-
arX
iv:1
108.
2012
v1 [
cond
-mat
.mes
-hal
l] 9
Aug
201
1
Electrically Controlled Adsorption of Oxygen in Bilayer Graphene
Devices
Yoshiaki Sato,1, ∗ Kazuyuki Takai,1 and Toshiaki Enoki1
1Department of Chemistry, Tokyo Institute of Technology, 2-12-1
Ookayama,
Meguro-ku, Tokyo, 152-8551, Japan
We investigate the chemisorptions of oxygen molecules on bilayer
graphene (BLG) and its elec-trically modified charge-doping effect
using conductivity measurement of the field effect
transistorchanneled with BLG. We demonstrate that the change of the
Fermi level by manipulating the gateelectric field significantly
affects not only the rate of molecular adsorption but also the
carrier-scattering strength of adsorbed molecules. Exploration of
the charge transfer kinetics reveals theelectrochemical nature of
the oxygen adsorption on BLG. [This document is the unedited
Au-thor’s version of a Submitted Work that was subsequently
accepted for publication in Nano Letters,c©American Chemical
Society after peer review. To access the final edited and published
work seehttp://dx.doi.org/10.1021/nl202002p .]
Keywords: Graphene; charge transfer; field effect transistor;
electron transport; mobility; band gap
It has been a central topic of surface science how tocontrol the
adsorption and desorption in order to tobring out desirable
features and functionalities by ad-sorbed molecules. Tuning the
electronic features of solidsurfaces has an important implication
in that molec-ular chemisorptions and catalytic reactions are
deter-mined by them1,2. In particular for graphene, the
two-dimensional honeycomb carbon lattice, in which the con-duction
π∗-band and the valence π-band contact to eachother at the “Dirac
point” giving a feature of zero-gapsemiconductor3, the control of
chemisorption is a criticalissue since chemisorption directly leads
to altering everyelectronic property of graphene. Other than the
elec-tron/hole doping4 owing to the charge transfer betweengraphene
and the adsorbed molecules, widely known arethe charged impurity
effect on the electron transport5–7,lattice deformation8, and
opening the band gap dueto asymmetric adsorption9–11. Aside from
the macro-scopic spatially-controlled adsorption that is achieved
us-ing nano-device fabrication technique12, microscopic con-trol of
adsorption structure is of great importance be-cause the
aforementioned adsorption effects are alteredby the local structure
of adsorbate, e.g., whether theadsorbed molecules are arranged in a
random or su-perlattice structure10,13, or whether the molecules
areadsorbed individually4,14 or collectively (in dimers15
orclusters16,17). For the first step to realize such anadvanced
control of adsorption, the methods to uti-lize the interaction
between the adsorbed molecules andgraphene for it are to be
explored.
The principal impetus in the present study is to con-trol the
charge transfer between graphene and the ad-sorbed molecules by
tuning the Fermi level of graphene,which is readily accomplished in
the field effect transis-tor (FET) structure. When SiO2/Si
substrate is usedas the back-gate insulator of the FET, the tuning
rangeof the Fermi level of graphene by the application of thegate
voltage is at the extent of several ±0.1 eV18 whichwould be
sufficient to alter the chemical reactivity onthe surface. Besides,
the additional charge and the gra-dient of electric potential
generated by the gate electric
SiO2SiO2SiO2
Vg,ad+−
−+
gatevoltage
200
240
280
320
360
0
0
100
12
34
5
200
300
400
500
600
Doping Density (×1012cm−2)
Mob
ility
(V
scm
−2 )
O2 E
xp
osu
re T
ime
(m
in)
−50 V
0 V
+40 V
+80 V
field are expected to change the polarization of
adsorbedmolecules19,20 and to modify the charge distribution
ongraphene layers and the adsorbed molecules21–25 leadingto, e.g.,
the change in the ease of migration of moleculesadsorbed on
graphene26. Some research27–29 argues thatthe change in the Fermi
level caused by a gate electricfield activates electrochemical
redox reactions and theaccompanying charge transfer causes
hysteresis of thesource–drain current in graphene FET, yet there
has beenno investigation that elucidates the relation between
thekinetics of adsorption to graphene and gate electric field.In
this study we investigated gate-tuned molecular oxy-gen adsorption
through systematic measurements of con-ductivity using mainly
bilayer graphene (BLG).The back-gated BLG-FETs were fabricated on
SiO2
(300 nm thick) on heavily n-doped silicon substrate bymeans of
photolithography. The channel length andwidth were 6 µm and 3.5 µm,
respectively. Prior to mea-surement, we repeated vacuum annealing
(210◦C, 10 h)to remove the adsorbed moisture and contaminants onthe
surface until no more changes in the gate-dependentconductivity σ
were eventually seen. After the anneal-ing, the BLG-FET exhibited
its pristine nature, that is,ambipolar transport properties with a
conductivity min-imum around Vg = V
0CNP < 8 V giving the “ charge neu-
trality point (CNP)” with electrons and holes in BLGbeing equal
in density. The Drude mobility µ(n) wasestimated to be ∼ 1 × 103
cm2V−1s−1 from the equa-tion µ(n) = σ/e|n|, where n is the carrier
density withn = (cg/e)(Vg − VCNP) (cg/e = 7 × 1010 cm−2V−1;
http://arxiv.org/abs/1108.2012v1http://dx.doi.org/10.1021/nl202002p
-
2
1 atmroom temperature
Vg,ad+
−
Vg(sweep)
VDSA
in vacuumin O2
measuring conductivity
0
0 40 80−80 −40
2
4
6
Vg−V0CNP (V)
0
2
4
6
0
2
4
6 pristine
0.5-min exposure
1-min exposure
+80 V
+80 V
+40 V
+40 V
−50 V
+80 V
+40 V
−50 V
−50 V
Vg,ad
Co
nd
uctivity (
×10
–4
Ω–
1)
−60 −40 −20 0 20 40 60 80
0
1
2
3
4
5
6
7
Co
nd
uctivity (
×1
0−
4Ω
−1)
Vg (V)
1 min
pristine
5.5 min
31 min
178 min
O2 Exposure
a
b
c
FIG. 1: (a) Schematic of the measurement cycle. First, the field
effect transistor channeled by bilayer graphene (BLG-FET) isexposed
to gaseous O2 while the gate voltage Vg,ad is applied (left panel).
