Electron transport in semiconducting carbon nanotubes with hetero-metallic contacts

0.24 MB·English

by  Yongqiang Xue

Electron transport in semiconducting carbon nanotubes with hetero-metallic contacts
Yongqiang Xue1,∗ and Mark A. Ratner2
1College of Nanoscale Science and Engineering, University at Albany,
State University of New York, Albany, New York 12203, USA
2Department of Chemistry and Materials Research Center,
5 Northwestern University, Evanston, Illinois 60208, USA
0 (Dated: February 2, 2008)
0
2 We present an atomistic self-consistent study of the electronic and transport properties of semi-
conducting carbon nanotube in contact with metal electrodes of different work functions, which
n
showssimultaneouselectronandholedopinginsidethenanotubejunctionthroughcontact-induced
a
charge transfer. We find that the band lineup in the nanotube bulk region is determined by the
J
effectivework function differencebetween thenanotubechanneland source/drain electrodes, while
1
electron transmission through the SWNT junction is affected by the local band structure modula-
2
tion at the two metal-nanotube interfaces, leading to an effective decoupling of interface and bulk

effects in electron transport through nanotubejunction devices.
]
l
l
a PACSnumbers: 73.63.-b,73.40.-c,85.65.+h
h
-
s Devices based on single-wall carbon nanotubes multaneously inside the channelby contacting with high
e
m (SWNTs)1,2 have been progressing in a fast pace, e.g., and low work function metals; (3) Since the metallurgy
the performance of carbon nanotube field-effect transis- of the metal-SWNT contact is different at the two in-
.
t tors (NTFET) is approaching that of the state-of-the- terfaces, the asymmetric device structure may facilitate
a
art silicon Metal-Oxide-Semiconductor field-effect tran- separatinginterfaceeffectonelectrontransportfromthe
m
sistors (MOSFET).3,4,5 But a general consensus on the intrinsic property of the SWNT channel.
-
d physical mechanisms and theoretical models remains to Thehetero-metallicSWNTjunctionisshownschemat-
n appear. ApointofcontinuingcontroversyinNTFEThas ically in Fig. 1, where the ends of an infinitely long
o been the effect of Schottky barriers at the metal-SWNT
SWNT wire are buried inside two semi-infinite metal-
c interface.6,7 Since SWNTs are atomic-scale nanostruc-
[ lic electrodes with different work functions. The em-
tures in both the axial and the circumferential dimen- bedded contact scheme is favorable for the formation of

1 sions, any barrier that may form at the interface has a
low-resistance contact. For simplicity, we assume the
v finitethicknessandafinitewidth.3,8,9 Ingeneralamicro-
embedded parts of the SWNT are surrounded entirely
8 scopic treatment of both the source/drainand gate field
by the metals with overall cylindrical symmetry around
3
5 modulationeffectwillbeneededtoaccountforfaithfully the SWNT axis.12 For comparison with previous work
the atomistic nature of the electronic processes in NT-
1 on symmetric SWNT junctions, we investigate (10,0)
0 FET. SWNTs (with work function of 4.5 eV1) in contact with
5 gold (Au) and titanium (Ti) electrodes (with work func-
Since thecharacteristicsofthe NTFETsdependsensi-
0
/ tively on the gate geometry,3 a thorough understanding tions of 5.1 and 4.33 eV respectively for polycrystalline
t materials13). Choosingtheelectrostaticpotentialenergy
a ofthe Schottkybarriereffectinthesimplertwo-terminal
inthemiddleofthejunctionandfarawayfromthecylin-
m metal-SWNT-metal junction devices is essential in elu-
drical surface of the SWNT as the energy reference, the
cidating the switching effect caused by applying a finite
-
d gate voltage.8 As a basic device building block, the two- Fermi-level of the Au-SWNT-Ti junction is the nega-
n terminal device is also of interests for applications in tive of the average metal work functions EF = −4.715
