Integrated digital inverters based on two-dimensional anisotropic ReS2 field-effect transistors

<jats:title>Abstract</jats:title><jats:p>Semiconducting two-dimensional transition metal dichalcogenides are emerging as top candidates for post-silicon electronics. While most of them exhibit isotropic behaviour, lowering the lattice symmetry could induce anisotropic properties, which are both scientifically interesting and potentially useful. Here we present atomically thin rhenium disulfide (ReS<jats:sub>2</jats:sub>) flakes with unique distorted 1T structure, which exhibit in-plane anisotropic properties. We fabricated monolayer and few-layer ReS<jats:sub>2</jats:sub> field-effect transistors, which exhibit competitive performance with large current on/off ratios (∼10<jats:sup>7</jats:sup>) and low subthreshold swings (100 mV per decade). The observed anisotropic ratio along two principle axes reaches 3.1, which is the highest among all known two-dimensional semiconducting materials. Furthermore, we successfully demonstrated an integrated digital inverter with good performance by utilizing two ReS<jats:sub>2</jats:sub> anisotropic field-effect transistors, suggesting the promising implementation of large-scale two-dimensional logic circuits. Our results underscore the unique properties of two-dimensional semiconducting materials with low crystal symmetry for future electronic applications.</jats:p>

section_content: T he scaling down of conventional metal-oxide-semiconductor FETs is approaching the limit of miniaturization due to severe short-channel effects 1. One approach to solve this problem is searching for atomically thin semiconductors, such as semiconducting two-dimensional (2D) materials [2] [3] [4] [5] [6]. Among the potential candidates, the family of transition metal dichalcogenides (TMDs) 7, 8 (MX 2, where M denotes a transition metal and X denotes a chalcogen) has attracted the most attention due to both its rich physics and tremendous potential for application. They are expected to exhibit a wide range of electronic structures and exotic transport properties arising from the various electron configurations of transition metals, such as superconductivity [9] [10] [11], half-metallic magnetism 12 and charge density waves [13] [14] [15]. 

Lattice structure and symmetry are vital in determining materials' fundamental properties. Most studied 2D TMDs exhibit isotropic behaviour due to high lattice symmetry; however, lowering the symmetry in TMDs could induce interesting anisotropic properties of both scientific and technologic importance. For example, in WTe 2, which is a semi-metallic TMD with a distorted lattice structure, a large non-saturating magnetoresistance effect along a principle axis (the direction of W chain formation) has been recently reported and has attracted considerable attention 16. In contrast, semiconducting 2D TMDs with low symmetry have remained unexplored. 

As the last stable element discovered in nature, the transition metal rhenium (Re) exhibits a wide range of oxidation states and crucial applications, such as superalloys and catalytic reforming. Its sulfide rhenium disulfide (ReS 2 ) is a semiconducting TMD that was recently discovered to have weak interlayer coupling and a unique distorted 1T structure 17. As shown by the side view and top view of the monolayer ReS 2 crystal structure in Fig. 1a, it consists of two hexagonal planes of S atoms (yellow) and an intercalated hexagonal plane of Re atoms (blue) bound with S atoms forming chains of parallelogram-shaped Re4 clusters. As highlighted by the red arrows in the top view, there are two principle axes, the b and a axes, which correspond to the shortest and second-shortest axes in the basal plane. They are 61. 03°or 118. 97°apart, and the b axis corresponds to the direction of the Re-Re atomic chain formed. Thus, ReS 2 offers an ideal material candidate for studying semiconducting 2D TMDs with low symmetry. 

In this work, we systematically investigate the in-plane anisotropic properties of atomically thin ReS 2. In addition to highly competitive FET performance, we also observe a large anisotropic ratio along its two principle axes, which is the highest among all experimentally investigated 2D layered materials. We also successfully demonstrate a digital inverter with good performance by integrating two anisotropic ReS 2 FET devices. Our results suggest that the lattice orientation can be used as an alternative design variable to tune device properties and optimize circuit performance in future 2D integrated circuits based on the anisotropic semiconducting materials.

