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Mesoscale Imperfections in MoS2 Atomic Layers Grown by Vapor Transport Technique

The success of isolating small flakes of atomically thin layers through mechanical exfoliation has triggered enormous research interest in graphene and other two-dimensional materials. For device applications, however, controlled large-area synthesis of highly crystalline monolayers with a low density of electronically active defects is imperative. Here, we demonstrate the electrical imaging of dendritic ad-layers and grain boundaries in monolayer molybdenum disulfide (MoS2) grown by vapor transport technique using microwave impedance microscopy. The micrometer-sized precipitates in our films, which appear as a second layer of MoS2 in conventional height and optical measurements, show 2 orders of magnitude higher conductivity than that of the single layer. The zigzag grain boundaries, on the other hand, are shown to be more resistive than the crystalline grains, consistent with previous studies. Our ability to map the local electrical properties in a rapid and nondestructive manner is highly desirable for optimizing the growth process of large-scale MoS2 atomic layers.

Single-layer molybdenum disulfide (MoS 2 ) is an atomically thin direct band gap (E g = 1.8eV) semiconductor [1,2]. Followed by the discovery of thickness dependent indirect-to-direct-gap transition [1,2] and valley quantum physics [36], many device prototypes, such as field-effect transistors [710], photo detectors [11,12], and floating gate memories [13], were reported on exfoliated MoS 2 samples. In order to meet the needs for next generation nanoelectronics, however, the production of large-area and high-quality monolayer MoS 2 films is a must. In the past few years, significant effort has been devoted to this research direction and the progress has been breathtaking [1420].
The amount of imperfections on the chemically grown monolayer MoS 2 is a good measure of the film quality. Point defects, including vacancies of the host atoms and unintentional impurity atoms, usually receive the most attention because they directly dope the semiconductor and shift its chemical potential [21,22]. There exist, on the other hand, defects in the mesoscopic (nanometer to micrometer) length scale. For example, several experimental and theoretical studies have investigated the influence of grain boundaries (GBs) on the local electronic properties [19][20][21]. Moreover, it is widely observed that micrometer-sized irregular ad-layers are overgrown on the MoS 2 monolayer [19,20]. If their electrical properties deviate significantly from the underlying single layers, these mesoscale imperfections could dominate the performance when the device dimension approaches the same length scale. It is thus crucial to perform spatially resolved electrical characterization, preferably in a rapid and nondestructive fashion, on various as-grown MoS 2 thin films.
In this study, the MoS 2 atomic films on SiO 2 (285nm)/Si substrates were prepared by the sulfurization of MoO 3 , a process similar to those described in references [15,19,20] (see Methods and Supporting Information S1 for details). Figure 1 shows the scanning electron microscopy (SEM) images of the deposited film at various distances away from the MoO 3 precursor. At the onset of monolayer growth, small isolated MoS 2 islands that are nearly round in shape are observed in Fig. 1(a). Moving towards the MoO 3 source, the flakes become bigger in size and more triangular in shape [ Fig. 1(b)]. As the size of individual triangles reaches 30~50m, neighboring grains start to merge [ Fig. 1(c)] and eventually form a pseudocontinuous film [ Fig. 1(d)]. From the SEM images, two types of mesoscale defects are clearly seen on the monolayer MoS 2 . As shown in Fig. 1(e), dendritic precipitates with various sizes are randomly distributed within individual grains. The merging of different islands is more complicated. As previously reported [20], the ad-layer overgrowth may or may not occur on the grain boundaries, both observed in our samples [ Fig. 1(f) and Fig. 1(g)]. While our current effort in growth aims to minimize the areal density of these defects, the goal of this work is to fully evaluate their electrical properties with respect to the underlying monolayer MoS 2 .
Figs. 2(a-c) show the conventional Raman and photoluminescence (PL) studies of a single domain monolayer MoS 2 (more details in Supporting Information S2). Due to its sensitivity to inter-layer coupling, the well-established Raman spectroscopy has become the standard technique to determine the number of layers in 2D van der Waals materials [23]. At the same time, the direct band gap in monolayer MoS 2 leads to a pronounced PL peak [1] when excited by the same laser in our Raman setup. As seen in the Raman and PL maps, the dendritic regions display a wider E 1 2g -A 1g frequency separation and a much weaker PL signal than the monolayer MoS 2 background. Combined with the atomic force microscopy [AFM, Fig. 2 bilayers.
