Electronic Properties of Graphene Encapsulated with Different Two-Dimensional Atomic Crystals

TL;DR: This work reports on the search for alternative substrates for making quality graphene heterostructures using atomically flat crystals and attributes the difference mainly to self-cleansing that takes place at interfaces between graphene, hBN, and transition metal dichalcogenides.

Abstract: Hexagonal boron nitride is the only substrate that has so far allowed graphene devices exhibiting micrometer-scale ballistic transport. Can other atomically flat crystals be used as substrates for making quality graphene heterostructures? Here we report on our search for alternative substrates. The devices fabricated by encapsulating graphene with molybdenum or tungsten disulfides and hBN are found to exhibit consistently high carrier mobilities of about 60 000 cm(2) V(-1) s(-1). In contrast, encapsulation with atomically flat layered oxides such as mica, bismuth strontium calcium copper oxide, and vanadium pentoxide results in exceptionally low quality of graphene devices with mobilities of ∼1000 cm(2) V(-1) s(-1). We attribute the difference mainly to self-cleansing that takes place at interfaces between graphene, hBN, and transition metal dichalcogenides. Surface contamination assembles into large pockets allowing the rest of the interface to become atomically clean. The cleansing process does not occur for graphene on atomically flat oxide substrates.

Summary

Summary

• Weak convergence, Chacon’s biting lemma, L1, Jacobians, determinants, divcurl lemma, maximal function, nonlinear elasticity, rank-one connections.
• However this lemma says nothing about weak continuity of sequences of functions with partial derivative constraints.
• This result depends heavily on the divergence theorem, hence cannot be used for problems where the authors only have det x on Q (see Proposition 3.3 below).
• Firstly, by Chacon’s biting lemma the authors have a subsequence on 0, and what they should prove is that x = u ~ w.

Figures

Figure 3. Capacitance spectroscopy of WS2/graphene/hBN/Au. (a) Ctot as a function of Vg in zero and quantizing B. For clarity, the 12T curve is offset by 15 fF. (b) Landau fan diagram Ctot(Vg, B). Scale: wine to white 0.105 to 0.120 pF.

Figure 1. Quality of hBN/graphene/hBN heterostructures fabricated by dry peel transfer. (a) Optical micrograph of a Hall bar device with two different types of contacts: overlapping (illustrated by the top inset) and edge (bottom). The scale bar is 5 µm. (b,c) Cross-sectional TEM image of an edge contact to an encapsulated bilayer graphene (BLG) and its HAADF elemental mapping. The images are obtained using thin slices of the contact areas, which were prepared by a focused ion beam.11 The scale is given by the interlayer distance of 3.4 Å. (d) Resistivity xx, conductivity xx (left inset) and mean free path l (right inset) as a function of n at different T for the device in (a). The green dashed line in the left inset corresponds to the 1/n dependence and illustrates the inhomogeneity n. The black dashed line in the right inset shows l expected if no scattering occurs at device boundaries. Acoustic phonon scattering leads to shorter l at elevated T as shown by the red and blue dashed curves. The theory curves were calculated following refs. 7,12.

Figure 5. AFM topology and TEM cross section image of graphene on various substrates. (a-g) Graphene on hBN, MoS2, WS2, mica, BSCCO and V2O5. All AFM scan sizes: 15 µm × 15 µm. Scale: black to white, 5.5 nm. The yellow dashed curves highlight edges of graphene flakes. Insets: 1.5 µm × 1.5 µm; black to white, 4 nm. Due to selfcleansing for graphene on hBN, MoS2 and WS2, hydrocarbon contamination is aggregated into bubbles seen in (ac) as bright spots connected by graphene wrinkles. (d) TEM cross section image of the graphene-on-hBN structure illustrating the hydrocarbon contamination bubble. The submicron-scale structures seen in the insets for (e,g) are probably due to a few monolayers of captured water.14-16 The small bright dots in (e-g) are a residue that is due to the use of acetone to dissolve PMMA at the final stage and is not at the graphene interface.

