Introduction

Two-dimensional (2D) Transition Metal Dichalcogenides (TMD) promise ultra-fast and highly scaled devices in the next generation information processing electronics1,2,3. However, promising device architectures like the GAA transistors4, hot electron transistors5,6, and avalanche transistors7,8 require operation in the high field regime, avalanche regime, or very close to the breakdown regime in some cases. Therefore, a thorough understanding of the high-field phenomena like Impact Ionization (II) and avalanche breakdown in TMD FETs is crucial. Moreover, avalanche multiplication also forms the basis of other semiconductor technologies like IMPATT diodes, avalanche photodiodes (used in image sensors, LIDAR sensors, optical fiber communication, etc.)9,10,11, and single-photon avalanche photodiodes (SPADs) in the emerging field of quantum technology to detect single photons for quantum computing, and communication applications12,13. Promising advances in 2D TMD-based avalanche transistors14 and avalanche photodetection15,16,17 are a significant push towards the heterogeneous integration of logic circuits, optoelectronics, and quantum technology in future electronics18. However, it also necessitates understanding avalanche multiplication in the 2D atomic limit with enhanced Coulomb interaction among charge carriers and defects due to the quantum confinement and the significantly reduced dielectric screening19. It is also suggested that because the conduction and valence bands in TMDs are narrow in energy (narrower than the bandgap), impact ionization is not expected in 2D TMDs20, yet it happens! Kang et al. demonstrated anisotropic impact ionization and critical electric field in the lateral and vertical multilayer WSe2 FETs21. Pak et al. demonstrated tuning the avalanche breakdown critical electric field and the impact ionization rate with the channel thickness, originating from the changing bandgap with the number of layers in MoS2 FETs22. Kim et al. demonstrated ambipolar transport and avalanche multiplication as two competing mechanisms of electrical breakdown in multilayer WSe2 devices using channel length modulation23. However, these works fail to establish the mechanism of avalanche multiplication in TMDs in light of the concerns formerly mentioned. Trap-assisted inverse auger effect is suggested to cause impact ionization in TMDs at high fields24; however, it has not been experimentally proven. Moreover, the reliability challenges associated with the defect-assisted impact ionization mechanism are unknown. In this paper, we employ rigorous electrical characterization and current transport mechanism analysis, with temperature dependence, to address the gaps mentioned in the understanding of high-field transport and avalanche multiplication in 2D TMDs. We also corroborate the observations using spatial high-field Electroluminescence (EL) mapping, which was employed for the first time to investigate the electric field distribution in the back-gated TMD FETs.

Results

Back-gated FETs on chemical vapor deposition (CVD) grown Bilayer (BL) MoS2 on SiO2/Si substrate are used in this work. The flake triangles are patterned and etched to form (rectangular) channels with uniform widths and thicknesses (BL) to minimize the device-to-device variability from the device dimensions (See Methods for more details). BL TMDs are advantageous for logic devices, providing good electrostatic control and higher mobility than monolayers25. Figure 1a shows the optical image of a sample fabricated device. The Photoluminescence (PL) peak position26 (Fig. 1b) and the peak position of the characteristic in-plane (E12g) and out-of-plane (A1g) Raman modes27 (Fig. 1c) confirm the chosen TMD to be MoS2. The channel is established to be of bilayer MoS2 from the AFM line scan (Fig. 1d), low energy indirect bandgap (IBG) peak (magnified in Fig. 1b), higher K-K direct bandgap than monolayer (ML) MoS2 (Supplementary Fig. 1a), and the optical contrast differentiating the chosen flake from the ML on the growth substrate. The fabricated FETs show n-type characteristics (Fig. 1e). A low metal-semiconductor Schottky barrier is evident from the linear output characteristics (ID-VD) at 295 K (RT) in Fig. 1f. To further eliminate the effect of the device-to-device variability plaguing the 2D TMD devices28, the FETs are biased in the sustainable breakdown regime by setting a current compliance level of 5μA/μm (refer to Supplementary Section A for more information) which ensured device recovery after high-field stress.

