Journal of Nanoparticle Research 5: 473–484, 2003.© 2003 Kluwer Academic Publishers. Printed in the Netherlands.

Three-terminal junctions of carbon nanotubes: synthesis,structures, properties and applications

L. ChernozatonskiiInstitute of Biochemical Physics, Russian Academy of Sciences, Moscow 119991, Russian Federation(Tel.: 7(095)1378347; Fax: 7(095)1378347; E-mail: cherno@sky.chph.ras.ru)

Received 20 March 2003; accepted in revised form 30 May 2003

Key words: carbon NTs, Y-junction, electronic properties, CVD method, topological defects, applications

Abstract

We summarize recent studies on the fabrication methods, structures and properties of three-terminal junctions ofcarbon nanotubes (NTs). Then, we present topological classifications of planar Y- and T-junctions of single-walledNTs. Finally, we discuss possible applications of these junctions.

Introduction

Individual carbon nanotubes (NTs) are perfectmolecular wires with well-known structural, elec-tronic, mechanical and transport properties (Harris,1999). They contain one graphitic layer (single-wallnanotubes, SWNTs) or at least two similar layers(multi-walled nanotubes, MWNTs). The electronicproperties of SWNTs, denoted as (n,m), depend onboth chirality that can be uniquely determined by thechiral vector (R = na1 + ma2) and NT diameter:d(n · m) = a

√n2 + m2 + nm/π , where n, m and q are

integers, and a = 0.246 nm is value of the unit cell basevector of the graphene sheet (Harris, 1999). SWNTscan be either metallic when (n,n) or when n−m = 3q,while NTs with n−m �= 3q are semiconducting. Thus,multi-terminal connections can be formed from NTswith different conductivities. In 1992, Dunlap (1992)and Chernozatonskii (1992a) independently consid-ered the possibility of forming continuous connectiontwo-carbon tubes by including pentagons, heptagonsor octagons in the hexagonal net of the carbon atoms.If two NTs, one semiconducting and the other metal-lic, are connected, a heterojunction is formed that willact as a rectifying diode. Such two-terminal hetero-junctions or rectifying diodes were first postulatedtheoretically (Lambin et al., 1995; Chico et al., 1996)

and recently observed in experiments (Han et al., 1998;Yao et al., 1999). For a typical two-terminal rectifyingdevice, the two-terminal junctions of NTs are difficultto make in experiments in any controlled way, muchless using these in any molecular electronic circuitryfor switching purposes. Moreover, the two-terminalrectifying devices also lack the versatility of the three-terminal devices where the third terminal could be usedfor controlling the switching mechanism, power gainor other transisting applications that are needed in anyextended molecular electronic circuit.

Connecting different NTs to form three-terminalNT junctions were proposed in 1992 (Scuseria, 1992;Chernozatonskii, 1992b), and observed first in 1995(Zhou & Seraphin, 1995). Recently, the use of car-bon NT T- and Y-junctions as three-terminal nanoscalemolecular electronic devices were reported (Menon &Srivastava, 1997).

Earlier experimental observations of carbon NTY-junctions (Zhou & Seraphin, 1995) did not attractmuch attention for electronics applications mainlydue to the difficulties associated with their synthe-sis and the complexities of their structures. In orderfor the Y-junctions to be useful from a device per-spective, controlled and high-yield production of thesejunctions is required. Very recently, experimental-ists have succeeded in developing template-based

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chemical vapor deposition (CVD) (Li & Papadopoulos,1999; Papadopoulos et al., 2000) and pyrolysis oforganometallic precursor with nickelocene and thio-phene techniques (Satishkumar et al., 2000) thatallows for the reproducible and high-yield fabrica-tion of carbon NT Y-junctions. The conductancemeasurements on Y-junctions have shown intrin-sic nonlinear and asymmetric current–voltage (I–V )behavior at room temperature (Papadopoulos et al.,2000). Recently, much interest has been focused onthree-terminal junctions that are envisaged as a unit ofnano-devices likely functioning as a transistor or a rec-tification element (Andriotis et al., 2001; 2002; Menonet al., 2003).

Here, we first review different methods for the prepa-ration of NT Y-junctions. Then, possible mechanismsfor the formation of NT Y-junctions are discussed. Wedetail the topological defects and the classification ofSWCN Y-junctions. Finally, transport properties areconsidered, including also the ballistic switching appli-cations of SWNT Y-junctions. Other properties andapplications of multi-terminal junctions are discussedin the Conclusion.

Synthesis

At present, there are seven known methods to prepareNT Y-junctions.

