Tunable reverse rectification of layed Janus MSeS (M = Hf, Zr) and SnS2 heterojunctions

Two-dimensional (2D) Janus transition metal dichalcogenides (JTMDs) exhibit suitable band gaps and strong visible light absorption, which are extensively applied to the field of optoelectronic devices. Here, we investigate the electronic properties of 2D JTMDs MSeS (M = Hf, Zr) and SnS2 van der Waals heterojunction through density functional theory. The calculated electronic properties reveal that ZrSeS/SnS2 heterojunction has a type-I band alignment, while HfSeS/SnS2 heterojunction has a type-II band alignment. We build the diodes based on the MSeS (M = Hf, Zr)/SnS2 heterojunctions and study the electronic transport. The currents of the devices exhibit asymmetry, and the negative turn-on voltages suggest that constructed devices are backward diodes. Moreover, it is found that the gate voltage can modulate the rectifying ratio, and the rectifying performance of ZrSeS/SnS2 is better than that of HfSeS/SnS2..


Introduction
The successful separation of atomic layers of single-layer graphite materials (graphene) [1] has attracted intensive research in the field of two-dimensional (2D) materials. Therefore, many researchers began to study new two-dimensional semiconductor materials, such as carbon nitride [2,3], boron nitride [4,5], black phosphorus [6][7][8], transition metal dichalcogenides materials (TMDs) [9][10][11] and the III-V compounds [12,13]. Moreover, through vertically stacking different 2D materials together to form van der Waals (vdW) heterojunctions [14], it is possible to integrate the properties of a single layer while creating properties that are superior to those of single-layer material. The rich physical properties and ultra-thin thickness of 2D materials are conducive to high-density integration of devices in the vertical direction, and are easier to control than three-dimensional bulk materials, enabling further reduction in device size. Therefore, 2D heterojunctions have been recently investigated for different device applications such as transistors [15,16], photodetectors [17,18], photovoltaics [19,20], and excitonic solar cells (XSCs) [21,22].
The most ubiquitous and fundamental p-n diodes are essential building blocks of electronics and optoelectronic devices. After the advent of atomically thin van der Waals 2D materials, numerous heterostructure-based diodes have been fabricated. In fact, several high-performance diodes have been demonstrated. And TMDs have been widely used in 2D vdW heterojunction diodes. For example, vdW heterojunction photodiodes composed of BP and PdSe 2 exhibit ultra-high-tunable rectification and photoresponsivity [23]. Recently, a MoTe 2 /ReS 2 heterojunction diode has been reported, and the feasibility of constructing a photodetector has been examined [24]. The gate-tunable WSe 2 /SnSe 2 backward diode has an impressive rectification ratio [25], etc. Nevertheless, there has not been much research on new material Janus TMDs (JTMDs) heterojunction diodes.
TMDs are considered to be very promising channel materials due to their thin atomic thickness, absence of dangling bonds, and good gate control capability [26]. However, in recent years, the novel Janus TMDs with asymmetric structure has attracted extensive attention due to their unique properties for important applications in energy conversion technology, quantum science, and spintronics, becoming an interesting class of 2D semiconductors [27]. Due to the layered structure and narrow atomic layer thickness of 2D Janus TMDs, the 2D Janus TMDs have good tunability of electrical and optical properties and excellent mechanical flexibility. Moreover, the difference in electronegativity of sulfur-group elements, ML Janus TMDs possess an intrinsic built-in electric field, which can induce the separation of carriers [28]. Therefore, the material system has applications in microelectronics, optoelectronics, and energy devices. And there are relatively many researches on MoSeS or WSeS [29,30], so this paper selects MSeS (M = Hf, Zr) for research. Through the chemical decomposition method, a new material called Janus TMDs (JTMDs) was synthesized experimentally [31,32], in which a layer of sulfur in MoS 2 was completely replaced by selenium. Similar JTMDs have been proven to exhibit suitable band gaps and strong light absorption from the ultraviolet to the visible light regions [33]. The experimental synthesis of MoSeS opened up a new direction for the study of layered materials. In this work, several other layered Janus transition metals dichalcogenides, HfSeS and ZrSeS are studied [34,35]. HfSeS and ZrSeS monolayers have an indirect band gap and an ideal band gap for absorbing sunlight, which makes them suitable for electronic and optoelectronic devices. Currently, tin-based transition metal dichalcogenides (SnS 2 ) have attracted extensive research interest due to their environmental friendliness, low cost, excellent chemical stability, semiconducting properties, high carrier mobility, and tunable electronic properties [36]. In this work, study the electronic properties and transport of MSeS (M = Hf, Zr)/SnS 2 van der Waals (vdW) heterojunctions using first-principles calculations. The calculations show that the designed heterojunctions are backward diodes with an extremely high reverse rectification ratio. Moreover, we find that the gate voltage can effectively modulate the rectifying performance of the heterojunctions.
