Introduction

Integrated circuits (ICs) have dramatically changed people’s lives in the past few decades. Nowadays, almost all electronic products possess a high packing density with ICs of numerous functions. In this era of rapid development of ICs, electronics performance has made significant progress in terms of size, efficiency, and cost. Nevertheless, the development of next-generation electronics is a vital issue and has received widespread attention in recent years. With the 2004 discovery of graphene, an extended honeycomb network of single carbon atoms, research on two-dimensional (2D), layered electronics has opened a window for transcending the current limit of Moore’s Law1. Electronics constructed with channels layered in semiconducting transition metal dichalcogenides, such as MoS2, are among the most promising candidates, with related research showing substantial advances2,3,4,5,6. To develop reliable 2D electronics, the electrical mechanisms of layered materials in contact with metals or metal-like graphene have been studied7,8,9. Previous authors have already demonstrated the existence of a Schottky barrier at the interface of the metal and the layered material, where charge carriers overcome this barrier at higher temperatures and show thermally-assisted tunnelling at lower temperatures7. However, it has now been experimentally proven that the small work function difference between graphene and layered materials allows graphene as a transistor contact to reduce the contribution of contact resistance and then form an Ohmic contact, achieving superior device performance10,11,12,13,14. Recently, these transistors with layered conducting channels connected in-plane have been surpassed by van der Waals heterostructures, formed by the layer-by-layer integration of various 2D materials in the vertical direction. This development has opened a whole new class of materials in condensed matter physics, some of which are being recognized as building blocks for the framework of novel three-dimensional (3D) artificial structures14,15,16,17,18. Pioneering achievements using these vertically stacked heterostructures have been demonstrated in diverse applications, such as logic devices19, atomically thin p-n junctions20, van der Waals memristors21, tunnelling transistors22, and even multifunctional electronics17,19,23. Although atomically thin 2D electronics present rosy prospects for the future, we still lack a complete understanding of performance difference as well as charge transport for carrier passing through parallel/vertical conducting channels24,25,26,27.

In the present work, a layered MoS2 van der Waals heterostructure with thin graphite acting as contacting electrodes was designed and fabricated by mechanical exfoliation and dry-transfer methods. The unique configuration, with two drains and one source, can conduct through both parallel and vertical channels in the same MoS2 flake. This configuration thus provides insight into charge transport mechanisms and shows the differences in electrical properties between the different transport directions. We emphasize that the use of thin graphite as contacting electrodes reduces the impact of contact resistance on electronics and further exposes the electrical contribution of interlayer resistance between adjacent MoS2 layers in the vertical conducting channel. Through a careful analysis of temperature dependence of current-voltage (Ids − Vds) behaviors in our layered MoS2 heterostructure, electrical performance was systematically compared between parallel and vertical channels. Unlike the electrical contribution from contact potential in the previous works16,28, here the electrical properties of charge transport are dominated mainly by the MoS2 conducting channels. We found that the operation of the MoS2 heterostructure under a drain-source voltage (Vds) of 25 mV was characterized by a current on/off modulation of ~106 for parallel conducting channels but less than 102 for vertical conducting channels. In addition, mobility variation with decreasing temperature displayed obvious upward and downward trends, respectively, for parallel and vertical electronics. This pattern suggests the domination of interlayer resistance in the vertical conducting channel. In addition to quasi-static measurements, dynamic current fluctuation measurements were also carried out to re-address the influence of interlayer resistance. Although a clear 1/f noise dependence was observed for both parallel and vertical channels, an additional resistor contribution was found for charge transport in the vertical direction, strongly indicating the existence of interlayer resistance. The MoS2 heterostructure used in this work offers a simple configuration to probe charge transport in both parallel and vertical conducting paths. The experimental observations not only provide a basic understanding of electrical properties for layered electronics, but also pave the way for using van der Waals heterostructures to develop future 3D artificial configurations.

