Investigation of the impact of mole-fraction on the digital benchmarking parameters as well as sensitivity in GaXIn1-XAs/GaYIn1-YSb vertical heterojunctionless tunneling field effect transistor


 GaXIn1-XAs/GaYIn1-YSb vertical heterojunctionless tunneling field effect transistor (VHJL-TFET) has been suggested to optimize the digital benchmarking parameters. In the proposed VHJL-TFET with type II heterostructure (i.e. X=0.8, Y=0.85), slight changes in gate voltage cause switching from OFF-state to ON-state. As a result, the electrical properties of Ga0.8In0.2As/Ga0.85In0.15Sb VHJL-TFET are excellent in the sub-threshold region. The heterostructure with III-V semiconductors in the source-channel region increases the ON-state current (ION (of the VHJL-TFET. Comparing the results of Ga0.8In0.2As/Ga0.85In0.15Sb VHJL-TFET with the simulated devices with type I heterostructure (i.e. X=0.9, Y=0.1) and type III heterostructure (i.e. X=0.1, Y=0.4) shows the improvement by 26% and 15% in the average subthreshold slope (SS). Sensitivity analysis for VHJL-TFET with the type II heterostructure shows that the sensitivity of OFF-state current (IOFF) to the body thickness (Tb) and doping concentration (ND) is more than the sensitivity of the other main electrical parameters. The Ga0.8In0.2As/Ga0.85In0.15Sb VHJL-TFET with a channel length of 20 nm, Tb=5 nm, and ND=1×1018cm-3 showed the SS=4.4mV/dec, ION/IOFF=4E14, and ION=8mA/um. As a result, Ga0.8In0.2As/Ga0.85In0.15Sb VHJL-TFET can be a reasonable choice for digital applications.


Introduction
Subthreshold slope (SS) of less than 60mV/dec and low leakage current of tunneling field effect transistor (TFET), respectively, causes an increase in switching speed and causes a reduction in static power consumption in digital circuits performance [1][2][3]. As a result, TFET device has attracted the attention of many researchers for digital applications [4,5]. However, the ultra-sharp doping concentration gradient in the source/channel and the drain/channel junctions complicates the fabrication process of TFET device in nanometer regime [6,7]. Recently, a junctionless TFET (JLTFET) has been proposed, in which issues caused by ultra-sharp doping concentration gradient in the source/channel and the drain/channel junctions are eliminated [6][7][8][9][10][11][12]. JLTFET is a heavy doped thin film semiconductor, in which the type and level of doping are unchanged throughout the device. In fact, in JLTFET device, the advantages of conventional TFET and junctionless field effect transistor are combined [7,13].
Silicon-based JLTFET such as conventional silicon based TFET, is suffering from issues caused by low ON-state current (ION) due to tunneling mechanism [7,14]. The reason is that the forbidden band width is so large that it reduces the electron tunneling probability in tunneling junction [6,11]. With the recent progress, the low ION problem in JLTFET has been resolved by various strategies, such as using small band gape materials [15,16] gate engineering [17,18]. and hetero-gate dielectric [11,19]. The use of III-V materials with staggered/broken bandgaps is suggested to increase ION in JLTFET [20][21][22][23]. III-V materials have improved the performance of the JLTFET device, due to high mobility as well as lower band gap [22,24]. JLTFET device with hetero structure is called HJL-TFET. In previous works, HJL-TFET structures are presented horizontally [20][21][22][23]. It is very complex to create horizontal heterojunction structures in HJL-TFET device. Use of vertical heterojunction in HJL-TFET is feasible and can reduce the chip consumption level in integrated circuits [25].
In this paper, a vertical heterojunctionless tunneling field effect transistor with III-V materials is proposed, which is called VHJL-TFET. GaXIn1-XAs and GaYIn1-YSb are recommended as a drain-channel material and as the source material, respectively in the proposed structure. The main goal of this study is to optimize the digital benchmarking parameters of GaXIn1-XAs/ GaYIn1-YSb VHJL-TFET in terms of the ION/IOFF ratio and SS by varying the mole fraction of X and Y.
