Scaling and carrier transport properties of monolayer MoS$_{2}$ transistors

2D crystals of layered~transition metal dichalcogenides~such as MoS$_{2}$ are ideal candidates for aggressive miniaturization of field-effect transistors (FETs) to the single digit nanometer scale. This class of materials can benefit from their atomically thin body with dangling-bond-free surfaces. In particular, monolayer-MoS$_{2}$, because of its bandgap of 1.8 eV yields high I$_{on}$/I$_{off\, \, }$ratio FETs, while its atomically thin body, t $\approx $ 0.7 nm, facilitate the reduction of characteristic scaling length. In this work, we first demonstrate the fabrication and electrical characteristics of a MoS$_{2}$ FET using single-layer graphene as the source/drain contacts and a channel length of 15 nm. The MoS$_{2}$ FET had an I$_{on}$/I$_{of\, \, }$of $\approx $10$^{6}$ with an I$_{on}$ \textasciitilde 50 $\mu $A/$\mu $m and minimum subthreshold slope of 90 mV/dec. Next, by exploiting the semiconducting to metallic phase transition in MoS$_{2}$, we demonstrate a 7.5 nm transistor channel length by patterning of MoS$_{2}$ in a periodic chain of semiconducting and metallic-phase MoS$_{2}$ regions. The transistor chain shows I$_{on}$/I$_{off} \quad \approx $10$^{5}$ with I$_{off} \quad \approx $100 pA/$\mu $m. Modeling of the resulting characteristics reveals that the 2H/1T' MoS$_{2}$ homojunction has a resistance of 75 $\Omega $.$\mu $m while the 2H-MoS$_{2}$ exhibits low-field mobility of \textasciitilde 25 cm$^{2}$/V.s and carrier injection velocity of \textasciitilde 10$^{6}$ cm/s.