Growth of forest of single-walled carbon nanotubes at inhomogenious fluxes from plasma
The growth of forest of single-walled carbon nanotubes (SWCNTs) in plasma-enhanced chemical vapor deposition (PECVD) is studied using a deposition model. The inhomogeneity in deposition of neutrals from plasma on the SWCNTs, which is typical for growth of the nanostructures in PECVD, is accounted fo...
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nasplib_isofts_kiev_ua-123456789-821472025-02-23T19:53:46Z Growth of forest of single-walled carbon nanotubes at inhomogenious fluxes from plasma Рост леса однослойных углеродных нанотрубок при неоднородных потоках из плазмы Ріст лісу одношарових вуглецевих нанотрубок за неоднорідних потоків із плазми Burmaka, G.P. Denysenko, I.B. Azarenkov, N.A. Низкотемпературная плазма и плазменные технологии The growth of forest of single-walled carbon nanotubes (SWCNTs) in plasma-enhanced chemical vapor deposition (PECVD) is studied using a deposition model. The inhomogeneity in deposition of neutrals from plasma on the SWCNTs, which is typical for growth of the nanostructures in PECVD, is accounted for. It is investigated how the growth rate and the residence time of carbon atoms on SWCNT surfaces depend on the SWCNT length and the decay length characterizing deposition of neutral fluxes on the SWCNTs. The obtained results can be used for optimizing the synthesis of related nanoassembles in low-temperature plasma-assisted nanofabrication. Изучен рост леса однослойных углеродных нанотрубок (ОУНТ) в процессе плазменно-химического осаждения (ПХО) на основе разработанной теоретической модели для описания этого осаждения. При этом учтена неоднородность осаждения нейтральных частиц из плазмы на поверхности ОУНТ, которая характерна для роста этих наноструктур в процессе ПХО. Исследовано, как скорость роста ОУНТ и время жизни атомов углерода на их поверхности зависят от длины ОУНТ и глубины проникновения потока нейтральных частиц в лес ОУНТ. Полученные результаты могут быть использованы для оптимизации синтеза различных наноструктур в низкотемпературной плазме. Вивчено ріст лісу одношарових вуглецевих нанотрубок (ОВНТ) у процесі плазмово-хімічного осадження (ПХО) на основі розробленої теоретичної моделі для опису цього осадження. При цьому враховано неоднорідність осадження нейтральних частинок із плазми на поверхні ОВНТ, яка є характерною для росту цих наноструктур у процесі ПХО. Досліджено, як швидкість росту ОВНТ та час життя атомів вуглецю на їх поверхні залежать від довжини ОВНТ та глибини проникнення потоку нейтральних частинок до лісу ОВНТ. Здобуті результати можуть бути використані для оптимізації синтезу різних наноструктур у низькотемпературній плазмі. 2015 Article Growth of forest of single-walled carbon nanotubes at inhomogenious fluxes from plasma / G.P. Burmaka, I.B. Denysenko, N.A. Azarenkov // Вопросы атомной науки и техники. — 2015. — № 1. — С. 184-186. — Бібліогр.: 5 назв. — англ. 1562-6016 PACS: 52.77.Dq, 81.16.Hc, 81.07.De https://nasplib.isofts.kiev.ua/handle/123456789/82147 en Вопросы атомной науки и техники application/pdf Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Низкотемпературная плазма и плазменные технологии Низкотемпературная плазма и плазменные технологии |
| spellingShingle |
Низкотемпературная плазма и плазменные технологии Низкотемпературная плазма и плазменные технологии Burmaka, G.P. Denysenko, I.B. Azarenkov, N.A. Growth of forest of single-walled carbon nanotubes at inhomogenious fluxes from plasma Вопросы атомной науки и техники |
| description |
The growth of forest of single-walled carbon nanotubes (SWCNTs) in plasma-enhanced chemical vapor deposition (PECVD) is studied using a deposition model. The inhomogeneity in deposition of neutrals from plasma on the SWCNTs, which is typical for growth of the nanostructures in PECVD, is accounted for. It is investigated how the growth rate and the residence time of carbon atoms on SWCNT surfaces depend on the SWCNT length and the decay length characterizing deposition of neutral fluxes on the SWCNTs. The obtained results can be used for optimizing the synthesis of related nanoassembles in low-temperature plasma-assisted nanofabrication. |