Full text

ORE Open Research Exeter
TITLE
Electronic properties of graphene encapsulated with different two-dimensional atomic crystals.
AUTHORS
Kretinin, AV; Cao, Y; Tu, JS; et al.
JOURNAL
Nano Letters
DEPOSITED IN ORE
21 October 2016
This version available at
http://hdl.handle.net/10871/24014
COPYRIGHT AND REUSE
Open Research Exeter makes this work available in accordance with publisher policies.
A NOTE ON VERSIONS
The version presented here may differ from the published version. If citing, you are advised to consult the published version for pagination, volume/issue and date of
publication

1
Electronic Properties of Graphene Encapsulated with Different
Two-Dimensional Atomic Crystals
A. V. Kretinin,
*,1
Y. Cao,
1
J. S. Tu,
1
G. L. Yu,
2
R. Jalil,
1
K. S. Novoselov,
2
S. J. Haigh,
3
A. Gholinia,
3
A.
Mishchenko,
2
M. Lozada,
2
T. Georgiou,
2
C. R. Woods,
2
F. Withers,
1
P. Blake,
1
G. Eda,
4
A. Wirsig,
5
C.
Hucho,
5
K. Watanabe,
6
T. Taniguchi,
6
A. K. Geim
1,2
and R. V. Gorbachev
1
1
Centre for Mesoscience and Nanotechnology, University of Manchester, Manchester M13 9PL, UK
2
School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester, M13 9PL, UK
3
School of Materials, University of Manchester, Oxford Road, Manchester, M13 9PL, UK
4
Graphene Research Centre, National University of Singapore, 6 Science Drive 2, Singapore 117546
5
Paul Drude Institut für Festkörperelektronik, Hausvogteiplatz 5-7, 10117 Berlin, Germany
6
National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044 Japan
KEYWORDS
Graphene, boron nitride, transitional metals dichalcogenides, layered oxides, carrier mobility,
capacitance spectroscopy
Hexagonal boron nitride is the only substrate that has so far allowed graphene devices exhibiting
micron-scale ballistic transport. Can other atomically flat crystals be used as substrates for
making quality graphene heterostructures? Here we report on our search for alternative
substrates. The devices fabricated by encapsulating graphene with molybdenum or tungsten
disulphides and hBN are found to exhibit consistently high carrier mobilities of about 60,000 cm
2
V
-1
s
-1
. In contrast, encapsulation with atomically flat layered oxides such as mica, bismuth
strontium calcium copper oxide and vanadium pentoxide results in exceptionally low quality of
graphene devices with mobilities of ~1,000 cm
2
V
-1
s
-1
. We attribute the difference mainly to self-
cleansing that takes place at interfaces between graphene, hBN and transition metal
dichalcogenides. Surface contamination assembles into large pockets allowing the rest of the
interface to become atomically clean. The cleansing process does not occur for graphene on
atomically flat oxide substrates.

2
Until recently, the substrate of choice in microfabrication of graphene devices was oxidized Si
wafers. This was due to their availability and versatility, excellent dielectric properties of
thermally grown SiO
2
, and easy visualization and identification of monolayer and bilayer
graphene on top of such substrates.
1
However, it has soon become clear that the quality of
graphene-on-SiO
2
devices was limited by several factors including surface roughness, adatoms
acting as resonant scatterers and charges trapped at or near the graphene-SiO
2
interface.
1-3
Search for better substrates had started
4
and eventually led to the important finding that
cleaved hexagonal boron nitride (hBN) provides an excellent substrate for graphene.
5, 6
Typically, graphene-on-hBN exhibits a tenfold increase in the carrier mobility, µ, with respect to
devices made on SiO
2
.
5
This quality of graphene has made it possible to observe the fractional
quantum Hall effect
6
and various ballistic transport phenomena.
7, 8
Although hBN is now widely
used for making increasingly complex van der Waals heterostructures,
9-11
it remains unclear
whether it is only the atomic flatness of hBN that is essential for electronic quality or other
characteristics also play a critical role. Even more important is the question whether hBN is
unique or there exist other substrates that may allow graphene of high electronic quality.
In this Letter we report on our studies of various layered materials as atomically flat
substrates for making graphene devices and van der Waals heterostructures. By using transport
and capacitance measurements, we assess the electronic quality of monolayer graphene
encapsulated between transitional metal dichalcogenides (TMD), such as MoS
2
and WS
2
, and
several layered oxides such as muscovite mica, bismuth strontium calcium copper oxide
(BSCCO) and vanadium pentoxide (V
2
O
5
), on one side and hBN on the other. As a reference for
electronic quality, we use graphene-on-SiO
2
and hBN/graphene/hBN heterostructures. In the
latter case, we can usually achieve µ of 100,000 cm
2
V
-1
s
-1 7, 12
and, with using the ‘dry-peel’
transfer,
12
µ can go up to 500,000 cm
2
V
-1
s
-1
, allowing ballistic devices with scattering occurring
mainly at sample boundaries.
7, 12
The MoS
2
/graphene/hBN and WS
2
/graphene/hBN structures
are also found to exhibit high quality (µ 60,000 cm
2
V
-1
s
-1
) and high charge homogeneity,
which makes MoS
2
and WS
2
a good alternative to hBN. Regarding atomically flat oxides, their
use results in dismal electronic quality, which is lower than that observed for atomically rough
surfaces such as oxidized Si wafers. This is despite large dielectric constants of the tested
oxides, which should suppress scattering by charged impurities.
1-4
Our observations indicate
that several mechanisms contribute to charge carrier scattering in graphene and the dominant
one may change for a different substrate. Nonetheless, we argue that the crucial role in
achieving ultra-high electronic quality is the self-cleansing process previously reported for
graphene on hBN
11
and now observed for graphene on the disulphides. In this process, van der
Waals forces squeeze contamination adsorbed at contacting surfaces into sizeable pockets,
leaving the rest of the interface atomically clean.
11
We expect this self-cleansing to occur for all
layered TMD.
9, 13
No self-cleansing is observed for cleaved oxide substrates where
contamination (including monolayers of adsorbed water
14-16
) remains distributed over the
entire graphene interface.