Fig. 1: BL MoS2 FET - Material and Device Characteristics.
figure 1

a Optical microscope image of a back-gated MoS2 FET with Ni (30 nm)/Au (30 nm) contacts on Bilayer (BL) MoS2 (marked in dashed white lines); Scale bar = 5 μm. Channel Length (LCh) = 3 µm, and Channel Width (WCh) = 2 µm. The CVD-grown BL MoS2 was etched from the unwanted regions using O2 plasma etching. b PL spectrum showing the A exciton, B exciton, and the 10× multiplied Indirect Bandgap (IBG) peaks. c Raman spectrum in the channel region with the insets schematically presenting the origin of the observed peaks in the spectrum. d AFM topography line scan confirming the layer thickness to be of bilayer TMD. e ID-VG confirms n-FET on BL MoS2. The inset shows the schematic of the back-gate FET device structure. f The linear output characteristics of the device suggest a low metal-semiconductor Schottky barrier height at the contacts.

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A sudden spike in the IDS with VDS indicates avalanche breakdown, and the decreasing critical breakdown voltage (VCr) with increasing gate voltage (VGS) dependence confirms the electron injection-initiated impact ionization (Fig. 2a). The log plot in the inset shows current saturation with increasing bias below VCr, beyond which the slope of the ID-VD curve rises rapidly with a dynamic on-resistance (Ron) till the current compliance level. High-field dielectric breakdown is ruled out as the gate current doesn’t reach the compliance level (Supplementary Fig. 2).

Fig. 2: Electrical Breakdown Characteristics and FET parameter shifts.
figure 2

a Critical breakdown voltage VCr decreases with increasing electrostatic n doping. Log plot in the inset shows current saturation before the sudden rise with increasing VDS. b Linear region in the ln(1-1/M) vs ln(V) plot indicating impact ionization in accordance with the empirical model. c For smaller depletion region width the maximum field exceeds EII at smaller external voltage but the impact ionization index is smaller. d Temperature dependence of VCr for varying VGS indicating that the increase in VCr saturates with temperature and confirming impact ionization. e Change in the device ID-VG characteristics due to the VDS sweep up to the current compliance for varying VGS. f Negative VTh shift magnitude decreases with increasing VGS. g Variation in the SS, and h Variation in the ON current for constant over-drive voltage, from that of the pristine device.

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The observed high-field breakdown was analyzed using the theoretical model for avalanche multiplication where the Multiplication factor (M = IDS/Isat; Isat is the saturation current) is defined by ref. 29: \(M={\left(1-{\left(V/{V}_{B}\right)}^{n}\right)}^{-1}\). It can be rewritten in the linear form as \({ln}\left(1-1/M\right)=n\left({ln}\left(V\right)-{ln}\left({V}_{B}\right)\right)\), where \(n\) is the ionization index, and \({V}_{B}\) is the critical voltage, which are fitting parameters. The linear fitting regime in the ln(1-1/M) vs. ln(VDS) in Fig. 2b confirms avalanche multiplication to be the cause of the unstable current at VCr. The extracted \({V}_{B}\) and \(n\) decrease with increasing VGS (Supplementary Fig. 3). While \(n\) (impact ionization index) was reported to be independent of VGS earlier23, we observed a clear VGS dependence. The calculated \(n\) value (range 6–16) is considerably higher than for silicon30, confirming more efficient avalanche multiplication in MoS2, possibly due to the quantum confinement and reduced dielectric screening, which increases the electron-hole interaction. Section B in the Supplementary information also confirms Fowler Nordheim Tunneling (FNT) of the electrons in the channel as the extrinsic source of electron injection for triggering impact ionization in the device (Supplementary Fig. 4a) where the effective FNT barrier height reduces with increasing VGS (Supplementary Fig. 4b). The consistency of the electrical characteristics is confirmed in Supplementary Fig. 5. The VGS dependence of \(n\) and \({V}_{B}\) indicate either (i) decreasing size of the high field region (or depletion region) with increasing electrostatic n-doping, as a smaller depletion region ensures reaching the threshold field for impact ionization (EII) at a smaller external voltage but also reducing the probability of ionizing collisions (and hence the impact ionization index \(n\)) in the region (Fig. 2c)31, or (ii) increasing n-doping reducing the impact ionization efficiency due to the electrostatic screening, or (iii) both.

