1. Introduction

Atomic thick two-dimensional (2D) layered materials, such as semi-metallic graphene and semiconductive transition metal dichalcogenides (TMDCs), have emerged as an attractive candidate for future electronic and optoelectrical materials^[1-6]. Among them, molybdenum disulphide (MoS₂) is a typical member of TMDCs and considered as a promising candidate for various device applications, mainly due to its prolific, thickness-dependent band structures^[7-10]. The single-gated field-effect transistors (SG-FETs) based on MoS₂ exhibit excellent carrier mobility (~ 200 cm²/(V·s)), high current on/off ratio (> 10⁸), and low subthreshold swing approaching the fundamental thermal limit at room temperature^[2]. The short channel effects (SCE) can also be suppressed due to the ultra-thin channel body^{[7, 11]}.

Since the bandgap size is dependent on the MoS₂ layer number^[12-14], bilayer (BL) or multilayer (ML) MoS₂ tend to achieve higher mobility to carry larger driving current than that of monolayer MoS₂. However, the BL or ML-MoS₂ suffer from the degradation of SS and the current on/off ratio due to weaker channel electrostatic control. To overcome such a problem, the dual-gated (DG) structure, similar to that of Fin-FET technology, provides better electrostatic control over the channel region and is more achievable for 2D-TMDCs^[15-18]. Liu et al. achieved a back-gate mobility of up to 517 cm²/(V·s) and an on/off ratio higher than 10⁸ based on SiO₂, Al₂O₃ as the back-gated and top-gated dielectric^[19]. Our previously reported results based on a DG-FET with symmetrical back and top gates also indicate that the DG structure is able to modulate the threshold voltage (V_TH) and SS by tuning back and top gates separately, and a superior channel current (I_D) modulation can be achieved under the DG gating^[20-22]. Nevertheless, the charge transport and current distribution influenced by DG structure have not been systematically discussed in TMDCs devices.

Here, we successfully fabricate the MoS₂ DG-FETs with symmetric back gate (BG) and top gate (TG) based on monolayer and multilayer MoS₂ films. The thickness-dependent charge transport in our MoS₂ DG structure is revealed by a four-probe electrical measurement which excludes the contact influence, and TCAD simulation shows that the impact of quantum confinement effect exists in thin MoS₂ sheet sandwiched by the DG. Such effect attenuates with larger thickness, but still exist in a 5-nm-thick channel. The temperature-dependent electrical measurement of our device also indicates that transport of multilayer MoS₂ DG-FET is in the phonon-limited transport regime, while single layer MoS₂ device shows typical Coulomb impurity (CI) limited regime.

2 Device structure and material characterization

The cross-sectional schematic of MoS₂ DG-FET is depicted in Fig. 1(a). The fabrication process for such devices starts from the deposition of a 200-nm-thick Al₂O₃ layer by atom layer deposition (ALD, MNT-100-4) on a heavily doped Si substrate, which acts as a BG dielectric layer. Then multilayer MoS₂ flakes are mechanically exfoliated on top of Al₂O₃, and a typical optical microscopic image is shown in Fig. 1(b). Uniform and rectangular shaped MoS₂ sheets are selected for subsequent device fabrication. Raman characterization (laser excitation wavelength of 514 nm) is then carried out to confirm the layer number and crystalline quality, as shown in Fig. 1(c). To avoid lithography contamination, electrical contacts (5 nm Ti/30 nm Au) are patterned using a stencil mask technique^[23]. Immediately after the contact deposition, another layer of 200-nm-thick Al₂O₃ is deposited by ALD as TG dielectric, followed by the formation of TG electrodes by traditional photo-lithography, metal evaporation, and lift-off. Electrical transport measurements are performed under an ambient condition with a semiconductor analyzer (Agilent, B1500a). Temperature-dependent measurement was carried out in a cryogenic vacuum probe-station.