section_name: Results

section_content: Figure 1b,c shows typical optical microscopy and atomic force microscope images of a monolayer ReS 2 film (see Methods for the material details), respectively. The inset of Fig. 1c shows that the thickness of the monolayer film is B0. 8 nm. In this study, we focus on monolayer and few-layer ReS 2, with thicknesses ranging from 0. 8 to 5 nm (1-7 layers with interlayer spacing of B0. 7 nm). Micro Raman scattering experiments were performed on monolayer, five-layer and bulk ReS 2. Due to the low symmetry of ReS 2, 18 Raman modes were observed as shown in Fig. 1d. The peak positions of our three samples are close to each other, same to the reported results 17. In Fig. 1d, we labelled two low frequency A glike modes (located at 136. 8 and 144. 5 cm À 1 ) corresponding to the out-of-plane vibrations of Re atoms and four E g -like modes (located at 153. 6, 163. 4, 218. 2 and 238. 1 cm À 1 ) corresponding to the in-plane vibrations of Re atoms. The rest 12 higher frequency Raman modes are vibrations mainly from lighter S atoms 18. The peak intensity ratio could be dependent on the polarization due to the low lattice symmetry 19. The band structures of monolayer, trilayer and five-layer ReS 2 calculated by an ab initio method are shown in Fig. 1e FET performances. We first examine the device performances of monolayer and few-layer ReS 2 FET devices (see Supplementary Note 1 for details). The inset of Fig. 2a presents the optical image of a typical monolayer device. The FET transfer curve was obtained by monitoring the source-drain current I ds while sweeping the back gate voltage V bg. A fixed 100-mV source-drain bias voltage V sd was applied across the channel during all of the measurements. We first measured a couple of monolayer ReS 2 devices, all of which behaved as excellent n-type FET devices with the back gate swept between À 50 and þ 50 V. As shown in Fig. 2a, the current on/off ratio reached 10 7, which meets the requirement of many applications, such as digital logic computation. When the back gate voltage reached þ 50 V, the I ds approached saturation. Few-layer ReS 2 transistor devices, ranging from bilayer to seven-layer, were studied as well. Similar n-type FET behaviour but a slightly larger on/off ratio was observed. The results from a trilayer device with the same back gate sweep range are shown in Fig. 2a for comparison. We note that all of the above measurements were carried out under vacuum (B10 À 5 mbar) at room temperature, and ambipolar behaviour can be observed by introducing the ionic liquid gating technique (see Supplementary Note 2 for details). On the basis of the transfer curves, we can also measure the subthreshold swing. For the monolayer ReS 2 FET device shown in Fig. 2a, swing is B310 mV per decade. The subthreshold swing becomes steeper for thicker flakes, reaching B100 mV per decade for the trilayer device shown in the same figure. The measured subthreshold swing values approach those measured in top-gated MoS 2 transistors 7 and outperform black phosphorus devices 5. This can be further improved by increasing the gate capacitance after introducing thinner high-k dielectric materials. 

The monolayer and few-layer ReS 2 FET devices (with Ti/Au electrodes) have also shown good contact behaviour. As shown in Fig. 2b, for a typical monolayer device, the source-drain current I ds varies linearly with the bias V ds in the ± 1 V range at different back gate voltages (V bg ¼ À 40, À 20, 0, 20 and 40 V, respectively), indicating ohmic contact behaviour in the n-doped regime under consideration (see Supplementary Note 3 for more details). 

We further extracted the mobility of all of the FET devices we measured and studied its dependence on the number of layers of the ReS 2. The mobility was determined by taking the steepest slope in the two-terminal I ds -V bg curves. The results for 17 devices (from monolayer to seven-layer) are plotted in Fig. 2c. Similar to the reported results based on MoS 2 thin flakes 20, 21, the device mobility generally increases with an increasing number of layers, implying that the electrons likely independently transport through different layers in thin ReS 2 flakes. The mobility of a monolayer device varies between 0. 1 and 2. 6 cm 2 V À 1 s À 1, and the highest mobility value obtained is 15. 4 cm 2 V À 1 s À 1 for a sixlayer device. These values were measured without any material treatment or device optimization. With further improvement in crystal quality, post-fabrication treatment 22 and dielectric engineering 7, 22, considerable enhancement of mobility to approach application requirements should be expected. Here the scattering of mobility values for flakes with the same number of layers could be induced by device quality variations or the anisotropic property, as will be discussed below. 

Anisotropic properties of ReS 2. We now focus on the in-plane anisotropic properties of monolayer and few-layer ReS 2 flakes induced by low lattice symmetry. As described in Fig. 1a, the a and b axes are the two directions with the shortest axes in the basal plane, thus differentiating them from other lattice orientations. Such a feature is often associated with the in-plane anisotropic properties of structural stiffness and electronic transport. Interestingly, during our experiments, exfoliated thin ReS 2 flakes commonly appear in a quadrilateral shape with inner angles of B60°or 120°, as shown by a typical flake in Fig. 3a. 

