The band gap of a semiconducting single wall carbon nanotube decreases and
eventually vanishes leading to metalization as a result of increasing radial
deformation. This sets in a band offset between the undeformed and deformed
regions of a single nanotube. Based on the superlattice calculations, we show
that these features can be exploited to realize various quantum well structures
on a single nanotube with variable and reversible electronic properties. These
quantum structures and nanodevices incorporate mechanics and electronics.Comment: 7 pages, 4 figures, To be appear in PR

Ciraci, S.

Gulseren, O.

Kilic, C.

Yildirim, T.

English

arXiv

The band gap of a semiconducting single wall carbon nanotube decreases and eventually vanishes leading to metalization as a result of increasing radial deformation. This sets in a band offset between the undeformed and deformed regions of a single nanotube. Based on the superlattice calculations, we show that these features can be exploited to realize various quantum well structures on a single nanotube with variable and reversible electronic properties. These quantum structures and nanodevices incorporate mechanics and electronics

Kılıç, Ç.

Çıracı, Salim

Gülseren, O.

Bilkent University Institutional Repository

RAPID COMMUNICATIONSPHYSICAL REVIEW B 15 DECEMBER 2000-IIVOLUME 62, NUMBER 24Variable and reversible quantum structures on a single carbon nanotubeÇ. Kılıç,1 S. Ciraci,1 O. Gülseren,2,3 and T. Yildirim21Physics Department, Bilkent University, Ankara, Turkey2NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 208993Department of Materials Science, University of Pennsylvania, Philadelphia, Pennsylvania 19104~Received 9 October 2000!The band gap of a semiconducting single wall carbon nanotube decreases and eventually vanishes leading tometalization as a result of increasing radial deformation. This sets in a band offset between the undeformed anddeformed regions of a single nanotube. Based on the superlattice calculations, we show that these features canbe exploited to realize various quantum well structures on a single nanotube with variable and reversibleelectronic properties. These quantum structures and nanodevices incorporate mechanics and electronics.rer, tcicnopalx-o-th-thoinersicco-ntthoednreumnc-niceftreThed,ledUnusual properties of electrons in the quantum structuwhich were realized by using semiconductor heterostructu(AnBm) have initiated several fundamental studies.1 Owingto the band offsets of the semiconductor heterostructuresenergies of the band states of one semiconductorB may fallinto the band gap of the adjacent semiconductorA. Accord-ing to the effective mass approximation~EMA!, the height~depth! of the conduction~valence! band edge ofA from thatof B, DEC (DEV), behaves as a potential barrier for eletrons~holes!. For example,m layers ofB betweenn layers oftwo A’s form a quantum well yielding confined electronstates. The depth of the well and the width of the barrier awell ~in terms of number of layersn andm, respectively! arecrucial parameters to monitor the resulting electronic prerties. Multiple quantum well structures~MQW’s! or reso-nant tunneling double barrier structures~RTDB’s! can betailored from the combination ofA andB, and from variousstacking sequence ofn andm.Single wall carbon nanotubes2 ~SWNT’s! can display me-tallic or semiconducting character depending on their chirties and diameters.3,4 Similar to the aforementioned idea eploited extensively in crystals,1 quantum structures can alsbe produced in SWNT’s.5–9 It has been experimentally demonstrated that a rectifying behavior can be achieved byjunction of two different SWNT’s.6 Furthermore, the transport measurements on the ropes7 and individual nanotubes8have indicated a resonant tunneling behavior. Recently,quantum dot behavior has been also observed.9 Like thesemiconductor heterostructures, a different electronic prerty requires each time the fabrication of a new device