The simulation results in the OFF-state show that, with changes in X and Y parameters, the type I, type II and type III hetero structures are formed in the source/channel interface. By choosing X=0.8 and Y=0.85 in the proposed VHJL-TFET device, the type II hetero structure is formed. As a result, with slight changes in gate voltage, the electron tunneling will occur from source valence band to channel conduction band, which can effectively improve the SS and ION. Our simulation results show that selecting a material with larger band gap in the drain-channel region as well as a material with smaller band gap in the source region in VHJL-TFET device drastically reduce the ambipolarity behavior. Based on the simulation results, the improvement of the SS and ON-state current to OFFstate current (ION/IOFF) ratio of VHJL-TFET structure with Y=0.85 and X=0.8 is noticeable compared to the recently proposed structures [11,12,18,21,22,26]. With changes in X and Y, in addition to energy band gap and electron affinity, the electron tunneling effective mass and hole tunneling effective mass are also changed [27]. We considered these changes in our simulations. In the VHJL-TFET structure with Y=0.85 and X=0.8, the effect of changes in structural parameters, such as doping concentration, body thickness, and spacer width between the auxiliary gate and control gate, is investigated on the main electrical parameters. Finally, the performance of the proposed VHJL-TFET device is compared with that of the recently proposed devices.
This article is organized in 4 Sections. The structure of the device and the simulation models are described in Section 2. In Section 3, the simulation results of the VHJL-TFET structure are presented. Finally, the conclusion is provided in Section 4. Figure 1 shows the structure of the simulated VHJL-TFET device in this paper. In the simulated structure to increase gate control over the channel, double gate technology is used. In the VHJL-TFET structure shown in Fig. 1, the source, channel, and drain doping is considered the same and of the donor type with value of ND=1×10 18 cm -3 . GaXIn1-XAs is selected as a drain-channel material and the source is composed of GaYIn1-YAs. As shown in Fig. 1, the channel length, body thickness (Tb), and gate dielectric thickness (TOX) are 20nm, 5nm, and 2nm, respectively. Drain/source extension length is 20nm. HfO2 is considered as a gate dielectric with K=25. In the proposed structure, SiO2 acts between control gate (c-gate) and auxiliary gate (p-gate) as the isolation layer with the thickness of WSiO2=2nm. The p-gate work function is 5.9ev and is achieved by considering Pt as the gate electrode [28]. The cgate work function is 4.3eV and can be obtained as metal using molybdenum with nitrogen implant dose [28]. The structural parameters of the VHJL-TFET device proposed in Fig. 1 are the same as those of HJL-TFET device proposed in [23] and [22] VHJL-TFET device shown in Fig. 1 is called GaXIn1-XAs/GaYIn1-YSb VHJL-TFET.

Device structure and simulation setup
In order to simulate the GaXIn1-XAs/GaYIn1-YSb VHJL-TFET, a commercial tool is used. The nonlocal band to band tunneling (BTBT) model is considered to determine the electrical properties of the proposed device. Nonlocal BTBT model considers spatial variations of energy bands and quasi-fermi levels in tunneling path [22,29]. The Hansch model is used to consider the quantum confinement effect as well as interface defects of oxide/semiconductor [12,29]. The dependence of the mobility on the vertical electric field, doping concentration, and temperature is considered using Lombardi model [22,29]. The direct generation/recombination model as well as Shockley-Read-Hall (SRH) recombination model is considered to determine the accurate leakage current value in the simulated devices [22,29]. Given the high doping density in the proposed device, the band gap narrowing model is used [29,30]. With changes in X and Y, in addition to changing energy band gap and electron affinity, the electron tunneling effective mass and hole tunneling effective mass are varied [27]. These changes are calculated based on [27] and are considered in the simulation. The effects of defects and nonsmoothness in the interfacial regions of GaXIn1-XAs/GaYIn1-YSb layers are neglected in our simulations. These effects in real devices flat the ID-VGS characteristics due to high electric field effects [30]. In GaXIn1-XAs/GaYIn1-YSb VHJL-TFET device, instead of doping junctions in regular TFET devices, there is a junction between two semiconductors with the same doping. Therefore, GaXIn1-XAs/GaYIn1-YSb VHJL-TFET is still categorized as a junctionless device In order to show the accuracy of our simulations in this paper, we simulated the HJL-TFET with the structural parameters reported in [23]. The HJL-TFET device reported in [23] contains GaAs material in both drain and channel regions, and Ge material in the source region. Figure 1b shows a comparison between our numerical simulations and simulation reported in [23]. Our numerical simulations are performed under the same conditions reported in [23]. As can be seen, the results of our numerical simulations are reasonably consistent with the simulation results reported in [23]. Therefore, the models used in the simulation in this study are sufficiently accurate.