The field-effect mobility μ is a crucial factor to characterize the FET performance. For most TMDCs-based FETs, the effective value of μ is mainly governed by the contact rather than the channel itself^{[24, 25]}. In order to isolate the intrinsic mobility, we compensate for this effect by utilizing a four-terminal structure to exclude the contact effect. The upper graph of Fig. 1(d) is an optical image of our four-terminal device and the lower graph is a schematic diagram where the two inner voltage probes V₁ and V₂ are used to gauge the voltage drop. Then the four-terminal conductivity ${\sigma }_{4\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{b}}=\dfrac{{I}_{\mathrm{D}}}{{V}_{1}-{V}_{2}}\dfrac{L}{W}$, where I_D is the channel current and L and W are the length and width of the MoS₂ channel inside the inner voltage probes, respectively.

3   Experimental result and discussion

The measured σ_4prob as functions of BG, TG and DG modes are shown in Fig. 2(a). It is noted that results from BG and TG modes are highly coincident due to their symmetric gating capability, while a weak mismatch at negative gate voltage region can also be observed, which may result from their different dielectric-MoS₂ interfaces. As for the BG, MoS₂ is directly transferred on to the pre-deposited Al₂O₃, while for the TG, the interface quality degrades because of the absence of dangling bonds on MoS₂ for deposition of Al₂O₃.

It also shows that DG mode displays an improved channel electrostatic control than that of BG or TG. To further illustrate the gate modulation by BG and TG, a 2D contour plot of σ_4prob as functions of V_BG and V_TG is then plotted in Fig. 2(b). Such 2D diagram shows parallel diagonal contours with constant current, and the slope of these contours line is approximately 1, indicating that the BG and TG exhibit the same capability to modulate the channel, since the oxidation layer capacitance of the back gate and top gate is nearly symmetrical (C_BG /C_TG ≈ 1).

For SG structure, the field-effect (FE) mobility can be estimated by $\mu =\dfrac{1}{e{C}_{\mathrm{o}\mathrm{x}}}\dfrac{\mathrm{d}\sigma }{\mathrm{d}{V}_{\mathrm{G}}}$, where C_ox is the gate capacitance per unit area (40 nF/cm² for 200 nm of Al₂O₃), V_G is the gate voltage, and e is the elementary charge. While in the case of a symmetric DG structure and considering top and bottom surfaces of MoS₂ as parallel channels, we can estimate that the total conductivity σ’_DG = σ_BG + σ_TG. Since C’_ox-DG ≈ 2C_ox, we expect that the quantity μ’_DG = (μ_BG + μ_TG)/2 will be equal to μ_DG estimated by the σ_DG–V_DG curve. However, it appears that directly measured μ_DG is generally larger than μ’_DG, which indicates the inadequacy of this parallel channel model. We then use Δμ_DG = (μ_DG – μ’_DG)/μ’_DG to quantify the mobility enhancement of dual gating, and plot in Fig. 2(c) Δμ_DG and μ_DG as functions of the channel thickness. It is noted that both device mobility and Δμ_DG reach a maximum with the MoS₂ thickness in the range of 2–6 nm, and such thickness-dependent μ_DG deviates from previously reported results with only BG^{[24, 26, 27]}, indicating a different carrier transport mechanism in our DG-FETs.

Depending on the channel thickness, there is a competition of multiple mechanisms in our MoS₂ DG-FETs: 1) larger current carrying ability in thicker channels, but with considerable interlayer resistance^[24]; 2) current redistribution due to the DG induced quantum confinement effect; 3) electrical transport exposed to extrinsic Coulomb scattering from high-k dielectrics (e.g. Al₂O₃, HfO₂) and interface for ultra-thin channels. Therefore, the experimental results exhibit their overall competitional effects. While the first and the third factors may have a negative effect on the mobility, we now focus on the quantum confinement effect, which may avoid the interfacial scattering and enhance the carrier mobility.

To ravel the impact from quantum confinement effect, the carrier density, and distribution of the DG-FETs are then simulated by using the van Dort model, the 1D Schrödinger equation, the density gradient model, and the modified local-density approximation (MLDA). The van Dort model computes the impact of electric field normal to the channel interface on the carrier density modification due to the quantization. Based on the energy band structures in the channel, the 1D Schrödinger equation was solved self-consistently with the Poisson equation. The eigenvalues and wave functions for electrons and holes were obtained with consideration of multi valleys in conduction and valence bands. The density gradient model added the quantum correction to the carrier distribution at interfaces in the device by introducing the reciprocal thermal energy, mass-driving term, and the smoothed potential^[28]. In this model, the bandgap narrowing effect and apparent band-edge shifts caused by multistate configurations were involved. The MLDA model calculates the distribution of confined carriers near the dielectric/channel interface. In our simulation, the multi valley properties of conduction and valence bands were considered in MLDA model.