With the increase in temperature, VCr increases irrespective of the VGS (Fig. 2c), further confirming avalanche breakdown. However, with increasing temperature, the VCr saturates due to increasing thermionic emission of the carriers (ID-VD plots in Supplementary Fig. 6). The VCr for avalanche breakdown increases with the temperatures due to the enhanced optical and acoustic phonon scattering, which decreases the average energy of the field accelerated carriers, increasing the EII. However, while the impact ionization threshold voltage has a positive temperature coefficient, and FNT is a temperature-independent process, the thermionic emission across the Schottky barrier increases with temperature. The resulting temperature dependence of the breakdown I-V is a cumulative effect of the three factors.

Mechanism of impact ionization in TMDs

For developing devices with efficient avalanche multiplication, it is also essential to understand the fundamental process of impact ionization in the atomically thin 2D TMDs in light of the quantum confinement, reduced dielectric screening19, increased effective electron and hole mass32,33, and a different band structure from conventional semiconductors20. The BL MoS2 band structure calculated using the Density Functional Theory (Supplementary Section C) in Supplementary Fig. 7 shows that the conduction bands are narrow in energy compared to the semiconductor bandgap. Therefore, to gain the threshold energy for impact ionization (ET\(\,\approx\) 1.5\(\,\times \,\)EG), electrons must scatter (inter-valley and inter-band) and tunnel across bands multiple times – lowering the chances of impact ionization34. The observation of NDC due to e-s scattering to the higher energy and higher effective mass \(\Sigma\) valley (Supplementary Section D) suggests a further reduction in electron mobility. However, the observation of avalanche multiplication indicates that a few “lucky electrons” gain some threshold energy ET associated with the mid-gap states35,36,37,38 in the lattice, resulting in the observation of impact ionization in the semiconductor.

Probing the Role of Defects in the Impact Ionization Process in TMD FETs

We recorded the device's transfer characteristics (ID-VG) before and immediately after the compliance current hit during the ID-VD avalanche soft breakdown (SB) sweep. For all applied VGS, the ID-VG changes from the pristine behavior (Fig. 2e). To our best knowledge, all the previous reports on avalanche multiplication fail to report this effect on the electrical characteristics of TMD FETs post-SB, disregarding the effect of impact ionization on the device characteristics. A left threshold voltage (VTh) shift is observed (Fig. 2f), with the magnitude decreasing with increasing VGS (constant current method (IDS = 66 nA) is used for the VTh extraction39). However, the subthreshold swing (SS) and the ON current variation do not align with the VTh shift (Fig. 2g, h). It is important to note that the device ID-VG recovers with time (VGS-dependent recovery data in Supplementary Fig. 9), ruling out the amorphization of the channel region40 or the field-induced generation of defects41 as the origin of the shift. The Negative Bias Temperature Instability (NBTI) effect results in the left VTh shift and an improved SS42 for negative VGS. However, the degraded SS and reduced ON current (for the same overdrive voltage), with left VTh shift for VGS = 0, 25 V (semi-ON state), must be explored further.

To determine whether the change in the device characteristics is associated with the current instability due to the avalanche breakdown, we ramp the bias up in steps of 5 V (for VGS = 25 V, with a dual sweep (DS)) and investigate the evolution in the device ID-VG, recovering the device before the next sweep if any shift is noted (Fig. 3a). It is observed that below VCr, there is a non-significant change in the ID-VG, and the reverse sweep near traces the forward sweep; only a small clockwise hysteresis is visible in the log plot. The clockwise hysteresis results from trapping of the carrier in the lower mobility (\(\Sigma\)) valley during the reverse sweep because it only comes into effect over the range of VDS where NDC is observed24 and is absent for larger VDS (Supplementary Fig. 10). However, as soon as the bias hits the VCr (critical voltage for avalanche multiplication), a significant anticlockwise hysteresis is noted43. Simultaneously, in the ID-VG after DS (for VDS = 1 V), degrading SS and left VTh shift is observed (Fig. 3b). The consistency of the results is confirmed in Supplementary Fig. 11. For VDS = −1 V (Fig. 3c), a continuous decrease in the n-branch of the ID-VG is also noted. After a high VDS sweep with opposite polarity, the n branch in ID-VG decays for VDS = 1V (Supplementary Fig. 12). Irrespective of the VGS, a similar effect was observed (Supplementary Fig. 13). The resulting mutation in the FET (i) reduces the VCr for positive VDS, where anticlockwise hysteresis in ID-VD is also observed, and (ii) reduces IDS for negative VDS, highlighting the asymmetric effect of the impact ionization in the FET (Supplementary Fig. 14) - decrease in the Schottky barrier for electron injection at the source contact, and increase at the drain contact (Fig. 3d). Therefore, the asymmetric change in the Schottky barrier for electron injection is confirmed as the mechanism for the bipolar resistive switching observed in lateral TMD FETs43.

