# Fileset [PhysRevResearch.6.033011.pdf](https://mdr.nims.go.jp/filesets/d911de95-c8bf-4146-a545-c6a52be8aaba/download) ## Creator Seiya Kawasaki, [Kei Kinoshita](https://orcid.org/0009-0005-4586-734X), [Rai Moriya](https://orcid.org/0000-0001-7471-7432), [Momoko Onodera](https://orcid.org/0000-0001-9457-6796), [Yijin Zhang](https://orcid.org/0000-0003-1127-1124), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Takao Sasagawa](https://orcid.org/0000-0003-0149-6696), [Tomoki Machida](https://orcid.org/0000-0002-1938-7415) ## Rights [Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/) ## Other metadata [Minigap-induced negative differential resistance in multilayer

Mo S_{2}

-based tunnel junctions](https://mdr.nims.go.jp/datasets/3ed473d5-cceb-44ea-a05a-50d1465daadd) ## Fulltext Minigap-induced negative differential resistance in multilayer ${\rm{Mo}}{{{\rm{S}}}_2}$-based tunnel junctionsPHYSICAL REVIEW RESEARCH 6, 033011 (2024)Minigap-induced negative differential resistance in multilayer MoS2-based tunnel junctionsSeiya Kawasaki,1 Kei Kinoshita ,1 Rai Moriya ,1,* Momoko Onodera ,1 Yijin Zhang ,1 Kenji Watanabe ,2Takashi Taniguchi ,3 Takao Sasagawa ,4 and Tomoki Machida 1,†1Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro, Tokyo 153-8505, Japan2Research Center for Electronic and Optical Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan3Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan4Laboratory for Materials and Structures, Tokyo Institute of Technology, 4259 Nagatsuta, Yokohama, Kanagawa 226-8503, Japan(Received 16 January 2024; accepted 23 May 2024; published 1 July 2024)Despite extensive research, the high-energy band properties of transition metal dichalcogenides remain unex-plored. Here, we reveal that a multilayer MoS2-based tunnel junction exhibits substantial negative differentialresistance (NDR) owing to the presence of a minigap, which is the energy gap between the upper and lower bandsof the valence band at the � point. We fabricated a highly p-doped multilayer p+-MoS2/h-BN/p+-MoS2 tunneljunction. When a bias is applied across the junction, holes at the Fermi level at the � point in the valence band ofthe source-side p+-MoS2 resonantly tunnel to the drain-side p+-MoS2 with momentum conservation. When theenergy of the injected hole coincides with the minigap of the drain-side p+-MoS2, the tunneling conductance issuppressed; thus, NDR is observed in the current-voltage characteristics. We identified minigap-induced NDRover a broad range of MoS2 thicknesses, including the bulk, that was observable even at room temperature.DOI: 10.1103/PhysRevResearch.6.033011I. INTRODUCTIONNegative differential resistance (NDR) devices based onvan der Waals (vdW) heterostructures of two-dimensional(2D) materials are becoming increasingly important becausesuch heterostructures enable the utilization of a wide va-riety of 2D materials without being restricted by latticemismatches at the interfaces [1]. As NDR devices play a cru-cial role in high-frequency electronics for upcoming wirelesscommunication systems [2,3], it is imperative to develop high-performance NDR devices utilizing vdW heterostructures.This creates new opportunities for practical applications. Todate, NDR in 2D materials has been demonstrated in var-ious ways, such as via resonant tunneling through discreteenergy levels [4–15] and in Esaki tunnel diodes [16–20].Most of these previous studies have suggested that the use ofvertical junctions constructed from monolayer to few-layer-thick 2D materials is crucial for the demonstration of NDR.This places severe limitations on device fabrication because(1) the thickness of the 2D material needs to be controlledwith monolayer precision [21], (2) the twist angle betweenthe source and drain layers