Analysis of Work-Function Variation Effects in a Tunnel Field-Effect Transistor Depending on the Device Structure

Metal gate technology is one of the most important methods used to increase the low on-current of tunnel field-effect transistors (TFETs). However, metal gates have different work-functions for each grain during the deposition process, resulting in work-function variation (WFV) effects, which means that the electrical characteristics vary from device to device. The WFV of a planar TFET, double-gate (DG) TFET, and electron-hole bilayer TFET (EHBTFET) were examined by technology computer-aided design (TCAD) simulations to analyze the influences of device structure and to find strategies for suppressing the WFV effects in TFET. Comparing the WFV effects through the turn-on voltage (Vturn-on) distribution, the planar TFET showed the largest standard deviation (σVturn-on) of 20.1 mV, and it was reduced by −26.4% for the DG TFET and −80.1% for the EHBTFET. Based on the analyses regarding metal grain distribution and energy band diagrams, the WFV of TFETs was determined by the number of metal grains involved in the tunneling current. Therefore, the EHBTFET, which can determine the tunneling current by all of the metal grains where the main gate and the sub gate overlap, is considered to be a promising structure that can reduce the WFV effect of TFETs.

However, TFETs suffer from low-level on-current (I on ) as an alternative of MOSFETs. Therefore, there have been much research to improve the I on of TFETs by modifying the materials and structures of TFETs [23][24][25][26][27][28][29][30][31]. Among them, metal gate technology, which is also widely used in MOSFETs, can improve the gate controllability and increase I on by eliminating the polysilicon depletion effect [32]. However, metal gates have different work-functions for each grain due to different grain orientations during the deposition process. This results in a work-function variation (WFV) effect that causes variations in the threshold voltage (V th ) and other electrical characteristics of TFETs [33]. In this study, the WFV effects of a planar TFET, a double gate (DG) TFET, and an electron-hole bilayer TFET (EHBTFET) are compared using technology computer-aided design (TCAD) simulations to analyze the effects of the structure and to find a way to improve the WFV of TFETs. In the case of the planar TFET and DG TFET, a tunneling current occurs along the channel (lateral tunneling) at the source junction. On the contrary, the tunneling current of the EHBTFET is generated across the channel (vertical tunneling) at the body between two gates, and the electrical characteristics of this structure have been actively studied through TCAD simulations and modeling [34][35][36][37][38].  Table 1. In the modern integrated chip (IC) process, the grain size of the metal gate has a range of approximately 5 to 20 nm [39,40]. The grain size decreases when the DC (direct current) power of the sputtering process increases [40]. On the other hand, the grain size increases when the process temperature increases during or after the deposition process [39,41]. In this research, TiN (titanium nitride) was applied as the gate metal for the WFV effect analysis. In the case of TiN, it is also known that the grain size can be reduced by incorporating Cu or C when the TiN layer is deposited [42,43]. In this simulation and analysis, each metal grain was assumed to be a cube with a side length of 10 nm within the general range of the modern IC process. With regard to the WF value distribution of TiN, much research is still on-going, in order to develop a better understanding of the WF variation in TiN (e.g., considering the work-function (WF) of the grain boundary [44] and increment of the high-WF grain portion with the increased process temperature [41]). In this study, it was assumed that 60% of TiN grains were crystallized in <200> with 4.6 eV WF and 40% were crystallized in <111> with 4.4 eV WF, which are generally accepted values [39]. The blue arrows in Figure 1 indicate the positions where the tunneling mainly occurs in the on-state of each structure. Unlike the planar TFET and DG TFET, where tunneling occurs at the boundary between the source and channel region, EHBTFET has a tunneling current between the main gate (MG) and the sub gate (SG), as shown by the arrow in Figure 1d.
