peak at$\sim$385cm$^{-1}$ and the A$_{1g}$ at$\sim$409cm$^{-1}$ correspond to in-plane and out-of plane vibrations of Mo and S atoms[@VerbPRL1970; @WietPRB1971]. Their difference, Pos(E$_{2g}^1$)-Pos(A$_{1g}$), is often used to monitor N[@LeeACS2010]. However, for N$\geq$4, the variation in Pos(E$_{2g}^1$)-Pos(A$_{1g}$) between N and N$+$1 approaches the instrument resolution[@LeeACS2010] and this method is no longer reliable. Thus, we use the low frequency modes ($<100$cm$^{-1}$) to monitor N[@ZhanPRB2013; @TanNM2012]. The shear (C) and layer breathing modes (LBM) are due to the relative motions of the atomic planes, either perpendicular or parallel to their normal[@ZhanPRB2013]. Pos(C) and Pos(LBM) change with N as[@ZhanPRB2013; @TanNM2012]: $$\label{Eq1}
\mathrm{Pos(C)_N}=\frac{1}{\sqrt{2}\pi c}\sqrt{\frac{\alpha_{\parallel}}{\mu_m}}\sqrt{1+\cos\left(\frac{\pi}{N}\right)}$$ $$\label{Eq2}
\mathrm{Pos(LBM)_N}=\frac{1}{\sqrt{2}\pi c}\sqrt{\frac{\alpha_{\perp}}{\mu_m}}\sqrt{1-\cos\left(\frac{\pi}{N}\right)}$$ where $\alpha_{\parallel}\sim$2.82$\cdot$10$^{19}$N/m$^3$ and $\alpha_{\perp}\sim$8.90$\cdot$10$^{19}$N/m$^3$ are spring constants for C and LBM modes, respectively, $c$ is the speed of light in vacuum, $\mu_m\sim$3$\cdot$10$^{-6}$Kg/m$^2$ is the 1L mass per unit area[@ZhanPRB2013; @TanNM2012]. Fig.\[figure:Raman\] shows a C mode at$\sim$30cm$^{-1}$ and an LBM at$\sim$22cm$^{-1}$. These correspond to N$=$4 using Eqs.\[Eq1\],\[Eq2\]. Fig.\[figure:Raman\] also plots the Raman measurements after device fabrication, deposition of the ionic liquid, low-T measurements, $V_{LG}$ removal and warm-up to room T (red curve). We still find Pos(C)$\sim$30cm$^{-1}$ and Pos(LBM)$\sim$22cm$^{-1}$, the same as those of the pristine flake, suggesting no damage nor residual doping.

Four-probe resistance and Hall measurements are then performed 