Nanoscale enhancement of photoconductivity by localized charge traps in the grain structures of monolayer MoS2

We report a method for mapping the nanoscale anomalous enhancement of photoconductivity by localized charge traps in the grain structures of a molybdenum disulfide (MoS2) monolayer. In this work, a monolayer MoS2 film was laterally scanned by a nanoscale conducting probe that was used to make direct contact with the MoS2 surface. Electrical currents and noise maps were measured through the probe. By analyzing the data, we obtained maps for the sheet resistance and charge trap density for the MoS2 grain structures. The maps clearly show grains for which sheet resistance and charge trap density were lower than those of the grain boundaries. Interestingly, we found an unusual inverse proportionality between the sheet resistance and charge trap density in the grains, which originated from the unique role of sulfur vacancies acting as both charge hopping sites and traps in monolayer MoS2. In addition, under light illumination, the larger the trap density of a region was, the larger the photocurrent of the region was, indicating anomalous enhancement of the photocurrent by traps. Since our method provides valuable insights to understand the nanoscale effects of traps on photoconductive charge transport, it can be a powerful tool for noise studies and the practical application of two-dimensional materials.

while mapping the electrical currents and noise through the probe. Then, the measured current and noise maps were analyzed to obtain maps for the sheet resistance and localized charge trap distributions in the MoS 2 grain structures. The maps clearly show multiple MoS 2 grains with rather low sheet resistances and charge trap densities compared with their boundaries. Interestingly, unlike other common conducting channels, the sheet resistance inside the grains was found to be inversely proportional to the charge trap density, which was attributed to the unique role of sulfur vacancies working as both charge hopping sites and charge traps in MoS 2 . Furthermore, under light illumination, regions with larger charge trap densities exhibited larger photocurrents, indicating that photocurrents were enhanced by charge trap sites. This method provides a valuable insight for the nanoscale effects of charge traps on the photoconductive charge transport, and, thus, can be utilized for various electrical noise research and practical device applications based on two-dimensional materials.

Results and Discussion
Experimental setup. Figure 1 shows the schematic diagram of our current and noise measurement setup.
A MoS 2 monolayer film was grown onto a SiO 2 /Si substrate by a chemical vapor deposition (CVD) method. For the noise microscopy measurement, a Pt-based conducting probe (25Pt300B, Park Systems) installed in an AFM (XE-70, Park Systems) was used to make a direct contact with the surface of the MoS 2 film under ambient conditions. Then, a direct current (DC) bias voltage of 5 V was applied to the Pt probe using a DC power supply (DS345, Stanford Research Systems). The current through the Pt probe was measured and converted to amplified voltage signals by a low-noise preamplifier (SR570, Stanford Research Systems). Simultaneously, electrical noise (the fluctuating component of a current signal) was collected using a band-pass filter (6 dB) in the SR570 preamplifier. We utilized a homemade root mean square (RMS)-to-DC converter to obtain the RMS power of the noise. The absolute noise power spectral density (PSD) at the central frequency of the band-pass filter was obtained by dividing the square of the measured RMS noise power with the bandwidth of the band-pass filter. Using this setup, two-dimensional maps for the topography, current and noise PSD were obtained at the same time by scanning the AFM probe on the MoS 2 sample. The mapping data were analyzed to obtain maps of the sheet resistance and charge trap density. In addition, we measured changes in the current and noise maps by white light illumination using a light source (LS-F100HS).