Fig. 3: IdVd Anti-clockwise hysteresis and the Role of Defects.
figure 3

a ID-VD dual sweep (DS) with the end-point of the forward sweep increasing in steps of 5 V shows a significant hysteresis for bias beyond VCr. ID-VG of the device pre and post the bias sweep up to different voltages in the breakdown regime (b) for VDS = 1 V shows a degrading SS and a left VTh shift (c) for VDS = −1 V shows a degrading SS and a right VTh shift. d High field stress reduces the Schottky barrier at the source contact and increases the Schottky barrier at the drain contact. The Schottky barrier height symbolized as the size of the diode in the schematic. e Spatial photocurrent mapping confirms higher electric field on the source edge than at the drain edge from the higher photocurrent with the laser illumination. f Schematic band diagram from point a to b in the inset device schematic, showing the mechanism of the source contact effective barrier lowering due to the high electric field induced local ionization of the deep donor levels, and its impact on the electric field distribution in the channel.

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A possible mechanism that we hypothesize for the left VTh shift, degraded SS, and the anticlockwise hysteresis is the impact ionization of chalcogenide vacancy-induced deep donor states37,44,45,46,47 in MoS2 near the source contact edge due to the defect-assisted impact ionization process. It is known that a depleted junction forms at the source contact for positive VDS48,49 and VGS > VF (flat band voltage), which results in a localized high electric field in the channel. The high field on the source is confirmed by spatial photocurrent measurement (Fig. 3e), with maximum photoresponsivity reaching 10.2 A/W, when the laser (P = 0.98 μW, λ = 532 nm, 50X objective) is illuminated on the source edge. The maximum photoresponsivity with minimum dark current is observed at VCr, where it can be biased for efficient avalanche photodiode applications. The mechanism leading to the left VTh shift due to the deep donor ionization from the impact ionization process is explained in Fig. 3f. Positive VDS generates a high electric field on the source edge (reverse biased Metal-Semiconductor Schottky junction) impact ionizing the electrons from deep traps in the semiconductor and thereby reducing the effective barrier height due to the increased positive fixed charge concentration resulting from the ionization of sulfur vacancies. This results in the observed left VTh shift and reduced VCr. The degraded SS results from (i) positive fixed charges that interfere with the gate modulation, (ii) change in the electric field profile, turning ON of the different regimes in the channel over a larger VGS range, and (iii) vacancy-assisted electron hopping transport in the OFF and semi-ON bias condition50. It is to be noted that we do not consider the inverse piezoelectric effect-induced degradation in the device characteristics because BL MoS2 has a preserved inversion symmetry51. The anticlockwise hysteresis in the ID-VD results from the ionization of the electrons trapped in the sulfur vacancy sites at VCr, which lowers the source edge Schottky barrier responsible for electron injection. The increase in the drain edge Schottky barrier results from the accumulation of the electrons during ejection to the drain electrode. During the temporal recovery, the occupancy of the vacancy sites is restored to the equilibrium state.