Then the system is evacuated and the source–drainconductivity of
the BLG-FET is measured by sweeping the gate voltage Vg (right
panel). Subsequently gaseous O2 is againintroduced, and the cycle
is repeated. The gas introduction and evacuation are completed in a
shorter time than ∼ 10 s toprevent additional gas from adsorption.
The whole cycle is executed at room temperature. (b) Change of the
field effectbehavior due to the O2 exposure with Vg,ad = 0 V (run
1). The gate voltage giving the minimum conductivity (the
chargeneutrality point), is shifted from Vg = V
0CNP (< 8 V) (marked by a brown triangle, before O2 exposure)
to the positive direction
(green triangles) upon O2 exposure. Circles on the curves
represent the conductivity at the hole density of 2.5 × 1012
cm−2
that are used to calculate Drude conductivity shown in Figure
4a. (c) The same measurement as in the panel (b) with applyingthe
finite Vg,ad . All the curves are shifted by −V
0CNP (V
0CNP = 13, 9, and 11 V for the run of Vg,ad = +80, +40, and −50
V,
respectively) in Vg direction, i.e., the charge neutrality
points of the pristine graphene without the adsorbed oxygen are
taken aszero gate voltage. The top panel of (c) represents the σ vs
Vg −V
0CNP for the pristine graphene. The changes of σ vs Vg −V
0CNP
curve after a single and a double exposure to O2 (the time
duration of a single exposure is 30 s) are shown in the center
andthe lower panel of (c), respectively. Filled circles indicate
Vshift = VCNP − V
0CNP (the shift of the CNP) for each curve.
cg is the capacitance per unit area for the back-gatedgraphene
FET on 300 nm-thick SiO2 )
22, It is in therange of the values for BLG-FET in two-probe
config-uration previously reported6, and therefore we confirmthat
the graphene of the present BLG-FET has few de-fects that may
extremely enhance the chemical reactivityof graphene30.
Next we exposed the BLG-FET to 1 atm of high-purity
(>99.9995%) oxygen in the measurement cham-ber at room
temperature. Instead of measuring conduc-tivity with graphene kept
in the O2 environment, weperformed the short-time interval
exposure–evacuationcycles schematically shown in Figure 1a; O2
exposurewas done under the dc gate voltage Vg,ad, followed byrapid
evacuation in less than 10 s (the physisorbed O2molecules would be
removed immediately without chargetransfer), and eventually the σ
vs Vg measurement was
done with sweeping Vg under vacuum. In this cycle, wecan rule
out the possibility of the additional oxygen ad-sorption during
sweeping gate voltage for the σ vs Vgmeasurement since the system
was evacuated then. Inaddition, we found that the σ vs Vg curve did
not varyunder vacuum at room temperature at least for morethan
several hours, so that we can also rule out the pos-sibility of the
oxygen desorption during σ vs Vg mea-surement (taking ca. 10 min to
obtain a single σ vsVg curve). Therefore, just repeating the cycles
substan-tially realizes the long-time O2 exposure under Vg,ad,
thelength of which is denoted by total O2 exposure time,t. Figure
1b shows the change in σ vs Vg by repeat-ing the O2
exposure-evacuation cycles without applyinggate voltage during O2
exposure (run 1, Vg,ad = 0 V).The shift of the charge neutrality
point by the amountof Vshift(t) = VCNP(t) − V 0CNP toward the
positive di-
-
3
---- --
++
+
0
10
20
30
40
50
60
70
O2 Exposure Time (min)
0.1 1 10 100 1000 10000
1
2
3
4
5
0
no
x (
×1
01
2 c
m−
2)
Vg,a
d =
−50
V
Vg,a
d =
+80
V
Vg,a
d =
+40
V
Vg,a
d =
0V
electrondominant
hole dominant
Vsh
ift (V
)
Run 1
Run 4
Run 5
Run 2
Run 3
2
5
3
FIG. 2: Time dependence of Vshift and doping density nox with
doping due to the O2 exposure under application of variousVg,ad.
