Table Of ContentDetermination of substrate pinning in epitaxial and supported graphene layers via
Raman scattering
∗
Nicola Ferralis, Roya Maboudian, and Carlo Carraro
Department of Chemical and Biomolecular Engineering,
University of California, Berkeley, California 94720†
(Dated: January 26, 2011)
The temperature-induced shift of the Raman G line in epitaxial graphene on SiC and Ni sur-
1 faces, as well as in graphene supported on SiO2, is investigated with Raman spectroscopy. The
1 thermal shift rate of epitaxial graphene on 6H-SiC(0001) is found to be about three times that of
0 freestanding graphene. This result is explained quantitatively as a consequence of pinning by the
2 substrate. In contrast, graphenegrown on polycrystalline Nifilms is shown tobeunpinned,i.e., to
behaveelasticallyasfreestanding,despitetherelativelystronginteractionwiththemetalsubstrate.
n
Moreover, it is shown that the transfer of exfoliated graphene layers onto a supporting substrate
a
J can result in pinned or unpinnedlayers, dependingon thetransfer protocol.
4
PACSnumbers: 65.80.Ck,68.65.Pq,63.22.Rc
2
]
l Graphenefilmsoninsulatingsubstrateshavegreatpo- 0.1% strained monolayer
al tentialforrealizationofhighspeedelectronicdevices[1], 1595 0.5% strained monolayer
h as demonstrated recently by graphene transistor opera- -1m]
s- tionnearterahertzfrequencies[2]. Comparedtoresearch on [c1590
e into graphene’s remarkable electronic properties, much siti
m less is known about its mechanical properties. Yet, the k po1585
a
e
t. responseofgraphenefilmstomechanicalstimuliisanim- G p
a portant fundamental topic, with potentially far reaching an 1580
m m
applications. Noteworthyamongtheseisstrainengineer- Ra
- ing,whichoffersthetantalizingprospectofmanipulating 1575
d
n graphene’s electromagnetic properties [3, 4]. Moreover,
300 350 400 450 500 550
o mechanical energy transfer processes dominate the re- Temperature [K]
c sponse(andhence,dictatethedesign)ofgraphene-based
[ nanomechanical transducers and actuators [5]. Lastly, FIG. 1. Raman thermal line shift of the G vibrational mode
forepitaxial graphenefilms, preparedwith differentamounts
1 thesuccessofmanypromisinggraphene-on-insulatorfab-
of strain on 6H-SiC(0001).
v rication processes hinges on suitable mechanical manip-
3
ulation of single layers of material [6–8].
7
6 Modeling of a graphene film as an elastic continuum onto an oxidized Si substrate results in either pinned or
4 can offer much valuable insight into its mechanical re- unpinnedfilmsdependingonthetransferprotocol. These
.
1 sponse [9, 10]. The constitutive ingredients of such results may seem surprising at first, given that graphene
0 model, namely Young’s modulus and bending rigidity, onSiCisknowntogrowontopofa“buffer”layer,which
1 are known experimentally [11]. However boundary con- decouples it from the substrate [12–15], while on metals,
1
ditionsmustalsobespecifiedinordertosolvethemodel. strong interactions involving hybridization of electronic
:
v These are determined by the complex interactions be- orbitals are believed to exist [16]. The explanation of
Xi tween graphene film and substrate, which ultimately re- this apparent paradox resides likely in the nature of the
sult into pinned or unpinned films. A pinned layer im- potential energy landscape on semiconductor vs metal
r
a pliescontinuityoftangentialdisplacements,whileanun- surfaces, the former having a highly corrugated poten-
pinned layer implies zero tangential stress. tial,thelatteramuchsmootherone. Itisthestrengthof
In this Letter, we show that information about film thelateral,ratherthanthevertical,interactionsbetween
pinning is obtained unambiguously from measurements film and substrate that is responsible for pinning.