Slew-rate dependence of the avalanche breakdown

The VCr decreases (Fig. 4a), and the left VTh shift and SS degradation are enhanced due to the decreasing slew rate (Fig. 4b) of the ID-VD sweep. This further confirms the role of mid-gap states in the impact ionization process. The Isat reduces for a smaller slew rate because of the increased phonon scattering. A smaller slew rate will increase the ionization of the mid-gap states, and therefore, the impact ionization process will also be affected. The FNT plots in Fig. 4c, for VDS > Vt (Vt: transition voltage from Direct Tunneling to FN Tunneling), can be fitted with two linear fitting regimes with different slopes (irrespective of the slew rate), indicating changing effective barrier height for FNT with the increasing bias. At the onset of FNT (@Vt), the effective electron barrier height is lesser for a smaller slew rate (marked in oval shape) because of the increased defect state ionization on the source edge, which reduces the electron tunneling barrier width and results in reduced VCr. Supplementary Fig. 15 confirms the consistency of the observation. Also, the impact ionization index (slope of the linear fit in the ln(1-1/M) vs. ln(V) plot) is larger for a higher slew rate (Fig. 4d) because of the larger depletion region width (explained in Fig. 2c). The olive, blue, and magenta dashed lines in Fig. 4a, c, d define the different regimes in the breakdown current for slew rate = 1 V/s. Avalanche Multiplication (AM) of FN tunneled electrons is dominant from olive to blue dashed lines. Then, there is no AM (or AM with a small ionization index evident from the low slope linear fitting in Fig. 4d), and no FNT between the blue-magenta dashed lines. Beyond the magenta dashed line, the FNT transport dominates the AM-generated current. A transition from the AM to the FNT dominant regime occurs irrespective of the slew rate, albeit at different voltage ranges. We hypothesize that this dynamic evolution of the transport mechanism from AM to FNT results from the dynamic redistribution of the electric field in the channel with increasing lateral bias if the electric field is not uniformly distributed in the channel.

Fig. 4: Slew Rate Dependent Electrical Breakdown and High Field Electroluminescence.
figure 4

a Slew rate dependent breakdown; VCr and Isat increase with the slew rate. b Larger negative VTh shift (or a degraded SS) is observed from a smaller slew rate. The VTh shift is found to be recoverable after every sweep. c FNT plot showing F-N tunneling current in the device in the breakdown regime of operation. d ln(1-1/M) vs ln(VDS) plot where the linear fitting suggests impact ionization in the bias regime. A higher ionization index is observed for larger slew. Olive, blue, and Magenta dashed lines in the plots mark different breakdown regimes in the device as explained in the text. e VDS dependent EL intensity at the source and the drain edge for VGS = 25 V. f Temporal rise of IDS shows a negative activation energy suggesting the role of hot carrier in the ionization of the deep donor levels. g The increase in the temporal current is accompanied by increase in the EL intensity. h The EL spectrum acquired for VGS = 40 V shows low energy trion recombination dominating over excitonic recombination because of the high electrostatic n-doping. The trion recombination confirms K-K electron -hole pair generation and recombination in the impact ionization regime.

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High field electroluminescence in TMD FETs

We also confirm the electric field redistribution resulting from the competition between the impact ionization of sulfur vacancies and the e--filling of the vacancy sites by FN tunneled electrons (due to non-uniform electric field distribution) from the spatial EL evolution with VDS. For VGS = 25 V, in the AM regime, the EL is first observed at the center of the channel, which shifts to the drain edge with increasing bias. EL migration possibly happens from the source to the drain edge, but the camera's sensitivity for lower current at lower bias limits the observation. The emission then diminishes, and with further increasing bias the intensity increases again on the drain edge. In the FNT regime, the EL intensity also initiates on the source edge (Fig. 4e). This increase, decrease, and increase of the EL intensity aligns with the AM to FNT transition observed in the I-V characteristics. The evolution of the EL with increasing source-drain voltage can be seen more clearly from the Supplementary Movie 1a (for VGS = 25 V). In the AM regime, EL is observed in the localized high-field regions in the channel depending on the band-bending due to the applied VGS (between olive and blue dashed lines (mentioned earlier)). The dependence of the EL brightness (B) on the applied bias in the inset also confirms FNT as the source of free carriers responsible for the observation of high-field EL (Fig. 4e inset). With the increasing bias, the electric field redistributes (reducing electric field in regions with localized high carrier concentration), dimming the free carrier source and lowering the ionization index due to the lower overall electric field (between blue and magenta dashed lines). Further increase in the bias enables FN tunneling of electrons from the source edge, which acts as the source of free carriers and results in the EL at the source edge (beyond the magenta dashed line). The large EL intensity at the drain edge is due to the high field from the junction termination effect when the field reaches the drain edge. In the OFF state at negative VGS, EL was only observed at the drain edge with a consistent indication of AM to FNT transition (Supplementary Section D and Supplementary Movie 1 (b–d)).

