Inhomogeneous hysteresis in local STM tunnel conductance with gate-voltage in single-layer MoS$_2$ on SiO$_2$
Santu Prasad Jana Suraina Gupta Anjan Kumar Gupta



Department of Physics, Indian Institute of Technology Kanpur, Kanpur 208016, India
anjankg@iitk.ac.in




  September 9, 2024

§ ABSTRACT 
Randomly distributed traps at the MoS_2/SiO_2 interface result in non-ideal transport behavior, including hysteresis in MoS_2/SiO_2 field effect transistors (FETs). Thus traps are mostly detrimental to the FET performance but they also offer some application potential. Our STM/S measurements on atomically resolved few-layer and single-layer MoS_2 on SiO_2 show n-doped behavior with the expected band gap close to 2.0 and 1.4 eV, respectively. The local tunnel conductance with gate-voltage V_ g sweep exhibits a turn-on/off at a threshold V_ g at which the tip's Fermi-energy nearly coincides with the local conduction band minimum. This threshold value is found to depend on V_ g sweep direction amounting to local hysteresis. The hysteresis is, expectedly, found to depend on both the extent and rate of V_ g-sweep. Further, the spatial variation in the local V_ g threshold and the details of tunnel conductance Vs V_ g behavior indicate inhomogenieties in both the traps' density and their energy distribution. The latter even leads to the pinning of the local Fermi energy in some regions. Further, some rare locations exhibit a p-doping with both p and n-type V_ g-thresholds in local conductance and an unusual hysteresis.







Keywords: TMDs, MoS_2, Interface Traps, Hysteresis, Scanning Tunneling Spectroscopy.





Inhomogeneous hysteresis in local STM tunnel conductance with gate-voltage in single-layer MoS_2 on SiO_2
    Santu Prasad Jana, Suraina Gupta & Anjan Kumar Gupta
    Received 16 July 2024; accepted 04 September 2024
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§ INTRODUCTION

In recent years, transition metal dichalcogenides (TMDs) have gained significant interest for next-generation semiconductor devices <cit.>. Molybdenum disulfide (MoS_2) is a promising TMD with a direct bandgap of ∼1.9 eV in monolayer form and an indirect bandgap of ∼1.3 eV in bulk form <cit.>, making it an excellent candidate for transistor <cit.>, logic <cit.>, high-frequency <cit.>, circuit integration <cit.> and optoelectronic <cit.> applications. However, MoS_2 single layer exhibits decreased charge carrier mobility compared to graphene due to its poor dielectric screening, inherent structural defects, and quantum confinement effects <cit.>. Interface traps between atomically thin MoS_2 and dielectric substrate and intrinsic defects are prevalent issues that impact electrical transport characteristics. For instance, a persistent photoconductivity is observed in MoS_2 photo-transistors <cit.> due to the photo-charge trapping by intrinsic localized band-tail states and extrinsic interface trap states. 

The traps are also responsible for the observed hysteresis in the transfer characteristics, i.e. drain-source current I_ DS Vs gate voltage V_ g, of MoS_2 field effect transistors (FETs). This has been studied by several research groups <cit.> and as a function of gate bias stress, gate sweeping range, sweeping time, sweeping direction and loading history in different conditions such as high and low temperature, vacuum and different gas environments. Hysteresis reported in single and multi-layer MoS_2 has been ascribed to several possibilities including the absorption of water and gas molecules on top of MoS_2 <cit.>, charge traps at the metal-semiconductor interface of the contacts <cit.>, the intrinsic structural defects <cit.>, the extrinsic traps at the MoS_2/SiO_2 interface <cit.>, oxide traps close to MoS_2/SiO_2 interface <cit.>, oxide traps close to p^ + Si/SiO_2 interface <cit.> and mobile ions (Na^ + and K^ +) in the oxide <cit.>. In bulk transport, the threshold V_ g value at which the channel conduction starts/stops and its change between the two opposite V_ g-sweep directions give an averaged information about the traps that are actually non-uniformly distributed. Traps also have potential in memory devices as some recent work illustrates <cit.>.

