Double Negative Differential Resistance Device Based on Hafnium Disulfide/Pentacene Hybrid Structure

Abstract Recently, combinations of 2D van der Waals (2D vdW) materials and organic materials have attracted attention because they facilitate the formation of various heterojunctions with excellent interface quality owing to the absence of dangling bonds on their surface. In this work, a double negative differential resistance (D‐NDR) characteristic of a hybrid 2D vdW/organic tunneling device consisting of a hafnium disulfide/pentacene heterojunction and a 3D pentacene resistor is reported. This D‐NDR phenomenon is achieved by precisely controlling an NDR peak voltage with the pentacene resistor and then integrating two distinct NDR devices in parallel. Then, the operation of a controllable‐gain amplifier configured with the D‐NDR device and an n‐channel transistor is demonstrated using the Cadence Spectre simulation platform. The proposed D‐NDR device technology based on a hybrid 2D vdW/organic heterostructure provides a scientific foundation for various circuit applications that require the NDR phenomenon.

Fabrication process of HfS 2 /pentacene heterojunction structure Figure S1. Figures S1 (a) -(d) illustrate the fabrication process of HfS 2 /pentacene heterojunction structure with insets of optical images for each step. The HfS 2 flake was mechanically exfoliated onto a 90nm thick SiO 2 /Si substrate by using an adhesive tape in Figure S1 (a). The electrodes were patterned by photolithography, and Ti/Au (10/30nm) layers were deposited using an ebeam evaporation method. Then, a lift-off process was conducted in an acetone bath for 1h. The formed metal electrodes are shown in Figure S1 (b). Next, the HfS 2 /pentacene heterojunction regions were defined by PMMA pattern via an e-beam lithography shown in Figure S1 (c).
Finally, the pentacen layer was deposited in a thermal evaporator, as shown in Figure S1 (d).
No region suspected of oxidized HfS 2 was found, and the oxygen concentration (O atom) was negligibly low at the HfS 2 /pentacene interface.
Energy band structures of HfS 2 and pentacene via UPS measurement Figure S3. UPS spectrum of (a) pentacene and (b) HfS 2 . (c) Energy band alignment of the pentacene and HfS 2 obtained from UPS measurement.
We conducted Ultraviolet photoelectron spectroscopy (UPS) analysis to find the energy band structures for the HfS 2 /pentacene heterojunction. However, it is not easy to analyze the binding energies at junction interfaces through the UPS measurements unless the materials forming the junction are very thin. This is because the maximum penetration depth of the beam is only 2.5 nm in used UPS system. Thus, it was impossible to inspect the junction interface region of our heterojunction consisting of 50 nm pentacene and 37 nm HfS 2 . The only data we could obtain from the UPS measurements were the energy band properties of the two substances (pentacene and HfS 2 ), as shown in Figure S3 (a) -(c) [S1] . The data were used to verify once again that the materials have energy band properties suitable for forming a type-III broken heterojunction.
Energy band information and I-V characteristic curves of Pentacene-TMDs Figure S4. (a) Energy band information of pentacene and vdW TMD materials.
(b) Comparison of I-V characteristic curves of four kinds of heterojunction diodes.
In Figure S4 (a), the energy band information of organic pentacene and four 2D vdW TMD materials (HfS 2 , ZrS 2 , SnS 2 , and SnSe 2 ) was examined [S2] . Although all the vdW materials were expected to form a broken gap with pentacene, only an HfS 2 /pentacene junction experimentally presented the NDR phenomenon, as shown in Figure S4 (b).
Current-voltage characteristics of four different HfS 2 /pentacene NDR devices Figure S5. HfS 2 /pentacene NDR devices. These four devices were designed to have the same distance of 5 µm between anode and edge of HfS 2 /pentacene heterojunction, consequently being expected to cause the same pentacene resistance value of 100 GΩ. The average values of V PEAK , V VALLEY , and PVCR for the four NDR devices were 0.56 V, 1.08 V and 1.63 (A/A), respectively, and the corresponding standard deviations were 0.11, 0.10 and 0.57, as shown in Figure S5 (e).
We prepared HfS 2 /pentacene NDR device samples and conducted I-V measurements twice at three different temperatures of 300, 250, and 200 K. As decreasing the measurement-temperature, the PVCR value was reduced approximately from 2.38 to 1.46 due to an increase in the series resistance of the pentacene region (see Figure S6 (a)). The suppression of carrier generation at a low temperature increased the series resistance, consequently reducing the current level and shifting the peak/valley voltages to the right (see Figures S6 (b) and (c)).  pentacene TFTs at V DS = 1 V and -1 V, respectively [S3-S6] . Because the proposed HfS 2 /pentacene NDR device operates under zero gate bias condition, the sheet resistance values of HfS 2 and pentacene were extracted from the I D -V D curves shown in Figures S7 (b) and (c). From the measured I D of HfS 2 and pentacene TFTs, which are 0.98 nA and 5 pA, the sheet resistance values of 3 GΩ/sq and 600 GΩ/sq are estimated, respectively. Owing to the larger sheet resistance values of pentacene compared to that of HfS 2 , pentacene was selected as a controlling factor for shifting the NDR peak/valley, where we varied the distance between the anode and the edge of HfS 2 /pentacene heterojunction.