However, TFETs suffer from low-level on-current (Ion) as an alternative of MOSFETs. Therefore, there have been much research to improve the Ion of TFETs by modifying the materials and structures of TFETs [23][24][25][26][27][28][29][30][31]. Among them, metal gate technology, which is also widely used in MOSFETs, can improve the gate controllability and increase Ion by eliminating the polysilicon depletion effect [32]. However, metal gates have different work-functions for each grain due to different grain orientations during the deposition process. This results in a work-function variation (WFV) effect that causes variations in the threshold voltage (Vth) and other electrical characteristics of TFETs [33]. In this study, the WFV effects of a planar TFET, a double gate (DG) TFET, and an electron-hole bilayer TFET (EHBTFET) are compared using technology computer-aided design (TCAD) simulations to analyze the effects of the structure and to find a way to improve the WFV of TFETs. In the case of the planar TFET and DG TFET, a tunneling current occurs along the channel (lateral tunneling) at the source junction. On the contrary, the tunneling current of the EHBTFET is generated across the channel (vertical tunneling) at the body between two gates, and the electrical characteristics of this structure have been actively studied through TCAD simulations and modeling [34][35][36][37][38].  Table 1. In the modern integrated chip (IC) process, the grain size of the metal gate has a range of approximately 5 to 20 nm [39,40]. The grain size decreases when the DC (direct current) power of the sputtering process increases [40]. On the other hand, the grain size increases when the process temperature increases during or after the deposition process [39,41]. In this research, TiN (titanium nitride) was applied as the gate metal for the WFV effect analysis. In the case of TiN, it is also known that the grain size can be reduced by incorporating Cu or C when the TiN layer is deposited [42,43]. In this simulation and analysis, each metal grain was assumed to be a cube with a side length of 10 nm within the general range of the modern IC process. With regard to the WF value distribution of TiN, much research is still on-going, in order to develop a better understanding of the WF variation in TiN (e.g., considering the work-function (WF) of the grain boundary [44] and increment of the high-WF grain portion with the increased process temperature [41]). In this study, it was assumed that 60% of TiN grains were crystallized in <200> with 4.6 eV WF and 40% were crystallized in <111> with 4.4 eV WF, which are generally accepted values [39]. The blue arrows in Figure 1 indicate the positions where the tunneling mainly occurs in the on-state of each structure. Unlike the planar TFET and DG TFET, where tunneling occurs at the boundary between the source and channel region, EHBTFET has a tunneling current between the main gate (MG) and the sub gate (SG), as shown by the arrow in Figure 1d.   In order to compare and analyze the WFV effects of each structure, three-dimensional (3D) simulations were conducted using Synopsys Senataurus TM (Ver. K-2015.06-SP1, Synopsys, Mountain View, CA, USA) [45]. Fermi-Dirac statistics, doping concentration dependent mobility, Shockley-Read-Hall (SRH) recombination, and modified local density approximation (MLDA) models were used to calculate and extract the electrical characteristics of TFETs in the simulation. For an accurate calculation of band-to-band tunneling (BTBT), a dynamic non-local BTBT model was applied with theoretically calculated parameters [46] generally used in recent TFET research [47][48][49]. The metal grain profiles of the gate area were randomly generated by the randomization algorithm provided in the Sentaurus tool, depending on the TiN grain orientation. Thirty samples with uniquely randomized metal gate grain profiles for each structure were used for the simulation and the WFV effect analysis in this research. In the case of the EHBTFET in Figure 2c, a voltage of −0.67 V was applied to the SG to transport the holes from the source region to the channel region near SG and generate BTBT between the MG and the SG. For a comparison of the WFV effects, the average and standard deviation of Vth, SS and Ion for each