I. INTRODUCTION

With the development of integrated circuits, the number of transistors on a chip and the operating frequency are increasing. Although these improve the chip performance, they also increase the power consumption ^[1]. Because complementary metal-oxide-semiconductor devices rely on thermal injection as the carrier emission mechanism, their subthreshold slope (SS) cannot be lower than 60 mV/decade at room temperature, owing to Boltzmann's tyranny ^[2], resulting in a transistor that does not satisfy both the high-performance and low-power consumption requirements. Fortunately, tunneling field-effect transistors (TFETs) that utilize quantum-mechanical band-to-band tunneling (BTBT) can overcome Boltzmann's tyranny and obtain sub-60 mV/decade SSs ^{[3,4,5,6,7,8,9]}. However, conventional TFETs have drawbacks, such as their low on-state currents ($I_{\rm ON}$) ^[10,11]. In many proposed TFETs structures, such as L-TFETs ^[12,13], U-TFETs ^[14], and Z-TFETs ^[15], $I_{\rm ON}$ is increased by increasing the BTBT area. In particular, the performance of L-shaped channel TFETs has been improved via doping or the addition of ferroelectric layers ^{[16,17,18,19]}. Doping engineering can achieve abrupt switching by mitigating the BTBT at the corner edge of the source region in a negative-capacitance TFET (NCTFET) ^[18]. Recently, an L-shaped gate InGaAs/GaAsSb heterojunction TFET was presented that extends the source to increase the BTBT area between source and channel for increasing $I_{\rm ON}$ ^[20]. However, few studies have focused on L-shaped gate heterojunction TFETs (LG-HJ-TFETs).

In the present study, an L-shaped gate negative-capacitance Si/Ge heterojunction tunneling field-effect transistor with channel doping (NCHJ-CD-LTFET) was developed and investigated via technology computer-aided design (TCAD) simulations with calibrated model parameters ^[21]. Compared with the LG-HJ-TFET, the NCHJ-CD-LTFET has a far lower threshold voltage ($V_{\rm TH}$). The energy bands of the corner doping region are modulated via channel doping, which reduces the tunneling barrier between the source and the channel and the ferroelectric layer can amplify the internal gate voltage to increase the electric potential of the channel surface. Meanwhile, the negative-capacitance effects can suppress BTBT at $V_{\rm GS} = 0$ V and reduce the off-state current ($I_{\rm OFF}$). The doping concentration of the channel corner region ($N_{\rm CH,CO}$) and the ferroelectric-layer thickness ($T_{\rm FE}$) can be adjusted to optimize the electrical performance of the device, lowing power consumption and improving drive capability.

II. STRUCTURE AND MECHANISM OF THE NCHJ-CD-LTFET

Fig. 1(a) shows a schematic of the proposed NCHJ-CD-LTFET structure. The tunneling junction consists of a p${}^{+}$ Ge source and an n${}^{+}$ Si channel. The drain is a silicon material, and the doping concentration of the source, drain and channel are $2 \times 10^{19}$, $1 \times 10 ^{17}$ and $1 \times 10 ^{18}$ cm${}^{-3}$, respectively. The source and drain are separated by a 4-nm-thick HfO${}_{2}$ barrier layer. The gate dielectric is a 1-nm-thick HfO${}_{2}$ layer with a dielectric constant of 22. A ferroelectric layer is deposited above the horizontal gate dielectric. In addition, the work function of the gate is 4.2 eV and the structural parameters are presented in Table 1. Fig. 1(b) shows the brief process flow for the fabrication of NCHJ-CD-LTFET.

Fig. 2 presents the electrostatic potential of the corner doping region. As shown, the electrostatic potential along the diagonal direction decreases faster than the vertical and horizontal potentials, and at the same distance from the gate, the diagonal electrostatic potential is lower than the vertical and horizontal potentials. Therefore, the energy bands can be modulated via heavy doping in this region. Figs. 3(a) and 3(b) present the energy bands with and without heavy doping, respectively. As shown, with heavy doping in the corner-doping region, the energy bands bend downward, and the bandgap between the source and doping region is reduced. Therefore, BTBT can occur at lower gate voltages ($V_{\rm GS}$).

Fig. 1. (a) Structure of the proposed NCHJ-CD-LTFET. (b) The brief process flow for the NCHJ-CD-LTFE.

