Negative Differential Conductance & Hot-Carrier Avalanching in Monolayer WS2 FETs

The high field phenomena of inter-valley transfer and avalanching breakdown have long been exploited in devices based on conventional semiconductors. In this Article, we demonstrate the manifestation of these effects in atomically-thin WS2 field-effect transistors. The negative differential conductance exhibits all of the features familiar from discussions of this phenomenon in bulk semiconductors, including hysteresis in the transistor characteristics and increased noise that is indicative of travelling high-field domains. It is also found to be sensitive to thermal annealing, a result that we attribute to the influence of strain on the energy separation of the different valleys involved in hot-electron transfer. This idea is supported by the results of ensemble Monte Carlo simulations, which highlight the sensitivity of the negative differential conductance to the equilibrium populations of the different valleys. At high drain currents (>10 μA/μm) avalanching breakdown is also observed, and is attributed to trap-assisted inverse Auger scattering. This mechanism is not normally relevant in conventional semiconductors, but is possible in WS2 due to the narrow width of its energy bands. The various results presented here suggest that WS2 exhibits strong potential for use in hot-electron devices, including compact high-frequency sources and photonic detectors.

. Identification of the different devices used in this study. Labeling scheme used to identify, and the dimensions of, the different devices investigated in the main paper. Shown left is the device (Device A) of Fig. 2(a) of the main paper, with its key dimensions indicated. The table on the right indicates these dimensions for Devices A -C. While the main focus of the main paper is on the high-field properties of the transistors, we have also studied their low-field mobility, by utilizing the features of their transconductance. While not too much faith may be placed in these measurements, due to the influence of contact resistance, S1 inferred values at room temperature are typically in the range of 1 -10 cm 2 /Vs, consistent with other studies. S2

Fig. S1
. Other examples of negative differential conductance and associated instabilities. Both plots were obtained under the same measurement conditions as described in the main paper, following modest annealing for around an hour. The upper plot was obtained for Device A, the bottom one for Device B. Filled symbols correspond to up sweeps of the drain voltage, open ones to down sweeps.
In Fig. S1 we show examples of negative differential conductance measured in other devices. As with the results presented in the main manuscript, these data were obtained for partial annealing of the device (anneal times around 1 hour), for which the drain-current level remains in the sub-µA range. The data shown here exhibit clear similarities with those presented in the manuscript. Negative differential conductance is observed, along with pronounced hysteresis as a function of sweep direction and enhanced noise. In the lower panel, the overall current level remains below 100 nA and the linear slope to the current at large drain voltages has the effect of "pulling up" the region of negative differential conductance so that it is less pronounced. Nonetheless, in spite of these device-dependent variations, the similarity in behavior between Figs. 3(a) and Fig. S1 is, we believe, very clear. Kaasbjerg et al. S3 A potential issue here arises from the influence of the polar LO modes, which one would expect to be present in the monolayer. Scattering by these modes has the same basic energy dependence as the nonpolar ones, so can be included by a modification of the coupling constant for the latter process. A potential weakness of this approach is that the role of nonequilibrium phonons (both optical and acoustic) is not addressed in the simulations. Nonetheless, in spite of this omission, our simulations confirm the presence of negative differential conductance due to intervalley transfer. The obtained agreement with experiment suggests that the influence of nonequilibrium phonons should largely be a higher order effect. Nonetheless, a fully complete microscopic model should properly account for the role of nonequilibrium phonons, including the decay of nonequilibrium optical modes into the acoustic ones that ultimately transfer energy to the heat sink.
In addition to the influence of the various phonon modes, our Monte-Carlo calculations also account for Coulomb scattering from remote ionized impurities in the SiO 2 gate dielectric, and from the polar surface modes of the SiO 2 . These impurities are taken to be present at a nominal density in the range of 0.3 -1.0 ´ 10 12 cm -2 , with a uniform distribution on the surface of the oxide.
A novel concept introduced in the main paper is of the idea of a trap-assisted inverse Auger process that may serve as a pathway to avalanching at high electric fields. Whereas the normal inverse-Auger interaction varies as (E -E T ), where E T > E g is some threshold energy, we expect the trap-assisted (second-order) process to vary as (E -E T ) 2 . However, as we have no solid theory for the two step interaction, we have to take experiment to suggest its strength. Breakdown is observed to occur at a given electric field, which means that the ionization coefficient at that field should satisfy α(! BD )L ≥ 1, where ! BD is the breakdown electric field and L is the FET channel length. The impact ionization process is characterized by a generation rate (per carrier per second) for ionizing collisions, which is related to the ionization coefficient as g(!) ~ α(!)v d (!), with v d the electron drift velocity. Thus, having an observed breakdown field from experiment, we can adjust the ionizing collision rate to yield an appropriate value for the generation rate at that field. We may then examine the generation rate at other fields without