Harnessing defects for high-performance MoS2 tunneling field-effect transistors

ABSTRACT The two-dimensional (2D) materials-based tunneling field-effect transistors (TFETs) suffer from low driving currents. In contrast to the prevailing wisdom that defects are detrimental, we proposed to harness the ubiquitous defects in MoS2 to overcome the problem of the low on-state current in TFET. The existence of certain molybdenum-related vacancies and sulfur vacancy in appropriate positions confers the higher driving currents without compromising the low-power benefits. Such performance enhancements are related to the defect-assisted resonant Zener tunneling mechanism introduced by the mid-gap states of the vacancy defects. These unveiled hidden defect benefits could provide new opportunities for boosting the performance of 2D TFETs. GRAPHICAL ABSTRACT IMPACT STATEMENT The defect-assisted resonant Zener tunneling mechanism in TFET introduced by the mid-gap states of the vacancies in MoS2 is beneficial for enhancing the on-state current.


Introduction
Integrated circuit (IC) technology is advancing in the direction of miniaturization, ultrahigh speed, low-power consumption and high performance. Field-effect transistor (FET) is the most basic working unit in ICs, and the reduction of its physical size guarantees the exponential development of chip integration and the continuous improvement of the chip performance [1,2]. However, the resulting short channel effects [3][4] and other quantum effects may degrade the performance of the conventional FETs and therefore new design space has to be explored. For a FET, the subthreshold swing SS = dV G /dlog 10 I D is an important figure of merit that reflects the steepness of the slope of the I-V transfer curve upon the transition between the off and on state, where V G is the gate voltage and I D is the drain current. In a conventional FET, the SS cannot be smaller CONTACT  than 60 mV/decade at room temperature because of the avoidable thermionic emission of carriers in the offstate (known as the Boltzmann limit) [5], preventing the device power from further reduction. To enable denser integration and power up a lot more computing cores, it is necessary to use new devices with steeper subthreshold slopes.
In early this century, a new type of FET, the tunnel field-effect transistor (TFET), was proposed utilizing the Zener tunneling mechanism rather than thermal injection [6][7][8][9]. The electron (hole) carrier transport in an n-type (p-type) TFET is from valence (conduction) band of p-doped (n-doped) source through the source-channel energy barrier via tunneling to the conduction (valence) band of channel, i.e. the band-to-band tunneling (BTBT). Because of the tunneling nature of carrier transport, SS less than 60 mV/decade and lower subthreshold leakage current can be achieved. However, due to the low transparency of the tunneling barrier, TFET suffers from low on-state current, usually orders of magnitude lower than that of the conventional MOSFET, which becomes a severe obstacle for TFET application in high performance IC. In the past decades, significant efforts have been made to investigate the solutions to the enhancement of the on-state current, such as the use of thinbody TFET structure to improve gate controllability, the use of low bandgap source, and the use of low-bandgap and small reduced-effective-mass channel materials [10][11][12][13][14][15].
Two-dimensional (2D) semiconductors, such as MoS 2 , are emerging channel materials for future FETs [16,17]. Their natural ultra-thin bodies can improve gate controllability, making them also attractive for TFETs. Unfortunately, most of the experimentally fabricated 2D semiconductors have severely degraded carrier mobilities, impeding the realization of high on-state current [18][19][20]. Unlike most conventional semiconductors with band-like transport [21][22][23][24], the carrier transport in MoS2 has often been found to exhibit the characteristics of variable-range hopping [25][26][27]. This unique property has been associated with the existence of rich defects. Direct observations of various vacancy defects have been reported in monolayer MoS 2 grown by chemical vapor deposition method [28]. S vacancies (V S ) are common in all samples. Mo-related vacancies are also abundant, usually presented as V MoS3 defect complexes, each with three V S around a V Mo .
In contrast to the common wisdom that defects are detrimental, Zhang et al. [29] recently found that by tailoring the sulfur vacancy defects to an optimum density of 4.7% in monolayer MoS2, an unusual mobility enhancement can be obtained and a record-high carrier mobility is achieved. In this paper, we report more than two orders of magnitude enhancements of the on-state currents in TFETs in the presence of V Mo , V S and V MoS3 . This is found to be due to the inelastic defect-assisted resonant Zener tunneling. Our findings suggest a generic defect engineering strategy for boosting the performance of 2D TFETs for highperformance ICs.

