Utilizing an innovative combination of scanning-probe and spectroscopic techniques, supported by first-principles calculations, we demonstrate how electron-beam exposure of field-effect transistors, implemented from ultrathin molybdenum disulfide (MoS), may cause nanoscale structural modifications that in turn significantly modify the electrical operation of these devices. Quite surprisingly, these modifications are induced by even the relatively low electron doses used in conventional electron-beam lithography, which are found to induce compressive strain in the atomically thin MoS. Likely arising from sulfur-vacancy formation in the exposed regions, the strain gives rise to a local widening of the MoS bandgap, an idea that is supported both by our experiment and by the results of first-principles calculations. A nanoscale potential barrier develops at the boundary between exposed and unexposed regions and may cause extrinsic variations in the resulting electrical characteristics exhibited by the transistor. The widespread use of electron-beam lithography in nanofabrication implies that the presence of such strain must be carefully considered when seeking to harness the potential of atomically thin transistors. At the same time, this work also promises the possibility of exploiting the strain as a means to achieve "bandstructure engineering" in such devices.

We use transient electrical measurements to investigate the details of self-heating and charge trapping in graphene transistors encapsulated in hexagonal boron nitride (h-BN) and operated under strongly nonequilibrium conditions. Relative to more standard devices fabricated on SiO 2 substrates, encapsulation is shown to lead to an enhanced immunity to charge trapping, the influence of which is only apparent under the combined influence of strong gate and drain electric fields. Although the precise source of the trapping remains to be determined, one possibility is that the strong gate field may lower the barriers associated with native defects in the h-BN, allowing them to mediate the capture of energetic carriers from the graphene channel. Self-heating in these devices is identified through the observation of time-dependent variations of the current in graphene and is found to be described by a time constant consistent with expectations for nonequilibrium phonon conduction into the dielectric layers of the device. Overall, our results suggest that h-BN-encapsulated graphene devices provide an excellent system for implementations in which operation under strongly nonequilibrium conditions is desired.

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