Direct Measurement of Folding Angle and Strain Vector in Atomically Thin WS₂ Using Second-Harmonic Generation

Structural engineering techniques such as local strain engineering and folding provide functional control over critical optoelectronic properties of 2D materials. Local strain engineering at the nanoscale level is practically achieved via permanently deformed wrinkled nanostructures, which are reported to show photoluminescence enhancement, bandgap modulation, and funneling effect. Folding in 2D materials is reported to tune optoelecronic properties via folding angle dependent interlayer coupling and symmetry variation. The accurate and efficient monitoring of local strain vector and folding angle is important to optimize the performance of optoelectronic devices. Conventionally, the accurate measurement of both strain amplitude and strain direction in wrinkled nanostructures requires the combined usage of multiple tools resulting in manufacturing lead time and cost. Here, we demonstrate the usage of a single tool, polarization-dependent second-harmonic generation (SHG), to determine the folding angle and strain vector accurately and efficiently in ultrathin WS₂. The folding angle in trilayer WS₂ folds exhibiting 1-9 times SHG enhancement is probed through variable approaches such as SHG enhancement factor, maxima and minima SHG phase difference, and linear dichroism. In compressive strain induced wrinkled nanostructures, strain-dependent SHG quenching and enhancement is observed parallel and perpendicular, respectively, to the direction of the compressive strain vector, allowing us to determine the local strain vector accurately using a photoelastic approach. We further demonstrate that SHG is highly sensitive to band-nesting-induced transition (C-peak), which can be significantly modulated by strain. Our results show SHG as a powerful probe to folding angle and strain vector.