Design and Investigation of Double Gate Field Effect Transistor Based H2 Gas Sensor Using Ultra-Thin Molybdenum Disulfide

In this article, a low-power hydrogen (H2) gas sensor has been proposed using a two-dimensional (2D) material based Double Gate Field Effect Transistor (2D-FET). It is imperative to highlight that the conventional three-dimensional (3D) materials cannot be scaled down to an ultra-low dimension due to the presence of dangling bonds, surface roughness scattering etc. This creates a major challenge in developing low-dimensional sensors for next generation sensing and computing. In this context, we have developed an extensive simulation model, which articulates the physical phenomena behind a catalytic metal gate-based hydrogen gas sensor using a 2D-FET. A 5 nm thin Molybdenum disulfide (MoS2) film has been used as the channel material for the proposed 2D-FET based gas sensor. The sensor has been modelled by emphasizing on the catalytic metal (Palladium) gate approach, where the work function of the gate metal deposited on top of the channel region varies after the absorption of the hydrogen gas. Moreover, the Technology Computer Aided Design (TCAD) based gas sensor model has been developed by considering a change in the pressure of H2 gas as well. We have also highlighted the effect of Metal/MoS2 contact on sensor performance. In terms of the performance, a maximum threshold voltage (Vth) shift of 100 mV has been obtained against a gas pressure of 10−10 torr, whereas the maximum percentage of change in ION/IOFF is 100. Lastly, the authors have shown the thermal noise characteristics of the gas sensor.


Introduction
Field effect transistors (FETs) are extensively used and closely packed to develop logic gates or any other integrated circuit for the last two decades. These devices are also developed to sense different gas molecules [1] at room temperature and have gained a lot of popularity in the research community. Low power consumption, CMOS compatibility, reconfigurability etc. make a FET based gas sensor efficient and attractive. It must be mentioned that the change in the metal (gate) work function against the adsorption of the gas molecules is the backbone of the FET based gas sensors, where the dipole generation changes the work function of the metal [2]. In addition, the change in the metal work function gets reflected on the threshold voltage of the FET, which shifts significantly. For the past few years, there have been multiple gas sensor models reported in the literature with an emphasis on different FET architectures. A gate-all-around nanowire junctionless transistor was proposed to work as a hydrogen gas sensor based on the catalytic metal gate approach [2]. Similarly, the scientists have also proposed an alternative to the MOSFET based gas sensors, where they have considered Tunnel FETs (TFETs) to minimize the short channel effects and to reduce the sub-threshold slope of the device [3]. It is imperative to say that planar MOSFET, gate all-around MOSFET [4], TFET [5] based gas sensors have shown a lot of promise, but all these devices are prone to scaling challenges as most of them are made of 3D materials [6]. On the other hand, to design and develop low-dimensional nanoelectronic devices for next generation sensing primitives, we need semiconducting materials that can be thinned down even to the atomic scale. It is to be noted that the 2D materials [7] have gained a lot of attention in the vast area of semiconductor devices owing to the atomically thin body, which also opens an opportunity for aggressive scaling of the device dimension. Moreover, the 2D materials such as the transition metal dichalcogenides (TMDs) are immune to surface roughness scattering as there are no dangling bonds present in the material [8], which makes them an ideal choice in terms of developing low-dimensional FETs for ultra-low power sensing/circuit applications [9,10] and non-von-Neumann computing [11].
In this paper, we have tried to articulate the gas sensing behavior of a MoS 2 based double gate FET by considering the catalytic metal gate approach. It is imperative that pressure plays a crucial role in changing the electrical characteristics of the device as it changes the work function of the gate metal. After the metal (Pd) gate is exposed to the H 2 gas, a decomposition of the gas molecules take place at the metal surface and then the disassociated molecules diffuse into the metal gate. Moreover, an electrical dipole layer gets generated at Pd/HfO 2 interface due to the adsorption of the gas molecules into the gate metal and thus the metal work function changes accordingly. In this context, we have evaluated the performance of the proposed device in terms of shift in threshold voltage and I ON /I OFF ratio. Furthermore, we have also depicted the potential distribution along the channel and the density of states.
In addition, we have also included the effects of a Schottky contact between MoS 2 and source/drain metal (Ag) contacts on the sensor performance for different gas pressures in our simulation framework.

