The effects of source doping concentration and doping gradient on the ON-state current of Si nanowire TFETs

The tunnel field-effect transistor (TFET) is considered a promising next-generation transistor due to its potentially limit-breaking low subthreshold swing and better immunity against short-channel effects. However, the low ON-state current (ION) of TFETs has been a critical problem. In this work, we investigated the effects of the source doping concentration and the source doping gradient (SDG) on the ION of n-type Si gate-all-around (GAA) nanowire (NW) TFETs using an ATLAS device simulator. Unexpectedly, we found that increasing the source doping concentration does not necessarily improve ION, especially for TFETs with a large SDG. Moreover, although reducing the SDG indeed increases ION, for TFETs with low source doping concentration (e.g., 1 × 1019 cm−3), the improvement in ION by reducing the SDG becomes insignificant.


Introduction
The tunnel field-effect transistor (TFET) is regarded as a promising candidate for next-generation transistors of lowpower digital circuitry [1][2][3][4][5]. The main advantage of the TFET is its potential for breaking through the subthreshold swing limit of traditional metal-oxide-semiconductor fieldeffect transistors (MOSFETs), which is about 60 mV/decade at room temperature. This is because the subthreshold current of TFETs is determined by band-to-band tunneling (BTBT) rather than thermionic emission as in MOSFETs. Another advantage of TFETs is their immunity against shortchannel effects (SCEs), since the drain current is dominated by the BTBT process at the source/channel interface [6,7]. Moreover, for silicon-based TFETs, compatibility with the conventional complementary metal-oxide-semiconductor (CMOS) process may be considered an advantage because TFETs can be viewed as MOSFETs with opposite doping types in the source and drain. Nevertheless, the main drawback of the TFET is its low ON-state current (I ON ) due to the nature of the tunneling process. Numerous studies have been undertaken to increase the I ON of TFETs [8][9][10][11][12][13][14][15][16][17]. Most of them involved improvement of the gate geometric configuration [8][9][10][11][12][13], the adoption of narrow-bandgap material at the BTBT region [13][14][15] or the use of high-κ gate dielectrics [16,17]. In addition, novel TFET structures such as charge-plasma-based dopingless TFETs [18,19] and negative capacitance (NC) TFETs with a ferroelectric gate insulator [19,20] have been proposed for further boosting the device performance. Fundamentally, the source doping concentration and source doping gradient (SDG) are the basic parameters for the source engineering and consequent I ON improvement of TFETs. Intuitively, increasing the source doping concentration and sharpening the SDG will improve the I ON of the TFET. Some simulation and experimental works have separately investigated the effects of the source doping concentration [7] and SDG [21] on TFET performance. However, the combined effects of both the source doping concentration and SDG for TFETs have rarely been examined in detail. In this work, we conduct a comprehensive simulation study on the effects of the source doping concentration and SDG for n-type Si nanowire (NW) gateall-around (GAA) TFETs using the ATLAS device simulator (Silvaco Group, Inc.). The Si NW GAA TFET showed experimentally good performance [22,23] and hence was chosen as the TFET device configuration to investigate the effects of the source doping concentration and SDG.

Device structure and simulation approach
We use the ATLAS device simulator (version 5.26.1.R) to simulate the device performance. The device structure is given as follows. A schematic diagram of the simulated Si NW GAA TFET is presented in Fig. 1. Figure 2 shows the cross section of the Si NW GAA TFET along the radial direction. The radius of the Si NW is 10 nm, which results in negligible quantum confinement effects. The gate length is 100 nm, and the length of the source/ drain is 50 nm. Note that the gate length can be further shortened without changing the device performance due to the aforementioned immunity to SCEs. The gate dielectric is SiO 2 , and the thickness is 1 nm, resulting in effective oxide thickness (EOT) equal to 1 nm. An aluminum gate is used in our simulation. Figure 3 shows the one-dimensional (1D) net doping profile of the Si NW GAA TFET prototype along the channel direction. The default values of the source and drain doping concentrations are p-type 1 × 10 20 and n-type 1 × 10 20 cm −3 , respectively. The doping concentration of the channel is p-type 1 × 10 17 cm −3 . Note that there existed a doping gradient with a default value of 10 nm/decade at the source/channel and drain/ channel interfaces of the prototype TFET. In this work, we simulated four different S/D doping concentrations for the prototype TFET, i.e., 1 × 10 20 (default value), 5 × 10 19 , 2 × 10 19 , and 1 × 10 19 cm −3 , as shown in Fig. 4. For each S/D doping concentration, we simulated three different    Here, the doping gradient is 10 nm/decade doping gradients for the prototype TFET, i.e., 15, 10 (default value), and 5 nm/decade, as shown in Fig. 5.
