Bias-controlled multi-functional transport properties of InSe/BP van der Waals heterostructures

Van der Waals (vdW) heterostructures, consisting of a variety of low-dimensional materials, have great potential use in the design of a wide range of functional devices thanks to their atomically thin body and strong electrostatic tunability. Here, we demonstrate multi-functional indium selenide (InSe)/black phosphorous (BP) heterostructures encapsulated by hexagonal boron nitride. At a positive drain bias (VD), applied on the BP while the InSe is grounded, our heterostructures show an intermediate gate voltage (VBG) regime where the current hardly changes, working as a ternary transistor. By contrast, at a negative VD, the device shows strong negative differential transconductance characteristics; the peak current increases up to ~5 μA and the peak-to-valley current ratio reaches 1600 at VD = −2 V. Four-terminal measurements were performed on each layer, allowing us to separate the contributions of contact resistances and channel resistance. Moreover, multiple devices with different device structures and contacts were investigated, providing insight into the operation principle and performance optimization. We systematically investigated the influence of contact resistances, heterojunction resistance, channel resistance, and the thickness of BP on the detailed operational characteristics at different VD and VBG regimes.


Results and discussion
describes the structure of our hBN/InSe/BP heterostructure device with Au/Ti electrodes (InSe-BP-Ti device), accompanied by its optical micrograph. The hBN/InSe/BP heterostructure was achieved using the conventional dry transfer method 2,3 . Individually exfoliated BP and InSe flakes were successively transferred on 300 nm-thick SiO 2 , followed by encapsulation with a pre-patterned hBN flake. InSe and BP are vulnerable to the air, but the hBN encapsulation allows improved stability and decent mobility 26,30 . Before the transfer, the hBN encapsulating layer was patterned using electron beam (e-beam) lithography and plasma etching to have eight openings. These allowed the InSe and BP to be partially exposed for metallization even after having the hBN cover on them. Four metal contacts on the InSe and BP were then defined by e-beam lithography, followed by Au(80 nm)/Ti(10 nm) deposition and lift-off. Figure 1b shows the atomic force microscopy (AFM) image,  Figure 1c shows the three distinct Raman spectra measured on the InSe, BP, and InSe/BP overlap regions (excitation wavelength = 514 nm).
The four peaks at 114 cm −1 , 175 cm −1 , 198 cm −1 , and 225 cm −1 from InSe, and the three peaks at 364 cm −1 , 440 cm −1 , and 467 cm −1 from BP are consistent with those previously reported 31,32 , confirming the high quality of our flakes encapsulated by hBN. The Raman spectrum on the overlapped region shows the same peak positions originating from the InSe and BP. The Raman peak intensity is slightly weakened in the InSe/BP overlap region, compared to that in InSe/SiO 2 . This Raman quenching is attributed to the weak but finite van der Waals coupling between the InSe and BP 33,34 . Nearly consistent peak positions and the ratio of A 1 (LO) peak to E 1 2g peak intensity suggest that the degree of strain and doping induced by having the heterostructure is negligible 30 . Electrical characterization was performed on the BP and InSe individually via the two-terminal and fourterminal methodology, as illustrated in the schematic in Fig. 1a 26,35 . Figure 1d shows the two-terminal conductances (G 2pt ) of the InSe (G 2pt InSe ) and BP (G 2pt BP ), and the channel conductances (G 4pt ) of the InSe (G 4pt InSe ) and BP (G 4pt BP ) as a function of back-gate voltage (V BG ), where G 2pt = I D /V D , G 4pt = (I D /V 4pt )(L 4pt /L 2pt ), I D is the measured drain current, V D is the drain bias applied on the InSe or BP, V 4pt is the voltage difference between the two inner contacts on the InSe or BP, and L 4pt (L 2pt ) is the distance between the two inner (outer) contacts. While the BP shows an ambipolar characteristic, the InSe shows an n-type semiconducting behavior, similar to those of prior reports 25,26 .
