Temperature dependence of Coulomb oscillations in a few-layer two-dimensional WS2 quantum dot

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received: 18 June 2015

accepted: 08 October 2015

Published: 05 November 2015

# Temperature dependence of Coulomb oscillations in a few-layer two-dimensional WS2 quantum dot

Xiang-Xiang Song 1,2 , Zhuo-Zhi Zhang 1,2 , Jie You 1,2 , Di Liu 1,2 , Hai-Ou Li 1,2 , Gang Cao 1,2 ,
Ming Xiao 1,2 & Guo-Ping Guo 1,2

Standard semiconductor fabrication techniques are used to fabricate a quantum dot (QD) made of
WS2, where Coulomb oscillations were found. The full-width-at-half-maximum of the Coulomb peaks
increases linearly with temperature while the height of the peaks remains almost independent of
temperature, which is consistent with standard semiconductor QD theory. Unlike graphene etched
QDs, where Coulomb peaks belonging to the same QD can have different temperature dependences,
these results indicate the absence of the disordered confining potential. This difference in the
potential-forming mechanism between graphene etched QDs and WS2 QDs may be the reason for the
larger potential fluctuation found in graphene QDs.

After demonstrating a variety of electronic applications on graphene 1, graphene-like two-dimensional
layered materials have attracted the increasing attention of researchers because of their unique properties 2,3 . Compared with traditional semiconducting materials, two-dimensional layered materials have the
advantages of inherent flexibility and an atomically-thin geometry. Moreover, because their interfaces
are free of dangling bonds, two-dimensional layered materials can easily be integrated with various substrates. They can also be fabricated in complex sandwiched structures 4 or even suspended to avoid the
influence of the substrate 5 .

Transition metal dichalcogenides (TMDCs) are considered one of the most promising two-dimensional
post-graphene materials for electronics owing to the presence of a band gap ranging from 1 to 2 eV 6,7 .
This band gap results in high on–off ratios in classical electronic devices made out of TMDCs 8 . A variety
of electronic devices have been demonstrated on TMDCs, such as field-effect transistors 9–13, heterostructure junctions 14,15 and photodetectors 16,17 .

Meanwhile, from the aspect of quantum nano-devices, TMDCs have advantages over graphene as
well. Unlike etched quantum dots (QDs) made on semimetallic graphene 18,19, semiconducting TMDCs
have a band gap large enough to form a QD using the electric field. This QD decreases the influence
of the edge states, which are a major aspect limiting the performance of graphene nano-devices 20,21 .
Recently, theoretical predictions using QDs on TMDCs as qubits have been proposed 22, and experimental studies of QDs on WSe2 have been performed as well 23 . However, a detailed study of QDs in TMDCs,
and especially the behavior of the Coulomb oscillations, is still not yet available.

Tungsten disulfide (WS2) is a typical semiconducting TMDC material that has a direct band gap of
2.0 eV in a monolayer and an indirect band gap of 1.4 eV in the bulk crystal 6 . Theoretical models predict
that WS2 should have the highest mobility among the semiconducting TMDCs because of the reduced
effective mass 24 . Several previous studies have shown that the typical carrier mobility of WS2 is in the
range of 20–300 cm 2 /(V·s) 11,25,26 .

In this letter, we use standard semiconductor fabrication techniques to fabricate a QD made of
WS2, where Coulomb oscillations are observed. The temperature dependence of the Coulomb peaks is

1Key Laboratory of Quantum Information, CAS, University of Science and Technology of China, Hefei, Anhui
230026, China. 2 Synergetic Innovation Center of Quantum Information & Quantum Physics, University of Science
and Technology of China, Hefei, Anhui 230026, China. Correspondence and requests for materials should be
[addressed to G.-P.G. (email: gpguo@ustc.edu.cn)](mailto:gpguo@ustc.edu.cn)