Results

Device structures

Figure 1(a) schematically illustrates the parallel and vertical MoS2 electronics, stacked with one multilayer MoS2 channel and three thin graphite electrodes. Thanks to both the particular device configuration and the thin graphite composition of the electrodes, it is possible to ignore the contribution of contact resistance and to more precisely explore transport differences between parallel and vertical channels in the same device. To modulate the position of the MoS2 Fermi level as well as carrier concentrations, a heavily doped Si substrate was used as the back-gate electrode (Vbg). Figure 1(b) shows an optical image of the van der Waals heterostructure device on a Si/SiO2 substrate. The shape of the MoS2 channel is outlined in solid white, while those of the thin graphite (Gr) electrodes are outlined in dashed orange. In the process of device fabrication, thin graphite 1 (Gr1) was first mechanically exfoliated and transferred on a heavily n-doped silicon substrate with a silicon oxide surface coating of 300 nm thickness; this surface served as the bottom electrode for the MoS2 channel. The MoS2 flake was then stacked on top of the Gr1 using the same technique. After that, thin graphite 2 (Gr2) and graphite 3 (Gr3) were sequentially stacked on the MoS2 channel without overlapping, acting as the source/drain electrodes for the parallel MoS2 channel. The overlapping portion of the Gr1/MoS2/Gr2 sandwich sets the position of the vertical electronics. For the purpose of characterizing electrical mechanisms, several outside pads were finally pattered on the top of Gr1, Gr2, and Gr3, using standard electron-beam lithography, followed by thermal evaporation of Ti/Au (5/50 nm thick). In this work, because of the limited density of states and weak electrostatic screening effect of thin graphite16, the MoS2 Fermi level should be effectively modulated through the back-gate electrode. Typical thicknesses of the MoS2 channel and thin graphite electrodes were further determined by atomic force microscopy (AFM). From the line profile of the AFM image, as shown in Fig. 1(c), the thickness of the MoS2 channel used in this work was about 6 nm, which is consistent with the height of a 9-layer MoS2 stack, while the thickness of thin graphite electrodes was determined to be 7 nm. Noticed that the thickness for Gr1, 2 and 3 is intentionally selected to be similar for making an easy comparison in electrical properties.

Figure 1
figure 1

(a) Schematic diagram of the layered MoS2 van der Waals heterostructure with a circuit diagram overlaid. (b) Optical microscopic image of the MoS2 heterostructure, composed of three thin graphite (outlined in dashed orange lines), a MoS2 channel (outlined in solid white lines), and Ti/Au metal electrodes. (c) Typical thickness of the MoS2 conducting channel and thin graphite as measured by atomic force microscopy line profile.

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Electrical characteristics

Ids − Vds curves for both parallel and vertical electronics were examined at room temperature and are shown in Fig. 2(a) and its inset, respectively. The observed linear features of the Ids – Vds curves in both parallel and vertical electronics strongly imply that contact resistance at the metal-semiconductor interfaces can be neglected, allowing electrical properties as well as carrier transport to be attributed mainly to the MoS2 conducting channel. It is emphasized that the contact resistance brings out by the Y-function method to be 3.4 × 104 Ω/μm, which is much smaller than the total resistance of 6.25 × 105 Ω/μm. Injected carriers can easily pass through from one thin graphite electrode to the other due to the formation of the Ohmic contact between the electrodes and the layered MoS2 channel. It should be emphasized that the adoption of a four-probe method to double-check the behavior of the Ohmic contact is too difficult to be realized because of the use of mechanical exfoliation. Ids − Vbg relationships for the electronics under different Vds values are further provided in Fig. 2(b) on a logarithmic scale. Under modulation of Vbg values, the parallel MoS2 electronics exhibit n-type behavior. The current on/off ratio at Vds = 25 mV can reach ~106, which fully matches the requirements for use as a switch. In striking contrast, the vertical MoS2 electronics were characterized at room temperature by almost Vbg-independent Ids variation, or a slight increase with the increase of Vbg. In addition, because the ~6 nm vertical conducting channel is much shorter than the 1.5 μm parallel channel, the current density in the vertical channel is significantly larger by 1–2 orders of magnitude at room temperature. Unlike the use of parallel electronics for switching, such Ids variations in vertical electronics depend only on Vds rather than Vbg (shown in the inset of Fig. 2(b)), and thus show potential for future low-range amplification electronics. In comparison with the previous reports for similar vertical electronics16,28, such the weak Vbg dependence is attributed the absence of tunable Schottky barriers on the contacts. For easy comparison of device performances, effective carrier mobility (μ) and subthreshold swing (SS) were respectively estimated using conventional equations \(\mu =(d{I}_{ds}/d{V}_{bg})\cdot (L/{C}_{ox}\cdot W\cdot {V}_{ds})\) and \(SS=d{V}_{bg}/d(\log \,{I}_{ds})\),29 where L and W are the channel length and width, respectively, which has been determined by its optical images. Cox of 1.15 × 10−8 F∙cm−2 is the capacitance per unit area between the MoS2 channel and the gate electrode. Notice that although the equation for carrier effective mobility is built for planar transistors, the value estimated from the vertical electronics can be taken as a direct and easy comparison for device performances in between. Respective carrier mobilities for parallel and vertical electronics at room temperature were about 37.06 and 0.31 cm2∙V−1∙s−1. Such lower effective mobility is extracted in the vertical MoS2 electronics, suggesting the existence of interlayer resistance between adjacent MoS2 layers in the vertical conducting channel. In this channel, carriers have to consume more energy for charge transport, leading to a redundant voltage drop as well as scattering. Although the vertical channel is much shorter than the parallel channel, the electrical contribution of interlayer resistance still significantly restricts Ids variations, dominating the transport mechanism. Respective SS values of ~1.21 and ~1000 V/decade were estimated for parallel and vertical electronics. The unreasonably large SS value for the vertical electronics, consistent with observations seen in the Ids − Vbg curves (Fig. 2(b) inset), again indicates that the inherent contribution from interlayer resistance causes inevitable charge transport scattering and weakens electrostatic control. The performance difference between the two device configurations provides a valuable perspective for the development of complex, stacked 2D electronics.

