Substrate-induced array of quantum dotsin a single-walled carbon nanotubeHyung-Joon Shin1,2, Sylvain Clair1,3†, Yousoo Kim1* and Maki Kawai1,2,3*

Single-walled carbon nanotubes are model one-dimensionalstructures1–6. They can also be made into zero-dimensionalstructures; quantum wells can be created in nanotubes byinserting metallofullerenes7, by mechanical cutting8–10 or bythe application of mechanical strain11. Here, we report thatquantum dot arrays can be produced inside nanotubes simplyby causing a misalignment between the nanotube and thek100l direction of a supporting silver substrate. This methoddoes not require chemical or physical treatment of either thesubstrate or the nanotube. A short quantum dot confinementlength of 6 nm results in large energy splittings.

Forty years ago, Esaki and Tsu12 proposed using periodic dopingor compositional change to engineer the band structure of a super-lattice, which can now be realized by state-of-the-art fabricationprocesses. Manipulating the electronic structure of materials hasbecome a fundamental technique for obtaining various functional-ities in electronic devices. To modify the electronic structure ofmatter, it is possible to construct junctions between materials ofdifferent electronic structures, dope semiconductors or make useof low-dimensional structures13. However, these methods are diffi-cult to apply to nanotubes. Their sidewalls are chemically stable,so controlled functionalization or chemical doping is difficult, par-ticularly in local regions. Lee and colleagues demonstratedquantum-well structures in nanotubes by manipulating the localbandgap through the insertion of metallofullerenes inside the nano-tubes (Fig. 1a)7. The band structure of such nanotubes resemblessuperlattices in which the bandgap energy (Eg) is periodicallymodulated12. In this Letter, we report the observation of anothertype of quantum-well structure in a pristine single-walled carbonnanotube: periodic bandgap modulations maintaining constant Eg(Fig. 1b). This is analogous to the band structure of a periodicallydoped superlattice12. When the degree of charge transfer is nothomogeneous along the nanotube axis due to registration con-ditions with the substrate, that is, lattice mismatching between thenanotube and the surface, the nanotube reveals periodic modu-lations in both topography and electronic structure. Our resultsindicate that the influence of the substrate on the electronic struc-ture of nanotubes can be much stronger than expected.

We investigated the electronic structure of single-walled carbonnanotubes on Ag(100) using scanning tunnelling microscopy(STM) and scanning tunnelling spectroscopy (STS) at cryogenictemperatures. The dry contact transfer (DCT) technique was suc-cessfully applied to deposit individual nanotubes on the Ag(100)surface in an ultrahigh-vacuum (UHV) chamber14–17. Figure 2a,bshows a nanotube on the terrace of the silver substrate.Interestingly, a long-range corrugation developed in the topographyalong the entire length of the nanotube (.300 nm). The period ofthe modulation is 6.42+0.57 nm and the height difference

between peak and valley is �9 pm (Fig. 2c,d). This value can varyslightly depending on bias voltage, but the positions of the peaksand valleys remain constant. We observed periodic modulationsnot only in the topography but also in the electronic structure.Figure 2e is a dI/dV map at a bias of 1.0 V, acquired simultaneouslywith the image of the topography (Fig. 2c), showing the same periodof modulation as the topography. The topographic valley positions(marked by arrows in Fig. 2d–f) have higher conductance than thepeak positions. This indicates that the topographic modulations inthe STM image arise mainly from structural corrugation of thenanotube. To acquire more detailed information about the spatialvariations in the electronic structure of the nanotube, we performeda spatially resolved STS (SR-STS) map. This revealed remarkable be-haviour in the electronic structure of the nanotube along the axis(Fig. 2f). As previously observed16, the position of the Fermi level(EF) of the nanotube is shifted toward the conduction band andthe midgap is positioned at negative energy due to the smallerwork function of Ag(100) when compared with that of the nano-tube. Although the EF of the nanotube was shifted toward the con-duction band, consistent with other measurements on differentnanotubes on the silver substrate, here, the degree of this shiftdiffered according to position. At the peak topographical position,EF shifted around 480 meV, and shifted �550 meV towards theconduction band at the valley relative to the midgap. As a result,the electronic band structure oscillated along the axis every 6.4 nm.

