T-Channel Field Effect Transistor with Three Input Terminals (Ti-TcFET)

In this paper, a novel T-channel field effect transistor with three input terminals (Ti-TcFET) is proposed. The channel of a Ti-TcFET consists of horizontal and vertical sections. The top gate is above the horizontal channel, while the front gate and back gate are on either side of the vertical channel. The T-shaped channel structure increases the coupling area between the top gate and the front and back gates, which improves the ability of the gate electrodes to control the channel. What’s more, it makes the top gate have almost the same control ability for the channel as the front gate and the back gate. This unique structure design brings a unique function in that the device is turned on only when two or three inputs are activated. Silvaco technology computer-aided design (TCAD) simulations are used to verify the current characteristics of the proposed Ti-TcFET. The current characteristics of the device are theoretically analyzed, and the results show that the theoretical analysis agrees with the TCAD simulation results. The proposed Ti-TcFET devices with three input terminals can be used to simplify the complex circuits in a compact style with reduced counts of transistors compared with the traditional complementary metal–oxide–semiconductor/ fin field-effect transistors (CMOS/FinFETs) with a single input terminal and thus provides a new idea for future circuit designs.


Introduction
Because of short-channel effects, the size of metal-oxide-semiconductor (MOS) devices is seriously restricted. In order to continue Moore's law, many new device structures have been proposed, such as silicon-on-insulator metal-oxide-semiconductor field-effect-transistors (SOI MOSFETs) with a single-gate structure, fin field-effect transistor (FinFETs) with a double-gate structure [1], and tri-gate field effect transistors (FETs) [2], Ω-gate FETs [3], and Gate-All-Around (GAA)FETs with a multi-gate structure. Among these devices, FinFET has been widely used in chip fabrication since it can considerably improve the ability of the gate electrode to control the channel and thus suppress the short-channel effects.
Most of the multi-gate devices mentioned above have only one input terminal. However, previous studies have shown that designing a circuit with devices with multiple input terminals is more flexible and efficient than using single-input ones [4,5]. The two-input low-threshold FinFET device proposed in the literature [6][7][8][9][10] is equivalent to two parallel transistors, while the two-input high-threshold FinFET device is equivalent to two series transistors. Therefore, the circuit can be simplified to reduce the transistor count by using two-input low-threshold and high-threshold FinFETs, thus reducing power consumption and the chip area. If a device has more input terminals, it is possible to achieve more flexible and efficient circuit designs.
This paper proposes a novel T-channel field effect transistor with three input terminals (Ti-TcFET). The invented T-type channel structure allows the device to have three independent input gates: the top This paper proposes a novel T-channel field effect transistor with three input terminals (Ti-TcFET). The invented T-type channel structure allows the device to have three independent input gates: the top gate, front gate, and back gate. Because of the device structure with a T-type channel, the coupling areas among the top gate and the front and back gates are increased, which increases the control capability of the gates to the channel. This unique structure design brings a unique function in that the device is turned on only when two or three inputs are activated. Compared with traditional FinFETs with a single input terminal, the proposed Ti-TcFET devices with three input terminals can provide more flexible circuit realizations in a compact style. The proposed Ti-TcFET devices can be fabricated by adding only a small number of process steps on the basis of the current mainstream FinFET process.
This paper is organized as follows. In Section 2, the structure of the proposed device is introduced, and its device parameters are presented. The key processing steps of Ti-TcFET devices are also included in Section 2. In Section 3, the current characteristics of the device are theoretically analyzed, and Silvaco technology computer-aided design (TCAD) simulations are used to verify the accuracy of theoretical analysis. In Section 3, we illustrate how to carry out performance optimization for the proposed Ti-TcFET devices, and device performances are analyzed and evaluated in terms of turn-on and turn-off currents and switching current ratio. The compact circuits based on Ti-TcFET devices are also included in Section 3. We show that Ti-TcFET devices can be used to simplify complex circuits in a compact style with reduced transistor counts compared with the traditional complementary metal-oxide-semiconductor/ fin field-effect transistors (CMOS/FinFETs) with a single input terminal. Finally, the work of this paper is summarized in the last section.

Device Structure and Description
This section takes an N-type Ti-TcFET as an example to present the structure and parameters of the proposed device. We also give the fabrication process of Ti-TcFET devices in this section. Figure 1a shows a 3D diagram of the N-type Ti-TcFET, while Figure 1b is a cross-sectional diagram of the N-type Ti-TcFET. As seen in Figure 1a, the device has three independent input gates, termed the top gate, front gate, and back gate. From Figure 1b, we can see that the T-type channel of the Ti-TcFET is divided into horizontal and vertical sections. HFin1 and TSi1 are the fin height and thickness of the vertical channel, respectively, while HFin2 and TSi2 are the fin height and thickness of the horizontal channel, respectively. By adjusting the fin height HFin2 of the horizontal channel, the contact area between the top gate and the horizontal channel can be changed, thus changing the coupling strength between the top gate and the front and back gates. The gate-to-channel control capability can be varied by adjusting the gate work function and the thickness Tox of the high-K dielectric hafnium(IV) oxide (HfO2).   In this work, SiO 2 is used as the substrate material for the device. The channel material is silicon, and the gate oxide material employs high-K dielectric HfO 2 . The device parameters of the Ti-TcFET are shown in Table 1. The optimum values of H Fin1 T Si1 , H Fin2 , T Si2 , T OX (HfO 2 thickness), and L g (channel length) are listed in Table 1. The doping concentrations N drain and N source of the source and drain regions are 2 × 10 20 cm −3 , and the channel doping concentration N channel is 1 × 10 16 cm −3 . The gate work function Φ m of the N-type Ti-TcFET is set to 4.95 eV, while the gate work function of the P-type Ti-TcFET is selected to be 4.55 eV.