Characterization of CVD-grown monolayer MoS 2 . Figure 2(a) shows the optical microscopy image of a MoS 2 film. The MoS 2 was synthesized via CVD on a SiO 2 /Si substrate. The MoS 2 film exhibited a darker purple color than the SiO 2 region. The constant color contrast of the MoS 2 region implies that the thickness of the MoS 2 film was rather uniform 18 . The image indicates that the surface of the MoS 2 sample was uniform and clean. The layer number of the MoS 2 film was characterized by Raman spectroscopy (Fig. 2(b)). We used a Raman microscope (XperRam 200, Nanobase) with a 532 nm laser. The Raman spectrum of our MoS 2 film shows two major peaks at 383.4 and 403.7 cm −1 . The interval for the peaks is approximately 20.3 cm −1 . These two peaks correspond to the E 1 2g (383.4 cm −1 ) and A 1g (403.7 cm −1 ) modes of MoS 2 18 . It is known that the interval for the two major peaks decreases as the number of layers in MoS 2 decreases, being ~20 cm −1 in the case of a monolayer 19 . Hence, the Raman spectrum indicates that the MoS 2 film consisted of a single atomic layer. The topography image of the MoS 2 film obtained by AFM measurement also supported the observation of monolayer formation in our film (Fig. S1 in the Supplementary Information). Figure 2(c) shows the current-voltage (I-V) characteristics of our MoS 2 sample. A bias voltage was applied to the Pt probe and swept from −5 to 5 V. The I-V graph exhibits asymmetric and nonlinear behavior. The nonlinear curve implies that Schottky contacts are formed between the MoS 2 layer and the electrode, presumably due to the large band gap of MoS 2 20 . Since the work function of the Pt probe is larger than that of the Au/Ti electrode, a negative bias on the Pt probe would worsen the Schottky barrier between the MoS 2 film and the Au/Ti electrode, resulting in a low current level. This result shows the Schottky barrier at the MoS 2 -metal contacts may have a  Figure 2(d) shows a back gate effect on the sample at a source-drain bias voltage of 3 V. The gate voltage (V G ) was swept from −40 to 40 V using the SiO 2 substrate as a back gate. The result shows an increasing current as the gate voltage was swept from negative to positive values, indicating typical n-type behavior for the MoS 2 channel 1,11-14 . The threshold voltage (V Th ) (the minimum gate voltage required to form a conducting channel) was obtained from the curve. The threshold voltage (V Th ) was estimated to be ~−40 V, which is the V G -axis intercept of the extrapolated line for the maximum slope region in the curve. The electrical properties of the MoS 2 sample were comparable to those found in a previous study 18 , confirming the uniform quality of our MoS 2 film. In Fig. 2(e), the frequency dependence of the current-normalized noise PSD (S I /I 2 ) is plotted on a log scale. A spectrum analyzer (SR780, Stanford Research Systems) was utilized to measure the noise spectrum. The S I /I 2 exhibited a 1/f noise behavior, as reported in previous noise studies on MoS 2 devices [11][12][13][14] . In our previous work, we showed that noise PSDs exhibited 1/f 2 (or Lorentzian) noise behavior when a current noise was generated by a few trap states that had rather uniform trapping times 15,17 . However, noise spectra exhibited 1/f behavior [15][16][17] when there were many trap states with various trapping times. The 1/f noise behavior in our plot implies that the noise was generated by many different noise sources such as charge traps in the MoS 2 sample.
Previously, a 1/f noise was suggested to originate from mobility fluctuations or carrier number fluctuations and that in each case S I /I 2 is differently related to carrier density 10,11,22,23 . To clarify a dominant origin, we measured S I /I 2 at different gate voltages (V G ) since the carrier density can be modulated by V G . Fig. 2(f) shows a plot of S I /I 2 values over V G . The S I /I 2 was measured while a V G ranging from −20 to 40 V was applied to the SiO 2 back gate. The slope of the fitted line in the log-log plot is estimated to be −1.994, which is close to −2, as expected for carrier number fluctuations 14,22,23 . This implies that carrier number fluctuations were the dominant mechanism for noise generation in our MoS 2 sample, as reported previously 12,14 . Charge trap distribution in the grain structure of monolayer MoS 2 . Figure 3(a) shows the AFM topography image of a MoS 2 monolayer. The surface area (3 × 3 μm 2 ) was scanned by an AFM probe. In the image, dark regions (film thickness <1 nm) are distinguished from bright