3
To set up a standard of electronic quality for graphene on a substrate, we start with
encapsulated hBN/graphene/hBN devices. Their fabrication is described in refs. 5-12 and in
Supporting Information.
17
Briefly, graphene and thin hBN crystals required for making such
heterostructures were mechanically cleaved onto a film consisting of two polymer layers (PMGI
and PMMA) dissolving in different solvents. We lifted the top polymer together with the chosen
crystals off the wafer by dissolving the bottom layer. The resulting flake is placed onto a circular
holder and loaded face down into a micromanipulation setup where it can be precisely aligned
with another 2D crystal prepared on a separate wafer, which later serves as a base substrate for
the final device. Unlike in the previous reports,
5-11
we no longer dissolve the PMMA carrier film
but peel it off mechanically.
12
Mutual adhesion between graphene and hBN crystals is greater
than either of them has with the polymer. After the transfer of graphene onto a selected crystal,
the structure is immediately encapsulated with another hBN crystal (5-20 nm thick) using the
same dry-peel transfer. This allows us to avoid any solvent touching critical surfaces. The final
heterostructures are shaped into the required geometry by plasma etching. One of our
hBN/graphene/hBN Hall bars is shown in Fig. 1a.
Figure 1. Quality of hBN/graphene/hBN heterostructures fabricated by dry peel transfer. (a) Optical
micrograph of a Hall bar device with two different types of contacts: overlapping (illustrated by the top inset)
and edge (bottom). The scale bar is 5 µm. (b,c) Cross-sectional TEM image of an edge contact to an
encapsulated bilayer graphene (BLG) and its HAADF elemental mapping. The images are obtained using thin
slices of the contact areas, which were prepared by a focused ion beam.
11
The scale is given by the interlayer
distance of 3.4 Å. (d) Resistivity

xx
, conductivity

xx
(left inset) and mean free path l (right inset) as a function
of n at different T for the device in (a). The green dashed line in the left inset corresponds to the 1/n
dependence and illustrates the inhomogeneity 
n. The black dashed line in the right inset shows l expected if
no scattering occurs at device boundaries. Acoustic phonon scattering leads to shorter l at elevated T as shown
by the red and blue dashed curves. The theory curves were calculated following refs. 7,12.

4
Electric contacts to encapsulated graphene can be made using two different approaches. In
the conventional one,
5-11
the heterostructures is designed in such a way that some areas of
graphene are left not encapsulated and Cr/Au (4/80 nm) contacts could be deposited later (top
inset of Fig. 1a). In the second approach,
12
the same metallization is evaporated directly onto
the etched mesa that had no exposed graphene areas as schematically shown in the bottom
inset of Fig. 1a. The latter method allows ohmic contacts with resistivity of 1 kOhm/µm over a
wide range of charge carrier densities n and magnetic fields B, similar to traditional (top-
evaporated) contacts.
5-11
The quality of ‘edge’ contacts is surprising because graphene is buried
inside hBN and exposed by less than one nanometer along the edge. The edge geometry is
visualized in Figs. 1b,c using transmission electron microscopy (TEM) and high-angle annular
Figure 2. Graphene devices fabricated on a MoS
2
substrate. (a) Optical micrograph of a typical
MoS
2
/graphene/hBN Hall bar. The MoS
2
/graphene heterostructure is encapsulated with a thin hBN layer
that serves as a top gate dielectric. Scale bar, 10 µm. (b) Resistivity and conductivity in zero B for the
MoS
2
/graphene/hBN device. (c) Its Landau fan diagram