All structural relaxation and calculations in this work are carried out by using the density functional theory (DFT) and non-equilibrium Green's function method (NEGF) in the QuantumATK [37]. We use the generalized gradient approximation (GGA) [38,39] of Perdew-Burke-Ernzerhof (PBE) [40] to describe the exchange-correlation potential. The vdW interaction is corrected with the Grimme DFT-D3 functional. The density mesh cut-off is set to 105 Hartree and the electron temperature 300 K. The k points used in the optimization of the structure and the calculations of the electronic transport properties were: 1 × 15 × 15, 5 × 1 × 150, respectively. The heterojunctions are relaxed until the forces of all atoms are less than 0.05 eV/Å. In order to avoid the interaction between adjacent layers, enough vacuum (25 Å) is added in the out-of-plane directions.

Results and discussion
We calculate the band structures of the pristine HfSeS, ZeSeS and SnS 2 monolayers through DFT. The calculated band gaps of the monolayer HfSeS, ZeSeS and SnS 2 are 0.80 eV, 0.76 eV and 1.56 eV, respectively, which agree with  Fig. 2. The result shows that the HfSeS/SnS 2 heterojunction is a semiconductor with a direct bandgap of 0.29 eV, which is smaller than the band gaps of these two monolayers, indicating that the formation of the vdW heterostructure reduces the band gap. And the narrow bandgap is conducive to electron transition. The conduction band minimum (CBM) and valence band maximum (VBM) of the HfSeS/SnS 2 heterojunction are determined by SnS 2 and HfSeS, respectively, so the heterojunction is a type-II band alignment, and its structure is favorable for charge separation. The ZrSeS/SnS 2 heterojunction is a semiconductor with a direct band gap of 0.13 eV, and the CBM and VBM of the ZrSeS/SnS 2 heterojunction are both determined by ZrSeS, indicating a type-I band alignment.
Then, we calculate the corresponding projected density of states (PDOS) of MSeS (M = Hf, Zr)/SnS 2 heterojunctions, as shown in Fig. 3. One can see that the VBM of the HfSeS/SnS 2 heterojunction is mainly dominated by the Se-p orbital of HfSeS, and the CBM is mainly dominated by Sn-s and S-p orbitals of SnS 2 . It indicates the characteristic of a well-defined type-II semiconductor. However, the VBM and CBM of the ZrSeS/SnS 2 heterojunction are dominated by the Se-p and Zr-d orbitals of ZrSeS, respectively. This type of valance and conduction localization is type-I band alignment. This result agrees with the projected energy bands in Fig. 2.
The device model is shown in Fig. 4a, the MSeS (M = Hf, Zr) region electrode is p doping, the SnS 2 region electrode  Fig. 4. It can be seen that the I ds -V ds of devices displays asymmetry. The current is almost zero in the bias voltage − 0.5-1 V, while I ds -V ds exhibits the linear scale at the bias voltage of -1-− 0.5 V. The negative turn-on voltages suggest that constructed devices are backward diodes. In addition, the current of ZrSeS/SnS 2 is larger than HfSeS/ SnS 2 at the negative bias. Thus, the rectifying performance of device ZrSeS/SnS 2 is better than HfSeS/SnS 2 . The negative turn-on voltage is the same when the bias interval is 0.1 V. But due to the different band gaps of the HfSeS/SnS 2 and ZrSeS/SnS 2 heterojunctions, the negative turn-on voltages of the two devices may be different. Therefore, we recalculate the I ds -V ds curve in the negative turn-on voltage range by reducing the point interval from 0.1 to 0.05 V, as shown in the inset of  Fig. 5a. When a small negative bias is applied, electrons flow from the VBM of MSeS (M = Hf, Zr) to the CBM of SnS 2 via the band-to-band tunneling (BTBT) as shown in Fig. 5b. As the negative bias voltage increases in Fig. 5c, the energy band of MSeS rises further, while that of SnS 2 falls, resulting in a larger tunneling window and ultimately a larger reverse current. Under the positive bias in Fig. 5d, the tunneling window will vanish owing to the decline of the energy band of MSeS (M = Hf, Zr) and the rise of SnS 2 . At the same time, the band bending also limits the carrier migration. Therefore, at the positive bias, the forward current is very small.