Figure 2
figure 2

(a) Ids − Vds curves for parallel and vertical (inset) conducting channels at various Vbg values from −60 V to 60 V. (b) Ids − Vbg curves for parallel and vertical (inset) conducting channels at various Vds values from 5 mV to 25 mV. (c) Schematic illustration of charge transport for parallel (i) and vertical (ii) conducting channels of MoS2 electronics, while the shading denotes the main path.

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Figure 2(c) illustrates the corresponding transport mechanisms for (i) parallel and (ii) vertical electronics. The blue areas denote the main path of current flow in the conducting channel, while its color shading denotes the intensity thereof. Charge transport in the parallel channel can be explained by a resistor network model based on Thomas-Fermi charge screening and interlayer coupling30. A charge distribution exists in the layered MoS2 channel, and the bulk of the charge distribution in the parallel electronics moves to the top layers with increasing Vbg. In on-current states (as shown in part (i) of Fig. 2(c)), carriers are transported mostly on the top and mutual-parallel layers of MoS2 channels. Thus, interlayer resistance does not dominate the transport mechanism, allowing layered electronics to represent their intrinsic electrical properties. As for the vertical electronics, carriers must substantially overcome the obstruction of interlayer resistance, resulting in device performance reduction, as shown in part (ii) of Fig. 2(c).

Temperature dependent electrical properties

Analysis of Ids − Vds characteristics of electronics at room temperature alone cannot provide a complete understanding of charge transport or elucidate the microscopic nature of inherent resistance formation31,32. Therefore, investigations of temperature dependence were also carried out. Figure 3(a,b) reveal Ids − Vds and Ids − Vbg behaviors at different temperatures for both electronics in different configurations. With decreasing temperature, the Ids − Vds curves for both electronics maintain linear form, again implying the formation of an ignored contribution of Schottky barrier at the thin graphite-MoS2 interface. Because of the semiconducting nature of the MoS2 channel, Ids values at a fixed Vbg and Vds for both electronics gradually decrease with decreasing temperature. As for Ids − Vbg behaviors (Fig. 3(b)), the current on/off ratio for parallel electronics indicates weak temperature dependence, consistent with the previous report33. On the other hand, the current on/off ratio for vertical electronics increases with decreasing temperature. At 100 K, the current on/off modulation can even reach ~102 for the vertical electronics (see Fig. 3(c)). To provide further insight into the performance difference of both electronics, temperature-dependent mobilities were extracted from 300 K down to 80 K (Fig. 3(d)). It has to be emphasized again such the estimation in mobilitis can offer an opportunity for rough comparison in device performance for both electronics. For parallel electronics, the temperature dependence was characterized by a maximum value around 200–180 K. Above 200 K, a strong decrease in mobility from the maximum value of ~54 cm2∙V−1∙s−1 was observed, attributable to the domination of electron-phonon scattering at higher temperatures. This part of the mobility trend was further fitted by the \(\mu \sim {T}^{-\gamma }\) formula, where the exponent depends on the dominant phonon scattering mechanism. From the fit, the value of \(\gamma \sim 1.43\) is in high agreement with theoretical predictions for a layered MoS2 channel34. Below 180 K, we found a decrease in mobility, consistent with transport being limited by scattering from charged impurities35. As for the vertical MoS2 electronics, mobility drastically decreased with decreasing temperature, due to presumable interlayer resistance in the conducting paths. This behavior is akin to the formation of potential barriers between adjacent MoS2 layers, which increases charge scattering. At higher temperatures, carriers with higher energy can easily surpass these barriers and exhibit higher mobility. Based on the present evidence, we conclude that, in parallel MoS2 electronics, charge transport is dominated by the layered, in-plane 2D channel, which causes effective utilization of 2D material advantages.

