Marulanda J.M. (ed.) Electronic Properties of Carbon Nanotubes
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Carbon Nanotube Based Magnetic Tunnel Junctions (MTJs) for Spintronics Application
515
The ~ null current in the CB region and the CS beyond CB region are clear indications of the
SET phenomena. The SET phenomena and the associated MR occur only if the transport of
electrons from one electrode to another is inhibited due to the extremely high electrostatic
energy e
2
/2C (e = charge of electron and C is the capacitance) of a single electron compared
to the thermal energy k
B
T. When the bias voltage increases and exceeds the threshold V
th
=
e/2C, the current starts to increase. If the resistance of two junctions are similar (R1≈ R2), the
current increases smoothly with bias voltage. A fluctuation in current is expected if there is
difference between the resistances of two junctions. Interestingly, if the difference between
the two junction resistances is very large (R1»R2 or R1«R2), the current increases stepwise
(CS) with bias voltage depending on the number of electrons accumulated on the spacer. In
that case, the tunnelling process in a current-biased junction is no longer random, but
becomes more or less coherent (single electron tunnelling), at a frequency ν = I/e. As a result
the voltage across the junction will oscillate with the same frequency, and could in principle
be used to define a quantum standard for the current.
Fig. 15. (a) I–V
b
curves of the sample at H = 0 and H =2 T at 300 K, (b) themagnification of
the I- V
b
(c) the dI/ dV vs. Vb plot of the sample at H= 0 T. (d) The MR% calculated from I–
V
b
curves. The inset of (c) shows the I–Vb curve in the range -1.9 to -1 Vb.
The calculation of capacitance C is also crucial in determining the TMR effect. We have
calculated the capacitance C from the period of dI/dV curve. The peaks show a periodic
pattern with a period of ∆V = 102.0 ±1.8mV. Assuming ∆V = e/C, the capacitance is
calculated as 1. 5705 × 10
-18
F. Our result is in agreement with the work of A. B Mantel et al.
49
who has studied the spin injection in a single cobalt nanoparticle tunnel junction and they
Electronic Properties of Carbon Nanotubes
516
obtained C value as 1.14 10
-18
F. The C value calculated by us is consistent with the
ferromagnetic nanoparticle tunnel junctions which confirm that the MR effect is due to the
spin injection from nickel electrode into the non ferromagnetic CNT and spin detection by
the nickel nanoparticle. The MR of the sample was also confirmed by low field
measurements (Figure 16). The low field measurements were performed from 100 to 100 Oe
and back to 100 Oe. The resistance peak appears as the field moves through zero and it
shows a change of resistance from the parallel to antiparallel alignment of the
magnetizations.
Fig. 16. Schematic of spintronic device showing vertically aligned carbon nanotubes (VCNT)
deposited with nickel nanoparticles.
7. Conclusion
The development of room temperature spintronic devices is very motivating for future
digital world. Spintronic devices can lead to advances in microelectronics creating faster and
high capacity data storage-devices with less power consumption. The spin of the electrons
can easily be manipulated in MTJ structures achieving novel phenomena of TMR and SET.
However, bringing new or improved MTJs to market requires theoretical modeling and
rapid assessment of the effect of enhanced material properties. Carbon nanotubes (CNTs)
are ideal spin transporters due to their unique electronic properties.
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24
Mechanisms of Single-Walled Carbon Nanotube
Nucleation, Growth and Chirality-Control:
Insights from QM/MD Simulations
Alister J. Page
1
, Ying Wang
2
, K. R. S. Chandrakumar
1
,
Stephan Irle
2
and Keiji Morokuma
1,3
1
Fukui Institute for Fundamental Chemistry, Kyoto University,
2
Institute for Advanced Research and Department of Chemistry, Nagoya University
3
Cherry L. Emerson Centre for Scientific Computation and Department of Chemistry,
Emory University,
1,2
Japan
3
U.S.A.