Results and Discussion
Equation 1 shows the probability of tunneling in a TFET device, in which Wentzel-Kramers-Brillouin approximation is used [12,16].
Where E g is energy band gap, h is Planck constant, q is electron charge, λ is screening length, T ox is gate dielectric thickness, and T ch is channel thickness. ε channel and ε oxide are relative permittivity of channel and gate dielectric, respectively. ∆φ is the energy difference between the valence band of the source and the conduction band of the channel, and m * is tunneling effective mass [16]. In fact, Equation 1 shows that both parameters E g and m * play an important role in the performance of the TFET device.
One of the main motivations for this study is to improve performance of GaXIn1-XAs/GaYIn1-YSb VHJL-TFET device proposed with changes in X and Y mole fractions. By changing the X and Y parameters, the electron tunneling effective mass (me * ), hole tunneling effective mass (mh * ), energy band gap and electron affinity (χ) in source, channel and drain regions of GaXIn1-XAs/GaYIn1-YSb VHJL-TFET device are affected, followed by changes in electrical properties of the simulated device.
Equations 2 and 3 show the electron tunneling effective mass and hole tunneling effective mass, respectively, in the drain-channel region (GaXIn1-XAs) and source region (GaYIn1-YSb) [27]. Where m0 is the free electron mass, mhh is heavy hole mass, and mlh is light hole mass. In Equations 2 and 3, at various X and Y, GaXIn1-XAs and GaYIn1-YSb have direct band gap. Therefore, the electron effective mass is used at Г valley in the simulation [27].
Equations 4 and 5 show the energy band gap (Eg) and electron affinity (χ), respectively, in the drain-channel region (GaXIn1-XAs) and source region (GaYIn1-YSb) [27]. As shown in Fig. 2a, for a given value of X=Y, the energy band gap in the source region (GaYIn1-YSb) is lower than that in the channel region (GaXIn1-XAs). Also, for a given value of X=Y, with the simultaneous increase in mole fractions, the difference in energy band gap between source (GaYIn1-YSb) and channel (GaXIn1-XAs) is increased. The difference in electron affinity between GayIn1-ySb and GaxIn1-xAs is reduced for a given value X=Y with an increase in mole fractions and, for X=Y=1, the electron affinity of the two materials overlaps. Figure 2b shows that for a given value of X=Y with an increase in mole fractions, the tunneling effective mass of the electron and hole is increased for both materials and also the increased effective mass in GayIn1-ySb is negligible.

Performance evaluation of the VHJL-TFET device for various mole fractions
In this section, for the proposed structure GaXIn1-XAs/GaYIn1-YSb VHJL-TFET, X mole fraction is increased from 0 to 1 with steps of 0.05; for each step of X, Y mole fraction is varied from 0 to 1. For various X and Y changes, the digital benchmarking parameters of GaXIn1-XAs/GaYIn1-YSb VHJL-TFET are investigated.
There are authoritative references [31] that considered ION as a drain current for bias conditions VGS=VDS=VDD and, IOFF as a drain current for bias conditions VGS=0V and VDS=VDD. In this study, VDD is considered to be 1V. Therefore, the drain current for bias conditions VGS=0V and VDS=1V is considered as IOFF and the drain current for bias conditions VGS=VDS=1V is considered as ION [31]. Also, the gate-source voltage for drain current 10 -7 A/um is considered as the threshold voltage [31]. Examinations in this study show that changes in X and Y parameters, in addition to changing electron tunneling effective mass and hole tunneling effective mass, would change the energy band profile in the source/channel interface. The changes in energy band profile are in a way that type I, type II, and type III hetero structures are created in the source/channel interface in the OFF-state (see Figure 3 to 6).  Figure 3a shows 2D matrix of IOFF changes and Fig. 3b shows 2D matrix of ION changes with variations of X and Y parameters. As seen, with changes in X and Y parameters, ION changes are one order of magnitude and IOFF changes are fourteen orders of magnitude. As a result, sensitivity of IOFF to changes in X and Y parameters, is higher than that of ION. The regions of type I, type II and type III hetero structures in OFF-state are shown in Fig. 3a. Accordingly, for some X and Y values in the region related to type III hetero structure, IOFF is larger than 10 -7 A/um. Therefore, in bias conditions VGS=0V and VDS=1V, the device is not located in the sub-threshold region. Comparison of Fig. 3a and Fig. 2a shows that, with an increase in X=Y in the region related to type II hetero structure, the electron and hole tunneling effective mass increases. As a result, the probability of tunneling based on Equation 1 is reduced and, consequently, IOFF is decreased. Our simulation results show that the tunneling width is reduced in ON-state for the values of X and Y in the red region in Fig. 3b. As a result, ION is increased in this region for the proposed GaXIn1-XAs/GaYIn1-YSb VHJL-TFET device.