needs to be aligned to within afew degrees to achieve matching of the in-plane momentumbetween the layers [22], and (3) in Esaki tunnel diodes, the*Contact author: moriyar@iis.u-tokyo.ac.jp†Contact author: tmachida@iis.u-tokyo.ac.jpPublished by the American Physical Society under the terms of theCreative Commons Attribution 4.0 International license. Furtherdistribution of this work must maintain attribution to the author(s)and the published article’s title, journal citation, and DOI.carrier density of the 2D material needs to be precisely con-trolled to realize broken-gap type III band alignment at theheterointerface. Furthermore, 2D-material-based Esaki diodeshave only been achieved using air-sensitive materials, thus de-vice fabrication in inert environments is required [18,20,23].Thus different approaches to realize NDR without these re-strictions are required. In this study, we demonstrate that atunnel junction fabricated without using monolayer materials,twist angle control, or broken-gap band alignment, using ahighly hole-doped multilayer (ML) MoS2 (ML p+-MoS2)electrode, exhibits NDR.II. RESULTSFirst, we discuss the band structure of monolayer-to-multilayer 2H-MoS2, as shown in Fig. 1(a). The bandstructure was calculated using density functional theory(DFT) using a calculation method presented in our previousreport [10]. The origin of the band energy (E = 0) was setat the top of the valence band (VB). While one-layer (1L)MoS2 features a direct band gap at the K point, multilayerMoS2 exhibits an indirect band gap between the conductionband (CB) at the Q point (the point between the � and Kpoints) and the valence band (VB) at the � point. In addition tothese band-gap changes, the structure of the VB includes otherinteresting features. First, the VB of MoS2 contains upperand lower bands [blue and orange solid lines, respectively,in Fig. 1(a)], and the number of upper bands at the � pointin the VB changes with the number of MoS2 layers. Thesesubbands arise owing to the out-of-plane quantum confine-ment in few-layer-thick MoS2; the number of subbands inthe VB at the � point corresponds to the number of layersN [24–28]. Second, the band structure of bulk MoS2 exhibits2643-1564/2024/6(3)/033011(9) 033011-1 Published by the American Physical Societyhttps://orcid.org/0009-0005-4586-734Xhttps://orcid.org/0000-0001-7471-7432https://orcid.org/0000-0001-9457-6796https://orcid.org/0000-0003-1127-1124https://orcid.org/0000-0003-3701-8119https://orcid.org/0000-0002-1467-3105https://orcid.org/0000-0003-0149-6696https://orcid.org/0000-0002-1938-7415https://ror.org/057zh3y96https://ror.org/026v1ze26https://ror.org/026v1ze26https://crossmark.crossref.org/dialog/?doi=10.1103/PhysRevResearch.6.033011&domain=pdf&date_stamp=2024-07-01https://doi.org/10.1103/PhysRevResearch.6.033011https://creativecommons.org/licenses/by/4.0/SEIYA KAWASAKI et al. PHYSICAL REVIEW RESEARCH 6, 033011 (2024)FIG. 1. (a) DFT-calculated band structures of MoS2 for different numbers of layers N from N = 1 to the bulk. For each N, E = 0 was set atthe top of VB (valence band maximum, VBM). For the band structure of the bulk (right-most plot), the bands with out-of-plane components(kz > 0) are projected onto the K-�-M plane as gray-colored bands. (b) Left: Positions of the band energies at the � point (k = 0) in thevalence band (VB) for different N (2 L to bulk). Right: Schematic illustration of the VB of bulk MoS2 showing upper continuous band, lowercontinuous band, and minigap.an energy gap between the upper and lower bands of the VBat the � point. In the bulk MoS2 (right-most plot), the bandswith out-of-plane components (kz > 0) are projected onto theK-�-M plane as gray-colored bands. There is an energy gapbetween the upper and lower bands of the VB at the � point,which has the form of a characteristic down-pointing triangle(see the bottom-right panel of Fig. 1). Because this energygap is smaller than the band gap of MoS2, we refer to it asa minigap. The band energies at the � point in the VB areplotted with respect to N in Fig. 1(b); for multilayer MoS2(2–22 L), the energies of the subbands are plotted. For bulkMoS2, the continuous upper and lower bands are representedby solid lines. These calculation results suggest that the mini-gap exists for all values of N and the center of the minigap islocated −1.2 eV below the top of VB at the � point. The sizeof the minigap is approximately 0.13 eV in the bulk MoS2.This is in stark contrast to the subband structure at the � pointin the VB: the number of subbands and their energy levels(thus, the center between the levels) are strongly dependenton N. We note that a similar down-pointing-triangle mini-gap was observed in previous angle-resolved photoemissionspectroscopy (ARPES) studies of bulk MoS2 [29,30], how-ever, thus far, no serious attempt has been made to investigatethe properties of the gap. In this study, we used momentum-conserved resonant tunneling to access the minigap throughtransport measurements.We fabricated a tunneling junction device with a highly p-doped multilayer p+-MoS2/few-layer h-BN/p+-MoS2 struc-ture, where p+-MoS2 was the electrode and few-layerh-BN was the tunnel barrier, as illustrated in Fig. 2(a).We used Nb-doped p+-MoS2 with a hole density of ∼3 ×1020 cm−3 [10,31]. Different devices using different numbersof p+-MoS2 layers ranging 6–50 were fabricated. Four toeight layers of h-BN were used as the tunnel barrier. Duringfabrication, we did not intentionally align the crystallographicorientation between the p+-MoS2 layers, thus it was assumedthat these layers were misaligned. Further details on the de-vice fabrication procedure are presented in Appendix A. Thecurrent-voltage (I-Vsd) characteristics of the junction weremeasured at T = 300 K under the application of a bias033011-2MINIGAP-INDUCED NEGATIVE DIFFERENTIAL … PHYSICAL REVIEW RESEARCH 6, 033011 (2024)FIG. 2. (a) Schematic illustration of thedevice structure for highly p-doped multilayer(ML) p+-MoS2/few-layer h-BN/ML p+-MoS2vdW tunnel junction. (b) Current-voltage (I-Vsd) characteristics of the device measuredat T = 300 K. (c) Schematic illustration ofresonant tunneling between hole-doped MLp+-MoS2 electrodes. Hole tunneling from thesource-side p+-MoS2 [ p+-MoS2 (S) ] to thedrain-side MoS2 [p+-MoS2 (D) ] is illustrated.Three different conditions (A, B, and C) ofinterlayer bias Vsd between p+-MoS2 (S) andp+-MoS2 (D) are considered.Vsd between the p+-MoS2 layers, with the measurement ofthe current I through the device; positive Vsd was definedas hole tunneling from the source-side p+-MoS2, p+-MoS2(S), to the drain-side p+-MoS2, p+-MoS2 (D). The resultsfor the device in which the p+-MoS2 (S) and p+-MoS2 (D)layer numbers are 22 and 45 L, respectively, are shown inFig. 2(b) (see Appendix B for the detailed device structure).The I-Vsd characteristics features a peak, dip, and negativedifferential resistance (NDR), suggesting the occurrence ofresonant tunneling. We attribute positions A, B, and C inthe I-Vsd curve [Fig. 2(b)] to the resonant tunneling of holesillustrated in panels A, B, and C, respectively, in Fig. 2(c).Since the Fermi energy EF of p+-MoS2 was estimated tobe ∼30 meV below the top of the VB at the � point (seeAppendix C for details of the determination of the EF ofp+-MoS2), the holes in MoS2 (S) have momentum only inthe vicinity of the � point of p+-MoS2 (S), contributing toenergy- and momentum-conserved tunneling. Therefore, inthe following analysis, we only consider tunneling betweenthe � point bands of p+-MoS2 (S) and p+-MoS2 (D). Asthe