Device Description and Simulation Methodology
In this article, we have tried to evaluate the electrical performance of a 2D-FET as a hydrogen gas sensor, and the transistor schematic is depicted in Fig. 1(a). A palladium (Pd) gate metal is used to sense the hydrogen gas molecules with a work function (ϕ m ) of 5.22 eV. The gate metal is deposited on top of a high-k oxide stack, where a 1 nm SiO 2 is the low-k dielectric layer, and the high-k dielectric layer is a 2 nm HfO 2 . Moreover, a 5 nm thin MoS 2 film has been considered as the channel material and the length of the channel is 10 nm. It must be mentioned that the MoS 2 film is intrinsic here with a carrier concentration of 10 14 atoms/cm 3 . Figure 1(a) shows the dipole formation mechanism at and near the Pd/ HfO 2 interface after the adsorption of the gas molecules. It must be noted that the hydrogen gas molecules undergo a significant amount of dissociation and adsorption at the gate metal surface and therefore some of the hydrogen atoms diffuse through the gate metal, which ultimately forms the dipole at and near the interface followed by a change in the metal work function. In this context, the change in the metal work function has been shown in Fig. 1(b) as a function of the hydrogen gas pressure. Moreover, the metal work function reduces as we increase the pressure due to the increased surface coverage of the hydrogen gas on the metal surface. Thus, it is observed that the |Δϕ m | or |ΔWF| increases with increasing gas pressure [1]. In this work, the 2D-FET has been simulated using the SILVACO ATLAS TCAD tool [10] at room temperature. The carrier transport mechanism in the 5 nm thin MoS 2 channel has been captured through NEGF simulations. Furthermore, the Schrodinger-Poisson equation is generally coupled with the NEGF formalism for extracting the electron density and eventually current [10]. In addition, the material parameters have been defined in ATLAS to develop the simulation framework, where the electron affinity of 5 nm thin MoS 2 is 4.0 eV, electron and hole effective mass is 0.52m o and 0.64m o . Also, the permittivity of MoS 2 is 11 and the bandgap is 1.6 eV [12]. The NEGF model used in our work has been calibrated [13] here to capture the carrier transport as well as the MOS electrostatics, which has been considered by the Schrodinger-Poisson solver coupled with NEGF.

Fabrication Process Flow
To start with, the 2D-FET can be fabricated over a conventional SiO 2 /Si substrate. For the deposition of bottom gate metal, sputtering must be used to deposit palladium (Pd) and should be patterned using e-beam lithography. Atomic layer deposition (ALD) technique should be used to grow the bottom gate dielectric stack (HfO 2 /SiO 2 ). Moreover, the 5 nm thin MoS 2 can be mechanically exfoliated [14] on to the bottom gate dielectric stack of HfO 2 / SiO 2 followed by e-beam lithography and dry etching using SF 6 to pattern the channel region. Furthermore, the ALD process should be used to grow the top gate dielectric stack followed by sputtered palladium as the top gate metal. Finally, the top gate metal can be patterned using e-beam lithography.

