Tunneling transport of mono- and few-layers magnetic van der Waals MnPS$_3$

We have investigated the tunneling transport of mono- and few-layers of MnPS3 by using conductive atomic force microscopy. Due to the band alignment of indium tin oxide/MnPS3/Pt-Ir tip junction, the key features of both Schottky junction and Fowler-Nordheim tunneling (FNT) were observed for all the samples with varying thickness. Using the FNT model and assuming the effective electron mass (0.5 me) of MnPS3, we estimate the tunneling barrier height to be 1.31 eV and the dielectric breakdown strength as 5.41 MV/cm.

exception of the High-Tc superconductor Bi2Sr2CaCu2O8+d. 5,6 Without citing numerous contributions magnetic materials have made over past many decades, if not centuries, to the fundamental physics as well as the industrial applications, the magnetic vdW systems, once discovered, will form an invaluable part of applications in fields like spintronics. 7 And then, there is huge potentials yet untapped when it is used in tandem with other vdW materials as components of vdW heterostructures. 8 Thus it is an interesting and welcome development to see the recent entry of new magnetic vdW materials to the field in the name of transition metal phosphorus tri-chalcogenide (TMPX3). One of the big advantages with TMPS3 is that it can host several transition metal elements at the TM sites with correspondingly diverse physical properties: TM = Mn, Fe, Co, and Ni. A passing note, nonmagnetic Zn and Cd at the TM site also form in the same phase. Different TM elements lead to different magnetic ground states and varying transition temperatures although all of them exhibit an antiferromagnetic ordering of one type or another with the transition temperature around 80 -150 K. 9 For instance, MnPS3 has an antiferromagnetic order of type II below TN = 78 K. 10 Moreover, one can also replace S by Se while keeping the same crystal structure, adding more flexibility to the choice of materials. This diversity of different physical properties in these materials will turn out to be extremely useful from a materials' point of view when it comes to actual applications. More importantly, successful exfoliation has been recently demonstrated down to monolayer of these newly discovered vdW materials. [11][12][13] With the successful initial works, it now needs further in-depth studies of its physical properties.
So far all the initial characterization has been made by using Raman and AFM, leaving many of the physical properties literally unexplored. For example, there has been no report of the transport characteristics of few-layer thick flakes of TMPX3, let alone monolayer although it is an essential step for future device applications. To measure current through ultrathin nanostructures such as thin oxide layers 14,15 , molecules 16 , and vdW materials 17,18 , conductive atomic force microscopy (C-AFM) has become an instrument of choice. The imaging mode and the spectroscopic mode of C-AFM have been proven extremely useful for studying electronic properties on nanoscale.
Especially, C-AFM is now an invaluable tool for mechanically exfoliated materials due to the small sample size of often microns or smaller. In this paper, we report on the tunneling transport properties of several exfoliated MnPS3 flakes with thickness varying from monolayer to a few tens of layers by the spectroscopic mode of C-AFM. Using these data, we estimated several key parameters of MnPS3 down to monolayer such as a tunneling barrier height and a dielectric breakdown strength.
In order to optimize the optical contrast between mono-layer MnPS3 and Si substrate, we deposited 70 nm of transparent conductive indium tin oxide (ITO) on top of Si substrates: from our simulation we found this 70 nm thickness to give the maximum contrast between the substrate and the sample. All our single crystal samples of MnPS3 were synthesized by a chemical vapor transport method: we put a quartz ampoule containing the raw materials into a horizontal 2-zone furnace with a temperature difference of 780 ℃ (hot zone) and 730 ℃ (cold zone). Details of the synthesis conditions can be found in literature [11]. Using these crystals and scotch tape, we exfoliated several samples with varying thickness from mono to a few tens of layers onto the substrate. We then carefully screened different parts of the samples by optical microscope and the thickness is confirmed by topological scans as shown in Figures 1(a) and 1(b). We found that thin MnPS3 flakes are stable in air and no sign of degradations has been observed by optical and AFM images for a week when kept inside a desiccator after exfoliation. Topological and current scans were performed by C-AFM (Asylum Research Cypher S ORCA Conductive AFM) with a Pt-Ir coated Si tip (Nanosensors PPP-NCHPt). During the I-V measurement of the ITO/MnPS3/Pt-Ir tip junction, bias voltage was applied to the substrate with the tip kept grounded. All measurements were performed within 4 hours after cleaving the samples.
We show the typical optical and topological images of mono-to 6 layers MnPS3 in Figures 1(a) and 2(b). As one can see in the figures, atomically flat MnPS3 was successfully isolated and the flake size is found to be bigger than 1 μm. The optical image was subsequently obtained using a closed aperture stop to enhance the contrast and each individual flakes are clearly distinguishable from one another in the images. The profile line in Figure 2(b) also shows that the thickness changes along the dashed line with the numbers representing the estimated thicknesses (nm) of mono-, bi-, and tri-layer flakes. Layer numbers were then determined by using the interlayer distance (0.65 nm) of MnPS3, 19 and they are labeled accordingly in Figure 1(c). We note that the measured thickness is slightly larger than the expected value probably because of a thin water layer or a difference in the interaction force of tip with the substrate and MnPS3 flake as discussed in Ref. [11]. A similar observation has been often made in other mechanically exfoliated vdW materials like graphene, 1,20 TMDCs, [21][22][23] and NiPS3. 11,13 It is rather common to observe carrier transport in a metal/insulator/metal junction being affected by a band alignment in accordance with the Schottky-Mott theory. 24  Therefore, we can determine the barrier height ΦB from a difference between an electron affinity s of MnPS3 and a work function of Pt-Ir (5.4 eV). Due to the large barrier height at the surface of MnPS3, we expect that the thick flakes are almost insulating as shown in Figure 1(c). In fact, our data show that even mono-layer MnPS3 shows a very high resistance value while the ITO-coated substrate shows good conductivity during the fast current scan (1 Hz, 256 lines).