1. Introduction
The experimental characterisations of carbon nanotubes (CNTs) (Iijima, 1991) and in
particular single-walled CNTs (SWNTs) (Iijima & Ichihashi, 1993) in the early 1990s were
landmark moments in 20
th
century science. The potential uses of these remarkable
nanostructures are now becoming realised, as their synthesis is now routinely performed on
the industrial scale. The initial successes in this respect were generally experimental
techniques that were previously well established in other fields. This is particularly true of
the chemical vapor deposition (CVD) and arc-discharge processes. The original
experimental characterisation of SWNTs was in fact accomplished using nanotubes
synthesised with the former method (Iijima & Ichihashi, 1993). The understanding of the
way in which CNTs nucleate and grow was therefore synergic with the evolution and
refinement of these synthetic methods. Indeed, the original mechanisms of CNT nucleation
and growth were conceived from experimental observations. The most prevalent of these
today is the vapor-liquid-solid (VLS) mechanism (Saito, 1995). According to this mechanism,
SWNT nucleation growth is postulated to consist of three distinct stages. The first of these
features a mixed carbon/catalyst vapor phase, from which co-condensation yields liquid
catalyst-carbide nanoparticles. Typical catalysts in the growth of SWNTs are traditionally
transition metals such as Fe, Ni, Co, Mo, and alloys thereof (see (Journet et al., 1997; Moisala
et al., 2003; Harris, 2007), and references therein). The precipitation of atomic carbon from
this liquid carbide phase takes place once the carbide phase is saturated with carbon. This
precipitation yields the formation of solid phase CNTs. Due to the inherent limits in spatial
and temporal resolutions that are furnished by experimental techniques and
instrumentation, there inevitably remain questions regarding the VLS mechanism and CNT
growth that, for now, cannot be answered from an experimental standpoint. There are
several infamous examples in this respect. For instance, the mechanism of so-called
‘catalyst-free’ SWNT nucleation growth remains unknown, following the recent
Electronic Properties of Carbon Nanotubes
522
experimental reports demonstrating the growth of CNTs in the absence of a transition metal
catalyst. The factors that govern ‘chirality-controlled’ growth (i.e. growth that produces a
specific (n,m) chiral SWNT, as opposed to a broad distribution of (n,m) SWNTs) have also
remained elusive to date.
It is in this respect that theoretical models of CNT growth have recently come to the fore by
complementing, and in some cases pre-empting, experimental understanding of SWNT
nucleation and growth. The most notable theoretical approach in this respect is molecular
dynamics (MD). In this work, we will highlight the recent advances made in our
understanding of SWNT nucleation and growth mechanisms gained from quantum
mechanical MD (QM/MD) simulations. Following a brief review of experimental SWNT
synthesis (§1.1) and previous theoretical investigations of SWNT nucleation and growth
(§1.2), we will briefly outline the quantum chemical approach used in our simulations (§2).
A discussion of QM/MD simulations of SWNT nucleation on both Fe and Ni catalysts will
be presented in §3. SWNT nucleation as the result of gas-phase acetylene, C and C
2
adsorption, as well as the decomposition of the Fe- and Ni-carbide phases will be considered
here. More recent simulations concerning the mechanism of SWNT nucleation on Si-based
catalysts, particularly SiO
2
, SiC and Si, will then be discussed in §3.4. In §4 we will discuss
QM/MD simulations concerning the continued growth of SWNTs on Fe and Ni catalysts.
Finally, insights gained from recent QM/MD simulations regarding the issue of chirality-
controlled growth will be the subject of §5.
1.1 Experimental synthesis of SWNTs
An exhaustive review of experimental techniques of CNT and SWNT synthesis lies beyond
the scope of the current work. Instead, we will provide a cursory overview of two relevant
experimental techniques pertinent to the simulations presented in this work, viz. the CVD
and arc-discharge techniques on transition metal catalysts. We will also briefly summarise
recent experimental reports concerning the synthesis of CNTs on ‘non-traditional’ catalysts
such as SiO
2
, SiC and Al
2
O
3
. For more extensive reviews of this area, we direct the reader to
the several books (Dresselhaus et al., 1996; Dresselhaus et al., 2001) and reviews (Teo et al.,
2004; Yoshinori, 2004) that are concerned with experimental synthesis.