Average SS in TFET is one of the most important parameters to evaluate switching performance from IOFF to ION. In  this study, the average SS is considered between a point where the drain current is raised with an increase in gate voltage and threshold voltage [22,32]. Figure 4a shows the contour of the changes in average SS by changing the X and Y parameters. The lower average SS in GaXIn1-XAs/GaYIn1-YSb VHJL-TFET indicates higher switching rate [15,22,32].
In this study, the optimal selection of X and Y values to improve the digital benchmarking parameters of GaXIn1-XAs/GaYIn1-YSbVHJL-TFET device are carried out by considering the following priorities: 1. IOFF must be of the fA/um order or smaller, because in TFET devices, the IOFF is expected to be of the fA/um order at the most [32].
2. Average SS must be smaller than 10mV/dec, because the TFET device with SS<10mV/dec is very suitable for sub-0.5V supply voltage applications [11,33].
3. ION must be of the mA/um order, because in TFET devices with ION from mA/um order, it can be said that the problems caused by the decreased ION are eliminated [15][16][17][18]22].
According to the priorities mentioned above, the optimal mole fractions are selected equal to X=0.8 and Y=0.85 to improve the performance of the proposed GaXIn1-XAs/GaYIn1-YSb VHJL-TFET structure. In Ga0.8In0.2As/Ga0.85In0.15Sb VHJL-TFET device shown in Fig. 1, we have IOFF=0.02fA/um, ION=8mA/um, SS=4.4mV/dec. The contours of Fig. 3a show that, for X=0.8 and Y=0.85, the IOFF is reduced compared to other values of X and Y. The contours of Fig. 3b also show that, for X=0.8 and Y=0.85, ION of the proposed device is reasonable compared to the other values of X and Y. As a result, in the proposed device for X=0.8 and Y=0.85, ION/IOFF ratio is increased. The contour of Fig. 4a also shows the average SS of Ga0.8In0.2As/Ga0.85In0.15Sb VHJL-TFET device is smaller than 10mV/dec, and is improved compared to other values of X and Y.
For studying the band structure of the proposed GaXIn1-XAs/GaYIn1-YSb VHJL-TFET device, it is not possible to display the energy band profile for all X and Y values. In this study, X=0.9, Y=0.1 and X=0.8, Y=0.85, and X=0.1, Y=0.4 are considered for the hetero structure of type I, type II, and type III, respectively. Fig. 4b shows the currentvoltage input characteristic of the simulated devices for different values of X and Y. As seen: 1. IOFF of the simulated device with X=0.8, Y=0.85 is much lower than the other simulated devices.
4. The simulated device with X=0.1 and Y=0.4 has the IOFF larger than 7A/um. Therefore, it will not turn off at VGS=0V. Figure 5a and Fig. 5b show the energy band profile for simulated structures with X=0.8 and Y=0.85 (type II hetero structure) and X=0.9 and Y=0.1 (type I hetero structure) in bias conditions of OFF-state. In addition, the energy band profile in bias conditions of OFF-state for X=0.1 and Y=0.4 (type III hetero structure) is shown in Fig. 6. Figure 7a compares the energy band diagram of type I, type II, and type III hetero structures in vicinity of the source/channel interface in OFF-state for the simulated structures.
