Carrier mobility and scattering lifetime in electric double-layer gated few-layer graphene

0.41 MB·

by  E. Piatti

Carrier mobility and scattering lifetime in electric double-layer gated few-layer
graphene
∗
E. Piatti, S. Galasso, M. Tortello, J. R. Nair, C. Gerbaldi, D. Daghero, and R. S. Gonnelli
Dipartimento di Scienza Applicata e Tecnologia, Politecnico di Torino, 10129 Torino, Italy
M. Bruna+ and S. Borini+
Istituto Nazionale di Ricerca Metrologica (INRIM), 10135 Torino, Italy
7
1 We fabricate electric double-layer field-effect transistor (EDL-FET) devices on mechanically ex-
0 foliated few-layer graphene. We exploit the large capacitance of a polymeric electrolyte to study
2 the transport properties of three, four and five-layer samples under a large induced surface charge
density both above and below the glass transition temperature of the polymer. We find that the
n
carrier mobility shows a strong asymmetry between the hole and electron doping regime. We then
a
J employ ab-initio density functional theory (DFT) calculations to determine the average scattering
lifetime from the experimental data. We explain its peculiar dependence on the carrier density in
0
terms of thespecific properties of the electrolyte we used in our experiments.
1
Keywords: Few-layer graphene - EDL gating - Liquid gating - Transport properties - Scattering lifetime -

] Surfacemodification
l
l
a
h I. INTRODUCTION as liquid gating). Indeed, after the first results on stron-
-
s tiumtitanate[5],EDLgatinghassoonbeenemployedon
e the prototypical 2D materials, first on SLG [6] and soon
m Since its discovery in 2004 [1], graphene has attracted
after on double and three-layergraphene (2LG and 3LG
a widespread interest from the scientific community due
. respectively)[7]. However,the properties of liquid-gated
t to its peculiar physical and electronic properties. More-
a few-layer graphene of higher number of layers have only
m over, it has soon been discovered that graphene crystals
recently been explored in our earlier work of Ref. [8]. In
having a different number of layers effectively behave as
- that paper we focused on the low-temperature transport
d completelydifferentelectronicsystems,approachingbulk
properties of 3LG, 4LG and 5LG.
n graphite for a number of layersN &8 [2]. While a lotof
In the presentwork,we focus instead onhow the elec-
o
effort has been devoted to the characterizationof single-
c tric transport properties of few-layer graphene are mod-
layer graphene (SLG), few-layergraphene (FLG) has re-
[ ified by EDL gating at higher temperatures, both im-
ceived a smaller attention [3]. Furthermore, most of the
mediately above and below the glass phase transition of
1 investigations has been restricted to the relatively small
ourelectrolyte. Wefindthatoursamplesshowamarked
v
carrier density range close to the Dirac point, where the
1 asymmetry in the response to electron and hole doping,
relativistic properties of the graphene quasiparticle ex-
0 i.e. toapositiveornegativeappliedgatevoltage. Inpar-
citations diverge more strongly from those of standard
7 ticular,whilethemobilityissuppressedinourdevicesby
2 semiconductors. bothpositiveandnegativeappliedgatevoltages,thesup-
0
The investigation of carrier-density ranges further pression in the electronic side is much more pronounced
.
1 away from the Dirac point requires a larger tunability than in the holonic one. By combining our experimental
0 of the Fermi level in a reproducible way. This can be findings with ab-initio density functional theory (DFT)
7
achievedby the technique of electric double-layer(EDL) calculations, we determine how the average scattering
1
gating, which has been introduced in the field of solid- lifetime in our devices is affected by the strong modu-
:
v state physics since the second half of the 2000s. With lation of the carrier density. We discover that the asym-
i respect to standard field-effect techniques, EDL gating metry in the response is even more pronounced for the
X
is able to access values of carrier density previously scattering lifetime than for the mobility. In addition a
r
a unattainable inchemically undoped insulatorsandsemi- difference in the carrier-density dependence of the scat-
conductors [4]. This strong increase in the tunability of tering lifetime emerges between 4LG and 5LG. Finally,
the carrier density in a field effect transistor (FET) ar- we propose a qualitative explanation for these findings,
chitecture is made possible by the strong increase in the in which we link the asymmetry in the transport prop-
gatecapacitance. Inturnthisisobtainedbysubstituting erties of the material to the asymmetry in the physical
thesolidgateoxidewithaliquidorpolymericelectrolyte dimensions of the active ions composing our electrolyte.