Solid and dotted curves are the fits based on the H kinetics and
the P kinetics (see text), respectively. The curve fittingis made
in the range of exposure time below 2000 min. The electron-dominant
region, where the Fermi level of BLG is higherthan the CNP (Vg,ad
> VCNP), is painted blue and the hole-dominant region (Vg,ad
< VCNP) is painted white. Carrier type isinverted between
electron and hole at the point indicated by arrows (numbers aside
correspond to the run number) during theevolution of the oxygen
adsorption.
rection was observed (Figure 1b), which represents holedoping to
graphene. Prolonged exposure brought furtherhole doping, and
eventually the doping density (inducedcharge by the oxygen
adsorption) nox(t) = (cg/e)Vshift(t)reached more than 5 × 1012 cm−2
within a time scaleof 103 min. Note that any hysteresis as observed
ingraphene FET in moist atmosphere29,31–34 was not foundin the
observed σ vs Vg curve, so that we can uniquely de-termine VCNP(t)
as a function of t. Another remarkablefeature is the hole
conductivity in highly doped regime,Vg − VCNP(t) < −40 V (i.e.,
|n| > 3 × 1012 cm−2). Theσ vs Vg curve distorted and exhibited
the sublinear de-pendence in this regime for the pristine BLG-FET
as canbe seen in Figure 1b. Yet it disappeared only after
theexposure to O2 for 1 min, whereas the carrier doping hasnot
proceeded much at that time. Thus this rapid changein conductivity
feature is discriminated from the slowerchange causing the shift of
the CNP; one possibility isthat the former is due to rapid
oxidation of the metal–graphene interface35,36, which does not
shift the Fermilevel of graphene but asymmetrically varies the
conduc-tivity.
Both VCNP and the mobility of the BLG-FET withthe oxygen
adsorbed were reset to the value for the pris-tine BLG-FET by
annealing the O2-exposed BLG-FETin vacuum at 200 ◦C, indicating
that O2 desorption read-ily proceeds at high temperature without
making anydefects. By virtue of this reversibility of the oxygen
ad-
sorption, we can repeat the conductivity measurementsin the
exposure–evacuation cycles as described above forthe same device
and compare the results. We addition-ally carried out four
consecutive measurements under thesame condition except that a
finite gate voltage Vg,ad wasapplied during O2 exposure; Vg,ad was
+80 V (run 2 andrun 3), −50 V (run 4) and +40 V (run 5). Figure
1crepresents the change of the gate-dependent conductiv-ity σ vs Vg
− V 0CNP at the initial step of the runs 2, 4,5: before O2
exposure, (i.e., after vacuum annealing)and after the first and
second exposure–evacuation cy-cles (the duration time for O2
exposure in each cycle is30 s, i.e., t = 0.5, 1 min, after the
first and second cycle,respectively). All the σ vs Vg − V 0CNP
curves collapsedonto almost the identical curve in the pristine
grapheneas shown in the top panel of Figure 1c. Since V 0CNP
waswithin 10±3 V for each run (see the caption of Figure 1),the
BLG-FET was realized to exhibit its pristine featurebefore O2
exposure. After the O2 exposure (the centerand the bottom panel of
Figure 1c) the gate-dependentconductivity changes similarly as was
also observed forrun 1 (Figure 1b), but the effect of applying
Vg,ad duringO2 exposure is marked by the clear difference in
Vshift(t).There is a tendency that Vshift(t) is larger for higher
Vg,adand smaller for lower Vg,ad, indicating that hole
dopingproceeds more intensively to graphene with higher Fermilevel.
This trend is pronounced on the increase in the ex-posure time, as
confirmed by comparing the center and
-
4
+80 V
+40 V
±00 V
−50 V
Vg,ad
0.1 1 10 100 1000
1013
1012
1011
1010
109
O2 exposure time (min)
dn
ox
/ d
t (c
m−
2 m
in−
1)
FIG. 3: Double logarithmic plot of time dependence ofdnox/dt.
Symbols are taken in common with Figure 2. Weestimate dnox/dt from
the differential between the neighbor-ing data points for each run
in Figure 2. Lines are linear fitsfor all the differential data.
The slope of each curve gives u =1.02, 0.91, 0.86, and 0.77
(dnox/dt ∝ t
−u) for the gate voltageVg,ad = +80, +40, 0, and −50 V,
respectively.
the bottom panel of Figure 1(c).
We tracked the temporal evolution of the gate-dependent
conductivity over a wide time range between100–103 min. Figure 2
represents Vshift for runs 1–5 withrespect to O2 exposure time, in
which the correspond-ing doping density owing to the oxygen
adsorption, nox,is also shown in the right axis. The tendency that
thehigh Vg,ad leads to rapid doping can be seen clearly overa whole
time range; e.g., to reach the doping level ofVshift = 40 V, it
took ca. 300 min for nonbiased BLG-FET. In contrast, hole doping is
so enhanced for theBLG-FET of Vg,ad = 80 V that it took only 4 min,
on theother hand so suppressed for that of Vg,ad = −50 V thatit
took more than 1000 min. The doping density increasesalmost
linearly with respect to log t for Vg,ad = +80 Vand +40 V, whereas
superlinearly for Vg,ad = 0 V and−50 V. The plots for runs 2 and 3,
having commonVg,ad = +80 V, are completely on the same line,
whichverifies that the thermal annealing in vacuum for the
re-producing of the undoped state in the BLG does notaffect the
behavior of adsorption.
Figure 3 shows the time dependence of the dopingrate dnox/dt
estimated from the differential betweenthe neighboring data points
in Figure 2. It is obvi-ous that the doping rate changes in
accordance withdnox/dt ∝ t−u. The power u is dependent on Vg,ad; u
≈ 1for Vg,ad = +80 V and it decreases for the runs withlower Vg,ad.
This deviates from the conventional Lang-murian kinetics for
molecular adsorption which wouldgive dnox/dt ∝ exp(−t/τ) with a
constant τ .Careful verification is necessary to inquire the
gate-
voltage-dependent and non-Langmurian temporal change
of the molecular doping since the rate for doping densitydnox/dt
is related to both of the rate for the chemisorp-tion of molecules
(dNox/dt, whereNox is the areal densityof the adsorbed oxygen
molecules) and the transferredcharge per adsorbed molecule (the
charge/molecular ra-tio, Z). Therefore, we analyze the mobility
that in-cludes the information of the scattering mechanism ofthe
conducting electrons and the charge of the adsorbedmolecules.