o eV. The SWNT channel length investigated ranges from
electromechanicalandelectrochemicalsensors,wherethe
c L=2.0,4.1,8.4,12.6,16.9nm to 21.2 nm, corresponding
conductionpropertiesofthe SWNT junctions aremodu-
:
v lated by mechanical strain10 or molecular adsorption re- to number of unit cells of 5,10,20,30,40 and 50 respec-
Xi spectively.11 Previous works have considered symmetric tively. We calculate the transport characteristics within
SWNTjunctionswithdifferentcontactgeometries.8Here the coherent transport regime, as appropriate for such
r short nanotubes.14
a weconsiderSWNT incontactwithmetallicelectrodesof
different work functions. Such hetero-metallic junctions Using a Green’s function based self-consistent tight-
are of interests since: (1) The electrode work function binding (SCTB) theory, we analyze the Schottky bar-
difference leads to a contact potential and finite electric rier effect by examining the electrostatics, the band
field (built-in field) across the junction at equilibrium. lineup and the transport characteristics of the hetero-
A self-consistent analysis of the hetero-metallic junction metallic SWNT junction as a function of the SWNT
can shed light on the screening of the applied field by channel length. The SCTB model is essentially the
the SWNT channelandthe correspondingbandbending semi-empiricalimplementationofthe self-consistentMa-
effect even at zero bias; (2) For SWNTs not intention- trix Green’s function method for ab initio modeling of
ally doped, electron and hole doping can be induced si- molecular-scale devices,15 which takes fully into account
2
the three-dimensionalelectrostaticsandtheatomic-scale transferinducedelectrostaticpotentialchangeδV decays
electronicstructureoftheSWNTjunctionsandhasbeen rapidlyinthedirectionperpendiculartotheSWNTaxis.
describedindetailelsewhere.8,16 TheSCTBmodelstarts Thishasledtoadifferentphysicalpictureofbandbend-
with the semi-empirical Hamiltonian H of the bare ing in symmetric SWNT junctions.8 In particular, the
0
(10,0) SWNT wire using the Extended Huckel Theory bandlineupinside the SWNT channelhasbeenfoundto
(EHT) with non-orthogonal (sp) basis sets φ (~r).17 We depend mainly on the metal work function, while inter-
m
describethe interactionbetweenthe SWNT channeland action across the metal-SWNT interface modulates the
the rest of the junction using matrix self-energy opera- bandstructureclosetotheinterfacewithoutaffectingthe
tors and calculate the density matrix ρ and therefore band lineup scheme in the middle of the channel. Simi-
ij
the electron density of the equilibrium SWNT junction larphysicalpictureappliestothe hetero-metallicSWNT
from junction, where we find that the bandlineup in the mid-
dle of the Au-SWNT-Ti junction is essentially identical
GR = {(E+i0+)S−H −Σ (E)−Σ (E)−Σ (E)−Σ (E)}−(11,)
L L;NT R toR;tNhTatoftheSWNTjunctionwithsymmetriccontactto
dE metals with workfunction of 4.715eV. This is examined
ρ = Imag[GR](E)f(E−E ). (2)
Z 2π F throughthelocal-density-of-states(LDOS)oftheSWNT
channel as a function of position along the SWNT axis
Here S is overlap matrix and f(E −E ) is the Fermi
F in Figs. 3 and 4.
distribution in the electrodes. Compared to the sym-
The coupling across the metal-SWNT interface and
metric SWNT junctions, here the Hamiltonian describ-
the corresponding strong local field variation immedi-
ing the SWNT channel H =H +δV[δρ]+V includes
0 ext
ately adjacent to the Ti-SWNT interface has a strong
the contact potential V (taken as linear voltage ramp
ext
effectontheSWNT bandstructurethere,whichextends
here) in addition to the charge-transfer induced electro-
to∼4nmawayfromtheinterface(Fig. 3(a)). Theband
static potential change δV (δρ is the density of trans-
structure modulation at the Au side is weaker. For the
ferred charge).