| format |
Article |
| author |
Burmaka, G.P. Denysenko, I.B. Azarenkov, N.A. |
| author_facet |
Burmaka, G.P. Denysenko, I.B. Azarenkov, N.A. |
| author_sort |
Burmaka, G.P. |
| title |
Growth of forest of single-walled carbon nanotubes at inhomogenious fluxes from plasma |
| title_short |
Growth of forest of single-walled carbon nanotubes at inhomogenious fluxes from plasma |
| title_full |
Growth of forest of single-walled carbon nanotubes at inhomogenious fluxes from plasma |
| title_fullStr |
Growth of forest of single-walled carbon nanotubes at inhomogenious fluxes from plasma |
| title_full_unstemmed |
Growth of forest of single-walled carbon nanotubes at inhomogenious fluxes from plasma |
| title_sort |
growth of forest of single-walled carbon nanotubes at inhomogenious fluxes from plasma |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2015 |
| topic_facet |
Низкотемпературная плазма и плазменные технологии |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/82147 |
| citation_txt |
Growth of forest of single-walled carbon nanotubes at inhomogenious fluxes from plasma / G.P. Burmaka, I.B. Denysenko, N.A. Azarenkov // Вопросы атомной науки и техники. — 2015. — № 1. — С. 184-186. — Бібліогр.: 5 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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2025-11-24T19:57:03Z |
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2025-11-24T19:57:03Z |
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| fulltext |
ISSN 1562-6016. ВАНТ. 2015. №1(95)
184 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2015, № 1. Series: Plasma Physics (21), p. 184-186.
GROWTH OF FOREST OF SINGLE-WALLED CARBON NANOTUBES AT
INHOMOGENIOUS FLUXES FROM PLASMA
G.P. Burmaka, I.B. Denysenko, N.A. Azarenkov
V.N. Karazin Kharkiv National University, Kharkiv, Ukraine
E-mail: gennadyburmaka@yahoo.com
The growth of forest of single-walled carbon nanotubes (SWCNTs) in plasma-enhanced chemical vapor
deposition (PECVD) is studied using a deposition model. The inhomogeneity in deposition of neutrals from plasma
on the SWCNTs, which is typical for growth of the nanostructures in PECVD, is accounted for. It is investigated
how the growth rate and the residence time of carbon atoms on SWCNT surfaces depend on the SWCNT length and
the decay length characterizing deposition of neutral fluxes on the SWCNTs. The obtained results can be used for
optimizing the synthesis of related nanoassembles in low-temperature plasma-assisted nanofabrication.
PACS: 52.77.Dq, 81.16.Hc, 81.07.De
INTRODUCTION
Plasma-enhanced chemical vapor deposition
(PECVD) techniques have been successfully used for
production of different nanoscale materials including
carbon nanofibers (CNFs) and carbon nanotubes
(CNTs) [1, 2]. These carbon nanostructures, formed by
PECVD, have better alignment and can be grown at
higher deposition rates and lower substrate temperatures
than those synthesized by thermal chemical vapor
deposition (CVD) or other methods.
In this paper, we study formation of a SWCNT forest
in plasma, using a deposition model, that is based on
mass balance equations for adsorbed species on the
single-walled carbon nanotube (SWCNT) surfaces. This
model is an extension of the model previously used for
description of the growth of an isolated SWCNT, where
it was assumed that plasma particles were deposited
homogeneously on the surfaces of SWCNTs [3]. We
account for the inhomogeneity in deposition of neutrals
from plasma on the SWCNTs. The model equations are
solved using the WKB (Wentzel-Kramers-Brillouin)
approach, and an analytical expression for the growth
rate of the SWCNT forest is obtained as a function of
parameters of the SWCNTs and ion and neutral fluxes.
We investigate how the growth rate depends on the
SWCNT length and the decay length characterizing the
deposition of neutral fluxes on the SWCNTs.
