The Opposite Anisotropic Piezoresistive Effect of ReS2 | ACS Nano

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The Opposite Anisotropic Piezoresistive Effect of ReS2 Chunhua An, Zhihao Xu, Wanfu Shen, Rongjie Zhang, Zhaoyang Sun, Shuijing Tang, YunFeng Xiao, Daihua Zhang, Dong Sun, Xiaodong Hu, Chunguang Hu, Lei Yang, and Jing Liu ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.8b09161 • Publication Date (Web): 06 Mar 2019 Downloaded from http://pubs.acs.org on March 7, 2019

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The a and b axes of ReS2 show positive and negative piezoresistive effect, respectively. 197x83mm (96 x 96 DPI)

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The Opposite Anisotropic Piezoresistive Effect of ReS2 1Chunhua

An, 1Zhihao Xu, 1Wanfu Shen, 1Rongjie Zhang, 1Zhaoyang Sun, 2Shuijing Tang, 2Yun-

Feng Xiao, 1Daihua Zhang, 3Dong Sun, 1Xiaodong Hu, 1Chunguang Hu, 4,5Lei Yang* and 1Jing Liu* 1State

Key Laboratory of Precision Measuring Technology and Instrument, School of

Precision Instruments and Opto-electronics Engineering, Tianjin University, 92 Weijin Rd., Tianjin, 300072, China. 2

State Key Laboratory for Mesoscopic Physics and School of Physics, Peking University; Collaborative Innovation Center of Quantum Matter, Beijing 100871, China

3

International Center for Quantum Materials, School of Physics, Peking University, NO. 5 Yiheyuan Road, Beijing, China, 100871 4

5

Max-Planck-Institut für Eisenforschung GmbH, Düsseldorf 40237, Germany.

WPI Nano Life Science Institute (WPI-NanoLSI), Kanazawa University, Kakuma-machi, Kanazawa 920-1192, Japan. Corresponding author emails: L.Y.: [email protected]; J. L.: [email protected]


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Abstract:

Mechanical strain induced changes in the electronic properties of two-dimensional (2D) materials is of great interest for both fundamental studies and practical applications. The anisotropic 2D materials may further exhibit different electronic changes when the strain is applied along different crystalline axes. The resulted anisotropic piezoresistive phenomenon not only reveals distinct lattice-electron interaction along different principle axes in low-dimensional materials, but also can accurately sense/recognize multi-dimensional strain signals for the development of strain sensors, electronic skin, human-machine interfaces and etc. In this work, we systematically studied the piezoresistive effect of an anisotropic 2D material of rhenium disulfide (ReS2) which has large anisotropic ratio. The measurement of ReS2 piezoresistance was experimentally performed on the devices fabricated on a flexible substrate with electrical channels made along the two principle axes, which were identified non-invasively by the reflectance difference microscopy developed in our lab. The result indicated that ReS2 had completely opposite (positive and negative) piezoresistance along two principle axes, which differed from any previously reported anisotropic piezoresistive effect in other 2D materials. We attributed the opposite anisotropic piezoresistive effect of ReS2 to the straininduced broadening and narrowing of the bandgap along two principle axes, respectively, which was demonstrated by both reflectance difference spectroscopy and theoretical calculations.

Keywords: ReS2, anisotropy, piezoresistive effect, reflectance difference microscopy, reflective difference spectroscopy


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Mechanical strain induced deformation is well-known to effectively change the band structure of semiconducting crystals.1–6 This effect becomes even more profound as the thickness of the crystal reduces to a few atomic layers, which provides insights into the lattice-electron interaction in low dimensional systems.7 Two-dimensional (2D) materials are the layered crystalline solids with thickness at the atomic level, which include graphene and its relevant hybrid,8 transition metal dichalcogenides (TMDs), hexagonal boron nitride (h-BN) and emerging monoatomic buckled crystals known as MXenes.9 They have drawn tremendous attentions since discovery, due to their excellent mechanical, electrical, optical properties and etc., which are ideal for various applications such as flexible optoelectronics,10 radiation (terahertz) detection,11 physical chemistry and nanotechnologies. Among these properties, extensive studies have been focused on the mechanical,12–15 mechano-electrical16,17 and mechano-optoelectrical18 characteristics of 2D materials. Examples include large piezoresistive/electric effect,2,7,19,20 strain-induced continuous bandgap modulation19–24 and anisotropic mechanical characteristic14,25 of 2D materials, which indicate promising applications of 2D materials in strain sensors,26 flexible electronics27 and straintunable photo-detection/voltaic devices.28–30 Rhenium disulfide (ReS2) is one of the 2D materials that belongs to the transition metal dichalcogenides (TMDs) sub-group.31,32 It crystallizes in a distorted 1T diamond-chain structure with the triclinic symmetry,31–33 which presents thickness-independent direct bandgap and anisotropic physical properties.34,35 The two anisotropic axes of ReS2 correspond to the crystal directions with the shortest (b-axis) and second-shortest (a-axis) axes in the basal plane intersecting at an angle of ~60 degree as shown in Supplementary Fig. S1, which have the maximum and minimum field effect mobilities, respectively.32 Meanwhile, theoretical calculations predict that the


