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Jian Liao, [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), Jiamin Xue

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This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Jian Liao, Takashi Taniguchi, Kenji Watanabe, Jiamin Xue; Probing thickness-dependent tip-induced band bending in MoS2. Appl. Phys. Lett. 17 March 2025; 126 (11): 113101 and may be found at https://doi.org/10.1063/5.0252812.[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

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[Probing thickness-dependent tip-induced band bending in MoS2](https://mdr.nims.go.jp/datasets/5a57fa8a-1c74-442d-830e-9728897e5f75)

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Probing thickness-dependent tip-induced band bending in MoS2Jian Liao1, Takashi Taniguchi2, Kenji Watanabe3, and Jiamin Xue1*.*Corresponding author: Jiamin XueEmail: xuejm@shanghaitech.edu.cnAffiliations1School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China. 2Research Center for Materials Nanoarchitectonics, National Institute for Materials Science,  1-1 Namiki, Tsukuba 305-0044, Japan3Research Center for Electronic and Optical Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, JapanABSTRACT: Scanning tunneling spectroscopy (STS) has played an important role in determining the electronic band structures of semiconductors. However, the tip-induced band bending (TIBB) could strongly affect the measured valence and conduction band edges, which are of vital importance for a semiconductor. In the literature, the presence or absence of the TIBB effect in a given STS measurement is often not discussed thoroughly. In this work, we quantitatively investigate the TIBB effect in MoS2 with varying thicknesses using light-modulated contact-mode STS. Our results demonstrate that the TIBB effect is strongly dependent on the thickness of MoS2. With thin MoS2 of a few atomic layers (several nanometers), the TIBB approaches zero, and the measured STS can accurately reflect the band edges. While for thicker MoS2 of ~100 nm, the TIBB can be as large as ~1 eV. This work clarifies the ambiguity about the TIBB effect and provides a foundation for the interpretation of STS data on atomically thin semiconductors.TEXTScanning tunneling spectroscopy (STS) has been an important tool for studying semiconductors. Combining millielectronvolt energy resolution and subnanometer spatial resolution, STS has provided a large amount of information about semiconductors regarding the band structures,1–3 doping,4,5 defects,6,7 and so on. However, there is an important side effect that needs to be considered properly when applying STS to the study of semiconductors, i.e., the tip-induced band bending (TIBB) effect.8,9 Due to the limited charge densities in semiconductors, the electric field induced by the bias voltage between the tip and sample is not efficiently screened on the sample side and has a finite penetration depth inside the semiconductor, causing the band to bend on the sample surface. This effect will make the measured band gap appear to be larger than the real gap, resulting in inaccurate measurement.10–12In the development of two-dimensional (2D) materials, STS has been playing an important role in determining the band structures of various 2D materials with different layer numbers.13,14 It is often assumed that TIBB does not affect the measured band gaps. The validity of this assumption is sometimes checked by varying the tip-sample distance and inspecting the possible variations of the I-V curves.15–17 If the band edges determined from the I-V curves remain the same at different tip-sample separations, it is taken as an indication that the TIBB is absent in the measurement. As we will show later, however, this method may not be able to reflect the real TIBB. In this work, we use light-modulated contact-mode STS (CMSTS) to detect the TIBB on a representative 2D semiconductor, MoS2, with different thicknesses. The van der Waals structure of MoS2 makes the study of thickness-dependent TIBB more feasible than that with conventional bulk semiconductors. We find that the TIBB is almost absent in atomically thin semiconducting MoS2 and increases with thicker MoS2 flakes. Electrostatic calculations are used to explain the experimental observations. Our results strengthen the foundation of applying STS to the study of 2D semiconductors.In conventional STS, the presence or absence of the TIBB effect is determined by varying the tip-sample distance and inspecting if the STS