Results and Discussions
In this article, we have assessed the electrical characteristics of the proposed 2D-FET based H 2 gas sensor based on the catalytic metal gate approach, where the absorbed gas molecules on the palladium gate metal, cause a modulation in the work function of the metal.
Here, the potential distribution has been shown in Fig. 1d along the channel for different Δϕ m values. It has been depicted in Fig. 1c that the maximum change in ϕ m is close to 120 meV, when the gas pressure (P) is 10 −10 torr. The potential distribution shows that with an increase in the Δϕ m , the surface potential also increases at and near the channel region. Moreover, the relative change is almost 15% when P is 10 −10 torr with respect to no gas molecules absorbed. The electric field distribution has been depicted in Fig. 1e for different Δϕ m values. In this case, the maximum electric field near the source/ channel and drain/channel interface has increased with an increase in the Δϕ m , where the work function (ϕ m ) of the Pd metal has reduced with an increase in the gas pressure. It is a known fact that, the electric field is nothing but a differential quantity of the surface potential and thus the electric field profile follows the slope of the surface potential. Figure 2a shows the transmission probability in linear and log scale across the filled energy levels and it illustrates that for different Δϕ m , there is a clear transition in the transmission probability, and it attains a lower energy level as ϕ m reduces after the gas molecules are absorbed at the metal surface. Moreover, the relative change in the occupied energy levels with a specific transmission probability is not very significant for different Δϕ m . Furthermore, the variation in the density of states (DOS) has been shown with respect to the energy levels at source, channel and drain regions of the 2D-FET. It must be noted that the change in the DOS as a function of occupied energy levels depicts the modulation in the band gap (E G ) and carrier density across the 2D-FET. Figure 2b shows the change in density of states for different Δϕ m , where a reduction in the metal work function reduces the filled energy level of the first sub-band that reduces the E G of MoS 2 .
Here, the transfer characteristics has been shown in Fig. 3(a) for different gas pressures (P = 10 −14 , 10 −12 and 10 −10 torr etc.) at a drain-to-source voltage or V DS of 0.2 V. It has been already shown in Fig. 1(c) that the metal work function, ϕ m , changes with the change in the gas pressure. We have assessed that ϕ m reduces gradually as the gas pressure increases from 10 −15 torr to 10 −10 torr due to catalytic reactions between the gas and the metal. The threshold voltage of the 2D-FET reduces with an increase in the gas pressure as shown in Fig. 3(b). Moreover, the I ON /I OFF ratio reduces significantly with an increase in the gas pressure as the off-state current (I OFF ) increases as ϕ m goes down as shown in Fig. 3(b). It must be noted that the on-state current of the 2D-FET does not get affected largely by the catalytic reaction between metal and the gas as the change in ϕ m is less as a function of the gas pressure. Furthermore, the transfer characteristics of a 2D-FET is expected to get affected by the interface trap charges (N it ) localized at and near the SiO 2 / MoS 2 interface due to defect states. Figure 3(c) shows that the transfer characteristics has shifted significantly due to the trapped charges (positive) and the threshold has reduced by 400 mV, when N it is 5 × 10 12 /cm 2 before the absorption of any gas molecules at the metal surface. Furthermore, the I ON /I OFF ratio has also shifted significantly by 7 orders of magnitude as shown in Fig. 3(d) against the variation of N it from 1 × 10 11 to 5 × 10 12 /cm 2 . Additionally, the variation in the transfer characteristics, threshold voltage and I ON /I OFF ratio has also been illustrated in Fig. 4(a-c) for different gas pressures to validate the sensing characteristics against the variation of N it . Figure 5(a) shows the threshold voltage sensitivity (S Vth ) as a function of both gas pressure (P) and interface trap charges (N it ). The maximum percentage of S Vth is nearly 100. In addition to this. The change in the I ON /I OFF ratio has also been considered as a sensing metric and the maximum percentage of S ION/IOFF is 100 for P = 10 −10 torr as shown Fig. 5(b). Although most of the previously reported FET (MOSFET or TUNNEL FET) based gas sensors have shown high sensitivity values while sensing H 2 , NH 3 or NO 2 , but the channel materials used in those devices do suffer from either quantum confinement [15] or surface roughness scattering [16] or both. In an ultra-thin Si based FET, the quantum confinement phenomena play an important role as it increases the effective band gap of silicon and thus, we observe a decrement in the current. Most of the previously published papers on FET based gas sensors have not really considered the effect of metal/semiconductor contact while evaluating the sensing behavior. In a 2D-FET based gas sensor, the interface between the MoS 2 and the source/drain metal contacts plays a crucial role in the carrier injection mechanism [17] and thus can govern the sensing behavior as well. It must be noted that the MoS 2 /metal interface is immensely affected by the Fermi level pinning [18] phenomena near the CB (conduction band) of MoS 2 as shown in Fig. 6(a). As we know that, the formation of a Schottky barrier (SB) takes place due to the difference between the metal (source/drain) ϕ mc and the electron affinity (χ) of the semiconductor and in our case the Schottky barrier height (Φ SBH ) is roughly 0.3 eV as ϕ mc is 4.3 eV. Moreover, the selection of the source/drain metal contacts plays a pivotal role in determining the amount of carrier injection and metals with low work functions would be a better. Figure 6(b) shows the surface potential distribution across the channel for different Δϕ m . We can say that the maximum change in the potential value is around 0.1 V by