Key Processing Steps for the Ti-TcFET Device
On the basis of a traditional SOI-independent FinFET process [11], Ti-TcFET devices can be fabricated by adding a few processing steps. A key fabrication process is shown in Figure 2.
Micromachines 2020, 11, x FOR PEER REVIEW 3 of 15 In this work, SiO2 is used as the substrate material for the device. The channel material is silicon, and the gate oxide material employs high-K dielectric HfO2. The device parameters of the Ti-TcFET are shown in Table 1. The optimum values of HFin1 TSi1, HFin2, TSi2, TOX (HfO2 thickness), and Lg (channel length) are listed in Table 1. The doping concentrations Ndrain and Nsource of the source and drain regions are 2 × 10 20 cm −3 , and the channel doping concentration Nchannel is 1 × 10 16 cm −3 . The gate work function Φm of the N-type Ti-TcFET is set to 4.95 eV, while the gate work function of the P-type Ti-TcFET is selected to be 4.55 eV.

Key Processing Steps for the Ti-TcFET Device
On the basis of a traditional SOI-independent FinFET process [11], Ti-TcFET devices can be fabricated by adding a few processing steps. A key fabrication process is shown in Figure 2. (c) the extra part of gate oxide was etched back; (d) a Si3N4 gate electrode mask was deposited and patterned; (e) the gate pattern was etched into the Si3N4 and through the TiN to form the gate electrodes; (f) the high-K dielectric was deposited by using atomic layer deposition (ALD) processing; (g) a suitable horizontal channel structure was established by using smart-cut processing; (h) the high-K dielectric layer was deposited by using ALD processing; (i) the gate pattern was etched into the silicon and through the TiN to form the top gate electrodes. (f) the high-K dielectric was deposited by using atomic layer deposition (ALD) processing; (g) a suitable horizontal channel structure was established by using smart-cut processing; (h) the high-K dielectric layer was deposited by using ALD processing; (i) the gate pattern was etched into the silicon and through the TiN to form the top gate electrodes.
A SiO 2 film was firstly grown as a mask for the silicon fin etching, and then the hard-mask and SOI layers were etched down to the buried oxide layer to produce the bodies of the devices, as shown in Figure 2a [11]. A high-K dielectric layer was deposited by using atomic layer deposition (ALD) processing. Next, chemical mechanical polishing (CMP) processing was used to remove the extra part of gate oxide above the top of the fin, as shown in Figure 2b. The extra part of gate oxide was etched back, and only the required part on the two sides of the fin remained, as shown in Figure 2c [11]. Thereafter, a Si 3 N 4 gate electrode mask was deposited and patterned, as shown in Figure 2d. The gate pattern was etched into the Si 3 N 4 and through the TiN to form the gate electrodes, as shown in Figure 2e. The high-K dielectric was deposited by using ALD processing, as shown in Figure 2f. In order to reduce the difficulty of the process, the horizontal channel and vertical channel were separated by HfO 2 , as shown in Figure 2g. Figure 2g shows how a suitable horizontal channel structure was established by using smart-cut processing. In order to establish the gate oxide layer of the top gate, the high-K dielectric layer was deposited by using ALD processing, as shown in Figure 2h. A Si 3 N 4 gate electrode mask was deposited and patterned, and finally, the gate pattern was etched into the silicon and through the TiN to form the top gate electrodes, as shown in Figure 2i.

Results and Discussion
In this section, the current characteristics of the device are theoretically analyzed by modeling the threshold voltage of Ti-TcFETs, and then Silvaco TCAD simulations are used to verify the accuracy of the theoretical analysis. The Lombardi constant voltage and temperature (CVT), Fermi-Dirac carrier statistics (FERMIDIRAC), Shockley-Read-Hall (SRH) models, and the Bohm quantum potential (BQP) models were considered in these TCAD simulations [12]. The performance optimizations for the proposed Ti-TcFET devices were carried out by selecting the channel thickness, gate oxide thickness, and gate work function, and device performances were evaluated in terms of turn-on and turn-off currents and switching current ratio. The several basic logic cells such as the "majority-not" [13,14], NOT-AND (NAND), and NOT-OR (NOR) logic cells, and the full adder realized by using the proposed Ti-TcFET devices are illustrated, showing that Ti-TcFET devices can be used to simplify complex circuits in a compact style with reduced transistor counts.