usSWNT junctions.In this work, we propose a practical and interesting altnative, and show that various quantum structures can eabe realized on an individual SWNT, and their electronproperties can bevariably and reversibly monitored. Wepredict and use the feature that the band gap of a semiducting SWNT can be modified by radial deformation10 asdescribed in Fig. 1~a!. More importantly, if such a deformation is not uniform but has different strength at differezones, each zone displays different band gap. Owing toband offsets at the junction of different zones, MQW’sRTDB’s of the desired electronic character can be formand novel electronic nanodevices can be engineered osingle nanotube. This scheme is quite different from the pPRB 620163-1829/2000/62~ 4!/16345~4!/$15.00seshe-d-i-eep-g-ilyn-er,a-vious constructions of SWNT heterostructures or quantdots,5 where one had to fabricate each time a different jution or topological defects to satisfy the desired electrocharacter.First-principles calculations are carried out within thgeneralized gradient approximation~GGA! using planewaves~PW! with a cutoff energy of 500 eV and ultrasopseudopotentials.11,12Constrained structure optimizations aperformed on the SWNT under transversal compression.zigzag~7,0! tube is a semiconductor when it is undeformeFIG. 1. ~a! Top and side view of~primitive! unit cells of the~7,0! SWNT under different degrees of elliptic~circumferential!deformation. Undeformed tube with circular cross section is labetype I. ~b! Variation of the energy band gapEg , and~c! density ofstates at the Fermi energy,D(EF) with deformationa/b calculatedby the first-principles PW method.~d! Variation ofEg , and~e! firstand second states at the edge of the conduction band (c1 , c2), andfirst and second states at the edge of the valence band (v1 , v2) witha/b calculated by the TB method.R16 345 ©2000 The American Physical Societyicsersmb-lytrmrtireinane,uan-nailamieindeTBthisdcur-Ms,ialedontoofthealthf allt in-de-em-tieson-nlyndi-alandn.e-ononin-rsedvealxis.ingramffRAPID COMMUNICATIONSR16 346 PRB 62KILIÇ , CIRACI, GÜLSEREN, AND YILDIRIMbut its band gapEg is modified upon introducing an ellipticdeformation, which is quantified by the ratio of the elliptmajor axis to the minor axisa/b. The band gap decreasewith increasinga/b, and eventually vanishes fora/b;1.28@see Fig. 1~b!#. After the onset of metalization upon thclosure of the band gap, the density of states at the Feenergy D(EF) increases with further increase ofa/b, asshown in Fig. 1~c!. Relatively stronger radial deformationare required for the closure of the gap of~8,0! and~9,0! tubes. The radial deformationa/b, the strain energyper atomEs , and the compressive force on the fixed atoFc at the closure of the band gap are calculated to(a/b51.28; Es518 meV; Fc50.32 eV/A), (a/b51.54;Es538 meV; Fc50.31 eV/A), and (a/b51.36; Es518meV; Fc50.25 eV/A) for ~7,0!, ~8,0!, and ~9,0! tubes,respectively.12 The armchair~6,6! SWNT maintains the metallic behavior despite the radial deformation. Remarkabthe induced deformations, in particular those causinginsulator-metal transition, are elastic. Our results confithat the atomic structure and hence the electronic propereturn to the original, undeformed state when the compsive stress is lifted.Normally, as the radiusR→` the electronic structure of aSWNT near the band edges becomes similar to that obtaby folding the p* and p bands of graphene. However,singlet state at the band edge of a (n,0) SWNT with smallRinvolves significants* -p* hybridization.3 This state occursabove thep* band (n59), but falls in the gap (n57,8) andeventually closes the gap (n56) asn decreases.3,12 Appar-ently, the estimate ofEg based on the simple extrapolatiousing the experimental gaps of SWNT with relatively largradius4 is not valid for the~7,0! tube. In the present caseintroducing radial deformation and hence increasing the cvature at both ends of the elliptic major axis reduces the bgap of the~7,0! SWNT owing