A. The Effect of SDG under Different S/D Doping Concentrations
Figure 6 shows the ID-VG curves of the TFETs with 3 different doping gradients (15, 10, and 5 nm/decade) under the S/D doping concentration of 1×1020 cm-3. In this work, the VDD and also the drain voltage, VD, is set to be 1 V. The swing range of the gate voltage, VG, is − 1 to 1 V. The ON-state current, ION, and the OFF-state current, IOFF, are defined by the drain currents under VD = 1 V with VG = 1 V and 0 V, respectively. Note that the drain current in this work is divided by the Si NW periphery and hence the unit is A/µm. From Fig. 6, we observed that reducing SDG from 15 to 5 nm/decade significantly increases ION. The ambipolar behavior is noticeable in Fig. 6 and can be suppressed by gate-drain underlap [6] which is beyond the scope of this work. Figure 7 shows the ON-state electron tunneling rates of the TFETs with 3 different doping gradients (15, 10, and 5 nm/decade) under the S/D doping concentration of 1×1020 cm-3. From Fig. 7, BTBT is basically distributed over the radius of Si nanowire around the interface between 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 8 shows the ON-state energy-band diagrams of the TFETs with 3 different doping gradients (15, 10, and 5 nm/decade) under the S/D doping concentration of 1×1020 cm-3 along the interface of Si and gate oxide as well as the central part of Si nanowire. Note that in this work, the energy-band diagrams along the channel direction were obtained at two locations: one is 0.1 nm below the interface of Si and gate oxide (referred to as the interface, unless other specifying), and the other is 2 nm away from the center of 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. 8, as the doping gradient became sharper, the minimum barrier width became narrower for both the interface and the central part.
Next, we will examine the effects of SDG when the S/D doping concentration is reduced from previous 1×1020 to 1×1019 cm-3. Figure 9 shows the ID-VG curves of the TFETs with 3 different doping gradients (15, 10, and 5 nm/decade) under the S/D doping concentration of 1×1019 cm-3. From Fig. 9, we found that reducing SDG from 15 to 5 nm/decade merely increases ION slightly. Again, we checked the ON-state electron tunneling rates of the TFETs with 3 different doping gradients (15, 10, and 5 nm/decade) under the S/D doping concentration of 1×1019 cm-3 as shown in Fig. 10. Unlike the TFETs with the S/D doping concentration of 1×1020 cm-3, for the TFETs with the S/D doping concentration of 1×1019 cm-3, BTBT occurs more locally and mainly at the interface of Si and gate oxide as well as at the source-end edge of 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 11 shows the ON-state energy-band diagrams of the TFETs with 3 different doping gradients (15, 10, and 5 nm/decade) under the S/D doping concentration of 1×1019 cm-3 along the interface of Si and gate oxide as well as the central part of Si nanowire. In Fig. 11, the minimum barrier width at the interface is obviously smaller than that at the central part and hence much higher electron tunneling rate appeared at the interface. Besides, the minimum barrier widths at the interface for the 3 different doping gradients are almost the same and difficult to be discriminated in Fig. 11, which resulted in the close electron tunneling rates for the 3 different doping gradients as shown in Fig. 10.
B. The Effect of S/D Doping Concentration under Different SDGs
Figure 12 shows the ID-VG curves of the TFETs with 4 different S/D doping concentrations (1×1020, 5×1019, 2×1019, and 1×1019 cm-3) under the SDG of 15 nm/decade. Surprisingly, the TFET with S/D doping concentration of 2×1019 cm-3 has the largest ION. Further increasing S/D doping concentration decreases ION instead. Figure 13 shows the ON-state electron tunneling rates of the TFETs with the previous four S/D doping concentrations under the SDG of 15 nm/decade. The TFET with S/D doping concentration of 2×1019 cm-3 has highest electron tunneling rate which occurred at the interface and therefore also has highest ION. Figure 14 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 interface of Si and gate oxide as well as the central part of Si nanowire. In Fig. 14, for the TFETs with S/D doping concentrations of 2×1019 and 1×1019 cm-3, the minimum barrier width at the interface is obviously smaller than that at the central part and hence much higher electron tunneling rate appeared at the interface. However, further increasing S/D doping concentration broadens the minimum barrier width at the interface as shown in Fig. 14(a) and (c) and consequently the tunneling process at the central part dominates the tunneling rate. Note that, in Fig. 14(a) and (c), the longitudinal electric fields at the source-end gate edge are higher than those of Fig. 14(e) and (g), but the electrons in the valence band at the source see a wider barrier width instead. That means higher longitudinal electric field does not necessarily lead to higher tunneling rate and accompanying higher ION. That also implies the local BTBT models would be problematic since the tunneling rates of local BTBT models are determined by the electric field.
