Crumpled Monolayer Semiconductors: Investigating electronic and transport properties of non-uniformly strained MoS₂

Wrinkles and nanobubbles are ubiquitous in two-dimensional (2D) semiconductors, particularly in monolayer and few-layer systems, where they strongly influence electronic, optical, and electrical properties. However, quantitatively correlating spatially non-uniform strain with local electronic structure remains challenging. Here, we develop a multiscale framework that combines density functional theory (DFT) with a recurrent neural network (RNN) to reconstruct the spatially resolved electronic structure of strained monolayer MoS₂ directly from experimentally measured strain maps. Local strain is extracted from atomic force microscopy (AFM) topography and Raman spectroscopy, with AFM providing nanometre-scale spatial resolution. DFT calculations show that biaxial bending-induced strain is substantially more effective than uniaxial bending or in-plane strain in tuning electronic and dielectric properties. A biaxial bending strain of only 0.35% reduces the band gap by 22% and increases the dielectric constant by 7%, compared to a 5% band-gap reduction and 1% dielectric enhancement for equivalent uniaxial bending. The resulting spatially varying band structure also creates pronounced carrier-density inhomogeneities.

To validate these predictions, monolayer MoS₂ is conformally draped over nanopillar- and nanohole-patterned substrates to generate controlled non-uniform strain. Wrinkle morphology is shown to depend on nanostructure geometry, material stiffness, and substrate interaction. Spatially resolved photoluminescence, Raman, and conductive AFM (dI/dV) measurements closely match the electronic structure predicted by the DFT-RNN framework, confirming that strain features modify the local band gap, dielectric response, carrier distribution, and charge transport. Comparison of wrinkle formation on amorphous and atomically flat substrates further enables quantitative estimation of sample–substrate interaction. Extending this approach to suspended bilayer MoS₂ reveals hierarchical wrinkle networks, while controlled folding of CVD-grown TMDC flakes creates ultrahigh-strain, low-band-gap one-dimensional channels. This framework is readily applicable to a wide range of 2D materials and van der Waals heterostructures for understanding and engineering strain-driven electronic phenomena.