We calculate the transmission spectra to study the electronic transport of the devices in Fig. 6. It is known that the current depends on the integral area of the transmission spectra within the bias window. It is clear that the integral areas of both devices at − 0.8 V are large than those at 0.8 V. This causes the large currents of the devices  Fig. 6b.
We further analyze the electronic transport by calculating the transmission eigenstates at ± 0.8 V in Fig. 7. One can see that the devices HfSeS/SnS 2 and ZrSeS/SnS 2 exhibit the localization at 0.8 V, compared with the devices at − 0.8 V. Thus, the currents of devices at 0.8 V are larger than those at − 0.8 V, accounting for the reverse rectification. Furthermore, it is notable that there are more transmission eigenstates for ZrSeS/SnS 2 at − 0.8 V than HfSeS/SnS 2 at − 0.8 V. Consequently, the current of ZrSeS/SnS 2 at the negative bias is larger than HfSeS/SnS 2 as shown in Fig. 4b.
The I ds -V ds characteristics of the devices at different gate voltages are shown in Fig. 8. It is clearly found that the gate voltage can effectively modulate the currents of both devices at the negative bias. But the currents hardly change at the positive bias. Thus, the gate voltage does not change the characteristics of reverse rectification of both devices. Moreover, the negative gate voltage causes a significant variation of current compared with the positive gate voltage; thus, negative gate voltage can improve rectifying performance.
The reverse rectifying ratio ( R(V) = |I(−V ds )∕I(V ds )| ) is plotted as a function of gate voltage and |V ds | in Fig. 9. It can be seen that the gate voltage can modulate the rectifying ratio. The device ZrSeS/SnS 2 has better rectifying performance than the device HfSeS/SnS 2. Notably, the rectifying ratios at negative gate voltage are larger than at positive gate voltage for both devices, which is consistent with the characteristics of the I ds -V ds. The rectifying ratio of the device can reach an order of magnitude of 10 7 . The reverse rectification ratio of our device is several order magnitudes higher than conventional backward diodes based on bulk materials and vdW heterojunctions backward diodes based on other 2D materials as shown in Fig. 9c. Thus, the gate voltage can modulate the rectifying performance of the device.  Fig. 10. Both devices exhibit more eigenstates at − 0.5 V than at 0.5 V. The reduction in the eigenstates leads to the reduced current at positive gate voltage, as shown in Fig. 8. In addition, the device ZrSeS/SnS 2 has more eigenstates than HfSeS/ SnS 2 at the gate voltage of − 0.5 V, consequently the current of ZrSeS/SnS 2 is larger than HfSeS/SnS 2 . As a result, the negative gate voltage induces better electron transmission than the positive gate voltage, which induces larger rectifying ratios at the negative gate voltage.

Conclusions
In summary, we have studied the electronic properties and transport of the MSeS (M = Hf, Zr)/SnS 2 heterojunctions by first-principles calculations. The ZrSeS/SnS 2 heterojunction shows the type-I band alignment, while HfSeS/ SnS 2 displays the type-II band alignment. The I ds -V ds curves of the MSeS (M = Hf, Zr)/SnS 2 heterojunctions display the rectifying behaviors. The larger currents of both devices at negative gate voltage than at positive gate voltage indicate that the constructed heterojunction devices are backward diodes. The rectifying performance of ZrSeS/SnS 2 is better than that of HfSeS/SnS 2. Furthermore, the negative gate voltage can significantly change the currents of the devices, especially for ZrSeS/SnS 2, and improve the rectifying performance of the device. The rectifying ratio can reach up to 10 7 . The results will provide Fig. 9 a and b reverse rectifying ratio of the two devices as a function of bias and gate voltage. c Comparison of rectification ratio of different backward diodes made of conventional bulk materials Si [44], GsAs [45], GaN [46], and 2D heterojunctions WSe 2 /MoS 2 [47], AsP/ InSe [48], WSe 2 /SnSe 2 [25], BP/MoS 2 [49], SnS 2 /SiO 2 [50]