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bandgap of ReS2 can be effectively modulated by the applied mechanical strain.35,36 In addition, the two anisotropic directions respond differently to the uniaxial strain, which indicates distinct strainelectronic structure interaction along different crystalline directions, and thus, anisotropic piezoresistive effect.36 This property is ideally useful in accurate detection and recognition of multidimensional strain/stress and gestures, which has wide applications in the fields of electronic skin,26,37,38 human-machine interfaces,27,39 strain sensors26 and etc. Although several other types of TMDs, such as ReSe2, WTe2, MoTe2, have also been reported possessing anisotropic properties,40– 43

the anisotropic piezoresistive effects of TMDs are rarely studied. Therefore, the systematic study

on anisotropic piezoresistance of ReS2 with the largest anisotropy ratio32 among semiconducting TMDs will be very helpful in both understanding the mechanism and developing piezo-functional devices. In this work, we experimentally characterized the anisotropic piezoresistive effect of ReS2 and investigated the underline mechanism. First, we used reflectance difference microscopy (RDM) to identify the a and b axes of a ReS2 flake in a non-invasive way.44,45 Then, we transferred the ReS2 flake on the flexible substrate for piezoresistance measurement. Since standard photo-lithography method can be hardly applied on flexible substrate, we developed a low-cost method to fabricate flexible ReS2 devices, which used tapered optical fiber(s) as the shadow mask. The measured results revealed that the two anisotropic directions of the ReS2 had completely opposite piezoresistive effect, which exhibited positive and negative piezoresistance along a and b axes, respectively. This observation differs from the previously reported piezoresistive effects of other 2D materials,19–22 which are either positive or negative along all principle axes. For instance, the anisotropic material of black phosphorus shows positive piezoresistance along both principle axes.19 In order to


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investigate the underline mechanism of such distinct piezoresistive effect of ReS2, we used reflectance difference spectroscopy (RDS) to probe the bandgap change of ReS2 under uniaxial tensile strain along the two anisotropic axes,46,47 respectively, which indicated that under uniaxial tensile strain, the bandgap along a and b axes increased and decreased, respectively. This result was also consistent with our DFT calculations, which further revealed that the anisotropic bandgap change was due to the different dispersion behaviors of the top valence band along two principle axes under tensile strain dominated by the Re dyz and dx2-y2 orbitals. Results and discussion Device fabrication. The fabrication process of the ReS2 device on the flexible substrate is illustrated in Scheme 1a, the details of which can be found in the Materials and Methods section. Briefly, ReS2 flakes were mechanically exfoliated from bulk ReS2 crystals and transferred onto a flexible polyimide (PI) substrate. Two optical fibers with diameters of ~2 m were transferred onto the ReS2 flake as shadow masks, each of which was perpendicular to one of the anisotropic axes of ReS2. The atomic force microscopy (AFM) image and Raman spectroscopy of a ReS2 flake and the AFM image of a tapered optical fiber on PI substrate are presented in Supplementary Fig. S2. After that, titanium/gold (Ti/Au) electrodes with thickness of ~8 nm/~100 nm were deposited, followed by optical fiber lift-off process. Finally, the Ag wires were connected to the electrodes for the further measurement. Scheme 1b displays the schematic of a ReS2 device on flexible PI substrate, the channels of which are along the two principle axes of the ReS2 flake, respectively.


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Scheme 1. Schematic of the device fabrication process (a) and configuration (b). Anisotropic measurement by both optical and electrical methods.