In Figure 2(a) we present some representative I-V spectroscopic data with various layer numbers of MnPS3 flakes, which exhibits the typical Schottky junction behavior. For example, there is clear linear behavior at a low-bias voltage region while the current increases rapidly above the breakdown voltage. We comment that small asymmetric I-V characteristics observed in Figure 2(b) probably arises from the asymmetric band alignment of the junction in Figure 1(d). The breakdown voltages in the positive bias are little larger than that in the negative bias region because the barrier height of the tip is higher than that for the ITO. We also show in Figure 2(c) the dielectric breakdown voltage as a function of thickness, at which the current reaches a typical value of 1 nA. 25 From the slope in the linear fitting, we can determine the dielectric breakdown strength of thin MnPS3 flake as 5.41 MV/cm. This value is smaller than that of SiO2 (8-10 MV/cm) 26 and h-BN (7.89 MV/cm) 17 , but it is a large enough value to make MnPS3 a good insulating vdW material down to monolayer.
We also display the I-V characteristics for mono-, bi-, and tri-layer MnPS3 in Figure 2 where Aeff and d are an effective contact area and thickness of MnPS3, respectively: q, me, and h are electron charge, free electron mass, and Plank constant, respectively. Thus, Eq. (1) naturally 6 explains the exponential decay of the tunneling conductance as a function of d. According to our experiment, this direct tunneling is almost suppressed for samples thicker than 6 layers.
On the other hand, at high bias voltage the I-V curve does no longer show a linear dependency.
Instead, as the tunneling barrier is deformed by the applied high electric field, the field-emitted electrons flow across the sample and the current becomes a non-linear function of applied voltage.
This behavior can be understood by a Fowler-Nordheim tunneling (FNT) theory. In this case, the current can be expressed in the following formula: 14-18,28 * exp where m* is the effective electron mass for MnPS3. Because of the lack of experimental and theoretical results for the effective mass of MnPS3, we used m* = 0.5 me for our analysis to be followed below. For comparison, a similar value of the effective mass (0.56 me) was theoretically found for MnPSe3 29 and the effective mass of MoS2 is also known to be 0.35 me for mono-layer and 0.53 me for bulk. 18 Given the same crystal structure for both compounds, we anticipate that the real value of the effective mass of MnPS3 may not be that different from MnPSe3. With this assumption, Eq.
(2) can be re-arranged as follows: Using this equation, we show the plot of ln(I(V)/V 2 ) versus 1/V from mono-to 9 layers MnPS3 in Figure 3(a). Linear dependency observed in this plot indicates that the tunneling current at high bias voltage can be well explained by the FNT theory as expected.
Using the measured thickness of the sample and the assumed effective mass, we can calculate the effective contact area and the tunneling barrier height from the linear fitting shown in Figure  3(a). To get an independent verification of this approach and the values obtained, we have also separately carried out a direct FNT fitting by using Eq.
(2) with the raw I-V data as shown in Figure   3(b). A good agreement between the two approaches gives us further confidence in the analysis we adopted here (see inset of Fig. 3(c)). The thus calculated barrier heights between the Pt-Ir tip and MnPS3 are plotted as a function of thickness in Figure 3(c). From this curve, we obtain the barrier height value of 1.31 eV (0.01) for samples thicker than 9 layers, which gets decreased with decreasing the layer number. This value is larger than that between Pt-Ir tip and MoS2 (0.64 eV) 18 and smaller than that between Pt tip and h-BN (3.07 eV). 17 Our estimate of electron affinity is 4.09 eV for MnPS3. We note that a similar reduction of the barrier height was previously reported for MoS2 18 , which may well come from the contribution of the direct tunneling in few layer thick samples. We further remark that a small mismatch was found in Figure 3(b) between the fitting curve and the experimental data just before the breakdown voltage. We think that it is most likely to come from the direct tunneling that decreases as the layer number gets increased. Therefore, the FNT model must overestimate the current for our thinner samples, and this results in the underestimated barrier height. The inset of Figure 3(c) shows the linear dependence of tunneling barrier term ФB 3/2 d with a number of layers. From this analysis, we get an averaged effective contact area from mono-to 6 layers around 3.76 nm 2 , which is a reasonable value considering the actual tip radius of 7 nm. 18 In summary, we report the tunneling transport of mono-and few layers MnPS3 exfoliated on top of ITO coated Si substrate. By using C-AFM, we could study the thickness dependence of the tunneling transport from a few tens of layers down to monolayer. From the I-V spectroscopy, we  A slight deviation from the fitting at low voltage is most likely to be due to the direct tunneling and it gets suppressed as the thickness increases. (c) Calculated barrier height from both linear fit and direct fit. The barrier height was calculated as 1.31 eV (0.01) for samples thicker than 9 layers, whereas for samples thinner than 6 layers the barrier height decreases as the number of layer decreases. Inset of (c) shows linear dependency of tunneling barrier term (ФB 3/2 d) on the number of layer.