We note that the two-terminal field-effect mobilities of the InSe and BP are ~20 cm 2 V −1 s −1 and ~65 cm 2 V −1 s −1 , respectively, and the four-terminal field-effect mobilities of the InSe and BP are ~370 cm 2 V −1 s −1 and ~120 cm 2 V −1 s −1 , respectively ( Figure S1). The two-terminal mobilities are obtained via ((1/C)(L 2pt /W) (dG 2pt /dV BG )) and the four-terminal mobilities are obtained via ((1/C)(L 2pt /W)(dG 4pt /dV BG )), where C is the back-gate capacitance and W is the channel width. The two-terminal mobilities are smaller than the four-terminal values due to contact resistances 36 , as is particularly notable for the InSe. Figure 1e shows the channel resistivities (ρ) of the InSe (ρ InSe ) and BP (ρ BP ), and the contact resistances (R C ) for the InSe (R C InSe ) and BP (R C BP ), where ρ = (1/G 4pt )(W/L 2pt ) and R C = (1/G 2pt − 1/G 4pt )/2 37 . R C BP (R C InSe ) occupies a large portion of the two-terminal resistance, 1/G 2pt BP (1/G 2pt InSe ). Figure 1f also provides I D vs V D output characteristics for the InSe and BP. The BP shows a linear dependence at high carrier density and even at charge neutrality (at V BG = 50 V and 0 V), suggesting ohmic contacts, but the InSe shows a nonlinear characteristic, indicating Schottky contacts. Figure 2a describes the measurement setup for the bias-controlled MVL and NDT properties of the InSe-BP-Ti device. While applying V D to the BP and grounding the InSe, the two-terminal conductance between the source and drain (G 2pt InSe−BP = I D /V D ) was measured in our device. Figure 2b,c show the measured G 2pt InSe−BP as a function of V BG at positive and negative V D , respectively (Fig. 3a also provides the corresponding I D as a function InSe−BP vs V BG of the InSe-BP-Ti device measured at a backward V D regime, which shows a strong NDT behavior with PVCR reaching ~ 10 2 at V D = −1 V. The dashed line represents (R InSe + R BP + R C BP ) −1 , which is comparable to the G 2pt www.nature.com/scientificreports/ of V BG ). In the positive V D regime, we note the particular region where the G 2pt InSe−BP hardly changes, creating an intermediate state "1/2" (at −6 V < V BG < 0), accompanied by a state "0" (at V BG < −20 V) and a state "1" (at V BG > 25 V). Several studies have demonstrated ternary inverters based on NDT 5,6,14,22,27,28 , where the potential inside of the constituent semiconductor barely changes within the negative transconductance region. However, this methodology is limited to the inverting logic and indeed not suitable for versatile CMOS circuitry design. Ternary transistors are indispensable to design versatile ternary-data-processing CMOS integrated circuits. In the negative V D regime, a strong NDT behavior is observed, achieving a peak conductance (G peak ) of 140 nS and a peak-to-valley current ratio (PVCR) of ~ 10 2 at V D = −1 V. Figure S2 shows transfer characteristics of our another InSe-BP-Ti device, which are qualitatively similar to those in Fig. 2b,c.
In the InSe-BP-Ti device, the total two-terminal resistance from source to drain can be approximately modeled as serially connected resistors (Fig. 2a), which can include R C InSe , R C BP , the channel resistances of the InSe (R InSe ), and of the BP (R BP ). Each of these components is acquired via the four-terminal measurements at V D = 1 V, as discussed in Fig. 1e. R InSe (R BP ) corresponds to ρ InSe (ρ BP ) multiplied by the appropriate dimension of the InSe (BP) region of the InSe-BP-Ti device; Figure S3 provides schematics and a table to define the multiple parameters we introduced more specifically. We assume that most of the current flows along the InSe rather than the BP in the InSe/BP overlap region. The InSe region that sits above the BP is not effectively gate-controlled due to the thick BP underneath, and thus, the InSe resistivity is assumed to be constant as ρ InSe at V BG = 0 V, which is smaller than ρ BP regardless of the applied V BG (Fig. 1e). We also remark that the resistance at the heterojunction between the InSe and BP is not taken into account, which is further discussed below.
As described in the lower schematics of Fig. 2a, four different equivalent circuits are compared with our experimental data: We present conductance rather than drain current in Fig. 2b,c for the comparison of the measurement to these series circuit models; there exist finite errors between them, which are discussed below. In the case of (R InSe + R BP ) −1 without any R C (black solid in Fig. 2d,e), a superior NDT peak arises at V BG ~ −4 V, which simply corresponds to when R BP + R InSe becomes a minimum in the p-side of the BP (see Fig. 1d). When V BG < −4 V, the (R InSe + R BP ) −1 value is strongly governed by R InSe , which is in an insulating state. As the V BG increases, R InSe decreases and correspondingly (R InSe + R BP ) −1 increases, reaching the NDT peak at V BG ~ −4 V. (R InSe + R BP ) −1 then rapidly decreases and shows a valley as the BP reaches its charge neutrality, which is followed by an increase of (R InSe + R BP ) −1 as the n-side of the BP turns on with increasing V BG . The overall characteristic behavior of (R BP + R InSe ) −1 is analogous to that of our experimentally measured G 2pt InSe−BP at negative V D , but the G peak of (R BP + R InSe ) −1 is much higher than the experimental values. By contrast, the calculated (R C InSe + R InSe + R BP + R C BP ) −1 value, including the R C components, yields a largely reduced G peak , which is even lower than the experimental values at both negative and positive V D regimes.