In Fig. 1, we used optical

measurement to assist identifying the principle directions of ReS2, so that we can easily fabricate separate anisotropic ReS2 devices. As reported previously, the ReS2 lattice tends to break along the lattice directions along a and b axes, respectively. Therefore, the exfoliated flakes usually have two boundaries intersecting at an angle of ~ 60o, according to which we can roughly determine the directions of the two principle axes of the ReS2 flake. However, it is difficult to further differentiate the a and b axes, which is critically important for fabricating anisotropic devices, since the two axes possess distinct physical properties from each other. By incorporating the optical anisotropic measurement, we can identify the a and b axes through a non-destructive means. The optical anisotropy of the ReS2 was measured by reflectance difference microscopy (RDM) developed in our lab. Its working principle has been described in detail in previous literatures.32–35,48,49 Briefly, it measures the normalized reflectance difference (N) of two polarized portions of light, s and p, as light normally incidents on a sample. The N value can be calculated by the following equation: 𝑁=1

𝑟𝑠 ― 𝑟𝑝 2(𝑟𝑠 + 𝑟𝑝)

(1)

where rs and rp are the reflectance from s and p portions, respectively. Consequently, the RDM


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signal will achieve the maximum/minimum value, when the polarization direction of s/p light matches the principle axis of the sample that has the strongest light-ReS2 coupling coefficient. In other words, the direction with maximum N value is parallel to the principle axis of ReS2 with strongest interaction with light, while the direction with minimum N value is perpendicular to that principle axis, since the polarization directions of s and p are perpendicular to each other. We transferred a ReS2 flake of around 8 nm thick to SiO2/Si substrate through mechanical exfoliation for sequential optical and electrical anisotropy measurements. Figure 1a shows the RDM images of the same ReS2 flake when the polarization direction of the s/p light rotates from 0o to 180o as marked in Fig. 1b. According to this figure, we plotted the measured N values in a polar coordinate system as shown by hollow blue squares in Fig. 1d by shifting the minimum N value to zero. The blue line in the figure is the theoretical fit of the data. It shows that the N value achieves the maximum value at 170o, which indicates that the principle direction of ReS2 with the strongest light interaction is along 170o. The minimum N value is achieved at around 80o, which is perpendicular to the direction of the maximum N value. This is consistent with the in-plane anisotropic optical absorption and photoluminescence spectra of ReS2 reported by Ho et al.50–52 After measuring the optical anisotropy of ReS2, we further measured the electrical anisotropy of the ReS2 by depositing 12 electrodes of Ti /Au (thickness was 5 nm/50 nm) on the same ReS2 flake for optical measurement with a spacing of 30° along the directions as shown in Fig. 1b. The optical image of the fabricated device is shown in the inset of Fig. 1c. AFM image of the device was shown in Supplementary Fig. S3. We performed transport characteristic measurements on this device (after it was annealed in the gas mixture of nitrogen and hydrogen (v:v = 98:2) at 300 ° C for 5 min) along different directions by applying the same bias of 2 V on each electrode pair separated by 180° and sweeping the back gate


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voltage. The Ids-Vg curves of the ReS2 device along different directions are plotted in Fig. 1c, based on which the angle-resolved field effect mobilities of ReS2 are calculated and presented by red hollow dots in Fig. 1d. The result shows that the direction corresponding to the maximum field effect mobility of 2.90 cm2/V·s (b-axis) is at 170°, while the direction corresponding to the minimum field effect mobility of 1.38 cm2/V·s (a-axis) is at 110°. We fabricated and tested another device which exhibited similar anisotropic behavior (see Supplementary Fig. S4). These results are consistent with previous work reported by Liu et al.32 It should be noted that previous report has observed the lowest and highest in-plane resistivity of p-type ReS2 along and perpendicular to b axis, respectively.53 Combining the optical and electrical measurement results, we can conclude that the principle direction with the strongest light interaction and highest field effect mobility (along 170o) corresponds to b-axis of ReS2, while the a-axis of ReS2 is separated by 60o from the b-axis.32 As a result, we can identify the a and b axes of ReS2 flake by combining its physical fracture boundary and the RDM measurement result: the boundary of the ReS2 flake that parallel to the maximum RDM value corresponds to the b-axis, while the other boundary corresponds to the aaxis. We tested the principle axes of another ReS2 sample with thickness of 70 nm by optical and electrical measurements, the results of which were consistent with the 8 nm thick sample. This conclusion is also confirmed by previous works on the in-plane anisotropic mechanical property of ReS2, which demonstrate that the ultimate tensile strength of ReS2 along the directions perpendicular to a and b axes are much lower than those along other directions (the direction perpendicular to b axis has the minimal ultimate tensile strength). Therefore, the cleavage edges are preferentially along a and b axes (with the longer edges along the b-axis).54–56