regions (film thickness ~2 nm). Additionally, there is a bright dot near the center of the grain. From the reported thickness of a MoS 2 monolayer (~0.7 nm) 1 , we can consider the dark area as grains of MoS 2 and the bright area as grain boundaries. The dot near the center of the grain would be a precursor for the CVD process of a MoS 2 film, as reported previously 24 . The difference in thickness between grain and boundary regions can be explained via a boundary formation mechanism. Typically, the growth of individual grains is known to stop when chemical bonds are formed between the grains 25 . However, it is common that the neighboring grains proceed to grow even after they encounter each other, forming additional layers. Thus, layer-overlapping without chemical bonds can occur, resulting in thicker boundaries 25 . The topography image indicates the cleanliness of the film, which showed no wrinkles or severely rough surface regions. Figure 3(b) shows a current map for the MoS 2 sample. The current was measured through the conducting probe while a DC bias voltage of 5 V was applied to the Au/Ti electrode. During the measurement, the sample was held under dark conditions to exclude photocurrents. In the map, bright and dark regions are clearly distinguished. The dark regions (~10 −6 A), which correspond to boundary regions, showed lower currents compared to the grain regions (~10 −5 A). This current difference could arise from structural disorder in the boundaries, which obstructs current flow. In a grain boundary region, the atomic structure could be different with that inside the grain due to the different orientation of adjacent grains, or grain overlapping and ruptures. Previous works show that various defects in boundaries, such as line dislocations and complex atomic ring structures, induce mid-gap states and decrease the band gap [26][27][28][29] . In addition, grain overlapping and ruptures could generate grain edges with unsaturated bonds, which lead to the intrinsic modification of the electronic structure due to the loss of periodicity 28 . The result shows success mapping of localized currents via a stable contact between the probe and the MoS 2 film, which is important for reliable electrical measurements. Figure 3(c) shows a S I /I 2 map (at 17.3 Hz) obtained from a noise PSD map measured simultaneously with the current map ( Fig. 3(b)). Here, the noise PSD map (S I ) at 17.3 Hz was divided by the square of the current (I) map. The S I /I 2 values were ~1.12 × 10 −7 Hz −1 inside a grain (arrowed by (i)) and ~3.96 × 10 −7 Hz −1 inside a boundary (arrowed by (ii)), indicating a higher noise level in the boundary than in the grain. The high S I /I 2 in the boundary implies that a large electrical noise was generated in the grain boundaries. Previously, it was reported that defects and disorders in a MoS 2 layer induce localized states within a band gap 30 , which can act as traps 31,32 and generate current noise by trapping and detrapping charge carriers. Hence, the large electrical noise from boundaries can be attributed to rather high density of defects in the area. It is remarkable that noise contributions from each localized area for the monolayer MoS 2 could be distinguished in our result, providing important information about how noise levels differ in grain structures. Figure 3(d) shows a sheet resistance (R s ) map of the monolayer MoS 2 film. To obtain the R s distribution, we performed computer calculations based on an iterative method developed in our previous work 15 . In brief, we calculated the R s map, which reproduced the measured current map in Fig. 3(b), via an iterative method. In the map, grains and their boundaries exhibit a clear difference in R s . The R s values were ~8.28 × 10 5 Ω sq −1 inside a grain (arrowed by (i)) and ~2.05 × 10 6 Ω sq −1 inside a boundary (arrowed by (ii)), showing ~2.5 times higher values in boundaries than in grains. The result was consistent with the reported R s values for CVD-grown monolayer MoS 2 (10 5 -10 6 Ω sq −1 ) 6,26,33 . The large R s of the boundary regions could originate from numerous scattering centers due to structural disorder 25,34 . Additionally, the R s difference between grains and boundaries was similar to that measured for intra-and inter-grain channels in field effect transistors (FETs) in a previous study 26 . However, it should be mentioned that previous measurements had difficulty in clearly distinguishing the localized resistance values for the grains and boundaries since the FET channels included both regions.
