Ferroelectric gating of graphene 5

Chapter 5
Quasi-periodic nanoripples in
graphene grown by chemical vapor
deposition and its impact on
charge transport
In the last chapter, we utilized mechanically exfoliated graphene to demonstrate a
novel non-volatile memory device. However, it is impossible to use mechanically
exfoliated graphene for large-scale applications. Ultimately, It needs to b e replaced
by large scale graphene, such as CVD graphene.
This chapter will be devoted to a better understanding CVD graphene. We ob-
served a new type of quasi-periodic nanoripple arrays in CVD graphene. The impact
of these ubiquitous nanoripple arrays to the charge transp ort of CVD graphene was
also studied.
The results discussed in this chapter have been published in ACS Nano [100].
61
62
5.1 Introduction and background
The technical breakthrough in synthesizing graphene by chemical vapor deposition
methods (CVD) has opened up enormous opportunities for large-scale device appli-
cations [44, 50]. In order to improve the electrical properties of CVD graphene grown
on copper (Cu-CVD graphene), recent efforts have focussed on increasing the grain
size of such polycrystalline graphene films to 100 micrometers and larger (Fig. 5.1)
[44, 50]. While an increase in grain size and hence, a decrease of grain boundary
density is expected to greatly enhance the device performance, here we show that the
charge mobility and sheet resistance of Cu-CVD graphene is already limited within
a single grain. We find that the current high-temperature growth and wet trans-
fer metho ds of CVD graphene result in quasi-periodic nanoripple arrays (NRAs).
Electron-flexural phonon scattering in such partially suspended graphene devices in-
troduces anisotropic charge transport and sets limits to both the highest possible
charge mobility and lowest possible sheet resistance values. Our findings provide
guidance for further improving the CVD graphene growth and transfer process.

Currently, CVD growth typically require high temperature of 1000-1050
◦
C, very
close to the melting point of Cu at 1083
◦
C. This leads to Cu surface reconstruction
and local surface melting [101, 102], during graphene growth, making high density
Cu single-crystal terraces and step edges ubiquitous surface features. Taking into
account the negative thermal expansion coefficient of graphene, this leads to new
surface corrugations in CVD graphene during the cool down process [103]. Previously
grain boundaries have been identified as one of the main limiting factors to degrade
graphene quality [104]. While the heptagon and pentagon network [104, 105] at grain
boundaries does disrupt the sp
2
delocalization of electrons in graphene, it remains
63
b
35 µm
Graphene
Cu (001)
Cu (111)
[001]
b
d
Figure 5.1: (a) Scanning electron microscopy (SEM) image of CVD graphene on
copper. By tuning the growth conditions, more than 100 µm graphene domain size is
obtained. Cited from R. S. Ruoff group[106]. (b) Electron backscatter diffraction of
sub-monolayer CVD graphene on Cu, revealing Cu(111) patch on Cu(001) surface.
to be seen whether this is indeed the most relevant charge scattering source most
relevant for device applications.

Here, we show that Cu single-crystal step edges lead to the formation of quasi-
periodic nanoripple arrays (NRAs) after transfer on Si/SiO
2
substrates. Such surface
corrugations suspend up to 20 % of the graphene and give rise to flexural phonon
scattering [107]. In particular at room temperature and density levels of the order of
10
12
/cm
2
this leads to a strong anisotropy in the room-temperature (RT) conductivity
depending on the relative orientation between NRA’s and current flow direction. More
importantly, flexural phonon scattering within the nanoripples sets a lower bound on
the sheet resistance and upper bound on the charge carrier mobility even in the
absence of grain boundaries. Our findings provide guidance for further improving the
CVD graphene growth and transfer process.
64
5.2 Sample fabrications
The detailed synthesis and transfer of large-scale CVD graphene are discussed in
Chapter 3.2. Electron backscattering diffraction reveals that the annealed Cu(001)
substrates have single-crystal patches of Cu(111) and Cu(101), BLG coverage up to
40% (Fig. 5.1b) or SLG-dominant samples (>95%). Raman spectra (Fig. 5.2c)
show insignificant defect peaks demonstrating the high quality of both SLG and A-B
stacked BLG. Except for areas with optically visible wrinkles, Raman imaging with
micrometer resolution also shows that on this scale strain is negligible.
GFET Hall bars and four-terminal devices ranging in size from 1.2×0.8 to 100×10
µm
2
were patterned by e-beam lithography (EBL) for metal contacts (5 nm Cr/30
nm Au) and O