spectrum changes.15–17 By reducing the tunneling current setpoint, the tip-sample distance is enlarged. The voltage drop inside the vacuum gap increases and the TIBB effect, if present, would reduce. As a result, the measured band gap would become smaller. Such a change is seldom observed in the study of 2D semiconductors,15–17 which has been taken as an indication of the absence of the TIBB effect. However, the tunneling current drops exponentially with tip-sample distance. Roughly one order of magnitude reduction in tunneling current only results in 1  increase of the tip-sample distance,18 which is not expected to change the TIBB noticeably since the tip-sample vacuum gap in normal STS is in the order of ~1 nm. To verify this expectation, a computer program numerically solving the three-dimensional tip-semiconductor electrostatic problem19 was employed (see the supplementary material for a list of relevant parameters used in the calculation). Figs. 1a and b present the computation results of potential distribution and tunneling current density at different tip-sample distances (ranging from 0.5 nm to 1.0 nm), with a tip radius of 3 nm and sample bias voltage Vb = +1 V. In the calculation, the semiconductor is taken to be half-infinite for  (blue region), while the tip is located in the vacuum (, purple region) with varying distances away from the surface of the semiconductor at . Far inside the semiconductor, the electrostatic potential  is taken to be zero, and  at  is taken to be the TIBB. Notably, an increase in the tip-sample distance from 0.5 nm to 1 nm results in a four-order-of-magnitude decrease in the tunneling current density (Fig. 1b), while  only decreases from 0.391 eV to 0.299 eV (Fig. 1a) and the decreasing rate slows down for larger tip-sample distances. Due to the relatively small change in , the calculated dI/dV does not show noticeable changes (Fig. 1c). Another calculation with a larger tip radius shows similar behavior (see Fig. S1 in the supplementary material). These calculation results indicate that the common way of detecting the TIBB has its limitations.FIG. 1. Calculation results of distance-dependent tunneling behaviors with a tip radius of 3 nm. . (a) Schematic showing where the potential distribution profiles are taken. (b) The potential distribution along the z direction at different tip-sample distances (from 0.5 nm to 1.0 nm) with a tip radius of 3 nm. The purple region () represents the vacuum, and the blue region () represents the MoS2. The MoS2 extends to positive infinite. (c) The calculated tunneling current density (Jt) at different tip-sample distances with , showing an exponential decay of the current. (d) Normalized dI/dV at different tip-sample distances. The similarity between all these curves indicates that the traditional method of detecting TIBB may not be sufficient.To detect the TIBB more accurately, we use the light-modulated STS (LM-STS),20–25 which has been used to detect charge carrier dynamics in bulk p-n junctions22,23 and photon-induced band movement in hybrid perovskite.21 In this technique, STS spectra are taken under dark and light-illuminated conditions. If there exists a TIBB, the two spectra will be different due to photo-excited carriers on the surface. The experimental setup for LM-STS is schematically depicted in Fig. 2(a). Thanks to its easy thickness tunability, MoS2 is chosen as a model semiconductor to study thickness-dependent TIBB. In addition, a modified STS technique is used, namely the contact-mode STS,26 instead of the conventional STS. In the contact-mode STS, the vacuum tunneling gap is replaced with a thin hexagonal boron nitride (hBN) flake, and a conductive atomic force microscope (CAFM) in mechanical contact with the hBN/MoS2/Au stack is used to detect the tunneling current. Since the tip position is stabilized by keeping track of the force between the tip and sample instead of the sensitive tunneling current as in a conventional STS, the tunneling junction in the contact-mode STS is more immune to mechanical, thermal or light-induced fluctuations and more suitable for studying microscale devices.27–29In the experiment, MoS2 flakes were exfoliated onto Au films, and 1.4 nm hBN flakes were transferred on top as the tunneling junction. A sample bias voltage (Vb) was applied to the Au substrate with the CAFM tip grounded. Unlike the conventional STS, which typically operates under ultrahigh vacuum and low temperatures, our experiments were conducted under ambient conditions. This setup allows easy light modulation of the surface