## 3 Results and Discussion
The N\({}_{\text{it}}\) was calculated using the following equation:  
\[\text{N}_{\text{it}}=\left[\frac{\text{SSlog(e)}}{\frac{\text{KT}}{\text{q}}}- 1\right]\frac{\text{C}_{\text{ox}}}{\text{q}}\]  
Figure 2: (**a**) Transfer curves (at V\({}_{\text{D}}\) = 1 V), (**b**) optical image, (**c**) AFM height profile (inset: AFM image), (**d**) current on/off ratios versus air annealing time, and (**e**) output curves (at V\({}_{\text{G}}\) = 0 V) of MoTe\({}_{2}\) FET #1.  
where K is the Boltzmann constant, T is absolute temperature, q is elementary electron charge, and C\({}_{\text{ox}}\) is the oxide capacitance. The SS value is extracted from the maximum slope in the transfer characteristics. Raman spectroscopy measurements of the freshly exfoliated multi-layered MoTe\({}_{2}\) devices were obtained to investigate the changes in Raman modes after continuous air exposure and air heating to examine the effect of O\({}_{2}\) molecules on MoTe\({}_{2}\) with respect to molecular vibrations inside the material (Figure 3a,b). Under continual exposure to air, MoTe\({}_{2}\) is strongly affected by defect sites resulting from O\({}_{2}\) molecules [29]. Only a few reports have elucidated the effects of air exposure on MoTe\({}_{2}\)[29] and MoTe\({}_{2}\)-based FETs [30]. Most studies on air-exposed 2D TMDs have been conducted on large-area chemically grown films rather than exfoliated flakes [31; 32; 33]. Figure 3 shows the three prominent Raman modes of MoTe\({}_{2}\), each corresponding to the A\({}_{\text{1g}}\), E\({}^{\text{1}}\)\({}_{\text{2g}}\), and B\({}^{\text{1}}\)\({}_{\text{2g}}\) modes with 532 nm laser excitation. Changes in the three dominant peaks of MoTe\({}_{2}\) after 2 days, 1 week, 2 weeks, and 4 weeks in chronological order are demonstrated. The in-plane (E\({}^{\text{1}}\)\({}_{\text{2g}}\)) vibrational mode of the pristine state had a relatively higher energy than the out-of-plane (A\({}_{\text{1g}}\)) mode, indicating that the exfoliated MoTe\({}_{2}\) is multi-layered [34]. As the air exposure time was increased, the E\({}^{\text{1}}\)\({}_{\text{2g}}\) peaks exhibited gradual red shifts, revealing the p-doping effect from the adsorbed oxygen molecules on the surface. All three vibrational modes of the MoTe\({}_{2}\) flakes exhibited red shifts, regardless of the intrinsic properties or thicknesses, indicating hole doping. The tendency of MoTe\({}_{2}\) to transition towards p-type behaviour in air has been previously proven by density functional theory calculations and Kelvin probe force microscopy [35]. As depicted by the purple curve in Figure 3a, after a certain duration, major peaks of MoTe\({}_{2}\) became undetectable due to undesirable adsorption of molecules besides oxygen. However, we inferred that the material remained physically intact since its peaks were all recovered from surface rinsing with toluene (Supplementary Figure S7), which is known to induce desorption of dopant molecules on surface channels [36]. The instability of air-exposure as a doping method can also be seen in device performance (Supplementary Figure S8). Device #2 with a channel height of 6 nm also demonstrated a similar doping effect; after 2 h of air heating, Device #2 reached its neutral state with an improved current on/off ratio. After 2 h of air heating, the on/off ratio increased from 1.02 \(\times\) 10\({}^{4}\) to 1.28 \(\times\) 10\({}^{5}\). The charge neutrality point was observed at \(-\)21 V before air heating and at \(-\)5 V after 2 h of heating. After 6 h of air heating, the performance of Device #2 began to degrade significantly (Supplementary Figure S2). Both the on and off currents steeply increased with a significantly increased SS after that point.