(1) The first observation of branching carbon NTs byhigh-resolution electron microscope (HREM) demon-strated the formation of L-, Y - and T -junction NTs.Zhou and Seraphin (1995) used an arc-dischargemethod with specific conditions: helium atmosphere of500 Torr and a hollow anode. The NT diameters of thesejunctions were in the order of 10 nm and the junction

lengths were ∼100 nm. Recently (Klusek et al., 2002;Osvath et al., 2002), scanning tunneling microscopy(STM) and scanning tunneling spectroscopy (STS)measurements on a Y-branched carbon NT produced bythe arc-discharge method were reported under slightlydifferent conditions. A drilled out graphite rod filledwith a nickel/yttrium particle mixture was used as ananode in the arc chamber under 660-Torr He atmo-sphere (Osvath et al., 2002). Straight MWNTs andlong (∼1 µm) asymmetrical Y-branches were foundin a sample taken from the cathode deposit. Asmeasured by STM, the Y-junctions have low appar-ent heights in the range of 1 nm. This may be anindication that these NTs have only a few walls,or possibly they are single-walled. In these studies,several defects were observed along the Y-branchedNT and some knees before branching. We will takethese results into account during the discussion ofthe Y-junction growth mechanism. The arc-dischargeformation of these different junctions was totallyrandom.

(2) Macro-scale Y-junction synthesis was real-ized first by using an alumina membrane withsplitting Y-shaped channels (Li & Papadopoulos,1999; Papadopoulos et al., 2000). In these studies,MWNTs were produced in aligned arrays (density∼1010 cm−2) with adjustable ‘stem’ (∼50 nm) and‘branch’ (∼35 nm) diameters and 6–10 µm totallength. Cobalt particles were used as catalysts atthe bottom of the channels during the pyrolysis ofacetylene at 650◦C. This CVD method allows thereproducible fabrication of carbon NT Y-junctionswith a controlled length (∼10 µm) and tube branches(15–100 nm) with an acute angle between them resem-bling ‘tuning forks’ (Figure 1a). However, this methodrequires the use of a special template.

(a) (b) (c)

Figure 1. Electron microscope images of carbon NT Y-junctions: (a) acute angle ‘fork’ junction with stem 100 nm and branched ∼50 nmin diameter (Papadopoulos et al., 2000); (b) obtuse angle ‘slingshot’ junction with arms 200 nm in diameter (Li et al., 2001), (c) T-junctionof welded single-walled tubes ∼1 nm in diameter (Terrones et al., 2002).

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(3) The pyrolysis method produced multipleY-junctions with angles between the arms varyingin the range of 90◦–150◦ from junction to junction(Satishkumar et al., 2000), where a two-stage fur-nace system was used. The nickeletone boat waslocated in the first furnace with heating up to 350◦C.Nickeletone vapor with hydrogen–thuophene (sulfuradditive) vapors were introduced into the second fur-nace at 1000◦C. Here, carbon deposits accumulatedafter the pyrolysis process. The TEM image showsmultiple Y-junctions, where the arms were fishbone-type tubes with diameters ranging from 15 to 100 nm.The yield of such structures was in the order of 70%.During this time period Y-junction carbon NTs wereobtained in a hot-filament CVD system where evapo-rated copper was used as catalyst during the pyrolysisof acetone bubbled by H2 (Gan et al., 2000a,b). Most

of the Y-junctions had similar geometry with 50◦–80◦

between branches of fishbone-type tubes too.A procedure similar to that described by Satishkumar

et al. (2000) was carried out to obtain the growth ofthe same Y-junction NTs by the pyrolysis of thiopheneover a Ni(Fe)/SiO2 catalyst (Deepak et al., 2001). In thisstudy, larger quantities of Y-junctions were producedthan obtained earlier.

(4) Straight identical Y-junction NTs have been syn-thesized by the pyrolysis of methane (CH4) togetherwith N2 over cobalt supported on a special calcinedmaterial of magnesium oxide supported Co (Li et al.,2001) (Figure 1b). The growth normally lasted for1 h after reducing Co catalysts at 1000◦C in flowinggases of H2 (40 sccm) with N2 (100 sccm) at a pres-sure of 200 Torr, and post-replacing the N2 with CH4

(10 sccm). The Y-junctions had very straight arms with

(a) (b)

(c) (d)

Figure 2. Modeling of Y-junction growth mechanism in floated CVD method: (a) first step of reaction – ‘floated’ nanosize iron particle(dark atoms on the right) is deposited on surface defects of main two-walled carbon NT, which has began to form on another metal clustersome time before (on the left) during pyrolysis of CH4 (small molecules); (b) outer (9,9) tube and inner (4,4) tube with pentagon andheptagon defects before formation of Y-junction; (c) third step of reaction – growth of the main tube and branch (d) Y-type outer (9,9)tube and inner (4,4) tube with the heptagon and octagon rings shown in dark shade.

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uniform ∼200 nm diameters (and ∼10 nm inner diam-eters), and the angles between the three arms were closeto 120◦ (Figure 1b). They had generally a short branch(∼0.5 µm) and some longer ones (up to ∼10 µm).Some NTs branched several times to form multipleY-junctions, which still keep their arms straight.