In the absence of traps, the oxide capacitance and the MoS_2 quantum capacitance dictate the carrier density of the MoS_2 channel <cit.> in response to V_ g. The presence of the interface charged-traps, lead to a spatially inhomogeneous electrostatic channel potential that dictates the local charge density and overall carrier mobility. A non-uniform density and energy-distribution of trap states lead to a spatially inhomogeneous, and V_ g dependent, screening of the gate electric field. This can cause a non-uniform change in carrier density and unpredictable changes in mobility with V_ g. For instance, a local peak in traps' density of states can pin the MoS_2 Fermi energy keeping the carrier density unchanged over significant V_ g range.

In this paper, we report on hysteresis and its inhomogeneities with gate sweep in the local tunnel conductance of atomically resolved single and few-layer MoS_2 on SiO_2 by using a scanning tunneling microscope (STM). The measured tunnel conductance spectra, i.e. dI/dV_ b Vs bias voltage V_ b, show the expected band-gap while the dI/dV_ b Vs V_ g curves, at a fixed V_ b, exhibit spatial inhomogeneities including that in V_ g-threshold. This threshold is found to differ during forward and backward sweeps of V_ g with this difference being dependent on the extent and rate of V_ g-sweep. A rare p-doped region, confirmed from spectra, is found to show unusual hysteresis. These findings are discussed using traps with an inhomogeneous density and energy distribution.



§ EXPERIMENTAL DETAILS



 §.§ MoS_2 Exfoliation, characterization and device fabrication 

Single and few-layer MoS_2 flakes were mechanically exfoliated from natural bulk crystal (from SPI) using a Scotch tape <cit.> and transferred on SiO_2/Si substrate by dry transfer technique <cit.> employing a PDMS membrane (Gel film from Gel Pak) as a viscoelastic stamp under an optical microscope. Acetone/IPA cleaned, highly doped Si acting as back gate with 300 nm thermal SiO_2 is used as substrate. The number of MoS_2 layers on SiO_2/Si substrate was determined by optical microscope and Raman spectroscopy.

Figure <ref>(b) shows a separation between the  E^ 1_ 2g and A_ 1g Raman peaks as 18.5 cm^ -1, which is comparable to that reported <cit.> in single-layer MoS_2.

A clean surface, free of resist and wet chemicals' residue, is required for STM/S studies. Therefore, we use mechanical masking to make 50 nm thick gold film contacts by placing and aligning the MoS_2 flake underneath a 25 μm diameter tungsten wire using an optical microscope and then depositing Au. This is followed by a second wire alignment, nearly perpendicular to the previous, and Au deposition to surround MoS_2 with Au from all sides as shown in figure <ref>(a). This helps in aligning the STM tip on MoS_2 under an optical microscope. The contact resistance was estimated to be about 5 kΩ-μm^2 from separate multi-probe transport measurements on samples made by e-beam lithography.



 §.§ STM measurement details

The STM/S measurements were done in a homemade room temperature STM in a cryo-pumped vacuum better than 10^ -4 mbar. Electrochemically etched and HF cleaned tungsten wire was used as STM tip with an apex radius between 20 and 50 nm as confirmed by scanning electron microscope. Figure <ref>(b) depicts the STM/S measurement schematic with the bias voltage V_ b applied to MoS_2 while the tip stays at virtual ground potential. Thus, at a positive sample bias electrons tunnel from the tip's filled-states to the vacant-states of MoS_2. The gate voltage V_ g is applied to the heavily doped Si-substrate with a 10 kΩ series resistance. Before doing the STM/S measurements on MoS_2, we have taken atomic resolution images on HOPG sample to ensure good tip conditions.