(this is the reason why the technique is also referred to
II. DEVICE FABRICATION
∗Electronicaddress: [email protected]
+Current address: Nokia Technologies, CB30FA Cambridge, We obtained the few-layer graphene samples via me-
UnitedKingdom chanical exfoliation of highly oriented pyrolitic graphite
2
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FIG.1: (a)AFMtopographic imageincontact modeof a3LGdevicebeforePES drop-casting,and(b)zoom onitsupperleft
corner. Inset shows the height signal step in correspondence to the graphene edge. While signs of electrical damage occurred
duringpreliminarymagnetoresistance measurementsappearinthelowerpartofthedevice,theentiremiddle-to-upperregions
arefreefromwrinklesandfolds. TheAFM-estimatedthicknessagreeswellwiththeresultsobtainedviaopticalcharacterization.
(c) Sketch of a complete device after PES drop-casting. Gate voltage is applied between the platinum wire and the negative
current contact. (d) Sheet conductance vs gate voltage transfer curves for a 4LG sample in the [-3V, +3V] range at room
temperature. Top scale shows thecorresponding induced charge density estimated from DSCC.
(HOPG) and transferredthem onto standardSiO on Si corresponding to a 3LG sample [16]) estimated at the
2
substrates. The number of layers of each flake was de- edge (see inset to Figure 1b) agrees well with the results
termined by optical contrast analysis [11]; Raman spec- obtained from the optical characterization.
troscopywasalsoemployedtoindependentlyconfirmthis Afterwirebondingwedrop-castedtheliquidprecursor
number and to determine the stacking sequence [12–15]. of the polymer electrolyte system (PES) onto the com-
Allthesamplesthatwillbediscussedinthefollowingare plete devices in the controlledatmosphere of a dry room
3LG,4LGand5LGpresentingBernalstacking. We real- in order to avoid contamination from water molecules
ized the electrical contacts for the four-wire resistance and other chemicals that may affect the performance of
measurements via the standard microfabrication tech- the electrolyte. We employed the same Li-TFSI based
niques, i.e. photolithography, Cr/Au thermal evapora- PESusedinourearlierexperimentsongold[9]andother
tion and lift-off. Subsequently we patterned the devices noble metals [10] due to its record amount of charge in-
into a Hall-bar shape by reactive ion etching. An ad- duction. Figure 1c shows a sketch of a device, where the
ditional windowing was finally realized on the device by few-layer graphene flake acts as the working electrode of
photoresistinordertoleaveuncoveredonlyapartofthe the electrochemical cell, while a Pt wire is immersed in
contact pads (for wire bonding) and the gated channel the PES and acts as the counter electrode. The elec-
over the flake. The photoresist mask was hard-baked at trical connections for longitudinal (R ) and Hall (R )
xx xy
145°C for 5 minutes to improve its electrochemical sta- resistance measurements are shown as well.
bility. Figure 1a shows an AFM image of a complete de-
vice after it underwent a preliminary magnetoresistance
characterization, while Figure 1b shows a magnification
III. EXPERIMENTAL RESULTS
of the upper left corner of the device to allow for eas-
ier thickness determination. The AFM characterization
shows that the device is free from intrinsic defects such We performed gating and transport measurements in
as wrinkles and folds. The flake thickness (≈ 1.4 nm, a Cryomechr PT405 pulse-tube cryocooler. After PES
3
drop-casting the devices were rapidly transferred inside Sheet carrier d ensity (e-/cm2)
the cryostat in order to minimize their exposure to air.
-4x1014-2x1014 0 2x1014 4x1014 6x1014 8x1014
We left the devices in vacuum at room temperature for
)
S
a few hours to degas before performing the actual mea- m T = 220 K
surements. The gate voltage was then applied at room e (
c
temperature both in form of ramps and step perturba- n 10
a
tions, and the response of the samples resistance and of ct
u
the gate-current was recorded. Slow gate-voltage ramps d
n
were employed to assess the ambipolar nature of the o
c
field effect in all our samples. It means that we always et
detected the electron (hole) conduction in the channel e
Sh (a)
uponapplicationofasufficientlylargepositive(negative)
3LG
1
bias between the gate electrode and the sample. Step- 4LG
like gate-voltage applications were instead used to allow 5LG
)
fordouble-stepchronocoulometry(DSCC)measurements -1s103
1
abletodeterminetheinducedcarrierdensityinthechan- -V
2
nel of our devices. A detailed analysis of this technique, m
c
tmheenctso,mapnadristohnesawsistehsstmheensttaonndatrhdeHreapllroedffuecctibmilietyasuarned- bility (102
purely electrostatic nature of the gating technique can o
M
be found in our earlier work [8]. The total sheet carrier (b)
density in the system n2D is determined by adding the 101
induced carrier density to the pristine density measured -4x1014-2x1014 0 2x1014 4x1014 6x1014 8x1014
by Hall effect. Sheet carrier density (e-/cm2)
Figure 1d shows a typical sheet conductance response
of a 4LG device both as a function of the applied
gate voltage and of the induced carrier density in the FIG. 2: Electrical transport characterization of the device
[−3V,+3V] voltage range. The small negative hysteresis at T = 220 K, below the glass transition of the electrolyte.