2
plasma etching. The completed device image are shown in Fig.
5.2e. For very large-scale GFETs of 1.2× 1.2 mm
2
devices, it were first etched into
van der Pauw geometry by EBL followed by metal contact evaporation using shadow
masks (Fig. 5.2d). To precisely define four contacts either perpendicular or parallel
with the nanoripple arrays (NRAs), Au alignment mask arrays were pre-patterned
using standard EBL processes followed by systematic non-contact mode atomic force
microscopy (AFM) scanning. For the systematic investigation of the origin of NRAs,
Au alignment mask arrays were also pre-patterned on Cu-CVD graphene using EBL
processes followed by the systematic SEM and AFM scanning.
For the AFM measurements, both high-resolution contact mode and tapping mode
AFM technique have been utilized to characterize graphene morphology on top of
copper and on top of the Si/SiO
2
substrate. For contact mode AFM, ultrasharp tips
with radii as small as 10 nm were used, limiting the error to be less than 10 % error
when measuring the 100 nm nanorippled area in Fig. 5.3. However, the contact
65
mode AFM tips are more vulnerable to surface contaminations. Thus, for large-scale
characterization, tapping mode AFM was used.
The devices were finally thermally annealed at 400 K in high vacuum level (10
5
mbar) for 2 hours to clean the graphene working channel. Electrical transport mea-
surements were done in vacuum in a four-contact configuration using a lock-in ampli-
fier with an excitation current of 100 nA. T-dependent measurements were done from
350 to 2 K in varable temperature insert (VTI) using standard four-contact lock-in
techniques. In total, eight SLG devices and three BLG devices have been measured.
Here we discuss five (two) representative SLG (BLG) devices in more detail.

5.3 Results and discussions
Utilizing these large grain size CVD graphene, we first compare the RT resistivity vs
gate voltage (ρ vs V
BG
) characteristics in four GFETs of very different dimensions,
ranging from the µm scale to the mm scale. The resistivities of these devices, fabri-
cated from the same batch of CVD graphene, are presented in Fig. 5.2f. Surprisingly,
except introducing stronger charge inhomogeneity, increasing the device channel area
by 6 orders of magnitude does not significantly alter the charge carrier mobility; RT
mobilities vary generally speaking independent of samples size between µ ∼ 4000-
6000 cm
2
/Vs. This excludes grain boundaries (10-20 per mm, see Fig. 5.2a) as the
main limiting factor for µ in our CVD graphene, and strongly suggests that the main
scatterers are identical to the ones in exfoliated graphene: adatoms and/or charged
impurities. Similar conclusions have recently been reached also by others [108].
However, high resolution contact mode atomic force microscopy (AFM) of CVD
graphene SiO
2
with ultrasharp tips reveals a new type of surface corrugations (Fig.
66
20 µm
b
c
e
f
Cu
a
20 µm
Raman Shift (cm )

-1
2000 2400 28001600
SLG
Wrinkle
BLG
>4L
G
2D
D
Intensity (a.u.)
n (10 cm )
12 -2
2-2-4 0
σ−σ
min
e /h
2
0
20
40
60
3 1 µm
2
100 10 µm
1.2 1.2 mm
1.2 0.8 µm
2
2
2
500

