Imaging quantum dot formation in MoS2 nanostructures

Among two-dimensional materials, semiconducting ultrathin sheets of MoS2 are promising for nanoelectronics. We show how a scanning probe microscope (SPM) can be used to image the flow of electrons in a MoS2 Hall bar sample at 4.2 K allowing us to understand device physics at the nanoscale. The SPM tip acts as a movable gate and capacitively couples the SPM tip to the device below. By measuring the change in device conductance as the tip is raster scanned across the sample, spatial maps of the device conductance can be obtained. We present images showing the characteristic ‘bullseye’ pattern of Coulomb blockade conductance rings around a quantum dot formed in a narrow contact as the carrier density is depleted with a backgate. These images show 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.


Introduction
Ultrathin sheets of MoS 2 , which are only a few atoms thick, conduct well and display electronic properties including a thickness-and strain-dependent bandstructure, valley Hall effects and spin-valley physics [1][2][3][4][5][6]. For graphene, covering both sides of a graphene sheet with layers of hexagonal boron nitride (hBN) greatly enhances the carrier mobility, resulting in ballistic transport [7]. However, the measured mobility in hBN-encapsulated MoS 2 devices is limited to moderate values (500-2000 cm 2 V −1 s −1 ) by scattering from lattice defects, charged impurities, and substrate adsorbates [8][9][10][11][12][13][14][15]. Direct imaging of electron motion in MoS 2 devices can give us vital information about device physics at the nanoscale, helping us to develop better devices. In previous research, we used our cooled SPM to image quantum dots formed in a GaAs 2DEG [16] and in an InAs/InP nanowire [17] by using the tip as a scanning gate to tune the number of electrons on the dot, creating rings of high conductance about the dot that correspond to Coulomb blockade conductance peaks [16,17].
In this paper, we have adapted our SPM technique to image electron flow and characterize disorder in a MoS 2 device. We present conductance images that reveal quantum dot formation in a three layer MoS 2 device at 4.2 K, by using the tip to locally gate the quantum dot. The device is a hBN-MoS 2 -hBN sandwich patterned into a Hall bar geometry, shown in figure 1(a). As the carrier density is reduced toward the charge neutral point, we find that quantum dots are created in the small side contact indicated in figure 1(a)  Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. white square, characterized by 'bullseye' pattern of Coulomb conductance peaks around each dot. From the spacing between the conductance rings and their dependence on backgate, we locate each dot and determine its radius.

Device fabrication
Using a dry transfer technique, we assembled a van der Waals heterostructure consisting of a few layer MoS 2 sheet contacting graphene sheets on all sides encased by two insulating hBN layers. The assembly is then transferred to a heavily doped silicon wafer covered with a SiO 2 layer that is 285 nm thick. The device is subsequently vacuum-annealed at 350°C to reduce structural inhomogeneity. Finally, the Hall bar geometry is defined by reactive ion etching and a 1D edge contact 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 MoS 2 sample; the white square indicates the regions of image scans. The Hall bar is patterned from a hBN/MoS 2 /hBN sandwich. It has dimensions 5.0×11.0 μm 2 , with two narrow (1.0 μm) contacts along each side, separated by 3.0 μm, and large source and drain contacts (width 3.0 μm) at either end. The heavily doped Si substrate acts as a backgate, covered by a 285 nm insulating layer of SiO 2 . The backgate capacitance is C G =11.5 nF. The density n can be tuned by applying a voltage V G between the backgate and the MoS 2 channel. The density n is determined by hall measurements, using the side contacts.

Cooled scanning probe microscope (SPM)
We use a home-built cooled SPM to image quantum dot formation in our sample [16,17]. The microscope assembly consists of a head assembly where the tip is attached and a cage assembly enclosing the piezotube translator that scans a sample fixed on top in the X, Y and Z directions. Scans are performed by actuating the piezotube with home-built electronics including an X-Y position controller for scanning, and a feedback Z controller for topological scans of the sample surface. The microscope assembly is placed in an insert inside a liquid He Dewar; the insert is filled with 3.0 mbar of He exchange gas to cool the sample and SPM. For the transport measurements, standard lock-in amplifiers are used. For the scanning gate measurements, an SPM tip of 10 nm radius was held at a fixed height 10 nm above the BN surface, which is approximately 50 nm above MoS 2 layer.
To image quantum dot formation using our cooled SPM, a voltage V s is applied between a side contact and the grounded source of the device. At each tip position, the sample conductance G=I s /V s is measured by the current I s . The work function on the tip changes the chemical potential of a dot located inside the MoS 2 channel with a corresponding potential ( figure 1(b)) that tunes the number of electrons in the dot, producing a change ΔG in the conductance. An image of rings of high conductance about the dot corresponding to Coulomb blockade conductance peaks is created by displaying ΔG as the tip is raster scanned above the sample at a constant height h.