Triangular amorphous particles consisting of Ca, Si,Mg and O were always found right at the junctioncenters, and some branches with open tips were filledMgO rods crystallizing during the cooling process. Theauthors assumed that the existence of Ca and Si is prob-ably from the impurities in the starting materials; thetriangular particles at the center of the Y-junction resultfrom the split of the catalyst particles due to the ther-mal fluctuations during growth and left behind duringthe tube growth.

(5) The growth of Y- and H-junctions and three-dimensionally connected NTs using a simple thermalCVD method has been reported very recently (Ting &Chang, 2002). A single crystal silicon wafer as the sub-strate was first scratched, cleaned ultrasonically, andthen placed in a horizontal tube of a thermal CVDfurnace. A ceramic boat carrying iron powers as the cat-alyst source was positioned at a distance of 5 cm awayfrom the substrate upstream. The arrangement allowsevaporation–deposition of the iron powders to occur atdesired temperatures such that nanosize iron catalystswere seeded on the Si substrate. Junctions of carbonNTs with uniform diameters (∼40 nm) were grownthrough the pyrolysis of methane on the catalysts at atemperature of 1100◦C.

(6) Y branchings were first observed by STM incarbon SWNTs grown by thermal decomposition ofC60 fullerenes in the presence of the following transi-tion metals: Ti, Cr, Fe, Co, or Ni (Nagy et al., 2000).The catalyst powder and fullerenes were mechanicallymixed and heated to 450◦C at 2 × 10−6 Torr pres-sure. Y-shaped SWNTs with ∼1 nm diameter and 120◦

angles between branches were obtained in the mate-rial evaporated and condensed on the graphite surface.However, this method does not allow reproducing ofY-junctions with high yield.

(7) Another preparation method of stable SWNTjunctions of various geometries (see, for example,Figure 1c) were obtained by electron beam weldingafter a few minutes of irradiation at specimen tempera-tures of 800◦C (Terrones et al., 2002). The NT behaviorwas monitored under usual imaging conditions in atransmission electron microscope: 1.25 MeV electronenergy beam with an intensity of ∼10 A/cm2. This tech-nique could be regarded as an alternative to possible

chemical functionalization, which, on the other hand,has limitations to provide epitaxial SWNT junctionsthat are mechanically robust. The junctions were cre-ated via vacancies and interstitial defects, induced bythe focused electron beam, that promote the formationof intertube links. The authors have assumed that elec-tron beam exposure at high temperatures induces struc-tural defects, which promote the joining of SWNTs viacross-linking of dangling bonds. They have modeledthis process by molecular dynamics simulations thathave shown that the creation of vacancies and inter-stitials induces the formation of junctions involvingseven- or eight-membered carbon rings between thetubes creating vacancies in the crossing region, and pro-viding a picture of an intermediate state of the ‘welding’process.

Growth and formation mechanisms

The various synthesis methods considered aboverequire the examination of several different forma-tion mechanisms of three-terminal junctions. We can-not decide on the process because (1) arc-dischargemethod has low productivity and is poorly control;(2) template growth mechanism of MWNT’s junctionsdoes not present peculiar difficulties in its comprehen-sion (Li & Papadopoulos, 1999). It can be described inthe framework of the CVD growth model of ordinaryMWNT’s in the presence of catalysts (Harris, 1999).The process begins with the growth of ‘branches’ insmall-diameter channel holes. These tubes grow upduring the pyrolysis of hydrocarbon molecules on cat-alytic particles previously imbedded at the bottom ofthe holes. Two particles rising in two small chan-nels arrive at the ‘stem’ hole and combine into oneparticle – from this place the growth of a tube pro-gresses in the template hole with a larger diameter andup to the entrance on the template surface. The joiningof the particles leads to the formation of a NT connectorin the place of channel connection. It can be assumedthat the changing of tube layer structure does not occuron the smooth sides of the ‘fork’ connector – all the tubetopological defects accumulate between the branchesas is shown in the next paragraph.

Zhu et al. (2000) have supported the followinggrowth mechanism of Y-junctions prepared by a float-ing catalyst method with sulfur additive. They placespecial significance on the presence of sulfur as a crit-ical factor for the growth, similar to the role playedby sulfur in the growth of carbon NTs and filaments

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(Kim et al., 1993; Ci et al., 2000). Their viewpoint isthat selective sulfur poisons the surface of the catalystparticles, and prevents its deactivation by the growth ofa carbonaceous layer so that the solution of hydrocar-bons can efficiently proceed. When sulfur atoms on theouter part of the iron particle surface are at an optimalcoverage, the catalysts will have high activity. At thesame time, carbon atoms from the pyrolysis of hydro-carbon molecules attach to catalyst surfaces and willgrow into a tube-stem. The curvature of the oppositeside becomes larger under the stress of the depositedgraphite layers, so it is difficult here for the deposi-tion of the graphite layers. When the particle surfacehas optimal sulfur coverage, the growth of the stem isstopped, but the selective graphite layers could depositon the side of the particle, leading to the growth of thebranch. After some time, the graphite layers come backto the original site, continue the growth of the mainstem, and stop the elongation of the branch.