To acquire the tunnel conductance dI/dV_ b spectra, an AC modulation voltage of 20 mV and 2731 Hz frequency was added to the DC bias voltage and the in-phase component of the AC tunnel current was measured using a Lock-in amplifier. The dI/dV_ b curves presented here are averages of twelve such curves unless stated otherwise. For the local dI/dV_ b measurements, the feedback loop is turned off to keep a fixed tip-sample separation. A standby gate voltage V_ g=30 V is also used to ensure sufficient bulk conductivity of MoS_2 after the spectra acquisition is stopped and before the feedback loop is turned on. This used positive V_ g is above the typical threshold voltage for bulk conduction as found from separate transport measurements.


The STM images were taken in constant current mode and at a V_ b value well above the conduction band edge of MoS_2 and also at a positive V_ g above the bulk conduction threshold. The latter ensures the tunnel current conduction from the tunnel junction to the Au contacts with an in-between voltage drop much less than the applied V_ b. Further, the junction resistance is typically kept as 20 GΩ or higher for imaging which is significantly larger than the typical off-state bulk resistance of about 1 GΩ. The local dI/dV_ b at large negative V_ g values is found to be still measurable when MoS_2 is in the off-state. This is presumably due to the presence of defects and traps that lead to a non-infinite resistance and smaller than tunnel junction resistance. This made it possible to acquire dI/dV_ b data, as discussed later, in a rare p-doped region. Only a very few <cit.> STM studies of MoS_2 on insulating substrates have been reported so far as opposed to those on conducting metals <cit.> presumably due to the complication arising from lack of tunnel current conduction in the off state. The off-state of an ultra-clean and trap-free MoS_2 can be expected to be highly insulating which can make such STM/S studies even more challenging.



§ RESULTS AND DISCUSSIONS



 §.§  STM topography and atomic resolution image and local dI/dV_ b spectra 

Figure <ref>(a) shows a topographic image of a single-layer MoS_2 on SiO_2/Si substrate acquired using constant current mode with I=50 pA, V_ b = 2 V and V_ g = +30 V. This observed corrugation of about 1 nm is same as that of the thermal SiO_2 on Si as reported by AFM measurements <cit.>. This could indicate that single layer MoS_2 adheres well to the SiO_2 surface although some of this corrugation can also be attributed to the electronic inhomogeneities. We also found that few layer MoS_2 exhibits a substantially smaller corrugation. A zoomed-in atomic resolution image, see Fig. <ref>(b), taken on relatively flat region of a few-layer MoS_2 shows a triangular lattice of sulfur surface atoms with a lattice constant of about 0.3 nm, in good agreement with the literature <cit.>.

Figure <ref> shows the dI/dV_ b-V_ b spectra acquired on the single layer and few-layer MoS_2 surfaces at V_ g = 30 V. No hysteresis was found in these spectra with respect to the V_ b-sweep direction. These spectra were acquired several microns away from the metal contacts to avoid their influence. The spectra on both single as well as few-layer MoS_2 exhibit a clear gap. For the used bias configuration, see Fig. <ref>(b), the sharp rise at V_ b>0 in these spectra corresponds to the conduction band minimum (CBM) and the one at V_ b<0 represents the valence band maximum (VBM) with the separation between the two edges representing the band-gap. The marked band-gaps of about 1.4 eV and 2.0 eV for few-layer and single-layer MoS_2, respectively, in figure <ref>, agree with the reported values <cit.>. The V_ b=0 point corresponds to the Fermi energy of MoS_2, which is close to the CBM in figure <ref> indicating that both these few-layer and single layer MoS_2 flakes are n-doped semiconductors. Electron rich sulfur vacancies and other n-type dopant impurities in natural MoS_2 crystals are believed to be responsible for this n-type nature <cit.>.