Fig. 2. Electrostatic potential of the corner doping region.

Fig. 3. Band energy diagrams (a) with and (b) without heavy doping.

Fig. 4. (a) Calibration of the BTBT parameters using simulated transfer characteristics ($I_{\rm DS}$-$V_{\rm GS}$) of the referenced NCTFET ^[18]. (b) Calibration of the L-K model matched to referenced result ^[25].

To accurately analyze the electrical characteristics of the NCHJ-CD-LTFET, the nonlocal BTBT and Landau-Khalatnikov (L-K) models were used. The Kane model parameters were $F _{0} = 1$ V/m, $P = 2.5$, $A _{Si} = 4.0 \times 10^{14}$ cm${}^{-3}\cdot$s${}^{-1}$, $B _{Si} = 9.9 \times 10^{6}$ V$\cdot$cm${}^{-1}$ ^[24], and the L-K model parameters were $\alpha = - 1.299 \times 10 ^{11}$ cm/F, $\beta = 6.4952 \times 10 ^{20}$ cm${}^{5}$/(FC${}^{2}$) and $\gamma = 5.0 \times 10 ^{30}$ cm${}^{9}$/(FC${}^{4}$) ^[25,26]. Meanwhile, both the nonlocal BTBT model and L-K model parameters were matched to the reference ^[18], as shown in Fig. 4(a). Fig. 4(b) shows the simulated ${P}$-${E}$ curve matched to the reference data ^[25]. Furthermore, the oldSlotboom, Fermi, Shockley-Read-Hall recombination, High-field saturation, e-normal and doping dependences models are also used. Here, the turn-on voltage ($V_{\rm ON}$) was defined as the $V_{\rm GS}$ at $I_{\rm DS} = 2 \times 10 ^{-13}$ A/$\mu$m ^[18]. The $V_{\rm TH}$ was extracted at $I_{\rm DS} = 1 \times 10^{-7}$ A/$\mu$m and the average subthreshold slope ($SS_{\rm AVE}$) was calculated by averaging the SS in the $I_{\rm DS}$ range of $2 \times 10^{-13}$ to $1 \times 10^{-7}$ A/$\mu$m.

III. RESULT AND DISCUSSION

1. Channel Doping Engineering

To enhance the realizable of the simulation, we consider the actual corner shape in fabrication and replace the vertical corner with a curved corner. As shown in Fig. 5(a), electrical properties are virtually unchanged. Meanwhile, the interface defect states between the HfO${}_{2}$ and the channel are also taken into consideration. Acceptor-type traps are added at the interface (for n-type transistors) with trap concentrations ranging from $1\times 10 ^{11}$ to $1\times 10 ^{13}$ cm${}^{-2}$eV${}^{-1}$ ^[27]. The transfer characteristic curves are shown in Fig. 5(b) and curves remained almost unchanged with an increasing concentration of traps. In addition, we also consider the impact of Gaussian doping and Uniform doping of the source on transistor performance. The Gaussian doping has a peak concentration of $3 \times 10 ^{19}$ cm${}^{-3}$, a background doping of $1 \times 10 ^{19}$ cm${}^{-3}$, and a junction depth of 6 nm as shown in Fig. 6(a). The results indicate that the curve of Gaussian doping is slightly degraded in the subthreshold region and increased in $I_{\rm ON}$. This is because as the doping concentration changes, the energy band of the source also changes. The $V_{\rm ON}$ decreases as the source doping concentration increases, due to the downward bending of the energy band. The $I_{\rm ON}$ is determined by the junction depth and the background concentration of Gaussian doping. This work focuses on optimizing transistors through corner doping and the ferroelectric layer, so, in summary, we use vertical corner, no interface trap, uniformly doped transistors as the object of study.

Besides, Fig. 6(b) compares the transfer characteristic curves of using low-k material (SiO${}_{2}$) and using HfO${}_{2}$ as a barrier layer. The result shows that using HfO${}_{2}$ as a barrier layer results in lower $I_{\rm DS}$ at $V_{\rm GS}$ below 0.06 V. Therefore, we choose to use HfO${}_{2}$ as our barrier layer.