structure were obtained and are summarized in Table 2. The Vth of MOSFET is defined as the gate voltage when VD is 0.5 V and the drain current is 10 −12 A. Instead of Vth, the turn-on voltage (Vturn-on) of TFETs is defined as the gate voltage when BTBT starts to occur at the source junction and the drain current increases compared to the leakage current, and is extracted when VD is 0.5 V and the drain current is 10 −18 A. In this research, Vturn-on was used for the WFV analysis instead of Vth, because the drain current of TFETs is much lower than that of MOSFETs, the definition of Vth in TFETs is controversial [50,51], and the SS variation effect of TFETs  In order to compare and analyze the WFV effects of each structure, three-dimensional (3D) simulations were conducted using Synopsys Senataurus TM (Ver. K-2015.06-SP1, Synopsys, Mountain View, CA, USA) [45]. Fermi-Dirac statistics, doping concentration dependent mobility, Shockley-Read-Hall (SRH) recombination, and modified local density approximation (MLDA) models were used to calculate and extract the electrical characteristics of TFETs in the simulation. For an accurate calculation of band-to-band tunneling (BTBT), a dynamic non-local BTBT model was applied with theoretically calculated parameters [46] generally used in recent TFET research [47][48][49]. The metal grain profiles of the gate area were randomly generated by the randomization algorithm provided in the Sentaurus tool, depending on the TiN grain orientation. Thirty samples with uniquely randomized metal gate grain profiles for each structure were used for the simulation and the WFV effect analysis in this research. In the case of the EHBTFET in Figure 2c, a voltage of −0.67 V was applied to the SG to transport the holes from the source region to the channel region near SG and generate BTBT between the MG and the SG. For a comparison of the WFV effects, the average and standard deviation of V th , SS and I on for each structure were obtained and are summarized in Table 2. The V th of MOSFET is defined as the gate voltage when V D is 0.5 V and the drain current is 10 −12 A. Instead of V th , the turn-on voltage (V turn-on ) of TFETs is defined as the gate voltage when BTBT starts to occur at the source junction and the drain current increases compared to the leakage current, and is extracted when V D is 0.5 V and the drain current is 10 −18 A. In this research, V turn-on was used for the WFV analysis instead of V th , because the drain current of TFETs is much lower than that of MOSFETs, the definition of V th in TFETs is controversial [50,51], and the SS variation effect of TFETs is large [33]. SS is defined as an average swing when the drain current is increased from 10 −12 to 10 −10 A (MOSFET) or 10 −18 to 10 −16 A (TFET). I on is defined as the drain current when V G is average V turn-on (average V th in MOSFETs) + 0.6 V and V D is 0.5 V. As shown in Figure 2 and Table 2, the σV turn-on of the planar TFET has the largest value (20.1 mV). In the case of the DG TFET, σV turn-on is reduced by −26.4% in comparison to the planar TFET. Moreover, in the EHBTFET, the σV turn-on is drastically reduced to −80.1% compared to the planar TFET, showing the smallest σV turn-on among the three types of TFET structures. The σSS and normalized σI on also show the same tendency as σV turn-on .

Results and Discussions
is large [33]. SS is defined as an average swing when the drain current is increased from 10 −12 to 10 −10 A (MOSFET) or 10 −18 to 10 −16 A (TFET). Ion is defined as the drain current when VG is average Vturn-on (average Vth in MOSFETs) + 0.6 V and VD is 0.5 V. As shown in Figure 2 and Table 2, the σVturn-on of the planar TFET has the largest value (20.1 mV). In the case of the DG TFET, σVturn-on is reduced by −26.4% in comparison to the planar TFET. Moreover, in the EHBTFET, the σVturn-on is drastically reduced to −80.1% compared to the planar TFET, showing the smallest σVturn-on among the three types of TFET structures. The σSS and normalized σIon also show the same tendency as σVturn-on.  