The Threshold Voltage of Ti-TcFET Devices
The Ti-TcFET device has three inputs. The threshold voltage of any gate is affected by the bias voltage of the other two gates because of the coupling effect among the three gates. In other words, the threshold voltage of a gate is a function of the voltages of the other two gates. Taking the threshold voltage of the top gate of the N-type Ti-TcFET as an example, the relationship between the threshold voltage and other gate voltages (front gate and back gates) is analyzed.
The relationship between the threshold voltage of the top gate and the bias voltages of the front gate and back gate can be measured by introducing the coupling coefficients γ top-gate and γ top-back [15,16], as shown in Equations (1) and (2).
where V THt is the threshold voltage of the top gate, V front-gate and V back-gate are the voltages of the front gate and back gate, respectively, C oxf , C oxb , and C oxt are the oxide capacitance of the front gate, back gate, and top gate, respectively, C si and T si are the body capacitance and thickness of the channel, respectively, and T oxf and T oxb are e thickness of the front and back gates, respectively.
TCAD simulation show that the threshold voltage V THt of the top gate is not completely linear to the bias voltages of the front and back gates. After considering the secondary effect, the threshold voltage V THt of the top gate can be written as Equation (3).
where V TH0 is the threshold voltage of the top gate when both V front-gate and V back-gate are at 0 V, and α and β are the fitting parameters. The threshold voltage of the top gate versus the voltages of the front gate and the back gate is shown in Figure 3. In Figure 3, the points are the threshold voltages of the Ti-TcFET device obtained by the TCAD simulations, while the lines are the theoretical calculation results obtained by Equation (3) in different voltages of the front and back gates. The results show that the theoretical formula of the threshold voltage agrees with the TCAD simulation results.
where VTH0 is the threshold voltage of the top gate when both Vfront-gate and Vback-gate are at 0 V, and α and β are the fitting parameters. The threshold voltage of the top gate versus the voltages of the front gate and the back gate is shown in Figure 3. In Figure 3, the points are the threshold voltages of the Ti-TcFET device obtained by the TCAD simulations, while the lines are the theoretical calculation results obtained by Equation As the size of nanoscale devices decreases, quantum mechanical effects will begin to affect device performance. The threshold voltage drift ΔVTH caused by the quantum mechanical effect can be written as follows [17]: where vT = kT/q is the thermal voltage-where k is Boltz constant, T is the thermodynamic temperature, and q is the electronic charge quantity-and S is the subthreshold swing of the device. ΔΨ is where Ψ QM S and Ψ

CL S
are the potential at the silicon-oxide interface when considering the quantum models and semi-classical models, respectively.
The Ti-TcFETs have been simulated considering both the Bohm quantum potential (BQP) models and semi-classical models. The threshold voltage of the device is reduced by 0.018 V when considering the BQP quantum compared with semi-classical models. Studies have shown that the amount of threshold voltage drift caused by quantum effects will become obvious when the channel silicon thickness is very thin (<2 nm) [18]. For undoped devices with a bulk silicon thickness (>4 nm), the threshold voltage drift caused by quantum effects is small [18]. As the size of nanoscale devices decreases, quantum mechanical effects will begin to affect device performance. The threshold voltage drift ∆V TH caused by the quantum mechanical effect can be written as follows [17]: where v T = kT/q is the thermal voltage-where k is Boltz constant, T is the thermodynamic temperature, and q is the electronic charge quantity-and S is the subthreshold swing of the device. ∆Ψ is where Ψ

QM S
and Ψ CL S are the potential at the silicon-oxide interface when considering the quantum models and semi-classical models, respectively.
The Ti-TcFETs have been simulated considering both the Bohm quantum potential (BQP) models and semi-classical models. The threshold voltage of the device is reduced by 0.018 V when considering the BQP quantum compared with semi-classical models. Studies have shown that the amount of threshold voltage drift caused by quantum effects will become obvious when the channel silicon thickness is very thin (<2 nm) [18]. For undoped devices with a bulk silicon thickness (>4 nm), the threshold voltage drift caused by quantum effects is small [18].

Drain Current of the Ti-TcFET
The drain current I D of the Ti-TcFET device can be expressed by Equation (6).
where I S and λ are fitting parameters. For short-channel devices, the range of λ is about 1.3 to 1.5 [19]. The drain current of the Ti-TcFET device versus the voltages of the top gate is shown in Figure 4, where V DS is 0.8 V, V front-gate is 0 V, and V back-gate changes from 0.2 V to 0.8 V. In Figure 4, the points are obtained by the TCAD simulations, while the lines are the theoretical calculation results of the drain current for different voltages of the top gate. The results show that the theoretical formula of the drain current agrees with the TCAD simulation results.

Drain Current of the Ti-TcFET
The drain current ID of the Ti-TcFET device can be expressed by Equation (6).
where IS and λ are fitting parameters. For short-channel devices, the range of λ is about 1.3 to 1.5 [19]. The drain current of the Ti-TcFET device versus the voltages of the top gate is shown in Figure  4, where VDS is 0.8 V, Vfront-gate is 0 V, and Vback-gate changes from 0.2 V to 0.8 V. In Figure 4, the points are obtained by the TCAD simulations, while the lines are the theoretical calculation results of the drain current for different voltages of the top gate. The results show that the theoretical formula of the drain current agrees with the TCAD simulation results.