However, this mechanism does not explain the for-mation of long branches – in this case branch growthshould be in the presence of the catalytic particle. Thisprocess requires division of the initial catalyst parti-cle into two particles of smaller sizes, one of whichprovokes the growth of the long branch NT. MWNTssynthesized by the CWD method have ordinarily adiameter approximately equal to that of the catalyticparticles (see, for example, Kukovitsky et al., 2003).So, a small particle should lead to the growth of a branchwith smaller diameter than that of the stem, but it is notobserved in the CVD methods (4–6) considered for thepreparation of Y-junctions. The Zhu mechanism doesnot also explain the experiments (Li et al., 2001; Ting &Chang, 2002) without sulfur participation.

We think that the basis of the MWST Y-junctionfloating CVD methods is the process of hydrocar-bon pyrolysis on catalytic particles attached to thestrain parts of stem-NTs, which have been organizedin previous time moments. This results in the presenceof catalytic particles with smaller sizes in the flow ofreagents. During the long time quasi-stationary pro-cess of Y-junction preparation (from minutes (Deepaket al., 2001) up to hours (Li et al., 2001)) particleswith approximately the same diameters are generated.It is known (Harris, 1999) that different defects areformed on the surface of rising MWNTs, so the otherfloating catalytic particles can stick to them and actas the beginning point of the growth of branches withapproximately equal diameters.

Thus, we can assume the following scenario ofMWNT Y-junction formation during floating CVD

synthesis. The first step is the growth of the usualmulti-walled tube on the catalytic particle of the initialflow and the formation of tube surface defects eitherchanging the tube direction or not visibly changing thedirection; during the second post-flow, iron catalystsare seated on the surface NT defects – the destroyedsite on the surface can provide dangling bonds to whicha metal particle is attached (Figure 2a). The third stepis ‘suction’ of carbon atoms into the particle fromthe tube defect area and the atoms, generated underpyrolysis of hydrocarbons, and the beginning of branchgrowth. In this step, distortion of the main tube nearthe particle attachment site can possibly occur becausethe process takes place at high temperature ∼1000◦C(Satishkumar et al., 2000; Deepak et al., 2001; Ting &Chang, 2002), where defects can occur in the hexagonalcarbon layers of the NT. The fourth period is simul-taneous growth of the main tube and the branch witha diameter close to that of the tube-stem, since thereare equal conditions for their growth (Figure 2c). Thelast period is the completion of the Y-junction growthunder cooling similar to the usual CVD NT preparation

Figure 3. The types of Y-junctions made up of zigzag NTs:(a) (14,0),(7,0)FH6 symmetrical ‘fork’ with six heptagons inacute angle between (7,0) tubes – indexes S, L and R denotestem, left, and right branches, respectively; (b) (8,0)S3H6 –‘slingshot’ of C3 symmetry; (c) (17,0),(7,0)(10,0)FH6 – non-symmetrical ‘fork’; (d) another (17,0) stem branching into (7,0)branch and (10,0) ‘bough’ – (17,0),(7,0)(10,0)BH2O2 junction.The atoms forming the heptagons and octagons are shown in darkshade.

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Figure 4. Simulation results showing different steps leading up to the formation of (10,0)–(5,5) T-junction. The defect rings are shownin dark and include five-, seven- and eight-fold rings. All the atoms in the junction region are sp2 bonded. The final structure contains sixheptagons and no pentagons.

with preliminary precipitation of catalytic particles ona substrate (Harris, 1999; Kukovitskii et al., 2003).

This mechanism may be expected in the case ofgrowth of Y-junctions with angles ∼120◦, when hot-filament CVD methods (Gan et al., 2000a, b), pyrolysisof cobaltocene and ferrocene (Deepak et al., 2001)pyrolysis of CH4 (Li et al., 2001), or thermal CVDmethods (Ting & Chang, 2002) are used without anytemplate. A similar mechanism can take place in theCVD process under special electrodeposition of metalat the present NT and NT junctions (Austin et al., 2002).

Further, we look at the process of Y-junction for-mation under electron beam welding of SWNTs. Theschematic of this process would be the following: Thefirst period is heating of the area of adjoining the NTs,perhaps with the generation of defects on the closedparts of these tubes, and covalent coupling of the closedatoms of the neighboring parts of the adjoining tubes(Chernozatonskii et al., 2001; Terronis et al., 2002;Zhao et al., 2002). The second period of reaction isbond rotation (Stone & Wales, 1986), resulting in theformation of the NT connector of the hexagon net withtopological defects (Terronis et al., 2002; Zhao et al.,2002; Menon et al., 2003).

