Local Semiconducting Transition in Armchair Carbon Nanotubes: The Effect of Periodic Bi-site Perturbation on Electronic and Transport Properties of Carbon Nanotubes

0.16 MB·English

by  M. J. Hashemi

APS/123-QED
Local Semiconducting Transition in Armchair Carbon Nanotubes: The Effect of
Periodic Bi-site Perturbation on Electronic and Transport Properties of Carbon
Nanotubes
M. J. Hashemi, K. Sa¨a¨skilahti, and M. J. Puska
Department of Applied Physics, Aalto University,
P.O. Box 11100, FI-00076 AALTO, Finland
(Dated: January 4, 2011)
1
Incarbonnanotubes,themostabundantdefects,causedforexamplebyirradiationorchemisorp-
1
tiontreatments,aresmallperturbingclusters,i.e. bi-sitedefects,extendingoverbothAandBsites.
0
2 The relative positions of these perturbing clusters play a crucial role in determining the electronic
propertiesof carbon nanotubes. Usingbandstructureandelectronic transport calculations, we find
n
out that in the case of armchair metallic nanotubes a band gap opens up when the clusters fulfill
a
a certain periodicity condition. This phenomenon might be used in future nanoelectronic devices
J
in which certain regions of single metallic nanotubes could be turned to semiconducting ones. Al-
3 thoughinthisworkwestudyspecificallytheeffectofhydrogenadatomclusters,thephenomenonis

generalfordifferenttypesofdefects. Moreover,westudytheinfluenceofthelengthandrandomness
]
l of thedefected region on the electron transport through it.
l
a
h PACSnumbers: 73.63.Fg,72.10.Fk
-
s
e I. INTRODUCTION
m
.
t Carbon based materials, carbon nanotubes and
a
graphene, are considered as the most promising can-
m
didates for many future technological applications be-
-
d cause of their unique electronic, mechanical and optical
n properties.1 In the case of single wall carbon nanotubes
o (SWCNTs), the chirality and diameter determine if a
c SWCNT is metallic or semiconducting2. In particular,
[
armchair nanotubes with the (n,n) -type chiral vectors

1 are metallic, enabling their use as ultimate leads in na-
v noelectronics.
9 Assumingthepossibilityofchirality-sensitiveselection
1
of nanotubes the first step towards single-SWCNT na-
5
noelectronic devices is the formation of rectifying metal-
0
semiconductorjunctions. Occasionally,thiskindofjunc-
.
1
tionsarerealizedduetopentagon-heptagondefectsmak-
0
ing a seamless junction between nanotubes of different
1
chiralities3,4. More intentionally, nanotubes of different
1
: character can also be electron-beam welded at elevated FIG.1: (Coloronline)Threedifferenthydrogenclusters(blue
v temperatures to form X-, T-, and Y-junctions5. More- circles) used in the calculations. They are shown on a piece
Xi over, recently Lee et al.6 suggested the joining of differ- of an armchair SWCNT’s surface. The unit vectors of the
graphenesheet(~aand~b),theAandBsublattices, theFermi
ent types of nanotubes with covalent peptide linkages.
r wavelength (λF = 3a), and a vector connecting the adjacent
a Another route is to modify the electronic bandstructure
hydrogen clusters are also given. The unit cell (UC) of the
of a single SWCNT spatially by functionalization with
pristine tube, as well as superlattice unit cells correspond-
defects, adatoms or molecules, or by controlled defor- ingtotwodifferentperiodicityofthehydrogenatedSWCNTs
mation. The use of modulating (saturation) hydrogen (SC5H4 and SC6H4) are shown.
