† Corresponding author. E-mail:

Project supported by the National Natural Science Foundation of China (Grant Nos. 61574109 and 61204092).

Trap-assisted tunneling (TAT) has attracted more and more attention, because it seriously affects the sub-threshold characteristic of tunnel field-effect transistor (TFET). In this paper, we assess subthreshold performance of double gate TFET (DG-TFET) through a band-to-band tunneling (BTBT) model, including phonon-assisted scattering and acoustic surface phonons scattering. Interface state density profile (*D*_{it}) and the trap level are included in the simulation to analyze their effects on TAT current and the mechanism of gate leakage current.

Tunnel Field-Effect Transistors (TFETs) are a new concept of device that has been proposed as a promising option to conventional MOSFET. Owing to different operating principles, the TFETs have attracted much attention because of their steep subthreshold swing (SS < 60 mV/dec).^{[1–4]} One significant task for TFETs is to study which factors deteriorate sub-threshold characteristics. However, in many papers just the effects of the trap density on subthreshold swing (SS) and off-state current (*I*_{off}) were studied, and interface traps (ITs) and phonon scattering were considered for TFET by a few authors.^{[5–9]} Furthermore, there are few reports of physically detailed effect of gate leakage current on TFET.

In general, the tunneling happens uniformly along the gate on the source side, and high-*κ* gate insulator as well as lattice mismatch in source-channel junction could induce those traps existing at the interface. Such an important issue is that the influences of trap level and phonon-assisted tunneling on the DG-TFET need further physical insight. In this paper, we focus on the TAT and gate leakage current behavior in DG-TFET. It is shown that different positions of trap and phonon scattering can result in the degradations of the SS and TAT current.

In this paper, the device structure under investigation is an all Si double-gate n-TFET (DG-nTFET), as illustrated in Fig. *κ* (*t*_{ox} = 2 nm, *κ* = 21) double-gate structure. The gated channel length (*L*_{g}) is 20-nm doped source region length and doped drain region length are both 20 nm. It consists of a thin (*T*_{Si} = 10 nm) intrinsic source (n-type, 10^{15} cm^{−3}), p-type source (10^{20} cm^{−3}), and n-type drain (10^{20} cm^{−3}). The metal gate work function used is 4.1 eV. For simplicity, abrupt doping profiles are used, and we assume semiconductor/oxide interface and source/channel interface where ITs are most likely located.

To elucidate the relationship between TAT current and phonon scattering, and that between gate leakage current and tunneling in DG-nTFET, the device simulation setup includes the dynamical nonlocal-path band-to-band tunneling (BTBT) model, dynamic nonlocal path trap-assisted tunneling, enhanced Lombardi model with high-*κ* degradation, a fully quantum-mechanical gate leakage current tunneling model, and hot-carrier injection model. When oxide is thinner than 3 nm, the gate leakage and mobility degradation must be considered. In the TAT simulations, a constant tunneling mass (*m*_{e} = 0.19*m*_{0}, *m*_{h} = 0.2*m*_{0}) is used, and nonlocal BTBT model (*A* = 4×10^{14} cm^{−3}·s^{−1}, *B* = 2×10^{7} V·cm^{−1}) is also adopted. Carrier bulk lifetime and trap capture cross section are 0.1 μs and 10^{−10} cm^{2} respectively. In addition, carrier injection model calculates the hot-carrier injection current by using the nonequilibrium energy distribution which contributes to distinguishing the influences of two different mechanisms on gate leakage current. Even more importantly, the influences of optical phonon (OP) assisted inelastic tunneling and acoustic phonon (AP) scattering on the carrier mobility could be effectively studied. In all DG-nTFET simulations in this paper we assume *V*_{DS} = 0.5 V.

The simulated TAT currents in this work are plotted in Fig. *V*_{DS} = 0.5 V, TAT current deteriorates by increasing *D*_{it}, owing to more traps that introduce greater trap-assisted tunneling numbers. However, when those traps are located at the source/channel interface for different temperatures, trap-assisted tunneling through trap (location see Fig. *V*_{GS} values ranging from −0.2 V to 0.2 V, TAT current is mainly due to trap-assisted tunneling, and the recombination rate is proportional to exp[−(*E*_{F,n}−*E*_{C})/*κT*].^{[10]} Hence, TAT current can be effectively suppressed at low temperatures.

To obtain further insight, we study the influence of trap levels on TAT characteristics of DG-nTFET with *D*_{it} = 10^{10} cm^{−2}·eV^{−1}. When trap level turns closer to valence band at the gate/channel interface in source region, the simulation results display that TAT current would increase as shown in Fig.

Here, a close match with experimental data is obtained when considering BTBT component and TAT component^{[12]} as shown in Fig.

*N*

_{op}= exp(

*ε*

_{op}/

*kT*− 1)

^{−1}is the phonon number and

*D*

_{op}is deformation potential,

*k*is the Boltzmann constant, and

*T*the device temperature.