Subthreshold Current of the Ti-TcFET
Referring to the literature [20,21], the subthreshold leakage current Isub of the Ti-TcFET device can be calculated by Equation (7) where Iw, m, b1, b2, and b3 are fitting parameters and n is subthreshold slope parameter. The drain current of the Ti-TcFET device versus the voltages of the top gate is shown in Figure  5, where VDS is 0.8 V, Vfront-gate is 0 V, and Vback-gate changes from 0 V to 0.5 V. In Figure 5, the points are obtained by TCAD simulations, while the lines are the theoretical calculation results of the drain current for different voltages of the top gate. The calculated subthreshold drains agree well with the simulated subthreshold current for Vtop-gate > 0.1 V.

Subthreshold Current of the Ti-TcFET
Referring to the literature [20,21], the subthreshold leakage current I sub of the Ti-TcFET device can be calculated by Equation (7): where I w , m, b1, b2, and b3 are fitting parameters and n is subthreshold slope parameter. The drain current of the Ti-TcFET device versus the voltages of the top gate is shown in Figure 5, where V DS is 0.8 V, V front-gate is 0 V, and V back-gate changes from 0 V to 0.5 V. In Figure 5, the points are obtained by TCAD simulations, while the lines are the theoretical calculation results of the drain current for different voltages of the top gate. The calculated subthreshold drains agree well with the simulated subthreshold current for V top-gate > 0.1 V.

Performance Optimization of the Ti-TcFET Devices
In order to obtain high-performance Ti-TcFET devices, the following two goals should be achieved. If only one gate is activated, the current should be as small as possible. If any two of the three gates are activated, the current should be as large as possible. In other words, the maximum turn-off current Ioff should be small and the minimum turn-on current Ion should be large. In this subsection, we study the influence of device size and parameters on device performance by changing the channel thickness, gate oxide thickness, and gate work function, and then select the optimized device size and parameters.
In order to achieve the first goal, Ti-TcFET devices should have a high-threshold voltage when only one gate is activated. The threshold voltage of a Ti-TcFET is approximated by Equation (8): where Vinv is a constant, Φm is the work function difference of the electrode and the silicon, QD is the channel depletion charge, Cox is the oxide capacitance of the front gate, back gate, and top gate, and V QM and V SCE are the threshold voltage increase caused by quantum-mechanical effect models and short-channel effects, respectively. From Equation (8), the threshold voltage of the device can be adjusted by selecting a suitable Φm and Cox.
In order to achieve the second goal, Ti-TcFET devices should have a low subthreshold slope, so that the device achieves a large turn-on current with a small turn-off current. The subthreshold slope S is given by Equation (9) where ψSi is the surface potential at the gate electrode. The subthreshold slope can be approximated by Equation (10 From Equation (10), we can get the relationship between the subthreshold slope S, channel thickness TSi, and gate oxide thickness Tox, which can be used to optimize the performances of Ti-TcFET devices.

Performance Optimization of the Ti-TcFET Devices
In order to obtain high-performance Ti-TcFET devices, the following two goals should be achieved. If only one gate is activated, the current should be as small as possible. If any two of the three gates are activated, the current should be as large as possible. In other words, the maximum turn-off current I off should be small and the minimum turn-on current I on should be large. In this subsection, we study the influence of device size and parameters on device performance by changing the channel thickness, gate oxide thickness, and gate work function, and then select the optimized device size and parameters.
In order to achieve the first goal, Ti-TcFET devices should have a high-threshold voltage when only one gate is activated. The threshold voltage of a Ti-TcFET is approximated by Equation (8): where V inv is a constant, Φ m is the work function difference of the electrode and the silicon, Q D is the channel depletion charge, C ox is the oxide capacitance of the front gate, back gate, and top gate, and V QM and V SCE are the threshold voltage increase caused by quantum-mechanical effect models and short-channel effects, respectively. From Equation (8), the threshold voltage of the device can be adjusted by selecting a suitable Φ m and C ox . In order to achieve the second goal, Ti-TcFET devices should have a low subthreshold slope, so that the device achieves a large turn-on current with a small turn-off current. The subthreshold slope S is given by Equation (9) [22]: where ψ Si is the surface potential at the gate electrode. The subthreshold slope can be approximated by Equation (10) [23]: From Equation (10), we can get the relationship between the subthreshold slope S, channel thickness T Si , and gate oxide thickness T ox , which can be used to optimize the performances of Ti-TcFET devices. Figure 6 shows the effect of channel thickness T si on current characteristics at V front-gate = 0 V and V back-gate = 0.8 V. When the voltage V top-gate of the top gate is set as 0.8 V, the two inputs of the N-type Ti-TcFET are at 0.8 V, and thus the device should be turned on. Its drain current is named as I on (turn-on current). When the voltage of the top gate V top-gate is 0 V, only one input of the Ti-TcFET is at 0.8 V, and thus the device should be turned off. Its drain current is named as I off (turn-off current). Figure 6 shows the effect of channel thickness Tsi on current characteristics at Vfront-gate = 0 V and Vback-gate = 0.8 V. When the voltage Vtop-gate of the top gate is set as 0.8 V, the two inputs of the N-type Ti-TcFET are at 0.8 V, and thus the device should be turned on. Its drain current is named as Ion (turn-on current). When the voltage of the top gate Vtop-gate is 0 V, only one input of the Ti-TcFET is at 0.8V, and thus the device should be turned off. Its drain current is named as Ioff (turn-off current).