An AFM-based microwave impedance microscope (MIM) was employed to study the local conductivity of the synthesized MoS 2 atomic layers. MIM is the GHz-frequency analogue of near-field scanning optical microscopy (NSOM) and measures the local electronic rather than optical responses [24][25][26]. Compared with DC probes, however, microwave frequency is high enough so that no contact electrode is needed for the imaging, therefore nondestructive to the sample. This unique capability allows us to rapidly map out the electrical properties of many dendritic features for statistical analysis. During the measurements, an excitation signal at 1GHz is delivered to the metallic tip of a special cantilever probe through the electrically shielded center conductor [27]. The local variation of the sample permittivity and conductivity modifies the effective tip impedance, which results in small changes of the reflected microwave [28]. The shaped bilayers are much closer to the monolayers than the dendritic ad-layers. We therefore conclude that, in terms of electrical properties, the irregular dendrites are very different from triangular bilayers with good crystallinity.
For a quantitative understanding of the dendritic precipitates and monolayer MoS 2 in our films, we have performed the finite-element analysis (FEA) [28] using a numerical software COMSOL4.3 and the result is shown in Fig. 3(d). The simulation takes the experimental geometry and other known parameters, e.g., the permittivity of SiO 2 and monolayer MoS 2 [29,30], to calculate the effective tip impedance. In this case, the MIM-Re and MIM-Im signals are proportional to the real and imaginary parts of the change of tip admittance (reciprocal of impedance), which allows a direct comparison between the experimental data and the simulation results. Due to the scattered data points and complicated nature of the near-field interaction, it is difficult to accurately quantify the sample conductivity (). However, as detailed in Supporting Information S5, using reasonable assumptions of the tip geometry and tip-sample contact condition, an order of magnitude estimate of the local conductivity is feasible within the measurement and statistical error. For the monolayer MoS 2 flakes, the modeling yields a low  of 1~10 S/m or a sheet resistance of 10 8~1 0 9 . The MIM data on the dendritic ad-layers, however, suggest a much higher  of 10 2~1 0 3 S/m. This value, while still much lower than that of a typical metal, implies a substantial amount of carriers in the ad-layers. Due to the relatively high local conductivity, the quasi-static potential drop within the ad-layer is small, which explains the fact that the MIM signals roughly scale with the areas (Supporting Information S5).
Since the lateral dimensions of these mesoscale patches are comparable to the sizes of typical nano-devices, their effects are certainly not negligible for electronic applications. Much more work is needed to determine whether similar dendritic regions in other CVD-grown films have the same conductivity as reported here.
Finally, we briefly discuss the MIM imaging of MoS 2 grain boundaries. Theoretical and experimental work has been carried out to understand the atomic structure and electronic property of various GBs in MoS 2 monolayers [19][20][21]. In our samples, most GBs are covered by a second layer, which complicates the interpretation of MIM data in terms of the underlying GBs.
We did, however, observe some flat GBs without the overgrown layer. As seen in Fig. 4, the zigzag GB appears darker than the grains in the MIM-Re data. Although the GB width is obviously broadened due to our limited spatial resolution, the result suggests that the local conductivity near the zigzag GB can be one order of magnitude lower than the background, consistent with previous transport and DFT calculations [19]. Because of the finite resolution of the MIM imaging, either the GB itself or defect segregation around the GB could contribute to the observed high local resistance.
In summary, we report the nanoscale impedance microscopy of two types of mesoscopic electrical imperfections in MoS 2 atomic layers grown by vapor transport technique. The micrometer-sized dendritic ad-layers, being identical to bilayer MoS 2 from conventional structural and optical measurements, display ~2 orders of magnitude higher conductivity than that of the monolayer. The zigzag grain boundaries, on the other hand, lower the local conductivity of MoS 2 . Compared with transport measurements, the MIM provides direct nanoscale electronic information without the need for fabricating ohmic contacts or other cumbersome sample preparations. We suggest that such capability will be particularly useful for the fast growing field of 2D van der Waals materials.