Figs. 3(a) and 3(b) indicate that heavy doping (n${}^{+}$-doping for an n-type TFET) can modulate the energy bands of the corner doping region and reduce the tunneling barrier. To optimize the performance, the effects of $N_{\rm CH,CO}$ were assessed from $1 \times 10 ^{18}$ to $1.5 \times 10 ^{19}$ cm${}^{-3}$.

Fig. 7 shows the $I_{\rm DS}$-$V_{\rm GS}$ curves of the LG-HJ-TFET with channel doping (HJ-CD-LTFET) at different $N_{\rm CH,CO}$ values. As $N_{\rm CH,CO}$ increases, the curves in the subthreshold region shift to the left, and the saturation curves move upward. Fig. 8(a) indicates that as $N_{\rm CH,CO}$ increases from $1 \times 10^{18}$ to $1.1 \times 10 ^{19}$ cm${}^{-3}$, $I_{\rm OFF}$ remains nearly constant, and $I_{\rm ON}$ increases, as shown in Fig. 7; thus, the switching current ratio ($I_{\rm ON}$/$I_{\rm OFF}$) increases. However, at $N_{\rm CH,CO} = 1.3 \times 10 ^{19}$ cm${}^{-3}$, the off-state current ($I_{\rm OFF}$) increases rapidly, and $I_{\rm ON}$/$I_{\rm OFF}$ decreases. The same trend is more obvious at $N_{\rm CH,CO} = 1.5 \times 10 ^{19}$ cm${}^{-3}$. Fig. 8(b) shows that $V_{\rm TH}$ continuously decreases, and the rate of reduction increases with increasing $N_{\rm CH,CO}$. Meanwhile, ${SS}_{\rm AVE}$ remains almost unchanged when $N_{\rm CH,CO}$ increases from $1 \times 10 ^{18}$ to $1.3 \times 10 ^{19}$ cm${}^{-3}$.

This is because with an increase in $N_{\rm CH,CO}$, the energy bands of the corner doping region bend downwards, as shown in Fig. 9(a). When $N_{\rm CH,CO}$ ranges from $1 \times 10^{18}$ to $1.27 \times 10 ^{19}$ cm${}^{-3}$, the conduction band bottom of the channel gradually approaches the valence band top of the source, allowing electrons to tunnel from the source to the channel at a lower voltage. Fig. 9(b) confirms that as $N_{\rm CH,CO}$ increases, significant changes in the band-to-band generation increase fast at a low $V_{\rm GS}$, and the total band-to-band generation is enhanced. Simultaneously, the energy bands do not overlap, and the band-to-band generation remains nearly constant at $V_{\rm GS} = 0$ V. Thus, $V_{\rm TH}$ and $V_{\rm ON}$ decrease, and $I_{\rm ON}$ increases. Fig. 10 shows that the BTBT in the corner of HJ-CD-LTFET (${BTBT}_{\rm CO}$) does not occur at $N_{\rm CH,CO}$ from $1 \times 10^{18}$ to $1.27 \times 10^{19}$ cm${}^{-3}$. As the $N_{\rm CH,CO}$ continues to increase, the energy band continues to bend downwards and partial overlap occurs between the valence band at the top of the source and the conduction band at the bottom of the channel at $V_{\rm GS} = 0$ V, as shown in Fig. 9(a). Therefore, as indicated by Fig. 10, ${BTBT}_{\rm CO}$ occurs at $N_{\rm CH,CO} = 1.28 \times 10^{19}$ cm${}^{-3}$ and as $N_{\rm CH,CO}$ continues to increase, $BTBT_{\rm CO}$ increases significantly and total band-to-band generation also appears a significant increase at $V_{\rm GS} =0$ V. So, $I_{\rm OFF}$ increases rapidly. Furthermore, as $N_{\rm CH,CO}$ increases, the $V_{\rm TH}$ and $V_{\rm ON}$ decrease. Therefore, ${SS}_{\rm AVE}$ fluctuates within a certain range.

Fig. 5. (a)Transfer characteristics at $V_{\rm DS}$ = 0.5 V with curved corner and vertical corner. (b) Transfer characteristics at $V_{\rm DS}$ = 0.5 V with different acceptor-type traps concentrations.

Fig. 6. (a) Transfer characteristics at $V_{\rm DS}$ = 0.5 V with different doping methods for source region. (b) Transfer characteristics at $V_{\rm DS}$ = 0.5 V with SiO${}_{2}$ barrier and HfO${}_{2}$ barrier.

