Electron Ptychography for Atom-by-Atom Quantification of 1D Defect Complexes in Monolayer MoS₂

Defect complexes can induce beneficial functionalities in two-dimensional (2D) semiconductors. However, understanding their formation mechanism with single-atom sensitivity has proven to be challenging for light elements using conventional transmission electron microscopy (TEM) techniques. Here, we demonstrate the atom-resolved formation of various one-dimensional (1D) defect complexes─consisting of rhenium dopants, sulfur interstitials, and sulfur vacancies─in monolayer MoS₂ by applying electron ptychography to our four-dimensional scanning transmission electron microscopy (4D-STEM) data sets. Our image resolution of 0.35 Å and a spatial precision of 2 pm allow us to achieve accurate matching between experimental structures and density functional theory (DFT) simulations at the atomic level. Additionally, we utilize out-of-focus ptychography to observe defect formation processes at dose rates comparable to those used in conventional TEM imaging, while maintaining a large field of view. This study demonstrates the systematic application of electron ptychography to extensive 4D-STEM data sets for quantitative defect imaging in 2D materials. We provide direct, atomically precise evidence that critical defect densities govern the formation of extended 1D defect complexes. For instance, we show that sulfur single-vacancy lines form when the vacancy density reaches 5 × 10¹³ cm^-2 and transform into double-vacancy lines beyond 8 × 10¹³ cm^-2. Rhenium-dopant lines emerge at a dopant concentration higher than 3 × 10¹³ cm^-2, where metastable sulfur interstitial-vacancy lines also form as the cumulative electron dose reaches 3 × 10⁵ e/Ų, initiating a local nucleation of the 1T' phase. Our results highlight the potential of electron ptychography for high-precision defect characterization and engineering in ultrathin 2D materials.