Graphite Edge Controlled Registration of Monolayer MoS2
Crystal Orientation
Chun-I Lu,1 Christopher John Butler,1 Jing-Kai Huang,2 Cheng-Rong Hsing,2
Hung-Hsiang Yang,1 Yu-Hsun Chu,1 Chi-Hung Luo,1 Yung-Che Sun,1 Shih-Hao
Hsu,1 Kui-Hong Ou Yang,1 Ching-Ming Wei,2 Lain-Jong Li,2 and Minn-Tsong Lin1,2
1
Department of Physics, National Taiwan University, Taipei 10617, Taiwan
2
Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan
Supplemental material
Sample preparation and measurement
Single-layer MoS2 was produced by the CVD process by using MoO3 and S powders as
reactants in a nitrogen environment. In variance with the procedure from Lee et al,1 the MoS2
was grown on an HOPG substrate without any prior treatment such as reduced graphene oxide
(rGO), PTAS or PTCDA solution. After deposition in the CVD chamber, the sample was transferred
in air to the fast-entry-lock of an ultra-high vacuum system with a base pressure lower than 5 ×
10-11 mbar.
STM measurements were performed at 4.5 K, also in a base pressure lower than 5 ×10-11
mbar, using a chemically etched tungsten tip. For analysis of moiré patterns, x-y calibration of
atomically resolved topography maps was performed using parameters obtained by measuring
the HOPG lattice 0.246 nm. After calibration, the 2D-FFT methods were used to measure the
averaged periodic structures and the unit cell vectors’ directions.
In the Figure S1, we show the I(V) and dI/dV(V) curves acquired on a clean MoS2 surface
and averaged over an area of approximately 25 nm2, representing the electronic properties of the
MoS2 thin film. The observed energy gap corresponds to an n-type semiconductor with a band
gap of about 1.9 eV, which is consistent with the properties of monolayer MoS2.2
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dI/dV Signals (arb. unit)
Tunneling Current (nA)
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1.0
Bias Voltage (Volt)
Figure S1: I(V) and dI/dV(V) curves taken on MoS2 island, in an area of approximately 25 nm2
(using a setpoint of Vbias = -1 V, Iset = 1 nA, and a bias modulation of Vmod = 30 mV), showing
n-type behavior semiconductor with the band gap width around 1.9 V.
Thin film quality and grain boundaries
Figure S2, shows STM topography images taken at several different scales, providing an
overview of the quality of the CVD MoS2 thin films. Some spots appear on the MoS2 triangular
island at Figure S2(a). Due to the growth method and the lack of any in situ cleaning procedure,
the contaminants are attributed to exposure to the atmosphere before loading into UHV. Despite
this, the atomic structure and moiré pattern can clearly be seen in the Figures S2(b) and (c), with
some protuberant point defects also visible. In Figure S2(d), the grain boundary between two
MoS2 islands can be seen.
The edge of an MoS2 island on an HOPG terrace is shown in Figure S2(e). We suppose that
the rough edge is due to contaminations resulting from the incomplete bonds of the Mo or S
atoms having reactions with other molecules while in atmospheric conditions.
The measured apparent height of the MoS2 island (as measured from the HOPG terrace to
the island interior in FIG. 1) is close to the c-axis lattice parameter of MoS2. (The apparent height
observed in STM may be lower than that observed using AFM, as STM constant current maps
represent a mixture of topographic and spectroscopic information. In this case the topographic
contrast may be slightly reduced due to the lower integrated density of states of the
semiconducting adlayer as compared to the metallic substrate.) The observed apparent height
indicates that the island consists of one MoS2 monolayer, and also precludes the possibility of
significant intercalated impurities in the MoS2/HOPG interface. Considering this, and the fact that
the existence of a moiré pattern already indicates a weak interaction between the MoS 2 and a
well-ordered crystalline substrate, we conclude that the interface is the expected MoS 2/HOPG van
der Waals hetero-structure. Furthermore, we note that the island interior is remarkably free of
point defects, which would result from non-stoichiometry.
Figure S2: A series of STM topography images showing the quality of the CVD grown MoS2
thin films. (a) Iset = 1 nA, Vbias = -1 V, 90 x 90 nm2 (b) Iset = 0.5 nA, Vbias = -0.5 V, 40 x 40 nm2, (c)
Iset = 5 nA, Vbias = -0.2 V, 17.5 x 17.5 nm2 (d) Iset = 0.5 nA, Vbias = -0.5 V, 375 x 375 nm2 (e) Iset =
0.5 nA, Vbias = -0.5 V, 50 x 50 nm2. The inset in panel (e) shows the line profile along the white
dashed line in the image.