of the temperature dependence of the Raman G line po- Figure1showsthevaluesofthefrequencyofthezone-
sition,whichallowonetoseparateout“spurious”effects, center optical phonon of graphene (the G line) [17, 18]
like chargeor strain,thatdominate the absoluteline po- recordedontwoepigraphenemonolayersamplesgrownin
sition at any given temperature. The significance of the ultrahigh vacuum by sublimation of Si from the (0001)
resultisillustratedinthreedifferentsystems. Growthby face of a 6H-SiC crystal under Si flux [19]. Note that
sublimationon SiC(0001)is shownto yieldpinned films. epigraphene films on SiC can be deliberately produced
Growth by chemical vapor deposition on Ni films yields with different amounts of internal stress at room tem-
unpinned films. Finally, transfer of an exfoliated film perature, and hence, the G line frequency at room tem-
2
peraturecouldtake onanyvalue between1580and1605 5
−1
cm in a given sample, depending on sample prepara-
tion[20]. ThesamplesinFig.1hadstrainvaluesof0.1% 0
and 0.5% at room temperature. Previous measurements
1]
on freestanding graphene monolayers produced by exfo- -m
c -5
lrieadtsiohniftfrroamteHofO-P0.G01c6rycsmta−l1s/[K21i,n22th]eobtesemrvpeedraatnuraevrearnaggee hift [
s
100K<T <300K,inagreementwiththeoreticalcalcu- y -10
c
n
lations on 2D graphene [23]. The redshift rates observed e
u
inepigraphenearealmostthreetimesaslarge,regardless eq-15
of the amount of internal stress in the films observed at Fr "Freestanding" graphene - ref. [21]
room temperature. Thus, the slope of the curves is in- "Freestanding" graphene - this work
-20 "Freestanding" graphene - calculation, ref. [23]
dependent of the initial amount of stress present in the Epitaxial graphene on SiC - this work
film, while the absolute position of the G line can vary Epitaxial graphene on SiC - calculation, this work
-25
for several reasons (such as engineered strain [24, 25] or 100 200 300 400 500
Temperature [K]
doping [26, 27]), which are decoupled from the thermal
redshift. This implies that a single measurement at con-
FIG. 2. Comparison between theoretical and experimental
stant temperature is not sufficient to determine whether
thermal G-line shifts for freestanding and epitaxial graphene
a film is pinned to the substrate or not. Pinning is in-
films(re-plottedfromFig.1). Thethermallineshiftsinboth
stead ascertainedby performing measurements at differ- thetheoretical curvesand theexperimentaldataarereferred
ent temperatures. to theposition of theG line at absolute zero.
To understand the behavior of the thermal line shift,
recall that at constant pressure, the rate of change of
phonon frequency with temperature is given by the sum Note that the integration constant, ω(T0) (where T0
of two terms, isanarbitraryreferencetemperature),neednotcoincide
with the line position of a freestanding film in equilib-
dω
=χ (T)+χ (T) (1) rium: its value may be shifted due to engineered stress
T a
(cid:18)dT(cid:19)P or charge effects, for example. The results of the calcu-
lations are shown in Fig. 2, along with the data. For
where:
comparison, we also plot the calculated thermal G-line
∂ω ∂a ∂ω shift of free graphene[23], along with experimentalmea-
χ (T)= ; χ (T)= . (2)
T (cid:18)∂a(cid:19) (cid:18)∂T(cid:19) a (cid:18)∂T(cid:19) surement from ref. [21], which we have augmented here
T P a
byperformingmeasurementsonfreefilmsathighertem-
Phonon frequencies depend on temperature in two peratures.
ways, explicitly and implicitly through the lattice con-
The agreement between theory and experiment con-
stanta. Theexplicitdependenceiscontainedinthecon-
firms thatonthe SiC(0001)surface,substrate effects are
stantspecificareatermχ ,whichisduetomany-phonon
a entirely accounted for by using the boundary conditions
interactions: it reflects the anharmonicity of the C-C
appropriate for a pinned monolayer. However, as shown
potential in the graphene lattice. The implicit depen-
below, this is not to be regarded as a forgone conclu-
dence, χ , is given by the product of the rate of change
T sion: we have observed strikingly different behavior on
of frequency with lattice constant a, times the rate of
different substrates.
lattice thermal expansion. It is this latter term that is
Graphene monolayer growth by chemical vapor depo-
affected by pinning of the layer to the substrate, i.e., by
sition (CVD) has been demonstrated on several metal
boundary conditions at the substrate-film interface. For
surfaces, including Ni substrates [6], where strong film-
the pinned layer,we assume continuity of tangential dis-
substrate interactions have been observed [29, 30]. In
placements, and calculate the frequency shift of the G
some cases, interactions lead to the suppression of the
lineinepigraphenebyusingthecoefficientoflinearther-
Raman signal, possibly owing to the hybridization be-
mal expansion (CTE) of SiC, αSiC [28], but keeping for tween the metal d bands and the carbon p bands [31].
z
all other terms the ab initio values appropriate for free-
On polycrystalline Ni films, perfect epitaxy is not ex-
standing graphene (denoted by the the subscript “free”
pected,andinfact,aRamansignalisalwaysobserved[6].
and taken from ref. [23]):
We have measured the thermal line shifts for graphene
T monolayersgrownby CVD on thin Ni films (300 nm) on
′ ′
ω(T)=ω(T0)+ dT χa,free(T ) SiO2/Si substrates [32]. The results are shown in Fig. 3,
Z
T0 (3) along with calculated values for freestanding graphene
T ′ ′ αSiC(T′) [23], for graphene on Si, and for graphene on bulk Ni.
+ZT0 dT χT,free(T )αfree(T′). We emphasize that the mechanical behavior of a well
3
Sample dω/dT T range Ref. Theory Ref.