Within a standard Boltzmann approach37,the mobility is changed
inversely proportional to thedensity of the scattering centers
(i.e., the adsorbedmolecules), Nox. In the realistic case, the
inverse mobil-ity is given as a function of Nox and the carrier
densityn, which reads5
1
µ(n,Nox)=
NoxC(n)
+1
µ0(n)(1)
Here µ0(n) represents the mobility of the pristinegraphene
without the adsorbed oxygen. The coefficientC(n) represents the
feature of carrier scattering by theadsorbed oxygen. On the one
hand, the charged-impurityscattering38 gives C(n) ∝ [1 + 6.53√n (d+
λTF)]/Z2for the BLG in the low-carrier-density regime andin the
limit of d → 0 within the Thomas–Fermiapproximation38, where d is
the distance between theimpurities and the center of the two layers
of the BLG(see the inset of Figure 4a for the definition), and
thescreening length λTF = κh̄
2/4m∗e ≈ 1 nm (κ: dielectricconstant)38. On the other hand, the
short-range delta-correlated scatterers give the constant C(n) ≡
Cs38, orthe strong impurities with the potential radius R giveC(n)
∝ [ln(R√πn)]2 in the off-resonance condition39,which is a
decreasing function of n in the regime ofn ∼ 1012 cm−2 taking R to
be several angstroms. As forthe relation between the concentration
of the adsorbedoxygen molecules Nox and the O2-induced doping
den-sity nox, we assume that the charge Ze of each adsorbedoxygen
molecule dopes the carriers −Ze in the BLG, no-tably, nox = −ZNox.
To be exact, the amount of theinduced charge is not such a simple
function6 propor-tional to the number of adsorbed molecules due to
theenergy-dependent DOS of BLG40,41 and the anomalis-tic screening
effect therein5,6,42. Yet in the low energyregime of BLG where the
DOS is envisaged to be con-stant, the assumption above is
appropriate.Figure 4a shows the inverse Drude mobility µ−1 vs
nox plots at the carrier density of n = 2.5 × 1012 cm−2(marked
by the open circles in Figure 1b for run 1:Vg,ad =0 V) for Vg,ad =
+80, +40, 0, and −50 V. Linear increasein µ−1 with respect to nox
was found. This, along withthe linearity between µ−1 and Nox given
by Eq. (1), im-plies that Z is not a function ofNox, i.e.,
invariant againstthe increase of the adsorbed molecules.
Interestingly, theslope of µ−1 vs nox plot (the inverse of the
slope corre-sponds to C(n)|Z| in Eq. (1)) depends on Vg,ad.
Notethat before O2 was introduced (nox = 0), we observedµ−1 ≈ 28 V
sm−2 irrespective of Vg,ad, and thus the dif-ference in the
mobility by Vg,ad genuinely results from
-
5
10 5
50
40
30
20
2 3 4
Doping density, nox (×1012 cm−2)
1/μ
(V
sm
−2
)
SiO2 AdsorbedMolecules
BLGd
Ze Ze Ze Ze Ze
+80 V
+40 V
0 V
−50 V
+80 V
+40 V
±00 V
−50 V
Vg,ad
Vg,ad
a
b
0 1 2 3 4 5 60
2
4
6
C|Z
| (×
10
15 V
−1
s−
1)
Carrier density, n (×1012 cm−2)
FIG. 4: (a) Inverse mobility µ−1 vs the doping density noxfor
each run in Figure 2. Symbols are taken in common withFigure 2.
Lines are linear fits (as for Vg,ad = +80 V, thedata for both run 2
and run 3 are included). Inset: Adsorbedoxygen species with charge
Ze positioned at the distance daway from the center of BLG. (b)
C|Z| vs the carrier densityn (see Eq. (1)). For Vg,ad = +80 V, C|Z|
is acquired bygathering the data for run 2 and run 3. Theoretical
resultsbased on a charged-impurity scattering mechanism are
shownwith the various distance d and charge/molecular ratio Z:
thesolid line represents the result for d = 0.43 nm and Z =
0.38,the dashed line for d = 0.73 nm and Z = 0.38, and the
dottedline for d = 0.43 nm and Z = 0.28, respectively.
the adsorbed oxygen instead of other unintentional im-purities
on the BLG or the SiO2 substrate. In Figure 4b,the inverse of the
slope, C(n)|Z|, is shown for the var-ious carrier densities, n.
Therein we omit the data inthe low carrier regime of n < 2.5 ×
1012 cm−2, in whichthe residual carriers due to electron–hole
puddles can-not be disregarded and the carrier density n (and
thusalso the Drude mobility) cannot be correctly estimatedonly by
considering the gate electric field effect43. Sim-ilarly to the
charged impurity model rather than oth-erwise, C(n)|Z| is
increasing with n. The dependenceexperimentally observed, however,
still deviates from thetheoretical calculated results within the
charged impuritymodel plotted in Figure 4b for various d and Z
(assumingd and Z are invariant to n).