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Figure 1. Optical and electrical anisotropic measurements. (a) RDM images of a ReS2 flake on SiO2/Si substrate as the direction of s/p light rotates from 0o to 180o as marked in (b). (b) Optical microscopy image of the ReS2 flake for optical and electrical measurements. The directions measured optically and electrically are marked on the flake. Scale bar: 10 μm. (c) Transfer curves of the ReS2 flake measured by the diagonally paired electrodes along different directions as marked in (b). Scale bar: 10 μm. (d) Angle-resolved N values from RDM measurement and mobilities of the same ReS2 flake plotted in polar coordinates. The N values and mobilities are presented by blue hollow squares and red hollow dots, respectively. The blue line is the theoretical fitting of the N values. The red arrows represent the a and b axes of the ReS2 flake. Anisotropic piezoresistive effect of ReS2. Figure 2 exhibits the anisotropic piezoresistance of ReS2. The devices used for piezoresistance measurement were fabricated by the same process as described in Scheme 1, during which the a and b axes of the ReS2 flakes were identified according to the RDM measurement results. The channel directions of the devices were made along a- and/or b-axis. The strain was applied on the ReS2 flake by clamping the two ends of the PI substrate on two stages. One of the stages was fixed, while the other stage was controlled to move towards the fixed stage at a certain speed. The strain experienced


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by the ReS2 flake was measured by a commercial strain gauge attached to the same lateral position as the ReS2 device on the PI substrate (the schematic testing setup is illustrated in Supplementary Fig. S5). Figure 2a and b are the real-time relative resistance change of two ReS2 devices under uniaxial tensile strain with channels and the applied strain along the a and b axes, respectively. The movable stage moved towards the fixed stage and then returned to the original location with a step of 0.5 mm. The original length of the PI substrates in Fig. 2a, b and c were 39 mm, 39 mm, 29 mm, respectively. As shown in Fig. 2a, the resistance of the ReS2 device along a-axis increased as the movable stage moved towards the fixed stage, corresponding to the increase of the tensile strain. When the moveable stage returned to the original position, the resistance completely recovered to the original value. The average resistance change corresponding to each step was 10.28 Ω. On the other hand, as shown in Fig. 2b, the resistance of the ReS2 devices along b-axis decreased/increased as the strain increased/decreased, which trend is opposite to the response along a-axis. We then tested the piezoresistance responses of the ReS2 on several other devices (see Supplementary Fig. S6), the result of which were all consistent with the observation that a/b-axis showed positive/negative piezoresistance. We also tested the resistance of the device under compressive strain, which increases/decreases along b/a axis as the compressive strain increases as shown in Supplementary Fig. S7. Furthermore, we fabricated a ReS2 (~56 nm thick) device with two channels along a and b axes, respectively, as shown in Fig. 2c. Figure 2d shows the relative resistance change of this ReS2 device along a and b axes, respectively, as a function of the strain. As expected, the a/b axis showed positive/negative piezoresistance and almost linear change with the strain. Thus, we calculated the gauge factors (GFs) of ReS2 along a and b axes to be around 50.14 ± 0.10 and 60.49 ± 0.37, respectively, resulting in a gauge factor ratio along a and b axes to be approximately


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-1:1.21. Figure 2e exhibits the repeatability of the piezoresistance response of ReS2, which shows almost non-degraded response over 28 bending cycles, indicating that the nanoflakes was deformed in the elastic regime.16 Open circuit voltage measurement (as shown in Figure S8) and dynamic current measurement (as shown in Figure S9) demonstrated that the phenomenon is piezoresistive effect instead of piezoelectric effect. The piezoresistive effect is mainly as a consequence of strain induced bandgap modulation, which has been observed in BP, even-layer MoS2, et al.19,20 Piezoelectricity, in comparison, mainly results from strain-induced lattice distortion and charge polarization of the materials with polarization domains or non-centrosymmetric structure, which behaves as oscillating voltage or current outputs under periodic strain.20,57 If the 2D material exhibits asymmetric lattice structure, it usually exhibits piezoelectric effect under strain, such as monolayer h-BN, odd layer MoS2 and monolayer to bulk α‑In2Se3, et al.20,57 We further investigated the piezoresistive coefficient () of ReS2, which is defined as the relative resistance change per stress and expressed by Eq 2: 𝜋=

△ R/R (2) 𝜌

where ρ is the stress experienced by ReS2, and ΔR/R is the relative resistance change of ReS2. Since stress relates strain (ε) through elastic modulus (E) by the following equation: 𝜌 = 𝐸𝜀 (3) The piezoresistive coefficient can be calculated by: 𝜋=

△ R/R 𝐸𝜀

G

=𝐸

(4)

We calculated the elastic modulus of ReS2 by density functional theory (DFT), which is presented as a 3 × 3 matrix in Eq. 5. The details of the DFT calculation is presented in Supplementary Information.


