As the feature size is being scaled down, metal-oxide-semiconductor field-effect transistors (MOSFETs) are facing serious problems. The short-channel effects are one of the most intractable challenges. Because of thermodynamic restrictions, the subthreshold swing (SS) of MOSFET devices must have a minimum value of 60 mV/dec at room temperature. This causes high power dissipation. Tunnel field-effect transistors (TFETs) have been attracting much attention because of their new operating mechanism. The TFETs are driven by band-to-band tunnelling (BTBT), and their SS values are no longer limited to 60 mV/dec; thus, the power consumption can be reduced greatly.^[1–5] However, the BTBT mechanism inevitably causes the on-state current of TFETs to be lower than that of MOSFETs by approximately two to four orders of magnitude, limiting the applications of TFETs.^[6–11] In addition, contrary to the theoretical prediction, it has been shown experimentally that the SS values of many fabricated TFET devices are much higher than 60 mV/dec.^[12–14] Therefore, new channel materials and innovative device structures, such as narrow band-gap materials,^[15–17] green FETs,^[18] multi-gate TFETs,^[19–21] and line TFETs (LTFETs)^[22] have been developed to overcome the shortcomings of the TFETs. On one hand, compared to bare Si TFETs, the Ge- and SiGe-channel TFETs have been verified to be potential candidates because of the higher tunnelling rates resulting from the narrow band gaps of Ge.^[23–27] On the other hand, many investigations have shown that the LTFETs perform well in terms of the on-state current because of the enlarged tunnelling area.^[28–30] However, both suffer from relatively large off-state leakage currents, which degenerate the on/off current ratio. Previously, a heteromaterial-gate (HMG) structure had been proposed and applied to the design of point TFETs to improve their device performance by energy-band profile modulation.^[31,32] Few studies have also reported the implementation of the HMG configuration in LTFETs.

In this work, a novel Si/Ge heterojunction LTFET device combined with a symmetric HMG structure is proposed and investigated through two-dimensional (2D) numerical simulations. The results show that the HMG LTFET has much lower off-state currents and superior subthreshold characteristics compared to the traditional single-material-gate (SMG) LTFETs. The lateral energy-band modulation effect induced by the HMG is examined in detail. The work-function mismatch of the HMG has significant impacts on the off-state leakage current and subthreshold characteristics, because of the modulation of the degree of depletion in the gap region. To achieve better performance, the dopant type and doping concentration in this region are also optimized considering the theoretical calculations for the width of the depletion layer. All numerical simulations are carried out using Sentaurus TCAD (Synopsys, San Jose, CA).^[33]

Figure 1(a) and 1(b) show the cross-sectional views of a conventional SMG LTFET and the proposed HMG LTFET, respectively. The source/pocket junction is the main region where vertical BTBT occurs in the on state, and the gap region connects the pocket and drain regions. The lengths of the pocket and gap regions are 20 nm and 5 nm, respectively, and both are 5 nm thick. The source is B-doped (10¹⁹ cm Ge. The pocket, gap, and drain regions are all abrupt P-doped Si with doping concentrations of 10¹⁷ cm , 10¹⁵ cm , and 10²⁰ cm , respectively. The metal gate of the proposed HMG LTFET is composed of one pocket gate and two symmetrical gap gates; the pocket gate in the pocket region is M1 with a fixed work function of φ ₁, and the gap gate in the gap region is M2 with a tuneable work function of φ ₂. Hence, the proposed HMG LTFET is equivalent to a series connection of a vertical tunnelling junction controlled by M1 and a lateral n-type junctionless transistor (JLT) gated by M2.^[34] HfO₂ with a thickness of 2 nm serves as the gate oxide. The main physical model used to describe the operating principle of this proposed LTFET in the simulation is the dynamic non-local BTBT model, which offers an analytical expression for the tunnelling rate using the Kane model^[33]

(1)

Fig. 1.

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Fig. 1. (color online) Schematic structures of (a) conventional single-material-gate (SMG) line TFET (LTFET) and (b) proposed heteromaterial-gate (HMG) LTFET based on a Si/Ge heterojunction. The channel of the HMG LTFET consists of three parts: the pocket region above the source and the two gap regions connecting the pocket and drain regions. The pocket gate and gap gate are named M1 and M2. The green dashed box shows the equivalent lateral n-type junctionless transistor (JLT) gated by M2.