Next, we investigate the effect of S/D doping concentration when the SDG is reduced from aforementioned 15 to 5 nm/decade. Figure 15 shows the ID-VG curves of the TFETs with 4 different S/D doping concentrations (1×1020, 5×1019, 2×1019, and 1×1019 cm-3) under the SDG of 5 nm/decade. We found that the TFET with S/D doping concentration of 1×1019 cm-3 has approximately one-order-of-magnitude lower ION than those of the TFETs with S/D doping concentration higher than 2×1019 cm-3. Figure 16 shows the ON-state electron tunneling rates of the TFETs with the preceding four S/D doping concentrations under the SDG of 5 nm/decade. In Fig. 16, the ON-state electron tunneling rate of the TFET with S/D doping concentration of 1×1019 cm-3 is obviously lower than those of the TFETs with S/D doping concentration higher than 2×1019 cm-3 and hence results in lower ION. Besides, as the S/D doping concentration increases, the dominant tunneling process at the source/channel interface spreads from the Si/SiO2 interface to the entire central region. Figure 17 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 interface of Si and gate oxide as well as the central part of Si nanowire. In Fig. 17, the minimum barrier width at the interface is basically smaller than that at the central part. For the TFET with S/D doping concentration of 1×1019 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 concentration higher than 2×1019 cm-3 and therefore give rise to lower electron tunneling rate. In addition, as the S/D doping concentration increases, the minimum barrier width at the central part decreases and consequently increases the electron tunneling rate at the central part.
C. Summary of the Effects of S/D Doping Concentration and SDG on TFETs
Table I summarized the ION under aforementioned four S/D doping concentrations and three doping gradients. Basically, reducing the doping gradient can improve ION especially when the S/D doping concentration is high such as 1×1020 cm-3. As the S/D doping concentration decreases, the ION improvement by decreasing the doping gradient becomes more and more insignificant. For the TFETs with the S/D doping concentration of 1×1019 cm-3, the dominant BTBT process occurs locally at the interface of Si and gate oxide as well as at the source-end edge of gate. Therefore, the doping gradient has little effect on ION which is consistent with our previous work [22] where the S/D doping concentration is also 1×1019 cm-3. On the other hand, for the TFETs with the S/D doping concentration of 1×1020 cm-3, the BTBT process spreads within the radius of Si nanowire along the interface between source and channel. Consequently, the doping gradient has strong effect on ION. Figure 18(a) and (b) shows the longitudinal electric field of the TFETs with the S/D doping concentration of 1×1019 and 1×1020 cm-3, respectively, under the doping gradient of 10 nm/decade. For the TFET with the S/D doping concentration of 1×1019 cm-3, the depletion region encroaches into the source region and the maximum longitudinal electric field appears at the interface of Si and gate oxide as well as at the source-end edge of gate where the dominant BTBT process occurs. However, for the TFET with the S/D doping concentration of 1×1020 cm-3, the depletion region is pushed back to the interface between source and channel which makes the doping gradient play an important role in determining the tunneling current.
TABLE I The TFET ON-State Current (ION) for Different S/D Doping Concentrations and Doping Gradients
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S/D doping of 1×1020 cm-3
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S/D doping of 5×1019 cm-3
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S/D doping of 2×1019 cm-3
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S/D doping of 1×1019 cm-3
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SDG of 15 nm/decade
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0.0638
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0.160
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4.03
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1.21
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SDG of 10 nm/decade
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0.689
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0.856
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5.58
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1.32
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SDG of 5 nm/decade
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10.4
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12.4
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10.4
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1.58
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The ON-state current, ION, is defined by the drain current under VD = VG = 1 V and the unit is μA/μm.
As to the effect of S/D doping concentration on ION, unexpectedly, increasing the S/D doping concentration does not necessarily increase ION especially when the doping gradient becomes larger. That means, for a given doping gradient, there exists an optimized S/D doping concentration which maximizes ION. For the TFETs with the doping gradient of 15 nm/decade, the optimized source doping concentration for maximizing ION is 2×1019 cm-3. Further increasing source doping concentration broadens the minimum barrier width at the interface as shown in Fig. 14(a) and (c) and hence decreases ION. As the doping gradient was reduced to 5 nm/decade, the optimized source doping concentration for maximizing ION became 5×1019 cm-3. From Figs. 13 and 16, in principle, for the high source doping concentration, the tunneling process occurred throughout the nanowire central region along the interface between source and channel. However, for the low source doping concentration, the dominant tunneling process occurred locally at the interface of Si and gate oxide as well as at the source-end edge of gate. For the high source doping concentration, reducing the doping gradient can increase the longitudinal electric field as shown in Fig. 19(a) and (b) as well as the tunneling rate as shown in Fig. 7. Nevertheless, for the low source doping concentration, the doping gradient has little effect on the tunneling rate and ION as discussed previously. In a word, the tunneling rate and ION are determined by the combined effect of the source doping concentration and the doping gradient which cannot be treated individually.