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[

]

𝑐bb = 203.5 𝑐ba = 40.5 𝑐bc = 1.0 Elastic modulus matrix （GPa） 𝑐ab = 40.5 𝑐aa = 205.1 𝑐ac = 1.0 (5) 𝑐cb = 1.0 𝑐ca = 1.0 𝑐cc = 1.8 where cij (i,j = a, b, c) is the elastic modulus in i-axis direction under the stress along j-axis. Equation 5 shows that the values of caa and cbb are almost the same, which indicates that the elastic modulus of ReS2 does not show anisotropic property. Then, the piezoresistive coefficient of the device in Fig. 2c are calculated to be πa=~ (2.44±0.05) ×10-10 m2/N and πb=~ (-2.97±0.18)×10-10 m2/N along a and b axes, respectively, with a ratio of -1:1.22, which is similar to the ratio of the GF. Usually, 2D and 1D materials possess larger piezoresistive effect than bulk metals but close to that of bulk single crystal silicon. By comparing 1D and 2D materials, the maximum GF of ReS2 measured in this work is 124.85 (along b-axis), which is larger than the GF of carbon nanotubes (0.82)58 and silver nanowires (1)59 induced by pieozresitive effect, but smaller than the GF of ZnO (1250)60 and ZnSnO3 (3740)61 induced by piezoelectric effect, and the GF of InAs (2200)62 induced by coexistence of piezoelectric and piezoresistive effects. However, 2D materials have symmetric/asymmetric in-plane piezoresistive effect, which is ideally for direction-sensitive strain sensing, such as gesture identification.


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Figure 2. Anisotropic piezoresistance response of the ReS2 flakes. (a, b) Real-time piezoresistance response curve of the ReS2 devices with channel direction along a-axis (a) and b-axis (b), respectively. The strain was applied along the channel direction. The insets are the optical microscopy images of the devices. The thicknesses of the flakes were ~11 nm (a) and ~106 nm (b), respectively. (c) Optical microscopy image of the device with two channels along a and b axes, respectively. The thickness of the device was ~56 nm. Principle axes were marked by red arrows. (d) The relative resistance changes of the device in (c) along two axes as a function of strain. (e) Repeatability of the piezo-resistance response of a ReS2 flake. (f) Schematic of a ReS2 device fabricated on flexible PI substrate under strain. Mechanism of anisotropic piezoresistive effect Figure 3 shows the band gap variation of ReS2 under different tensile strains by DFT calculations and RDS measurement. Figure 3a, b and c are the DFT calculated band structures of bulk ReS2 under no strain, 0.6% uniaxial strain (εb) along b-axis, and 0.6% uniaxial strain (εa) along a-axis, respectively. Without any strain, the ReS2 exhibits a direct band gap of 1.36 eV at the Γ point, which agrees with the theoretical result in Ref. 30. When 0.6% strain is applied along b-axis (Fig. 3b) and a-axis (Fig. 3c), the band gap remains direct, but is narrowed by 0.035 eV and broadened by 0.003


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eV, respectively. When the strain applied along a-axis increases to 3.0%, the direct band gap evolves to be indirect (see Supplementary Fig. S10). The transition behavior agrees with the results reported by Yu and co-workers on monolayer ReS2,36 except that the direct-to-indirect band structure transition occurs at a lower strain εa = 0.3% in their work. However, they reported that the band gap decreased under both a-strain and b-strain. This discrepancy may come from the different strainelectronic structures between monolayer and bulk material. We then performed RDS measurement to experimentally probe the band gap change under different strains. The ReS2 sample (~87 nm thick) for RDS measurement was exfoliated and transferred onto the flexible PI substrate, the principle directions of which were identified by RDM measurement. Then, the sample was deposited with electrodes of Ti/Au (thicknesses were 5 nm and 100 nm, respectively) to prevent slippery of the ReS2 flake on the PI substrate. The strain was induced by attaching the substrate on the cylinders with diameters of 25 mm and 37 mm to obtain strain of 0.22% and 0.28%, respectively, along both a and b axes. The RDS measurement is similar with the RDM measurement, both of which measure the reflectance difference of the two polarized portions of the incident light (s and p) with polarization directions perpendicular to each other. However, the RDS measurement fixes s/p polarization direction along the b-axis of ReS2, instead of rotating the polarization direction, while sweeps the incident photon energy from 1.44 eV to 1.53 eV (the directions of the s/p polarization, principle axes of ReS2 and applied strain is plotted in Supplementary Fig. S11). Figure 3e presents the RDS signals (Ns( λ )) of the device under tensile strain along p polarization direction and with s portion polarized along b-axis of ReS2 (see Supplementary Fig. S11a). The Ns( λ ) value can be calculated by: 𝑁𝑠(𝜆) =