Extraction of sheet resistance values from electrical measurement of HfS
Carrier-transport mechanism of double-peak NDR device   Figure S8. (a) I-V characteristics of 1 st NDR device with R lateral (blue), 2 nd NDR device with R lateral + R vertical (red), and double-peak NDR device (black). The carrier transport mechanism of the 1 st NDR, 2 nd NDR, and double-peak NDR devices in (b) slope-1, (c) slope-2 and (d) slope-3 regions, respectively. Figure S8 (a) presents the I-V characteristic curve of double-peak NDR device including the predicted characteristic curves of the 1 st NDR and 2 nd NDR devices. This double-peak NDR curve can be explained by the carrier-transport mechanism based on tunneling and diffusion [S8] . Figure S8 (b) shows the double-peak NDR curve consisting of the tunneling currents of 1 st and 2 nd NDR paths, resulting in the largest I-V slope (slope-1 region). The current in the slope-2 region is composed of the diffusion current of 1 st NDR path and the tunneling current of 2 nd NDR path, as shown in Figure S8 (c), and therefore, the I-V slope is decreased when compared to the slope-1 region. Lastly, Figure S8 (d) shows the smallest I-V slope. This is because the current in this slope-3 region is determined by the diffusion currents of 1 st and 2 nd NDR paths. Figure S9. Influence of (a) energy bandgap and (b) electron affinity of HfS 2 on the NDR characteristics.

Influence of energy bandgap and electron affinity of HfS 2 on the NDR characteristics
As depicted in Figure S9, the influence of energy bandgap (E g ) and electron affinity (χ) of HfS 2 on the NDR characteristics was theoretically investigated by using our analytical NDR device model constituting the tunneling and diffusion current equations detailed below.
NDR device's total current (I total ) is the sum of two currents: the tunneling (I tunnel ) and diffusion (I diff ) currents (I total = I tunnel + I diff ). Here, the tunneling current is based on the Landauer expression for a two-dimensionally confirmed system and is expressed as follows: where q is the elementary charge, h is Plank's constant, E V_Pentacene is the valence band maximum energy of pentacene, α is the fitting parameter, E C_HfS2 is the conductance band minimum energy of HfS 2 , and V is the applied voltage. DOS Pentacene (E) and DOS HfS2 (E) represent the density of states of pentacene and HfS 2 , respectively, and f Pentacene (E) and f HfS2 (E) represent the density of states and the Fermi-Dirac distribution functions of pentacene and HfS 2 , respectively. The diffusion current is given as where I 0 is the saturation current, n is the ideality factor, k B is the Boltzmann constant, and T is the temperature. The calculation was performed via MATLAB simulator.
When the χ is fixed and the E g is varied, no changes in the peak/valley voltages are observed because the broken bandgap is not changed. If the tunneling is considered from the valence band of HfS 2 (filled states) to the valence band of pentacene (empty states), a current level beyond the valley point might be changed. However, we ignore the tunneling between the valence bands of the two materials because it does not affect the peak/valley points. When E g is fixed and χ is varied, the peak/valley voltages shift to the right because the filled states in the HfS 2 conduction band require a higher voltage to get into pentacene's bandgap region. As χ increases from 5.4 eV to 5.42 eV, the peak/valley voltages increase from 0.2/0.44 V to 0.255/0.54 V. In particular, the peak current level increases because the empty states in the HfS 2 valence band and the filled states in the pentacene conduction band are increased at the equilibrium state.
Specifications of the n-channel transistor in controllable-gain amplifier circuit Figure S10. We used the n-channel transistor that is provided by the library of the simulation tool Cadence. The geometric information of the n-channel transistor, comprising channel length, width, and oxide thickness, is listed in Figure S10 (a). Figure S10  Then, to explain the amplification of the AC input voltage signal, as depicted in section [2] of Figure S11, a small-signal equivalent circuit was prepared, where v in , R in , v gs , g m , R D , and v out denote AC input voltage signal, input resistance, gate-source voltage, transconductance of the nchannel transistor, total output resistance, and AC output voltage signal, respectively. Because the output resistance of the n-channel (r O,Q ) is expected to be larger than that of the D-NDR device (r D-NDR,Q ) at every operating node, the total output resistance is approximately R D-NDR (see Figure S11 inset The proposed controllable-gain amplifier operated well in the 1 kHz -10 MHz frequency range, as shown in Figure S12. Double-NDR-device-based ternary inverter The proposed double-NDR device can be made into a ternary inverter. Figure S13 (a) shows the circuit configuration of the ternary inverter, where the supply (V DD ) and input (V IN ) voltages were connected to the drain and gate electrodes of the p-channel transistor, respectively. Figure   S13 (b) presents the V IN vs V OUT characteristic of the ternary inverter. As V IN varies from 0 V to 5 V, V OUT displays three distinct logical states: "2," "1," and "0". The load-line analysis of the ternary inverter circuit under different gate bias conditions is shown in Figure S13 (c). For the state "1," owing to the low slope of the I-V curve, the distribution of the output voltage is excessively wider than that for the other states.
Performance comparison of various 2D material-based NDR devices Table S1. NDR devices benchmarking table