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S Bhandari, K Wang, [K Watanabe](https://orcid.org/0000-0003-3701-8119), [T Taniguchi](https://orcid.org/0000-0002-1467-3105), P Kim, R M Westervelt

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[Imaging quantum dot formation in MoS2 nanostructures](https://mdr.nims.go.jp/datasets/be06c1a8-f69b-4d46-a93b-7f04a11e9cdb)

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Imaging quantum dot formation in MoS2 nanostructuresNanotechnologyLETTER • OPEN ACCESSImaging quantum dot formation in MoS2nanostructuresTo cite this article: S Bhandari et al 2018 Nanotechnology 29 42LT03 View the article online for updates and enhancements.Related contentScanning gate imaging of quantum dots in1D ultra-thin InAs/InP nanowiresErin E Boyd, Kristian Storm, LarsSamuelson et al.-Imaging electron motion in grapheneSagar Bhandari and Robert M Westervelt-Scanning gate imaging of two coupledquantum dots in single-walled carbonnanotubesXin Zhou, James Hedberg, YoichiMiyahara et al.-This content was downloaded from IP address 144.213.253.16 on 19/08/2018 at 02:46https://doi.org/10.1088/1361-6528/aad79fhttp://iopscience.iop.org/article/10.1088/0957-4484/22/18/185201http://iopscience.iop.org/article/10.1088/0957-4484/22/18/185201http://iopscience.iop.org/article/10.1088/1361-6641/32/2/024001http://iopscience.iop.org/article/10.1088/0957-4484/25/49/495703http://iopscience.iop.org/article/10.1088/0957-4484/25/49/495703http://iopscience.iop.org/article/10.1088/0957-4484/25/49/495703http://oas.iop.org/5c/iopscience.iop.org/307808967/Middle/IOPP/IOPs-Mid-NANO-pdf/IOPs-Mid-NANO-pdf.jpg/1?LetterImaging quantum dot formation in MoS2nanostructuresS Bhandari1 , K Wang2, K Watanabe3, T Taniguchi3, P Kim1 andR M Westervelt11 School of Engineering and Applied Sciences and Department of Physics, Harvard University, MA 02138,United States of America2 School of Physics and Astronomy, University of Minnesota, MN 55455, United States of America3National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, JapanE-mail: sbhandar@fas.harvard.eduReceived 21 May 2018, revised 26 June 2018Accepted for publication 2 August 2018Published 14 August 2018AbstractAmong two-dimensional materials, semiconducting ultrathin sheets of MoS2 are promising fornanoelectronics. We show how a scanning probe microscope (SPM) can be used to image theflow of electrons in a MoS2 Hall bar sample at 4.2 K allowing us to understand device physics atthe nanoscale. The SPM tip acts as a movable gate and capacitively couples the SPM tip to thedevice below. By measuring the change in device conductance as the tip is raster scanned acrossthe sample, spatial maps of the device conductance can be obtained. We present images showingthe characteristic ‘bullseye’ pattern of Coulomb blockade conductance rings around a quantumdot formed in a narrow contact as the carrier density is depleted with a backgate. These imagesshow that multiple dots are created by the disorder potential in MoS2. From these SPM images,we estimate the size and position of these quantum dots using a capacitive model.Keywords: scanning probe microscope, MoS2, quantum dots, imaging quantum dots(Some figures may appear in colour only in the online journal)1. IntroductionUltrathin sheets of MoS2, which are only a few atoms thick,conduct well and display electronic properties including athickness- and strain-dependent bandstructure, valley Halleffects and spin-valley physics [1–6]. For graphene, coveringboth sides of a graphene sheet with layers of hexagonal boronnitride (hBN) greatly enhances the carrier mobility, resultingin ballistic transport [7]. However, the measured mobility inhBN-encapsulated MoS2 devices is limited to moderate values(500–2000 cm2 V−1 s−1) by scattering from lattice defects,charged impurities, and substrate adsorbates [8–15]. Directimaging of electron motion in MoS2 devices can give us vitalinformation about device physics at the nanoscale, helping usto develop better devices. In previous research, we used ourcooled SPM to image quantum dots formed in a GaAs 2DEG[16] and in an InAs/InP nanowire [17] by using the tip as ascanning gate to tune the number of electrons on the dot,creating rings of high conductance about the dot that corre-spond to Coulomb blockade conductance peaks [16, 17].In this paper, we have adapted our SPM technique toimage electron flow and characterize disorder in a MoS2device. We present conductance images