considering the SB effect. Figure 6(c) shows the transfer characteristics of the 2D-FET, and the on-state current has reduced a bit due to the Φ SBH of 0.3 eV compared to Fig. 3(a). Furthermore, the change in the threshold voltage is 85 mV for a Δϕ m of 100 meV, whereas it was 100 mV in Fig. 5(a) without the SB effect. Therefore, we can say that it is imperative to carefully consider the SB effect in 2D-FET and assess the sensor performance. However, if the ϕ mc is low, then we can minimize the Φ SBH further and carrier injection will be more. Thus, it is very much crucial to consider this non-ideal effect while designing a 2D-FET based gas sensor [19]. Figure 7 shows the thermal noise characteristics of the 2D-FET for different gas pressures against the variation of V GS . Thermal noise analysis of a FET based gas sensor is extremely crucial as it dictates the noise immunity of the device and depicts a clear picture of the thermally generated (carrier to carrier scattering in the channel) noise characteristics, which can have a significant impact on the electrical performance of the FET based gas sensor. It is quite evident that the S I, Thermal reduces with an increase in the V GS . As we increase the pressure of the gas, it results into a change in the gate metal work function and the S I, Thermal reduces. In addition, the thermal noise characteristics of the 2D-FET based gas sensor have been evaluated in presence of fixed interface trap charges at the SiO 2 /MoS 2 interface as shown in Fig. 8(a-c) for different gas pressures. Moreover, the S I, Thermal changes (reduces) significantly as N it changes from 1 × 10 11 /cm 2 to 5 × 10 12 /cm 2 .
It must be mentioned that the demonstration of a hydrogen gas sensor through TCAD simulation is to establish and validate the catalytic metal gate approach in presence of a 2D material as the channel, where the work function of palladium (Pd) changes after the absorption of hydrogen gas molecules. Many experimental demonstrations [20,21] have shown that Pd is an ideal candidate to sense hydrogen gas molecules and thus for a proof of concept we had decided to perform extensive simulations to sense hydrogen by using a 2D-FET with Pd metal gate [22]. Furthermore, it can be said that by using the catalytic metal gate approach we can design any gas sensor apart from a hydrogen sensor [23] as it an ubiquitous method. In addition, it must be highlighted that Fig. 9 shows the relative sensitivity against different gases by considering different gate metals for P = 10 −10 torr. In our case, we have depicted the sensitivity metric against H 2 , PH 3 , NH 3 and O 2 , where Pd offers the highest sensitivity in terms of sensing H 2 . In addition, we would like to highlight that the sensitivity of the 2D-FET based hydrogen gas sensor increases as we thin down the channel material (MoS 2 ) to an atomic scale as shown in Fig. 10(a). It must be mentioned that the sensitivity increases in case of a monolayer MoS 2 , which attributes to the increasing gate control over the channel [24]. However, the maximum change in the sensitivity for P = 10 −10 torr is 30%, where P is the pressure of the gas. On the other hand, the sensitivity of the 2D-FET based hydrogen gas sensor decreases as we reduce the channel length of the device as shown in Fig. 10(b). In our work, the fundamental building block of the sensor is the catalytic reaction between the gas and the gate metal. Thus, the sensitivity reduces by 75% as the effective area of the gate metal gets shorten P = 10 −10 torr. Note that, the gate length here is the same as the channel length and a larger gate length device can absorb a greater number of gas molecules compared to its shorter counterparts, which ultimately enhances the sensitivity of gas sensor.
It is quite well known that in all TMDC based 2D-FETs, the metal/MoS 2 (source/drain and semiconductor) interface is Schottky in nature, where the carrier transport relies on the type (low or high work function) of the contact. In our case, it is very important to assess the performance of the 2D-FET based gas sensor as a function of the gas pressure and Schottky contact. As shown in Fig. 6(a), the Schottky barrier height at the metal/MoS 2 interface does not change as the gas pressure changes. Figure 11(a-b) shows the contour plot of electron current density for P = 10 −15 torr and P = 10 −10 torr, where the Schottky barrier height is 0.3 eV. It must be highlighted that the distribution of the current due to electron transport does not change significantly throughout the channel against the variation of the gas pressure. However, the current density profile shows both edge and vertical injection of carriers into the channel from the source contact. Thus, it can be inferred that the impact of gas pressure on the Schottky contact is largely insignificant and the pivotal reason behind the change in sensitivity is the catalytic reaction between the gate metal and the gas molecules. Furthermore, if we vary the source/drain contact metals, then a significant change in sensitivity can be overserved as shown in Fig. 12.
In most of the 2D-FETs, the source/drain metal contacts play a pivotal role in deciding the nature of the carrier  transport. It must be noted that the MoS 2 /metal interface is immensely affected by the Fermi level pinning phenomena near the CB (conduction band) of MoS 2 as shown in Fig. 6(a) and the pinning phenomena appears as the deciding factor as far as the carrier injection is concerned. In our work, we have demonstrated the effect of different contact metals on the sensor performance at P = 10 −10 torr, and it is evident that metals (source/drain) with higher work function reduces the sensitivity as shown in Fig. 12. The reduction in the sensitivity attributes to the increase in the Schottky barrier height as we increase the metal work function [25]. However, the relative change in the sensitivity is about 41% as a function of the variation in metal work function. Besides, the surface morphology of the MoS 2 /metal interface cannot be captured in a commercial TCAD simulator.