The reduction in the WFV effect on the DG TFET and EHBTFET compared to the planar TFET can be interpreted as a result of an increase in the number of metal grains that affect Vturn-on determination. It is known that as the number of metal grains affecting Vturn-on increases, the WFV effect is suppressed by a higher averaging effect [52][53][54]. When the number of grains changes, the variance of the WF distribution (var(ΦM)) according to the number of grains (N) can be expressed as the following equation [55]:  The reduction in the WFV effect on the DG TFET and EHBTFET compared to the planar TFET can be interpreted as a result of an increase in the number of metal grains that affect V turn-on determination. It is known that as the number of metal grains affecting V turn-on increases, the WFV effect is suppressed by a higher averaging effect [52][53][54]. When the number of grains changes, the variance of the WF distribution (var(Φ M )) according to the number of grains (N) can be expressed as the following equation [55]: where Φ i and P i represent the WF value of each grain and the probability of achieving the WF value. As can be seen from (1), var(Φ M ) and the resulting WFV effects change when N changes. For example, as the grain size of the metal gate increases during the fabrication process (e.g., increase in the heat budget), the number of grains affecting the characteristics of the device decreases and the WFV effects increase. If the grain size is large enough that the overall gate area is filled by one metal grain, the V turn-on of 60% of devices is determined by a metal grain with a 4.6 eV WF and the V turn-on of the other 40% of devices is determined by a metal grain with a 4.4 eV WF. On the other hand, when the grain size of the metal gate is reduced during the fabrication process (e.g., by incorporating carbon into TiN), the WFV effects can be reduced [43]. If the grain size is continuously reduced and the metal gate reaches an almost amorphous state, it can be considered that there is no difference among the grain distributions of each device and the V turn-on values of all the devices converge to the average V turn-on .
As the grain size controlled by the process condition can affect the number of grains and the WFV effects, the device structure of TFETs can also affect the WFV effect if the structure can change the grain number, having effects on the V turn-on determination. In order to analyze the reason why the σV turn-on of the TFETs is different, depending on the structures, the metal grain distributions and the energy band diagrams were compared for the lowest and highest V turn-on among the simulated results of planar TFETs with the randomly generated metal grain profiles. Figure 3a,b show the metal grain distributions of planar TFETs, with the highest value of V turn-on at 0.367 V and the lowest value at 0.289 V, respectively. In the gate region of Figure 3a,b, a red color represents metal grains with WF of 4.6 eV, while a blue color shows other grains with WF of 4.4 eV. Comparing Figure 3a,b, there is a clear difference between the two samples in terms of the distribution of metal grains adjacent to the source region. Figure 3a, with high V turn-on , shows that most of the metal grains close to the source region have a WF of 4.6 eV, while Figure 3b, with low V turn-on , shows that there are more metal grains with a WF of 4.4 eV around the source region. where Φi and Pi represent the WF value of each grain and the probability of achieving the WF value. As can be seen from (1), var(ΦM) and the resulting WFV effects change when N changes. For example, as the grain size of the metal gate increases during the fabrication process (e.g., increase in the heat budget), the number of grains affecting the characteristics of the device decreases and the WFV effects increase. If the grain size is large enough that the overall gate area is filled by one metal grain, the Vturn-on of 60% of devices is determined by a metal grain with a 4.6 eV WF and the Vturn-on of the other 40% of devices is determined by a metal grain with a 4.4 eV WF. On the other hand, when the grain size of the metal gate is reduced during the fabrication process (e.g., by incorporating carbon into TiN), the WFV effects can be reduced [43]. If the grain size is continuously reduced and the metal gate reaches an almost amorphous state, it can be considered that there is no difference among the grain distributions of each device and the Vturn-on values of all the devices converge to the average Vturn-on.