5 G"Frraepehsetanned oinng N" gi-rfialmph/SeinOe2 /-S cialculation ref. [23] [cm−1/K] [K]
Graphene on Si - calculation, this work Freestanding -0.009±0.002 150-250 [21] -0.011 [23]
0 Graphene on Ni - calculation, this work
-1cm] -5 Pressed on SiO2/Si --00..001552±±00..000034 330000--440000 [2∗∗1] --00..004167∗ [2∗∗3]
hift [ On Au/SiNx/Si -0.040±0.002 400-500 [38] -0.052∗ ∗∗
y s-10 Epi-G on SiC -0.043±0.013 300-400 ∗∗ -0.048 ∗∗
quenc-15 ∗ Calculation trea∗ts∗tThheissuwbosrtkra.te as puresilicon.
e
Fr-20
TABLE I. Comparison between values of the thermal line-
-25 shiftratesdω/dT measuredoverdifferenttemperatureranges
for graphene films prepared by different methods and calcu-
250 300 350 400 450 500 550 600 650 700 lated values from Eq. 3.
Temperature [K]
FIG.3. TheexperimentalthermallineshiftsoftheRamanG 10 "Freestanding" graphene - calculation ref. [23]
lineforamonolayergraphenegrownviaCVDonaNi/SiO2/Si "Freestanding" graphene - this work
substrateiscompared tothecalculated valuesofthethermal 5 Graphene pressed on SiO2/Si - this work
Graphene on Au/SiN/Si - ref. [38]
shifts for freestanding graphene, graphene pinned to Si, and x
graphene pinned to Ni (from Eq. 3, using the linear thermal -1m] 0 Strongly interacting graphene on Si - calculation, this work
expansion coefficient of Si[33] and Ni[34], respectively.) c
hift [ -5
s
y
c
adhered thin film (or thin film stack) on a thick sub- en-10
u
strateisdictatedbythe propertiesofthe bulksubstrate. q
e
When comparing to our experiment, the relevant CTE Fr-15
to be used in Eq. 3 is that of Si [33], since the Si wafer
thickness is 500 µm vs. 300 nm Ni film thickness. The -20
good agreement between the experimental data and the
theoretical curve for freestanding graphene, rather than 250 300 350 400 450 500 550 600 650 700
Temperature [K]
for graphene on Si substrate, indicates that on polycrys-
talline Ni films, graphene is completely unpinned from
FIG.4. ExperimentalthermallineshiftsoftheRamanG-line
the substrate and it behaves essentially like a freestand-
forfreestandinggrapheneandforgraphenefilmspressedonto
ing layer. This free-like behavior can be rationalized by a SiO2 and Au/SiNx [38] substrates.
considerations of surface potential corrugation, which is
usually much smaller on metal surfaces compared to in-
sulators(orsemiconductors). Since filmpinning involves showsthethermallineshiftsmeasuredforthesetwosam-
tangential displacements, it is plausible that graphene ples(solidandemptysquares,respectively). Forcompar-
monolayersgrownonmetalsurfaces,arefreetoslidelat- ison,data correspondingto graphenelayerspressedonto
erally, the rather strong electronic interactions with the Au/SiN /Si substrates are plotted from ref. [38]. A vi-
x
substrate notwithstanding. sual inspection shows very similar thermal line shifts for
Otherfabricationmethodsinvolvetransferofgraphene graphenepressedonSiO2/SiandAu/SiNx/Sisubstrates
layersontoan inertsubstrate, usually aninsulator [6–8]. (Figure4). The experimentaldataiscomparedwithcal-
The question then arises whether these supported layers culationsforfreestandinggrapheneandgraphenepinned
are free or pinned. Interestingly, two different transfer to a Si substrate, (solid and dashed lines in Fig. 4, re-
methods leadconsistently to contrastinganswers. In the spectively). Agreement between theory and experiments
first method, we produced graphene films by mechanical points out that only the films dispersed from solution
exfoliation of HOPG crystals [35]; the substrate die (a behaveasfreestanding,whereaspressingorstampingre-
300 nm thick thermal oxide film on Si) was dipped in sults in pinned films. Consistent with our discussion of
a toluene solution where graphene flakes were dispersed. tangential vs vertical interactions, we believe pinning of
Graphene layers thus collected are referred to as “free- pressed films is brought about by their better conforma-
standing.”Inthesecondmethod,graphiteplateletswere tion to nanoscale surface roughness, as well as by the
exfoliated from HOPG samples using ScotchTM tape, squeezing out of liquid-like layers at the film-substrate
and immediately pressed against the SiO2/Si substrate interface (e.g., physisorbed water [39]). The values of
die. After sonication of the die to remove the larger dω/dT and their corresponding temperature ranges are
flakes,∼1µmsingleanddoublelayersofgraphene(char- reported in Table I.
acterized by Raman spectroscopy [36] and optical mi- In summary, we have shown that the position of the
croscopy[37])remainedattachedtothesurface. Figure4 Raman G line of graphene monolayers at a given tem-
4
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