Depending on the polarity of V D , the R C on the other side (R C InSe or R C BP ) can be more effective due to the asymmetric nature of Schottky barriers 38,39 . In particular, the channel of our InSe-BP-Ti device consists of two different materials, InSe and BP, which leads to strong asymmetric characteristics, depending on the polarity InSe−BP at negative V D . This is because when V D > 0, electrons generally see a barrier at the junction between the Au/Ti contact and the InSe 40 . By contrast, when V D < 0, carriers generally see a barrier at the junction between the contact and the BP. The band diagrams further describe which side of the contact resistances, R C InSe or R C BP , is more effective, depending on the polarity of V D (Fig. 3b-e). Figure 3b represents the band parameters we used to build the band diagrams [41][42][43] . The Schottky barrier for electrons at the junction between the 4-nm thick BP and Au/Ti contact was presumed to be ~0.2 eV 43 , and the Schottky barrier at the junction between the InSe and Au/Ti contact was roughly presumed to be ~0.3 eV 44 , as previously reported. Figure 3c-e describe the band diagrams at V D = 0, V D > 0, and V D < 0 and at points (i), (ii), and (iii), marked in Fig. 3a. At V D > 0 (Figs. 2b, 3d), the electrons entering the InSe/BP channel experience a barrier at the junction between the source and the InSe, resulting in R C InSe . The slightly smaller G 2pt InSe−BP compared to the (R C InSe + R InSe + R BP ) −1 at point (i) is presumably due to the underestimated R C InSe value in the subthreshold region of the InSe. As the V BG decreases, the R C InSe dramatically increases (Fig. 1e) 26 , exceeding the reasonable range measurable via the conventional four-terminal methodology. The slightly higher G 2pt InSe−BP , compared to the (R C InSe + R InSe + R BP ) −1 at point (ii), is due to the minority carriers drifting in the BP injected from the InSe, a typical characteristic of a p-n diode at a forward bias. G 2pt InSe−BP agrees well with (R C InSe + R InSe + R BP ) −1 at point (iii), where the n + -n junction is made. At V D < 0 (Figs. 2c, 3e), electron carriers generally see a barrier at the junction between the drain and the BP, experiencing R C BP . Distinctively, at point (i), electrons can be injected from the BP valence band, full of electrons, into the InSe via band-to-band tunneling (BTBT) 11 . This leads to the reduced impact of R C BP and the corresponding enhanced NDT peak compared to (R InSe + R BP + R C BP ) −1 (Fig. 2c). At points (ii) and (iii), the measured G 2pt InSe−BP agrees well with (R InSe + R BP + R C BP ) −1 . The band diagrams also explain the backward rectification at point (i) and the forward rectification at point (ii). The rectification ratio (I D at positive V D divided by I D at negative V D ) values of our multiple InSe-BP-Ti devices are provided in Figure S4, where the backward rectification ratio reaches up to 10 5 .