40-unit cell (16.9 nm) SWNT, the band structure in the
The calculated charge transfer per atom and electro-
middle of the SWNT junction remains essentially unaf-
static potential change along the cylindrical surface of
fected. This is shown in Fig. 4, where we compare the
the SWNT for the Au-SWNT-Ti junction are shown in
Fig. (2). Previous works8 have shown that by con- LDOS of the Au-SWNT-Ti junction in the left end, the
rightend and the middle of the SWNT channelwith the
tacting to the high (low)-work function metal Au (Ti),
corresponding LDOS of the Au-SWNT-Au, Ti-SWNT-
hole(electron)dopingisinducedinsidetheSWNTchan-
Ti junction and the bulk (infinitely long) SWNT wire
nel. Here we find simultaneous electron and hole dop-
respectively. Since the magnitude of the build-in elec-
inginsidetheSWNTchannelforthehetero-metallicAu-
tricfieldissmallerthanthecharge-transferinducedlocal
SWNT-Ti junction (lower figure in Fig. 2(a)). Since
fieldatthe metal-SWNT interface,the LDOSatthe two
the magnitude of hole doping inside the Au-SWNT-Au
junction (≈−5.6×10−4/atom)is much largerthan that ends of the SWNT channel remain qualitatively similar
tothatofthesymmetricSWNTjunction(Figs. 4(a)and
of the electron doping inside the Ti-SWNT-Ti junction
(≈ 3×10−5/atom) due to the larger work function dif- 4(c)). Note that the LDOS plotted here has been ener-
getically shifted so that the SWNT bands in the middle
ference, the majority of the channel remains hole-doped
of the hetero-metallic junction line up with those of the
inside the Au-SWNT-Ti junction. Due to the localized
symmetric SWNT junctions.
nature of interface bonding, the charge transfer pattern
immediately adjacent to the Au(Ti)-SWNT interface re- The above separation of band lineup scheme at the
mains similar to that of the Au-SWNT-Au (Ti-SWNT- interface and in the interior of the SWNT junction im-
Ti) junction both in magnitude and shape. The short- plies that in NTFETs, the gate segments controlling the
wavelength oscillation in the transferred charge inside device interiors affect the device operation through ef-
the SWNT channel reflects the atomic-scale variation of fective modulation of the work function difference be-
charge density within the unit cell of the SWNT.8,18 tween the source/drain electrode and the bulk portion
Thecontact-induceddopingaffectsthetransportchar- of the SWNT channel (applying a finite gate voltage to
acteristics by modulating the electrostatic potential pro- the SWNT bulk leads to an effective modulation of its
file along the SWNT junction. We find that inside the work function relative to the source/drain electrodes),
SWNT channel, the built-in electric field is screened ef- while the gate segments at the metal-SWNT interfaces
fectively by the delocalized π-electron of carbon. So affect the device operation by controlling charge injec-
the net electrostatic potential change along the cylindri- tion into the device interior through local modulation of
cal surface (V + δV[δρ]) is much more flat than the the SWNT band structure and Schottky barrier shapes
ext
linear voltage ramp denoting the contact potential ex- includingheight,widthandthickness,inagreementwith
cept close to the metal-SWNT interface (lower figure of recentlateralscalinganalysisofgate-modulationeffect19
Fig. 2(b)), where its shape remains qualitatively simi- and interface chemical treatment effect in Schottky bar-
lar to that at the Au (Ti)-SWNT interface of the Au- rierNTFETs.20 Notethatsincethebandstructuremod-
SWNT-Au(Ti-SWNT-Ti)junction. Due tothe confined ulation at the metal-SWNT interface can extend up to
cylindrical structure of the SWNT channel, the charge- ∼4nmintotheinterioroftheSWNTjunction,itmaybe
3
readily resolved using scanning nanoprobe techniques.21 duetothereducedtransmissionclosetothevalence-band
The Schottky barrier effect at the metal-SWNT inter- edge (Fig. 4(d)) caused by the band structure modula-
face can also be analyzed through the length-dependent tion at the Ti-SWNT interface. Due to the finite num-
conductance and current-voltage (I-V) characteristics of ber of conduction channels, the increase of the conduc-
the Au-SWNT-Ti junction, which are calculated using tance with temperature is rather slow (Fig. 5(b)).8 The
the Landauer formula15 G = 2e2 dET(E)[−df (E − relativecontributionoftunneling andthermal-activation
h dE
E )] = G +G and I = +∞RdE2eT(E,V)[f(E − to the room-temperature I-V characteristics is shown in
F Tu Th −∞ h Figs. 5(c) and 5(d) for the 20- and 40-unit cell long
(E + eV/2)) − [f(E − (E R− eV/2))] = I + I
F F Tu Th (8.4and16.9nm)SWNTrespectively,whereweseethat
andseparatedintotunnelingandthermal-activationcon-
thermal-activation contribution increases rapidly with
tributions as G = 2e2T(E ),G = G − G and
Tu h F Th Tu biasvoltageforthe20-unitcellSWNTjunctionwhilethe
I = 2e EF+eV/2T(E,V)dE,I =I −I .8,22 thermal-activation contribution dominates the I-V char-
Tu h EF−eV/2 Th Tu
In genReral the transmission function is voltage- acteristicsatallbiasvoltagesforthe40-unitcellSWNT.