adsorption7orradialdeformation8 hasbeensuggestedto
beusedtocreatequantumwellstructuresforchargecar-
riers. Asapotentialmethod,WallandFerreira9modeled the electronictransmissionthroughnanotubes14–19. The
alsotheeffectsofhelicalwrappingofpolymericmolecules carbon atoms of a nanotube belong to two sublattices,
around SWCNT’s. A and B, and then in the case of more than one adsor-
Imperfections, their causes and effects in SWCNTs bate the effect on the transmission strongly depends on
have been a subject of detailed studies for a long whether the adsorbates are on the same sublattice, A
time10–13. For instance, point-like vacancies,defects and or B, or on the different ones, A and B, as well as on
adsorbed atoms are known as a source of reduction in their relative positions16,19,20. In a recent study, Garc´ıa-
2
Lastra et al.20 showed that the relative position depen- SC1H0 SC4H4 SC5H4 SC6H4
1.5
dence obeys a certain rule if the adsorbates are on the
Pristine
same sublattice, while they did not find any trend for Perturbed
adsorbates on different sublattices. Considering the dif-
ficulty of realizing such site-selective perturbations and
the abundance of extended bi-site perturbations in ex-
F
periments, it is alsoimportant to understand how defect E
clusters (collectively) affect the electronic properties of E - 0
carbon nanotubes.
Inthisarticlewediscusstheeffectofperturbingdefect
clustersspanningboththeAandBsublatticesandwere-
fer to them as bi-site perturbances or bi-site defects. In (a) (b) (c) (d)
particular we discuss how undoped armchair SWCNTs -1.5
can locally be turned from metallic to semiconducting
by periodic bi-site perturbations. We study the effects FIG. 2: (Color online) Effect of the periodically-repeated H4
of repeated small hydrogen clusters (Fig. 1) on SWC- clustersonthebandstructureofthe(8,8)SWCNT.Theband
NTs, but our main qualitative results are valid also for structure of (a) the pristine nanotube SC1H0 is compared
arbitrary bi-site perturbance. We discuss how the elec- to those for nanotubes with H-atom clusters and different
trontransportthrougharmchairSWCNTs isaffected by supercell lengths, i.e., for (b) SC4H4, (c) SC5H4, and (d)
bi-site perturbations of different number, strength and SC6H4(ForthenotationseethetextandFig.1). Thedotted
lines in (b) - (d) denote the band structure of the pristine
periodicity along the SWCNT. Our calculations for the
nanotubefoldedaccordingtothelengthofthesupercell. The
metallic armchair SWCNTs show that when a certain
(blue) dashed lines in panel (a) are band or Brillouin zone
rule for the relative positions of the defect clusters is
folding lines for SC3H0. For any SC(3*M) with an integer
fulfilled, an energy gap around the Fermi level opens
M,theselinesare twoofthe3M-1folding lines. Therefore in
gradually by increasing the length of the periodically
allofthesecases, theFermipointisplaced, afterthefolding,
defected region. We study the robustness of this effect near theΓ-point.
against randomness in the cluster size and geometry as
well as in their relative positions. Hydrogen clusters are
realistic defect candidates because calculations and ex- drogen atoms would lead to similar effects. Because we
periments show that adsorbed hydrogen atoms tend to are interested in the main qualitative results and want
cluster on SWCNTs’ sidewalls21–23. The rapid devel- to avoid the complication due to spin effects we neglect
opment in pattern making, e.g. using block copolymer these odd-atom clusters in our studies.
nanolithography24,25, and in fine tuning and manipulat-
The electronic structures are solved with the density
ing structures even in the ˚Angstrom scale26 may make
functionaltheory(DFT)withinthePBEgeneralizedgra-
regular defect systems feasible and relevant also in the dientapproximation27 fortheelectronexchangeandcor-
experimental and practical sense. relation. We employ the SIESTA package28 with non-
Theorganizationofthepresentarticleisasfollows. In local norm-conserving pseudopotentials29 and a double-
Sec. IIwepresentthesystemsstudiedandtheirnotation
zeta plus polarization (DZP) atomic orbital basis set.
as well as the methods used in electronic structure and
The atomic geometry and the supercell size are relaxed
transportcalculations. Sec. IIIcomprisesourresultsand until all atomic forces are less than 0.02 eV/˚A. C-C and
their discussion. Sec. IV is a short summary.
