional to the crystallite size and is caused by a breakdown of the k‐selection rule. The intensity of this band allows an estimate of the crystallite size in the surface layer of any carbon sample. Two in‐plane force constants are calculated from the frequencies.

9,373 citations

Journal ArticleDOI
TL;DR: In this article, a unified scheme combining molecular dynamics and density-functional theory is presented, which makes possible the simulation of both covalently bonded and metallic systems and permits the application of density functional theory to much larger systems than previously feasible.
Abstract: We present a unified scheme that, by combining molecular dynamics and density-functional theory, profoundly extends the range of both concepts. Our approach extends molecular dynamics beyond the usual pair-potential approximation, thereby making possible the simulation of both covalently bonded and metallic systems. In addition it permits the application of density-functional theory to much larger systems than previously feasible. The new technique is demonstrated by the calculation of some static and dynamic properties of crystalline silicon within a self-consistent pseudopotential framework.

8,852 citations

Journal ArticleDOI
TL;DR: A model potential-energy function comprising both two- and three-atom contributions is proposed to describe interactions in solid and liquid forms of Si, suggesting a temperature-independent inherent structure underlies the liquid phase, just as for ``simple'' liquids with only pair interactions.
Abstract: A model potential-energy function comprising both two- and three-atom contributions is proposed to describe interactions in solid and liquid forms of Si. Implications of this potential are then explored by molecular-dynamics computer simulation, using 216 atoms with periodic boundary conditions. Starting with the diamond-structure crystal at low temperature, heating causes spontaneous nucleation and melting. The resulting liquid structurally resembles the real Si melt. By carrying out steepest-descent mappings of system configurations onto potential-energy minima, two main conclusions emerge: (1) a temperature-independent inherent structure underlies the liquid phase, just as for ``simple'' liquids with only pair interactions; (2) the Lindemann melting criterion for the crystal apparently can be supplemented by a freezing criterion for the liquid, where both involve critical values of appropriately defined mean displacements from potential minima.

4,345 citations

Journal ArticleDOI
TL;DR: An empirical many-body potential-energy expression is developed for hydrocarbons that can model intramolecular chemical bonding in a variety of small hydrocarbon molecules as well as graphite and diamond lattices based on Tersoff's covalent-bonding formalism with additional terms that correct for an inherent overbinding of radicals.
Abstract: An empirical many-body potential-energy expression is developed for hydrocarbons that can model intramolecular chemical bonding in a variety of small hydrocarbon molecules as well as graphite and diamond lattices. The potential function is based on Tersoff's covalent-bonding formalism with additional terms that correct for an inherent overbinding of radicals and that include nonlocal effects. Atomization energies for a wide range of hydrocarbon molecules predicted by the potential compare well to experimental values. The potential correctly predicts that the \ensuremath{\pi}-bonded chain reconstruction is the most stable reconstruction on the diamond {111} surface, and that hydrogen adsorption on a bulk-terminated surface is more stable than the reconstruction. Predicted energetics for the dimer reconstructed diamond {100} surface as well as hydrogen abstraction and chemisorption of small molecules on the diamond {111} surface are also given. The potential function is short ranged and quickly evaluated so it should be very useful for large-scale molecular-dynamics simulations of reacting hydrocarbon molecules.

3,588 citations