relative energy between p+-MoS2 (S) and p+-MoS2 (D)changes with Vsd, conditions A, B, and C occur. ConditionsA and C correspond to resonant tunneling into the upper andlower bands of p+-MoS2 (D), respectively, and the tunnelingconductance is high in these cases. In contrast, under con-dition B, the tunneling conductance was suppressed becausethere were no available states at the � point within the mini-gap. Thus, the I-Vsd curve exhibited a dip at this position.The dip is located at Vsd ≈ 1.3 V; this value is close to theenergy separation between the top of the VB at the � pointand the minigap [1.2 V below the top of the VB at the �point, as shown in Fig. 1(a)]. Therefore, these results suggestthat minigap-induced NDR can be detected from energy- andmomentum-conserved resonant tunneling.We believe that the momentum-conserved resonant holetunneling between the � points of p+-MoS2 (S) and p+-MoS2(D) is crucial for observing minigap-induced NDR. Toconfirm this hypothesis, we fabricated a reference device:monolayer WSe2/few-layer h-BN/38L p+-MoS2 (see Ap-pendix D, for details of the device structure). The differencebetween this device and the device shown in Fig. 2 is thatmonolayer WSe2, in which the Fermi energy is located inthe VB at the K point, was used as the source electrodeinstead of p+-MoS2 (S). We then consider hole tunneling fromthe source-side hole-doped monolayer WSe2, p-WSe2 (S), top+-MoS2 (D), as illustrated in Fig. 3(a). Because the Fermienergy of monolayer p-WSe2 is close to the top of the VB atthe K point, momentum-conserved tunneling between the �points of the VBs is prohibited, as illustrated by the dashedarrow in the figure. Indeed, the I-Vsd curve measured for thedevice [Fig. 3(b)] does not show apparent NDR at T = 300K within the measured Vsd range. The small inflection in theI-Vsd curve near Vsd = +1.2 V is attributable to tunneling fromthe VB at the K point in p-WSe2 (S) to the VB at the � pointof p+-MoS2 (D); however, this is not momentum-conservedtunneling, and thus does not show NDR. This finding is fur-033011-3SEIYA KAWASAKI et al. PHYSICAL REVIEW RESEARCH 6, 033011 (2024)FIG. 3. (a) Schematic illustration of tunneling process from ahole-doped monolayer WSe2 to ML MoS2. The crystallographicorientations of the monolayer WSe2 and p+-MoS2 layers were suchthat they were considered to be misaligned. (b) I-Vsd characteristicsof the device measured at T = 300 K.ther evidence of the cruciality of using momentum-conservedhole tunneling between the � points of the VBs to observeminigap-induced NDR, as shown in Fig. 2.We now address the impact of the number of layers N ofMoS2 (D) on the NDR. We fabricated p+-MoS2 (S)/few-layerh-BN/p+-MoS2 (D) with different N values from 45 to 6L, and the I-Vsd curves were measured at different temper-atures from 20 to 300 K; these are compared in Fig. 4(a)(see Appendix E for details of the device structures of thedifferent devices). The N = 45 L device (the same device isshown in Fig. 2), the data for which are featured at the top ofFig. 4(a), exhibits minigap-induced NDR, as highlighted bythe green shaded area, that is nearly temperature-independent.For smaller N values of 16, 9, and 6, the I-Vsd curves exhibitdifferent behaviors. Specifically, the curves exhibit oscillatorybehavior, showing NDR as highlighted by the blue shadedareas. The peaks of the oscillation are marked by blue squares,circles, triangles, diamonds, and pentagons. The position ofthe oscillation peaks changed with N, and the amplitude ofFIG. 