charge carriers without affecting the tunneling junction, i.e., the hBN. Light from a laser diode (532 nm) with energy above the MoS2 band gap was positioned 60˚ off-normal to the sample surface and focused onto the tunneling junction area with a spot diameter of ~0.2 mm. Contact-mode STS spectra were measured under dark, light-on (illuminated), and light-off (back to dark) conditions, yielding corresponding tunneling current (It) versus Vb curves. Fig. 2(b) presents a typical result for a 20 nm MoS2 sample. At positive Vb, the It measured under light-on conditions (red curve) is significantly larger than that under dark conditions (black and yellow curves), with enlarging differences as Vb increases. In contrast, the two curves nearly overlap for negative Vb. These behaviors reveal the existence of TIBB in the positive Vb range.22,23 After turning the light off (in 1~3 minutes), the It-Vb curve is measured again (yellow curve in Fig. 2(b)), which falls on top of the curve obtained before illumination, indicating that the light did not cause any unwanted damage to the sample.FIG. 2. Principles of LM-CMSTS. (a) Schematic of the LM-CMSTS setup. The tip is grounded, and the bias voltage Vb is applied to the sample. (b) Tunneling current (It) versus Vb curves were obtained on a 20 nm thick MoS2 under dark (black), illuminated (red), and light-off (yellow) conditions. The blue arrow indicates the magnitude of SPV at Vb = +2 V. (c) One-dimensional energy band diagrams of the tunnel junction for an n-type MoS2 with the same tunneling current under dark (left) and light-on (right) conditions (Vb＞0 V). Regions shaded with diagonal lines represent the electron states of the tip that produce the tunneling current. Excess electrons (blue circles) and holes (red circles) generated by light illumination are separated by the electric field originating from the TIBB and reduce the band bending at the surface. (d) Light-intensity dependence of SPV at Vb = +2 V measured on MoS2 with a thickness of 70 nm.Two schematic band diagrams in Fig. 2(c) explain the observations in Fig. 2(b). In the dark condition shown in Fig. 2(c) left, a negative tip voltage (equivalent to a positive sample bias, denoted as Vbdark) repels electrons and induces holes at the surface of MoS2. Due to the n-type doping of MoS2, its surface band will be bent up, resulting in a space charge region that blocks some of the tunneling paths (represented by the red arrow in the schematic). When the light is on (Fig. 2(c) right), a large number of photo-excited charge carriers populate the surface. Driven by the built-in electric field in the TIBB region, the newly generated holes accumulate on the surface and flatten the band there. As shown in Fig. 2(c), when the same tunneling current (It) is achieved under dark and illuminated conditions, the latter requires a smaller sample bias voltage, denoted as Vblight. The difference between Vbdark and Vblight for achieving the same It is defined as the surface photovoltage (SPV), which is an increasing function of Vbdark. The blue arrow in Fig. 2(b) shows the SPV at Vbdark = +2 V. The SPV is also a function of incident light intensity. When the light is sufficiently strong, a “flat band” condition is achieved, where the measured SPV equals the magnitude of TIBB at that specific Vbdark. Further increasing the light intensity should no longer increase the SPV. To confirm this, a light-intensity dependence of SPV at Vb = +2 V is measured on a 70 nm MoS2 flake (Fig. 2(d)). As expected, the SPV reaches a saturation value of 1.20 V when the light intensity exceeds 1.13 mW. Throughout this work, we chose the SPV at Vbdark = +2 V as a measure of the TIBB strength.For negative Vbdark, the tip electric field causes electron accumulation near the sample surface. Since MoS2 is rich in electrons, the field is efficiently screened with little band bending. As a result, no SPV is expected in the negative Vbdark range, as seen in the data of Fig. 2(b). This observation also rules out the possibility of light-induced thermal effect since that would affect both the positive and negative biases.30To investigate the thickness dependence of TIBB, the SPV of MoS2 with different thicknesses is measured. As illustrated in Figs. 3(a)-(d), It -Vb curves are obtained for MoS2 with thicknesses of 96, 66, 13, and 3 nm, respectively. These curves exhibit two consistent characteristics similar to those in Fig. 2(b). First, the It -Vb curves obtained under light-off conditions (yellow curves) closely align with the ones measured under dark