Further results of all inner angles measured on over 20 thin flakes is shown in Fig. 3b, with 460% of the specimens showing these two angles. The inner angles of 60°and 120°match the angles between the a and b axes (118. 97°or 61. 03°) with high accuracy. This can be readily explained by the fact that the breaking strength is the weakest along these two axes, which are the two most strongly bonded orientations 17, 23, and suggests that two sides of the quadrilateral shape with 60°or 120°inner angles correspond to the a and b axes, respectively. The in-plane stiffness anisotropy-induced quadrilateral shape makes it feasible to determine the two axes of ReS 2 flakes via convenient transport measurements instead of other highly sophisticated tools, such as scanning tunnelling microscopy. Early studies on bulk materials reported that the b axis is more conductive than other crystalline orientations 24, 25. We then patterned the electrodes to be perpendicular to two sides (A and B directions) of a quadrilateral-shaped five-layer ReS 2 with a 60°i nner angle (as shown in the top inset of Fig. 3c ). The transfer curves in two directions are shown in Fig. 3c, and anisotropic FET behaviour was observed. The B direction appears to be noticeably more conductive than the A direction, suggesting that the A and B directions correspond to the a and b axes, respectively. The conductance ratio of the two directions is gate dependent, with values of B8. 2 when V bg ¼ À 50 V and B2 when V bg ¼ 50 V. To evaluate the influence of contact resistance, we performed fourterminal measurements (see Supplementary Note 3 for more details). The four-terminal results of the same device are shown in the lower inset of Fig. 3c, indicating that the anisotropy arises from the intrinsic properties of ReS 2. 

We further systematically studied the anisotropic properties of thin ReS 2 flakes through angle-resolved transport measurement. As shown in the inset of Fig. 3d, a six-layer device was fabricated with 12 electrodes (5 nm Ti/50 nm Au) evenly spaced at 30°apart. We measured the transfer curves of each pair of diagonally positioned electrodes separated by 4. 5 mm at 180°apart and extracted the renormalized field-effect mobility of each direction, with the results plotted in Fig. 3d (red dots) in polar coordinates. Measurements on each pair of electrodes lead to two data points that are 180°apart by swapping source-drain current directions. 

Here we define the direction with the lowest mobility to be the 0°(or 180°) reference. The field-effect mobility is highly angle dependent, with the largest value in the direction of 120°( or 300°), which is 60°from the direction with the lowest value. The anisotropic ratio of mobility m max /m min is B3. 1, which is noticeably larger than that reported in other 2D anisotropic materials, such as 1. 8 for thin-layer black phosphorus 26. 

To fully understand our observations, we calculated the effective mass and mobility of monolayer ReS 2 along three crystalline orientations (a axis, b axis and perpendicular to the a axis) using an ab initio technique (see Supplementary Note 4 for details), with the results plotted in the same graph (blue dots with right axis). Here we set the direction with the lowest mobility (a axis) to be the 0°(or 180°) reference as well. By comparing with experimental data, the calculation results offer a qualitative explanation that for the device with polar coordinates, the direction of 0°(or 180°) approaches the a axis with the lowest mobility, 120°(or 300°) approaches the b axis with the highest mobility and 90°(or 270°) approaches the direction perpendicular to the a axis with a moderate mobility value between the two extremes. The quantitative discrepancies between the experimental and theoretical results imply that with continuous improvement of sample quality and material engineering, it is possible to achieve intrinsic properties that approach the real potential of ReS 2 in high-performance device applications. 

Digital inverter based on anisotropic ReS 2 FETs. Anisotropic ReS 2 FET devices with expected high mobility could have important applications in future nanoscale electronics, especially on 2D logic circuits [27] [28] [29] [30] [31] with demanding requirements of scalability (o10 nm) and large-scale integration. In contrast to conventional complementary metal-oxide-semiconductor technologies, tailoring material properties and integrated circuit design variables (such as the channel width/length ratio) 32 to optimize circuit performance on such a rigorous scale will remain a significant challenge. In this context, the lattice orientation could be used as an alternate design variable to tune device transport properties and optimize circuit performance in future 2D integrated circuits based on anisotropic semiconducting materials. 