Figure 3
figure 3

(a) Ids − Vds curves at different temperatures for parallel and vertical (inset) conducting channels at Vbg = 60 V. (b) Ids − Vbg curves for parallel and vertical (inset) conducting channels at Vds = 25 mV. (c) Current on/off modulation as a function of temperature for parallel and vertical conducting channels. (d) Temperature-dependent mobilities for parallel and vertical (inset) conducting channels.

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Low-frequency noise

To go further in characterizing charge transport, we turned to low-frequency (LF) noise measurements using a Programmable Point-Probe Noise Measuring System (3PNMS) with a noise floor ≈ 1 × 1027 A2⋅Hz−1. These measurements, traditionally used in exploring dynamic carrier fluctuations in silicon-based field effect transistors36,37,38, have been widely adopted as a sensitive tool for identifying the influence of interface conditions, particularly for nanoscale electronics. To better understand the differences in transport mechanisms between parallel and vertical MoS2 electronics, we conducted LF noise measurements for both parallel and vertical electronics (Fig. 4). For parallel and vertical MoS2 electronics, respectively, typical power spectral densities of current fluctuation, SI, are shown in Fig. 4(a,b), as a function of the frequency at different applied Vbg. The Vds value was set at 40 mV while the frequency was swept from 101 to 104 Hz. It should be noted that to effectively reduce the contribution of thermal energy, the measurement temperature was kept at 100 K and monitored. The dashed line, showing an ideal 1/f dependence, is provided for comparison. Because of the obvious current on/off modulation, the SI for the parallel electronics can be significantly increased, with increasing Vbg, from the system noise floor of 1 × 10−27 up to 10−21 A2∙Hz−1 at 10 Hz. This behavior is consistent with Ids − Vbg observations shown in Fig. 3(b). The LF noise data were then analyzed using the formula \({S}_{I}\propto {I}_{ds}^{\alpha }/{f}^{\beta }\), where α and β are the exponent parameters for current and frequency, respectively39,40. Analytical values of β for both electronics approached unity closely, indicating the uniform distribution, in energy and space, of intrinsic structural defects such as sulfur vacancies in the conducting MoS2 channels. These defects lead to trapping/detrapping fluctuations of current flow. In contrast, analytical values of α differed between parallel (~2) and vertical (~1.5) electronics. The evidence used in determining the α values is shown in Fig. 4(b,c), where the SI value varies as a function of Ids across different frequencies. Such deviation from α = 2 in the vertical conducting path strongly implies that the existence of an additional resistance contribution incurs energy loss. As mentioned in the above discussion, thin graphite was used in the present study to form a free contact barrier at the thin graphite-MoS2 interface. Therefore, this additional contribution originates mainly from interlayer resistances. The SI value was further normalized by the square of the Ids value at different Vds values, as shown in Fig. 4(c,f) for parallel and vertical electronics, respectively. These plots clearly indicate that normalized SI cannot collapse into a single curve for the vertical electronics; this finding is consistent with the domination of LF noise by an additional resistor41, compared with LF noise in parallel electronics. By determining dynamic current fluctuations, LF noise expresses the difference between two-configuration electronics configurations while addressing the influence of interlayer resistance on charge transport.

Figure 4
figure 4

Power spectral densities of current fluctuation (SI) for (a) parallel and (d) vertical conducting channels as a function of frequency at 100 K. Dashed lines in (a,d) denote ideal 1/f dependence. (b,e) SI as a function of Ids at different frequencies for (b) parallel and (e) vertical conducting channels. Dashed lines in (b,e) denote the relationship \({S}_{I}\propto {I}_{ds}^{\alpha }\). (c,f) SI values normalized by the square of Ids at different Vds values for (c) parallel and (f) vertical conducting channels.

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Discussion

In conclusion, the vertical electronics displays almost Vbg independent Ids variation and lower mobility at room temperature, due to interlayer resistance between adjacent MoS2 layers in the vertical conducting channel. With decreasing temperature, mobility decreases from ~100 at 300 K down to ~10−2 at 100 K. Moreover, LF noise measurements in the vertical channel are consistent with an interlayer resistance contribution. Our study significantly provides fundamental information about electrical properties in layered 2D systems that will likely play an important role in the building of future electronics components as well as van der Waals stacking 3D artificial structures.