The transfer characteristics of our proposed HMG LTFET are compared with those of the SMG LTFETs at , in Fig. 2. The gate work function of the SMG LTFET was set to two different values of 4.1 eV and 4.5 eV, which were the values of φ ₁ and φ ₂ of the HMG LTFET. As expected, the shapes of the two – curves were mostly identical for the SMG devices. The difference in the gate work functions was evident only in the shift in the onset voltage, which was marked as ,^[31] indicating the switching of the transistor from the off state to the on state. However, for the HMG LTFET, the introduction of the HMG configuration made a big difference, achieving several advantages simultaneously: the off-state leakage current was lower by approximately three orders of magnitude, the SS was smaller, and no degradation was observed in the on-state current. The inset shows the point SS, which can be calculated as and which varies with the increasing drain current. It can be seen that the proposed HMG LTFET has the minimum point SS at approximately 10 mV/dec.

Fig. 2.

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	Fig. 2. (color online) Transfer characteristics of SMG and HMG LTFETs at . The latter shows the superior properties of lower off-state leakage current and steeper subthreshold slope. The inset displays the values of the point SS as a function of drain current.

The enhanced performance can be explained further by the change in the energy band diagram of the HMG LTFET in Fig. 3. was maintained at 0.6 V and was assigned several values to represent the different operating modes of the device. When , both the SMG and HMG LTFETs were in the off state and the drain leakage current was primarily from the lateral electron drift–diffusion. However, the work function of the gap gate, , was higher than that of the pocket gate, φ ₁, which pulled up the energy band in the gap region, resulting in a maximum conduction band ( ). Thus, a local electron potential barrier was formed, leading to a significant reduction in the off-state leakage current.

Fig. 3.

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	Fig. 3. (color online) Energy band diagram along a horizontal cutline for SMG ( eV) and HMG LTFETs ( , eV) at , 0.6 V, and 1.5 V. The cutline is 0.5 nm below the interface between the gate oxide and the Si channel.

When a positive larger than was applied to the gate, the two SMG LTFETs and the HMG LTFET were in the on state. The vertical tunnelling from the source to the pocket was dominant, and the tunnelling direction was perpendicular to the surface plane of the gate oxide. Because the energy band in the vertical direction was controlled by M1, the SMG and HMG LTFETs with had similar band profiles in this direction. Therefore, the difference in their drain currents was mainly caused by the modulated lateral JLT. The effect of the applied positive on the energy band contends with that of the higher work function of the gap gate. When the positive is relatively low (e.g., V), the raising of the energy band induced by the gap gate is dominant; therefore, the conduction band of the HMG device will be higher than that of the SMG device. However, when is high enough (e.g., , as shown in Fig. 3), the energy band of HMG LTFETs would be pushed down to a level lower than that of the SMG devices. In this case, the drain current of the HMG LTFET can surpass that of the SMG LTFET, with increase in .

To gain insight into the dependence of the work-function mismatch, a HMG LTFET with different gap-gate work functions is also studied, and the transfer characteristics are presented in Fig. 4(a). In the simulations, the values of φ ₂ are varied from 3.7 eV to 4.7 eV in increments of 0.2 eV, while φ ₁ is kept unchanged at 4.1 eV. The simulated results show that this variable has a remarkable influence on the performance of the HMG device. It can be seen intuitively that a lower work function of the gap gate causes deterioration in the SS and . Here, SS is defined as the average subthreshold swing, which can be expressed as:^[36]

(2)

Fig. 4.

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	Fig. 4. (color online) (a) Simulated – characteristics of the HMG LTFET, showing their dependence on various work functions of the gap gate at . (b) φ 2 dependence of SS and ratio extracted from these simulated devices.

On one hand, when φ ₂ was less than φ ₁, the smaller φ ₂ led to a lower energy band in the gap region; thus, a lower barrier height for electrons for drift–diffusion could cause a higher . However, this reduction in the band energy was favourable for boosting the drain current in the on state. Under a positive gate voltage, the lateral JLT was turned on. In this case, this JLT played the role of a series resistor, whose value was primarily adjusted by M2. The electron density in the surface of this region became larger as φ ₂ decreased, making this region a relatively lower resistance channel, and the on-state current was enhanced. Nevertheless, the discrepancy in the on-state current was very slight as increased. On the other hand, if φ2 was larger than φ ₁, the lateral JLT was in the off state under negative , and the leakage current was generated at the bottom of the channel, i.e., the gap region. In this case, the gap region was depleted and the width of the depletion layer increased as φ ₂ increased. Therefore, there was a minimum when the gap region became fully depleted with a critical value of φ ₂, and it could not be reduced further even when a higher φ ₂ was adopted. In addition, the excessive increase in φ ₂ was detrimental to the on-state current because of the lateral local potential barrier that was formed.