1. THEORETICAL MODEL
Let us consider close-ended growth of a forest of
SWCNTs with semi-spherical peaks. It is assumed that
the SWCNTs have the same length, and the catalyst
nanoparticles are anchored to the base (at x=LNT, where
x is the coordinate along the SWCNT axis and LNT is the
length) of a SWCNT. The plasma produced in a
C2H2/H2 gas discharge is located above the forest of
SWCNTs, and the main particles which interact with
surfaces of the SWCNTs are hydrocarbon neutrals
(C2H2), hydrocarbon ions (C2H2
+
) and atoms or
molecules of an etching gas (atomic hydrogen H). The
hydrocarbon neutrals and atomic hydrogen are adsorbed
and desorbed on the SWCNT surfaces as well as on the
substrate surface between the SWCNTs. We consider
the case when the distance between the SWCNTs is
small (≤1 µm), and, therefore, it is assumed that the
fluxes of neutral particles onto the surfaces of the
SWCNTs decrease exponentially (exp(-x/l
*
), where x is
the distance from the top of a nanotube, and l
*
is the
characteristic decay length [4].
The adsorption and desorption fluxes of the neutrals
can be presented as: jαads=jα(1-t) and jαdes=a0
exp(-Ea/kbTs), where 0 is the number of adsorption
sites per unit area, =СН and Н denote C2H2 and H
neutrals, respectively; jα=nathaexp(x/l*)/4 is the flux
density of impinging neutral particles; Ts is the SWCNT
surface temperature; asbtha mTk /8 is the thermal
velocity, kb is the Boltzmann constant, Еа is the
adsorption energy; na, a and ma are the plasma bulk
density, surface coverage, and mass of species α. The
ion flux is determined as ieii mTnj /~ , where Te is
the plasma electron temperature, and ni and mi are the
ion density and mass, respectively. Since ions have
essentially larger energies than neutrals, it is assumed
that ions are deposited homogeneously on the SWCNT
surfaces [5].
We suppose that the SWCNT surfaces and the
surface between nanotubes are covered by C2H2
molecules, C and H atoms. The total surface coverage
by the particles is t=CH+H+C. Carbon atoms can
appear on the SWCNT surfaces due to such reactions as
thermal dissociation, ion bombardment of adsorbed
C2H2 molecules and decomposition of C2H2+ ions.
We obtain the differential equation for the surface
density of carbon atoms nC on the SWCNT surfaces:
0/2/2 aCCs nQdx
c
ndD , (1)
where )/exp(2
0 sbds TkEaD is the surface diffusion
coefficient of carbon atoms on the SWCNT surfaces,
а0=0.14 nm is the interatomic distance in the nanotube,
δEd is the threshold energy of surface diffusion for
carbon on a SWCNT surface, 1310 Hz is the thermal
vibration frequency, QC=2(C1+ji) is the effective carbon
flux to the SWCNT surfaces,
,
//)/2(1
)/exp(0
1
CHCHH
isbi
jLKjLjM
jTkE
C
mailto:gennadyburmaka@yahoo.com
ISSN 1562-6016. ВАНТ. 2015. №1(95) 185
1
0
12
)exp(
C
j
Tk
E
Hads
sb
ev
a
is the time
characterizing the carbon loss, ads =6.8 10
16
cm
2
is
the cross section of the adsorbed-layer reaction,
Eev=1.8 eV is the evaporation energy for carbon atoms,
δEi=2.1 eV is the activation energy of thermal
dissociation, ),exp(0
sb
i
Tk
E
M
.)exp(
,)exp()exp(
00
000
Hads
sb
a
iHads
sb
i
sb
a
j
Tk
E
K
jj
Tk
E
Tk
E
L
Eq. (1) should be accompanied by boundary conditions.
We assume that:
,
,0
0 NT
CCsC
Lx
knn
x
D
x
n
x
(2)
where )/exp(0 sbinc TkEak , δEinc is the energy of
atom incorporation into the SWCNT wall.
In general, Eq. (1) cannot be solved analytically.
However, when the variation of the fluxes of neutrals
and ions along the SWCNTs is weak, the solution of
Eq. (1) can be found using the WKB approach. If the
surface diffusion length is smaller than l
*
, the SWCNT
growth rate is:
)cosh()/()sinh(
)sinh(
1
11
sD
aC
Lx
c
SNT
Dk
Qk
dx
dn
DV
NT
, (3)
where Ω is the area per unit C atom in a SWCNT wall,
11 asD D is the surface diffusion length at x=LNT
and
NTL
D dx
0
)/1( , τa1=τa(x=LNT).