to the enhanceds* -p* hy-bridization.We also perform tight binding~TB! total energy and electronic structure calculations for the undeformed and uformly deformed ~7,0! SWNT by using transferableparameters13 related to carbon 2s and 2px,y,z orbitals. Theradial deformation has been induced by approaching twooms of the unit cell at one end of the diameter to two simatoms at the other end indicated by dark atoms in Fig. 1~a!.Once the transversal strain is set by fixing these four atothe rest of the atoms are relaxed by the conjugate gradmethod. We consider undeformed (a/b51) and five differ-ent degrees of radial deformation (a/b.1). The variation ofEg , first and second states of the conduction band, (c1 andc2) and those of the valence band, (v1 andv2) are illustratedin Figs. 1~d! and 1~e!. Data points on the curves shownthese figures correspond to different degrees of ellipticformations from I to VI as described in Fig. 1~a!. We notedeviations between the first-principles PW and empiricalresults perhaps due to the differences in the details ofdeformations and limitations of the empirical method. Italso known that the band gapEg is usually underestimateby local density approximation~LDA ! calculations. On theother hand, as discussed before, thes* -p* hybridizationeffect is crucial for settingEg , and first-principles PW cal-culations described it better. While the present GGA callations for the undeformed~7,0! tube findsEg50.242 eV,an earlier LDA calculation3mie,oess-edrr-di-t-rs,nt-e-predictedEg50.09 eV. Our TB calculations using transfeable parameters predictEg;0.5 eV and hence relativelystronger deformation is required to reduce the TB gapEg to0.1 eV. Earlier TB calculations foundEg;1.0 eV for unde-formed tube.14 Comparison of band gaps measured by STspectroscopy6 with those calculated by different methodand an extensive analysis for their variation with the raddeformation applied on different SWNT’s will be presentelsewhere.12 Nevertheless, both methods~PW and TB! pre-dict here similar overall behavior for the band gap variatiwith the radial deformation. We will use the TB methodstudy MQW’s, since it allows us to treat a large numbercarbon atoms, which cannot be treated easily withpresent first-principles PW method. We will treat the~7,0!tube as a prototype system.ReducingEg and eventually the onset of insulator-mettransition, and further metallization of certain SWNT’s wiincreasing radial deformation, and the reversible nature othese sequence of physical events incorporate importangredients suitable to form quantum structures and nanovices. We investigate MQW’s as a generic system and donstrate that one can generate electronic properconvenient for various device applications. To start, we csider a~7,0! zigzag nanotube, that is pressed to squash oat certain regions. We assume that the undeformed regioAof n unit cells,15 and adjacent deformed regionB of m unitcells ~one interface atomic layer at both side has intermeary deformation! repeat periodically, so that the translationperiodicity along the axis of the tube involvesn1m516cells and 448 carbon atoms. This tube forms a (AnBm) su-perlattice of semiconductor heterostructure, where the bgap of A is larger than that ofB. Since Eg(A;a/b51).Eg(B;a/b.1), a band offset shall occur at the junctioThe (n58, m58) supercells of the superlattices are schmatically described for two different degrees of deformatiin Fig. 2. Note that at low degree of deformation the junctican be formed by using one interface layer, while moreterface layers may be necessary ifB is severely deformed oa graded junction is aimed.Experimental and theoretical methods have been propoin the past to determine the band offsets, and hence to rethe band diagram perpetuating along the superlattice aFor the present situation ambiguities exist in calculatalignments of the band edges and to determine band diagFIG. 2. Schematic descriptions of the (A8B8) supercells of thesuperlattices generated from the~7,0! SWNT. cs is the lattice pa-rameter.