Variation in the EF shifts of the nanotube indicate that theamount of charge transfer is not homogeneous along the nanotubeaxis. Figure 3a,b shows a part of the nanotube over one modulationperiod. It was identified as a (6, 2) nanotube with a diameter of�6.08 Å and chiral angle of 168 (nominally 5.65 Å and 16.18), forwhich the translational vector T is [5, 27]. It was misaligned�168 from the k100l direction of the substrate. In terms of thelength of the unit cell along the nanotube axis (jTj¼ 1.54 nm),the period of modulation corresponds to around four unit cells.To interpret the physical significance of this periodicity, we exam-ined the epitaxial relationship between the nanotube and theAg(100) substrate (Fig. 3c). The figure shows the hexagonalcarbon lattice of a nanotube unrolled onto the substrate. Thoseparts of the lattice that, when it is rolled into a tube, are closest toa silver atom, are shown as yellow hexagons. Among these, sixappear in an optimal epitaxial relationship with silver atoms(shown in pink), and the spacing between the two equivalentregions is 6.16 nm, which corresponds closely to the observedperiod. Thus, we assume that the enhanced charge transfer at theepitaxial sites is responsible for the larger local EF shift of the nano-tube. When the nanotube is doped with electrons or holes, not onlyelectronic but also structural modifications arise. Gartstein andcolleagues18 reported a theoretical calculation for charge-induced

1Surface Chemistry Laboratory, RIKEN, Wako, Saitama 351-0198, Japan, 2Department of Applied Chemistry, The University of Tokyo 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan, 3Department of Advanced Materials Science, The University of Tokyo 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8561, Japan;†Present address: Aix-Marseille Universite, Institut Materiaux, Microelectronique et Nanosciences de Provence, CNRS UMR 6242, Campus de Saint-Jerome,Case 142, F-13397 Marseille Cedex, France. *e-mail: ykim@riken.jp; maki@riken.jp

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distortion of nanotubes. Based on this model, the relative change innanotube radius for the electron-doped (6, 2) nanotube can beexpressed as dR/R¼ 0.286� dn (R, radius of nanotube; dn,amount of induced electrons). In our results, the peak in topographyshowed a more pronounced EF shift than the valley (Fig. 2d,f ). Thisis consistent with our assumption that the more electronic chargetransferred to the nanotube, the larger the EF shift andradial expansion.

As well as modulation of the bandgap along the nanotube axis,the spectroscopic image (Fig. 2f ) reveals another interestingfeature: regular patterns in the energy levels. Figure 4 plots a selectedspectrum from an SR-STS map. Clearly, there are evenly distributedconductance peaks in the spectrum, for which the average spacing is�247 meV. When we examined the conductance peaks at differentpositions, the average spacing was 247.4+16.4 meV. Peaks in thelocal density of states (LDOS) are strong indicators of confinedstates. Single-walled carbon nanotubes serve as ideal quantumwires in which electrons are able to move in only one dimension.Thus, local disorder in a nanotube can work as a scattering centrefor electrons, which can induce quantum confinement inside thenanotube6,19–21. If the epitaxial relationships with the substratefunction as quantum boundaries, we can consider this system asan array of disorder-induced quantum boxes. If we simplify thismodel as a one-dimensional quantum box, the energy splitting in aconfined system can be characterized by finite-size level spacing(DE) and charging energy (ECH). The energy splitting for a lengthL¼ 6.42-nm quantum box is given by DE¼ hvF/2L¼ 261 meV,where vF¼ 8.1� 105 m s21 is the Fermi velocity and h is Planck’sconstant. The estimated energy agrees with the measured value.The dI/dV map acquired at a bias of 1.0 V (Fig. 2e) reveals thatmore electronic states are developed at valley than at peak positionsof the STM topography. This also indicates that the commensuratesites function effectively as quantum interference boundaries alongthe one-dimensional conductor, so the DOS is enhanced inside theconfined region between boundaries. In addition, there are smallpeaks in the range of approximately 21.0 to 0.2 V; these are simi-larly equispaced by �71.1 meV (inset, Fig. 4). The average peakspacing is 72.6+7.1 meV over the entire length of the nanotube.

The charging energy is given by ECH¼ e2/C, where C is the capaci-tance. However, the capacitance of a confined region is not easy toquantify, because no quantum box is fully isolated electrically fromits neighbours. From the measured energy spacing (72.6 meV), thecapacitance of the nanotube is estimated to be 2.20 aF, and the

EC

EV

EC

EV

Figure 1 | Two types of quantum-well structures realized in single-walled

carbon nanotubes. a, Schematic of the modulation of conduction (EC) and

valence (EV) band edges of a nanotube peapod. b, Schematic of modulation

of EC and EV with constant Eg by means of periodic doping.