0
5
1
3
2
4
ρ ( Ω)
k
V - V (V)
BG
D
Graphene
1.2 mm
a
d
Figure 5.2: (a) SEM image of submonolayer graphene on Cu foil. (b) Optical image
of high BL coverage CVD graphene on 300 nm SiO
2
. The black, red, and blue
circles indicate the Raman measurement (0.4 µm in spot size) locations. Black arrows
indicate wrinkles formed during growth. (c) Raman spectroscopy of SLG, BLG, and
multilayer graphene. Raman on optical visible wrinkle shows significant broadening
in G and 2D peaks, indicating non-negligible strain. (d) Optical image of a millimeter
size GFET with van der Pauw geometry and (e) of micrometer size. Scale bar: 2 µm.
(f) Electrical measurements of square millimeter and square micrometer devices at
RT. Each curve is shifted by 20 V. Inset show the corresponding σ-σ
min
vs n.
5.3), whose influence on charge transport is not known. Distinct from the well known
low density strain-induced wrinkles (∼ 1 per 5 µm), we observe nanoripples of ∼ 3±1

nm in height of much higher density (∼ 10 per 5µm), which are typically arranged
in a quasi-periodic fashion (Fig. 5.3b). Each nanoripple location contains multiple
peaks of 10-20 nm width (Fig. 5.3e), thus making it possible that overall a section of
up to ∼ 100 nm, i.e. up to 20 % of the graphene sheet becomes effectively suspended.
67
d
a
b
Z (nm)
(nm)
Z (nm)
Distance (µm)
6
2
4
c


e
1
Figure 5.3: (a) AFM image of Cu surface, showing single-crystal terraces and step
edges (color scale, 0-60 nm; scale bar = 1 µm), and (b) CVD graphene on SiO
2
,
showing high-density nanoripples induced by Cu step edges (color scale, 0-15 nm;
scale bar = 1 µm). (c) Top: AFM cross section of Cu terraces. The typical width
of step edges is 100 nm. Bottom: AFM line scans of graphene after transfer to
Si/SiO
2
reveal nanoripple arrays which are closely correlated with the Cu terraces. (d)

Illustration of nanoripple formation, structure, and periodicity. (e) High-resolution
scan with ultrasharp tips shows that the nanoripple consists of multiple peaks of 10-20
nm width.
Systematic AFM studies on centimeter size samples further confirm that quasi-
periodic nanoripples arrays (NRAs) are a general feature of the CVD graphene-on-
SiO
2
surface morphology. To find out the origin of these NRAs, we did systematic
comparative SEM and AFM studies of the Cu films before transfer and the CVD
graphene sheets after transfer. The patterning of Cu substrate after graphene growth
with Au alignment mark arrays allows a direct comparison of the local Cu step edge
orientation and their density with the surface morphology of CVD graphene, once it
is transferred to Si/SiO
2
substrates. Systematic SEM studies before transfer (more
than 30 locations) on centimeter size Cu substrates confirm that single crystal step
68
edges and terraces are a ubiquitous surface feature of Cu foils after CVD graphene
growth. Here we pick two specific locations for illustration. In Fig. 5.4, we show
the comparison of CVD graphene morphology before and after wet transfer from two
different positions (namely Left and Right). Left-(a) shows an overview of an as-
grown CVD graphene on copper foil. The feature in the bottom right corner is Au
alignment mark. After wet transfer graphene to Si/SiO
2
substrate, the morphology
of CVD graphene in the same location were examined using AFM (Left-(b) and Left-
(c)). Both the nanoripple orientation and density follows closely the Cu-step edge
profile, as indicated by the dotted square region in Left-(a). Using the same strategy,
another different location was examined, as shown in the Right images. Right-(a)
shows the SEM image of CVD graphene before wet transfer. The black dotted square