2(𝑟𝑏(𝜆) + 𝑟𝑎(𝜆)𝑠𝑖𝑛𝜃 ― 𝑟𝑎(𝜆)𝑐𝑜𝑠𝜃) 𝑟𝑏(𝜆) + 𝑟𝑎(𝜆)𝑠𝑖𝑛𝜃 + 𝑟𝑎(𝜆)𝑐𝑜𝑠𝜃

(6)


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where ra and rb are the reflectivity of ReS2 along a and b axes, respectively. The 𝑟𝑎𝑐𝑜𝑠𝜃 and (𝑟𝑏(𝜆) + 𝑟𝑎(𝜆)𝑠𝑖𝑛𝜃) are the component of ra and rb along the p and s polarization directions, respectively, in which θ equals to 30o. When no strain is applied, the value decreases as the incident photon energy increases and achieves a minimum value at certain photon energy, which increases as the incident photon energy further increases. Since the variation of rb is larger than ra with the incident photon energy (b-axis has stronger interaction with light than a-axis as discussed previously), the change of Ns(λ) value is mainly determined by the change of rb. Consequently, Ns(λ) approaches the minimum value when rb becomes minimum, corresponding to the case when the incident photon energy matches the excitation energy of excitons along b-axis. This photon energy also matches the exciton energy along a-axis. When strain is gradually applied along p polarization direction, the position of the minimum value shifts towards high photon energy level. The shift of the minimum value is mainly caused by the change of ra, since the strain applied perpendicular to b axis does not cause much change in rb. Therefore, the shifting of the minimum value towards higher photon energy demonstrates the broadening of the band gap along a-axis. In contrast, Fig. 3d shows the RDS signals (Np(λ)) of the device when p portion polarized along the direction of applied strain and the b-axis of ReS2 (see Supplementary Fig. S11b), which can be expressed as: 𝑟𝑎(𝜆)𝑐𝑜𝑠𝜃 ― (𝑟𝑏(𝜆) + 𝑟𝑎(𝜆)𝑠𝑖𝑛𝜃)

𝑁𝑝(𝜆) = 2 𝑟𝑎(𝜆)𝑐𝑜𝑠𝜃 + 𝑟𝑏(𝜆) + 𝑟𝑎(𝜆)𝑠𝑖𝑛𝜃 (7) When no strain is applied, Np( λ ) increases as incident photon energy increases and reaches the maximum value at certain incident photon energy as plotted in the blue curve, which then decreases as photon energy further increases. Since the variation of Np( λ ) is also mainly determined by the variation of rb with incident photon energy, Np(λ) approaches the maximum value when rb becomes


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minimum, corresponding to the case when the incident photon energy matches the excitation energy of the excitons along b-axis. When strain is applied along b-axis (p polarization direction), the peak position of Np( λ ) shifts towards lower photon energy. In this case, the shift of the maximum value mainly attributes to the change of rb, since the applied strain is along b axis. It indicates the decrease of excitation energy of excitons, and thus, the narrowing of bandgap along b-axis. It should be noted that it is the trend of the shift of the peak position, rather than the measured photon energy at the peak position that we want to emphasize. These experimental observations are consistent with the DFT calculations. Therefore, we attribute the anisotropic piezoresistance effect to be the anisotropic bandgap variation under tensile strain.19–21

Figure 3. Strain-modulated bandgap of ReS2. (a, b, c) The DFT calculated band structures of bulk ReS2 under no strain, 0.6% uniaxial strain (εb) along b-axis, 0.6% and uniaxial strain (εa) along a-


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axis, respectively. (d) RDS of a ReS2 device (~87 nm in thickness) when the p portion polarized along b-axis, under no strain, 0.22% and 0.28% uniaxial strain applied along p polarization direction. (e) RDS of the same ReS2 device in (d) when the s portion polarized along b-axis, under no strain, 0.22% and 0.28% uniaxial strain applied along p polarization direction. The resistance change of the semiconductor caused by bandgap variation can be explained by the conductivity equation. In detail, at room temperature, thermally activated carrier transportation dominates the electrical current, during which electrons are thermally excited into the conduction band. In this case, the conductivity of the semiconductor is expressed as20