The difference in C(n)|Z| depending upon Vg,ad indi-cates that
the electronic polarity of graphene varies theadsorption states of
oxygen molecules, leading to the vari-ation of d and Z. When the
positive (negative) Vg,ad isapplied, negative (positive) carrier is
electrically inducedon graphene, which may modify the interaction
betweengraphene and the adsorbed oxygen molecules with thenegative
charge, e.g., the Coulomb interaction and theoverlap of the
orbitals. Eventually, the stable adsorptionstate is varied by
Vg,ad, leading to the difference in mo-bility. Besides, let us
recall that conductivity measure-ment process is set apart from the
O2 adsorption processand that constant Vg,ad is not applied when
the mobilityis measured (Figure 1a). Accordingly, whereas the
sta-ble adsorption state of oxygen during the
conductivitymeasurement may differ from that during adsorption,
theadsorbed oxygen molecules are kept in the former stateduring
conductivity measurement, and the mobility vary-ing by Vg,ad is
actually observed. This indicates that theenergetic barrier exists
for charge redistribution betweengraphene and the adsorbed oxygen
molecules (shown be-low), and once the adsorption is accomplished,
the chargeZe on each adsorbed oxygen molecules will not
immedi-ately change just after switching on/off the gate
voltage.One possible reason for the deviation between the
ex-perimental results and theoretical curve is that d
variesaccompanied with the change in n (or sweeping Vg).
Yetactually, since modifying d by several angstroms resultsin the
small change in (C(n)|Z|) as shown in Figure 4b,it is necessary to
investigate more about the behavior ofthe adsorbed oxygen molecules
in the gate electric fieldin a the future study.
It is controversial what kind of oxygen species does ac-tually
cause the hole doping to graphene. Because theelectron affinity of
O2 (0.44 eV
44) is much lower thanthe work function of graphene (4.6 eV45),
direct chargetransfer between them seems unfavorable. Instead,
withan analogy of the charge doping of diamond surface46,there is a
widely accepted28,33,47 hypothesis that the holedoping proceeds
through an electrochemical reaction46
such as: O2+2H2O+4e− = 4OH−, by which the charge
transfer is favorable due to the lowered free energy change∆G =
−0.7 eV28 on the condition that the oxygen pres-sure is 1 atm and
pH = 7. This electrochemical reactionneeds the aid of water that is
mostly eliminated in the ex-periment by annealing (we observed no
hysteresis in theσ vs Vg curve, that is, there are few charge traps
oftenattributed to residual moisture on graphene or its
sub-strate). Yet as for graphene deposited on the hydrophilicSiO2
substrate
32, it is possible that a small amount ofresidual water
molecules (more than the chemical equiv-alent of O2) are trapped on
SiO2 surface or voids, whichcannot be easily removed by the vacuum
annealing at200 ◦C in comparison with those on graphene surface.We
suggest that the electrochemical mechanism is plau-sible also in
our case, yet the adsorbed molecule couldbe other chemical species
than OH−, the charge of whichmay be dependent on Vg,ad.
-
6
e−
A
ζTS
ζG
ζCNP
‡E
ζads
T
∆G
Vg,ad > 0
cg
DOS of BLG
εF
0 0
‡E(εF(0))+ε
F(0)
‡E(εF(0))
‡E(εF(t))+ε
F(t)
DOS
nox
DOS
O2
εF(0)
εF(t)
‡E(εF(t))
a
b
FIG. 5: Schematic energy diagrams of the kinetics of
O2adsorption (H kinetics). (a) Path for electron transfer inthis
model is shown by the blue dotted arrow; electrons inBLG (the
electrochemical potential ζG) are transferred toO2 molecules via
the transition state (the circled T at thelevel of ζTS ), giving
the adsorbed oxygen species (the cir-cled A at the level of ζads).
The activation energy, the freeenergy change, and the level of the
CNP are denoted by ‡E,∆G and ζCNP, respectively. The Fermi level is
defined byεF = ζG− ζCNP. As a demonstration, the case for Vg,ad
> 0 ispresented. (b) Temporal change in the activation energy
andthe Fermi energy due to the adsorption of oxygen moleculesto BLG
negatively doped by the positive gate voltage (as incase of panel
a). The left panel represents the case beforeoxygen adsorption (t =
0), and the right panel represents theoxygen exposure for the time
t. Here the energy is measuredfrom the CNP. The red and the blue
tick marks denote thelevel for the transition state and the Fermi
level, respectively.Oxygen adsorption lowers the Fermi level,
accompanied withthe increase in hole doping of nox (equal to the
area of grayed
part,∫ εF(0)εF(t)
D(εF) dεF), and the activation energy increases
according to Eq. (2)
In light of the discussion above, the
electrochemicaldescription33,48 is expected to be applicable for
the ob-served adsorption kinetics of oxygen to the BLG. Herewe
premise that the molecular adsorption is determinedby the
electrochemical potential of graphene, and con-sider the charge
transfer kinetics in an approach basedon Butler–Volmer theory49,50.