indicates the zoom-in region shown in (b). Right-(c) shows the AFM image of CVD
graphene of the same location after transfer to a Si/SiO
2
substrate. The blue dotted
square indicates the zoom-in region shown in Right-(d) and Right-(e), respectively.
A direct relation between nanoripple array orientations, density with Cu step edges
is clearly seen. Thus, we conclude that the quasi-periodic nanoripple arrays in CVD
graphene do indeed originate from the Cu step edges and rule out any other potential
factors during the fabrication processes.
We now focus on T-dependent electrical transport measurements. In micron size
devices the QHE is well developed for both SLG and BLG, as shown in Fig. 5.5a and
5.5b, respectively. As we expected, SLG shows the anomalous quantization plateaux
of ±4e
2
/h(N +1/2), while BLG has the typical ±4Ne
2
/h quantization signatures.
From an application point of view, the zero field measurements of conductivity (σ)
vs charge density (n) are more relevant. They show a pronounced sublinear behavior,
69
8.0 µm
2.5 µm
Au marker
a
600 nm
b
c
a
Au marker
5.0 µm

b
1.0 µm
640 nm
270 nm
d
e
1.6 µm
36 nm
0 nm
c
Left: Right:
Figure 5.4: Two specific examples of CVD graphene morphology before and after
wet transfer. Left: SEM and AFM images of CVD graphene before and after wet
transfer. (a) Overview image of CVD Cu foil. The Au alignment markers (”11”) is
clearly visible. The dotted square indicates the zoom-in region shown in (b). (b) SEM
image of CVD graphene morphology at the boundary of two different Cu crystals.
(c) AFM image of CVD graphene of the same location after transfer to a Si/SiO2
substrate. Both the nanoripple orientation and density follows closely the Cu-step
edge profile. Note that the upper dotted region is shown in more detail in (d), while
the lower dotted region refers to the image shown in (e). The Right panel shows
another location on the same sample before and after transfer.
not only in CVD SLG but also in CVD BLG devices. The sublinearity is strongest
at RT and diminishes gradually with decreasing temperature, as shown in Fig. 5.5c
and 5.5d, respectively. This is best studied by plotting the T-dependent part of
the resistivity instead and represents the key finding of our experiments. Our data
reveal a superlinear T-dependent resistivity for T>50 K. Remarkably, such a metallic
behavior is observed in both SLG and BLG (Fig. 5.5e). Note that the dashed lines
correspond to a two-parameter fit to the data using ρ= ρ
0
+ 0.1T + γT

2
/ne, and
70
-0.3
0.3
0.0
4
6
8
d
a
b
BLG
BLG
BLG
SLG
SLG
SLG
SLG
BLG
Charge Density (10 cm )
12 -2
300 K
200 K
250 K
100 K
50 K
5 K
100 K
50 K

5 K
300 K
200 K
350 K
-2 -1 0 1 2 3 4
-2 -1 0 1 2 3
-3
T (K)
50 150 250 350 50 150 250
2.8 (10 cm )
12 -2
1 2 3
100
0
200
300
400
ρ (Ω)
s
0.4
0.5
1.4
1.6
1.8
1.4
1.2
1.0
0.2
0.8
3.8 (10 cm )

12 -2
0.5 (10 cm )
12 -2
0.5 (10 cm )
12 -2
0
40
80
120
V (V)
BG
BLG
B = 16 T
T = 2 K
SLG
B = 9 T
T = 3.5 K
0
40
20
60
σ
(e /h)
2
-8
-4
0
4
8
40

6020
0
-20
4
2
0
6
40
6020
0
-20
-40
0
4
2
0
6
8
ρ ( Ω)
k
xx
V (V)
BG
Charge Density (10 cm )
12 -2
Charge Density (10 cm )
12 -2
ρ ( Ω)
k
8

-8
16
σ
(e /h)
2
xy
σ
(e /h)
2
xy
σ
(e /h)
2
c
e
f
ρ ( Ω)
k
xx
Figure 5.5: (a) and (b) QHE of CVD SLG and BLG graphene on Si/SiO
2
substrate,
respectively. (c) and (d) T-dependent sub-linear behavior of a SLG and a BLG. Inset
of (c) and (d): Insulating behavior with n < 5 ×10
11
/cm
2
and AFM image of a flower
shaped CVD BLG, respectively. The scale bar is 1 µm. (e) ρ(T) at different doping
level for both SLG and BLG. (f) At RT, ρ