Figs. 3(a) and 3(b) compare the quantum-confinement impact on the simulated carrier redistribution in SG (V_BG  = 10 V) and DG (V_BG  = V_TG  = 10 V) structures. In the DG structure, quantum confinement effect is rather prominent, it repulses carriers away from dielectric-MoS₂ interfaces and confines carriers inside the channel, which can suppress phonon and Coulomb scattering at interfaces and contribute to the mobility improvement. On the opposite, the carriers in the SG structure are pushed towards one side of MoS₂, amplifying the interface scattering. Fig. 3(c) shows the calculated carrier distribution in MoS₂ DG device with a series of channel thicknesses, by considering quantum confinement effect. It is noticed that the impact of quantum confinement effect attenuates with larger thickness but still exist in a 5 nm thick channel.

Thus, a complete scenario for thickness dependence of MoS₂ DG-FET can be: thicker MoS₂ carries current larger but with less quantum confinement effect, and there are also trade-offs including large interlayer resistance and screening effect than weakens the gate control. For practical applications of MoS₂ FETs, considering critical parameters including μ, SS and current on/off ratio, a layer thickness in the range of 2–6 nm would be ideal by achieving overall satisfying μ, SS and current on/off ratio^[21], which is competitive comparing to best SOI^[29].

We then investigate the temperature-dependent electrical properties of our MoS₂ DG-FETs. Fig. 4(a) shows the temperature-dependent transfer curve from a multilayer MoS₂ device (~ 5 nm). The channel current increases when temperature decreases, while the threshold voltage V_TH hardly shifts when lowering the temperature. In the 4-terminal device architecture, mobility extraction is more accurate, as shown in Fig. 4(b). The mobility in a multi-layer MoS₂ DG-FET is as high as 763 cm²/(V·s) (n ≈ 10¹³ cm^–2) at 125 K (plotted by red point) and can be fitted by T^–γ for T > 100 K with γ = 2.5, which is in good agreement with theoretically predicted value (γ between 1.52 and 2.6)^{[30, 31]}. This indicates that our multilayer MoS₂ DG-FET is in the phonon-limited transport regime. While the temperature-dependent mobility of a monolayer MoS₂ device (grey points) shows typical CI limited regime, especially at low temperature. The CI limited mobility (μ_CI) can be well fitted by our calculation (plotted by gray dash) considering screening effect by surrounding dielectrics^{[32, 33]} (15-nm-thick HfO₂ for this device) with n ≈ 10¹³ cm^–2 and impurity density N_l ≈ 2 × 10¹³ cm^–2. Such difference can also originate from the quantum confinement effect but a more detailed investigation is necessary to achieve an in-depth understanding in the future.

4. Conclusion

We reported a systematic investigation of carrier transport in MoS₂ DG-FETs with a variation of MoS₂ channel thickness. DG structure provides better electrostatic control for the MoS₂ FETs. Moreover, quantum confinement plays an important role in the charge transport, as for a certain thickness of MoS₂, confinement of the charge in the center of the channel under DG mode reduces the scattering and thus boosts the mobility compared to single gating of a similar thickness layer. The TCAD simulation considering quantum confinement reveals that the impact of quantum confinement effect attenuates with larger thickness but still exist in a 5 nm thick channel. Furthermore, the phonon-limited transport regime and CI limited regime were revealed in multi-layer MoS₂ DG-FETs and single layer MoS₂ by temperature-dependent transfer curves, respectively. Such device architecture together with similar results can be extended to other TMDCs based devices.

Acknowledgements

This work was supported by the National Key Research and Development Program of China (2016YFA0203900, 2018YFA0306101), the National Natural Science Foundation of China (Grant No. 91964202), and Shanghai Municipal Science and Technology Commission (18JC1410300).