The transient evolution of the drain current (Supplementary Section E) also unfolded the role of the impact ionization of the mid-gap defects in the observed left VTh shift for positive VDS (Supplementary Fig. 17a, b). Initially, the drain current decreases due to the Positive Bias Temperature Instability (PBTI) effect; however, the time-dependent ionization of the defect states eventually leads to the increase in IDS. A strong VDS dependence on the rise in the IDS was also observed (Supplementary Fig. 17c). Most importantly, the defect emission showed an increasing emission time with temperature, indicating the role of hot electrons at the high electric field to be responsible for the impact ionization of the defect states (Fig. 4f). Supplementary Fig. 18 confirms further that the increasing emission time with temperature is not due to device degradation. The observation of negative activation energy indicates that due to the increased coulomb interaction (from quantum confinement and reduced dielectric screening), impact ionization dominates over thermal ionization or field-assisted Poole-Frenkel effect-induced ionization at high electric fields, which happens only at low temperatures in bulk semiconductors52. The high field current transient also shows increasing EL intensity with the increasing current (Fig. 4g) due to the triggering of the non-Arrhenius impact ionization process with time. The EL spectrum for VGS = 40 V (for enhanced EL emission to capture the spectrum) indicates trion recombination dominating over excitonic recombination in the ON state regime (Fig. 4h), which further confirms that the defect-assisted impact ionization process generates e-/h pair in the CB/VB which recombine at the (higher energy, direct bandgap) K point in the Brillouin zone in the indirect bandgap semiconductor (BL MoS2), emitting photons. The current instability is not merely due to Poole Frenkel emission of the defect states.

Unified electrical breakdown mechanism in 2D TMD FETs

While the observations establish the electrical breakdown mechanism for BL MoS2 FET, they do not unify the mechanism for all TMDs with different (n or p) doping, material bandgap, and layer number-dependent bandgap variation. For this, we analyze the VGS-dependent breakdown and the accompanying spatial EL distribution for BL MoSe2 FETs. It is observed that for 2D TMD FETs having ambipolar ID-VG, the high-field electrical breakdown mechanism is different from that in the device with unipolar behavior. In the BL MoSe2 FET, significant hole transport is observed at negative VGS (ID-VG in Fig. 5a). It suggests that the hole injection from the drain edge of the device is favorable despite the dominant n-doping of the FET. Various factors are known to boost hole injection in 2D TMD Schottky barrier FETs: (i) smaller semiconductor bandgap, (ii) higher work-function contact metal, and (iii) fermi level pinning of metal fermi-level close to the valence band of the semiconductor. Owing to the favorable hole injection, it is observed that in BL MoSe2 FET, the VCr decreases with VGS (Fig. 5b) because of the reduction in the hole injection barrier with decreasing VGS. This contrasts with MoS2 FETs, where the VCr increases with the decreasing VGS. While impact ionization was observed in BL MoS2 FET, it was not observed for BL MoSe2 FETs with the same device dimensions. This was because of the ambipolar nature of the FET, which allows hole injection with increasing VDS before the field reaches EII23. Moreover, the VGS dependence of the EL observed in MoSe2 FET with ambipolar characteristics significantly differs from that in MoS2 FET. Figure 5c shows that when MoSe2 FET is biased in the regime with dominant hole conduction, high field EL is observed on the source edge. When biased in the regime with dominant electron conduction, EL is observed on the drain edge. When electron and hole injection from the source and drain contacts are equally probable because of the similar effective electron and hole mass in TMDs [20], the injected e-h recombines at the center of the channel. The observation is due to the recombination of the majority carrier in the device with the injected minority carrier at high electric field, which can be understood more clearly from the schematic in Fig. 5d for the three discussed cases: (i) VGS \(>\) VF, (ii) VGS \(=\) VF, and (iii) VGS \(<\) VF, where VF can be defined as the flat-band voltage or more precisely the VGS allowing equal electron injection efficiency from the source edge and hole injection efficiency from the drain edge.

Fig. 5: High Field Electrical Breakdown in Ambipolar TMD FETs.
figure 5

a ID-VG for BL MoSe2 FET showing ambipolar behavior. b VCr increases with VGS, in contrast to the opposite observed for BL MoS2 FETs. c Spatial Distribution of EL in the breakdown regime for varying VGS in BL MoSe2 FET. d Schematic showing the mechanism for EL in MoSe2 FET at high enough VDS for ambipolar carrier injection and varying VGS. VF means the flat-band voltage for the Schottky Barrier diode.