[

𝜎 = 𝜎0𝑒𝑥𝑝 ―

]

𝐸𝐶 ― 𝐸𝐹 𝑘𝐵𝑇

(8)

where σ0 is the minimum conductivity defined by the hopping distance, EC is the conduction band edge, EF is the Fermi energy, kB is the Boltzmann constant, and T the temperature. Assuming a symmetric increasement/reduction of bandgap under strain, the conduction band would shift to higher/lower energies while the valence band edge would shift to lower/higher energies by the same amount. For small strains (up to 0.4% in our case), the bandgap is expected to change linearly and the conductivity can be written as20

[

𝜎𝑑𝑒𝑓𝑜𝑟𝑚 = 𝜎𝑟𝑒𝑙𝑎𝑥𝑒𝑥𝑝 ―

]

𝜀 ∂𝐸𝑔 (9) 2k𝐵𝑇 ∂𝜀

where σdeform and σrelax are the conductance of the flake in the deformed and relaxed state, respectively, ε is the strain, and ∂Eg/∂ε is the rate of bandgap change with strain. For positive/negative values of ∂Eg/∂ε, Eq. 9 predicts decreasing/increasing conductivity. Generally, compressive strain shortens chemical bonds, and thus, strengthens the interaction between the overlapped orbitals, leading to a broadened band width. The consequent dispersion of conduction band and valence band can result in a narrowed band gap, and even cause


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semiconductor-metal transitions.63–65 Conversely, the elongation of chemical bonds under tensile strain, in general, weakens the interaction between orbitals, and thus, leading to an increase of band gap.65–67 In this study, however, a decrease of band gap induced by tensile strain along b-axis was found. This abnormality explains the negative piezoresistive effect observed in our experiments through its influence on the electrical conductivity. To understand the origin of the negative correlation between band gap and strain along b-axis, we analyzed the variation of conduction band minimum (CBM) and valence band maximum (VBM) as a function of strain applied along a and b axes by DFT calculations. High-resolution transmission electron microscopy and X-ray diffraction (XRD) microscopy were also used to measure the change of the lattice constants of ReS2 in the flat and bent states (see Supplementary Fig. S12, S13, S14 and Table S1 for more details). As shown in Fig. 4a, both CBM and VBM decrease linearly as strain applied along a (in black line) and b (in red line) axes increases. This fits nicely with deformation potential theory, in which the strain induced band edge shift is proportional to the strain tensor. However, the decrease rates of CBM and VBM values with strain are different, leading to the change of bandgap. In the case of applying tensile strain along b-axis, the decrease of VBM is slower than that of CBM, leading to the narrowing of the bandgap (when compressive strain is applied, the bandgap is broadened and narrowed along the b and a axes, respectively, as shown in Supplementary Fig. S15). We further calculated the total density of states under 0 and 0.6% strain along b-axis by DFT to investigate the reason for slow VBM decrease with applied strain. The energy levels of CBM were adjusted to be the same for comparison. Figure 4b shows the energy dispersion of the total density of state, which indicates that the VBM raises under εb strain. It is responsible for the slow decrease of VBM with εb strain. By assigning these states according to partial densities of states, it is found that the top valence bands


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are dominated by Re dyz and dx2-y2 orbitals, whereas the bottom conduction bands are mainly composed of Re dz2 and dx2-y2 orbitals. From the partial densities of states of Re dyz and dx2-y2 orbitals as depicted in Fig. 4c and d, respectively, we indicated that the ~0.1 eV dispersion of the top valence bands is dominantly attributed to these two orbitals.

Figure 4. Variation of CBM and VBM modulated by strain. (a) The variation of CBM and VBM as functions of εa and εb. (b) Total energy states modulated by strain. (c, d) Partial density states of Re dyz and Re dx2-y2. Energy levels under εa = 0.6% were adjusted to be the same as ε = 0 for comparison. Insets show DOS in the ellipse around the Fermi energy which was artificially shifted to 0 eV. Conclusion

We used RDM combined with the physical fracture boundaries to successfully identify the a and b axes of the ReS2 flake non-invasively, which was confirmed by the electrical transport measurement. This capability enabled us to calibrate the anisotropic piezoresistance of ReS2 on separate devices. We fabricated anisotropic ReS2 devices on flexible substrate using optical fibers as the shadow