−2.0

Position x (nm)350

Ener

gy (e

V)

1.5

0

dI/dV (a.u.)

CB

VB

30

Hei

ght (

pm)

00 35

Position x (nm)

Figure 2 | Periodic modulations in a nanotube on Ag(100). a,b, Topographic

(a) and derivative (b) STM images of a (6, 2) nanotube (Vs¼ 1.4 V, sample

bias; I0¼ 250 pA, tunnelling current). Scale bars, 30 nm. c, Magnified

STM image of the nanotube (Vs¼ 1.0 V, I0¼ 250 pA). Scale bar, 7 nm.

d, Topographic height profile of the nanotube along the black dashed line

marked in c. Five modulation periods are clearly visible. e, Spectroscopic

map of dI/dV at 1.0 V, obtained simultaneously with the topography in c.

f, SR-STS map of the nanotube along the dashed line marked in

c (Vs¼0.7 V, I0¼ 250 pA). The pink wavy lines indicate the position of the

conduction and valence band edges. A differential conductance spectrum

along the vertical dashed line is shown in Fig. 4. The arrows in d–f represent

equivalent positions between figures.

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orders of capacitance and energy are reasonable compared withthose noted in previous reports6,8. Therefore, the two types ofenergy splittings seen in the STS can be attributed to quantum con-finement. We confirmed the epitaxial origin of this effect byobserving different periodicities of the modulations and differentenergy splittings depending on the registry conditions (seeSupplementary Information). It is surprising that the sub-10-nm-sized quantum confinement occurred in the form of one-dimen-sional arrays inside a long nanotube. The energy splitting is threetimes greater here than in the case of mechanically shortened nano-tubes8–10 due to the extremely small size of the confined region.Moreover, the broadening of the conductance peaks is less sensitiveto energy than previously reported8,10. We attribute this differenceto the strong correlations between the confined regions as well asto the size effect, which is not available for isolated nanotubes.Recently, a similar result was observed for a semiconductor super-lattice22. Considering the reflection coefficient of the resonant elec-tron scattering in the nanotube (�0.5) (ref. 21), the transmittedelectron wavefunctions from the neighbouring dots can be amongthe factors affecting the peak intensity inside the confined region.As a result, the decay of the peak intensities could be partly compen-sated for by this contribution.

There are two main reasons why it is difficult to find this effect inother nanotubes and why there have been no reports of such obser-vations to date. First, the diameter of the nanotube is an importantfactor in periodic modulations. With a larger diameter, more carbonatoms might face the substrate and have more chance of matchingwith substrate atoms owing to the curvature of the nanotube. Hence,the effect of inhomogeneous charge transfer along the nanotubeaxis becomes smaller for nanotubes of large diameter. The diameterof the nanotube showing modulations is exceptionally small com-pared with the diameters of most nanotubes used in this study.

Second, the way in which nanotubes are prepared on the substrateseems to have an important role. In a previous study we reportedselective adsorption of nanotubes along the k110l direction onAu(111) and Cu(111) surfaces and along k100l or k110l directionson a Cu(100) surface17. The strong interaction between nanotube

6.16 nm

Figure 3 | Epitaxial relationships between the (6, 2) nanotube of Fig. 2, and Ag(100). a,b, Topographic (a) and derivative (b) STM images of the same part

of a nanotube corresponding to one modulation period. The inset in b shows an STM image of the silver substrate (Vs¼ 80 mV, I0¼ 250 pA). Scale bars,

1 nm. c, Schematic of the atomic configuration of the (6, 2) honeycomb structure of carbon atoms and the Ag(100) surface. Spheres and hexagons represent

the silver atoms and carbon lattice, respectively. The yellow hexagons are those closest to the surface atoms when the carbon lattice is rolled into the tube.

The red and blue lines indicate the contact position between the nanotube and the substrate, each line corresponding to a translational vector of [5, –7]

(longitudinal unit cell of the nanotube). The pink spheres indicate the silver atoms of the lattice that best match the nanotube. The periodicity here matches

that of the experimental results in Fig. 2.

dI/d

V (a

.u.)

Sample bias (V)

−1.0 0−2.0 1.0

dI/d

V (a

.u.)

Sample bias (V)0−1.0

Figure 4 | Substrate-induced quantum confinement in the nanotube.