~a! RegionA is undeformed,B has elliptic cross section otype III. The interface layer has type-II deformation.~b! SeverelydeformedB has type-VI deformation with two interface layers otype-II and -IV deformation.nn,i-adl--on-TBceshends,dntedrstthet.,thelec-ailgerceon-tRAPID COMMUNICATIONSPRB 62 R16 347VARIABLE AND REVERSIBLE QUANTUM STRUCTURES . . .in real space including band bowing due to the charge trafer betweenA andB. Even if the band diagram were knowit is not obvious whether EMA is applicable for an indvidual, non uniformly deformed SWNT. Therefore, insteof applying EMA to the 1D band diagram, we directly caculate the electronic structure of the (AnBm) superlattice onan individual ~7,0! SWNT. The band alignment is not exFIG. 3. Upper panel: local density of statesL(E, j ); lowerpanel: the state densityuC i ,k( j )u2 at the cellj of the superlatticeswhich display MQW’s behavior.~a! (A8B8); ~b! (A4B12); ~c!(A12B4).s-plicit, but it is indigenous to the method and hence the cfined states shall be obtained directly from the presentsuperlattice calculations.16We performed calculations on three different superlattidescribed in Fig. 2~a!, i.e., (A8B8); (A4B12); (A12B4), andcalculated the electronic statesC i ,k(r ) with band energyEi ,k . Here,i andk are the band index and wave vector of tsuperlattice along its axis. Because of flat superlattice bawe considered only theG point in the superlattice Brillouinzone. Figure 3 illustrates the local~or cell! density of states,L(E, j )5( i ,k* jdr uC i ,k(r )u2d(E2Ei ,k) and the state densityuC i ,k( j )u25* jdr uC i ,k(r )u2 both integrated at each cellj inthe supercell.L(E, j ) with higher density near the banedges ofB ~i.e., small gap region! is due to quantum wellstates and hence is consistent with the discussion preseat the beginning. Second peak ofL(E, j ) in the conductionband occurs inA, and becomes well separated from the fipeak in the superlattice (A4B12). The well known behaviorof MQW’s is apparent with the confinement of states atband edges. The first states at the band edges ofB, i.e., c1and v1 are confined inB suggesting a normal band offseThe confinement of the second state in the valence bandv2is rather weak. On the other hand, the second state ofconduction band,c2 is not confined in the well ofB, but islocalized at the barrier ofA. It appears that the energy ofc2occurs above the well inB, and c2 cannot match with thenext higher energy state ofB. Similar to that observed inshort periodicity AlxGa12xAs superlattices,16 this situationdemonstrates that the description of the superlattice etronic structure in terms of one-dimensional~1D! multiplesquare well states obtained within the simple EMA can fowing to the band structure effects. The confinement ofc1and v1 states increases withn, i.e., with the length of thebarrier region. This is an expected result, since the lonbarrier prevents the tunneling of these states throughA. Alsothe energy ofc1 raises with decreasingm. This is a directconsequence of the uncertainty principle.Figure 4 shows the MQW’s behavior of the superlattidescribed in Fig. 2~b!, whereB is strongly deformed. Thestate density and local density of states indicate that the cfined statesc1 andv1 display relatively higher localization aFIG. 4. The same as Fig. 3~a! except thatB has type-VI crosssection shown in Fig. 1~a!.cfetu’sr-geizontehrnlfori-t thenc-beumofanderi-r-ofngtingh as-i-ndRAPID COMMUNICATIONSR16 348 PRB 62KILIÇ , CIRACI, GÜLSEREN, AND YILDIRIMthe interface. This situation originates from the interfaatomic structure connectingA to strongly deformedB. Dif-ferent band offsets can also be realized by setting up difent level of deformations at bothA andB. Again, dependingon the level of the deformationEg(B;a/b.1) can even bezero that makes a metal-semiconductor superlattice strucFurthermore, from the junction of two metalized SWNThaving differentD(EF) one can form a metal-metal supelattice.In