Charged defect scattering of electrons plays a critical role in determining a wide range of material properties. However, there is a lack of an accurate method to calculate the scattering, as all the existing methods require assuming a specific distribution for unscreened (i.e., bare) excess charge carried by the defect, which limits their accuracy. Here we develop a first-principles method to determine the bare charge distribution, which thus enables accurate calculations of the scattering. Using this method, we accurately calculate the electron mobility of 2D ${\mathrm{MoS}}_2$ under the scattering of charged sulfur vacancies and compare with that of charge-neutral oxygen substitutes of sulfur. Interestingly, we find that the charged defect-limited mobility exhibits a strong temperature dependence at low temperature and carrier concentration, in contrast to the neutral defect and the conventional belief that the defect-limited mobility is less sensitive to the temperature. This behavior arises from the free carrier screening of the long-range scattering potential of the charged defect. Our work offers new insights into the transport mechanism, and opens access to accurate calculation, understanding, and prediction of charged defect scattering and a broad range of associated properties.

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• Electrical conductivity
• Point defects
• Density functional theory development
• First-principles calculations