Effect of Channel Thickness on Current Characteristics
From Figure 6, it ca be seen that as the channel thickness reduces from 6 nm down to 3 nm, Ion/Ioff (the switching current ratio) increases. From Equation (10), the subthreshold slope S of the devices reduces when the channel thickness TSi reduces. The results show that the TCAD simulations agree with the theoretical formula. In order to have enough Ion and an acceptable Ion/Ioff, the optimized TSi is set to 4 nm.  Figure 7 shows the effect of gate oxide thickness TOX on current characteristics at Vfront-gate = 0 V and Vback-gate = 0.8 V according to the TCAD simulations. As the gate oxide thickness TOX increases from 2.0 nm to 3.5 nm, Ion/Ioff increases. As shown in Equation (10), when the gate oxide thickness TOX increases, the subthreshold slope S of the Ti-TcFET devices decreases, so that Ion/Ioff increases. The results show that the theoretical formula agrees with the TCAD simulations. In order to have enough Ion and an acceptable Ion/Ioff, the optimized gate oxide thickness TOX is set to 3 nm.   From Figure 6, it ca be seen that as the channel thickness reduces from 6 nm down to 3 nm, I on /I off (the switching current ratio) increases. From Equation (10), the subthreshold slope S of the devices reduces when the channel thickness T Si reduces. The results show that the TCAD simulations agree with the theoretical formula. In order to have enough I on and an acceptable I on /I off , the optimized T Si is set to 4 nm. Figure 7 shows the effect of gate oxide thickness T OX on current characteristics at V front-gate = 0 V and V back-gate = 0.8 V according to the TCAD simulations. As the gate oxide thickness T OX increases from 2.0 nm to 3.5 nm, I on /I off increases. As shown in Equation (10), when the gate oxide thickness T OX increases, the subthreshold slope S of the Ti-TcFET devices decreases, so that I on /I off increases. The results show that the theoretical formula agrees with the TCAD simulations. In order to have enough I on and an acceptable I on /I off , the optimized gate oxide thickness T OX is set to 3 nm.

Effect of Gate Oxide Thickness on Current Characteristics
Micromachines 2020, 11, x FOR PEER REVIEW 8 of 15 Figure 6 shows the effect of channel thickness Tsi on current characteristics at Vfront-gate = 0 V and Vback-gate = 0.8 V. When the voltage Vtop-gate of the top gate is set as 0.8 V, the two inputs of the N-type Ti-TcFET are at 0.8 V, and thus the device should be turned on. Its drain current is named as Ion (turn-on current). When the voltage of the top gate Vtop-gate is 0 V, only one input of the Ti-TcFET is at 0.8V, and thus the device should be turned off. Its drain current is named as Ioff (turn-off current).

Effect of Channel Thickness on Current Characteristics
From Figure 6, it ca be seen that as the channel thickness reduces from 6 nm down to 3 nm, Ion/Ioff (the switching current ratio) increases. From Equation (10), the subthreshold slope S of the devices reduces when the channel thickness TSi reduces. The results show that the TCAD simulations agree with the theoretical formula. In order to have enough Ion and an acceptable Ion/Ioff, the optimized TSi is set to 4 nm.  Figure 7 shows the effect of gate oxide thickness TOX on current characteristics at Vfront-gate = 0 V and Vback-gate = 0.8 V according to the TCAD simulations. As the gate oxide thickness TOX increases from 2.0 nm to 3.5 nm, Ion/Ioff increases. As shown in Equation (10), when the gate oxide thickness TOX increases, the subthreshold slope S of the Ti-TcFET devices decreases, so that Ion/Ioff increases. The results show that the theoretical formula agrees with the TCAD simulations. In order to have enough Ion and an acceptable Ion/Ioff, the optimized gate oxide thickness TOX is set to 3 nm.   Figure 8 shows the effect of the gate work function on current characteristics at V front-gate = 0 V and V back-gate = 0.8 V according to the TCAD simulations. From Figure 8, it can be seen that as the gate work function Φ m increases from 4.85 eV to 5.00 eV, I off decreases. As shown in Equation (8), a high-threshold voltage can be achieved by increasing the gate work function Φ m , so that I off decreases. The results show that the theoretical formula agrees with the TCAD simulations. In order to reduce I off , the optimized gate work function is set to 4.95 eV.

Effect of Gate Work Function on Current Characteristics
Micromachines 2020, 11, x FOR PEER REVIEW 9 of 15 Figure 8 shows the effect of the gate work function on current characteristics at Vfront-gate = 0 V and Vback-gate = 0.8 V according to the TCAD simulations. From Figure 8, it can be seen that as the gate work function Φm increases from 4.85 eV to 5.00 eV, Ioff decreases. As shown in Equation (8), a high-threshold voltage can be achieved by increasing the gate work function Φm, so that Ioff decreases. The results show that the theoretical formula agrees with the TCAD simulations. In order to reduce Ioff, the optimized gate work function is set to 4.95 eV.