First principles calculations
First-principles calculations were performed in accordance with density functional theory
(DFT)3,4 using the Vienna ab-initio simulation package (VASP).5,6 Valence wave functions were
treated by the projector augmented wave (PAW) method6 that uses pseudopotential operators
but keeps the full all-electron wave functions. The interlayer interaction is calculated by the local
density approximation (LDA).8 The plane-wave energy cutoff was at least 400 eV. We also
checked the convergence of k points and used meshes containing at least 549 points in the
primitive Brillouin zone (BZ) of graphene. A vacuum of 15 Å was used to eliminate spurious
interaction between supercells. We have also calculated the binding energies between MoS 2 and
graphene layer with vacuum spacing 2.0 nm and found the results of binding energies for the
same morié pattern are very close to each other (within 0.5 meV) except for the
MoS2(R7)/Graphene(R12) which is about 1 meV difference. Therefore, it is
safe to say 1.5 nm
(or 2.0 nm) is able to avoid spurious interaction among neighboring cells. For structural
optimization, all atoms were relaxed until the change of the energy and the force reaches 10 -5 eV
per cell and 10-2 eV/Å, respectively.
Assignment of moiré superstructure unit cells
Although it is tempting to assign lattice points of the moiré superstructure to the peaks of
the moiré pattern, this simple model does not reliably yield the correct relative rotation angles
between the MoS2 and graphite lattices upon trigonometric analysis. A detailed inspection of the
atomic lattice at and around the moiré pattern peaks shows that a larger superstructure unit cell
may be necessary, as adjacent moiré peaks may in general be slightly different (see FIGs 2 and 3),
and can be seen as non-equivalent lattice sites, which must be grouped into sets or sub-lattices.
The actual unit cells of the moiré superstructure may then contain one of each of these
non-equivalent moiré peaks. We demonstrate this in Figure S3, where we reproduce the image
from FIG. 3(a), and now highlight two of these sub-lattices of non-equivalent moiré peaks with
sets of green and blue triangles. The orientations of the triangles highlight the different relations
between the moiré peak positions and the S atomic lattice. In this case it is clear that in order to
fully represent the details of both the moiré pattern and the atomic lattice, a large moiré
superstructure lattice is necessary, accompanied by a basis of three different moiré peaks. The
white lines in Figure S3 show one choice of unit cell for the resulting superstructure lattice.
Figure S3: An atomically resolved topography map of a moiré pattern on MoS2 on HOPG
(reproduced from FIG. 3(a)). The blue and green triangles mark sets of equivalent sites of the
moiré superstructure.
Determination of relative rotational angles
In this section, we explain how the rotational angle between the two lattices is determined.
First, in an atomically resolved image of a moiré pattern, the lattice vectors of the moiré
superstructure are constructed using the atomic lattice vectors of MoS2 (or graphite) as a set of
basis vectors. A schematic diagram is drawn in the Figure S1. In this example, the red arrow in
Figure S4 represents the length of the superstructure period, and can be constructed as the
vector (1, 2) in the MoS2 lattice vector basis. In this case, the length is around 0.83 nm. The vector
with the most similar length constructed using the basis of graphite atomic lattice vectors is
0.246 nm x √12 = 0.852 nm, in which the √12 originates from applying the law of cosines to a
hexagonal lattice, and constructing the moiré lattice vector as a vector (2, 2) in the basis of the
graphite atomic lattice. We calculate the angles θ1 and θ2 by using the law of cosines, and the
rotational angle between the two lattices is the absolute value of |θ1 - θ2|. The analysis results
collected from the data shown in FIG. 2 and FIG. 3 in the manuscript are shown in Table S1, which
lists the relative rotational angle and the corresponding MoS2 lattice constants.
Figure S4: A schematic diagram of the construction of moiré superstructure lattice vectors from
a basis of MoS2 and graphite atomic lattice vectors. In this case, the superstructure is R(7/12).
The red arrow represents a superstructure lattice vector. The blue and black arrows represent
atomic lattice vectors of MoS2 and graphite, respectively. Both bases are the hexagonal
lattices. The rotational angle θ can be calculated by |θ1 - θ2|.
TABLE SI. Geometric information for five different moiré patterns found.
Interpretation of moiré pattern observed in HOPG substrate through a
MoS2 island
In FIG. 2(b), after accounting for the drift between the two consecutive images, the bright parts of
FIG. 2(a) and FIG. 2(b) are found to coincide with each other. Although the bottom HOPG layer
should be flat, the moiré pattern still appears in the image dominated by the HOPG layer. This
indicates that the moiré pattern is the result of a superperiodic modulation in the density of
states, rather than a purely topographic contrast. This is consistent with the effect described
theoretically by Kang et al., in MoS2/MoSe2 heterojunctions; moiré patterns induce a modulation
of the electronic structure of the system, even without significant topographic corrugation.9
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