Methods
The density functional theory and the non-equilibrium Green's function method implemented in ATK 2020 package were employed [30]. The double-ζ polarized basis set and Local Density Approximation exchange correlation were adopted. The k-point samples were 1 × 2 × 2 and 1 × 7 × 153 during the electronic structure and device transport calculations, respectively. A 20 Å vacuum layer was used in the x-direction, and the transport direction was along the z-axis. The energy difference was converged to 10 −5 eV/atom, and the maximum residual force was converged to 0.01 eV/Å. The real space mesh cutoff energy was set at 75 Hartree, and the temperature was 300 K. The driving current at a given bias voltage V SD and gate voltage V G was calculated by the special thermal displacement-Landauer method [31][32][33]: (1) where T (E, V ds , V g ) is the transmission coefficient, f S and f D are the Fermi-Dirac distribution functions for the source and drain, μ S and μ D are the electrochemical potentials.

Results and discussion
The calculated lattice constant of monolayer MoS 2 is 3.11 Å, and the LDA band gap is 1.83 eV, in reasonable agreement with the experiments [34]. Experimental observations have shown the existence of V S , V Mo and V MoS3 in MoS 2 [28,35], whose atomic structures are shown in Figure 1(a). The densities of states (DOSs) of the defect-free MoS 2 and defective MoS 2 are shown in Figure 1(b-e). It is seen that V Mo , V MoS3 and V S can all introduce mid-gap states, but with varying energy distributions. In particular, the states of V Mo tend to locate in the middle of the gap, while the states of V S locate near the edge of the conduction band. As expected, the states of V MoS3 are more broadly distributed in energy, from near the valence band edge to near the conduction band edge. Next, we simulate the carrier transport phenomena in three dual-gated MoS 2 homojunction TFETs, each containing one of these three types of point defects in the source region near the source-channel interface, as schematically shown in Figure 2(a). For the device model, the source and drain electrodes are p-type and n-type electrostatic doped by using the atomic compensation charges method, the doping concentration is 2.2 × 10 13 cm −2 . The length of the intrinsic channel region is 7.9 nm, the equivalent oxide thickness (EOT) was set to be 0.49 nm, and the dielectric constant was 3.9. Here, EOT indicates how thick a silicon oxide film would need to be to produce the same effect as the high-k material being used. In total, there are 492 atoms in a TFET model device. Each of the defective models contains only one defect on either the source side or the channel side of the source-channel heterojunction, which is equivalent to a defect density of 2 × 1013 cm −2 as normalized by the channel surface area. This defect density is comparable to that measured in experiment [28,35]. In addition, because there is at most one defect in the channel of the simulated device and the channel length is much greater than the localization length estimated from the variable-range hopping model [27], the mechanism of conduction in the channel of the simulated device is actually assumed to be band-like transport. In fact, band-like transport behavior can be observed in the high-carrier density linear region if the devices are carefully prepared and measured under conditions that minimize surface adsorbates [21][22][23][24].
The calculated transfer curves for the defect-free and defect-containing devices are shown in Figure 2(b). Compared to the defect-free device, the on-state currents of the V Mo and V MoS3 -containing devices are larger by nearly three orders of magnitude, while the off-state currents are only slightly higher. The SS values are calculated to be 31.0 mV/decade for V Mo -containing TFET and 30.7 mV/decade for V MoS3 -containing TFET. On the other hand, both the on-state and off-state currents of the V S -containing device are comparable to those of the defect-free device.
To better understand the origins of the performance enhancements achieved by introducing V Mo and V MoS3 into the source regions, analyses of the device densities of states (DDOSs) of the defect-free MoS 2 TFET (Figure 3 (a)), and of the devices containing V S , V Mo and V MoS3 defects (Figure 3 (b-d)) at their on-state are conducted. One can see from Figure 3(b,c) that there are many midgap states within the tunneling window localized at the source-channel interface. It is therefore expected that the defect-assisted resonant Zener tunneling can occur. To verify this hypothesis, we examine the atomic projected densities of states (PDOSs) and the transmission coefficients (T(E)s) in the on-state MoS 2 TFETs without and with point defects, as shown in Figure 3 (e-h). As can be seen, the source valance band (VB) and the channel conduction band (CB) overlap each other, opening up the BTBT window. Compared to the defect-free TFET (Figure 3(e)), one can find in Figure 4(f) that the existence of the V Mo defect dramatically increases the T(E), with the energies where T(E) peak coinciding with the V Mo defect energy levels. This indicates that the resonant tunneling occurs as assisted by the mid-gap defect states. Similar phenomena can be found in the case of V MoS3 , as shown in Figure 3(g). Compared to V Mo and V MoS3 , the existence of V S does not increase the on-state current (Figure 2 (b)). This can be understood by noticing that the V S mid-gap states locate outside the BTBT window, as expected from the high energy positions of the V S defect states near the CB edge of the source MoS 2 (Figure 3(d,h)).