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The observation, therefore, unifies the breakdown mechanism in 2D TMD FETs as a competition between the impact ionization induced and the ambipolar carrier injection-induced electrical breakdown in TMD FETs, which can be distinguished from the VGS-dependent breakdown voltage and the spatial EL information. VGS-dependent EL snapshots in FETs on exfoliated MoS2 (Supplementary Fig. 19) also confirm that the observed EL is not due to the junction termination effect at the drain contact but defines the electric field profile in the channel.

Discussion

Evident from CB-VB recombination in the EL spectrum, impact ionization in MoS2 can occur as a band-to-band inverse Auger process (blue arrows) or through a defect-assisted transition (black arrows: A-A’ + B-B’ transitions) (Fig. 6a). Therefore, while defects in the 2D lattice decrease the carrier mobility, they can also support the hot carrier phenomenon of impact ionization through the defect-assisted second-order transition - hence the “paradox” of defects. The defect-assisted process has no restrictions imposed by momentum conservation; therefore, the figure only shows one of the many possible impact ionization transitions. The defect-assisted process can become dominant in the TMDs due to (i) enhanced scattering of the electrons by the multiple bands within ET above the CB edge and (ii) quantum confinement-induced increased coulomb interaction between electrons, holes, and defects. However, considering that the (i) sulfur vacancy defect level is closer to the CB than the VB35,36, and (ii) in the lucky electron model, more hot electrons will be available for defect-to-CB transition, than for VB-to-defect transition, the dynamic change in the space charge field of the charged impurity centers with increasing bias may dynamically distort the electric field distribution in the device as confirmed in the text.

Fig. 6: Defect Assisted Impact Ionization in BL MoS2 FETs.
figure 6

a Possible transitions for impact ionization in semiconductors - blue arrows depict inverse auger band-to-band impact ionization, and black arrows depict deep level defect assisted (A-A’ + B-B’) second order impact ionization process. b Electron \({\alpha }_{i}\) as a function of the inverse of the electric field indicating an increasing slope of the linear fitting with decreasing VGS. c EL uniformly spread across the channel for VGS = 10 V, d Schockley model fitting for uniform EL distribution across the channel length: \({\alpha }_{i}\) vs inverse of the electric field; the electric field across the channel evaluated by subtracting the voltage drop due to the contact resistance (RC), where RC was evaluated for VGS = 10 V from the Y-function method.

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The VGS dependent ID – VD data also fits well with the Shockley model53: \({\alpha }_{i}\left(E\right)=\,{\alpha }_{0}\exp \left({-E}_{{no}}/E\right)\), where \({\alpha }_{i}\) is the impact ionization coefficient of electrons which is a function of the applied electric field (\(E\)), and \({E}_{{no}}={E}_{T}/e\lambda\) Here, \(\lambda\) is the mean free path of the electrons and \(\alpha\) is deduced from the multiplication factor (M) by \(\alpha =1/L\left(1-1/M\right)\) assuming a uniform electric field in length L = LCh, and approximately equal electron and hole impact ionization coefficients23. This is confirmed by the linear fit in \(\mathrm{ln}\left({\alpha }_{i}\left(E\right)\right){vs}1/E\) plot (Fig. 6b and Supplementary Fig. 20a). However, the decreasing slope of the linear fitting (\({E}_{{no}}\)) with increasing VGS (Supplementary Fig. 20b)) indicates either (i) decreasing size of the high field region (L), or (ii) an increasing mean free path of the electrons with increasing electrostatic n doping (because ET is independent of VGS). For an n-type Schottky barrier FET, the field is expected to become more spread for decreasing VGS approaching the flat band condition54. However, the screening effect can increase the mean free path of electrons with n-doping, indicating the role of impurity centers in the impact ionization process – especially in the quantum confinement regime in BL MoS2.