Drain-Induced Barrier Lowering (DIBL) and S of the Optimized Ti-TcFET Devices
The drain-induced barrier lowering (DIBL) can be calculated by using Equation (11): As shown in Equation (11), the DIBL is defined as the difference in threshold voltage when the drain voltage is increased. The drain current of the Ti-TcFET is shown in Figure 9 when Vfront-gate = 0 V and Vback-gate = 0.8 V. From Figure 9, the DIBL of the Ti-TcFET device is about 41.48 mV/V when Vfront-gate = 0 V and Vback-gate = 0.8 V. Our TCAD simulations show that the DIBL of the Ti-TcFET device is almost the same as the standard FinFET device when using the same device parameters.

Drain-Induced Barrier Lowering (DIBL) and S of the Optimized Ti-TcFET Devices
The drain-induced barrier lowering (DIBL) can be calculated by using Equation (11): As shown in Equation (11), the DIBL is defined as the difference in threshold voltage when the drain voltage is increased. The drain current of the Ti-TcFET is shown in Figure 9 when V front-gate = 0 V and V back-gate = 0.8 V. From Figure 9, the DIBL of the Ti-TcFET device is about 41.48 mV/V when V front-gate = 0 V and V back-gate = 0.8 V. Our TCAD simulations show that the DIBL of the Ti-TcFET device is almost the same as the standard FinFET device when using the same device parameters.
Micromachines 2020, 11, x FOR PEER REVIEW 9 of 15 Figure 8 shows the effect of the gate work function on current characteristics at Vfront-gate = 0 V and Vback-gate = 0.8 V according to the TCAD simulations. From Figure 8, it can be seen that as the gate work function Φm increases from 4.85 eV to 5.00 eV, Ioff decreases. As shown in Equation (8), a high-threshold voltage can be achieved by increasing the gate work function Φm, so that Ioff decreases. The results show that the theoretical formula agrees with the TCAD simulations. In order to reduce Ioff, the optimized gate work function is set to 4.95 eV.

Drain-Induced Barrier Lowering (DIBL) and S of the Optimized Ti-TcFET Devices
The drain-induced barrier lowering (DIBL) can be calculated by using Equation (11): As shown in Equation (11), the DIBL is defined as the difference in threshold voltage when the drain voltage is increased. The drain current of the Ti-TcFET is shown in Figure 9 when Vfront-gate = 0 V and Vback-gate = 0.8 V. From Figure 9, the DIBL of the Ti-TcFET device is about 41.48 mV/V when Vfront-gate = 0 V and Vback-gate = 0.8 V. Our TCAD simulations show that the DIBL of the Ti-TcFET device is almost the same as the standard FinFET device when using the same device parameters.  The drain current of the Ti-TcFET is shown in Figure 10 when V top-gate = V front-gate = V back-gate . From Figure 10, it can be seen that the subthreshold slope S of the Ti-TcFET devices is about 62.6 mV/dec. The TCAD simulations show that the subthreshold slope S of the Ti-TcFET device is also almost the same as the standard FinFET device when using the same device parameters.
Micromachines 2020, 11, x FOR PEER REVIEW 10 of 15 The drain current of the Ti-TcFET is shown in Figure 10 when Vtop-gate = Vfront-gate = Vback-gate. From Figure 10, it can be seen that the subthreshold slope S of the Ti-TcFET devices is about 62.6 mV/dec. The TCAD simulations show that the subthreshold slope S of the Ti-TcFET device is also almost the same as the standard FinFET device when using the same device parameters.

Scaling Factors of the Ti-TcFET Devices
The minimum turn-on current and maximum turn-off current are shown in Figure 11 as channel length Lg and fin height HFin scale down, where the scaling factor (SF) is set as 0.707. From Figure 11a, as the channel length Lg and fin height HFin scale down, the minimum turn-on current reduces slowly. From Figure 11b, as the channel length Lg and fin height HFin scale down, the maximum turn-off drain is almost a constant.

Performance Analysis of the Ti-TcFET Devices
The Ti-TcFET device has three input terminals, and each input terminal has two logic values with logic "1" (0.8 V) and logic "0" (0 V), so that the device has eight switching modes. Taking the N-type Ti-TcFET as an example, eight working modes are illustrated in Figure 12. When only one or fewer inputs are "1", the device is turned off, as shown in Figure 12a. In Figure 12a, there are four switching modes in the turn-off state. When two or three inputs are "1", the device is turned on, as shown in Figure 12b. In Figure 12b, there are also four switching modes in the turn-on state.

Scaling Factors of the Ti-TcFET Devices
The minimum turn-on current and maximum turn-off current are shown in Figure 11 as channel length L g and fin height H Fin scale down, where the scaling factor (SF) is set as 0.707. From Figure 11a, as the channel length L g and fin height H Fin scale down, the minimum turn-on current reduces slowly. From Figure 11b, as the channel length L g and fin height H Fin scale down, the maximum turn-off drain is almost a constant.
Micromachines 2020, 11, x FOR PEER REVIEW 10 of 15 The drain current of the Ti-TcFET is shown in Figure 10 when Vtop-gate = Vfront-gate = Vback-gate. From Figure 10, it can be seen that the subthreshold slope S of the Ti-TcFET devices is about 62.6 mV/dec. The TCAD simulations show that the subthreshold slope S of the Ti-TcFET device is also almost the same as the standard FinFET device when using the same device parameters.