The model is schemati-cally depicted in Figure 5. The probability
of the adsorp-tion reaction is determined by the electrochemical
poten-tial of graphene (ζG) and that in the equilibrium condi-tion
of the oxygen-chemisorption reaction (ζads). When
∆G = ζads − ζG < 0, the electrons favorably transferfrom of
graphene to the adsorbed oxygen (denoted by“A” in Figure 5a), and
the oxygen-adsorption reactionproceeds. For charge transfer, the
electrons should gothrough some energy barrier; we assume that
electronstunnel from BLG to the O2 molecules via a single
transi-tion state (denoted by “T”), whose electrochemical
po-tential is ζTS. The difference
‡E = ζTS − ζG correspondsto the activation energy of the
oxygen-chemisorption re-action, which determines the frequency of
the electrontransfer. Whereas ζG is dependent on the Fermi level
εFas ζG = εF+ ζCNP (ζCNP is the electrochemical potentialof the
CNP), we envisage that ζTS (or
‡E) is a functionof εF as well. In the framework of the
Butler–Volmertheory, we obtain the dependence of ‡E on εF as
‡E(εF + dεF) =‡E(εF)− α dεF, (2)
where α(> 0) is a constant related to the “transfer
coef-ficient” in the Butler–Volmer theory that associates
theactivation energy with the electrochemical potential (notthe
Fermi energy); thus herein we call α as “pseudo trans-fer
coefficient” (see Supporting Information for detail inthe
derivation). That is, we have the assumption thatthe activation
energy scales linearly with the Fermi en-ergy. Further assuming
that the molecular adsorptionrate dNox/dt is controlled by the
electron transfer pro-cess and is not strongly affected by other
contributionssuch as molecular diffusion14, it is given by
dNoxdt
= χD(
εF +‡E(εF)
)
f(
εF +‡E(εF); εF
)
, (3)
where D(ε) is the density of states (DOS) of BLG (ε isthe energy
measured from ζCNP) and f(ε; εF) = [1 +(ε− εF)/kBT ]−1 is the
Fermi–Dirac distribution func-tion. The coefficient χ does not
depend on εF (if thedistance between the adsorbing molecules and
BLG var-ied depending on εF or Vg,ad, the tunneling frequencywould
be affected so that χ might be dependent on themas well; yet herein
we ignore such effect for simplicity).The right-side of Eq. (3)
represents the tunneling rate ofthe electron from the graphene to
oxygen at the energylevel of transition state, ε = εF +
‡E(εF) = ζTS − ζCNP.According to Eq. (2) and Eq. (3), the
molecular adsorp-tion rate is dependent on the Fermi level of
graphene.Using them, we can explain both the temporal evolutionof
the doping rate and its dependence on the gate voltageVg,ad.Let us
discuss the temporal change in the doping rate.
The Fermi level of graphene is lowered with the increaseof the
adsorbed oxygen molecules, because the positivecharge is induced on
graphene by the charge Ze theypossess. Recalling that nox = −ZNox,
the doping rateis given by dnox/dt. Furthermore, since
‡E ≫ kBT isfulfilled as shown later, we also approximate that
f(εF+‡E(εF); εF) ≃ exp(−‡E(εF)/kBT ). Using the relationdnox =
−D(εF)dεF, we acquire a formula describing thetemporal change of
the Fermi level:
-
7
−D (εF(t))dεF(t)
dt=
pkBT
αteD
(
εF(t) +‡E (εF(t))
)
exp
(
αteεF(t)− εF(0)
kBT
)
, (4)
where εF(t) = εF(t, Vg,ad), expressing that the Fermilevel is a
function of the exposure time t and the gatevoltage Vg,ad, and
εF(0) = εF(0, Vg,ad), the Fermi levelat t = 0. We have specifically
defined two constants, thepseudo transfer coefficient αte (the
subscript “te” abbre-viates “temporal evolution”) and
p = −αteZχkBT
exp
(
−‡E (εF(0))
kBT
)
(5)
The right side of Eq. (4) represents the product of thecharge
transfer frequency and the amount of charge peradsorbed molecule,
whereas the left side does the resul-tant amount of the doped
charge. Because BLG (or alsosingle layer graphene) has the low DOS
around the CNPcompared to metal, the small amount of carrier
dopingresults in the large shift in the Fermi level, which
effec-tively controls the kinetics. Thus the adsorption kineticsis
well described by Eq. (4), the equation focusing on theFermi level.
When we envisage that the BLG is approx-imately described by
two-dimensional parabolic disper-sion of the free electron, the DOS
becomes constant asD ≡ DP = γ⊥/π(h̄vF)2, where vF = (
√3/2)γ0a/h̄ is the
Fermi velocity in SLG, a = 2.46 Å is the in-plane
latticeconstant, and γ0 = 3.16 eV and γ⊥ ≈ 0.4 eV51,52 are
theintrasheet and intersheet transfer integrals, respectively.In
this case (hereafter labeled as P kinetics), Eq. (6) isreadily
integrated, giving
nox(t) = −{εF(t)− εF(0)}DP =(
kBTDPαte
)
ln(1 + pt)
(6)Note that Eq. (6) satisfies dnox/dt ∝exp[−αtenox(t)/kBTD] and
is equivalent to the in-tegrated form of Elovich equation53,54, the
empiricalequation that is widely applicable to chemisorptionsonto
semiconductors. When the hyperbolic DOS ofBLG41 is reflected to Eq.
(4), more accurate but morecomplicated expression of εF(t) is
acquired (denoted asH kinetics), given by
− αtekBT
exp
(
αteεF(0)
kBT
)
S[εF(0), εF(t)] + pt = 0, (7)
where S[εF(0), εF(t)] is a function that depends on theDOS at
the Fermi level and that at the transition statelevel (derived in
the Supporting Information).We performed curve fitting of the
experimental results
of nox(t) with Eq. (6) and Eq. (7) for P kinetics andH kinetics,
respectively. The difference in Vg,ad by runsis simulated by the
dependence of εF(0) on Vg,ad firstwithout considering the
gap-opening effect55,56, that is,
we calculate εF(0) using the relation that the charge
ofcg(Vg,ad−V 0CNP) doped on BLG by applying Vg,ad is equalto
∫
εF(0)
0D(ε)dε. Irrespective of the kinetic models, All
the theoretical curves are well fitted to the
experimentalresults except those for run 4 in the range above
103
min. Eq. (4) is invalid in the first place in the long-time
regime in which the adsorption rate is almost aslow as the
desorption rate, since the present treatmentincludes no
contribution of desorption. The deviationis, however, contrary to
the expectation; the desorptionshould suppress the evolution of the
hole doping yet theenhanced doping was actually observed. Thus we
suspectthat it is due to long-time scale chemisorption of
oxygenonto graphene which is ubiquitously observed in
carbonmaterials57,58. Note that the several volts of offsets
areadded in Vshift (corresponding to the doping density of 2×1011
cm−2) to improve the fitting in the time range of t ≤100 min. This
small offset corresponds to a fast reactionthat finishes at the
very initial stage of adsorption, e.g.,due to the reactive
chemisorption of O2 to the defect oredge site of graphene59,60.