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masks to measure the anisotropic piezoresistive effect of ReS2 along a and b axes, which were found to be positive and negative, respectively, with the ratio of GF to be GFa :GFb=-1:1.21. According to the calculated Young’s modulus matrix, we further estimated the ratio of the piezoresistive coefficient to be πa:πb=-1:1.22. Both RDS measurements and DFT calculations revealed the mechanism of the completely opposite piezoresistive effect along two anisotropic axes, which was attributed to the distinct bandgap change along the two axes under uniaxial tensile strain: the bandgap increased/decreased along a-/b-axis under uniaxial tensile strain. This anisotropy effect

of ReS2 may be used as the gate to develop various homojunctions for strain involved applications. Materials and methods Device fabrication. The few-layer ReS2 nanoflakes were mechanically exfoliated from bulk crystal and then transferred onto a heavily doped silicon substrate with a 285 nm thick SiO2 dielectric layer. Prior to device fabrication, the substrate with ReS2 nanoflakes was soaked in acetone for 1 h to remove the tape residues. Bilayer PMMA e-beam resists (Micro Chem 950 A6) were spin coated (2000 rpm) onto the SiO2/Si substrate followed by baking on a hot plate at 180 ℃ for 90 s. E-beam lithography (Raith 150) was used to define the source/drain patterns, and 5 nm thick Ti and100 nm thick Au film was sequentially deposited using a thermal evaporator (Edward Auto 306) followed by lift-off process to form the S/D electrodes. The vacuum during evaporation was around 1×10-5 Pa. The PI used in the experiment was UPILEX-S of UBE. Sample measurements. AFM characterization was conducted by Dimension Icon (Bruker, German) in the tapping mode. Raman spectra were obtained from a Renishaw InVia Raman microscope with ∼1.38 mW excitation at 532 nm. HRTEM image were obtained from Talos F200 (200kV) and FEI


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Titan G2-800 (300kV). EDS mapping were obtained by Super-X EDS. XRD image were obtained by Rigaku XtaLAB Synergy. FIB fabrications were conducted by FEI Helios 600. The electrical characteristics of ReS2 devices were inspected by semiconductor parameter analyzer B1500 (Agilent). All of the Ids−Vg curves were obtained under a 2 mV source−drain bias, if not specially noted. All measurements were conducted in ambient conditions. Field effect mobility was calculated using the following equation 𝜇 =

𝑑𝐼𝑑𝑠 𝐿 𝑊𝐶ox𝑉ds 𝑑𝑉𝑔

where μ is the field effect mobility, L and W are the channel length and width, respectively.

𝑑𝐼𝑑𝑠 𝑑𝑉𝑔

is the transconductance, Cox is the gate oxide capacitance of 12 nF/cm2 for 285 nm thick dry thermal SiO2, and Vds is the source−drain voltage. Computational method. DFT calculations within the Purdue, Burke, and Ernzerhof (PBE) generalized gradient approximation68 as implemented in the Vienna Ab initio Simulation Package (VASP)69 were performed in our electronic structure calculations. The Re 5d66s1 and S 3s23p4 electron states were treated as valence electrons. Plane waves up to a cutoff energy of 650 eV formed the PAW basis set70,71 for the wave function expansion. 4×4×2 Monkhorst-Pack scheme72 was employed to sample the Brillouin zone. The tolerance of the self-consistent field was set as 1.0×10-6 eV/atom. Forces were relaxed below a threshold of 0.002 eV/ Å. Acknowledgements This project has been supported by the National Science Foundation of China (NSFC Grant No. 21405109) and Seed Foundation of State Key Laboratory of Precision Measurement Technology and Instruments (Pilt No. 1710). We thank the instrument analytical center at School of Pharmaceutical Science and Technology, Tianjin University, for providing the XRD analysis and


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Dr. Jun Xu and Prof. Xiangyang Zhang for the helpful discussions. ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: XXX. Crystal structure of ReS2, Raman and AFM characterization of ReS2 devices, electrical anisotropic of ReS2, testing setup for the strain measurement, response of ReS2 to tensile and compressive strain, measurement of piezoelectrical effect of ReS2, DFT calculation of the direct-to-indirect band structure transition of ReS2, alignment of the light polarization and principle axes of ReS2 under strain, characterization of lattice constants of ReS2 by HRTEM and XRD, calculation of elastic coefficients of ReS2.


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The Opposite Anisotropic Piezoresistive Effect of ReS2 | ACS Nano

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