S
vs. n for both CVD SLG and CVD BLG.
The solids curves correspond to fits of the form ρ
S
= a/n, where ρ
S
arises from both
FPs and RIPs. We used a = 1.57×10
18
Ω/m
2
and 2.87×10
18
Ω/m
2
for SLG and BLG,
respectively.
serve as guide to the eyes. Previous studies on supported exfoliated samples only
reported such a T-dependent resistivity in SLG, while BLG samples did not show
any T dependence away from the charge neutrality point (CNP) [109]. Such behavior
for BLG is expected only for suspended samples, where the T-dependent contribution
to ρ (n, T) scales as T
2
/n and is generally associated with electron-flexural phonon
(FP) scattering [110]. Indeed, the high density NRAs effectively decouple up to 20 %
of CVD graphene sheets from the substrates, activating low energy FP excitations in
both SLG and BLG even when the samples are overall supported on a substrate.
For CVD BLG, this clearly demonstrates that at RT NRAs will limit both R
✷
and µ due to FP scattering. However, the CVD SLG case is more ambiguous. Its

71
resistivity has additional T dependent contributions due to scattering from remote
interfacial phonons (RIP) of the SiO
2
substrate [34, 111] and possibly high energy
FPs arising from quenched 10 nm-wide nanoripples [112, 113]. On SiO
2
substrates
both the FP and RIP scattering mechanisms lead to a very similar T and n dependent
behavior over 50-350 K and 10
12
cm
−2
ranges (Fig. 5.5e and 5.5f) [34].
b
d
c
a
e
Charge Density (10 cm )
12 -2
Charge Density (10 cm )
12 -2
-2 -1 0 1 2 3
-3
-4
0
40
20
60

0
40
20
60
-2 -1 0 1 2
-3
-4
Charge Density (10 cm )
12 -2
T (K)
S1
S2
,
2.0 x 10 cm
12 -2
2.5 x 10 cm
12 -2
3.0 x 10 cm
12 -2
3.4 x 10 cm
12 -2
2.0 x 10 cm
12 -2
,
100 150 200 250 300
50
0
1 10 100
10
1

0.1
0.1
1 10
100
100
10
1
400
200
0
400
200
0
400
200
400
200
0
350
200
300
250
150
100
Parallel NRAs
Perpendicular NRAs
T (K)
Figure 5.6: (a-b) T-dependent σ for both ⊥ and ∥ NRAs configurations. Inset:
AFM image of graphene channel with clear ⊥ and ∥ NRAs orientations. The scale
bar is 1 µm. (c) Anisotropic resistivity results obtained with sample set S1 at n =

2.0 ×10
12
/cm
2
. (d) Estimate of the NRA impact on CVD SLG R and µ at n = 2
×10
12
/cm
2
. (e) ∆ρ(T) obtained from a second set of devices S2 for different charge
densities ranging from 2.0 ×10
12
/cm
2
to 3.4 ×10
12
/cm
2
.
To explicitly measure the influence of NRAs on CVD SLGs resistivity, we have
fabricated GFETs where the orientation of the electrodes is such that the current
is either perpendicular (⊥) or parallel (∥) to the NRAs (Fig. 5.6a and 5.6b). We
analyzed the corresponding transport data by assuming a resistivity ρ of the form:
ρ(n, T) = ρ
0
(n) + αT + ρ
S
(n,T), where ρ
0
(n) is the T-independent residual resistivity,

αT is the acoustic phonon (AP) induced resistivity (α= 0.1 Ω/K), and ρ
S
(n,T) the
72
superlinear part of the resistivity. In Fig. 5.6e, we directly compare ρ
S
(n,T) for the
⊥ and ∥ devices by computing ∆ρ
⊥
(n, T) =ρ
⊥
(n, T) - ρ
⊥
(n, 100K) - α(T-100K)
= ρ
S⊥
(n,T) - ρ
S⊥
(n,100K) and ∆ρ
∥
(n, T) = ρ
∥
(n,T) - ρ
∥
(n, 100K) - α(T-100K)
= ρ
S∥
(n,T) - ρ
S∥
(n,100K). Strikingly, ∆ρ