Let us consider the formation modeling of single-wall carbon NT T-junctions via the fusing of twoSWNTs by using tight-binding molecular dynamics(Menon et al., 2003). Energetically efficient path-ways for this process in which all atoms maintainthe sp2 arrangement throughout have been proposed.This consideration has been illustrated by the forma-tion of (10,0)(9,0) and (10,0)(5,5) T-junctions pro-posed earlier as elements for electronic nanodevices

(Menon & Srivastava, 1997). We next illustrate theformation of a (10,0)(5,5)TH6 junction by bringing acapped (10,0) NT near a (5,5) NT wall. In Figure 4,simulation results showing eight steps leading up to theformation of this T-junction is presented. It is knownthat SWNTs are very sensitive to electron irradiation atT ∼ 300–700◦C (Banhart, 1998). Thus, we take intoaccount this phenomena by including the first defectformation in the (5,5) tube which facilitates the bond-ing to the (10,0) tube (step 1). In step 2, the inter-NTconnectivity is through four bonds forming the sides offour octagons. This structure also contains defect ringsin the form of four pentagons and two heptagons. Instep 3, two of the octagons are annihilated, and addi-tionally, the structure contains four pentagons and sixheptagons in the junction region. In step 4, the rear-rangement of atoms causes the neck to widen. Thedefects are identical to step 3, but their positioningis different. The subsequent arrangement of defectsas we proceed toward the final structure are: six pen-tagons and 12 heptagons (step 5); four pentagons, sixheptagons and two octagons (step 6); and two pen-tagons and eight heptagons (step 7). The final structure(step 8) contains seven heptagons and no pentagons. Allstructures in this figure are fully relaxed and the totalenergy is calculated using the tight-binding moleculardynamics scheme (Menon et al., 1996).

More insights can be gained from a study of ener-gies at various steps leading to the formation of thetwo T-junctions. The relative energies at each step inthe formation of the two T-junctions are plotted inFigure 5. An initial increase in energy (indicating abarrier ∼2 eV) is followed by an almost monotonic

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Figure 5. Relative energies calculated using the GTBMD schemeat each step. Dotted curve belongs to the formation of (10,0)–(5,5)T-junction, full curve belongs to the formation of (10,0)–(9,0)T-junction (containing eight heptagons and two pentagons).

decrease in subsequent steps. The absence of large bar-riers is indicative of the energy efficiency involved inthe junction formation. Similar modeling has been car-ried out for fullerene-NT coalescence by Zhao et al.(2002). They also supported T-junction formation butwithout the estimation of the energetically profitableprocess.

Topological defects and classification ofthree-terminal NT junctions

For a good understanding of three-terminal junctions,a detailed characterization of the structure is required.Although pristine SWNTs contain only hexagonalarrangement of carbon atoms, the formation of a multi-terminal infinite net junction requires the presence oftopological defects in the form of pentagons, heptagonsand octagons (Harris, 1999). This is essential for main-taining sp2 configuration for all carbon atoms in order tomaximize stability. It is interesting to note that topolog-ical defects in SWNT junctions obey a generalization ofthe well-known Euler’s formula (Crespi, 1998). Crespi(1998) proposed by considering only non-hexagonalpolygons on the surface of a closed polyhedron in termsof the faces, vertices and edges, a consideration forthe formation of complex multiple junctions in termsof local bond surplus at the junction. The excess inthe number of polygonal sides due to non-hexagonalpolygons is called local bond surplus. For example,the presence of a pentagon in a hexagonal sheet con-tributes to a bond surplus of −1, while heptagons and

octagons contribute to bond surpluses of +1 and +2each, respectively. The consideration is that a junctionmade of N half-NTs has a bond deficit of 6(N− 2). Forall three-terminal junctions (such as Y- or T-junctions)this gives a bond surplus of +6, and for all four-terminaljunctions (such as X- or +-junctions) this gives a bondsurplus of +12 at the junctions. The Crespi formulacan be simply transformed into a modified equation:N(7) + 2N(8) − N(5) = 6(N − 2), where N(5), N(7),N(8) are numbers of pentagons, heptagons, octagons,and N is number of branches (open NT ends) of theN -terminal junction.

We classify here planar three-terminal junctions,which contain tube axes of both branches and stemin the same plane, i.e. the Y- and T-SWNT struc-tures generally observed in experiments (Figure 1).The later can be constructed only from ‘a’ – armchair(n, n) or ‘z’ – zigzag (n, 0) NTs. Thus, these junc-tions are considered only with ‘a,aa’, ‘a,az’, ‘a,zz’,‘z,zz’, ‘z,za’, ‘z,aa’ sets of NTs. The classification isbased on the geometry of different junction forms.We consider junctions with heptagon and octagondefects whose number is equal to N(7) + 2N(8) = 6.Modeling of three-terminal junctions with even num-ber of pentagon–heptagon extra pairs can be carriedout similarly (see, for example, (10,0)-(9,0) T-junctioncontaining eight heptagons and two pentagons inFigure 5).