4. (a) Left: I-Vsd characteristics for ML p+-MoS2/few-layer h-BN/ML p+-MoS2 tunnel junction with different N for drain-side MoS2.The I-Vsd curves for different temperatures (T = 20, 60, 100, 200, and 300 K for N = 45, 22, and 9. T = 20, 60, and 100 K for N = 16. T = 20,60, and 90 K for N = 6) are plotted. The peaks in the I-Vsd curve are highlighted by blue squares, circles, triangles, diamonds, and pentagons.Right: illustrations of VB structures of MoS2 (S) and MoS2 (D). (b) Left: Vsd positions of resonant tunneling peaks in the I-Vsd curves shownin panel (a). Right: Vsd positions of the dips in the I-Vsd curves marked by red solid squares in panel (a). The Vsd positions were obtainedfrom the data at T = 20 K except for N = 6, which was obtained from the data at T = 60 K. (c) Temperature dependence of PVR for (left)subband-induced NDR and (right) minigap-induced NDR.033011-4MINIGAP-INDUCED NEGATIVE DIFFERENTIAL … PHYSICAL REVIEW RESEARCH 6, 033011 (2024)oscillation decreased at higher temperatures (this is especiallyapparent in the data for N = 9); thus, these oscillations areboth N and temperature dependent. We recently observedsimilar oscillatory behavior as well as temperature-dependentbehavior in a multilayer p+-MoS2/h-BN/few-layer WSe2 [10]and few-layer WSe2/h-BN/few-layer WSe2 junction [11].Therefore, we assigned these peaks to resonant tunneling intothe quantized subbands of the VB at the � point, as illus-trated schematically on the right side of Fig. 4(a). Becausethe energy spacing between the subbands changes with N, thepeak position of the resonant tunneling also changes with N. Incontrast to the N-dependent behavior of the subband-inducedresonant tunneling, we found that minigap-induced NDR wasindependent of N and temperature. For example, the positionof the dip assigned to minigap-induced NDR, marked by thered solid square, is nearly identical for the junctions withdifferent N, and NDR is clearly seen even at 300 K. There-fore, minigap-induced NDR was found to be robust againstN and temperature changes. In addition to these features, weobserved that the I-Vsd curves exhibited other peaks that couldbe assigned to tunneling into the impurity band of Nb, asdiscussed in Appendix F.The Vsd positions of the peaks and dips were plotted versusN in Fig. 4(b). This plot further confirms that the peaks aris-ing from resonant tunneling into subbands depend on N (leftpanel), and the position of the dip due to minigap-inducedNDR does not depend on N (right panel). In addition, inFig. 4(c), the peak-to-valley ratio (PVR) of the NDR (peakI/dip I) is plotted versus temperature for the subband-inducedNDR (left) and minigap-induced NDR (right). The temper-ature dependence is substantially different for the minigap-and subband-induced NDRs. While the PVR of the subband-induced NDR decreased with increasing temperature anddisappeared (was <1) at 300 K, the PVR of the minigap-induced NDR remained the same across the entire temperaturerange. This difference can be attributed to the band structure ofMoS2 [Fig. 1(a)]. DFT calculations suggest that the separationbetween the subbands at the � point in the VB decreases withN and goes to zero at the bulk limit. This is in stark contrastto the minigap, which exists for all values of N and in the bulkmaterial (additional data sets for the detailed N dependence ofminigap-induced NDR features are presented in Appendix G).Taken together, the results discussed above reveal theunique properties of minigap-induced NDR, which includethe following: (1) a wide range of thicknesses of multilayerMoS2 can be used to demonstrate NDR because it is insensi-tive to the thickness of MoS2, (2) resonant tunneling betweenthe VBs at the � points does not require alignment of thecrystallographic orientations of MoS2 (S) and MoS2 (D) [11],and (3) as long as both p+-MoS2 (S) and p+-MoS2 (D) areconductive, there are no serious restrictions on the dopinglevel of the p+-MoS2 layers. We believe that these are sig-nificant advantages for constructing high-frequency