However, because the field is not uniformly distributed in the channel for all VGS, the fitting was more comfortably done for the case where the EL intensity is uniformly distributed across the channel in the impact ionization regime (Fig. 6c). We also estimate the phonon scattering limited mean free path of electrons in the device from the resultant fitting. For VGS = 10 V, the electric field did not redistribute due to the impact ionization taking place over the entire channel. To estimate the electric field across the channel, we subtract the voltage drop at the contacts from the applied voltage: VCh = VDS – IDS*RC; RC: total contact resistance. We use the Y-function method55 to determine the contact resistance (Supplementary Fig. 21) and use the value at VGS = 10 V to determine the channel electric field, E = \({V}_{{Ch}}/{L}_{{Ch}};\) \({L}_{{Ch}}\): Channel length = 3 μm. From the slope of the linear fit in the \(\mathrm{ln}\left({\alpha }_{i}\left(E\right)\right){vs}1/E\) plot (in accordance with the Schockley “lucky electron” model), and \({E}_{T}=\) 2.114 eV, the mean free path of the electrons is obtained equal to 38.58 nm. The threshold electron energy for impact ionization is calculated by \({E}_{T}={E}_{G}\left(\left(2+\gamma \right)/\left(1+\gamma \right)\right)\); \(\gamma ={m}_{h}/{m}_{e}\), where EG = 1.57 eV is obtained from the PL spectrum, and \(\gamma\) is calculated from the DFT calculated BL MoS2 band structure for electrons in Q valley and holes in Γ valley. Even with the possible overestimation of the contact resistance using the Y-function method56, the calculated mean free path value is unrealistic57. This confirms a lower \({E}_{T}\), possibly belonging to the defect assisted process for impact ionization in MoS2 (also indicated by the VGS dependence of the \({\alpha }_{i}\) ; indicating increasing mean free path of electrons with increasing n-doping).

In conclusion, this work analyses the crucial role of defects in the electrical breakdown mechanism in 2D TMD based FETs. It highlights the fundamental limitation for impact ionization in MoS2 imposed by the material band-structure and the role of defect states in facilitating a defect-assisted second order impact ionization process. The observation of anti-clockwise IDS-VDS hysteresis, left VTh shift, increased subthreshold slope, and the slew-rate and gate voltage dependence of the breakdown confirm the role of defects in the breakdown mechanism while also indicating the reliability challenges associated with the defect enabled hot-carrier process. The non-Arrhenius temporal breakdown manifested due to the increased carrier-defect interaction in the 2D quantum confinement regime confirms the role of hot carriers in the breakdown process. The spatial and spectral distribution of the high field electroluminescence are revealed as an indispensable characterization method to determine the electric field distribution in different FET operating regimes, and to distinguish avalanche breakdown from ambipolar injection induced breakdown in TMD FETs. The observations in this study serve as a stepping stone for the development of robust next generation 2D electronics and optoelectronics, and for a reliable adoption of 2D device technologies based on avalanche phenomena.

Methods

Device fabrication

CVD-grown bilayer MoS2 triangles on SiO2/Si substrate were first patterned and etched into (rectangular) channels with uniform dimensions = 2 μm × 9 μm. This was accomplished by spin-coating bilayer PMMA 495 A4/ 950 A2 positive resist, e-beam lithography patterning of unwanted region in the triangular flake, MIBK: IPA (1:3) development and oxygen plasma etching in the Plasma Asher chamber for 40s at 20 sccm O2 flow, RF Power = 20 W. Positive resist was used in the case instead of negative resist to prevent resist hardening induced contamination. The sample die was kept in acetone for 24 h after etching to remove all resist contamination from the desired flake region. Ni (30 nm)/Au (30 nm) contacts were deposited using e-beam lithography and e-beam deposition. The devices in the paper have a channel length (source-drain distance, LCh) = 3 μm, channel width (WCh) = 2 μm, oxide thickness of 285 nm, and contact length of 0.6 μm.

Measurement setup

All electrical measurements were carried out using 26XX Keithley SMUs in a Faraday cage-enclosed probe station in ambient. Unless mentioned otherwise, all the DC I-V sweeps were done with a slew rate of 1 V/s in steps of 0.2 V. The temperature-dependent measurements were done on the Linkam stage with a PID controller feedback loop to ensure a stable temperature at the set value during the measurements. The EL measurements were done by equipping the Optical Microscope with a high-sensitivity CCD camera with Peltier cooling from Andor Technology. For the best spatial EL resolution, a long working distance 100X objective was used to focus on the device area (additional 2X magnification from the microscope). The Raman and Photoluminescence measurements were done using a LABRam Horiba Spectrometer with 1800 and 600 grooves/mm grating, respectively.