Control of majority carrier type and concentration in transition metal dichalcogenides (TMDs) is an important goal for engineering and improving TMD-based devices. Monolayer and few-layer molybdenum disulphide (MoS2) is an n-type semiconductor due to the presence of electron-donating native defects whose distribution is strongly dependent on the processing history and ambient environment. However, the spatial heterogeneity of the charge carrier concentration has not yet been studied in MoS2 when implemented in devices such as field-effect transistors (FETs). Here, we present a method to extract the spatial distribution of charge carriers using Kelvin probe force microscopy of MoS2 FETs in operando. The carrier concentration in monolayer MoS2 exfoliated on SiO2/Si ranges from 1.2×1012 cm-2 to 2.3×1012 cm-2, corresponding to a three-dimensional concentration of 1018 cm-3 to 2.5×1018 cm-3. A comparable carrier concentration is obtained for few-layer MoS2, while for thicker MoS2 (>50 nm) it is an order of magnitude lower (2×1017 cm-3- 4×1017 cm-3). This finding is consistent with an increased concentration of electron-donating sulfur vacancies at surfaces compared to the bulk. Thus, the reported method for measuring the carrier concentration may advance strategies for doping and improve understanding of devices and defects in 2D materials.
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