Given the above findings and considering the two facts that the tunneling window is formed between the source VB edge and channel CB edge, and the energy positions of the V S defect states are near the CB edge of MoS 2 , it is natural to ask whether or not creating a V S defect in the channel region near the source-channel interface can enable defect-assisted tunneling and achieve high on-state current. To answer this question, TFET models without and with V S , V Mo and V MoS3 defects in the channel regions near the source-channel interface are built, as shown in Figure 4(a). Figure 4(b) shows the transfer characteristics of a monolayer MoS 2 TFET with such a V S located in the channel region. In line with our expectation, the TFET shows nearly two orders of magnitude increase in the onstate current compared to that of the defect-free device, with a low SS of 30 mV/decade. The DDOS, PDOS as well as the tunneling transmission coefficient (Figure 5(a,d)) further show that the energies where the transmission coefficient peaks coincide with the mid-gap defect levels  within the BTBT window, which is a key signature of the resonant Zener tunneling. The transfer characteristics of MoS 2 TFETs with V Mo and V MoS3 defects located in the channel region are also shown in Figure 4(b). It is seen that these two devices have on-state currents larger than that of the defect-free device as well, both with sub-60 mV/decade SSs. Figure 5 shows that there are also resonant mid-gap defect states within the BTBT windows whose energy levels coincide with those at which the transmission coefficients peak. The abilities of the V Mo and V MoS3 defects that locate at either position, i.e. in the source region or in the channel region, to assist BTBT can be understood as due to their near-middle of the gap or broadly distributed energy levels. The above findings provide new insights into the design of MoS 2 TFETs by engineering suitable defects into appropriate positions to overcome the problems of limited onstate currents in TFETs. Further improvements may be through other materials engineering approaches, such as the use of low-bandgap source, as recently demonstrated in experiment where record high I 60 (the current where SS becomes 60 mV/decade) was achieved [14]. In addition, the effects of defect density on V Mo -containing and V S -containing devices have been discussed in the Supporting Information.
Accordingly, we envision that the main practical challenge to implement this approach effectively is to precisely create the desired defects and control their positions. As for position-selective creation of defects, with the advancement of scanning transmission electron microscopy (STEM), the sub-angstrom-sized electron probe guarantees single-atom accuracy of the electron-matter interaction and allows electron-beam irradiation to precisely create defects in 2D MoS 2 [36]. Recently, Zhang et al. [29] also reported a method to tailor a single vacancy in 2D MoS 2 , involving a mild anneal in the high-pure hydrogen atmosphere. As for the creation of V Mo and V MoS3 defects with higher formation energies compared to that of V S defect, non-equilibrium growth techniques can be used, such as rapid cooling. It has also been found experimentally that under prolonged electron-beam irradiation V MoS3 can be generated, presumably via ionization, beam-induced chemical etching, ballistic displacement, or catalyzed by hydrocarbon surface contamination [28,36].

Conclusions
We have demonstrated that engineering defects in MoS 2 can be beneficial for assisting the BTBT process in the operating of the TFET. In particular, by introducing defects, whose mid-gap states lie close to conduction band edge, such as V S , into the channel region near the source-channel interface, or by introducing defects, whose mid-gap states lie close to the valence band edge, into the source region near the source-channel interface can enhance the on-state current of an n-type TFET because the mid-gap defect levels fall within the BTBT window and therefore can assist tunneling. Defects that have near-middle of the gap states or broadly distributed energy levels, such as V Mo and V MoS3 , can be engineering into both the source region and the channel region for the same purpose. The arguments developed in this work are very general and could be readily extrapolated to p-type TFETs (opposite 'defect level-defect position' design rule) and other materials systems. In our simulated cases, the introduction of suitable defects at appropriate positions enhances the driving currents without compromising the low-power benefits. Our work provides a new strategy to overcome the problem of the limited on-state currents in TFETs.

Disclosure statement
No potential conflict of interest was reported by the author(s).