Figure 6 shows the profiles of the fitting results.
Prac-tically, the fitting parameters are following two: αte andp,
but in order to derive the initial activation energy be-fore the
oxygen adsorption, ‡E(εF(0)), from p based onEq. (6), we briefly
assume that the charge/molecular ra-tio is independent of the gate
voltage and determine thatZχγ⊥ = 1×105 eV2 min−1 from the
pre-exponential fac-tor in the literature33, coxνκel ∼ 1017 cm−2s−1
(coxνκelin the literature corresponds to χγ⊥/π(h̄vF)
2 in this pa-per). Note that if we assume another value than
Zχγ⊥ =1 × 105 eV2 min−1, it results in a uniform shift of
thecalculated ‡E(εF(0)). In addition, the charge/molecularratio of
the adsorbed molecule Z is likely dependent onVg,ad from the
discussion about the mobility, but it leadsthe shift of ‡E(εF(0))
only by ∼ kBT = 0.026 eV. Onthe one hand, αte (representing the
temporal change ofthe activation energy) exhibits a significant
deviation be-tween the H kinetics and the P kinetics(Figure 6a), or
de-pends on the treatment of the DOS of BLG. This devia-tion is
understood as follows: H kinetics reflects the DOSof BLG that is a
monotonically increasing function withrespect to |εF| having a
minimum (D = DP) at the CNP(Figure 6(c)), yet P kinetics does not.
Since the down-ward shift of the Fermi level upon the oxygen
adsorptiondepends on the DOS at the Fermi level, the range of
thechange in the Fermi level differs between two kineticsmodels
(Figure 6(c)). Thus αte, related with the Fermilevel by Eq. (2), is
calculated differently. This result iscontrasted with the
conventional electrochemical reactionon the metal electrodes in
which the kinetics is not signif-
-
8
0 31 2DOS /DP
P H
0.2
0.1
0
+80 V+40 V0 V–50 V
–0.1
–0.2
–0.3
Vg,ad
εF (
eV
)
CNP
−50 0 50
0
2
4
Vg,ad (V)
αte
H
P
αgf
−0.2 0 0.2
0.5
0.4
0.3
εF(0) (eV)
‡E
(εF(0
))
(eV
)
H
P
a
c
b
FIG. 6: Summary of parameters obtained by the curve fittingin
Figure 2 with P kinetics (P) and H kinetics (H) compared.(a)
Dependence of the pseudo transfer coefficient αte on Vg,ad.The
pseudo transfer coefficient αgf acquired by the linear fit-ting to
panel b is also plotted. (b) Initial activation energy‡E(εF(0))
plotted as a function of εF(0) = εF(0, Vg). (c) (Leftpanel) Density
of states (DOS, solid line) for BLG as a func-tion of the Fermi
energy, where DP (DOS at the energy ofεF = 0) is taken as unit of
the DOS. The solid line denotesthe DOS applied for the H kinetics.
In P kinetics the DOSis treated as constant; D = DP (dotted line).
(Right panel)Change of the Fermi level by oxygen adsorption as a
functionof Vg,ad. Bars and boxes represent the range calculated
underP kinetics and H kinetics, respectively, assuming γ⊥ = 0.4
eV.The Fermi level before the oxygen adsorption (εF(0)) is at
thepoint indicated by triangles (black squares) for H (P)
kinetics,whereas the Fermi level shifts downward with the increase
ofthe adsorbed oxygen, and eventually reaches the bottom endof the
boxes (bars) in the end of the oxygen adsorption forthe H (P)
kinetics. The energy is measured from the CNP(dashed line), and the
gap-opening effect is not considered.
icantly affected by the DOS of the electrodes and is justowing
to the low DOS of the BLG with comparison to themetal. On the other
hand, we found that ‡E(εF(0)) is adecreasing function of εF(0) =
εF(0, Vg,ad) (shown in Fig-ure 6b, therein we plot ‡E(εF(0)) with
respect to εF(0)instead of Vg,ad). From Eq. (2), the slope of the
plots inFigure 6b corresponds to the pseudo transfer coefficientα,
and we found that αgf = 0.36 and 0.42 for P kineticsand H kinetics,
respectively (the subscript “gf” abbrevi-ates “gate electric
field”). Herein we distinguish αgf fromαte; being different from
αte that is calculated based on
the temporal Fermi level shift by oxygen adsorption (thusαte
inevitably includes the oxygen adsorption effect), αgfis acquired
by tuning the Fermi level electrically at t = 0before oxygen
adsorption. We found that αgf is muchsmaller than αte(≥ 1), or
rather near 0.5, a typical trans-fer coefficient for simple redox
reactions48,49 (Figure 6a).Specifically, the oxygen adsorption
effect included onlyin αte but not in αgf is attributed, e.g., to
the electricdipole layer61 formed between graphene and the
adsorbedmolecules and the Coulomb interaction between the ad-sorbed
oxygen molecules. We expect that these effectsalso raise the
activation energy roughly in proportionalto the number of molecules
Nox (or the doping densitynox), and thus we have the expression for
the additionaladsorption effect: d‡E = ξmoldnox =
−ξmolD(εF)dεF(ξmol: the proportional coefficient; herein we use
therelation dnox = −D(εF)dεF again). Then we acquireαte ≃ αgf +
ξmol〈D(εF)〉 (〈D(εF)〉 denotes the averageDOS in the range of the
Fermi level for each run), whichindicates that αte is large when
the DOS is large inthe level far away from the CNP (see Figure 6c).