Circuit model for tip-dot-backgate capacitance
Using a simple circuit model (figure 1(c)) we derive an expression to measure the radius of the quantum dot from the SPM images such as those shown in figure 4. The circuit includes the small tip-to-dot capacitance C td and the large backgate-to-dot capacitance C gd associated with the heavily doped Si substrate. The dot potential is V dot , the backgate potential is V G and the tip potential is V tip . Using a standard model, the conical tip is modeled by two conducting spheres at the same potential: a small sphere with the tip radius a tip and a much larger sphere representing the top of the cone. When the tip is scanned across the sample, the distance is larger than the tip diameter, but generally small compared with the large sphere radius; the tip motion provides the contrast, while the top of the cone provides a background level. The tip-to-dot capacitance is given by: where a dot is the dot radius, a tip is the tip radius, and r td is the distance between the tip and the dot. Similarly, the backgateto-dot capacitance is given by:

Experimental results
As the electron gas inside the MoS 2 device is depleted, the SPM images reveal the presence of quantum dots associated with pools of electrons at low points in the background potential. Figure 3(a) shows an image of ΔG taken inside the narrow contact at the upper left side ( figure 1(a)). A clear bullseye pattern of Coulomb blockade conductance peaks circle the location of a quantum dot; the tip is acting as a movable gate, and the number of electrons on the dot changes by one as the tip moves from one ring to the next. As the electron density is increased in figure 2(b), a second quantum dot appears. Similar images of quantum dots were recorded previously for dots formed by top gates in a GaAs/AlGaAs heterostructure [16] and for an InAs dot formed in a InAs/InP nanowire [17].

Estimation of dot radius
Cooled SPM images of bullseye pattern of conductance rings are shown in figures 2(a) and (b). In these images, the backgate voltage is kept fixed at V G =4.80 V and V G =5.29 V,  respectively. In figure 2(a), a single quantum dot is located at the center of the bullseye. Each conductance ring corresponds to an electron being added to the dot Δq dot =e, where e is the electron charge, by changing the tip-to-dot capacitance via tip motion. Using Method 1, from the spacing between these rings and their distance from the center, we can compute the size and position of the dot. In figure 3, the plot of the ring spacing Δr td versus r td 2 shows a linear dependence which agrees well with equation (5).
The slope determines the dot radius a dot =180 nm, using V tip = −1.00 V and a tip =10 nm. For Method 2, we keep the tip position fixed and change the backgate voltage V G . figures 4(a)-(h) shows a series of SPM images of ΔG in the same location as figure 4 for backgate voltages ranging from (a) V G =4.80 V to (h) V G =5.29 V. An additional quantum dot appears as the density is increased.
To measure the effect of changing V G , we pick a fixed tip position X=−0.5 μm, Y=0.5 μm. Figure 5 plots ΔG at this tip position versus V G . Figure 5 shows five peaks, and each peak corresponds to the addition of one electron charge e to the quantum dot. To get the peak spacing, the peak position in V G versus the peak number is plotted. The slope of this line gives the average peak spacing ΔV G =50 mV. By putting the average peak spacing in V G into equation (6), we obtain the quantum dot radius a dot =150 nm, in good agreement with the dot radius found by Method 1.

Conclusion
In our imaging experiment, a cooled SPM shows quantum dots formation in the narrow side contacts in a MoS 2 Hall bar device at low electron density. We observe the characteristic bullseye pattern of Coulomb conductance peaks from two quantum dots formed in the narrow contact at the upper left of figure 1(a). Using a capacitive model, we estimate the dot radius using two methods to be a dot =180 nm and a dot =150 nm, in good agreement. The quantum dots are presumably formed by pools of electrons at minima in the background potential.
This paper demonstrates how a cooled SPM can image the presence of quantum dots created at low densities by roughness in the background potential, giving their location and radius, using our previously developed technique [16,17]. By combining SPM imaging with photoluminescence and Raman microscopy, investigators will be able to probe the sources of non-uniformity in MoS 2 . This approach could be extended to sheets of other semiconducting transition metal dichalcogenide materials.  To get the peak spacing, the peak position in V G versus peak number is plotted and slope of this line gives average peak spacing ΔV G = 50 mV. Using the expression for charge induced in the quantum dot as V G is varied, the measured dot radius is a dot =150 nm in good agreement with figure 4.