As the grain size controlled by the process condition can affect the number of grains and the WFV effects, the device structure of TFETs can also affect the WFV effect if the structure can change the grain number, having effects on the Vturn-on determination. In order to analyze the reason why the σVturn-on of the TFETs is different, depending on the structures, the metal grain distributions and the energy band diagrams were compared for the lowest and highest Vturn-on among the simulated results of planar TFETs with the randomly generated metal grain profiles. Figure 3a,b show the metal grain distributions of planar TFETs, with the highest value of Vturn-on at 0.367 V and the lowest value at 0.289 V, respectively. In the gate region of Figure 3a,b, a red color represents metal grains with WF of 4.6 eV, while a blue color shows other grains with WF of 4.4 eV. Comparing Figure 3a,b, there is a clear difference between the two samples in terms of the distribution of metal grains adjacent to the source region. Figure 3a, with high Vturn-on, shows that most of the metal grains close to the source region have a WF of 4.6 eV, while Figure 3b, with low Vturn-on, shows that there are more metal grains with a WF of 4.4 eV around the source region.  Figure 4 shows the energy band diagrams of these two extreme cases of planar TFETs when VD is 0.5 V and VG is 0.4 V. Due to the difference in the distribution of the metal grains analyzed above, the energy band bending between the source and the channel region becomes larger in the case of Vturn-on = 0.289 V (red dash line) than in the case of Vturn-on = 0.367 V (black solid line). As a result, when the same VG is applied, there is a difference in the tunneling width of the two cases and accordingly, the Vth is also different. As described above, the planar TFET is relatively vulnerable to the WFV effect, as the Vth of the planar TFET is only determined by the energy band of the channel adjacent to the source region, while the Vth of the conventional MOSFET is determined by the entire channel under the gate [33]. In the metal grain distributions shown in Figure 3a Figure 4 shows the energy band diagrams of these two extreme cases of planar TFETs when V D is 0.5 V and V G is 0.4 V. Due to the difference in the distribution of the metal grains analyzed above, the energy band bending between the source and the channel region becomes larger in the case of V turn-on = 0.289 V (red dash line) than in the case of V turn-on = 0.367 V (black solid line). As a result, when the same V G is applied, there is a difference in the tunneling width of the two cases and accordingly, the V th is also different. As described above, the planar TFET is relatively vulnerable to the WFV effect, as the V th of the planar TFET is only determined by the energy band of the channel adjacent to the source region, while the V th of the conventional MOSFET is determined by the entire channel under the gate [33]. In the metal grain distributions shown in Figure 3a,b, planar TFETs have a ∆V turn-on of 78 mV (0.367 V-0.289 V) between the two cases. On the other hand, the DG TFET and EHBTFET show a ∆V turn-on of 65 mV (0.371-0.306 V) and 5 mV (0.685-0.679 V), respectively, when one of two gates has the same metal grain distribution, as shown in Figure 3a, show a ΔVturn-on of 65 mV (0.371-0.306 V) and 5 mV (0.685-0.679 V), respectively, when one of two gates has the same metal grain distribution, as shown in Figure 3a,b. As confirmed in the analysis of Figures 3 and 4, only seven metal grains near the source junction mainly affect the tunneling current and the Vturn-on of the planar TFET. Meanwhile, in the case of DG TFETs, the addition of another gate on the opposite side doubles the number of metal grains (14 metal grains) that affect the tunneling current and reduces the effect of WFV. Unlike the planar TFET or DG TFET, in the on-state of the EHBTFET, electrons are collected under MG and holes are collected under SG. As the bias of MG increases, energy band bending and a tunneling current are generated in the channel between the two gates. The EHBTFET has a tunneling current at the channel between MG and SG, and all of the metal grains (70 metal grains) where MG and SG overlap are included in Vturnon determination, which greatly reduces the effect of WFV.