We investigated multiple InSe-BP devices with different contacts and structures: (1) an InSe/BP heterostructure device with few-layer graphene (FLG) contacts (InSe-BP-FLG device, Fig. 4a-d), and (2) another device where InSe and BP are serially connected via Au/Ti contacts (InSe-Ti-BP-Ti device, Fig. 4e,f). As described in Fig. 4a, there are two FLG contacts on the InSe and two others under the BP in the InSe-BP-FLG device. Figure 4b shows the G 2pt InSe−BP measured using the inner two contacts, where the InSe and BP are vertically overlapped over the whole measured region. It is notable that the G 2pt InSe−BP barely depends on V BG , without NDT behavior. The InSe-BP-FLG device is also measured using the outer two contacts as source and drain (Fig. 4c). In contrast to the Fig. 4a setup, the individual non-overlapped InSe and BP regions are included in the Fig. 4c setup. Figure 4d shows the correspondingly measured G 2pt InSe−BP as a function of V BG . Note the NDT behavior, similar to that observed in the InSe-BP-Ti device at a negative V D regime. This contrasts remarkably with the G 2pt  www.nature.com/scientificreports/ using the ρ InSe at V BG = 0 V (data in Fig. 1e) and the dimension of the InSe region between the two inner contacts, without taking into account any of the BP region and the InSe/BP junction resistance. This suggests that the current flows mostly along the InSe, and the heterojunction resistance and FLG contact resistances are negligible compared to the InSe channel resistance. We thus neglect the InSe/BP junction resistance when considering the equivalent circuits of the InSe-BP-Ti device in Fig. 2. The low InSe/BP junction resistance even when the BP is p-type (at V BG < 0) and V D < 0 is due to BTBT between the InSe and BP, as described in the band diagram in Fig. 3e. The output characteristics of the individual InSe and BP regions with FLG contacts also reveal ohmic characteristics ( Figure S6), which contrasts with the Schottky behavior of Au/Ti contacts on the InSe. This leads to the transconductance behavior being nearly the same regardless of the polarity of V D ( Figure S7), distinct from the InSe-BP-Ti device. The schematic in Fig. 4e describes the InSe-Ti-BP-Ti device where InSe and BP are serially connected via Au/Ti contacts and the associated measurement setup. Figure 4f shows the G 2pt InSe−BP measured from the InSe-Ti-BP-Ti device as a function of V BG at different V D , ranging from -0.1 to -1 V. The NDT characteristics are also observed in this device, similar to the InSe-BP-Ti device and InSe-BP-FLG device. This further reveals that the NDT behavior originates from the individual InSe and BP parts rather than the vertically overlapped InSe/BP region. The measured G 2pt InSe−BP agrees well with ((G 2pt InSe ) −1 + (G 2pt BP ) −1 ) −1 (dashed line in Fig. 4f). However, we note the much lower G peak (~0.1 nS), compared to those of the InSe-BP-Ti device and the InSe-BP-FLG device (>0.1 μS). This is due to the additional Au/Ti contact resistances that exist between the InSe and BP, which are much larger than the InSe/BP vdW junction resistance. The thicknesses of the BP and InSe flakes in the InSe-Ti-BP-Ti device were 3 nm and 9 nm, respectively ( Figure S8).  Figure 5c,d show the extracted PVCR and subthreshold swing (SS) values of the devices, respectively. While the PVCR of the InSe-BP-Ti device increases as the V D increases, the PVCR of the InSe-BP-FLG device weakly depends on V D . In the InSe-BP-Ti device, as V D increases, R C BP decreases; thus, the PVCR increases and the SS decreases. By contrast, the low FLG contact resistance in the InSe-BP-FLG device leads to the PVCR and SS being less dependent on V D .
The transfer characteristics of the InSe-Ti-BP-Ti, InSe-BP-Ti, and InSe-BP-FLG devices can be compared to those calculated as (R InSe + R C InSe + R BP + R C BP ) −1 , (R InSe + R BP + R C BP ) −1 , and (R InSe + R BP ) −1 , respectively (Fig. 2a). The calculated conductances at their NDT valley points are similar (Fig. 2e), regardless of the inclusion of R C InSe or R C BP . This is because the valley point characteristic is dominated by the large R BP at the charge neutrality of BP. On the other hand, the conductance at the NDT peak strongly depends on whether R C InSe or R C BP is included. The additional R C InSe and R C BP existing in the InSe-Ti-BP-Ti device result in much lower PVCR and worse SS values due to reduced gate control. By contrast, the negligible vdW junction resistance renders better PVCR and SS values for the InSe/BP vdW heterostructure devices.
In many cases, ohmic contacts are more favorable than Schottky contacts. Our InSe-BP-FLG device also shows I Peak and PVCR values higher than those of InSe-BP-Ti device (Fig. 5). The ohmic symmetric contacts in InSe-BP-FLG device lead to the nearly the same NDT characteristics for both positive and negative V D regimes ( Figure S7). On the other hand, the asymmetric Au/Ti contacts to the InSe and BP in InSe-BP-Ti device can provide dissimilar operational properties depending on the polarity of V D , multi-valued transistor behavior at V D > 0 and NDT at V D < 0. Particularly at V D > 0, the high Schottky barrier (contact resistance) at the junction between Au/Ti contact and InSe becomes highly effective (point (i) in Fig. 3). This suppresses the current in that regime, leading to the intermediate state for the multi-valued transistor instead of a NDT peak (Figs. 2, 3, and Figure S2). Our study as a function of multiple device parameters, including contact type and heterojunction type, can provides an idea for fine manipulation of electronic device characteristics.