xx
(V
g
, B). Scale: navy to white, 0 to 
3 kOhm. (d)
Optical image of a typical MoS
2
/graphene/hBN/Au capacitor. The meandering shape of the top gate is to
maximize the active area by avoiding contamination bubbles (dark spots). Colored dashed lines outline
corresponding layers: green – is the MoS
2
substrate, red – is graphene and yellow is the thin encapsulating
hBN, which is also used as the gate dielectric. Scale bar, 15 µm. (e) Capacitance of a MoS
2
/graphene/hBN/Au
device in zero and quantizing B. For clarity, the curves are offset by 50 fF. (f) Fan diagram C
tot
(V
g
, B). Scale:
wine to white, 0.18 to 0.3 pF. The numbers and arrows above the plot mark the filling factors,

.

Frequently asked questions

Q1. What is the effect of the use of a heavy element on graphene?

Note that the use of substrates containing heavy elements may in principle lead to a proximity-induced spin-orbit gap in graphene. 

Q2. Why do the authors use them in testing different substrates?

Because capacitors are quicker and easier to fabricate and examine, the authors tend to employ themmore than Hall bars in testing various substrates, only checking their conclusions by transportmeasurements if necessary. 

Q3. What is the process of encapsulating graphene onto a selected crystal?

After the transfer of graphene onto a selected crystal,the structure is immediately encapsulated with another hBN crystal (5-20 nm thick) using thesame dry-peel transfer. 

Q4. How can the authors use semiconducting crystals as substrates?

1-8 Nonetheless, it is possible to use semiconducting crystals assubstrates if the gate voltage Vg is applied through a top dielectric layer. 

Q5. What is the onset of the oscillations in graphene?

In this particular device, the onset of magneto-oscillations isobserved at 1 T, which implies µq ~10,000 cm2 V-1 s-1, a factor of 2 lower than µq in MoS2/graphene/hBN in Fig. 

Q6. What is the way to assess graphene?

In conclusion, using transport and magnetocapacitance measurements, the authors have assessedelectronic quality of single-layer graphene devices fabricated on various atomically flatsubstrates. 

Q7. How many cm2 V-1 s-1 is the onset of magneto-os?

Weak Shubnikov – de Hass oscillations could be observed in B >10 T (Fig. 4c), which allows an estimate for µq as 1,000 cm2 V-1 s-1. 

Q8. How many gate voltages were applied to a particular device?

The range of gate voltages, Vg, applied to a particular device was dictated by dielectric strength of the hBN layer limited by typically 0.5 V/nm 2, 3. 

Q9. How can the authors achieve a of 100,000 cm2 V-1 s-1?

In the latter case, the authors can usually achieve µ of 100,000 cm2 V-1 s-1 7, 12 and, with using the ‘dry-peel’ transfer,12 µ can go up to 500,000 cm2 V-1 s-1, allowing ballistic devices with scattering occurring mainly at sample boundaries. 

Q10. What is the method for ohmic contacts?

The latter method allows ohmic contacts with resistivity of 1 kOhm/µm over awide range of charge carrier densities n and magnetic fields B, similar to traditional (topevaporated) contacts.5-11 

Q11. What is the DoS minimum for graphene on mica?

Despite such strong scattering, graphene on mica is practically undoped (the DoS minimum is near zero Vg; n 1011 cm-2), which is surprising and disagrees with the earlier Raman studies that inferred heavy p-dopingfor graphene on muscovite mica (1013 cm-2).15 Similarly low µ are observed forBSCCO/graphene/hBN in both transport and capacitance measurements (µq µFE 1,000 cm2 V-1 s-1). 

Q12. How much V-1 s-1 is graphene on SiO24?

In this case, the authors find µq 2,500 cm2 V-1 s-1, similar to graphene on SiO24 and notably higher than the values obtained using atomically flat oxides.