between an increasing or decreasing gate-voltage ramp Sheetconductance(a)andmobility(b)vscarrierdensityn2D
is typical of electrolyte-gated graphene devices and can for 3LG (green), 4LG (red) and 5LG (violet) devices. The
strongly asymmetric response of the system to electron and
be attributed to carrier transfer from the metal contacts
hole doping is readily distinguishable. Dashed lines act as
due to capacitive gating [17]. This also accounts for
guides to theeye.
the minimum in the conductance curves being shifted
to negative gate voltages (indicating that the sample is
n-doped). In fact Hall effect measurements performed
immediatelyafterdrop-castingshowedanativep-doping is beyond the scope of this paper and has been detailed
of the sample, as is to be expected in the case of traces elsewhere [8]. Here, we focus on the regime around 220
of residualwater adsorbedat the graphenesurface. Two K, i.e. where the sample is still relatively close to room
other features clearly emerge from these curves: first, temperaturebutthePEShasalreadyundergoneitsglass
both for electron and hole doping a sharp slope change transition. Thisensuresthattheionmovementinsidethe
arises for intermediate values of the applied gate voltage electrolyteiscompletelyfrozen,thusminimizingthefluc-
(VG ≈±1.5V). This behaviorhas alreadybeenobserved tuationsinthechargedensityaccumulatedatthesample
in 3LG [7] and linked to the rise of interband scattering surface.
due to the crossing of a Van Hove singularity when the
Figure 2a shows the dependence of the sheet conduc-
Fermilevelcrossesthe splitband T . Second, while the
2g tance on the sheet carrier density n2D at 220 K, as de-
curves are symmetric for low values of the applied gate
termined by DSCC, for both the 4LG and 5LG samples.
voltage, a strong asymmetry emerges for higher values.
Data from a 3LG sample are shown for comparison, but
The electron-doped branch saturates at almost half the
will not be discussed due to the small number of experi-
sheet conductance value with respect to the maximum
mental points. In the case of 4LG, the behavior at 220K
one in the hole-doped branch, even though the induced
closelyresemblesthe responseto the gatesweepatroom
carrier density is estimated to be significantly larger.
temperature. In particular, the sheet conductance on
Wethenstudiedinmoredetailthetransportproperties the electron side shows clear signs of saturation already
ofour samplesfor few selectedvalues ofthe appliedgate at relatively small values of carrier density, while on the
voltage. Foreachofthesevalues,thevoltagewasapplied holesideanincresingtrendisobservedintheentireden-
at room temperature in order to measure the DSCC re- sity range. As a consequence the maximum conductance
sponse,andthesamplewassubsequentlycooleddownto valueontheholebranchisalmostthreetimeslargerthan
thebasetemperatureofthecryogenicsystem. Ananaly- the one on the electron branch. Interestingly, the asym-
sisofthetransportpropertiesofFLGatlowtemperature metryismuchlesspronouncedinthecaseof5LG.Inthis
4
case no sign of saturation is evident also on the electron Sheet carrier density (e-/cm2)

side and the maximum conductance in the hole branch
-4x1014-2x1014 0 2x1014 4x1014 6x1014 8x1014
is only about twice as big as that in the electron one. 102
Thisdependenceofthedifferenceintheasymmetryon
the number oflayersis presentalsoin the dependence of
themobilityµ=σ2D/(en2D)onn2D,asshowninFigure )e
m
2b. The mobility decreases at the increase of the carrier
densityforbothelectronandholedoping,independently e /
(
of the number of layers. However, in the case of 5LG
101
the mobility rapidly reaches saturation. In the case of m / t
4LG instead, the mobility decrease is significantly more
(a)
pronounced, and signs of saturation are present only in
the hole branch. 10-13 45LLGG
T = 220 K
IV. DISCUSSION
) 10-14
Aswehaveseen,threepeculiarbehaviorsemergefrom (s
t
the carrier density dependence of the mobility. First, µ
decreaseswith increasingn2D for both electronand hole (b)
doping. Second, this dependence is strongly asymmetric
in the signof the chargecarriers. Third, this asymmetry 10-15
-4x1014-2x1014 0 2x1014 4x1014 6x1014 8x1014
is less pronounced in the case of 5LG with respect to Sheet carrier density (e-/cm2)
4LG.