Overlap of source valence band and channel conduction band for X=0.8 and Y=0.85 is small enough to not allow the electron tunneling from the source valence band to the channel conduction band (see Fig. 5a). Additionally, for X=0.8 and Y=0.85, electron tunneling effective mass and hole tunneling effective mass are increased (see Fig. 2b). As a result, in the OFF-state, the probability of electron tunneling from the source valence band to the channel conduction band based on Equation1 is reduced, followed by significant degradation in IOFF. Despite the increased   tunneling effective mass for X=0.8 and Y=0.85 compared to the other X and Y values, ION of the proposed device is reasonable. This is because for X=0.8 and Y=0.85 in ON-state, the increased tunneling effective mass is compensated for by reduced tunneling barrier width in source/channel interface. Given that Ga0.8In0.2As/Ga0.85In0.15Sb VHJL-TFET is turned on for gate voltage below 0.1V.
In the OFF state, high overlap of source valence band and channel conduction band in the type III hetero structure allows electron tunneling (see Fig. 6). As a result, the IOFF of GaXIn1-XAs/GaYIn1-YSb VHJL-TFET is increased with X=0.1 and Y=0.4. The simulation results show that the quantum well formed in the conduction band in the source/channel interface for the type I hetero structure (see Fig. 5b). Accordingly, electron concentration is increased in the source/channel interface, see Fig. 7b. As a result, channel conductance is increased, followed by IOFF increases. For simulated structures, IOFF of type I is larger than that of type II and less than that of type III.
By examining energy band profile of GaXIn1-XAs/GaYIn1-YSb VHJL-TFET with type II hetero structure (X=0.8, Y=0.85) in OFF-state, it can be said that with slight changes in gate voltage, the Zener breakdown occurs in source/channel interface. As a result, the device switches from IOFF to ION. Moreover, the IOFF in GaXIn1-XAs/GaYIn1-YSb VHJL-TFET with type II hetero structure is from fA/um order.
Our simulation results show that using a material with a larger band gap in the drain-channel region and a material with a smaller band gap in the source region in proposed VHJL-TFET (i.e. EgGaXIn1-XAs>EgGaYIn1-YSb) significantly reduces the ambipolarity behavior. This result is compatible with another study [23].

3.2.Importance of structural parameters in performance of VHJL-TFET device
Simulations carried out in this study show that the doping concentration (ND), body thickness (Tb), and spacer width between PG and CG (WSiO2) are among the most important design parameters for the performance of VHJL-TFET device.
ION/IOFF ratio as a function of Tb for different types of hetero structures is shown in Fig. 8a. As seen, the ION/IOFF ratio for a given type is increased by reducing Tb. Simulation results show by reducing Tb, the CG ability to deplete the channel is increased in the OFF-state. Consequently, channel resistance is increased by reducing Tb, and the IOFF is significantly reduced. This is reflected in the increased ION/IOFF ratio.
As shown in Section 3.1, the high overlap of the source valence band and channel conduction band in the simulated devices with type III hetero structure increases the IOFF. As a result, the increased ION/IOFF ratio by reducing Tb for Ga0.1In0.9As/Ga0.4In0.6Sb VHJL-TFET is negligible (see Fig. 8a). Also, Fig. 8a shows the ION/IOFF ratio for a given Tb for Ga0.8In0.2As/Ga0.85In0.15Sb VHJL-TFET is larger than the devices simulated with type I and type III hetero structures, because IOFF of the simulated device with type II hetero structure is less than other simulated devices.
Our simulation results show that the sensitivity of the IOFF to increased ND is higher than the sensitivity of ION. In fact, the channel resistance depends on ND, accordingly, ND plays an important role in determining drain current. Channel resistance has been decreased due to positive control gate voltage in the ON-state, and its value is smaller than channel resistance in the OFF-state. As a result, the sensitivity of the IOFF to increased ND is higher than the sensitivity of ION.
We investigated the performance of Ga0.8In0.2As/Ga0.85In0.15Sb VHJL-TFET in OFF-state for different NDs between 1E18 and 1E19. Figure 8b shows IOFF as a function of ND for different body thickness of Ga0.8In0.2As/Ga0.85In0.15Sb VHJL-TFET. Our simulation results for a given Tb show that, the channel resistance is reduced in OFF-state by increasing ND. As a result, the IOFF is increased (see Fig. 8b). Also, the CG ability to deplete the channel is increased by Tb reducing for a given ND in OFF-state; therefore, IOFF is decreased.