We look at two main classes of those junctions withone or two dissymmetrical planes. Class N containsY-junctions with only one dissymmetrical plane (P1)in which all axes of Y arm-tubes are situated. Class S

contains the junctions with P1 and the plane (P2) dis-secting the stem and its symmetrical structures in half.We make groups of junctions according to a type andposition of defects: group F (‘forks’ – Figure 3a and c)consists of Y-junctions with defects in an acute anglebetween branches; group S (‘slingshots’ – Figures 3band 2d) gathers junctions with obtuse angles betweenall three arms; the class N junctions are inclusive ofone branch-tube, continued from the stem-tube withoutdefects on one side, put together in group B – ‘boughs’(Figure 3d); the T-junctions of class S are constructedfrom the stem added perpendicularly to tube-crossbar.The presence of the dissymmetrical plane P1 in all theconsidered SWNT junctions points to fixed dispositionof defects – the structures with even number of hep-tagons (H6, H4O1 and H2O2) or only three octagonsare considered. So we subdivide each group into sub-groups of different defect types: the H6 subgroupcontains six heptagons in each junction, the H4O1

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junctions contain four heptagons and one octagon inthe each, and the H2O2 subgroup includes junctionswith two heptagons and two octagons, three octagonsare contained in each of the O3 subgroup junctions.

Thus, any Y-junction of class N can be denoted as:stem, right branch and left branch NT notations, groupnotation, and defect subgroup notation. For example,the ‘bough’ (Figure 3d) consisted of (17,0) tube-stem,(7,0) R-tube and (10,0) L-tube branches, with two hep-tagon and two octagon defects that could be denoted as(17,0),(7,0)-(10,0)BH2O2.

Any Y-junction of class S can be denoted as: stemand branch NT notations, F (either S or T) groupnotation, and defect subgroup notation. For example,the symmetric ‘fork’ (Figure 3a) consisted of (14,0)tube-stem, and two (7,0) tube branches, with six hep-tagons and could be denoted as (14,0),(7,0)FH6. C3h

symmetrical ‘slingshots’ of three equal tube arms con-tain six heptagons or three octagons only. This set ofY-junctions are denoted as S3. An example of a sim-ilar Y-junction, (8,0)S3H6, consisting of (8,0) NTs isshown in Figure 3b.

If a Y-junction contains four heptagon unionsthen it can be transformed into another by usingthe Stone–Wales bond rotation of type (7,7,7,7) ↔(8,6,6,8), when in the union a bond together withtwo C atoms rotate at 90◦, and two octagons andtwo hexagons are generated (Figure 6a). The inverseoperation with the (8,6,6,8) union is also possible.During another S–W rotation (7,6,6,8) ↔ (6,7,7,7) –Figure 6b – three adjoined heptagons are gener-ated. A pair of heptagons can rotate at 90◦ duringthe (6,7,6,7) ↔ (7,6,7,6) transformation. S–W bondrotations of the enumerated unions allow obtain-ing isomers of the examined Y-NT molecule. The(6,7,6,7) union can be transformed into the (6,8,6)union when we exclude two carbon atoms and form anoctagon (Figure 6c). The considered transformationsdo not change radically the forms of the concernedY-junctions. Thus, we can reorganize the set of defectswithout changing the structure of the NT junction armsby reforming the Y-subgroup, for example, from H6to H2O2 (under (7,7,7,7) → (8,6,6,8) transformation),and from H2O2 to H4O1 (under (6,7,7,7) → (7,6,6,8))or to O3 (under (6,7,6,7) → (6,8,6)).

The classification of all planar SWNT three-terminaljunctions (Chernozatonskii & Lisenkov, 2003) is givenin Tables 1 (class S) and 2 (class N ). Each line in thesetables determines the junction series from the initialstructure of NTs with minimal diameters when addi-tional indexes m, k, p are equal to zero (m, k, p = 0).

Figure 6. Defect transformations: (a) (7,7,7,7) ↔ (8,6,6,8)Stone–Wales bond rotation; (b) (7,6,6,8) ↔ (6,7,7,7) S–W rota-tion; (c) (6,7,6,7) ↔ (6,8,6) process of C2 arrival–leaving –octagon formation by exclusion of C2 cluster between two hep-tagons, or inclusion of C2 in the octagon center in the oppositeprocess. The defect rings are shown in dark shade.

The hand-picked (3,0) and (2,2) NTs have the small-est diameter. The condition m, k, p �= 0 means that them-hexagon strip is put in the middle of tube-stem, inone’s turn the k- and p-hexagon strips are put in leftand right sides of the considered Y-junction (in R andL branches, and stem), correspondingly.

Each of the tables consists of three columns. Thefirst column is the number of lines for reference, andthe second is the NT index of the stem. The thirdcolumn contains tube-branch indexes, notations ofgroup and possible subgroups of defects for the chosenjunction arms.