dependent due to the self-consistent screening of the
In conclusion, we have presented an atomistic real-
source-drain field by the SWNT channel at each bias
space analysis of Schottky barrier effect in the two-
voltage. Since in the case of voltage dropping mostly
terminal SWNT junction with hetero-metallic contacts,
across the interface, the transmission coefficient is ap-
whichshowsaneffectivedecouplingofinterfaceandbulk
proximately voltage-independent at low-bias,22 here we
effects. Further analysis is needed that treat both the
calculate the I-V characteristics using the equilibrium
gate and source/drain fields self-consistently in the real
transmission coefficient instead of the full self-consistent
space to achieve a thorough understanding of NTFETs.
calculation at each bias voltage. We find that the con-
ductance of the Au-SWNT-Ti junction shows a tran-
sition from tunneling-dominated to thermal activation-
dominatedregimewithincreasingchannellength,butthe
lengthwhere this occursis longerthan thoseofthe sym-
metric Au/Ti-SWNT-Au/Ti junctions (Fig. 5(a)). This
is partly due to the fact that the Fermi-level is closer to
themid-gapoftheSWNTbandinsidethechannel,partly
* Author to whom correspondence should be ad- McEuenPL2003Phys.Rev.Lett.90156401;CaoJ,Wang
dressed. E-mail: [email protected]. URL: Q and Dai H 2003 Phys.Rev. Lett. 90 157601
http://www.albany.edu∼yx152122. 11 Chiu P-W, Kaempgen M, and Roth S 2004 Phys. Rev.
1 DekkerC 1999 Phys. Today 52(5) 22 Lett. 92 246802; Chen G, Bandow S, Margine E R, Nisoli
2 BachtoldA,HaleyP,NakanishiTandDekkerC2001Sci- C,Kolmogorov AN,CrespiVH,GuptaR,Sumanasekera
ence 294 1317 G U, Iijima S and Eklund P C 2003 Phys. Rev. Lett. 90
3 AvourisPh,AppenzellaerJ,Martel R andWindS J2003 257403
Proc. IEEE 91 1772 12 Experimentallylow-resistancecontactscanbeobtainedei-
4 Javey A, Guo J, Wang Q, Lundstrom M and Dai H 2003 therbygrowingSWNT’sdirectlyoutofthepredefinedcat-
Nature 424 654; Javey A, Guo J, Paulsson M, Wang Q, alystislandsandsubsequentlycoveringthecatalystislands
Mann D, Lundstrom M and Dai H 2004 Phys. Rev. Lett. with metallic contact pads (Ref. 4) or by using standard
92 106804 lithographyandlift-offtechniqueswithsubsequentanneal-
5 Yaish Y, Park J-Y, Rosenblatt S, Sazonova V, Brink M ing at high-temperature (Ref. 7). In both cases, the ends
and McEuen P L 2004 Phys. Rev. Lett. 92 46401 of the long SWNT wires are surrounded entirely by the
6 XueYandDattaS1999Phys.Rev.Lett. 834844;Le´onard metalswithstrongmetal-SWNTsurfacechemicalbonding,
F and Tersoff J 2000 Phys. Rev. Lett. 84 4693; Odintsov although the exact atomic structure of the metal-SWNT
AA2000 Phys. Rev. Lett. 85 150; NakanishiT,Bachtold interface remains unclear.Contacts can also beformed by
A and DekkerC 2002 Phys. Rev. B 66 73307 depositing SWNT on top of the predefined metallic elec-
7 Heinze S, Tersoff J, Martel R, Derycke V, Appenzeller J trodes and side-contacted to the surfaces of the metals
andAvourisPh2002Phys. Rev. Lett. 89106801; Appen- (side-contactscheme),whichcorrespondstotheweakcou-
zeller J, Knoch J, Radosavljevi´c M and Avouris Ph 2004 pling limit due to the weak van der Waals bonding in the
ibid. 92 226802 side-contact geometry leading to high contact resistance
8 Xue Y and Ratner M A 2003 Appl. Phys. Lett. 83 2429; (Ref.3).Othertypesofcontactmayalsoexistcorrespond-
XueYandRatnerMA2004 Phys. Rev. B 69161402(R); ing to intermediate coupling strength. The contact geom-
Xue Y and Ratner M A 2004 Phys. Rev. B In Press etry chosen in this work thus serves as a simplified model
(Preprint cond-mat/0405465) of the low-resistance contact. A comprehensive study of