The slope of the IOFF versus ND curve increases by increasing ND, and this is more pronounced for larger body thicknesses, see Fig. 8b. First, the curve slope increases slowly and, then, increases rapidly. The rapid increase of slope for larger Tbs begins at smaller NDs. As a result, as Tb increases, the sensitivity of IOFF to ND increases. As expected, with an increase in ND for more CG control over the channel, the body thickness should be thinner.
The simulation results show that the performance of Ga0.8In0.2As/Ga0.85In0.15Sb VHJL-TFET is dependent on the WSiO2. In this study, to investigate the effect of WSiO2 on the performance of the proposed Ga0.8In0.2As/Ga0.85In0.15Sb VHJL-TFET in Fig. 1, WSiO2 is varied from 2nm to 6nm. Figure 9a shows the ID-VGS characteristic of Ga0.8In0.2As/Ga0.85In0.15Sb VHJL-TFET for various values of WSiO2. The inset of Fig. 9a shows the performance of Fig.9 (a) Drain current and (b) the total gate-to-gate capacitance as a function of gate bias of Ga0.8In0.2As/Ga0.85In0.15As VHJL-TFET for various WSiO2. The inset of Fig. 9(a) shows the ID-VGS of simulate device in above threshold region. The bias condition is VDS=1V. the simulated devices in the above threshold region. As WSiO2 increases, the slope of the energy band diagram at the tunneling junction is reduced in the source/channel interface. As a result, electron tunneling in ON-state is reduced followed by decreased ION. This is reflected in larger values by threshold voltage shift (see Fig. 9a). Based on the simulations, as WSiO2 varies from 2nm to 6nm, ION is reduced by 37%.
The total gate-to-gate capacitance (Cgg), plays an important role in determining the intrinsic gate delay of a transistor (τ) for digital applications [22]. Figure 9b shows Cgg as a function of VGS for Ga0.8In0.2As/Ga0.85In0.15Sb VHJL-TFET and for various values of WSiO2. We assume VDS=VDD=1V for calculating Cgg and sweep gate voltage between 0 and 1V at a frequency of 1MHz [22]. Our simulation results show that, with an increase in WSiO2, the gate-source capacitance decreases. As a result, Cgg is reduced, which is more evident in the above threshold region.

= (6)
Where VDD=1V refers to supply voltage and ION refers to ON-state current. Table 1 compares the values of τ, ION and Cgg in bias conditions VGS=VDS=1V. To calculate τ, the device width is considered to be 1μm [22,30]. As expected, with an increase in WSiO2, ION and Cgg are decreased. According to Equation 2, ION has a direct impact and Cgg has an  . 10 The ID-VGS characteristic in the presence of the defect in the source/channel interface. defect in the source/channel interface has negligible effects on the ON-state current, however, the OFF-state current has been affected noticeably by considering defect. inverse impact on τ. As a result, ION and Cgg are in competition to determine τ. The results in Table 1 show, in determination of τ, ION degradation overcome Cgg degradation. Consequently, as WSiO2 increases, τ is increased.
It should be noted that an increase in WSiO2 to values larger than 2nm might be a feasible way of bringing up the breakdown voltage of oxide between CG and PG; but the device performance is degraded. WSiO2 degradation to values smaller than 2nm might lead to oxide breakdown between CG and PG. As a result, WSiO2 is considered to be 2nm in our simulations.