Figure 1. Device characterization. ( a ) Scanning electron microscope image of the WS2 quantum dot
studied in this work. The WS2 flake is highlighted by the white dotted line, and the four top gates are labeled
as MG, LB, PG, RB. The scale bar represents 5 μ m. ( b ) Three-dimensional schematic view of the device. ( c )
Schematic cross-section of the device. The few-layer WS2 is deposited on a heavily-doped silicon substrate
covered with 100 nm of SiO2. The WS2 flake is separated from the four top gates (Ti/Au) by 100 nm of ALDgrown Al2O3. Two metal gates (Pd/Au) are connected to the flake and used as source-drain contacts.

investigated, showing that the behavior of Coulomb peaks is in agreement with standard semiconductor
QD theory: the full-width-at-half-maximum (FWHM) of the Coulomb peaks increase linearly while the
peak height remain almost unchanged when increasing the temperature. The Coulomb oscillations of
the QD on WS2 are different from those of the graphene etched QDs, wherein Coulomb peaks belonging
to the same QD can have different temperature dependences. Among these Coulomb peaks, only portions can be understood by the standard semiconductor QD theory, while most of the Coulomb peaks
of graphene etched QDs become broader and higher with increasing temperature. Our results indicate
the absence of the disordered confining potential, showing a difference between the potential-forming
mechanisms of graphene etched QDs and WS2 QDs, which may be the reason for the larger potential
fluctuation found in graphene QDs. Meanwhile, the results may be useful for the fabrication of QDs on
graphene-like two-dimensional layered materials.

Results
As shown in Fig. 1(a), the few-layer WS2 flake used in the experiment has an area of approximately
3 × 5 μ m 2, which is highlighted by the white dotted line in the scanning electron microscope image. A
schematic depiction of the device is shown in Fig. 1(b). The heavily doped silicon substrate worked as
the back gate, which was isolated from the WS2 by a 100 nm-thick layer of SiO2. Here, we used Pd/Au for
source-drain contacts (“source” and “drain” in Fig. 1(b)) of the WS2 flake. On the Al2O3 insulating layer,
four split electrodes (“top gates” in Fig. 1(b)) were fabricated using Ti and Au, corresponding to Middle
Gate (MG), Left Barrier (LB), Plunger Gate (PG) and Right Barrier (RB) in Fig. 1(a). The voltage applied
to MG, LB, and RB is mainly to form the confining potential to obtain quantum dot. The effect of PG is
not only for confining the dot, but also for tuning the energy levels in the quantum dot.

Figure 1(c) shows the schematic cross-section of the device. The experiment was performed in a
He3 refrigerator at a base temperature of 240 mK. We used the standard lock-in method to probe the
electronic signals.

First, we applied a dc voltage to the back gate to accumulate carriers in the WS2 device. The source-drain
current is obtained while sweeping the back gate voltage VBG. As shown in Fig. 2(a), the characteristic
behavior of an n-doped semiconductor is observed, that when tuning the back gate voltage to be more
positive, the current becomes nonzero around VBG = 5 V. Note that the puddles may be formed in our
device since some current oscillations are already evident. After we apply a dc voltage of −2 V to the top
gates, the current as a function of the dc bias voltage at varying back gate voltages is measured. As shown
in Fig. 2(b), over 20 consecutive Coulomb diamonds are observed from VBG = 13.2–14 V, indicating
the formation of a QD. The fact that the Coulomb diamonds are symmetric suggests equivalent tunnel

Figure 2. Transport measurement of the device. ( a ) Source-drain current flows through the WS2 devices
as a function of back gate voltage, VBG, showing the characteristic behavior of an n-doped semiconductor.
( b ) Over 20 consecutive Coulomb diamonds of a WS2 quantum dot. Symmetric Coulomb diamonds suggests
equivalent tunnel coupling to the source and drain leads. All of the top gates have an applied dc voltage of

- 2 V. ( c ) The relative peak position as a function of peak number p for the first 10 peaks of ( b ). The red
dashed line is the linear fit for the data (red open circles). ( d ) A Coulomb diamond measured as a function
of the plunger gate voltage VPG. Two black dotted lines mark the two sides of the diamond.

coupling to the source and drain leads. All of the Coulomb diamonds appear to have a similar charging
energy EC of approximately 0.75 meV in logarithmic plotting (Fig. S1 in the supplemental material).