Scaling Factors of the Ti-TcFET Devices
The minimum turn-on current and maximum turn-off current are shown in Figure 11 as channel length Lg and fin height HFin scale down, where the scaling factor (SF) is set as 0.707. From Figure 11a, as the channel length Lg and fin height HFin scale down, the minimum turn-on current reduces slowly. From Figure 11b, as the channel length Lg and fin height HFin scale down, the maximum turn-off drain is almost a constant.

Performance Analysis of the Ti-TcFET Devices
The Ti-TcFET device has three input terminals, and each input terminal has two logic values with logic "1" (0.8 V) and logic "0" (0 V), so that the device has eight switching modes. Taking the N-type Ti-TcFET as an example, eight working modes are illustrated in Figure 12. When only one or fewer inputs are "1", the device is turned off, as shown in Figure 12a. In Figure 12a, there are four

Performance Analysis of the Ti-TcFET Devices
The Ti-TcFET device has three input terminals, and each input terminal has two logic values with logic "1" (0.8 V) and logic "0" (0 V), so that the device has eight switching modes. Taking the N-type Ti-TcFET as an example, eight working modes are illustrated in Figure 12. When only one or fewer inputs are "1", the device is turned off, as shown in Figure 12a. In Figure 12a, there are four switching modes in the turn-off state. When two or three inputs are "1", the device is turned on, as shown in Figure 12b. In Figure 12b, there are also four switching modes in the turn-on state.
Micromachines 2020, 11, x FOR PEER REVIEW 11 of 15 Using the optimized parameters and device sizes listed in Table 1, the turn-on and turn-off currents of N-type and P-type Ti-TcFETs working in eight switching modes are listed in Table 2 and  Table 3, respectively.  Table 2 lists the turn-on current Ion and turn-off current Ioff of the N-type Ti-TcFET in the four turn-on modes and four turn-off modes, respectively. The normalized currents are listed in the rightmost column in Table 2. From Table 2, it can be seen that the maximum turn-off current among the four turn-off modes is 2.06 × 10 −8 A, while the minimum turn-on current among the four turn-on modes is 1.14 × 10 −5 A. In the worst case, Ion/Ioff (switching current ratio) is 553. In order to increase Ion/Ioff, some new materials such as ferroelectric materials and two-dimensional materials can be used. Ferroelectric materials can enhance the internal gate voltage through the negative capacitance effect, so that Ion/Ioff (switching current ratio) increases greatly and the subthreshold swing decreases below 60 mV/dec [24]. Two-dimensional (2D) semiconductors, such as transition metal dichalcogenides (TMDs), have the potential for ultra-scaled transistor technology beyond 10 nm node technology because of their atomically thin layered channel and low dielectric constant, which offer strong electrostatic control [25]. Table 2. The turn-on current and turn-off currents of the N-type Ti-TcFET.

State
Vtop  Table 3 shows the turn-on current Ion and turn-off current Ioff of the P-type Ti-TcFET in the four turn-on modes and four turn-off modes, respectively. The normalized currents are also listed in the rightmost column in Table 3. From Table 3, it can be seen that the maximum turn-off current among the four turn-off modes is 1.57 × 10 −8 A, while the minimum turn-on current among the four turn-on modes is 7.09 × 10 −6 A. In the worst case, the switching current ratio is 452. Using the optimized parameters and device sizes listed in Table 1, the turn-on and turn-off currents of N-type and P-type Ti-TcFETs working in eight switching modes are listed in Tables 2  and 3, respectively.   Table 3. The turn-on current and turn-off currents of the P-type Ti-TcFET.  Table 2 lists the turn-on current I on and turn-off current I off of the N-type Ti-TcFET in the four turn-on modes and four turn-off modes, respectively. The normalized currents are listed in the rightmost column in Table 2. From Table 2, it can be seen that the maximum turn-off current among the four turn-off modes is 2.06 × 10 −8 A, while the minimum turn-on current among the four turn-on modes is 1.14 × 10 −5 A. In the worst case, I on /I off (switching current ratio) is 553. In order to increase I on /I off , some new materials such as ferroelectric materials and two-dimensional materials can be used.

State
Ferroelectric materials can enhance the internal gate voltage through the negative capacitance effect, so that I on /I off (switching current ratio) increases greatly and the subthreshold swing decreases below 60 mV/dec [24]. Two-dimensional (2D) semiconductors, such as transition metal dichalcogenides (TMDs), have the potential for ultra-scaled transistor technology beyond 10 nm node technology because of their atomically thin layered channel and low dielectric constant, which offer strong electrostatic control [25]. Table 3 shows the turn-on current I on and turn-off current I off of the P-type Ti-TcFET in the four turn-on modes and four turn-off modes, respectively. The normalized currents are also listed in the rightmost column in Table 3. From Table 3, it can be seen that the maximum turn-off current among the four turn-off modes is 1.57 × 10 −8 A, while the minimum turn-on current among the four turn-on modes is 7.09 × 10 −6 A. In the worst case, the switching current ratio is 452.