Ions and neutral particles are deposited also between
nanotubes. Their deposition can be accompanied by
formation of carbon film. The film formation between
SWCNTs was studied in [3]. Here, we consider such
nanotube’s and plasma parameters when formation of
the film between nanotubes does not take place.
RESULTS
Using the analytical results presented in the previous
section, let analyze how the parameters which
characterize the growth of SWCNT forest [the
nanostructure growth rate (VNT) and the time
characterizing the carbon loss near the nanotube base
(
1a )] depend on the SWCNT length, the decay length
characterizing the deposition of neutrals on the
nanotube surfaces, and the substrate temperature. To
make this analysis, we vary the SWCNT length, the
decay lengths for neutral fluxes, as well as the substrate
temperature in our calculations, and then observe how
these changes affect the SWCNT growth parameters.
The growth rate of SWCNTs VNT is calculated from
Eq. (3) for different external conditions. In Figs. 1 and
2, the SWCNT growth rate VNT and the characteristic
residence time of carbon atoms τa1 are shown as
functions of the SWNT length LNT for different decay
lengths of neutral particle fluxes. The dependences are
obtained for the SWCNT surface temperatures
TS=800 K (see Fig. 1) and TS=1000 K (see Fig. 2),
assuming that ions are deposited homogeneously on the
nanotubes. One can see from Fig. 1,a that at low
temperatures the SWCNT growth rate VNT first increases
with increase of the length LNT, reaching a maximum at
a certain length, and then it decreases. At larger l
*
, the
maximum is observed for larger lengths. For long
nanotubes, the growth rate depends slightly on the
SWCNT length.
For nanotubes with the length in the range between
6l
*
and 10l
*
, the effective carbon flux to the nanotube
base decreases with an increase of LNT because of the
exponential dependence of the hydrocarbon flux on the
coordinate. At large lengths (>10 l
*
), the neutral particle
fluxes to the nanotube’s base are small, and the
production of carbon adatoms is mainly due to
decomposition of ions on the SWCNT surfaces. As a
result, for these lengths, the effective carbon flux and
the SWCNT growth rate are nearly independent on the
length LNT. For LNT>>l*, the residence time also
depends slightly on the SWCNT length (see Fig. 1,b)
because for large LNT the loss of carbon atoms near a
nanotube base is mainly due to their evaporation.
Fig. 1. Dependences of the SWCNT growth rate (a) and
time characterizing the carbon loss (b) on the
nanotube’s length LNT. The external parameters for (a)
and (b) are TS=800 K, nCH=10
15
cm
3
, ni=10
10
cm
3
,
jH=0.3jCH, and l
*
=1.0 (dotted line), l
*
=0. μm (dashed line),
l
*
=0.3 μm (solid line)
Fig. 2. The same as in Fig. 1, but for TS=1000 K
Due to decrease of the loss of carbon atoms, the
residence time τa1 becomes larger with increasing LNT
(see Fig. 1,b). At low Ts, the effect of etching gas on
processes on the SWCNT surfaces is essential, and the
difference in the residence times for small and large
nanotube lengths is very large (~ 100 times (see
Fig. 1,b)). Due to increase of τa1, the growth rate
becomes larger with increasing LNT for small SWCNT
a b
a b
186 ISSN 1562-6016. ВАНТ. 2015. №1(95)
lengths. For nanotubes of middle length (6l
*
<LNT<10l
*
),
the growth rate decreases with the length increase
because of decrease of QC at small variation of the
residence time.
For large surface temperatures (see Fig. 2), the effect
of etching gas on the loss of carbon adatoms from the
SWCNT surfaces is less pronounced and thermal effects
are more important. The difference in τa1 for small and
large LNT is small (see Fig. 2,b), comparing with this
difference for lower TS. For small LNT, VNT increases
with an increase of LNT. For 0.1μm<LNT<l
*
, QC decrease
is accompanied by an increase of τa1 and the growth rate
depends slightly on LNT (see Fig. 2,a). For l
*
< LNT < 10l
*
,
VNT decreases due to the decrease of QC. For large
nanotube’s lengths, the fluxes of neutral particles to the
nanotube’s base are small, and the growth rate is a
function only of the ion flux.