conditions (black curves), indicating the reliability of the measurement. Second, there is negligible SPV in the negative Vb range; while in the positive Vb range, the SPV increases with Vbdark. The light intensity used for each sample has been adjusted to make sure that the SPV saturates. Therefore, the SPVs obtained in Fig. 3 provide measures of the TIBB at any specific Vbdark for MoS2 with different thicknesses. From Fig. 3, it is clear that the TIBB on thicker MoS2 is significantly larger than that on thinner MoS2. FIG. 3. It versus Vb curves for MoS2 with different thicknesses under dark (black), illuminated (red), and light-off (yellow) conditions, respectively. (a) 96 nm. (b) 66 nm. (c) 13 nm. (d) 3 nm. The light intensity was adjusted to obtain saturated SPV for all the measurements.In Fig. 4a, the thickness-dependent SPV (TIBB) at Vbdark = +2 V is depicted, revealing that the SPV approaches 0 V for atomically thin MoS2 and increases sharply until saturation with a value of  V for thicker MoS2. To understand the experimental result, a simple one-dimensional electrostatic model is adopted. In the model, the tip is treated as a gold plate, as shown in the inset of Fig. 4b. The electrostatic potential  satisfies Poisson’s equation throughout the stack. In the hBN,  linearly depends on z as no spatial charge exists there. Within MoS2,  is determined by:where  is the electron charge,  is the charge density,  is the permittivity of vacuum, and  is the dielectric constant of MoS2 (taken as 6.9).31  in MoS2 is equal to the donor concentration  since the MoS2 is depleted of electrons at positive Vb. The boundary conditions for Eq. (1) differ in two scenarios. When MoS2 is so thin that the entire MoS2 is depleted, the electrostatic potential energy at the tip position , and at the surface of the Au substrate . Applying these boundary conditions and matching the electric field at the MoS2-hBN interface allows analytical solutions for Poisson’s equation within MoS2 and hBN. The resulting electric potential distribution is depicted in Fig. 4c for a 1 nm MoS2 sample. Here, the blue region represents MoS2 (), and the green region represents hBN (). The electrostatic potential energy at the MoS2-hBN interface (denoted as ) is the TIBB for MoS2 with this thickness.In cases where the thickness of MoS2 is larger than a depletion width , the boundary conditions for Eq. (1) change to  and the electrostatic potential energy at the boundary of the depletion width inside the MoS2 . Applying these boundary conditions to solve the Poisson’s equation, we derive the distribution of potential and the expression of : where  is the dielectric constant of hBN, and  is the tip-sample distance (equal to the thickness of hBN in this case). Taking ,31  cm-3, and  nm, we obtain  nm from Eq. (2). Fig. 4d shows the potential distribution for a 45 nm MoS2 sample. The majority of  (1.74 eV) drops within MoS2, with only a minor portion dropping across the hBN tunnel junction. When the thickness of MoS2 exceeds ,  becomes independent of the thickness and remains at 1.74 eV. Calculated results of the thickness-dependent TIBB (Fig. 4b) closely resemble experimental findings (Fig. 4a), despite some quantitative differences in the thickness at which TIBB reaches saturation and the maximum TIBB obtained. These differences may arise from the inaccuracy introduced by the one-dimensional approximation, zero-temperature condition, and some inaccurate parameters used in the calculation. It is also worth noting that the thickness of hBN could affect the measured TIBB as shown in Fig. S2. However, the trend that TIBB decreases with thinner MoS2 holds the same.FIG. 4. Thickness-dependent SPV and model calculations. (a) Experimental results of the thickness dependence of SPV at Vb = +2 V. (b) Calculation results of thickness dependence of the surface potential  of MoS2 with . The one-dimensional model used is depicted in the inset. (c, d) Calculated potential distribution for 1 nm and 45 nm MoS2 samples. The blue region () denotes the MoS2 region, and the green region () denotes the hBN region.TIBB is widely acknowledged as a primary source of measurement error affecting band edge positions in tunneling spectra.10–12 Since we have shown that TIBB depends on the sample thickness, it is natural to ask how that affects the measured band edges. To do that, numerical differentials of the It -Vb curves are used to obtain dIt/dVb. Following the conventions of band edge determination,15 the logarithm of the dIt/dVb are plotted in Figs. 5a and b for MoS2 with thicknesses