^{[11]}

*D*

_{op}and

*N*

_{op}are proportional to the optical phonon energy, but the scattering rate is inversely proportional to

*D*

_{op}and

*N*

_{op}. At small

*D*

_{op}and

*N*

_{op}values, Optical-phonon scattering rate increases, and thus, TAT current and off-state current increase at low gate voltage.

When the gate voltage is over threshold voltage, the remote phonons (RPs) scattering and acoustic phonons (APs) scattering begin to have an influence, which stem from the high-*κ* dielectrics. Carriers are scattered into trap level, followed by thermal emission into the conduction band. An increase in *V*_{DS} results in reducing the electron concentration in the channel, and the electrons are now pulled back to the end of the drain. The mobility would suffer RP scattering. Figure *V*_{GS} in the cases with and without (W/O) scattering. Elastic scattering due to acoustic phonon and remote phonon comes into effect at larger gate biases. As can be seen, the on-state current is obviously reduced by scattering because of acoustic phonon and remote phonon. First, the remote phonon scattering can affect the electron mobility, resulting in the significant decrease of drift-diffusion current. On the other hand, the acoustic phonon scattering can reduce the BTBT generation rate at the source/channel injunction, since part of the electrons entering into the drain are backscattered.

In many cases, there are few researchers to discuss the gate leakage current. On-state current can be effectively and easily improved by using a thinner high-*κ* gate dielectric. However, this method has a major disadvantage, that is, the gate leakage current. The leakage floor would reduce device reliability. For DG-nTFET, the leakage floor can be divided into hot-carrier injection current and direct tunneling current. Direct tunneling and hot-carrier injection are the main gate leakage mechanism for oxides thinner than 3 nm. With the decrease of the device size, hot carrier effect failure has received much attention nowadays, it becomes one of the main failure mechanisms, especially in TFET.

A comparison of the apparent shift in the onset of gate leakage among different *V*_{DS} values is shown in Fig. *V*_{DS} increases linearly. When *V*_{GS} is smaller than *V*_{DS}, carriers indirectly tunnel into the channel, followed by drift-diffusion into drain. Direct tunneling becomes limited by the indirect tunneling. Once *V*_{GS} is over *V*_{DS}, the gate direct tunneling current increases exponentially. Direct current density is:^{[14]}

*E*

_{F,S}, (0) and

*E*

_{F,M}, (0) denote the Fermi energy at the Si/SiO

_{2}interface and the gate Fermi energy, respectively;

*E*is the energy of the elastic tunnel;

*E*

_{C,ins}is the conduction band energy. Under the same gate voltage, the increased

*V*

_{DS}would suppress the direct tunneling.

When the gate oxide thickness reduces to 2 nm, oxide barriers are easily affected by the image force. The image force can reduce the tunneling barrier, hence, the gate direct tunneling current decreases as shown in the inset of Fig.

Figure _{f}O_{2} barrier for the DG-nTFET. Unless otherwise mentioned, the device dimensions and parameters are both kept unchanged for our simulations. The barrier height is a function of insulator field, and the insulator field can directly affect electron distribution function. The injection probability of hot-carrier into gate insulation would reduce due to higher barrier height. The probability can be written as^{[13]}

*ε*is the dielectric constant of H

_{f}O

_{2}material,

*λ*

_{r}is the redirection mean free path, and

*E*

_{B}is the Si–H

_{f}O

_{2}barrier. The probability with which the electron will be redirected would be reduced with increasing the height of the Si–H

_{f}O

_{2}barrier, as presented in Fig.

*λ*

_{r}can also affect the gate leakage floor. Scattering rate of carriers in oxide increases with increasing the redirection mean free path. The change of gate leakage current is clearly indicated in Fig.

In addition, the gate leakage current is also influenced by scattering mean free path *λ* in semiconductor. The probability is given by the following expression:^{[13]}

*P*

_{s}is the probability with which the electron travels a distance to channel/gate interface without losing any energy,

*P*

_{ε}is the probability with which the electron has energy in the oxide layer. The probabilities in semiconductor and high-

*κ*gate insulator, for different scattering mean free paths are shown in Fig.

*P*

_{ins}is defined as

*P*

_{ins}is the probability with which hot-carrier scatter stays in the image-force potential well,

*λ*

_{ins}is the scattering mean free path in the insulator,

*P*

_{ins}is analogous to

*P*

_{S+ε}. With increasing these scattering rates, the gate leakage floor increases. Figure

In this paper, we present the TAT current and gate leakage current characteristics of all-Si DG-nTFET. Based on different defect levels, phonon energies and trap densities, transfer characteristics of subthreshold which suffers the influence of phonon scattering are studied. The phonon with higher scattering energy and the phonon closer to the valence band would deteriorate SS and off-state current. The DG-nTFET leakage floor is vulnerable to not only barrier height of semiconductor/oxide, but also scattering mean free path. Leakage floor can be improved by increasing the barrier height and a robust surface processing.

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