Logic Cells Based on Ti-TcFET Devices
A single Ti-TcFET transistor can implement three input "majority-not" switch functions [26,27], and thus only one N-type Ti-TcFET and one P-type Ti-TcFET are needed to realize a "majority-not" logic cell, as shown in Figure 13a. From Figure 13a, the "majority-not" logic cell using traditional CMOS/FinFET devices needs 10 transistors. The transistor counts of the "majority-not" cell using the proposed Ti-TcFET devices is only one-fifth of that of the "majority-not" cell using traditional CMOS/FinFET devices, which shows that the proposed Ti-TcFET devices with three input terminals have a higher information processing capacity than traditional CMOS/FinFETs with a single input terminal.

Logic Cells Based on Ti-TcFET Devices
A single Ti-TcFET transistor can implement three input "majority-not" switch functions [26,27], and thus only one N-type Ti-TcFET and one P-type Ti-TcFET are needed to realize a "majority-not" logic cell, as shown in Figure 13a. From Figure 13a, the "majority-not" logic cell using traditional CMOS/FinFET devices needs 10 transistors. The transistor counts of the "majority-not" cell using the proposed Ti-TcFET devices is only one-fifth of that of the "majority-not" cell using traditional CMOS/FinFET devices, which shows that the proposed Ti-TcFET devices with three input terminals have a higher information processing capacity than traditional CMOS/FinFETs with a single input terminal. The Ti-TcFET devices can also be used to implement other logic gates in a compact style, such as NOR and NAND, as shown in Figure 13b and Figure 13c, respectively. For more complex logic circuits, such as a full adder, the circuit structure can also be simplified by using Ti-TcFET devices, as shown in Figure 14a. For comparison, Figure 14b shows the full adder using traditional CMOS/FinFETs. The Ti-TcFET devices can also be used to implement other logic gates in a compact style, such as NOR and NAND, as shown in Figure 13b,c, respectively. For more complex logic circuits, such as a full adder, the circuit structure can also be simplified by using Ti-TcFET devices, as shown in Figure 14a. For comparison, Figure 14b shows the full adder using traditional CMOS/FinFETs. The power consumption, delay, and power delay product of the one-bit full adder using Ti-TcFET devices and standard FinFET devices are compared in Table 4. From Table 4, the power consumption and power delay product of the one-bit full adder based on Ti-TcFET devices are smaller than standard FinFET devices, with an acceptable delay penalty.

Conclusions
In this paper, a novel T-channel field effect transistor with three input terminals (Ti-TcFET) is proposed. The T-channel structure increases the coupling area between the top gate and the front and back gates so that the device can realize the "majority-not" function well. By adjusting the gate work function, channel thickness, and the thickness of the gate oxide layer, the performance of the Ti-TcFET device is optimized. The results show that when the gate work function Φ of the N-type Ti-TcFET is 4.95 eV, TSi = 4 nm, and TOX = 3 nm, the minimum turn-on current Ion is 1.14 × 10 −5 A and the maximum turn-off Ioff is 2.06 × 10 −8 A, with the switching current ratio Ion/Ioff of 553. When the gate work function Φ of the P-type Ti-TcFET is 4.52 eV, TSi = 4 nm, and TOX = 3 nm, the minimum turn-on current Ion is 7.09 × 10 −6 A and the maximum turn-off current Ioff is 1.57 × 10 −8 A, with the switching current ratio Ion/Ioff of 452. The purpose of this paper was to propose a three input device to simplify the circuit structure and thus to provide a new idea for future circuit designs.
In the future, we will optimize the N-type and P-type Ti-TcFETs by applying new materials such as ferroelectric materials and two-dimensional materials, which should be helpful to increase the switching current ratio of the device and to decrease the leakage current.   The power consumption, delay, and power delay product of the one-bit full adder using Ti-TcFET devices and standard FinFET devices are compared in Table 4. From Table 4, the power consumption and power delay product of the one-bit full adder based on Ti-TcFET devices are smaller than standard FinFET devices, with an acceptable delay penalty.

Conclusions
In this paper, a novel T-channel field effect transistor with three input terminals (Ti-TcFET) is proposed. The T-channel structure increases the coupling area between the top gate and the front and back gates so that the device can realize the "majority-not" function well. By adjusting the gate work function, channel thickness, and the thickness of the gate oxide layer, the performance of the Ti-TcFET device is optimized. The results show that when the gate work function Φ of the N-type Ti-TcFET is 4.95 eV, T Si = 4 nm, and T OX = 3 nm, the minimum turn-on current I on is 1.14 × 10 −5 A and the maximum turn-off I off is 2.06 × 10 −8 A, with the switching current ratio I on /I off of 553. When the gate work function Φ of the P-type Ti-TcFET is 4.52 eV, T Si = 4 nm, and T OX = 3 nm, the minimum turn-on current I on is 7.09 × 10 −6 A and the maximum turn-off current I off is 1.57 × 10 −8 A, with the switching current ratio I on /I off of 452. The purpose of this paper was to propose a three input device to simplify the circuit structure and thus to provide a new idea for future circuit designs.
In the future, we will optimize the N-type and P-type Ti-TcFETs by applying new materials such as ferroelectric materials and two-dimensional materials, which should be helpful to increase the switching current ratio of the device and to decrease the leakage current.

Conflicts of Interest:
The authors declare no conflicts of interest.