Inasmuch as NT diameter strictly connects withtube index (see the section ‘Introduction’ and Harris,1999), we can determine from our tables a set ofdefects needed for constructing the three-terminal junc-tion in order to compare with the chosen experimentalexample.

For instance, we like to construct a ‘fork’ sym-metrical junction with (20,20) tube-stem and acuteangle between branches of (13,13) NTs (Figure 7a). InTable 1, we are looking for the crossing of ‘a’ stem

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Table 1. Class S of NT Y-junctions

Class S: Branches of equal tubesLine ‘z’ stem ‘zz’ branches: (3 + k,0)/group – defects

1 (4 + 4k ± 2m,0) S – H6; H4O1; H2O2, O32 (6 + 2k + 2m,0) F – H6; H4O1; H2O23 (12 + 2k + 6m,0) F – O3

‘z’ ‘aa’: (2 + k,2 + k)/1 (4 + 4k + 2m,0) S – H4O1; H2O22 (4 + 4k + 6m,0) S – H6

‘a’ ‘zz’: (3 + k,0)/1 (2 + 2k + 2m,2 + 2k + 2m) S – H6; H4O1; H2O2

‘a’ ‘aa’(2 + k,2 + k)/1 (2 + 2k ± 2m,2 + 2k ± 2m) S – H6; H4O1; H2O2; O3;2 (4 + 2k + 2m,4 + 2k + 2m) F – H6; H4O1; H2O23 (4 + 2k − 2m,4 + 2k − 2m) F – H6; H4O14 (6 + 2k + 2m,6 + 2k + 2m) F – O3

Class S: Three equal tube arms‘a’ arm Group – defects

1 (2 + 2k,2 + 2k) S3 – H6; O3S – H4O1; H2O2

‘z’ arm Type – defects1 (4 + 2k,0) S3 – H6; O3

S – H4O1; H2O2

Class S: Group of T-junctions‘a’ stem ‘a’ crossbar (2 + k,2 + k)/defects

1 (2 + 2k ± 2m,2 + 2k ± 2m) H6, H2O2‘z’ ‘z’ (3 + k,0)/

1 (4 + 2k ± 2m,0) H6, H2O2‘a’ ‘z’ (3 + k,0)/

1 (2 + 2k ± 2m,2 + 2k ± 2m) H6, H2O2‘z’ ‘a’ (2 + k,2 + k)/

1 (4 + 2k + 2m,0) H6, H2O2

Table 2. Class N of NT Y-junctions

Class N

Line ‘a’ stem ‘aa’ branches: (2 + k, 2 + k)(2 + p, 2 + p)/group – defects

1 (2 + k + p ± m, 2 + k + p ± m) S – H6; H4O1; H2O2; O3B – H6; H4O1; H2O2; O3

2 (6 + k + p + m, 4 + k + p + m) F – H6; H4O1; H2O23 (6 + k + p + m, 6 + k + p + m) F – O3

‘z’ ‘zz’: (3 + k, 0)(3 + p, 0)/1 (3 + k + 2p ± m, 0) B – H6; H4O1; H2O2; O32 (4 + 2k + 2p ± m, 0) S – H6; H4O1; H2O2; O33 (6 + k + p + m, 0) F – H6; H4O1; H2O24 (12 + k + p + 3m, 0) F – O3

‘a’ ‘zz’: (3 + k, 0)(3 + p, 0)/1 (2 + k + p ± m, 2 + k + p ± m) S – H6; H4O1; H2O2

‘z’ ‘aa’: (2 + k, 2 + k)(2 + p, 2 + p)/1 (4 + 2k + 2p ± m, 0) S – H6; H4O1; H2O2

‘a’ ‘az’: (2 + k, 2 + k)(3 + p, 0)/1 (2 + k + p ± m, 2 + k + p ± m) B – H6; H4O1; H2O2

‘z’ ‘za’: (3 + k, 0)(2 + p, 2 + p)/1 (4 + k + 2p ± m, 0) B – H6; H4O1; H2O2

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Figure 7. Transformation of Y-junction of (20, 20) tube-stem and (13, 13) tubes-branches under pressure treatment: (a) arrays show theforce action on the ‘fork’ in unstrained state; (b) ‘fork’ with stick together branches is in metastable state after unloading. The heptagonsare shown in dark shade.

line and ‘aa’ branch column with the necessary tubeindexes – this is crossing of branches with additionalindex k = 11 and line 3 of the stem with m = 3. Onthe other hand, we can chose this junction from anotherset of junctions with (8+2k′,8+2k′) stem and (7+ k′)branches, when k′ = 6, i.e. when we put two pairs threehexagon strip lateral insets in initial tube configuration(8,8)(7,7)SH6, but here the initial ‘slingshot’ convertsinto ‘fork’ (20,20)(13,13)FH6. That is why we do notuse this description in Table 1.