This analysis can be confirmed indirectly by comparing the probabilities of the most extreme theoretical cases of the planar TFET, DG TFET and EHBTFET. As discussed above, the Vturn-on of the planar TFET and DG TFET is controlled by the metal grains near the source. Therefore, the planar TFET has the maximum value of Vturn-on when all WFs of seven metal grains adjacent to the source are 4.6 eV and the minimum Vturn-on when they are all 4.4 eV; the probabilities are 2.8% (0.6 7 ) and 0.2% (0.4 7 ), respectively. Similarly, for the DG TFET, the probability of the maximum Vturn-on is 7.8 × 10 −2 % (0.6 14 ) and the probability of the minimum Vturn-on is 2.7 × 10 −4 % (0.4 14 ). In the case of the EHBTFET, as tunneling occurs from the valence band of the channel near SG to the conduction band of the channel near MG, the Vturn-on reaches the maximum when all MG grains have a WF of 4.6 eV and all SG grains have a WF of 4.4 eV where MG and SG overlap, as shown in Figure 5a; its probability is 2.0 × 10 −20 % (0.6 35 × 0.4 35 ). Additionally, in the opposite case, as shown in Figure 5b, the Vturn-on reaches the minimum and its probability is equal to the probability of the maximum Vturn-on. By comparing the probabilities of the most extreme cases in the three structures, it was confirmed that the EHBTFET has the smallest probabilities, and this difference is caused by the difference in the number of metal grains that affect the Vturn-on.  This analysis can be confirmed indirectly by comparing the probabilities of the most extreme theoretical cases of the planar TFET, DG TFET and EHBTFET. As discussed above, the V turn-on of the planar TFET and DG TFET is controlled by the metal grains near the source. Therefore, the planar TFET has the maximum value of V turn-on when all WFs of seven metal grains adjacent to the source are 4.6 eV and the minimum V turn-on when they are all 4.4 eV; the probabilities are 2.8% (0.6 7 ) and 0.2% (0.4 7 ), respectively. Similarly, for the DG TFET, the probability of the maximum V turn-on is 7.8 × 10 −2 % (0.6 14 ) and the probability of the minimum V turn-on is 2.7 × 10 −4 % (0.4 14 ). In the case of the EHBTFET, as tunneling occurs from the valence band of the channel near SG to the conduction band of the channel near MG, the V turn-on reaches the maximum when all MG grains have a WF of 4.6 eV and all SG grains have a WF of 4.4 eV where MG and SG overlap, as shown in Figure 5a; its probability is 2.0 × 10 −20 % (0.6 35 × 0.4 35 ). Additionally, in the opposite case, as shown in Figure 5b, the V turn-on reaches the minimum and its probability is equal to the probability of the maximum V turn-on . By comparing the probabilities of the most extreme cases in the three structures, it was confirmed that the EHBTFET has the smallest probabilities, and this difference is caused by the difference in the number of metal grains that affect the V turn-on . In order to prove that the WFV improvement of the EHBTFET is due to the large number of metal grains, the σVturn-on of the planar TFET, DG TFET, and EHBTFET was examined while reducing the LG of the EHBTFET, as shown in Figure 6. The WFV effects of the planar TFET and DG TFET were determined by the metal grains located at the edge between the source and the channel. Therefore, the σVturn-on of the planar TFET and DG TFET is not significantly affected by the change in the gate length. On the other hand, when the LG of the EHBTFET decreases, the number of metal grains in the overlapping areas of MG and SG decreases and the σVturn-on of the EHBTFET increases accordingly. By comparing when LG was 70 nm and when LG was 30 nm, it can be seen that the σVturn-on of the EHBTFET increased from 4.0 to 9.9 mV as the number of metal grains affecting the tunneling current decreased from 70 to 14, respectively. Therefore, if LG continues to decrease, the WFV effects of the EHBTFET are expected to be similar to those of other TFET structures. In addition, the electrical performance (e.g., Ion) also degrades as the tunneling area (i.e., overlap area between main and sub gates) of the EHBTFET decreases with the smaller LG. Consequently, when the scaling down of TFETs continues, it is necessary to maintain the LG by using a vertical channel [38] to maintain the advantages of the EHBTFET in the WFV effects. Figure 6. The σVturn-on of the planar TFET, DG TFET, and EHBTFET when the LG is changed. While reducing the LG, the LCH is reduced by the same length, and LUD and LUS are kept at 20 nm.