⊥
remains always significantly greater than
∆ρ
∥
. In other words, the RT CVD graphene resistivity is anisotropic. This is in sharp
contrast with the isotropic resistivity of exfoliated samples and clearly shows that the
phonon scattering rate is higher in the devices with the ⊥ configuration. Since FPs
are the only phonons which are activated upon suspension, this demonstrates that
NRAs contribute also in CVD SLG importantly to the T-dependence of ρ.
Assuming a simple resistor-in-series and resistor-in-parallel model, we estimate
the impact of NRAs on key figures of merit such as µ and R
✷
. In Fig. 5.6d, The solid
red and black curves represent the RT mobility µ against liquid Helium T mobility
µ
0
for CVD SLG in both ⊥ (solid red) and ∥ (solid black) NRAs configurations,
assuming electron-RIP scattering is suppressed. The dashed dotted curves represent
the FP-induced increase in R in ⊥ (red) and ∥ (black) orientations. Note that in
our model ρ
S
(n,T) arises from both electron-FP scattering (in the nanoripples) and
electron RIP-scattering events (between the nanoripples) independent of the NRAs
orientation. With this we write ρ
S⊥
= f·ρ
FP
+ (1-f)·ρ
RIP
and ρ

S∥
= (f/ρ
FP
+ (1-
f)/ρ
RIP
)
−1
, where f is the ratio of the typical ripple width w and the mean inter-ripple
spacing a. Besides, we assume ρ
FP
is of the form γT
2
/ne [13, 113, 114] and ρ
RIP
can
be written as (A/n)(g
1
/(Exp(E
1
/(k
B
T))-1) + g
2
/(Exp(E
2
/(k
B
T))-1)), where g
1

=
3.2 meV and g
2
= 8.7 meV are the respective coupling strengths of the SiO
2
RIP
modes of energies E
1
= 63 meV and E
2
= 149 meV. We can now estimate the two
free parameters A and γ setting the magnitude of ρ
FP
and ρ
RIP
by fitting the 12 curves
73
of Fig. 5.6e. This leads to A = 3·10
17
kΩ/(eV cm
2
), in reasonable agreement with
Refs ([111],[34]), and γ = 6∼ 10
−6
Vs/(mK)
2
. Interestingly, this extracted value of γ
matches well the experimental values recently obtained for fully suspended graphene
samples. With the extracted value of γ, its now possible to predict FP-induced limits
on CVD SLG µ and R

✷
. Fig 5.6d shows the calculated RT mobility as a function
of the Helium-T mobility µ
0
for CVD graphene with f = 20 % both in ⊥ and ∥
orientations. As µ
0
is unaffected by phonons, this is a convenient variable to gauge
the influence of FPs [115]. Including AP scattering NRAs limit the RT mobility to
40,000 cm
2
/Vs in ⊥ orientation and 80,000 cm
2
/Vs in ∥ orientation, independent of
the choice of substrate. In contrast, RT mobilities greater than 100,000 cm
2
/Vs have
already been achieved for exfoliated graphene encapsulated in h-BN [116].
5.4 Conclusion
In summary, we show that the current growth and transfer metho ds of CVD graphene
lead to a quasi-periodic nanoripple arrays in graphene. Such high density NRAs
partially suspend graphene giving rise to flexural phonon scattering. This not only
causes anisotropy in charge transport, but also sets limits on both the sheet resistance
and the charge mobility even in the absence of grain boundaries. At room temperature
NRAs are likely to play a limiting role also for the mobility of ultra-clean samples,
in particular when the graphene sheets are transferred onto ultraflat BN substrates
[35, 108]. On the other hand the controlled rippling of graphene may be useful for
graphene-based sensor applications as the ripples are more prone to adsorptions than
flat graphene [117]. Controlled rippling may also be instrumental for spin-based device
applications requiring surface modifications [118].