CONCLUSIONS
The theoretical model, describing the growth of a
SWCNT forest in PECVD, is developed. Using this
model, it is shown that the dependence for the growth
rate of the SWCNT forest on the nanotube’s length at
nonuniform deposition of neutrals on the surfaces of the
SWCNTs can be different from that in the case of their
uniform deposition. In the case of uniform deposition,
the growth rate becomes larger with an increase of LNT ,
until it reaches a maximum (at LNT ~ 0.1 m in [4]), and
VNT is independent on the length for large lengths. At
nonuniform deposition of neutrals and uniform
deposition of ions, the growth rate first becomes larger
with an increase of LNT for small lengths, reaches a
maximum at a certain length and then decreases, until it
reaches the magnitude, corresponding to the case, when
only ions are deposited on the nanostructures (see
Fig. 1,a). For long nanotubes, the loss of carbon atoms
near the SWCNT base is mainly due to evaporation. As
a result, the residence time of carbon atoms at x = LNT is
larger for long nanotubes than for short SWCNTs (see
Figs. 1,b and 2,b). Since the evaporation is more
intensive at large surface temperatures, the growth rate
of long nanotubes may increase with decreasing the
SWCNT surface temperature (Figs. 1,a and 2,a).
REFERENCES
1. M. Meyyappan. Carbon Nanotubes: Science and
Applications. Boca Raton: CRC Press, 2004, p. 304.
2. I. Denysenko, N.A. Azarenkov. Formation of
vertically aligned carbon nanostructures in plasmas:
numerical modeling of growth and energy exchange // J.
Phys. D: Appl. Phys. (44). 2011, p. 174031.
3. I. Denysenko, K. Ostrikov, M.Y. Yu,
N.A. Azarenkov. Effects of ions and atomic hydrogen in
plasma-assisted growth of single-walled carbon
nanotubes // J. Appl. Phys.(102). 2007, p. 074308.
4. O.A. Louchev, T. Laude, Y. Sato, H. Kanda.
Diffusion-controlled kinetics of carbon nanotube forest
growth by chemical vapor deposition // J. Chem. Phys.
(188). 2003, p. 7622.
5. E. Tam, K. Ostrikov. Catalyst size effects on the
growth of single-walled nanotubes in neutral and
plasma systems // Nanotechnology (20). 2009,
p. 375603.
Article received 20.10.2014
РОСТ ЛЕСА ОДНОСЛОЙНЫХ УГЛЕРОДНЫХ НАНОТРУБОК
ПРИ НЕОДНОРОДНЫХ ПОТОКАХ ИЗ ПЛАЗМЫ
Г.П. Бурмака, И.Б. Денисенко, Н.А. Азаренков
Изучен рост леса однослойных углеродных нанотрубок (ОУНТ) в процессе плазменно-химического
осаждения (ПХО) на основе разработанной теоретической модели для описания этого осаждения. При этом
учтена неоднородность осаждения нейтральных частиц из плазмы на поверхности ОУНТ, которая
характерна для роста этих наноструктур в процессе ПХО. Исследовано, как скорость роста ОУНТ и время
жизни атомов углерода на их поверхности зависят от длины ОУНТ и глубины проникновения потока
нейтральных частиц в лес ОУНТ. Полученные результаты могут быть использованы для оптимизации
синтеза различных наноструктур в низкотемпературной плазме.
РІСТ ЛІСУ ОДНОШАРОВИХ ВУГЛЕЦЕВИХ НАНОТРУБОК
ЗА НЕОДНОРІДНИХ ПОТОКІВ ІЗ ПЛАЗМИ
Г.П. Бурмака, І.Б. Денисенко, М.О. Азарєнков
Вивчено ріст лісу одношарових вуглецевих нанотрубок (ОВНТ) у процесі плазмово-хімічного осадження
(ПХО) на основі розробленої теоретичної моделі для опису цього осадження. При цьому враховано
неоднорідність осадження нейтральних частинок із плазми на поверхні ОВНТ, яка є характерною для росту
цих наноструктур у процесі ПХО. Досліджено, як швидкість росту ОВНТ та час життя атомів вуглецю на їх
поверхні залежать від довжини ОВНТ та глибини проникнення потоку нейтральних частинок до лісу ОВНТ.
Здобуті результати можуть бути використані для оптимізації синтезу різних наноструктур у
низькотемпературній плазмі.
|