MQW’s, the truly 1D states are normally propagatinwith the wave vectork, and form a band structure. Thbands become flatter with increasing, and eventually theband picture breaks down and states become totally localin the quantum well~or in B). This way the superlattice isexpected to experience a Mott metal-insulator transitiFurthermore, a randomly deformed SWNT can be an inesting system to investigate electron localization in 1D. Tmodulating ord doping of a MQW’s or QW’s~also quantumdots! may exhibit interesting effects on the transpoproperties.16 It is interesting to note that the resonance codition of a RTDB’s withAn8Bm8An8 having contacts to metareservoirs from both ends shall be monitored by the dectscetaldier-re.ed.r-et-r-mation and size ofB. Strain or pressure nanogauges or vaable nanoresistors can be developed based on the fact thametalization and hence the conductance of a~7,0! nanotubecan be changed with the applied deformation. Also a jution An8Bm8 with metallicB is expected to show a rectifyingbehavior. We also note that a 3D grid of MQW’s canconstructed by periodic stacking of tubes where quantwells occur at crossing points. The electronic propertiesthis system can be varied with the stacking sequenceapplied pressure. Finally, we point out that the recent expmental work17 which showed that the controlled local defomation can be achieved.In conclusion, we showed that the electronic propertiesa semiconducting SWNT can be modified by introduciradial deformation which can be used to produce interesquantum structures and devices on a single tube, sucMQW’s, RTDB’s, rectifying junction, and variable nanoresistor with continuously tunable electronic properties.This work was partially supported by the National Scence Foundation under Grant No. INT97-31014 aTÜBİTAK under Grant No. TBAG-1668~197 T 116!.odeintsed.1Highlights in Condensed Matter Physics and Future Prospe,edited by L. Esaki, Volume 285 of NATO Advanced ScienInstitute ~Plenum, New York, 1991!.2S. Iijima, Nature~London! 354, 56 ~1991!.3X. Blaseet al., Phys. Rev. Lett.72, 1878~1994!.4J. W. G. Wildöer et al., Nature~London! 391, 59 ~1998!; T. W.Odomet al., ibid. 391, 62 ~1998!.5L. Chico et al., Phys. Rev. Lett.76, 971~1996!; 81, 1287~1998!;R. Saito et al., Phys. Rev. B53, 2044 ~1996!; J.-C. Charlieret al., ibid. 53, 11 108~1996!.6P. G. Collinset al., Nature~London! 278, 100 ~1997!.7M. Bockrathet al., Science275, 1922~1997!.8S. J. Tanset al., Nature~London! 386, 474 ~1997!.9A. Bezryadinet al., Phys. Rev. Lett.80, 4036~1998!.10The s* -p* hybridization effects in Ref. 3 and the experimenresults in Ref. 9 have led to the band gap modifications by radeformation in the following studies: A. Rochefortet al., Chem.Phys. Lett.297, 45 ~1998!; Phys. Rev. B60, 13 824~1999!; C.Kilic, Ph. D. thesis, Bilkent University, 1999~unpublished!; C-J.alParket al., Phys. Rev. B60, 10 656~1999!; M. S. C. Mazzoniet al., Appl. Phys. Lett.76, 1561 ~2000!; L. Liu et al., Phys.Rev. Lett.84, 4950~2000!; P. E. Lammertet al., ibid. 84, 2453~2000!; L. Yang and J. Han,ibid. 85, 154 ~2000!.11First-principles calculations were performed by planewave cCASTEP; M. C. Payneet al., Rev. Mod. Phys.64, 1045~1992!. Inthe present calculations we used Monkhorst-Pack special powith 232320 k points mesh, and the total energies convergwithin 0.5 meV/atom.12O. Gülserenet al., ~unpublished!.13C. H. Xu et al., J. Phys.: Condens. Matter4, 6047~1992!.14N. Hamadaet al., Phys. Rev. Lett.68, 1579~1992!; V. H. Crespiand M. L. Cohen,ibid. 79, 2093~1997!.15A cell denotes the primitive unit cell of the~7,0! nanotube, thathas 28 carbon atoms. TheA8B8 supercell contains 16 such cells16S. Ciraciet al., Phys. Rev. Lett.58, 2114 ~1987!; Phys. Rev. B36, 1225~1987!; 38, R12 728~1988!.17T. W. Tombleret al., Nature~London! 405, 769 ~2000!.

Variable and reversible quantum structures on a single carbon nanotube

Abstract

Similar works

Full text

Available Versions

Bilkent University Institutional Repository

Crossref