The CVD process is widely used throughout the areas of material science and solid-state
physics. Put simply, it involves a substrate material being deposited and subsequently
exposed to a chemical reagent. This reagent subsequently decomposes or reacts on the
substrate surface, yielding a desired chemical deposit. In the context of SWNT synthesis, the
substrate is traditionally a thin (typically < 100 nm) layer of transition metal nanoparticles,
and the reagent is a carbonaceous gas such as methane, acetylene or ethanol. These gaseous
reagents are believed to decompose on the catalyst nanoparticle surface, thus providing a
source of atomic carbon, before dissolving and diffusing into the metal catalyst. As will be
shown in §3, however, there is currently a lack of consensus over exactly how these initial
stages of SWNT nucleation occur. The metal catalyst layer itself may be deposited via a
number of different techniques. However, SWNT synthesis is only successful with relatively
small nanoparticle diameters (ca. 5 nm or less) (Teo et al., 2004). The catalytic species that are
typically used for the synthesis, or growth, of SWNTs include first row transition metals
such as Fe, Ni, Co and Mo (Journet et al., 1997; Moisala et al., 2003; Harris, 2007). These
metals, and alloys thereof, are employed today in the industrial scale CVD synthesis of
SWNTs. However, the alkaline earth metals Mg and Ca, as well as Ir and W have also
shown catalytic capabilities in the context of CVD SWNT synthesis (Esconjauregui et al.,
2009). Most recently, so-called ‘catalyst-free’ synthesis of SWNTs has been reported (see
Mechanisms of Single-Walled Carbon Nanotube Nucleation,
Growth and Chirality-Control: Insights from QM/MD Simulations
523
(Homma et al., 2009), and references therein). In these cases, SWNTs have been synthesised
via CVD in the absence of the metal catalyst layer. It follows then that the
cracking/decomposition of the gaseous reagent takes place on the supporting substrate
itself. The precise mechanism underpinning this un-catalysed reagent decomposition is as
yet not unknown. While a number of such covalent CVD ‘catalysts’ have been reported
(including Ge (Takagi et al., 2007), Al
2
O
3
(Liu et al., 2008; Liu et al., 2010a) and even other
nanocarbon structures (Homma et al., 2009)) the majority of experimental investigation in
this area has so far focused upon SiO
2
(Bachmatiuk et al., 2009; Huang et al., 2009; Liu et al.,
2009a; Liu et al., 2009b; Liu et al., 2010b).
In the most general terms, the arc-discharge method involves an electrical discharge
between two electrodes through a particular gas (in the process of which this gas is broken
down). This method was employed in the synthesis of C
60
fullerene (Krätschmer et al., 1990;
Heath, 1992), before becoming a popular synthetic method for SWNTs. Indeed, the first
experimental characterisation of SWNTs (Iijima & Ichihashi, 1993) employed arc-discharge
synthesis. In both fullerene and CNT synthesis, the arc-discharge method involves the
electrical discharge between two carbon electrodes (one of which is vaporised), usually in
the presence of some inert buffer/carrier gas. In the case of SWNT synthesis however, it is
preferable that a metal-doped anode is used, otherwise multi-walled carbon nanotubes
(MWNTs) are formed. Thus, both the carbon and metal vapors may co-condense, forming
liquid phase metal carbide particles. In this sense, the arc-discharge technique constitutes a
‘pure’ example of the VLS mechanism of SWNT growth. The most common catalytic metals
employed in this arc-discharge SWNT synthesis are the same as those employed in the
traditional CVD synthesis of SWNTs (i.e. Fe, Co, Mo etc.) (Journet & Bernier, 1998). There is
great variability, however, regarding the yield and diameter distribution and of the
synthesised nanotubes with different catalyst metals. The same may be said regarding the
pressure and composition of the environmental buffer gas (Journet & Bernier, 1998; Farhat et
al., 2001).
1.2 Theoretical investigations of SWNT growth
The first foray of theoretical investigation aimed at understanding CNT nucleation and
growth took place in the 1990s (see (Irle et al., 2009), and references therein). Amongst the
first of these undertakings was that of Smalley et al., who demonstrated that a single metal
atom (Ni or Co) has the ability to prevent the closure of an extended sp
2
-hybridised carbon
structure, simply by ‘scooting’ around the open edge (Thess et al., 1996). Despite the
simplicity of this ‘scooter mechanism’, it revealed for the first time this most fundamental
property that is now commonly ascribed to the catalytic nanoparticle during SWNT growth.
Another early discovery made by Smalley et al. concerned the observation of SWNT growth
during the Boudouard reaction (2CO C + CO
2
) on nanoparticle Mo catalysts (Dai et al.,
1996). It was in this investigation that the now well-known ‘yarmulke’ mechanism was
proposed. This mechanism postulates that a SWNT ‘cap’ fragment exists on the catalyst
nanoparticle surface prior to the continued growth of the nanotube, a fact that has since
been corroborated independently on a number of occasions (see (Irle et al., 2009), and
references therein).