C-Hbondlengths inaclose agreementwith experiments
are obtained.
Thereafterstructuresforthetransportcalculationsare
II. SYSTEMS AND METHODOLOGY
made of two semi-infinite pristine (8,8) SWCNT leads
and a central region with a varying content. In order
First we perform a set of supercell band-structure cal- to see how prolongation of the periodically defected re-
culations in which supercells consist of a certain num- gion changes the influence of hydrogen clusters on the
ber of unitcells of a pristine armchair SWCNT and four electronic transport of nanotubes, we consider central
hydrogen atoms adsorbed on neighboring carbon atoms regions consisting of varying numbers of the different,
as shown in Fig. 1. In particular, we choose the (8,8) above-mentioned supercells. For example, we may have
nanotube which has a diameter close to that often seen tenSC5H4supercellswhichisdenotedasthe10(SC5H4)
in experiments. We adopt, for example, the notation scattering region. Finally, we have at each end of the
SC5H4 for the supercell comprising five (8,8) SWCNT central region a unitcell of the (8,8) SWCNT nanotube
unitcells (SC5)andanadsorbedclusteroffourhydrogen to ensure non-reflecting semi-infinite leads.
atoms (H4) as depicted in Fig. 1. The essential crite- Our transport calculations are done using the
rion for these clusters is that they have to perturb both Landauer-Bu¨ttiker formalism. We construct the Hamil-
the A and B sublattices in a plane perpendicular to the tonian matrix using the tight-binding method with
tube axis. Similar clusters with an odd number of hy- nearest-neighbor hopping. Because carbon atoms take
3
N = 1 N = 2 N = 5 N = 10
)
H4 6 Pristine
5
C Perturbed
S 4
(
N
f 2
o
)
E
T( 0
)
H4 6 DFT
6
C
S 4
(
N
f 2
o
)
E
T( 0
-1 0 1 -1 0 1 -1 0 1 -1 0 1
Energy (E - E)
f
FIG. 3: (Color online) Effect of the relative positions and the number of bi-site perturbations on the transmission coefficient
of armchair SWCNTs. The (red) solid curves in the upper and lower rows show the tight-binding results for central regions
N(SC5H4) and N(SC6H4), respectively. From left to right, N=1, 2, 5 and 10. The dotted black lines give the pristine
transmission function. The dashed (green) curve in the lower left panel gives the DFT result calculated by the Transiesta
program.
part in the transport process by the pz orbitals, the car- bation, e.g., as the number of the hydrogen atoms in
bon atoms using them in bonding with on-top adsorbed the cluster increases. Further calculations with super-
hydrogenatomswillnotparticipateinthetransportpro- cellscontainingseveralH-atomclustersshowthatsucha
cess anymore. In our tight-binding transport calcula- bandgapopeninghappens forallsupercellsinwhichthe
tions,wesimulatethiseffectbyremovingthehostcarbon relative positions of the adjacent adsorbate clusters, or
atomsbinding tohydrogenatoms. Forbenchmarkingwe more generally bi-site perturbations, fulfill the condition
comparethetransmissionfunctionsofasingleSC6H4su-
R~ =p~a+q~b, p−q =3M, |M ∈Z, (1)
percell obtained by the tight-binding method with that
calculated by the DFT Transiesta program30. When the where~a and~b arethe unit vectorsgivenin Fig. 1. Thus,
hopping parameter, t, has the value of 2.3 eV we find a
the clusters may be in different positions on the planes
verygoodagreementparticularlyaroundthe Fermi level
perpendicular to the tube axis as, for example, the dif-
(See the lower left panel in Fig. 3).
ferent clusters in Fig. 1. Eq. (1) is actually the condi-
tion that a pristine nanotube is metallic2. Moreover, it
was found by Garc´ıa-Lastraet al.20 to give also the rule
III. RESULTS AND DISCUSSION
that two molecules adsorbed on same sublattice sites of
a SWNT leave one of the two transmission channels un-
Fig. 2 shows our DFT results for the band structures affected.