9 Appenzeller J, Radosavljevi´c M, Knoch Jand AvourisPh the contact effects in SWNT junction devices is currently
2004 Phys. Rev. Lett. 92 48301 underway and will bereported in a futurepublication.
10 Minot ED,Yaish Y,SazonovaV,Park J-Y,Brink M and 13 1994 CRC Handbook of Chemistry and Physics (CRC
4
Press, Boca Raton) SalahubDRandAvourisPh 1999 J. Phys. Chem. B 103
14 Yao Z, Kane C L and Dekker C 2000 Phys. Rev. Lett. 641
84 2941; Park J-Y, Rosenblatt S, Yaish Y, Sazonova V, 18 Le´onard F and Tersoff J 2002 Appl. Phys. Lett. 81 4835
UstunelH,Braig S,AriasTA,BrouwerPandMcEuenP 19 WindSJ,AppenzellerJ,andAvourisPh2003Phys. Rev.
L 2004 Nano Lett. 4517 Lett. 91 58301
15 Xue Y, Datta S and Ratner M A 2002 Chem. Phys. 281 20 AuvrayS,BorghettiJ,GoffmanMF,FiloramoA,Derycke
151; See also Datta S 1995 Electron Transport in Meso- V,BourgoinJPandJostO2004Appl.Phys.Lett.845106
scopic Systems (Cambridge University Press, Cambridge) 21 Freitag M, Radosavljevi´c M, Clauss W and Johnson A T
16 The SWNT-metal interaction arises from one discrete 2000 Phys. Rev. B 62 R2307; Venema L C, Janssen J W,
cylindrical shell of metal atoms, surrounded by the bulk BuitelaarMR,Wild´’oerJWG,LemaySG,Kouwenhoven
metal and treated using the Green’s function method as L Pand DekkerC 2000 Phys. Rev. B 62 5238
detailed in Ref. 15. We use a SWNT-metal surface dis- 22 XueYandRatnerMA2003Phys.Rev.B 68115406;Xue
tance of 2.0(˚A), close to the average inter-atomic spacing Y and RatnerM A 2004 Phys. Rev. B 69 85403
in theSWNTs and metals.
17 Hoffmann R 1988 Rev. Mod. Phys. 60 601; Rochefort A,
5
FIG. 1: (Color online) (a) Schematic illustration of the Au-
SWNT-Ti junction. The ends of the long SWNT wire are
surroundedentirelybythesemi-infiniteelectrodes, withonly
afinitesegmentbeingsandwichedbetweentheelectrodes(de-
finedasthechannel). Alsoshownisthecoordinatesystemof
thenanotubejunction. (b)Schematicillustrationoftheband
diagram in the Au-SWNT-Ti junction. The band alignment
inthemiddleoftheSWNTjunctionisdeterminedbytheav-
erageofthemetalworkfunctions. W1(2),EF denotethework
functions and Fermi-level of thebi-metallic junction.