From the data in Fig. 2(f), we showed that the 1/f noise of our MoS 2 channel (Fig. 2(e)) was mainly generated by carrier number fluctuations. The number of carriers fluctuates since charge carriers are randomly trapped and detrapped by charge trap states, generating current noise 35 . Using the differential method developed in our previous study 15 , an effective charge trap density (N eff ) (the integrated value of the charge trap density over the thickness) of a small area ΔxΔy at (x, y) on a sample surface is obtained as where ΔC, I, f, k, T and ΔS I are the number of charge carriers, measured current, frequency, Boltzmann constant, temperature and noise PSD generated by the small area, respectively. In the case of 1/f noise, ΔS I (f, x, y) is proportional to 1/f. Then, f ΔS I becomes f-independent, resulting in a f-independent N eff (f, x, y), i.e., N eff (x, y). To estimate ΔS I , we considered a MoS 2 layer as a two-dimensional resistance network. This "network model" was shown to be a successful model in our previous study on graphene samples 15 . The ΔC in equation (1) was estimated from the charge carrier concentration. We calculated the charge carrier concentration (n) using n = C OX (V G − V Th )/e, where C OX is the gate capacitance of the SiO 2 layer (~1.48 × 10 −8 F/cm 2 ), V G is the gate voltage (0 V), V Th is the threshold voltage (~−40 V), and e is the elementary charge (1.60 × 10 −19 C). The calculated value for n was ~3.69 × 10 12 cm −2 . Then, ΔC could be calculated from ΔC = nΔxΔy, where ΔxΔy is the effective contact area of the conducting Pt probe (~2000 nm 2 ). Eventually, we could estimate N eff values at each point of the area scanned by a conducting AFM probe. Since N eff is an integrated value over a thickness, it will be a useful value representing the effective density of charge traps in two-dimensional materials. Figure 3(e) shows the effective charge trap density (N eff ) map of the MoS 2 monolayer. The map exhibits the areal density distribution of the charge traps on the sample. The N eff value was ~2.91 × 10 14 cm −2 eV −1 inside a grain (arrowed by (i)), while the boundary region (arrowed by (ii)) exhibited a N eff value of ~3.87 × 10 14 cm −2 eV −1 , which was ~1.3 times higher in value than that of the grain. In a MoS 2 film, charge traps can be induced by defects including atomic vacancies, dangling bonds and impurities [30][31][32] . Since defects in monolayer MoS 2 generate trap states within a band gap while defect-free monolayer MoS 2 shows no such states 30,36 , N eff corresponds to the density of traps generated by defects. The high N eff in the boundary implies the existence of abundant charge traps, which originate from structural disorder of the boundaries 25,34 . Charge traps in a MoS 2 sample can also be located in the underlying substrate. However, it should be noted that the N eff values in our map were 2-3 orders of magnitude higher than the reported oxide trap density associated with SiO 2 substrates 12,37 , indicating that the substrate was not the main origin for the generated noise. Instead, the N eff could be attributed to defects generated during the CVD process under high temperature (~750 °C) and low pressure (~10 Torr), as reported previously 38 . Previously, it was reported that the presence of defects such as sulfur vacancies significantly affects the band structure of monolayer MoS 2 by introducing localized mid-gap states near the Fermi level, leading to a transition from a direct to indirect band gap 30 . Our method provides a method to map localized density of charge traps in two-dimensional nanomaterials, which can be useful for studying charge traps in various other nanostructured materials. Figure 3(f) shows a scatter plot for the relationship between N eff and R s for monolayer MoS 2 on a log-log scale. Each data point in the plot is obtained from the pixel area in the N eff map (Fig. 3(e)) and the corresponding pixel area in the R s map (Fig. 3(d)). The data points for the grains and boundaries were distinguished using the R s map. The plot exhibits different tendencies for grain and boundary regions, showing a positive correlation in boundaries and a negative correlation in grains. The positive N eff -R s correlation in boundaries is similar to previously reported results on the relation between noise PSD and resistance in percolated systems [38][39][40][41] . Since boundaries are highly disordered regions with many trap states, each pixel region in the boundaries can be considered as a localized percolation channel. In such a system, it was reported that both resistance and its fluctuation have a power law dependence on (p − p c ), where p is the fraction of the conductive paths and p c is the percolation threshold 39 . Hence, the resistance of each pixel region (R s , in our case) is related to its fluctuation as follows , the relation N eff ~ (R s ) w is obtained, which explains the correlation between N eff and R s . In our result, the exponent w was approximately 