It was not until 2002 that MD simulations were employed successfully in simulating the
SWNT nucleation and growth processes. In a series of investigations, Shibuta and co-
workers simulated Ni-catalysed SWNT nucleation (Shibuta & Maruyama, 2002; 2003). The
roles of both Ni vapor and condensed Ni nanoparticles in the earliest stages of the SWNT
nucleation process were therefore established. These theoretical investigations proved
Electronic Properties of Carbon Nanotubes
524
remarkably consistent with contemporary experimental work. Moreover, the previous
prediction made by Smalley et al. regarding the catalyst preventing closure of the nascent
SWNT was realized in situ. In a somewhat different approach, Bolton and co-workers
investigated the relationship between diffusion and precipitation of carbon from Fe
nanoparticles, and SWNT nucleation in a series of investigations (Ding et al., 2004a; Ding et
al., 2004c; b; Ding et al., 2006a; Ding et al., 2006b). Notably, the nucleation of SWNTs from Fe
‘carbide’ was demonstrated at temperatures between 800 and 1400 K (Ding et al., 2004a).
According to this investigation, the formation of the SWNT cap structure was preceded by
three distinct stages: (1) the incorporation of carbon into the Fe nanoparticle bulk; (2) the
saturation of the Fe nanoparticle with atomic carbon, and (3) the formation of polyyne
chains and small graphitic ‘islands’ on the Fe nanoparticle surface. It was also noted that at
lower temperatures (below 600 K), encapsulation of the nanoparticle, rather than the
formation of a well-defined cap structure, took place. These efforts were complemented by
investigations in 2007 (Shibuta & Maruyama, 2007a; b) in which an inverse relationship
between the melting behaviors of catalyst nanoparticles and the carbon-catalyst interaction
was observed. This was in agreement with an earlier independent investigation (Ding et al.,
2006b). These authors have also investigated the relative behaviors of Fe-, Ni- and Co-
carbide nanoparticles (Shibuta & Maruyama, 2007b), and observed that the Co-C interaction
exceeds both the Fe-C and Ni-C interactions. This correlation suggests that a stronger
catalyst-carbon interaction may yield more defective synthetic SWNTs.
The pioneering MD investigations in this area relied on the reactive empirical bond order
(REBO) force field (Brenner, 1990; 1992; Brenner et al., 2002), which is itself based upon the
Tersoff interactive potential (Tersoff, 1988; 1989). While the use of this force-field makes MD
simulations on nanosecond timescales possible, it nonetheless has several notable
deficiencies with respect to the chemistry of SWNT nucleation. For instance, -conjugation
and aromatic stabilization of carbon (central to the formation and extension of an sp
2
-
hybridised carbon network, such as a CNT), charge transfer effects and the near-degeneracy
of transition metal d-orbitals (crucial in the case of transition metal catalysts) can not be
accurately described by the REBO or Tersoff potentials. One infamous outcome of the
former of these deficiencies is the overestimation and underestimation of the sp
3
- and sp-
hybridised carbon fractions, respectively, during the self-assembly of fullerenes at high
temperature (Zheng et al., 2004; Irle et al., 2006). On a few occasions (Gavillet et al., 2001; Raty
et al., 2005), more reliable simulations based on Carr-Parinello MD (CPMD) have been
reported. The description of atomic interaction and bonding in these latter investigations
relied on density functional theory (DFT), and so therefore significantly exceeded that given
by the REBO potential. However, this advantage incurs a substantial increase in the
computational cost of the calculation. Thus, these simulations employed generally
unphysical assumptions, or model systems, in order to alleviate these computational costs.
In addition, the timescales of these simulations were restricted to less than 25 ps, and as
such can hardly be considered to be sufficient in the context of SWNT growth. While these
simulations nevertheless represent Herculean efforts, relatively few conclusions regarding
the mechanisms of SWNT nucleation and growth have been gained as a result. Ideally, the
most suitable approach to the simulation of SWNT nucleation and growth would provide a
compromise between quantum mechanical accuracy, and the computational efficiency
provided by semi-empirical, or classical, force-field based methods. In the subsequent
section, we will turn to one such method, the density-functional tight-binding (DFTB)
method, and provide a brief picture of its formulation.