Fig. 7. Transfer characteristics at $V_{\rm DS}$ = 0.5 V with different $N_{\rm CH,CO}$ values.

Fig. 8. (a) $I_{\rm OFF}$, $I_{\rm ON}$/$I_{\rm OFF}$, (b) ${SS}_{\rm AVE}$, and $V_{\rm TH}$ of the proposed HJ-CD-LTFET with different $N_{CH,CO}$ values.

Fig. 9. (a) $I_{\rm OFF}$, $I_{\rm ON}$/$I_{\rm OFF}$, (b) ${SS}_{\rm AVE}$, and $V_{\rm TH}$ of the proposed HJ-CD-LTFET with different $N_{CH,CO}$ values.

Fig. 10. BTBT diagrams at different $N_{\rm CH,CO}$ with $V_{\rm GS}$ = 0 V in the corner of HJ-CD-LTFET.

2. Ferroelectric layer and parameter optimization

To further improve the device performance, a ferroelectric layer was deposited above the horizontal gate dielectric to form a negative capacitance HJ-CD-LTFET (NCHJ-CD-LTFET). Meanwhile, considering the influence of heavy doping, the effects of the ferroelectric-layer thickness ($T_{\rm FE}$) on the transistor performance were studied, with $N_{\rm CH,CO} = 5 \times 10 ^{18}$ cm${}^{-3}$.

Fig. 11 shows the $I_{\rm DS}$-$V_{\rm GS}$ curve of the NCHJ-CD-LTFETs with different $T_{\rm FE}$. When the ferroelectric-layer thickness was $< 1.5$ nm, the ferroelectric layer increased the internal gate voltage via negative-capacitance effects, reducing $V_{\rm ON}$. However, when the ferroelectric-layer thickness was 2 nm, $I_{\rm OFF}$ increased rapidly. This is because the polarization was unstable and fluctuated at $T_{\rm FE} = 2$ nm, as illustrated in Fig. 12(a). Fig. 12(b) shows that BTBT occurred at the polarization peak. Hence, $I_{\rm OFF}$ increased rapidly, as shown in Fig. 11.

Fig. 13(a) shows that the total capacitance (${C}_{\rm GG}$) increases as the ferroelectric thickness increases, with a capacitance peak occurring at $T_{\rm FE} = 1.5$ nm, when the negative capacitance effect is most apparent ^[28] and no hysteresis occurs ^[29]. Fig. 13(b) illustrates the position of NCHJ-CD-LTFET on the S-curve for gate voltages ranging from 0V to 0.8V. The NCHJ-CD-LTFET is operating in the negative capacitance region. Therefore, the 1.5 nm ferroelectric layer was used to investigate the impact of various doping concentrations on transistor performance.

According to the above analysis, the characteristics of the NCHJ-CD-LTFET with a 1.5-nm-thick ferroelectric layer and without a ferroelectric layer ($T_{\rm FE} = 0$ nm, HJ-CD-LTFET) were evaluated as $N_{\rm CH,CO}$ increased from $5 \times 10^{18}$ to $1.3 \times 10^{19}$ cm${}^{-3}$. As shown in Fig. 14(a), when the doping concentration was $5 \times 10 ^{18}$ and $9 \times 10^{18}$ cm${}^{-3}$, the $V_{\rm ON}$ with the ferroelectric layer was lower than that at $T_{\rm FE} = 0$ nm. However, ${C} _{GG}$ remains essentially unchanged as $N_{\rm CH,CO}$ increases as shown in Fig. 14(b). In addition, Fig. 15(a) shows that the $V_{\rm TH}$ of the NCHJ-CD-LTFET was lower than that without the ferroelectric layer. As shown in Fig. 15(b), ${SS}_{\rm AVE}$ decreases with an increase in $N_{\rm CH,CO}$ at $T_{\rm FE} = 1.5$ nm. In particular, when $N_{\rm CH,CO}$ was $1.3 \times 10 ^{19}$ cm${}^{-3}$, $I_{\rm OFF}$ with a 1.5-nm-thick ferroelectric layer decreased significantly, as shown in Fig. 15(b). This is because owing to the negative-capacitance effects, the ferroelectric layer amplified the internal gate voltage, increasing in channel surface potential, reducing $V_{\rm TH}$. Simultaneously, some electrons that could not initially tunnel in the subthreshold region could tunnel from the source to the channel. Thus, ${SS}_{\rm AVE}$ decreased. When $N_{\rm CH,CO}$ was $1.3 \times 10^{19}$ cm${}^{-3}$, the ferroelectric layer inhibited the tunneling of overlapping bands owing to heavy doping. As shown in Fig. 16(a), compared with the transistor without a ferroelectric layer, no electrons tunneled in the corner for the NCHJ-CD-LTFET at $V_{\rm GS} = 0$ V and $V_{\rm DS} = 0.5$ V.