As a simple example, we successfully demonstrated a ReS 2based prototype logic device, a 2D digital inverter. As schematically shown in Fig. 4a, the inverter can be fabricated by combining two anisotropic ReS 2 FETs along the a and b axes (with a Re atomic chain highlighted in red). In our experiment, a quadrilateral-shaped few-layer ReS 2 flake with a 60°inner angle was selected to fabricate two FETs along two axes. HfO 2 was then deposited with a thickness of 15 nm as the top dielectric, followed by the fabrication of two top-gate electrodes (30 nm Au). The optical image of a typical inverter device is shown in Fig. 4b. The transfer curves along the two directions are shown in the inset of Fig. 4c, which confirms the anisotropic behaviour and determines two axes as well. The circuit diagram is shown in the inset of Fig. 4b, where the top-gate voltage on the a axis is fixed at À 2 V, the top-gate voltage on the b axis is the input voltage V in and the middle shared electrode is the output voltage V out. Figure 4c shows the voltage transfer characteristics with excellent logic-level conservation of our digital inverter, while V in varies between À 4 and 2 V for three different V DD values (3, 2 and 1 V with different colours). When V in is above À 1 V, V out approaches 0 V, which denotes a digital 0. Similarly, when V in is below À 3 V, V out approaches V DD, which denotes a digital 1. The output swing (defined as the largest difference of V out ) is close to the supply voltage V DD. As the most important parameter of a digital inverter, the gain is defined as 7dV out /dV in 7, which represents the sensitivity of V out to the change in V in. For this device, the gain reaches 4. 4 when V DD ¼ 3 V (as shown in Fig. 4d ). The gain that we obtained is clearly larger than the unity gain (gain ¼ 1), which is required in integrated circuits consisting of multiple cascaded inverters, such as ring oscillators, and is comparable to the MoS 2 based inverters 29, 30. 

In conclusion, we have systematically studied the anisotropic properties of atomically thin ReS 2, a semiconducting 2D TMD with a distorted 1T structure. We fabricated monolayer and fewlayer ReS 2 FET devices that exhibit competitive performance, including a high current on/off ratio (B10 7 ) and a steep subthreshold swing (100 mV per decade) at room temperature. We also obtained an anisotropic ratio along the two principle axes of ReS 2 that is the highest obtained for all experimentally studied 2D materials. Finally, we successfully demonstrated a digital inverter device by integrating two anisotropic ReS 2 FET devices. Our results underscore the unique properties of semiconducting 2D materials with low symmetry, which can be exploited for novel applications in future electronics. 

During the preparation of this manuscript, we became aware of another work studying the FET properties of few-layer ReS 2 (ref. 33).
section_name: Material characterizations and ab initio calculations.

section_content: Materials and devices. Single crystals of ReS 2 were grown by the same Br 2 -assisted chemical vapour transport method described in ref. 17. We used a standard mechanical exfoliation method to isolate monolayer and few-layer ReS 2 films. The number of layers can be identified using the colour interference of a 285nm-thick SiO 2 wafer, and further confirmed by measuring the thickness of the flakes using a Bruker Multimode 8 atomic force microscope. Micro Raman scattering experiments (Horiba-JY T64000) were carried out under ambient conditions in the backscattering geometry. The incident laser wavelength was 514. 5 nm, and the power was o1 mW to minimize laser heating. Due to the limitations of the spectrometer, we only measured Raman modes above 100 cm À 1. 

A conventional electron-beam lithography process (FEI F50 with Raith pattern generation system) followed by standard electron-beam evaporation of metal electrodes (typically 5 nm Ti/50 nm Au) was used to fabricate monolayer and fewlayer ReS 2 FET devices. 

Ab initio calculations. Band structures for monolayer and few-layer ReS 2 were calculated using the generalized gradient approximation Perdew-Burke-Ernzerhof function, as implemented in the VASP code (Vienna ab initio Simulation Package) within the density functional theory (DFT) 34, 35. Projector-augmented wave potentials were adopted 36. The kinetic energy cutoff for the plane-wave basis set was 550 eV. The few-layer ReS 2 was simulated with a vacuum layer of 15 Å in the interlayer direction to ensure negligible interaction between its periodic images. In the self-consistent calculations, the Brillouin zone integration was performed on uniform Monkhorst-Pack of 24 Â 24 Â 1 for few-layer ReS 2 and 24 Â 24 Â 24 for bulk ReS 2. The convergence criterion of self-consistent calculations for ionic relaxations was 10 À 5 eV between two consecutive steps. The internal coordinates and lattice constants were optimized until the atomic forces became o0. 001 eV Å À 1 and the pressures on the lattice unit cell became o0. 5 kbr.
section_name: Methods

section_name: Acknowledgements

section_content: We thank Chun Ning Lau, Marc Bockrath and J. Joshua Yang for stimulating discussions. This work was supported in part by the National Key Basic Research Program of China ( 2015CB921600, 2013CBA01603 ), the National Natural Science Foundation of China ( 11374142 ), the Natural Science Foundation of Jiangsu Province ( BK20130544, BK20140017 ), the Specialized Research Fund for the Doctoral Program of Higher Education (20130091120040) and Fundamental Research Funds for the Central Universities. H. Y., H. Y. H. and Y. C. were supported by the Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under contract DE-AC02-76SF00515.
section_name: Acknowledgements

section_name: Author contributions

section_content: This work is licensed under a Creative Commons Attribution 4. 0 International License. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons. org/licenses/by/4. 0/
section_name: Author contributions