Figure 4(b) shows the SS and ratio as functions of φ ₂ for the simulated HMG LTFETs. was extracted as the drain current at and . Both of them change significantly when φ ₂ is lower than 4.3 eV. The ratio increases and SS decreases because of the decreasing . However, both of them change in an opposite manner when φ ₂ is increased further, which is because tends to saturate whereas reduces.

In addition to the work-function mismatch, the dopants in the gap region were also predicted to influence the performance of the HMG LTFET. It needs to be pointed out that the thicknesses of the gate oxide and gap region also have impacts on the device characteristics. The former affects the capability of gate control over the channel and the latter determines the leakage current in the off state. In this section, we modify these two parameters to further highlight the modulation effect of the gap gate on the gap region. The transfer characteristics with various dopant types and doping concentrations in the gap region of the HMG LTFET with a 3-nm-thick gap region and a 1-nm-thick gate oxide are depicted in Fig. 5(a). Because the same structure is used for the pocket region and the gate stack on top of it, the onset voltage and on-state current of all simulated devices are almost the same. The obvious difference is reflected in the off state, which depends primarily on the gap region. The HMG LTFETs with an n-type gap have a flat ambipolar window in a certain range of negative gate voltages, while those with a p-type gap transform immediately from forward operation to an ambipolar state. The inset shows the simulated hole current density of an HMG LTFET with a p-type (10¹⁸ cm gap region at . In this case, the p-type gap was accumulated and the hole drift–diffusion current was collected in the source region. As became more negative, a hole BTBT process from the drain to the gap region was induced by the higher energy band in the gap region, which also contributed to the ambipolar current. This caused the – curves of the HMG LTFET devices with a p-type gap to appear in the form of a ‘V’.

Fig. 5.

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Fig. 5. (color online) (a) – characteristics of HMG LTFETs with various dopant types and doping concentrations in the gap. The n-type dopants endow the transistor with a flat window. (b) – characteristics of HMG LTFETs with an n-type gap with increasing from 1019 cm to 1020 cm . (c) Electron current density diagram in the lateral direction for HMG LTFETs with cm and 1020 cm . (d) Calculated and extracted for HMG LTFETs with n-type gap as functions of .

For transistors with an n-type gap, it was noticeable that a relatively low doping level varying from 10¹⁵ cm to 10¹⁸ cm caused almost no difference in the off-state current. However, when the doping level was changed from 10¹⁹ cm to 10²⁰ cm , the off-state current increased dramatically, as can be observed in Fig. 5(b). Because was larger than zero, the n-type gap region was in a depleted state under the low negative , and the width of the depletion layer decreased with increasing doping concentration. Figure 5(c) presents a comparison of the electron current densities for the gap region with n-type doping of 10¹⁸ cm and 10²⁰ cm at . The distributions of electron current clearly show that the gap region is fully depleted with a relatively low doping level and that it becomes partially depleted as the doping level becomes sufficiently high.

To quantitatively estimate the width of the depletion layer, we use the depletion approximation. The gate voltage equation for the lateral JLT can be expressed as follows:

(3)

(4)

(5)

Figure 5(d) shows the calculated and leakage current ( of the HMG LTFETs extracted from Fig. 5(b) at . Based on the calculated results, the 3-nm-thick gap region was fully depleted when was less than cm , and accordingly, was almost unchanged in this range. When increased, the channel of the JLT became partially depleted. The electrons could drift and diffuse at the bottom of this region, and the non-depleted region for electrons to flow broadened with increasing , which caused the to rise sharply. This dependence of the off-state performance on the channel doping concentration was observed in some previous researches concerning JLTs.^[37–39] These results indicated that, to suppress the off-state leakage current, the gap-gate material and n-type doping level in the gap region should be simultaneously optimized to make the gap region fully depleted.

We proposed a symmetric HMG LTFET based on a Si/Ge heterojunction and demonstrated its properties through 2D numerical simulations. It was shown that the introduction of the gap gate with a work function different from that of the pocket gate significantly suppressed and improved SS because of the lateral energy-band profile modulation. On this basis, the work function mismatch between the pocket gate and the gap gate, the dopant type, and the doping level in the gap region could all be tuned to enhance the performance. By optimizing the off-state leakage current and retaining the advantages of the high on-state current of the LTFETs, this proposed HMG LTFET could demonstrate potential for low-power applications.