A differential conductance (dI/dV) spectrum sampled from the vertical dotted

line in Fig. 2f. The arrows indicate peak positions of 21.88, 21.65, 21.4, 21.16,

20.91, 20.63, 20.33, 20.07, 0.18, 0.39, 0.63, 0.87, 1.10 and 1.33 V. The green

arrows mark peak positions assigned in the magnified region (inset). The inset

shows a magnified region between 21.0 and 0.2 V. The arrows indicate peak

positions of 2980, 2910, 2870, 2810, 2760, 2680, 2630, 2560, 2460,

2400, 2330, 2250, 2160, 272, 18, 110 and 157 meV.

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and substrate resulted in the alignment of the nanotubes along theclose-packed directions of the face-centred cubic (fcc) substratewhen nanotubes were prepared by the DCT method. Nanotubesprepared by the solution droplet method, however, are unlikely toachieve a special orientational relationship with the substrate. Ifthe diameter of the nanotube is small, interaction with the substratemight be strongest when the close-packed direction of the substrate isaligned with the chiral angle of the nanotubes. For larger-diametertubes, on the other hand, the angle between the close-packed direc-tion of the substrate and the nanotube axis is more important. Ourresults also revealed alignment between the k100l direction of thesubstrate and the row of the carbon hexagons (Du� 2.48).

Graphene, another type of carbon allotrope in two-dimensionalform, is currently drawing the attention of many researchers23–25.Recent studies of the substrate-induced gap opening26, EF shiftson various metal substrates27, and inhomogeneous charge distri-bution28 have demonstrated the sensitivity of the electronic proper-ties of epitaxial graphene to the underlying substrate. Ourexperimental results reveal that the electronic structure of nanotubesis also very sensitive to the way they register on metal substrates. Thecommensurability of a nanotube with a substrate determines thelocal EF alignment, and thus the carrier transmission coefficientat the interface. This can give rise to quantum confinement inthe form of one-dimensional arrays over the whole length of thenanotube, as confirmed by the observation of quantized energylevel splittings in a nanotube. Our findings suggest that chargetransfer-induced doping of nanotubes29,30 can be applied as fardown as the sub-10-nm region if properly patterned, and wouldalso provide a possible general basis for designing and controllingthe architecture of molecular electronics based on one-dimensional nanomaterials.

MethodsThe experiments were performed in a UHV low-temperature scanning tunnellingmicroscope (Omicron LT-STM) at 4.7 K. The Ag(100) single crystal was cleaned bythe repetition of sputtering and annealing cycles. After sample cleaning, HiPCOsingle-walled carbon nanotubes (Carbon Nanotechnologies Inc.) were depositedonto the substrate in situ by the DCT technique under UHV at room temperature.A copper braid was macroscopically covered with nanotubes dispersed indichloroethane, then introduced into the UHV chamber and brought into directcontact with the clean surface at room temperature. By this method, we were able toprepare nanotubes with reduced contamination of the sample. We measured thedifferential conductance dI/dV with lock-in detection by applying a modulation of50 mV (r.m.s.) to the tunnelling voltage at 797 Hz. The SR-STS results were obtainedwith phase-sensitive detection using a lock-in amplifier, as a function of both theposition of the tip along the centre of the nanotube and the sample bias voltage. Thefixed tunnelling gap for dI/dV was set by the tunnelling current during the samplingtime period in the sample-and-hold mode.

Received 20 April 2009; accepted 9 June 2009;published online 13 July 2009

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AcknowledgementsThe authors wish to thank Young Kuk for helpful discussions. This work was supported bythe Grant-in-Aid for Young Scientists (A), ‘Single-molecule chemistry on the single-walledcarbon nanotubes’, and partially by the Grant-in-Aid for Scientific Research on PriorityAreas, ‘Electron transport through a linked molecule in nano-scale’, from the Ministry ofEducation, Culture, Sports, Science and Technology (MEXT), and in part by Global COEProgram (Chemistry Innovation through Cooperation of Science and Engineering),MEXT, Japan.

Author contributionsH.S., S.C. and Y.K. conceived and designed the experiments. H.S. and S.C. performed theexperiments and analysed the data. H.S. wrote the paper. All authors discussed the resultsand commented on the manuscript.

Additional informationSupplementary information accompanies this paper at www.nature.com/naturenanotechnology. Reprints and permission information is available online at http://npg.nature.com/reprintsandpermissions/. Correspondence and requests for materials should beaddressed to Y.K. and M.K.

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