3.3. Impact of Band-Tails on the subthreshold behavior of Ga0.8In 0.2As/Ga0.85In0.15Sb VHJLTFT Our simulation results show that band tailing due to defect in the source/channel interface is thus of importance on subthreshold performance in the proposed structure. Defects in the GaInAs/GaInSb interface can be of the donor or acceptor type, and their density may vary between 10 5 -10 7 cm -2 [34,35]. In this section, to investigate the effect of defect in the source/channel interface on the performance of Ga 0.8In 0.2As/Ga0.85In0.15Sb VHJLTFT, the donor type defect density is 10 6 cm -2 and the acceptor type defect density is10 7 cm -2 . Figure 10 shows the ID-VGS characteristic of the simulated devices. It can be seen that the interface defects increase the OFF-State current, followed by an increase in the subthreshold slope, see inset of Fig Figure 11(a) shows the square root of the product of the electron-hole density (np) 1/2 taken vertically across the tunneling junction of simulated devices in the OFF-state. As shown, (np) 1/2 by taking defects into account in the source/channel interface is higher than the (np) 1/2 when the defect is absent. Figure 11b compares the recombination rate taken vertically across the tunneling junction of simulated devices in the OFF-state. As can be seen, the defects have shifted the maximum recombination rate to the source/channel interface. Moreover, the maximum recombination rate by taking defects into account is higher than the maximum recombination rate when the defect is absent. In fact, the defects increase the product of the electron-hole density in source/channel interface, followed by an increase in the recombination rate. As a result, the OFF-state current by taking defects into account is higher than the OFF-state current when the defect is absent. The higher IOFF due to defect results in the deteriorating the subthreshold behavior of simulated devices.

3.4.Sensitivity analysis
The simulation results in this section have been presented without taking the defect of the source/channel interface into account. To obtain the sensitivity of the main electrical parameters of the Ga0.8In0.2As/Ga0.85In0.15Sb VHJL-TFET to structural parameters, such as Tb, ND and WSiO2, the sensitivity analysis is conducted. We considered ION, IOFF, ION/IOFF ratio, threshold voltage (Vth), and average SS as the main electrical parameters of VHJL-TFET. In this study, sensitivity is considered as standard deviation divided by mean. In calculating the sensitivity of a main electrical parameter to a given structural parameter, other structural parameters are considered constant. Figure 12 shows the sensitivity of main electrical parameters of Ga0.8In0.2As/Ga0.85In0.15Sb VHJL-TFET with respect to the structural parameters. To calculate the sensitivity of the main electrical parameters with respect to ND, it is assumed that Tb=5nm and WSiO2=2nm, and ND is varied from 5e17 to 1e19. The IOFF of the simulated device has higher sensitivity than other main electrical parameters with respect to the ND (see Fig. 12). As ND increases, the channel resistance decreases and, then, the IOFF is increased. To calculate the sensitivity of the main electrical parameters with respect to Tb, ND=1e18 and WSiO2=2nm are assumed and Tb is varied from 5nm to 10nm. Figure12 shows that IOFF has higher sensitivity to Tb than other main electrical parameters. The simulation results show, with an increase in Tb, the CG control over channel is decreased and, then, the IOFF increases.
To calculate the sensitivity of the main electrical parameters with respect to WSiO2, ND=1e18 and Tb=5nm are assumed and WSiO2 varies from 2nm to 8nm. As WSiO2 increases, slope of the energy band diagram in the source/channel interface is reduced and, then, ION is reduced. As seen in Fig. 9, ION has higher sensitivity to WSiO2 than other main electrical parameters.

Conclusion
In this paper, the effects of changes in indium mole fraction (X) in the drain-channel region and Y in the source region are comprehensively examined by numerical simulator to improve digital benchmarking parameters of GaXIn1-XAs/GaYIn1-YSb VHJL-TFET. With changes in X and Y, type I, type II and type III hetero structures are formed in the source/channel interface. For Ga0.8In0.2As/Ga0.85In0.15Sb VHJL-TFET (type II hetero structure), there is a small overlap between source valence band and channel conduction band in OFF-state. Additionally, electron and hole tunneling effective mass is increased. Thus, IOFF is decreased significantly. Simulation results for Ga0.8In0.2As/Ga0.85In0.15Sb VHJL-TFET in ON-state showed that electron and hole tunneling effective mass is compensated for by reducing tunneling barrier width. Moreover, in the proposed device, III-V semiconductors are used throughout the device. As a result, ION of Ga0.8In0.2As/Ga0.85In0.15Sb VHJL-TFET is reasonable, which meet the requirements of international technology roadmap for semiconductors. Ga0.8In0.2As/Ga0.85In0.15Sb VHJL-TFET with a 20nm channel length has ION/IOFF=4E14 and SS=4.4mV/dec and could be a good candidate for digital applications. Also, in the proposed device, we has ION=8mA/um and maximum transconductance is 19mS/um. As a result, the proposed device could be reasonable for analog applications.