0.4, which is similar to that observed in an FET channel including the grain boundary in monolayer MoS 2 40 . This kind of scaling behavior has been observed in many percolation systems where the exponents varied according to the material, geometry and temperature [38][39][40][41] . On the other hand, the unique negative correlation for the grain regions can be explained by the electrical transport mechanism in monolayer MoS 2 . It was suggested that the charge transport in few-layered MoS 2 is dominated by hopping through localized states, which originates from sulfur vacancies 14,30,42 . At room temperature (~300 K), the dominating transport mechanism in MoS 2 should be nearest-neighbor hopping 30 . In this mechanism, the conductivity (σ) is expressed as σ ~ exp (−1/a 2 kTN μ ), where 'a' is an average defect distance and N μ is the density of states near the Fermi level, which corresponds to N eff 30 . The equation indicates that if there are many sulfur vacancies in a region (high N eff ), the hopping probability for the carriers will be high due to the high density of vacancy-induced hopping sites, resulting in a high conductivity. In the plot, the data points for the grain regions are fitted well by the equation R s ~ exp (1/a 2 kTN eff ). As a fitting parameter, the average defect distance (a) was estimated to be ~1.97 nm, which was very close to the reported value of ~1.7 nm 30 . Previous observations based on transmission electron microscopy (TEM) revealed that sulfur vacancies are the most common defects in monolayer MoS 2 30,36 . Additionally, it should be mentioned that the reported density of trap states from sulfur vacancies was comparable to our N eff value 30 . Therefore, the negative correlation between N eff and R s for the grain regions could be attributed to the sulfur vacancies playing a key role for both charge transport and charge trap generation in monolayer MoS 2 .

Enhancement of photoconductivity by localized charge traps.
To investigate the effect of charge traps on photoconductive charge transport in monolayer MoS 2 , we measured the MoS 2 film under dark and illuminated conditions. Figure 4(a) shows a current map (I dark ) of the MoS 2 monolayer measured under the dark condition. A DC bias voltage of 5 V was applied to the Au/Ti electrode. In the map, many grains were observed since we scanned an area (10 × 10 μm 2 ) larger than that of individual grains. The grains and boundaries were distinguished by relatively high and low current values, respectively. Figure 4(b) is the map of the current changes (ΔI) caused by light illumination. We used a white light source (LS-F100HS, Light Bank) with an intensity of ~100 mW/cm 2 . Here, a current map was first measured under the dark condition, with the measurement repeated under illumination. After illumination, the currents in the grains were found to increase by more than 10 −5 A, resulting in ~7.5 times higher current values than before illumination. On the other hand, the currents in the boundaries increased by only a factor of ~4, indicating rather small changes (10 −6 -10 −5 A). The current increase was caused by photocarrier generation in the MoS 2 layer 9,43 . Previously, defects such as charge traps in MoS 2 were reported to assist the recombination of photogenerated carriers as recombination centers, and, thus, to reduce the photocurrents 43 , which explains the low photocurrent in boundaries. It is also notable that there were clear differences in current values between individual grains. The current differences between individual grains were as large as 30% of the average current value of all the grains. This inter-grain current difference can be attributed to an energy band modulation that presumably arises from the random crystal orientation and strain of MoS 2 grains grown via the CVD method 24,34 . Figure 4(c) shows a map of the charge trap density when the MoS 2 film was under the dark condition (N eff_dark ). The N eff_dark map was calculated using the current map ( Fig. 4(a)) and the noise PSD map at 17.3 Hz. The N eff_dark values were on the order ~10 14 cm −2 eV −1 and found to be higher in boundaries than in grains. This result is consistent with that shown in Fig. 3(e). The difference in N eff_dark between individual grains could arise from the grain-growing process, as mentioned in Fig. 4(b). Figure 4(d) shows a map of the charge trap density changes (ΔN eff ) in the MoS 2 film due to illumination. The map was obtained by subtracting the N eff_dark map (Fig. 4(c) Fig. 4b,c. In the plot, the data points for the boundary regions show no special correlation. However, a positive correlation between N eff_dark and ΔI is observed in the grain regions, as indicated by the yellow fitted line with a slope of ~0.9. Considering that traps were previously reported to act as recombination centers, resulting in a decreased photocurrent 46 , this result is quite unusual. One possible explanation for this anomalous enhancement of the photocurrent by charge traps is