of 3 and 38 nm, respectively. Vb = 0 V denotes the Fermi level and the sharp rises at negative and positive Vb correspond to the valence band maximum (VBM) and conduction band minimum (CBM), respectively (see Fig. S3 for details). The log(dI/dV) curves measured under dark and light-on conditions overlap for the negative Vb region, indicating that TIBB does not influence the VBM. However, changes in the CBM under dark and light-on conditions correlate with MoS2 thickness. For the 38 nm MoS2, the CBM changes  between light-on and dark conditions. Conversely, for the 3 nm MoS2, . The thickness-dependent behavior of  is illustrated in Fig. 5(c). It has a similar trend as the TIBB at Vbdark = 2 V in Fig. 4(a), i.e. increasing with thickness and approaching 0 for atomically thin flakes. This behavior can be understood with the schematic in Fig. 5(d). For thinner flakes, the TIBB is weak and the band edge can be determined accurately; while for thicker flakes, the TIBB is strong and the measured gap under dark conditions is enlarged compared to its real value.FIG. 5. Band edges affected by the TIBB. log (dI/dV) versus Vb curves obtained on MoS2 with thicknesses of (a) 3 and (b) 38 nm under dark (black), illuminated (red), and light-off (yellow) conditions, respectively. (c) Experimental results of thickness dependence of . (d) One-dimensional energy band diagrams of tunnel junctions with different thicknesses of MoS2 under the same positive Vb. The tunneling current It can directly tunnel through the narrow depletion region of thin MoS2 (left), but not for thick MoS2 (right) due to a wide depletion region.So far, we have measured MoS2 flakes on an Au substrate. For device applications, MoS2 flakes are typically placed on insulating substrates, such as SiO2. The thickness-dependent TIBB of this type of sample is also measured (see Figs. S3 and S4 in the supplementary material), and behaviors similar to MoS2 flakes on Au are obtained. Considering the totally different screening behavior between the SiO2 and Au substrates, the similarity is an intriguing phenomenon. To clarify the mechanism, a two-dimensional electrostatic model is needed which can be solved numerically. The results in Fig. S6 closely resemble the experimental results indicating that electrostatic consideration is enough to account for the observed thickness-dependent TIBB.To conclude, we used light-modulated contact mode STS to study the TIBB as a function of MoS2 thickness. We showed that the conventional way of varying the tip-sample distance and measuring the I-V curves may not reflect the real TIBB. With the help of light, we found that the TIBB and the band gap determined by STS have a sensitive dependence on the semiconductor thickness. For MoS2 of a few nanometers, the TIBB approaches zero. For thicker MoS2 of ~100 nm, the TIBB grows to ~1 eV. The absence of TIBB in atomically thin MoS2 flakes both on conductive (i.e. Au) and insulating (i.e. SiO2) substrates provides a solid foundation for applying STS in the study of 2D semiconductors.See the supplementary material for more data.The authors thank Dr. Wujun Shi and Prof. Baile Chen for computation support and the Soft Nano Fabrication Center at ShanghaiTech University for the equipment provided. J.L. and J.X. are funded by NSFC 12074256. K.W. and T.T. acknowledge support from the JSPS KAKENHI (Grant Numbers 21H05233 and 23H02052) and World Premier International Research Center Initiative (WPI), MEXT, Japan.AUTHOR DECLARATIONSConflict of InterestThe authors have no conflicts to disclose. Author ContributionsJian Liao: Experimental investigation; Modeling; Writing.Takashi Taniguchi: BN growth.Kenji Watanabe: BN growth.Jiamin Xue: Conceptualization; Writing.DATA AVAILABILITY The data that support the findings of this study are available from the corresponding authors upon reasonable request.REFERENCES(1) Zhang, C.; Johnson, A.; Hsu, C. L.; Li, L. J.; Shih, C. K. Direct Imaging of Band Profile in Single Layer MoS2 on Graphite: Quasiparticle Energy Gap, Metallic Edge States, and Edge Band Bending. Nano Lett. 2014, 14 (5), 2443–2447. https://doi.org/10.1021/nl501133c.(2) Zhang, C.; Li, M.-Y.; Tersoff, J.; Han, Y.; Su, Y.; Li, L.-J.; Muller, D. A.; Shih, C.-K. Strain Distributions and Their Influence on Electronic Structures of WSe2–MoS2 Laterally Strained Heterojunctions. Nature Nanotech 2018, 13 (2), 152–158. https://doi.org/10.1038/s41565-017-0022-x.(3) Zhang, Z.; Wang, Y.; Watanabe, K.; Taniguchi, T.; Ueno, K.; Tutuc, E.; LeRoy, B. J. 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