6
(a) Au−SWNT−Ti
0.1
m
o 0
t
a

r
e
p
−0.1
n 0 5 10 15 20
o
−5
r x 10
t
c 5
e
el 0

t
e −5
N
−10
−15
8 9 10 11 12
Position along NT axis (nm)
Au−SWNT−Ti
(b)
0
−1
)
V
e
−2
(

e
g 0 5 10 15
n
a
h
c
0.2
l
a
i
nt 0
e
t
o−0.2
P
−0.4
6 7 8 9 10 11
Position along NT axis (nm)
FIG. 2: Electrostatics of the Au-SWNT-Ti junction for
SWNT channels of different lengths. (a) Upper figure shows
transferred charge per atom as a function of position along
theSWNTaxisforSWNTchannellengthsof2.0,8.412.6,16.9
and 21.2 nm. Lower figure shows the magnified view of the
transferredchargeinthemiddleofthechannelforthelongest
(21.2 nm) SWNT studied. (b) Upper figure shows the elec-
trostatic potential change at the cylindrical surface of the 20
(8.4 nm) and 40- unitcell (16.9 nm) SWNTs studied. The
dotted line denote the linear voltage ramp Vext (contact po-
tential) due to the work function difference of gold and ti-
tanium. The dashed line show the charge-transfer induced
electrostatic potential change δV(δρ). The solid line shows
thenetelectrostaticpotentialchangeVext+δV. Lowerfigure
showsthemagnifiedviewoftheelectrostaticpotentialchange
in themiddle of the40-unitcell SWNTjunction.
7
FIG. 3: (Color online) Local density of states (LDOS) as a
functionofpositionalongtheSWNTaxisforSWNTchannel
length of 16.9nm. We show the result when self-consistent
SWNT screening of the build-in electric field is included in
(a). Forcomparisonwehavealsoshowntheresultfornonself-
consistent calculation in (b). The plotted LDOS is obtained
by summing over the 10 atoms of each carbon ring of the
(10,0) SWNT. Note that each cut along the energy axis at
a given axial position gives the LDOS of the corresponding
carbon ring and each cut along the position axis at a given
energy gives thecorresponding band shift.
8
(a) LDOS: Left End (b) LDOS: Middle
10 10
) )
V V
e e
s/ s/
e e
t t
a 5 a 5
t t
s s
( (
S S
O O
D D
L 0 L 0
−6 −5 −4 −3 −5.5 −5 −4.5 −4
t
(c) LDOS: Right End n (d)
e
) 10 i1.5
V c
e fi
s/ ef
e o 1
t c
a
st 5 on
(
S si0.5
O s
i
D m
L s
0 n 0
−6 −5 −4 a −5.5 −5 −4.5 −4
r
Energy (eV) T Energy (eV)
FIG. 4: Local-density-of-states (LDOS) and transmission
versus energy (TE) characteristics of the 40-unit cell Au-
SWNT-Ti junction. (a) LDOS at the 1st unit cell adjacent
to the Au side (left end) of theAu-SWNT-Tijunction (solid
line) and theLDOSat thecorresponding location of theAu-
SWNT-Au junction (dashed line). (b) LDOS in the middle
unit cell of the Au-SWNT-Ti junction (solid line) and the
LDOS of the bulk (10,0) SWNT (dashed line). (c) LDOS
at the 1st unit cell adjacent to the Ti side (right end) of the
Au-SWNT-Tijunction(solidline)andtheLDOSatthecorre-
spondinglocation oftheTi-SWNT-Tijunction(dashedline).
(d) TE characteristics of the Au-SWNT-Tijunction.
9
(a) Au−SWNT−Ti (b) x 10−7
)
S
S) Tunnel 6 L=16.9 (nm)
µ 100 Total µ (
( e
n c
o n 4
ti a
c t
u −10 c
d10 u 2
n d
o n
C o
C 0
0 10 20 100 200 300
SWNT Length (nm) Temperature (K)
(c) (d)
0.2
2 Total Total
) )
A Tunnel A Tunnel
0.1
n 1 n
( Thermal ( Thermal
nt 0 nt 0
e e
urr−1 L=8.4(nm) urr−0.1 L=16.9(nm)
C C
−2
−0.2
−0.5 0 0.5 −0.5 0 0.5
Voltage (V) Voltage (V)
FIG. 5: (a) Room temperature conductance of the Au-
SWNT-Ti junction as a function of SWNT channel length.
(b) temperature dependence of the conductance of the 40-
unit cell (16.9 nm) SWNT junction. The room tempera-
ture current-voltage characteristics of the 20- and 40- unit
cell SWNTjunctions are shown in (c) and (d) respectively.