Conclusion
In this article, we have tried to evaluate the electrical performance of a 2D-FET as a hydrogen gas sensor. One of the reasons behind selecting a 5 nm thin MoS 2 film as the channel material is the area efficiency as we can thin down a MoS 2 film up to the atomic scale and it does not suffer from surface roughness scattering or any quantum mechanical effect. The proposed 2D-FET has been modelled using SIL-VACO TCAD and the catalytic metal gate approach helped us to realize the gas sensing phenomenon. The maximum threshold voltage shift is 100 mV after the variation of the gas pressure. Moreover, we have tried to include the effect of interface trap charges and investigated the change in the electrical characteristics of the device. Furthermore, the study of the Metal/MoS 2 contact (source/drain) was included in the paper to highlight the effect of the Schottky barrier height and how we can minimize the barrier height to have more amount of carrier injection. Lastly, the thermal noise characteristics have also been depicted to highlight the effect of thermally generated noise on the sensor performance.

Author Contributions
The authors have investigated a Double Gate Field Effect Transistor Based H 2 Gas Sensor Using Ultra-Thin Molybdenum Disulfide in this work. All the authors have contributed to this work.
Funding The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

Data Availability
The presented work requires only the published research papers in the area.

Ethics Approval Yes
Informed Consent Not applicable.

Consent for Publication Yes
Research Involving Human Participants and/or Animals Not applicable.