Finally, the thickness of the ferroelectric layer and doping concentration of the corner doping region were adjusted to improve the electrical characteristics of the transistor, as shown in Fig. 16(b). Table 2 presents the key performance parameters of the LG-HJ-TFET, HJ-CD-LTFET and NCHJ-CD-LTFET.

Fig. 11. Transfer characteristics at $N_{\rm CH,CO}$ = 5 ? 10${}^{18}$ cm${}^{-3}$ with different $T_{\rm FE}$ values.

Fig. 12. (a) FE Polarization at $T_{\rm FE} = 2$ nm. (b) BTBT diagram at $V_{\rm DS} = 0.5$ V with $T_{\rm FE} = 2$ nm.

Fig. 13. (a)$C_{GG}$ of the NCHJ-CD-LTFET at different $T_{\rm FE}$ values. (b) S-curve of the NCHJ-CD-LTFET and the operating region for $V_{\rm DS} = 0.5$ V.

Fig. 14. (a) Transfer characteristics of the NCHJ-CD-LTFET with different values of $T_{\rm FE}$ and $N_{\rm CH,CO}$. (b) C${}_{GG}$ of the NCHJ-CD-LTFET at different $N_{\rm CH,CO}$ values.

Fig. 15. (a) $V_{\rm TH}$ of the NCHJ-CD-LTFET with different values of $T_{\rm FE}$ and $N_{\rm CH,CO}$. (b) $I_{\rm OFF}$ of the NCHJ-CD-LTFET with different values of $T_{\rm FE}$ and $N_{\rm CH,CO}$, and ${SS}_{\rm AVE}$ of the NCHJ-CD-LTFET with different values of $N_{\rm CH,CO}$ at $T_{\rm FE} = 1.5$ nm.

Fig. 16. (a) BTBT diagrams at $N_{\rm CH,CO} = 1.3 \times 10^{19}$ cm${}^{-3}$ with $T_{\rm FE} = 1.5$ nm and without the ferroelectric layer. (b) Transfer characteristics of the NCHJ-CD-LTFET and LG-HJ-TFET at $V_{\rm DS} = 0.5$ V.

Table 2. Key parameters of the LG-HJ-TFET, HJ-CD-LTFET and NCHJ-CD-LTFET.

	LG-HJ-TFET	HJ-CD-LTFET	NCHJ-CD-LTFET
ION (μA/μm)	13.02	16.87	20.58
ION/IOFF	1.016 × 108	1.282 × 108	1.555 × 108
VTH (V)	0.221	0.180	0.145
SSAVE (mV/decade)	28.08	28.78	24.92

IV. CONCLUSION

An NCHJ-CD-LTFET was developed on the basis of the L-shaped-gate TFET and analyzed using TCAD simulations. In contrast to the LG-HJ-TFET, channel doping can modulate the energy bands, narrowing the bandgap between the source and channel, and reducing the threshold voltage. Meanwhile, regulating the ferroelectric-layer thickness via heavy doping can further improve the electrical performance. In particular, when the energy bands overlap in the corner doping region at $N_{\rm CH,CO} = 1.3 \times 10^{19}$ cm${}^{-3}$ with $V_{\rm GS} = 0$ V, the ferroelectric layer can reduce $I_{\rm OFF}$ and the power consumption through negative-capacitance effects. Adjusting the doping concentration of the channel corner region and the thickness of the ferroelectric layer increased the $I_{\rm ON}$ and $I_{\rm ON}$/$I_{\rm OFF}$ of the NCHJ-CD-LTFET by 58% and 53%, respectively, and reduced $V_{\rm TH}$ and ${SS}_{\rm AVE}$ by 34% and 11%, respectively.