that reveal quantumdot formation in a three layer MoS2 device at 4.2 K, by usingthe tip to locally gate the quantum dot. The device is ahBN-MoS2-hBN sandwich patterned into a Hall bar geo-metry, shown in figure 1(a). As the carrier density is reducedtoward the charge neutral point, we find that quantum dots arecreated in the small side contact indicated in figure 1(a) by theNanotechnologyNanotechnology 29 (2018) 42LT03 (5pp) https://doi.org/10.1088/1361-6528/aad79fOriginal content from this work may be used under the termsof the Creative Commons Attribution 3.0 licence. Anyfurther distribution of this work must maintain attribution to the author(s) andthe title of the work, journal citation and DOI.0957-4484/18/42LT03+05$33.00 © 2018 IOP Publishing Ltd Printed in the UK1https://orcid.org/0000-0003-1007-9034https://orcid.org/0000-0003-1007-9034https://orcid.org/0000-0001-9836-3923https://orcid.org/0000-0001-9836-3923mailto:sbhandar@fas.harvard.eduhttps://doi.org/10.1088/1361-6528/aad79fhttp://crossmark.crossref.org/dialog/?doi=10.1088/1361-6528/aad79f&domain=pdf&date_stamp=2018-08-14http://crossmark.crossref.org/dialog/?doi=10.1088/1361-6528/aad79f&domain=pdf&date_stamp=2018-08-14http://creativecommons.org/licenses/by/3.0white square, characterized by ‘bullseye’ pattern of Coulombconductance peaks around each dot. From the spacingbetween the conductance rings and their dependence onbackgate, we locate each dot and determine its radius.2. Methods2.1. Device fabricationUsing a dry transfer technique, we assembled a van der Waalsheterostructure consisting of a few layer MoS2 sheet con-tacting graphene sheets on all sides encased by two insulatinghBN layers. The assembly is then transferred to a heavilydoped silicon wafer covered with a SiO2 layer that is 285 nmthick. The device is subsequently vacuum-annealed at 350 °Cto reduce structural inhomogeneity. Finally, the Hall bargeometry is defined by reactive ion etching and a 1D edgecontact to each graphene layer is fabricated with Cr/Pd/Au(1.5 nm/5 nm/120 nm) metal deposition.Figure 1(a) shows an optical image of the Hall bar MoS2sample; the white square indicates the regions of image scans.The Hall bar is patterned from a hBN/MoS2/hBN sandwich.It has dimensions 5.0×11.0 μm2, with two narrow (1.0 μm)contacts along each side, separated by 3.0 μm, and largesource and drain contacts (width 3.0 μm) at either end. Theheavily doped Si substrate acts as a backgate, covered by a285 nm insulating layer of SiO2. The backgate capacitance isCG=11.5 nF. The density n can be tuned by applying avoltage VG between the backgate and the MoS2 channel. Thedensity n is determined by hall measurements, using the sidecontacts.2.2. Cooled scanning probe microscope (SPM)We use a home-built cooled SPM to image quantum dotformation in our sample [16, 17]. The microscope assemblyconsists of a head assembly where the tip is attached and acage assembly enclosing the piezotube translator that scans asample fixed on top in the X, Y and Z directions. Scans areperformed by actuating the piezotube with home-built elec-tronics including an X–Y position controller for scanning, anda feedback Z controller for topological scans of the samplesurface. The microscope assembly is placed in an insert insidea liquid He Dewar; the insert is filled with 3.0 mbar of Heexchange gas to cool the sample and SPM. For the transportmeasurements, standard lock-in amplifiers are used. For thescanning gate measurements, an SPM tip of 10 nm radius washeld at a fixed height 10 nm above the BN surface, which isapproximately 50 nm above MoS2 layer.To image quantum dot formation using our cooled SPM,a voltage Vs is applied between a side contact and thegrounded source of the device. At each tip position, thesample conductance G=Is/Vs is measured by the current Is.The work function on the tip changes the chemical potentialof a dot located inside the MoS2 channel with a correspondingpotential (figure 1(b)) that tunes the number of electrons in thedot, producing a change ΔG in the conductance. An image ofrings of high conductance about the dot corresponding toCoulomb blockade conductance peaks is created by display-ing ΔG as the tip is raster scanned above the sample at aconstant height h.2.3. Circuit model for tip-dot-backgate capacitanceUsing a simple circuit model (figure 1(c)) we derive anexpression to measure the radius of the quantum dot from theSPM images such as those shown in figure 4. The circuitincludes