In-deed, as shown in Figure 6a, αte for H kinetics showsthe
V-shaped dependence on Vg,ad with the minimum forVg,ad = +40 V,
which gives the smallest average DOS.Though the kinetics for the
molecular adsorption is af-fected by various effects as mentioned
above, we representthem by the parameter αte and succeed in
accounting forthe observed kinetics in a facile way.
Finally let us account for the power-law dependenceof dnox/dt ∝
t−u shown in Figure 3. It is helpful tolook on the simpler P
kinetics for the assessment ofdnox/dt; from Eq. (6), we obtain
dnox/dt ∝ p/(1 + pt).Approximately we have dnox/dt ∝
(
u〈t〉u−1)
t−u where
u ≃ [1 + (1/p〈t〉)]−1 ≤ 1 (the time 〈t〉 is the center ofthe
expansion of ln(dnox/dt) in terms of ln t, and it is agood
approximation if p〈t〉 ≫ 1, or otherwise if p〈t〉 ≃ 1in the time
range such that t = [10−1〈t〉, 10〈t〉]). Sincep is intensively
dependent on Vg,ad (recall that (i) p isexponentially decaying
against ‡E(εF(0)) as representedin Eq. (5), (ii) ‡E(εF(0)) linearly
decreases with respectto εF(0) with the slope of −αgf as shown in
Figure 6c,(iii) εF(0) is an increasing function of Vg,ad. We
acquiredp =19.6, 2.9, 0.98 and 0.32 for Vg,ad = +80, +40, 0,and −50
V, respectively, by fitting within the P kineticsmodel), we can
find that u is almost unity for a positivelyhigh Vg,ad and tends be
smaller for negatively high Vg,adwithin the time range
experimentally scoped, which isconsistent with the observed
behavior. When the elec-trochemical mechanism governs the kinetics
of the oxy-gen adsorption, the activation energy of the charge
trans-fer continually increases with the O2 exposure time
in-creasing. This effect leads to non-Langmurian kineticsof the
oxygen adsorption and the power-law decrease ofdnox/dt, even though
neither the desorption process northe saturation limit of
adsorption are taken into consid-eration.
In BLG, it is known that a band gap opens due to theenergy
difference between two layers9. The gate electric
-
9
field as well as the adsorbed oxygen may produce sucha strong
energy difference that the eventual band gapshould affect the time
evolution of molecular adsorption.The band gap opening effect is
expected to exhibit mostprominently when the Fermi level goes
across the CNP(at the point shown by arrows in Figure 2), while we
can-not find such behavior obviously. We guess it is partly
be-cause most of the adsorbed oxygen molecules exist in
theinterface between graphene and the gate dielectric SiO2.For the
band gap opening effect to appear, it is neces-sary that the gate
electric field and the molecular fieldenhance each other when the
Fermi level is near the CNP(i.e., the charge induced by the gate
electric field and thatby the adsorbed molecules including
unintentional resid-ual impurities on the SiO2 substrate are
balanced), yet itis possible only when the molecules mainly adsorb
on thetop surface of BLG, and not for the molecules adsorbedin the
interface (Figure S2, Supporting Information). Orit may be partly
because the disordered potential dueto the impurities in the
substrate fluctuates the energylevel around which the band gap
exists62, eventually blur-ring band gap opening effects and
chemical reactivity63
of BLG. Details about the band-gap opening effects arediscussed
in the Supporting Information.In summary, we investigated the weak
chemisorption of
O2 molecules on bilayer graphene by measuring its trans-port
properties. The hole doping due to O2 chemisorp-tion is remarkably
dependent on the gate voltage, andthe amount of the doped carrier
increases with O2 ex-posure time, the rate of which is in
accordance with∝ t−u(u ≤ 1) rather than with conventional
Langmuiriankinetics. We conclude from these that an
electrochem-
ical reaction governs the O2 chemisorption process, inwhich the
rate of the chemisorption is determined bythe Fermi level of
graphene, and indeed succeed in ac-counting for the observed
kinetics by the analysis basedon the Butler–Volmer theory. We also
found that thechemisorbed molecules decrease the mobility of
graphene,and interestingly, the mobility change is dependent onthe
gate voltage applied during the adsorption, indicat-ing that the
adsorption state, e.g., transferred charge ordistance between a
molecule and graphene, can be mod-ified electrically. Graphene,
offering a continuously tun-able platform for study of
chemisorptions on it, realizesthe electrical control of the
adsorption by gate electricfield, a novel and versatile method in
which we wouldexplore extensively a wider variety of host–guest
interac-tions between graphene and foreign molecules.
Supporting Information. Additional descrip-tions about (i) the
experimental method, (ii) theelectrochemistry-based kinetics model
and the mathe-matical derivation for it, and (iii) an expanded
discussionabout the gap-opening effects.
Acknowledgments
The authors acknowledge support from Grant-in-Aidfor Scientific
Research No. 20001006 from the Ministryof Education, Culture,
Sports, Science and Technology,Japan. The authors thank M. Kiguchi,
T. Kawakami, K.Yokota, and Y. Kudo for useful discussion.
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