As mentioned previously, the BTBT process determines the drain current of the TFET, and hence, the BTBT model used in the simulation is crucial. In this work, the nonlocal BTBT model was used [24]. The bandgap narrowing caused by doping was also taken into account. Unlike the local BTBT models, which treat BTBT as a recombination-generation rate according to the electric field attributed to a certain spatial point, the nonlocal BTBT model calculates the tunneling current by quantum mechanical computation of the tunneling probability at certain electron energy and integration of the tunneling probability along the energy interval of the valence band electron within which the BTBT process is allowed. Further details about the nonlocal BTBT model can be found in our previous work [25]. The mobility model used in the simulation considers the high-field velocity saturation due to the longitudinal electric field as well as the mobility degradation caused by the transverse electric field and doping. Note that the drain current in this work is divided by the Si NW periphery, and hence, the unit is A/µm. We observe from Fig. 6 that reducing the SDG from 15 to 5 nm/ decade significantly increases I ON . The ambipolar behavior is noticeable in Fig. 6 and can be suppressed by gate-drain underlap [6,26]. This is confirmed by our simulation results as shown in Fig. 7. Note that the ON-state current was not affected by the gate-drain underlap. Since in this work we focus our attention on the effects of source doping concentration and its doping gradient on the ON-state current, we do not further investigate the optimization of gate-drain underlap. Figure 8 shows the ON-state electron tunneling rates of the TFETs with three different doping gradients (15, 10, and 5 nm/decade) under the S/D doping concentration of 1 × 10 20 cm −3 . It can be seen from Fig. 8 that the BTBT is basically distributed over the radius of the Si nanowire around the interface between the source and channel. The electron tunneling rate of the doping gradient of 5 nm/decade is obviously higher than that of the doping gradient of 15 nm/decade. Figure 9 shows the ON-state energy band diagrams of the TFETs with three different doping gradients (15, 10, and 5 nm/decade) under the S/D doping concentration of 1 × 10 20 cm −3 along the Si/gate oxide interface as well as the central part of the Si nanowire. Note that in this work, the energy band diagrams along the channel direction were obtained at two locations: one at 0.1 nm below the Si/gate oxide interface (referred to as the interface, unless otherwise specified), and the other 2 nm from the center of the Si nanowire (referred to as the central part). The BTBT current is expected to be dominated by the valence-band electrons, which see the minimum barrier width. In Fig. 9, as the doping gradient becomes sharper, the minimum barrier width becomes narrower for both the interface and the central part.