electronicdevices based on multilayer p+-MoS2.III. SUMMARYWe investigated the tunneling transport in a highly p-dopedmultilayer (ML) p+-MoS2/few-layer h-BN/ML p+-MoS2vdW junction. The results showed that in the presence ofenergy- and momentum-conserved tunneling, the gap betweenthe upper and lower bands within the VB of MoS2 gives riseto negative differential resistance at 300 K. We showed thatthe minigap-induced NDR is robust to changes in the MoS2thickness and temperature under our experimental conditions.Because this phenomenon was observed even when we usedalmost bulklike thick multilayer MoS2, our results providea direction for the development of electronics applicationsutilizing multilayer transition metal dichalcogenides (TMDs).ACKNOWLEDGMENTSThis work was supported by JST-CREST, JST-Mirai,and JST-PRESTO (Grants No. JPMJCR15F3, No. JP-MJCR20B4, No. JPMJMI21G9, and No. JPMJPR20L5);JSPS KAKENHI (Grants No. JP20H00127, No. JP20H00354,No. JP21H04652, No. JP21H05232, No. JP21H05233,No. JP21H05234, No. JP21H05236, No. JP21K18181,No. JP22H01898, No. JP22K18317, No. JP22K14559,No. JP22J22105, No. JP22KJ1104, and No. JP23H02052);the Kenjiro Takayanagi Foundation; the Inoue Foundationfor Science; Tokuyama Science Foundation; and SupportCenter for Advanced Telecommunications Technology Re-search Foundation.APPENDIX A: DEVICE FABRICATIONAND MEASUREMENT METHODSBulk crystals of both Nb-doped p-type MoS2 (p+-MoS2)and nondoped WSe2 were purchased from HQ GrapheneInc. High-quality h-BN bulk crystals were grown using ahigh-pressure, high-temperature method. First, thin crystalsof p+-MoS2, WSe2, and h-BN were exfoliated from the bulkcrystal and deposited on an 85- or 290-nm SiO2/Si sub-strate. The exfoliation procedure was reported in our previouspublication [11]. The thicknesses of the flakes were de-termined by means of optical contrast and atomic forcemicroscopy (AFM) measurements.vdW heterostructure devices were fabricated via apolymer-based van der Waals (vdW) pick-up method us-ing poly(bisphenol A carbonate) (PC) on a PDMS sheetas the polymer material. The fabrication procedure for thep+-MoS2/few-layer h-BN/p+-MoS2 device was as follows.First, the top h-BN layer (with a thickness of 30–60 nm) waspicked up with the PC on PDMS. Using this h-BN, the topp+-MoS2 (42–45 layers), tunnel barrier h-BN (4–8 layers),bottom p+-MoS2 (6–22 layers), and bottom h-BN (30–60 nmthick) were sequentially picked up. Finally, the heterostructureon the PC was transferred onto a 290-nm-thick SiO2/p-dopedFIG. 5. (a) Schematic illustration of the 45L p+-MoS2/4–5L h-BN/22L p+-MoS2 device structure. (b) Optical micrograph of thefabricated device.033011-5SEIYA KAWASAKI et al. PHYSICAL REVIEW RESEARCH 6, 033011 (2024)FIG. 6. (a) Band structure of bulk MoS2 calculated using DFT. (b) Fermi energies of electrons and holes as a function of carrier density n.Si substrate. During the flake pickup and the transfer of theheterostructure onto the SiO2/Si substrate, temperature wasmaintained at 130 and 180 °C, respectively.To fabricate the WSe2/few-layer h-BN/p+-MoS2 device,after the top h-BN layer, monolayer WSe2, tunnel barrier h-BN, and bottom p+-MoS2 layers had been picked up, anotherp+-MoS2 was picked up, and this was used to construct anOhmic contact with WSe2 [31]. Finally, the bottom h-BNwas picked up, and the heterostructure was transferred ontoa 290-nm-thick SiO2/p-doped Si substrate.To fabricate an electrical contact with the device, electrodepatterns were prepared by electron beam (EB) lithographyusing poly(methyl methacrylate) (PMMA) as a resist. Afterfabricating the PMMA pattern for the electrodes, reactiveion etching (RIE) (Samco, RIE200iP) with CF4 gas was per-formed to remove a part of the top h-BN and p+-MoS2 layers.After RIE, the sample was loaded into