We also investigate the peak spacing of the Coulomb peaks. Figure 2(c) shows the relative peak position as a function of peak number p, for the first 10 peaks of Fig. 2(b). The relative peak position can be
expressed as V(p)− V0, where V(p) is the voltage of the peak p and V0 is the voltage of the first peak.
The data was fitted by a linear function, as shown by red dashed line, suggesting a constant peak spacing
of 36.6 mV. Using the EC and peak spacing ∆V, the lever arm of the back gate αBG is calculated to be
0.0205 eV/V. It is also estimated that the average QD radius is 430 nm using the relationship _EC_ = _e_ 2 /
(8ε0εr _r_ ) 27, where εr = 7 is the relative permittivity of few-layer WS228 and _r_ is the radius of the QD. Note

(8ε0εr _r_ ) 27, where εr = 7 is the relative permittivity of few-layer WS228 and _r_ is the radius of the QD. Note

that because the estimated dot size is comparable to the thickness of the insulating SiO2 layer, the isolated
disk approximation should change to a parallel plate approximation. Thus, the result of the estimated QD
size should be considered as an upper limit, which is comparable to our geometric design of the top
gates.

Further, to confirm that the QD is formed because of the presence of top gates, we use a plunger gate
(PG) to tune the energy levels in the QD. As shown in Fig. 2(d), a Coulomb diamond is observed. These
results are similar to those obtained in previous experiments on WSe223. There are two reasons why we

results are similar to those obtained in previous experiments on WSe223. There are two reasons why we

don’t have a complete Coulomb diamond in Fig. 2(d): (1) The thickness of the insulating layer Al2O3 is
as larger as 100 nm. This will result in a relatively small lever arm α of the top gate, since α ~ ε /d, where
ε is the relative dielectric constant of the insulating layer, and d is the thickness of the insulating layer.
(2) Due to the limitation of ALD-growth quality, ε may also be smaller than theoretical expectation,
resulting in a smaller lever arm as well. Moreover, due to the growth quality limitation, applying high
voltage to top gates may lead to current leakage in the insulating layer (as shown in Fig. 2(d)). We only
applied the voltage to show a dependence on VPG. In fact, comparing the resonant tunneling point in
Fig. 2(b) to that in Fig. 2(d), we found a current difference of about ~10 pA, which means there may be
leakage between the source and the drain. We think the leakage is caused by the insulating layer of Al2O3.
Using the leak current ~10 pA, divided by the voltage applied on the top gates, we can estimate that the
resistance of the Al2O3 layer is about 5 × 10 11 Ω . Although the resistance is large, it may cause a leakage
of several pA, which can be measured in the experiment.

Next, we investigate the temperature dependence of the Coulomb peak to achieve a better understanding of the Coulomb oscillations in WS2. According to the standard theory of semiconductor QDs 29,
the line shape of the Coulomb peak in the weak coupling regime manifests in different forms for different
temperature regimes, such that

Figure 3. Temperature dependence of the Coulomb peaks. ( a ) A typical Coulomb peak of the QD on
WS2 fitted with a Lorentzian (red solid line) and cosh( _x_ ) (blue solid line). (Inset) Same figure plotted in
the logarithmic scale. ( b ) The FWHM (black open squares) and the peak height (blue open circles) of a
typical Coulomb peak as a function of temperature. The dashed lines are linear fits. ( c ) The FWHM of three
Coulomb peaks (labeled as peaks 1, 2, and 3) as a function of temperature. The dashed lines show the linear
fits for each peak, linearly increasing with temperature. ( d ) The peak height of the three Coulomb peaks
in ( c ) (labeled as peaks 1, 2, and 3) as a function of temperature. The peak heights are almost independent
of temperature. ( e ) Normalized Coulomb peak height as a function of temperature. The red (blue) dashed
line shows the temperature dependence of the peak height obtained from the QD (impurity trap) on WS2,
which lies in the classical (quantum) regime. The green solid line indicates the temperature dependence of a
common peak height obtained from a graphene etched QD taken from ref. 21.