The effect of SDG under different S/D doping concentrations
Next, we will examine the effects of SDG when the S/D doping concentration is reduced from 1 × 10 20 to 1 × 10 19 cm −3 . Figure 10 shows the I D -V G curves of the TFETs with three different doping gradients (15, 10, and 5 nm/decade) under an S/D doping concentration of 1 × 10 19 cm −3 . We can see that reducing the SDG from 15 to 5 nm/decade increases the I ON only slightly. Again, we checked the ON-state electron tunneling rates of the TFETs with three different doping gradients (15, 10, and 5 nm/decade) under the S/D doping concentration of 1 × 10 19 cm −3 , as shown in Fig. 11. Unlike the TFETs with the S/D doping concentration of 1 × 10 20 cm −3 , for the TFETs with the S/D doping concentration of 1 × 10 19 cm −3 , BTBT occurs more locally and mainly at the Si/gate oxide interface and at the source-end edge of the gate. The electron tunneling rate of the doping gradient of 5 nm/ decade is slightly higher than that of the doping gradient of 15 nm/decade in the central region. Figure 12 shows the ON-state energy band diagrams of the TFETs with three different doping gradients (15, 10, and 5 nm/decade) under the S/D doping concentration of 1 × 10 19 cm −3 along the Si/gate oxide interface and the central part of the Si nanowire. In Fig. 12, the minimum barrier width at the interface is obviously smaller than that at the central part, and hence, a much higher electron tunneling rate appears at the interface. In addition, the minimum barrier widths at the interface for the three different doping gradients are almost the same and are difficult to discriminate in Fig. 12,   Figure 14 shows the ON-state electron tunneling rates of the TFETs with the abovementioned four S/D doping concentrations under the SDG of 15 nm/decade. The TFET with S/D doping concentration of 2 × 10 19 cm −3 has the highest electron tunneling rate occurring at the interface, and therefore, also has highest I ON . Figure 15 shows the ON-state energy band diagrams of the TFETs with the four S/D doping concentrations under the SDG of 15 nm/decade along the Si/gate oxide interface and the central part of the Si nanowire. Here, for the TFETs with S/D doping concentrations of 2 × 10 19 and 1 × 10 19 cm −3 , the minimum barrier width at the interface is obviously smaller than that at the central part, and hence, a much higher rate of electron tunneling appears at the interface. However, further increasing the S/D doping concentration broadens the minimum barrier width at the interface, as shown in Fig. 15a and c, and consequently, the tunneling process at the central part dominates the tunneling rate. Note that in Fig. 15a and c, the longitudinal electric fields at the source-end gate edge are higher than those of Fig. 15e and g, but the electrons in the valence band at the source see a wider barrier width instead. This means that a higher longitudinal electric field does not necessarily lead to a higher tunneling rate and accompanying higher I ON . It also implies that the local BTBT models would be problematic, since the tunneling rates of local BTBT models are determined by the electric field. Note that in Fig. 13, the nonuniform I D -V G characteristics for the TFET with source doping of 5 × 10 19 cm −3 were caused by the two BTBT regions: the interface and the central part. At low gate voltage (V G < ~ 0.7 V), the BTBT process occurring at the central part dominated the drain current, as shown in Fig. 16. However, for high gate voltage (V G > ~ 0.7 V), the BTBT process taking place at the interface dominated the drain current, as shown in Figs. 14b and 15c. Next, we investigate the effect of the S/D doping concentration when the SDG is reduced from 15 to 5 nm/ decade. Figure 17 shows the I D -V G curves of the TFETs with the four different S/D doping concentrations (1 × 10 20 , 5 × 10 19 , 2 × 10 19 , and 1 × 10 19 cm −3 ) under an SDG of 5 nm/decade. We found that the I ON of the TFET with an S/D doping concentration of 1 × 10 19 cm −3 was approximately one order of magnitude lower than the I ON of the TFETs with S/D doping concentrations higher than 2 × 10 19 cm −3 . Figure 18 shows the ON-state electron tunneling rates of the TFETs with the four S/D doping concentrations under the SDG of 5 nm/decade. The ONstate electron tunneling rate of the TFET with the S/D doping concentration of 1 × 10 19 cm −3 is obviously lower than the rates of the TFETs with S/D doping concentrations higher than 2 × 10 19 cm −3 and, hence, results in lower I ON . In addition, as the S/D doping concentration increases, the dominant tunneling process at the source/ channel interface spreads from the Si/SiO 2 interface to the entire central region. Figure 19 shows the ON-state energy band diagrams of the TFETs with the four S/D doping concentrations under the SDG of 5 nm/decade along the Si/gate oxide interface and the central part of the Si nanowire. It can be seen in Fig. 19 that the minimum barrier width at the interface is basically