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

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 (ReS2) flakes with unique distorted 1T structure, which exhibit in-plane anisotropic properties. We fabricated monolayer and few-layer ReS2 field-effect transistors, which exhibit competitive performance with large current on/off ratios (∼107) 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 ReS2 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.


Supplementary Notes Supplementary Note 1: Few-layer ReS 2 FETs
We measured over 40 ReS 2 FETs with thicknesses ranging from 0.8 to 7.5 nm (1-10 layers with an interlayer spacing of approximately 0.7 nm). All of the FETs behaved similarly as excellent n-type FET devices with the back gate swept between -80 V and +80 V. Some of the data from few-layer devices are summarized and shown in Supplementary Figure 1. The current on/off ratio can reach up to 10 7 -10 8 , which is comparable to that of MoS 2 devices [1]. All measurements were carried out in a vacuum (approximately 10 -5 mbar) at room temperature.

Supplementary Note 2: Ambipolar behavior of ReS 2 electric double-layer transistor
To further explore the field effect of mono-and few-layer ReS 2 devices, an electric double-layer transistor (EDLT) using ionic liquid gating is introduced. In our experiments, the EDLT was fabricated by dropping a droplet of an ionic liquid, N,N-diethyl-N-(2-methoxyethyl)-N-methylammonium bis(trifluoromethylsulfonyl)imide (DEME-TFSI), onto the surface of a ReS 2 FET device. For more efficient tuning of carrier density, the side electrode pad of the ionic liquid was designed to have a larger area than the ReS 2 channel of the device. To avoid possible chemical reactions between the ionic liquid and ReS 2 , all measurements were performed at 220K and in a vacuum environment of approximately 10 -5 mbar. An ambipolar behavior was observed when we swept the ionic liquid gate voltage (V LG ), with a typical transfer curve measured from a seven-layer ReS 2 device shown in Supplementary Figure 2. When V LG is above -2 V, the device behaves as an n-type transistor. When V LG is below -3.2 V, a p-type transistor behavior appears, indicating the shift of Fermi-level E F to access the valence band.

Supplementary Note 3: Contact of ReS 2 FETs
During the fabrication of mono-and few-layer ReS 2 FETs, we used 5 nm Ti covered by 50 nm Au as electrodes to make the contact. These devices have shown good contact behavior. To estimate the influence of contact resistance, we compared the measurement results obtained from both two-probe and four-probe methods. As shown in Supplementary Figure 3a, the resistance measured by the two-probe method (R 2P ) is slightly larger than that of the four-probe method (R 4P ). The resistance difference (∆R) of R 2P and R 4P should be mainly attributed to the contact resistance. If as the weight of ∆R in R 2P , we found α is highly gate-tunable. In the n-doped regime as our work focused on, α is less than 10% (when V bg = -20 V) and decreases notably as the doping level increases, to be as low as 1% when V bg = 40 V.
We also used the transfer length method to estimate the contact resistance of the

Supplementary Note 4: Carrier mobility calculation
Our carrier mobility calculation was performed using the VASP (Vienna ab-initio Simulation Package) code [3,4]. The results presented in the following were obtained by using the generalized gradient approximation (GGA)-Perdew-Becke-Erzenhof (PBE) function [5], a 10×5×1 mesh for the Brillouin zone sampling and a cut-off of 500 eV for the plane-wave basis set. An orthogonal supercell was created for ReS 2 sheets, with the atomic plane and its neighboring image separated by a 36 Å vacuum layer. All of the structures were relaxed until the Hellmann−Feynman forces became less than 0.01 eVÅ -1 .
In 2D materials, the carrier mobility is given by the following formula [6,7]: where m * is the effective mass and T is the temperature (set to be 300K in our calculation). The term E 1 is the deformation potential constant, which denotes the shift in the band edges along the transport directions induced by strain  (calculated using a step of 1% where E total is the total energy and S 0 is the lattice volume at equilibrium for a 2D system.