The observed tunneling band-gap can actually be significantly larger than the actual one due to the tip-induced band bending (TIBB) <cit.>, the term used in the framework of 3D semiconductors. Further, the same effects, if significant, would also lead to hysteresis in dI/dV_ b-V_ b spectra as is the case with respect to V_ g which is discussed later. This can be expected as the local band bending will change the occupancy of the slow traps <cit.> in the vicinity. Lack of such hysteresis and the fact that the observed tunneling band-gap is close to the actual value indicate that effects due to TIBB are insignificant. This can be attributed to the following observations. 1) The occupancy of the traps, arising from defects, changes in response to V_ b change and amount to screening of tip's electric field that would reduce the band-bending. A significant density of states of fast traps ∼ 10^12 eV^-1cm^-2 can be inferred in such devices from the large values of the subthreshold swing <cit.>. A large density of slow traps can also be deduced from the typical hysteresis in the channel transport in such devices <cit.>. 2) The back gate is capacitively coupled to the channel with a capacitance equivalent to a quantum capacitance corresponding to a density of states κϵ_0/(e^2d) with κ as dielectric constant of SiO_2 gate, d as its thickness and ϵ_0 as free space permittivity. This works out to be 7.4×10^10 eV^-1cm^-2. This will also contribute towards reducing the TIBB as some of the electric-field lines due to the tip bias will terminate on the gate rather than the channel. 3) The STM tip size is much smaller than the typical screening length within the 2D-MoS_2. The latter will dictate the channel area over which the TIBB will spread. This will substantially reduce the local TIBB under the STM tip. In contrast, the back-gate voltage in the 2D-FET configuration affects whole of the 2D MoS_2 uniformly leading to significant band-bending. 4) It has been recently argued <cit.> that presence of lateral tunneling inside MoS_2 will also reduce the TIBB.

In figure <ref>, the sharpness of the spectra at the VBM is seen to be substantially more than that near CBM for both cases. This can be attributed to the band tail states (BTS) below the CBM. These BTS near CBM can reduce the effective band gap and severely affect the transport. The U-shaped spectra indicating BTS or band edge states near both VBM and CBM have been commonly seen in Si/SiO_2 and other conventional 3D semiconductors <cit.>. The presence of BTS near the CBM can arise from the presence of sulphur vacancies in MoS_2 <cit.> which are the most common defects. Although a single S vacancy state is expected to be 0.46 eV below the CBM by density functional theory calculations <cit.> but we did not find any peaks inside the band gap in our dI/dV_ b spectra even in the vicinity of defects inferred from the STM images. The observed continuum of BTS close to the CBM could arise from multiple S vacancies that interact with each other and possibly with other defects.



 §.§ Spatial variation of hysteresis in local dI/dV_ b with gate-sweep.

Figure <ref>(a) shows a set of twelve unprocessed individual dI/dV_ b versus V_ g curves at a specific location of single layer MoS_2 at a fixed V_ b=2 V and for forward and reverse V_ g sweeps between -60 and 60 V. The schematics in Figure <ref> illustrate the underlying physics. At V_ b= 2 V, the Fermi level of MoS_2 is 2 eV below that of the tip. The Fermi level of the tip, kept at virtual ground, is used as zero energy reference. As V_ g is increased, at fixed V_ b, from negative to positive during the forward sweep, the bands of MoS_2 will shift downward, see fig. <ref>. At certain threshold V_ g value, namely V_ th, the tip's Fermi level will be within a few k_ BT below the MoS_2 conduction band edge, see Fig. <ref>(d), leading to a sudden rise in dI/dV_ b as the electron start tunneling from the tip to the MoS_2 CB states. In Fig. <ref>, the threshold voltage V_ thf for the forward V_ g sweep is seen to be smaller than V_ thb, i.e threshold for the backward sweep. This amounts to a significant positive local hysteresis. Comparing with the bulk transport in similar and those with passivated interface samples <cit.>, this observed hysteresis is attributed to the local traps at the interface of MoS_2 and SiO_2. When V_ g is increased from negative extreme value, during the forward sweep, the interface traps are positively charged which induces a negative charge on MoS_2. This brings MoS_2 CBM closer to its Fermi energy as compared to when there is no trap charge and thus a smaller V_ g is needed to reach the threshold condition. For the backward sweep the traps will be negatively charged, which makes the threshold higher.