smaller than that at the central part. For the TFET with an S/D doping concentration of 1 × 10 19 cm −3 , the minimum barrier widths at both the interface and the central part are larger than those of the TFETs with S/D doping concentrations higher than 2 × 10 19 cm −3 and, therefore, give rise to a lower electron  : a, c, e, g) and the central part of Si the nanowire (right side: b, d, f, h) tunneling rate. In addition, as the S/D doping concentration increases, the minimum barrier width at the central part decreases, and consequently, the electron tunneling rate at the central part increases. especially when the S/D doping concentration is high (e.g., 1 × 10 20 cm −3 ). As the S/D doping concentration decreases, the improvement in I ON by decreasing the doping gradient becomes increasingly insignificant. In Table 1, the tunneling current becomes sensitive to the doping gradient when the doping concentration exceeds 5 × 10 19 cm −3 . This phenomenon can be attributed to the fact that, for the TFETs with S/D doping concentrations higher than 5 × 10 19 cm −3 , the BTBT process occurring at the Si/gate oxide interface was strongly influenced by the doping gradient, as shown in Fig. 20, where the minimum barrier width was greatly reduced as the doping gradient decreased. However, for the TFETs with S/D doping concentration lower than 2 × 10 19 cm −3 , the BTBT process occurring at the Si/gate oxide interface was only weakly affected by the doping gradient, as shown in Fig. 21, where the minimum barrier width remained almost the same as the doping gradient decreased. Thus, for low S/D doping concentration, the doping gradient has little effect on I ON , which is consistent with our previous work [25] where the S/D doping concentration was 1 × 10 19 cm −3 .

Summary of the effects of S/D doping concentration and SDG on TFETs
As to the effect of S/D doping concentration on I ON , unexpectedly, increasing the S/D doping concentration does not necessarily increase I ON , especially when the doping gradient becomes larger. Thus, for a given doping gradient, there exists an optimized S/D doping concentration which maximizes I ON . In Table 1, for the TFETs with doping gradients of 15 and 10 nm/decade, the optimized source doping concentration for maximizing I ON is 2 × 10 19 cm −3 . Further increasing the source doping concentration broadens the minimum barrier width at the interface, as shown in Fig. 15a and c, and hence decreases I ON . When the doping gradient was reduced to 5 nm/decade, the optimized source doping concentration for maximizing I ON was 5 × 10 19 cm −3 . From Figs. 14 and 18, in principle, for the high source doping concentration, the tunneling process occurred throughout the nanowire central region along the interface between the source and channel. The BTBT process which occurred at the interface became dominant only when the doping gradient was small enough that the minimum barrier width at the interface was narrower than that at the central part. However, for the low source doping concentration, the dominant tunneling process always occurred locally at the Si/gate oxide interface and at the source-end edge of the gate, and the doping gradient had very little influence on the minimum barrier width. In other words, the tunneling rate and I ON are determined by the combined effect of the source doping concentration and the doping gradient, which thus cannot be treated individually.

Conclusion
In this work, we simulated and examined in detail the effects of source doping concentration and doping gradient on n-type Si nanowire GAA TFETs. We found that for TFETs with high source doping concentration, BTBT occurred throughout the nanowire central region along the interface between the source and channel. The BTBT process which occurred at the interface became dominant only when the doping gradient was small enough that the minimum barrier width at the interface was narrower than that at the central part. However, for TFETs with low source doping concentration, the dominant BTBT always occurred locally at the Si/ gate oxide interface and the source-end edge of the gate, and the doping gradient had very little influence on the minimum barrier width. Therefore, for TFETs with high source doping concentration, reducing the doping gradient can increase the tunneling rate and I ON , while for TFETs with low source doping concentration, the doping gradient has little effect on the tunneling rate and I ON . Furthermore, for a given doping gradient, there exists an optimized source doping concentration which maximizes I ON . In summary, the I ON of the TFET does not monotonically increase with the doping concentration and the doping gradient. The tunneling rate and I ON of the TFETs are determined by two-dimensional (longitudinal and transverse) electrostatics, which are jointly affected by the source doping and its gradient. Therefore, the effects of the source doping and its gradient on the I ON of TFETs must be considered simultaneously.