of the pristine (8,8) SWCNT as well as those of (8,8) The above-mentioned metal to semiconductor transi-
nanotubes decorated periodically with H4 clusters. The tion can be understood as follows. When the length of
band structures are shown with the increasing super- the unit cell of a pristine armchair SWNT is artificially
cell length, i.e., they correspond to the SC1H0, SC4H4, tripled the energy band crossingpoint at the Fermi level
SC5H4,andSC6H4supercells. Theincreaseofthesuper- (corresponding to a K point in the first Brillouin zone
celllengthfoldsthe bandstructureofthepristinesingle- of graphene) is folded close to the Γ-point (see Fig. 2(a)
unit-cell nanotube as shown by dotted lines in panels forBrillouinzonefoldinglines). Therefore,perturbations
(b) - (d). There are qualitatively two different repeating withthisperiodicityaffectthebandstructureinthesame
bandstructureschemeswithrespecttothe bandcrossing way as the lattice potential in the nearly free electron
point at the Fermi energy represented by the SC4H4 or model and open up a band gap around the Fermi level.
SC5H4 supercells and the SC6H4 supercell. The band Thesamehappensforanyperiodicitylengthof3Mtimes
structuresoftheH-clusterdecoratednanotubeswithdif- the unit cell length and also when the condition of Eq.
ferent supercell lengths follow roughly those of the pris- (1) is fulfilled. But for the periodicity lengths of 3M+1
tine nanotube. However, there is an important quali- or 3M+2 times the unit cell length the band crossing
tative difference. In the case of the SC6H4 supercell a point does not coincide with a reciprocal lattice bound-
band gap opens around the Fermi energy. The size of ary and the armchair SWNT remains metallic even with
the band gap increases with the strength of the pertur- the bi-site perturbations.
4
2 0.25
T(E)f0.00.000.1111 HHH246 CCCllluuusssttteeerrrsss T(E)f 00..00..012155 68917(((0(SSSS(SCCCCC6666HHH6HH4444)))4)) 1N-8S-1N 2N-8S 8S-2N 3S-1N-3S-1N-2S4S-2N-4S Disaligned Different Clusters
0 5 10 15 0
Number of Supercells in the Central Region
FIG. 5: (Color online) Fermi-energy transmission coeffi-
FIG. 4: (Color online) Fermi-energy transmission coefficient cientfordifferentsystemsmadebymanipulatingtheoriginal
for N(SC6H2), N(SC6H4), and N(SC6H6) scattering regions 10(SC6H4) system by displacing two of the H4 clusters. In
as a function of N,thenumberof the perturbingsupercells. thenotationgivingthesequenceoftheclusters,SandNstand
for clusters Satisfying and Not−satisfying the condition
ofEq. (1). Sampleresultsduetochangingclusters’positions
To getanother viewpointaboutthe originof the band (Disaligned) around the circumference perpendicular to the
gap opening for certain periodic perturbations and to tube axis and due to replacing some of the H4 clusters by
see how periodic bi-site perturbations of finite lengths H6orH2clusters(DifferentClusters)arealsoshown. The
affect the transmission of the armchair SWCNT, we cal- solid (red)lineistheFermi-energytransmission valueforthe
original 10(SC6H4)system and the (black) dotted lines are,
culate the transmission functions of several nanotubes
for comparison, those for the N(SC6H4) systems with N=9,
withavaryingnumberofperturbedsupercellsinthecen-
8, 7 and 6.
tral region. With increasing number of atoms, the use
of DFT for transport calculations becomes prohibitively
cpu-time consuming and therefore we employ a simple
takes place for periodic central regions constructed, for
tight-binding method benchmarked against the DFT re-
example, from the SC6H4 supercells but not for those
sults. The upper and lower panels of Fig. 3 show the
containing, for example, SC5H4 supercells (See Fig. 1).