Properties and applications

The synthesis of carbon NTs with branching structuresis an important step in the development of carbon-basednano-electronic and micro-electromechanic devicesand because these materials are potentially able to bringin new mechanical and electrical properties.

Unusual Y-junction mechanic properties connectwith their geometric form. So ‘slingshots’ and ‘boughs’may be used as nanosprings under loading oftheir branches. Y-junctions will be good components

of polymer composites making their strengtheningproperties better.

Here, we present the marvelous effect arising underthe force influence upon the ends of a ‘fork’. Thisis the sticking effect for acute angle Y-junctions:processes of branches sticking together and openingof closed branches (Chernozatonskii & Ponomareva,2003). The modelings have been carried out by a mole-cular dynamic method with Brenner potential (Brenner,1990) and taking account van der Waals interaction(Brenner et al., 2002). Two (20,20)(13,13)F6H struc-tures (7014 and 11070 carbon atoms) with equal 7.7length tubes, stems and branches of 11.5 and 20.9 nmlengths, were obtained. A pressure of ∼0.1 GPa wasapplied to the ends of the branches as shown inFigure 7a. We have found sticking of branches tooccur when the arms of the ‘fork’ have approachedone another on the vdW distance, similar to whattakes place in the case of the effect of van der Waalsforces between two adjacent tubes touching each other(Rouff, 1993). After the force is removed the junc-tion maintains the new metastable state of the touchedbranches (Figure 7b) if we chose comparatively

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shorter branches (length/diameter ≥5). Naturally, thecritical branch’s opening angle of θ ◦ must exist,depending on a branch’s length, the excess over which(θ > θ ◦) results in the impossibility of the branchestouching each other in the normal room temperaturecondition. We have also modeled a heating of touchedbranch Y-junctions considered above, and detected theeffect of branch opening under 2700◦C heating duringan evolution time of ∼1000 of 0.0003-ps steps.

The effects of sticking and temperature openingof the ‘fork’ junctions may be used in differentnanomechanisms and nanoelectric circuits.

The introduction of topological defects in the hexa-gonal carbon atom net can be used to radically changethe NT configurations and their electronic proper-ties, especially in NT multi-terminal junctions. Thefirst conductance measurements on these template-made Y-junctions were observed by Papadopouloset al. (2000). Andriotis et al. (2001, 2002) havedetailed a mechanism for calculating the quantum con-ductivity of different types of three-terminal SWNTjunctions using the Green’s function approach inconjugation with an effective computational scheme

(Andriotis & Menon, 2001). In particular, I–V resultsobtained for different SWCN Y-junctions using thismethod revealed their asymmetric behavior.

We examined transport properties of the T-junctionin more detail (Menon et al., 2003). The junction’sleft (L) and right (R) parts of the (9,0) metallic crossbarand the semiconducting (10,0) stem (S) are shown inthe inset of Figure 8. The current direction is taken to bepositive when flowing towards the junction region andnegative otherwise. The current versus voltage (Is–Vs)characteristics shown in Figure 8 were calculated byapplying a voltage Vs on the stem, and a gate voltageVg on the L (or R) branch and keeping the R (or L)branch grounded. This configuration is similar to theY-junction observed by Papadopoulos et al. (2000) andanalyzed by Andriotis et al. (2001). A rectification ofthe current Is for positive Vs voltages is observed whenVg has not been applied. This is similar to the behaviorobserved earlier in the case of a symmetric Y-junctionwhere both branches were kept grounded and a voltageVs was applied only through the stem terminal. A sym-metric T-junction therefore behaves like a symmetricY-junction with the stem made of a semiconducting NT.

Figure 8. The I–V characteristics of the (10,0)(9,0)TH8P2 junction for different gate voltages applied at the stem (Menon et al., 2003).The current Is in the primary channel as a function of the bias voltage Vs for different values of the gate voltage Vg is shown. Asymmetryin the I–V behavior with current saturation for all positive Vs values is clearly indicated. The main effect of the variation in Vg is themodulation of the current.

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For Vs smaller than −0.6 eV the negative current startsto increase whereas no significant change in currentis observed for any positive value of Vs. The effectof introducing an asymmetry can be investigated bykeeping one of the branches grounded and applyingVg voltage through another branch. For negative Vg

smaller than −0.5 eV, significant modulation in thewhole Is–Vs curve is observed. This behavior may beused for current modulation in the primary channelby changing the gate voltage applied through the L orR branch.

Thus, three-terminal carbon NT junctions can beused as new elements of nanomechanical systems andnanoactuators, and nano-electronic devices.

Acknowledgements

The author is grateful to A.N. Andriotis, M. Menonand I.V. Stankevich for useful discussions. This workis supported by Russian programs ‘Actual lines incondensed matter physics’ (direction ‘Fullerenes andAtomic Clusters’) and ‘Low dimensional quantumstructures’ (grant 9.21), and INTAS (grant 00-237).

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