_G_ / _Gmax_ = 1 −2 _δ_  if _h_ Γ, ∆ _E_  _k_ _BT_  _e_ 2/ _C_, (classical regime
2 cosh . 2 5 _k_ _BT_ 

/ _Gmax_ = 1 −2 _δ_

2 cosh .



(1)

. 2 5

_B_

2 _δ_ if _h_ Γ, ∆ _E_  _k_ _BT_  _e_ 2

.2 5 _k_ _T_ 

_max_ = if _h_ Γ, ∆ _E_  _k_ _BT_  _e_ / _C_, (classical regime)

2 cosh . 2 5 _k_ _BT_  (1



if _h_ Γ, ∆ _E_  _k_ _BT_  _e_ 2/ _C_, (classical regime)



/ _Gmax_ = ∆ _E_ cosh−2 _δ_





_G_ / _Gmax_ = ∆ _E_ cosh−2 _δ_  if _h_ Γ  _k_ _BT_  ∆, _E_ _e_ 2/ _C_, (quantum regime
4 _k_ _BT_  2 _k_ _BT_ 

(2)



2 _δ_ if _h_ Γ  _k_ _BT_  ∆, _E_ _e_ 2

 2 _k_ _T_ 

_max_ = cosh if _h_ Γ  _k_ _BT_  ∆, _E_ _e_ / _C_, (quantum regime)

4 _k_ _BT_  2 _k_ _BT_  (2

_BT_  2 _k_ _B_



if _h_ Γ  _k_ _BT_  ∆, _E_ _e_ 2/ _C_, (quantum regime)



where _G_ is the conductance of the Coulomb peak, _Gmax_ is the maximum conductance at high temperature, Γ is the tunneling rate through the barriers connecting the QD and the reservoirs, _δ_ is the distance
to the peak center in terms of energy, ∆E is the average level spacing, and _e_ 2 / _C_ is the charging energy. If
the QD is in the strong coupling regime, the formula that describes the line shape of the peak changes
to the well-known Breit–Wigner formula,

2 ( _hΓ_ )2

_h_

2 _e_ 2 ( _hΓ_ )2

_h_ ( _hΓ_ )2 + _δ_

_Γ_

_G_ = 2 _he_ 2 ( _hΓ_ ( _h_ )2 _Γ_ +)2 _δ_ 2 if _T_ = 0, _e_ 2/ _C_  _h_ Γ, ∆. _E_ (3)

2 _he_ 2 ( _hΓ_ ( _h_ )2 _Γ_ +)2 _δ_ 2 if _T_ = 0, _e_ 2/ _C_  _h_ Γ, ∆. _E_ (3

_h_

2 _Γ_ +) _δ_ 2 if _T_ = 0, _e_ 2

( _hΓ_ )2 +

= 0, _e_ 2/ _C_  _h_ Γ, ∆. _E_

The Coulomb peaks in the regime _kBT_ ~ _h_ Γ have the Lorentzian lineshape of Eq. (3), where _kB_ is
Boltzmann’s constant and _T_ is the temperature 27 .

Figure 3(a) shows a typical Coulomb peak from the QD on WS2, where the data (blue open squares)
are fitted using both a Lorentzian curve (red solid line) and a cosh( _x_ ) curve (blue solid line). The peak is
also plotted in the logarithmic scale (Fig. 3(a) inset). The data decrease linearly at the tails of the peak,
showing a deviation from the Lorentzian line shape. Note that only when _kBT_ ≥ _h_ Γ does the slower decay
of the Lorentzian tails become clearly visible 27,30 . According to the fitting curve, it is estimated that _h_ Γ of
the QD is not dominated compared to the temperature.