that the photocurrent in few-layer MoS 2 is significantly affected by O 2 molecules on the MoS 2 surface 43,47 . Previous studies showed that both dark current and photocurrent levels for monolayer MoS 2 were much lower in ambient air than in vacuum, attributing the difference to chemisorbed O 2 molecules, which captured a large portion of the electrons from MoS 2 43,47 . When the MoS 2 was illuminated with light under ambient conditions, electron-hole pairs were generated by photoexcitation. Then, the photogenerated holes recombined with the electrons captured by some chemisorbed O 2 molecules, and the discharged O 2 molecules were desorbed from the surface 43,47 . In this case, the photogenerated electrons, which might be captured by the chemisorbed O 2 molecules, were now free and acted as a charge carrier. Thus, the number of free electrons in the MoS 2 channel increased, and the current increase (ΔI) should be proportional to the number of desorbed O 2 molecules generated by illumination. On the other hand, before illumination, the O 2 molecules were chemisorbed on sulfur vacancies 9 which were responsible for N eff_dark . In this case, the MoS 2 regions with more sulfur vacancies (or larger N eff_dark ) should have more chemisorbed O 2 molecules before illumination 30,36 , and, following light illumination, they should also have a larger number of desorbed O 2 molecules and a larger current increase. Therefore, the proportional relationships lead to the proportionality between ΔI and N eff_dark , explaining the fitted line with a slope close to 1 in the log-log plot. Our result revealed the anomalous enhancement of the photocurrent due to noise sources such as charge traps, which can be important in applications of MoS 2 to optoelectronics since electrical noise is often a key parameter determining device performance. Figure 4(f) shows a scatter plot showing the distributions of the N eff and R s values for the monolayer MoS 2 under dark and illuminated conditions. Each data point represents the N eff and R s values of each pixel area in the maps. There are two groups of data points obtained under dark (high R s ) and illuminated (low R s ) conditions. Each group consists of the data points from grains and boundaries, which were distinguished using R s maps (Fig. S2 in the Supplementary Information). The distribution of data points obtained under the dark condition was similar to that shown in Fig. 3(f), exhibiting different N eff -R s correlations between grains and boundaries. On the other hand, under illumination, R s was generally decreased while the distribution of N eff was broadened in both grain and boundary regions. The broadening of the N eff distribution was the result of a large increase in N eff in most regions and a decrease in N eff in only a few regions. The increase in N eff was mainly caused by defect generation due to absorbed photon energy 44,45 . Additionally, localized states filled with charges under the dark condition could trap charge carriers after photoexcitation of the occupied charges, contributing to the increase in N eff . On the other hand, the desorption of physically adsorbed O 2 molecules from the MoS 2 surface could decrease N eff . It is also worth mentioning that the N eff distribution is rather broadened by the light illumination, resulting in weakened N eff -R s correlation. Presumably, under dark conditions, most of the charge traps are sulfur vacancies contributing to charge conduction as a hopping site 30 . However, light illumination generated various charge traps, which may not work as a hopping site, such as Mo vacancies and large atomic holes 44 .

Conclusions
In conclusion, we successfully imaged how localized charge traps enhanced the photoconductivity in the grain structures of monolayer MoS 2 . By laterally scanning a conducting AFM probe used to make direct contact with a monolayer MoS 2 sample, electrical currents and noise transmitted through the probe were simultaneously mapped. The mapping data were analyzed to obtain the distribution maps for the sheet resistance and charge trap density in the grain structures of MoS 2 . The result showed that both the sheet resistance and charge trap density were higher in the grain boundaries than in the grains. We found a unique negative correlation between SCientifiC REPORTS | (2018) 8:15822 | DOI:10.1038/s41598-018-34209-w the charge trap density and sheet resistance, which was attributed to the role of sulfur vacancies acting as both hopping sites and charge traps in monolayer MoS 2 . Furthermore, the photocurrent exhibited a positive scaling relation with the charge trap density since photogenerated holes recombined with electrons captured by oxygen molecules absorbed on sulfur vacancies. Since our strategy enabled us to map the nanoscale effect of localized charge traps on the photoconductive carrier transport, it should be a versatile tool that can be used for basic noise studies and applications based on versatile two-dimensional materials.