transmissionfunctions for the N(SC5H4) andN(SC6H4)
central region systems, respectively. The lengths of the Next,weexplorewiththetight-bindingmodelthegen-
periodic regions increase from left to right with N=1, 2, erality of our finding of the opening of the transmission
5 and 10. It can be clearly seen that the transmission in gap at the Fermi level. We take the 10(SC6H4) central
theN(SC6H4)systemsdecaysandsharpensinthe shape region system and change the positions of two of the H4
around the Fermi energy with the length of the periodi- clusterssothattheydon’tsatisfyEq. (1). Dependingon,
cally perturbed region. which two of the clusters one chooses, the transmission
In contrast, for the N(SC5H4) systems, the transmis- changes, but not in a radical way. In all combinations
sion around the Fermi energy remains very close to that the general trend of the decreasing transmission is con-
of the pristine armchair SWCNT and actually the sev- served. In Fig. 5 the transmission at the Fermi level is
eral scatterings develop a nearly constant transmission shown for some of the combinations studied. The trans-
plateauwiththeincreasinglengthoftheperiodicallyper- mission is close to that of the 8(SC6H4) central region
turbed region. system when all the clusters satisfying Eq. (1) are ad-
We plot in Fig. 4 the transmission coefficient at jacent to each others. When the clusters satisfying Eq.
the Fermi energy for the N(SC6H2), N(SC6H4), and (1) are separated the transmission is close to that of the
N(SC6H6) central region systems as a function of N. 7(SC6H4) central region system.
Although the stability of this H6 cluster has not been The effects of randomness in the size of the clusters
established in contrast to H2 and H4 clusters21, we use as well as in their positions around the circumference
H6 cluster to qualitatively mimic the effect of stronger perpendicular to the tube axis are also studied in the
perturbations which cover a full hexagon. For long pe- case of the 10(SC6H4) system. First we replace some of
riodically perturbed regions, a nearly exponential decay the H4 clusters with the H2 or H6 clusters and see that
canbeseeninallthreecasesreflectingtunnelingthrough the transmission at the Fermi level stays low although
asemiconductingregion. Inanaturalmanner,thedecay the exact value depends on the particular combination
rate increases strongly as a function of the cluster size. in question. Next, in a set of separate calculations, we
We describe the above phenomena as follows. When move the H4 clusters around the nanotube on the same
the periodic perturbations occur with the separation of perpendicularplane. We findthataslongasthe clusters
nλF/2, where n is an integer, all the backscattered elec- fulfillEq. (1),thesamedestructiveeffectontransmission
tronwavesattheFermilevelinterfereconstructivelysup- occurs. Sample results labeled as Different Clusters and
pressingthetransmission. AsdepictedinFig.1theFermi Disaligned are included in Fig. 5. Our findings show
wavelength of an armchair SWCNT is 3a and therefore that the exact periodicity of the clusters is not playing
the constructive interference of the backscatteringwaves the main role and the cluster species and their position
5
around the tube may vary, for example, as depicted in nanotubes. Our calculations show that following a cer-
Fig. 1. tainrelative-positioncondition,anaturallymetallicnan-
Finally,we emphasizethatourqualitativefindingsare otube can turn into semiconducting. The phenomenon
valid regardless of the type of perturbations beyond the shows robustness against variations in the types of per-
adsorbateclusters. Forinstance,ourcalculationsforcar- turbingspeciesandalsotosomeextentintheirpositions.
bon nanobuds31,32, which can be viewed as an example The phenomenon is proposed as a means for creating
of perturbing a full hexagon, show exactly the same be- single-SWCNT electronic devices.
havior. Moreover, according to our calculations also dif-
ferent hydrogenated vacancy clusters result in the same
phenomenon.
V. ACKNOWLEDGMENT
IV. CONCLUSIONS
The work has been supported by Finnish Academy
through their Center of Excellence program. We are
Wehavestudiedtheeffectofmultiplebi-siteperturba- thankful to R.M. Nieminen, A-P Jauho and Maria
tions on electronic and transport properties of armchair Ganchenkova for useful discussions.
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