Conclusions
In this research, the WFV effects of the planar TFET, DG TFET, and EHBTFET were compared and analyzed by TCAD simulation. As a result of extracting the σVturn-on and examining the metal grain distributions, it was confirmed that the planar TFET has the greatest WFV effect because only a few metal grains around the source region affect the Vturn-on. On the other hand, the EHBTFET is the In order to prove that the WFV improvement of the EHBTFET is due to the large number of metal grains, the σV turn-on of the planar TFET, DG TFET, and EHBTFET was examined while reducing the L G of the EHBTFET, as shown in Figure 6. The WFV effects of the planar TFET and DG TFET were determined by the metal grains located at the edge between the source and the channel. Therefore, the σV turn-on of the planar TFET and DG TFET is not significantly affected by the change in the gate length. On the other hand, when the L G of the EHBTFET decreases, the number of metal grains in the overlapping areas of MG and SG decreases and the σV turn-on of the EHBTFET increases accordingly. By comparing when L G was 70 nm and when L G was 30 nm, it can be seen that the σV turn-on of the EHBTFET increased from 4.0 to 9.9 mV as the number of metal grains affecting the tunneling current decreased from 70 to 14, respectively. Therefore, if L G continues to decrease, the WFV effects of the EHBTFET are expected to be similar to those of other TFET structures. In addition, the electrical performance (e.g., I on ) also degrades as the tunneling area (i.e., overlap area between main and sub gates) of the EHBTFET decreases with the smaller L G . Consequently, when the scaling down of TFETs continues, it is necessary to maintain the L G by using a vertical channel [38] to maintain the advantages of the EHBTFET in the WFV effects. In order to prove that the WFV improvement of the EHBTFET is due to the large number of metal grains, the σVturn-on of the planar TFET, DG TFET, and EHBTFET was examined while reducing the LG of the EHBTFET, as shown in Figure 6. The WFV effects of the planar TFET and DG TFET were determined by the metal grains located at the edge between the source and the channel. Therefore, the σVturn-on of the planar TFET and DG TFET is not significantly affected by the change in the gate length. On the other hand, when the LG of the EHBTFET decreases, the number of metal grains in the overlapping areas of MG and SG decreases and the σVturn-on of the EHBTFET increases accordingly. By comparing when LG was 70 nm and when LG was 30 nm, it can be seen that the σVturn-on of the EHBTFET increased from 4.0 to 9.9 mV as the number of metal grains affecting the tunneling current decreased from 70 to 14, respectively. Therefore, if LG continues to decrease, the WFV effects of the EHBTFET are expected to be similar to those of other TFET structures. In addition, the electrical performance (e.g., Ion) also degrades as the tunneling area (i.e., overlap area between main and sub gates) of the EHBTFET decreases with the smaller LG. Consequently, when the scaling down of TFETs continues, it is necessary to maintain the LG by using a vertical channel [38] to maintain the advantages of the EHBTFET in the WFV effects. Figure 6. The σVturn-on of the planar TFET, DG TFET, and EHBTFET when the LG is changed. While reducing the LG, the LCH is reduced by the same length, and LUD and LUS are kept at 20 nm.

Conclusions
In this research, the WFV effects of the planar TFET, DG TFET, and EHBTFET were compared and analyzed by TCAD simulation. As a result of extracting the σVturn-on and examining the metal grain distributions, it was confirmed that the planar TFET has the greatest WFV effect because only a few metal grains around the source region affect the Vturn-on. On the other hand, the EHBTFET is the Main gate Figure 6. The σV turn-on of the planar TFET, DG TFET, and EHBTFET when the L G is changed. While reducing the L G , the L CH is reduced by the same length, and L UD and L US are kept at 20 nm.

Conclusions
In this research, the WFV effects of the planar TFET, DG TFET, and EHBTFET were compared and analyzed by TCAD simulation. As a result of extracting the σV turn-on and examining the metal grain distributions, it was confirmed that the planar TFET has the greatest WFV effect because only a few metal grains around the source region affect the V turn-on . On the other hand, the EHBTFET is the most immune from the WFV effect, as all of the metal grains where MG and SG overlap determine the V turn-on .