the small tip-to-dot capacitance Ctd and the largebackgate-to-dot capacitance Cgd associated with the heavilydoped Si substrate. The dot potential is Vdot, the backgatepotential is VG and the tip potential is Vtip. Using a standardmodel, the conical tip is modeled by two conducting spheresat the same potential: a small sphere with the tip radius atipFigure 1. (a) Optical image of the hBN/MoS2/hBN device patterned into (a) Hall bar geometry. The white outline indicates the region whereSPM imaging experiments were performed. (b) Schematic diagram showing the potential inside the MoS2 layer created by the SPM tip,which tunes the chemical potential of a quantum dot in the device below, changing the device conductance ΔG. An image is formed bydisplaying ΔG versus tip position as the tip is raster scanned across the sample. (c) Schematic circuit model of a quantum dot, showing thetip-to-dot capacitance Ctd and the backgate-to-dot capacitance Cgd (see equation (3)).2Nanotechnology 29 (2018) 42LT03and a much larger sphere representing the top of the cone.When the tip is scanned across the sample, the distance islarger than the tip diameter, but generally small comparedwith the large sphere radius; the tip motion provides thecontrast, while the top of the cone provides a backgroundlevel. The tip-to-dot capacitance is given by:Ca ar4, 1tdo dot tiptdp= ( )where adot is the dot radius, atip is the tip radius, and rtd is thedistance between the tip and the dot. Similarly, the backgate-to-dot capacitance is given by:Cad42. 2gdo dot2p= ( )From the circuit model in figure 4(c), the dot charge qdot is:q C V C V . 3dot td tip gd G= +( ) ( )We apply two methods to induce a change Δqdot in the dotcharge. Method 1 involves changing the tip position by Δrtd toinduce a change in dot charge Δqdot while keeping the backgatevoltage VG fixed. For this caseqdqdrrdCdrr . 4dotdottdtdtdtdtdD = D = D ( )Therefore, charge induced in the dot by a change in tip positionΔrtd becomesq V Va arr4. 5dot tip Go dot tiptdtd2pD = + D( ) ( ) ( )Method 2 involves inducing Δqdot by a change in thebackgate voltage VG keeping the tip position fixed. For thismethodqdqdVV C V . 6dotdotGG gd GD = D = D ( )3. Results and discussion3.1. Experimental resultsAs the electron gas inside the MoS2 device is depleted, theSPM images reveal the presence of quantum dots associatedwith pools of electrons at low points in the backgroundpotential. Figure 3(a) shows an image of ΔG taken inside thenarrow contact at the upper left side (figure 1(a)). A clearbullseye pattern of Coulomb blockade conductance peakscircle the location of a quantum dot; the tip is acting as amovable gate, and the number of electrons on the dot changesby one as the tip moves from one ring to the next. As theelectron density is increased in figure 2(b), a second quantumdot appears. Similar images of quantum dots were recordedpreviously for dots formed by top gates in a GaAs/AlGaAsheterostructure [16] and for an InAs dot formed in a InAs/InPnanowire [17].3.2. Estimation of dot radiusCooled SPM images of bullseye pattern of conductance rings areshown in figures 2(a) and (b). In these images, the backgatevoltage is kept fixed at VG =4.80 V and VG =5.29 V,Figure 2. (a) Display of conductance change ΔG versus tip position at the narrow contact (see figure 1) for VG =4.80 V, when the device isnearly depleted. The bullseye pattern of concentric rings are Coulomb blockade conductance peaks associated with a quantum dot at thecenter. (b) As the density is increased for VG =5.29 V an additional quantum dot appears at a different location.Figure 3. Spacing Δrtd between conductance rings versus radialdistance rtd between the tip and bullseye center. The measured dotradius is adot =180 nm.3Nanotechnology 29 (2018) 42LT03respectively. In figure 2(a), a single quantum dot is located at thecenter of the bullseye. Each conductance ring corresponds to anelectron being added to the dotΔqdot =e, where e is the electroncharge, by changing the tip-to-dot capacitance via tip motion.Using Method 1, from the spacing between these rings and theirdistance from the center, we can compute the size and position ofthe dot. In figure 3, the plot of the ring spacing Δrtd versus rtd2shows a linear dependence which agrees well with equation (5).The slope determines the dot radius adot =180 nm, using Vtip =−1.00 V and atip =10 nm.For Method 2, we keep the tip position fixed and change thebackgate voltage VG. figures 