an EB evaporator anda metal stack of Au (80 nm)/Pd (20 nm) was deposited toform Ohmic contacts with the p+-MoS2. Owing to the highNb doping of p+-MoS2, an Ohmic contact between Au/Pd andp+-MoS2 was obtained [31].To fabricate the top-gate electrode, PMMA patterns werefirst fabricated by EB lithography, and an Au (90 nm)/Cr(5 nm) stack was deposited using an EB evaporator.Transport properties were measured using a variable-temperature cryostat. The current-voltage (I-Vint)characteristics were measured by applying a source-drainbias Vint and the current flowing through the device wasmeasured using a current amplifier (DL instruments, Model1211). Vint and the top-gate voltage VG were applied using aKeithley 2400 source measurement unit.APPENDIX B: DETAILED STRUCTURE OFp+-MoS2/h-BN/p+-MoS2 DEVICE PRESENTEDIN FIG. 2The detailed device structure of the p+-MoS2/h-BN/p+-MoS2 device presented in Fig. 2 is shown in Fig. 5.APPENDIX C: DETERMINATION OF THE FERMIENERGY OF p+-MoS2The band structure, density of states (DOS), and Fermienergy calculated using DFT are shown in Fig. 6.APPENDIX D: DETAILED STRUCTURE OFWSe2/h-BN/p+-MoS2 DEVICE PRESENTED IN FIG. 3The detailed device structure of the monolayer WSe2/h-BN/p+-MoS2 device presented in Fig. 3 is shown in Fig. 7.FIG. 7. (a) Schematic illustration of the monolayer WSe2/few-layer h-BN/38L p+-MoS2 device structure. A top gate voltage Vtgof −10.5 V was applied to the top h-BN dielectric with a thicknessof 34 nm to hole-dope the WSe2 monolayer during the transportmeasurement. (b) An optical micrograph of the fabricated device.(c) An optical micrograph of the monolayer WSe2 on the 290-nmSiO2/Si substrate. (d) An optical micrograph of the thin h-BN flakeon the 290-nm SiO2/Si. Scale bars: 10 µm.033011-6MINIGAP-INDUCED NEGATIVE DIFFERENTIAL … PHYSICAL REVIEW RESEARCH 6, 033011 (2024)FIG. 8. (a)–(d) Left: optical micrographs of p+-MoS2 lakes on 290-nm SiO2/Si substrate used in the devices. Middle: optical micrographsof h-BN lakes on 290-nm SiO2/Si substrate used in the devices. Right: optical micrographs of fabricated devices. Scale bars: 10 µm.APPENDIX E: OPTICAL MICROGRAPHS OF ALL THEDEVICES AND p+-MoS2 FLAKES EXAMINED IN THISSTUDYOptical micrographs of the devices, exfoliated p+-MoS2flakes, and exfoliated h-BN flakes used in this study are sum-marized in Fig. 8.APPENDIX F: TUNNELING FEATURES RELATED TO THENb IMPURITY BAND IN MoS2The I-Vsd curves for N = 22, 16, and 9, shownin Fig. 9(a), exhibit additional peaks indicated by filledFIG. 9. (a) I-Vsd curves for N = 22, 16, and 9 measured at 20 K. (b) Schematic illustration of tunneling into Nb impurity band.033011-7SEIYA KAWASAKI et al. PHYSICAL REVIEW RESEARCH 6, 033011 (2024)FIG. 10. The width of the dip � in the I-Vsd curve is plotted fordifferent N.dark-yellow hexagons. This can be attributed to the Nbimpurity band formed in highly Nb-doped p+-MoS2, asschematically illustrated in Fig. 9(b). The presence of theNb impurity band has been previously reported in Nb-dopedp+-MoS2 crystals with similar hole densities [32].APPENDIX G: RELATIONSHIP BETWEENMINIGAP-INDUCED NDR AND DRAIN-SIDE p+-MoS2THICKNESSThe width of the dip in the I-Vsd curves for minigap-induced NDR was extracted for different N values, and theresults are shown in Fig. 10. The width decreases with N,as we expected from the N dependence of the minigap sizeshown in Fig. 1.[1] A. Chaves, J. G. Azadani, H. Alsalman, D. R. da Costa, R.Frisenda, A. J. Chaves, S. H. Song, Y. D. Kim, D. He, J. Zhou,A. Castellanos-Gomez, F. M. Peeters, Z. Liu, C. L. Hinkle,S.-H. Oh, P. D. Ye, S. J. Koester, Y. H. Lee, P. Avouris, X.Wang, and T. Low, Bandgap engineering of two-dimensionalsemiconductor materials, npj 2D Mater. Appl. 4, 29(2020).[2] S. 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