CVD Growth of MoS 2 :
The MoS 2 atomic layer films were grown by standard vapor transfer growth process. The inner diameter of the quartz tube is 25 mm. The starting materials were MoO 3 (15 mg) and sulfur (1g) powder that were loaded in alumina crucibles and placed inside the tube. The substrates (285nm SiO 2 on Si) were placed with the polished side facing the MoO 3 powder. The tube was then sealed and evacuated to a base pressure of 10 mTorr. After the base pressure was reached, the vacuum pump was shut off and N 2 gas was introduced into the tube at a flow rate of 200 sccm. Once the atmospheric pressure was reached, the N 2 gas flow was reduced to 10 sccm. At this point, the temperature of the furnace was raised to 850C at a rate of 50C/minute. The temperature of sulfur at one end of the furnace is roughly 350C. The growth continued for 5 minutes at 850C, after which the heater in the furnace was turned off and the N 2 flow rate was increased to 200 sccm for cooling down.     shown in the inset) can be found in Ref. [1]. The 1GHz excitation V 1GHz ~ 20mV (10W signal in the 50 transmission lines) is guided to the cantilever through a Z-match section [2], which converts the tip impedance (C ~ 1.2pF and R ~ 4) to 50. The reflection coefficient S 11 from the Z-match section is shown as the red curve in Fig. S3(b). The electronics operate at the frequency of minimum S 11 , which also corresponds to the maximum S 11 . During the scanning, the near-field interaction changes the effective impedance of the tip, which results a change of the reflected microwave voltage S 11 V 1GHz . The blue curve in Fig. S3(b) is a calculated frequency-dependent S 11 , assuming an admittance change of 1nS. The MIM circuit then amplifies this RF input by the RF amplifier, demodulates the RF signal, and further amplifies it as the final output. The amplifier response is shown in Fig. S3(c). In the experiment, the phase shifter in front of the mixer is adjusted such that the two orthogonal channels are aligned to the real and imaginary components of the tip-sample admittance, which can be simulated by FEA modeling ( Figure S5). Figure S4(a, b) shows the simultaneously taken AFM and MIM data on a monolayer MoS 2 sample with both randomly distributed dendritic ad-layers and a big triangular island in the middle. As seen clearly in the image and the line trace in Fig. S4(c), the ad-layers, although smaller in area, show much higher MIM signals than that of the triangular bilayer island. In other words, for MoS 2 bilayers with good crystallinity, the conductivity is only weakly higher than that of the monolayer and is considerably lower than that of the dendritic ad-layers. Similar results have also been seen in mechanically exfoliated samples (not shown). Our main result of the high local conductivity of ad-layers is therefore nontrivial and cannot be simply attributed to the thickness effect.

S5: Finite Element Analysis (FEA) modeling
FEA simulation using COMSOL4.3 is shown in Fig. S5. Since all dimensions here are much smaller than the wavelength (30cm) at 1GHz, the interaction is in the extreme near-field regime and can be modeled as lumped elements. The MoS 2 conductivity is the variable to be determined in the modeling. The fixed parameters are as follows -Tip: 300nm in diameter; SiO 2 : 285nm thick and  = 3.9; heavily doped Si:  = 10 5 S/m; MoS 2 monolayer: 0.6nm thick and  = 7 [3]; MoS 2 ad-layer: an extra height of 0.6nm on the monolayer, with a lateral radius of 0.7m.
Several nanometers of depletion region right underneath the tip apex are assumed to represent the non-Ohmic tip-sample contact. The software directly computes the admittance contrast with respect to the substrate as a function of the ad-layer conductivity. The MIM signals on the monolayer MoS 2 are barely above the noise level, corresponding to a low conductivity  monolayer 1 ~ 10S/m here. The dendritic ad-layer, on the other hand, is much brighter in the images with roughly equal MIM-Im and MIM-Re signals. The quasi-static potential distribution at  ad-layer = 10 2~1 0 3 S/m shows a nearly constant potential across the ad-layer, which also explains the linear areal dependence of the MIM signals. We note that since the experimental data are quite scattered and the simulation strongly depends on the above parameters, the deduced conductivity only serves as an order of magnitude estimate.