We first consider the decrease in mobility. In SLG the
mobility is expected to decrease moving away from the
FIG. 3: (a) Dependence of the mobility-over-scattering life-
Diracpoint. However,in2LGand3LGithasbeenshown
time ratio, µ/τ, as function of the carrier density n2D as es-
that the different density of states leads to an increasing
timated from DSCCmeasurements andDFT calculations, in
behavior, albeit in a smaller range of carrier densities
units of the elementary charge divided by the electron mass.
than the one considered in this paper [18]. On the other The behavior is symmetric with respect to electron and hole
hand, it is known that in two-dimensionalelectron gases doping and strongly depends on the number of layers only
(2DEGs) in general, and in graphene in particular, a re- in close vicinity to the Dirac point. (b) Average scattering
entrantmobilityatveryhighcarrierdensityisassociated lifetime τ vs carrier density n2D calculated by dividing the
to a crossover from a dominant scattering by screened experimentally measured mobility by µ/τ. The asymmetry
Coulomb charges to a scattering dominated by surface of τ between electron and hole doping is enhanced with re-
spect to that of the experimental mobility, and a qualitative
roughness (for 2DEGs in semiconductors [19]) or short-
differencein theresponse of 4LG and5LG is also readily ap-
range scatterers (in graphene [20]).
parent. Resultsare reportedfor 4LG(red) and5LG(violet).
Inorderto disentanglethe contributionsto the mobil-
Asin Figure2, dashed lines are guides to theeye.
ityduetothechangesintheDOSfromthosearisingfrom
changes in the scattering rates, we combine our experi-
mental results with ab-initio DFT calculations [21, 22]. and correlation terms we adopted the local density ap-
The bandstructure of 4LG and 5LG under strong dop- proximation(LDA)andthehexagonalBrillouinzonewas
ing conditions is calculatedby using the all-electronfull- sampledwitha28x28x1meshofk-points. Atotalenergy
potentiallinearisedaugmented-planewavemethodasim- toleranceof10−8Hartreewasusedforobtainingthecon-
plemented in the ELK code [23]. We model the FLG by vergence of the self-consistent field calculations.
building a 3D supercell with a value of the c-axis lattice Itiswellknownthattheeffectivemassm∗isnotagood
constant larger than 20 ˚A so that, in order to avoid in- quantity for the description of the massless relativistic
teractions, the periodic images of the structures are at quasiparticlesclosetotheDiracpointofgraphene. How-
least 10 ˚A apart. Independently of the number of lay- ever,anexpressionforthemobility-to-scatteringlifetime
ers the layer to layer distance is taken equal to 3.35 ˚A ratiocanbeobtainedknowingthetheoreticalbandstruc-
while the in-plane lattice constant is fixed to a = 2.46 tureandtheexperimentalvalueofn2D accordingto[26]:
˚A. As a first approximation we simulate the effect of
the EDLgatingbyintroducingextrachargecarriersinto
tbhaecksgyrsotuemndtcohgaertgheer(Jweiltlhiuma cmomodpeeln)s.atAingmhooremcoogmenpeloeutes µτ = τ1eσn22DD = n2eD Xi (Nk4iNsvF2iNi) (1)
model, that takes into account the intense electric field
at the EDL/graphene interface [24, 25] goes beyond the whereN andN arethevalleyandspindegeneracies,
ki s
scope of this paper. In order to describe the exchange respectively,v isthe FermivelocityandN the DOSat
Fi i
5
the Fermi level of the i-th band. The strong asymmetry of the conductance, the mobil-
Unsurprisingly, the symmetry of the bandstructure of ity,andthescatteringlifetime betweenelectronandhole
FLG aboveand below the Dirac point is reflected onthe doping in both 4LG and 5LG can instead be related to
symmetric dependence of the ratio µ/τ on the carrier the asymmetry in the size of the ions composing the Li-
density (Figure 3a). Thus, the strong asymmetry in the TFSIsalt. Infact,thestandardionicliquidsusedinEDL
doping dependence of the mobility cannot be attributed gating literature (e.g. DEME-TFSI), have cations and
to features in the bandstructure. However, the clear re- anionsthatarebothmadebycomplexmoleculesofcom-
ductionofµ/τ movingawayfromthe Diracpointcanbe parable size [4]. In the case of Li-TFSI instead, the Li+