In addition, we investigated the impact of BP thickness (t BP ) on the electrical characteristics of our InSe-BP-Ti devices. Figure 6a shows the I D of two InSe-BP-Ti devices (solid) with different t BP , 4 nm and 14 nm, as a function of V BG , shifted with respect to the V BG at the minimum I D of the BP. The most salient feature here is that the device with thinner BP shows significantly reduced I Valley , resulting in a highly improved PVCR. The transfer curve of the BP side of each InSe-BP-Ti device is also provided for comparison (dashed). The on/off current ratio of the 4 nm-thick BP is much higher than that of the 14 nm-thick BP due to the increased band gap, as  Figure S9). The performance also depends on the mobility and the initial doping level of BP. A few studies have reported PVCR values higher than ours, but these either applied much higher V D (≥10 V) or had a wider V BG width of the peak 18,19 .

Conclusion
In summary, we demonstrated bias-controlled MVL and NDT properties based on InSe/BP heterostructures. Due to the asymmetric nature of Schottky barriers at the junction between Au/Ti contact and InSe or BP, asymmetric electrical characteristics were developed depending on the polarity of V D . At positive V D , the InSe-BP-Ti devices worked as ternary transistors, but at negative V D , the devices showed NDT characteristics. The contributions of contact resistances and channel resistance were identified separately via four-terminal measurements performed on each layer. Multiple devices with different contacts and device structures were investigated, and we systematically discussed the influence of contact resistances, heterojunction resistance, channel resistances, and the thickness of BP on the detailed operational characteristics of InSe/BP-based vdW heterostructures. These results provide insight into the operation principle and further performance optimization of general 2D material-based vdW heterostructures.

Experimental
Fabrication of the InSe-BP-Ti device. InSe and BP flakes were mechanically exfoliated on polydimethylsiloxane (PDMS) film using cleanroom tape, while hBN was exfoliated on 300 nm-thick SiO 2 /Si substrate. Once appropriate InSe and BP flakes with the desired thicknesses were identified, the PDMS films with the flakes were cut into 10 mm × 10 mm pieces and then attached to a glass slide for transfer to a designated location. The BP and InSe flakes on PDMS film were then successively transferred on 300 nm-thick SiO 2 , thermally grown on a highly doped Si substrate, resulting in an InSe/BP stack. To minimize the surface contamination of the device, the exfoliation and stacking processes were performed entirely in a glovebox, keeping the oxygen level below 5 ppm. The separately exfoliated hBN flake suitable for top encapsulation was patterned before the transfer using conventional e-beam lithography and reactive ion etching using SF 6 gas to have eight openings. These allowed the InSe and BP to be partially exposed for metallization even after having the hBN cover on them. The patterned hBN flake was annealed at 400℃ for an hour in the Ar/H 2 atmosphere to remove polymethyl methacrylate (PMMA) residue, which also allowed the hBN to be easily picked up using a polypropylene carbonate (PPC)/PDMS stamp. The patterned hBN was then transferred onto the InSe/BP stack by melting the PPC   www.nature.com/scientificreports/ at ~120 ℃. Then the hBN/InSe/BP heterostructure was washed with acetone. Additional e-beam lithography was performed to define metal contacts for the InSe-BP-Ti device, followed by Au(80 nm)/Ti(10 nm) deposition via e-beam evaporation and lift-off. The device was annealed at 400℃ for an hour in the Ar/H 2 atmosphere to remove the remaining polymer residues.
Fabrication of the InSe-Ti-BP-Ti device. The fabrication process for the InSe-Ti-BP-Ti device was similar to that of the InSe-BP-Ti device. One distinction was that the BP and InSe flakes were ~5 μm apart from each other without InSe/BP vdW heterojunction.
Fabrication of the InSe-BP-FLG device. FLG and hBN flakes were mechanically exfoliated on Si/SiO 2 substrates. They were annealed at 400°C for an hour in the Ar/H 2 atmosphere. Individually exfoliated BP and InSe flakes were successively transferred on the FLG exfoliated on SiO 2 , similar to the transfer process employed for the InSe-BP-Ti device. Finally, hBN and top FLG flakes were successively picked up using a PPC/PDMS stamp. Then the hBN/FLG stack was transferred to the prepared InSe/BP/FLG heterostructure on SiO 2 . Au/Ti contacts were deposited on a non-encapsulated region of the FLG, followed by annealing in the Ar/H 2 atmosphere.