A trap-state is characterized by a potential barrier, which determines how fast it exchanges electrons with the channel <cit.>. The fast traps, which are strongly coupled to the channel, exchange electrons faster than the experimental time scale. These fast-traps act like dopants as their occupancy gets equilibrated fast and is dictated by the Fermi-energy of MoS_2. Further, their local areal density and energy distribution will determine the local V_ th value of the dI/dV_ b-V_ g curves but the fast traps will not contribute to the hysteresis. The extremely slow traps, with a large potential barrier, also do not contribute to the hysteresis. The slow traps that exchange electrons with the channel at a time scale comparable to the V_ g sweep time dominantly contribute to the positive hysteresis.

Assuming only one electron is captured or released per trap, the trap density responsible for the observed hysteresis in figure <ref>(a) can be estimated as: N_ tr= (V_ thb-V_ thf)C_ ox/e≈ 7 ×10^ 11cm^ -2. Here, C_ ox =κϵ_ 0/d≈ 12 nF/cm^ 2 is the capacitance of SiO_2. The few-layer MoS_2 is found to exhibit larger hysteresis and less steep changes in dI/dV_ b-V_ g curves than mono-layer MoS_2 for the same sweep parameters. This is, presumably, due to more defects and inter-layer traps. Note that the interface trap-states do not directly contribute to the tunnel conductance as the direct tunneling matrix element between the tip and interface-trap states will be negligible as compared to that between tip and MoS_2 states. The tunneling electrons' equilibration rate is expected to be much faster than the typical electron transfer rate between MoS_2 and the trap states. Thus the interface-traps affect the local dI/dV_ b only through the filling or the band-shift of the MoS_2 channel.


Different scales of inhomogeneities were observed in the sense of seeing the same nature of curves over scales of 100×100 nm^ 2 order but with variation in V_ th values, while over larger scales a change in the nature of these curves is also observed. Figure <ref>(b) displays three typical dI/dV_ b-V_ g curves in different regions, more than 100 nm apart. Other than the variation in V_ th and Δ V_ th=V_ thb-V_ thf, the details of the dI/dV_ b spectra markedly change for the same V_ g sweep parameters. These regions do not have any correlation with the topography images. Figures <ref>(c) and (d) show representative dI/dV_ b-V_ g curves from regions `1' and `3', respectively, which are taken at points 20 nm apart and along a straight line. Region `1' exhibits a sharper turn-on than Region `3' while region '2' shows a plateau-like feature in backward V_ g sweep. The V_ th values of forward sweep in these regions differ, by more than 18 V, which is more than that within a region. This implies a variation in trap density of ≈ 1.3×10^ 12 cm^ -2 over large scales.

Figure <ref> illustrates how the bands shift relative to the tip Fermi energy when V_ g is increased. Note that we use a convention where the MoS_2 Fermi energy E_ F and that of the tip, i.e. E_ F+eV_ b, are kept fixed. The MoS_2 bands and the trap-states (not shown in Fig. <ref>) shift together downward in response to a V_ g increase. This dictates the Fermi energy of the combined trap and MoS_2-band system through the charge induced on this system by back-gate. Thus the trap states effectively screen the gate electric field and slow down the shift of the bands in response to V_ g. The dI/dV_ b value at a given V_ g reflects the thermally smeared density states of MoS_2 at energy eV_ b above E_ F. The traps that contribute to hysteresis are the slow ones but both, the fast and slow, will contribute to the shift of the bands and thus to the details of dI/dV_ b-V_ g curves.