To give a rough estimation of the order of magnitude, we can estimate the average single particle
energy of the QD to be ∆E = 1.4 μ eV using Δ _E_ = _ħ_ 2 / _m_ * _r_ 2 27, where _r_ is the radius of the QD and
_m_ * = 0.3 _me_ is the effective mass in WS222. Because the temperature varies in the range 290 mK to 1K, it

can be estimated that _kBT_ ~ 50 μ eV, which suggests that the QD is in the classical regime (Δ _E_ ≪ _kBT_ ). We
fit the Coulomb peak at different temperatures using Eq. (1). Figure 3(b) plots the FWHM (black open
squares) and height (blue open circles) of a typical Coulomb peak as a function of temperature, as well
as the linear fits (dashed lines) of the data. The FWHM of the Coulomb peak increases linearly with the
temperature while the peak height remains almost constant.

Three typical Coulomb peaks in the range of VBG = 12.32–12.43 V are also tracked in the same way
(labeled as peaks 1, 2, and 3). The FWHM of these peaks as a function of the temperature is shown in
Fig. 3(c). The FWHM decreases linearly while lowering the temperature. Using the linear fitting slopes
and the previously obtained lever arm, we can estimate the FWHM to be (1.41 ± 0.07) _kBT_ .

Using Eq. (1), the FWHM is calculated to be 4.4 kBT in the classical regime, which is almost three
times the value measured in the experiment. The difference in slope between the theory and experiment
can be caused by many reasons, such as the tunneling rate broadening and larger effective electron temperature 27 . The deviation from the theoretical expectation suggests that the assumption that the effect of
hΓ can be neglected may not be appropriate. There may also be other reasons which need to be further
studied.

Figure 3(d) shows the Coulomb peak heights of the three peaks as a function of the temperature,
exhibiting a behavior that is almost independent of the temperature. This is the signature of Coulomb
peaks in the classical regime 29 . Moreover, when changing to the region where a large bias voltage, VSD,
is applied, another series of Coulomb diamonds with a charging energy _EC_ larger than 30 meV emerge
(Fig. S2 in the supplemental material). Because this series of Coulomb peaks has a much larger _EC_ and
is nearly independent of the gate voltages applied on the top gates, it is considered to be the result of an
impurity trap. The effective QD radius of this area is estimated to be 10 nm, resulting in the single particle
energy of ∆E = 2.6 meV. Compared to _kBT_ ~ 50 μ eV, Coulomb oscillations of the impurity trap lies in the
quantum regime ( _kBT_ ≪ Δ _E_ ). Similarly, we investigate the temperature dependence of two typical peaks
of the impurity trap (Fig. S3 in the supplemental material). The height of the Coulomb peak decrease
linearly with increasing temperature, which is the signature of a Coulomb peak in the quantum resonant
tunneling regime 29 .

Figure 3(e) shows the normalized peak heights as a function of temperature for Coulomb peaks
obtained from the QD (red dashed line) and the impurity trap (blue dashed line) on WS2. The peak
height of the impurity trap (quantum regime) has a much larger slope that decreases with temperature,
which is consistent with theoretical predictions 29 . Meanwhile, the nonzero slope of the QD (classical
regime) may be caused by the influence of the impurity in WS2 flake. However, although the impurity
trap exists in our device, the behavior of the Coulomb peaks is still in agreement with standard semiconductor QD theory. Note that these results are different from those found with graphene etched QDs,
wherein Coulomb peaks belonging to the same QD are able to have different temperature dependences.
Among these Coulomb peaks, only portions can be understood by the standard semiconductor theory, while most of the Coulomb peaks becoming broader and higher with increasing temperature 21,31 .
The temperature dependence of the normalized peak height of graphene etched QDs is also plotted in
Fig. 3(e) for contrast, using a green solid line (The data is from ref. 21.).