partly responsible for the similarly decreasing behavior cation (inducing electron doping) is significantly smaller
of the mobility. than its anion counterpart (inducing hole doping). This
We finally extract the average scattering lifetime τ by characteristiccanallowittopackattheelectrodesurface
dividing the measured mobility by the DFT-determined bothwithhigherdensityand,moreimportantly,incloser
ratio µ/τ (Figure 3b). In this case, the asymmetries in proximity. Thisinturnenhancesitscharge-inductionca-
the electron- and hole-doping branches are magnified, as pabilities with respect to the anion, as demonstrated by
well as the difference in the behaviour between 4LG and ourDSCCmeasurementsonbothgraphene[8]andnoble
5LG. In 4LG, the scattering lifetime monotonically de- metals[9]. Ontheotherhandthisfactmostlikelymakes
creases across the entire electron branch, while rapidly its efficiency as a scattering center sensibly larger than
saturatesafter aninitialdecreasein the hole branch. In- that of the bigger TFSI anion.
stead, in 5LG τ shows a nonmonotonic behavior in the
electron branch, decreasing rapidly for small values of
carrier density and increasing for larger ones, while in V. CONCLUSIONS
the hole branch it appears to be monotonically increas-
ing.
In conclusion, we characterized the electric transport
This very peculiar behavior cannot be simply asso-
propertiesof4LGand5LGfield-effectdevicesinthevery
ciated with modifications in the DOS, nor to a pure
high carrier-density regime achievable by EDL gating,
crossover from screened Coulomb scattering to short-
both above and below the freezing point of the elec-
range scattering. Instead, an intrinsically surface-
trolyte. We detected a peculiar asymmetry in the re-
sensitive, asymmetric scattering mechanism is required
sponse to hole and electron doping in both the conduc-
to account for our findings. In the following, we pro-
tanceandthemobilityofthesamples. Bycombiningour
poseapossibleexplanationthatisdirectlyrelatedtothe
experimentalresultswithab-initio DFT calculations,we
physical implementation of the EDL technique.
extracted the dependence of the average scattering life-
As we mentioned earlier, when the gate voltage is
time on both the number of layers and the carrier den-
applied, the solvated ions inside the polymeric matrix
sity. We haveinterpretedthe resulting trends as primar-
densely accumulate in close vicinity (. 1 nm) to the
ily due to the microscopic properties of our EDL gating
graphene surface, thus building a nanoscale capacitor
technique, i.e. the capability of the ions composing the
at the electrolyte/graphene interface. Since it has been
EDL to act as extra chargedscattering centers for carri-
shown [27] that charged impurities in close proximity to
ers at the surface of the device. In particular,the strong
the graphene surface create scattering centers for Dirac
asymmetry between electron and hole doping has been
quasiparticles, we can assume that the ions constituting
associatedwiththedifferenceinsizebetweencationsand
the EDL itself may behave in the same way.
anionsinthesolvatedsaltLi-TFSI.Theseresultsarerel-
As long as the electric transport is dominated by
evant in the framework of understanding the non trivial
screened Coulomb scattering, the average τ of the sys-
modificationsthe EDLtechniquecausesatthesurfaceof
tem is determined by a competition between two contri-
graphene and other two-dimensional materials.
butions. On one hand, the increasing number of charge
carriers introduced by gating improves the screening ca-
pabilities of the 2DEG and would enhance τ and µ. On
Acknowledgments
the other hand, the concomitant increasing number of
defects introducedbythe presenceofchargedionsatthe
graphene surface would decrease τ and µ. The reduced The authors acknowledge the support from the EU
suppression of the mobility with increasing carrier den- GrapheneFlagshipandGraphene@PoliTo. Wearegrate-
sity in 5LG would then be a direct consequence of its fultoE.Cappellutifortight-bindingcalculationsweused
reduced surface to volume ratio with respect to 4LG. to check the validity of DFT results.
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