4(a)–(h) shows a series of SPMimages of ΔG in the same location as figure 4 for backgatevoltages ranging from (a) VG =4.80 V to (h) VG =5.29 V. Anadditional quantum dot appears as the density is increased.To measure the effect of changing VG, we pick a fixed tipposition X=−0.5 μm, Y=0.5 μm. Figure 5 plots ΔG atthis tip position versus VG. Figure 5 shows five peaks, andeach peak corresponds to the addition of one electron charge eto the quantum dot. To get the peak spacing, the peak positionin VG versus the peak number is plotted. The slope of this linegives the average peak spacing ΔVG =50 mV. By puttingthe average peak spacing in VG into equation (6), we obtainthe quantum dot radius adot =150 nm, in good agreementwith the dot radius found by Method 1.4. ConclusionIn our imaging experiment, a cooled SPM shows quantumdots formation in the narrow side contacts in a MoS2 Hall bardevice at low electron density. We observe the characteristicbullseye pattern of Coulomb conductance peaks from twoquantum dots formed in the narrow contact at the upper leftof figure 1(a). Using a capacitive model, we estimate thedot radius using two methods to be adot =180 nm andadot =150 nm, in good agreement. The quantum dots arepresumably formed by pools of electrons at minima in thebackground potential.This paper demonstrates how a cooled SPM can imagethe presence of quantum dots created at low densities byroughness in the background potential, giving their locationand radius, using our previously developed technique[16, 17]. By combining SPM imaging with photo-luminescence and Raman microscopy, investigators will beable to probe the sources of non-uniformity in MoS2. Thisapproach could be extended to sheets of other semiconductingtransition metal dichalcogenide materials.Figure 4. Images that display ΔG versus tip position in the narrow contact at the same locations as figure 3 for a series of backgate voltagesindicated on the figure, ranging from (a) VG =4.80 V to (h) VG =5.29 V. The bullseye pattern of Coulomb conductance peaks in (a) showsthe existence of a quantum dot. A second dot is created as VG is increased.Figure 5. Plot of the conductance change ΔG from the series ofimages at tip position. X=−0.5 μm, Y=0.5 μm versus VG. To getthe peak spacing, the peak position in VG versus peak number isplotted and slope of this line gives average peak spacing ΔVG =50 mV. Using the expression for charge induced in the quantum dotas VG is varied, the measured dot radius is adot =150 nm in goodagreement with figure 4.4Nanotechnology 29 (2018) 42LT03AcknowledgmentsThe SPM imaging experiments and the ray-tracing simula-tions were supported by the US DOE Office of Basic EnergySciences, Materials Sciences and Engineering Division, undergrant DE-FG02-07ER46422. The MoS2 sample fabricationwas supported by Air Force Office of Scientific Researchcontract FA9550-14-1-0268 and Army Research Office con-tract W911NF-14-1-0247. Growth of hexagonal boron nitridecrystals was supported by the Elemental Strategy Initiativeconducted by the MEXT, Japan and a Grant-in-Aid for Sci-entific Research on Innovative Areas No. 2506 ‘Science ofAtomic Layers’ from JSPS. Nanofabrication was performedin the Center for Nanoscale Systems (CNS) at Harvard Uni-versity, a member of the National Nanotechnology Coordi-nated Infrastructure Network (NNCI), which is supportedby the National Science Foundation under NSF awardECCS-1541959.ORCID iDsS Bhandari https://orcid.org/0000-0003-1007-9034R M Westervelt https://orcid.org/0000-0001-9836-3923References[1] Kim S et al 2012 Nat. Commun. 3 1011[2] Mak K F, McGill K L, Park J and McEuen P L 2014 Science344 1489–92[3] Mak K F et al 2012 Nat. Nanotechnol. 7 494–8[4] Conley H J et al 2013 Nano Lett. 13 3626–30[5] Han P et al 2018 Nanotechnology 29 20[6] Zhang Y et al 2012 Nano Lett. 12 1136–40[7] Dean C R et al 2010 Nat. Nanotechnol. 5 722–6[8] Xiao D, Liu G-B, Feng W, Xu X and Yao W 2012 Phys. Rev.Lett. 108 196802[9] Baugher B W, Churchill H O, Yang Y and Jarillo-Herrero P2013 Nano Lett. 13 4212–6[10] Cui X et al 2015 Nat. Nanotechnol. 10 6[11] Oiu H, Pan L, Yao Z, Li J, Shi Y and Wang X 2012 Appl.Phys. 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Introduction 2. Methods 2.1. Device fabrication 2.2. Cooled scanning probe microscope (SPM) 2.3. Circuit model for tip-dot-backgate capacitance 3. Results and discussion 3.1. Experimental results 3.2. Estimation of dot radius 4. Conclusion Acknowledgments References