Discussion
The anomalous behavior of Coulomb peaks in a graphene etched QD is widely considered to be the
result of a disordered confining potential 32 since the edge states are formed in the narrow constrictions
connecting the QD and the reservoirs. Moreover, this disordered confining potential may limit the performance of the graphene etched QD because low-frequency noise experiments on graphene QDs exhibit
a larger fluctuation of potential 21 . Our results, which are consistent with standard semiconductor theory,
suggest the existence of an energy-independent tunneling barrier, which is different from the situation
existing in graphene QDs. The difference, which relates to the edge states, in the barrier-forming mechanisms of an graphene etched QD and a WS2 QD, may contribute to the larger noise level found in
graphene QDs. Meanwhile, the designed device structure used in our experiment, where a disordered
confining potential is absent, may be useful for the fabrication of QDs on graphene-like two-dimensional
layered materials.

In summary, we use standard semiconductor fabrication techniques to fabricate a QD on WS2, which
is one of the TMDCs materials. The FWHM of the Coulomb peaks increases linearly with temperature
while the height of the peaks remains nearly independent of temperature, showing that the behavior of
the Coulomb oscillations is consistent with standard semiconductor QD theory. Unlike etched graphene
QDs, where Coulomb peaks belonging to the same QD can have different temperature dependences, our
results indicate the absence of a disordered confining potential. This difference in the potential-forming
mechanisms of graphene etched QDs and WS2 QDs may be the reason for the larger potential fluctuation found in graphene QDs. Meanwhile, the designed device structure used in our experiment, which
is isolated from the edge states, illustrates the fabrication of QDs on graphene-like two-dimensional
layered materials.

Methods
The WS2 flakes were produced by mechanically cleaving a bulk WS2 crystal using the “Scotch tape”
method onto a highly-doped silicon substrate covered by 100 nm of SiO2, similar to the method used
to fabricate graphene devices 19,31 . Few-layer flakes were selected using an optical microscope. The flake
of the device studied in the experiment has a thickness of approximately 7–10 layers according to our
experience. The source-drain electrodes were formed using a standard electron beam lithography (EBL)
process followed by electron beam evaporation to deposit 10 nm of Pd and 90 nm of Au. After a standard
lift-off process, an atomic layer deposition (ALD) technique was used to make a 100 nm-thick insulating
Al2O3 layer. Then another EBL step was subsequently applied to form a pattern of four split top gates.
Using electron beam evaporation, 5 nm of Ti and 45 nm of Au was deposited to fabricate the top gates.
After the Al2O3 layer covering the source-drain contacts was etched, the device was bonded to the chip
carrier and was ready for measurements.

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Acknowledgements
This work was supported by the National Fundamental Research Program (Grant No. 2011CBA00200),
the National Natural Science Foundation (Grand Nos. 11222438, 11174267, 61306150, 11304301 and
91121014) and the Chinese Academy of Sciences.

Author Contributions
X.-X.S. fabricated the samples. X.-X.S., J.Y. and D.L. performed the measurements. X.-X.S., Z.-Z.Z., H.O.L., G.C. and M.X. provided theoretical support. Data are analyzed by X.X.S., J.Y. and Z.-Z.Z. The
manuscript is prepared by X.-X.S., Z.-Z.Z. and G.-P.G. G.-P.G. supervised the project. All authors
contributed in discussing the results and commented on the manuscript.

Additional Information
Supplementary information [accompanies this paper at http://www.nature.com/srep](http://www.nature.com/srep)

Competing financial interests: The authors declare no competing financial interests.

How to cite this article : Song, X.-X. _et al._ Temperature dependence of Coulomb oscillations in a fewlayer two-dimensional WS2 quantum dot. _Sci. Rep._ 5, 16113; doi: 10.1038/srep16113 (2015).

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