In region '1', a sharp rise in dI/dV_ b at the threshold and near saturation afterwards implies a sharp rise or a peak in traps' density of states. When the Fermi energy of MoS_2 and traps is well above this peak the bands and the traps states move down fast, in response to V_ g increase. This leads to a sharp rise in dI/dV_ b, until the traps' peak reaches E_ F where the bands stop shifting with V_ g and dI/dV_ b stays nearly constant. The dI/dV_ b can also decrease in case of the delayed reaction of the slow traps which can cause an upward shift with time of the bands with a fixed, or even with an increasing, V_ g. In region '3', on the other hand, the rise in dI/dV_ b is slow and without any saturation indicating a relatively constant trap density of states leading to a slow downward shift in bands with increasing V_ g. In region '2' the plateau-like feature can arise from a small peak in the trap density of states that checks the shift of bands over a range of V_ g. Furthermore, traps with energies within a few k_ BT of E_ F can randomly exchange electrons with the channel leading to the generation-recombination (g-r) noise <cit.> in dI/dV_ b, see figure <ref>(b).

An inhomogeneous distribution of traps can be understood as arising from various non-uniform distribution of defects. These defects include amorphous SiO_2 surface defects, surface dangling bonds, surface absorbers, immobile ionic charges, and foreign impurities adsorbed on the surface. Two major SiO_2 surface structures have long been recognized: a high-polarization silanol group (Si-OH) and a weak-polarization siloxane group (Si-O-Si) <cit.>. Negatively charged silanol groups will induce a positive charge on MoS_2 and increase local V_ th. H^ + ions of water molecules hydrogen bond with the OH^ - of the silanol while exposing O^ 2- to MoS_2, which can exchange electron with MoS_2 and alter V_ th. Water molecules on MoS_2 cannot be completely removed by pumping in a vacuum at room temperature even for extended periods <cit.>. The weak polarization siloxane groups (Si-O-Si) lead to hydrophobic nature <cit.> as no hydrogen bonding with water molecule is possible. The MoS_2 in such regions will exhibit a lower V_ th as compared to that on the silanol surface.

In addition, foreign impurity atoms present on the SiO_2/MoS_2 interface can also act as traps. A shallow donor trap state is produced just below the CBM of the MoS_2 when a foreign impurity atom is absorbed on the siloxane surface <cit.>. Even at low temperatures and with a low activation energy, it can transfer an electron to the MoS_2 conduction band and affect V_ th. In addition, intrinsic defects like sulphur vacancies, as discussed earlier, also affect V_ th. These are more likely to act as fast traps as these will be well coupled to MoS_2.



 §.§ Variation of hysteresis with gate voltage sweep range and sweep rate.

Figure <ref>(a) shows the dI/dV_ b-V_ g curves for different V_ g sweep ranges varying from ±20 V, i.e. Δ V_ g=40 V to ±80 V, i.e. Δ V_g=160 V. Negligible hysteresis is seen in the ±20 V sweep range and hysteresis, quantified by Δ V_ th=V_ thb-V_ thf, increases non-linearly with Δ V_ g, see the inset of figure <ref>(a). This is consistent with the bulk transport in similar devices <cit.>. For smaller Δ V_ g, the MoS_2 and traps Fermi energy changes by smaller amount and thus slow-traps in relatively narrower energy range change their charge state as compared to larger Δ V_ g. We can estimate the number of traps that change their charge state using Δ V_ th, as discussed earlier. Thus, for Δ V_g=160 V, 1.05× 10^ 12 cm^-2 traps change their charge state as compared to 6.58× 10^ 10 cm^-2 at Δ V_g=40 V in figure <ref>(a).


Figure <ref>(b) shows the change in hysteresis curves with V_ g sweep rate for fixed Δ V_ g and other parameters. At higher sweep rate more slow-traps will be able to change their charge state. This makes the hysteresis increase with reducing V_ g-sweep rate. A larger sweep-rate also increases the maximum value of the tunnel conductance as reduced traps' participation leads to higher change in channel Fermi energy or carrier density. Also, the slowly acquired dI/dV_ b-V _ g curves contain more generation-recombination noise, see Fig. <ref>(b), as more traps capture and release electrons randomly during the slow sweep



 §.§ Observation of a rare hole-doped nature in local tunnel conductance

Figure <ref>(a) shows a tunnel spectra, i.e. dI/dV_ b-V_ b at certain location with the bias voltage sweep at a fixed V_ g = 30 V. This shows the expected band gap but more band tail states near both VBM and CBM and with MoS_2 Fermi energy close to the valance band edge. This indicates a local p-type doping as opposed to the n-type which is more common. If the underlying SiO_2 is defect-free, it has also no influence on MoS_2's local conductance since its valence and conduction bands are far apart from those of MoS_2 <cit.>. No charge transfer occurs between SiO_2 and MoS_2 due to the high hole and electron barrier. Hence, the observed n-or p-type local conductance of MoS_2 on SiO_2 must arise from defects, impurities and local disorder at the MoS_2-SiO_2 interface. Regions with sulfur-rich or Molybdenum-deficiency can also make it p-type locally. The traps may also give rise to this behavior depending on their energy relative to the MoS_2 bands. Thermally created undercoordinated oxygen atoms (Si-O*) on the silanol (Si-OH) terminated surface can serve as an electron trap leading to p-doping in MoS_2. For such a defect it is reported that the empty acceptor state is generated at 0.9 eV above the SiO_2 VBM <cit.>.

Figure <ref>(b) shows dI/dV_ b-V_ g curves at the same location with a rather unusual hysteresis and with access to both electron and hole doped regimes through V_ g change. During the forward sweep, local conductance becomes non-zero at V_ g = 10 V and increases till V_ g=60 V and then it quickly drops to zero at the beginning of the backward sweep followed by a p-type threshold at around V_ g =-10 V. On further decreasing V_ g, conductance increases till V_ g = -35 V and then decrease again reaching zero at -50 V which stays at zero at the begining of forward sweep of V_ g. The nono-monotonic change in dI/dV_ b, and particularly a maximum near V_ g=-32 V can arise from the delayed reaction of the slow traps with energy near VBM which depletes the hole-type carriers from the channel.

Thus in this region of MoS_2, all five scenarios of Fig. <ref> seem to be accessible, presumably, due to a lower overall trap density leading to a wide variation of E_ F with V_ g spanning both CBM and VBM. This is more likely from much lower fast-trap density as the hysteresis, arising due to the slow traps, is still quite significant. Also the observation of a finite dI/dV_ b at a negative V_ g implies that the bulk of the MoS_2 in its insulating state is not too insulating to forbid the transport of tunnel current.




§ SUMMARY AND CONCLUSIONS

Figure <ref> summarized how the MoS_2 bands shift in response to V_ g at a given location with certain trap charge density. The local traps' charge configuration determines the local charge density σ_ tr arising from traps and thus the local band shift of MoS_2. This is illustrated in the schematic in figure <ref>. The overall electrochemical potential stays constant throughout the MoS_2 channel while the local filling or electrostatic potential or Fermi energy is inhomogeneous due to variations in local σ_ tr. One can thus have locally n- or p-doped regions as seen in this STM study. These schematics, however, do not capture the detailed behavior of traps in terms of their response time and energy distribution. The latter will affect the hysteresis in local dI/dV_ b-V_ g curves as well as the detailed V_ g dependence.

In conclusion, our STM/S investigation on single-layer MoS_2 surface shows hysteresis in local tunnel conductance with gate sweep at a constant sample bias voltage. The Δ V_ th, V_ th and the shapes of dI/dV_ b-V_ b and dI/dV_ b-V_ g curves also show inhomogeneities due to traps. Further, the hysteresis changes with V_ g sweep range and sweep rate. Energy-dependent interface trap-state density is spatially inhomogeneous and even pins the MoS_2 Fermi energy in some places. Finally, the dependence of dI/dV_ b-V b and dI/dV_ b-V b on the traps can be a valuable tool for studying traps and defects in 2D materials.


§ ACKNOWLEDGMENTS

The authors acknowledge SERB-DST of the Government of India and IIT Kanpur for financial support.


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