Machine Learning Assisted Reconstruction of Local Electronic Structure of Non-Uniformly Strained MoS2

Wrinkles and nanobubbles are an integral and often unavoidable part of integrating 2D van der Waals semiconductors into actual device architectures. Despite their ubiquitous nature, quantitative correlation between such spatially non-uniform strain and modifications to the local electronic structure remains challenging. Here, density functional theory is combined with a recurrent neural network to reconstruct the local electronic structure of monolayer MoS2 from strain maps derived from atomic force microscopy (AFM) topography and Raman spectral maps. The analysis reveals that biaxial bending induced strain is significantly more effective than both uniaxial bending or in-plane strain in modifying electronic and dielectric properties. A ~ 0.35% strain induced by biaxial bending results in ~ 22% reduction in band gap and ~ 7% increase in dielectric constant, compared to a ~ 5% reduction in band gap and ~ 1% increase in dielectric constant under comparable uniaxial bending. The modified band structure reveals band edge states that concentrate charge in regions of high curvature or strain. While conductive AFM measurements indicate increased local conductance (carrier density) at wrinkles and nanobubbles, the spatial band gap maps predicted by the model are validated against experimental photoluminescence peak energy maps. The results indicate that strained features like wrinkles and nanobubbles commonly present in real devices influence the band gap, carrier distribution, and dielectric response, which favourably affects electrical transport in such systems. The framework developed here can be readily extended to other 2D materials and heterostructures, offering a computationally efficient route for studying and exploiting strain effects.

💡 Research Summary

This paper presents a data‑driven framework that combines first‑principles density‑functional theory (DFT) with a recurrent neural network (RNN) to reconstruct the local electronic structure of monolayer MoS₂ subjected to non‑uniform strain such as wrinkles and nanobubbles. The authors first generate a DFT database by imposing three‑dimensional Gaussian‑shaped out‑of‑plane deformations on a 5 × 5 supercell, varying the central height h to produce biaxial bending strains up to ~0.35 % (h ≈ 1.33 Å). DFT results reveal that such bending dramatically modifies bond lengths, bond angles, and the S‑S interlayer distance, leading to a pronounced reduction of the band gap (≈22 % at 0.35 % strain) and a shift of the conduction‑band minimum and valence‑band maximum by 25 % and 20 %, respectively. Importantly, the same magnitude of band‑gap reduction would require 2–3 % planar biaxial strain, highlighting the superior efficiency of out‑of‑plane bending.

To overcome the prohibitive cost of exhaustive DFT calculations across the continuous strain field of real samples, the authors train an RNN on 50 DFT‑derived density‑of‑states (DOS) datasets spanning 0–0.33 % biaxial strain. The network, built with seven 1‑D hidden layers (up to 4000 neurons), achieves a mean‑squared error below 2 × 10⁻⁶ after 300 epochs, outperforming conventional polynomial interpolation. Once trained, the RNN can predict the full DOS, CBM, VBM, and band gap for any arbitrary strain value, enabling rapid, spatially resolved electronic‑structure mapping.

Experimentally, CVD‑grown MoS₂ monolayers are transferred onto SiO₂/Si substrates patterned with periodic gold nanopillars, inducing localized wrinkles and nanobubbles. Atomic‑force microscopy (AFM) provides high‑resolution topography, from which the out‑of‑plane strain component εzz is calculated using continuum elasticity theory. Raman spectral shifts are also used to generate complementary strain maps. Feeding these strain maps into the RNN yields spatially resolved band‑gap maps that are directly compared with photoluminescence (PL) peak‑energy maps; the two show strong agreement, validating the model. Conductive AFM measurements further confirm increased local conductance at highly strained regions.

The study also quantifies dielectric response: biaxial bending raises the in‑plane static dielectric constant εr by ~7 %, whereas comparable uniaxial bending yields only ~1 % increase. This enhancement, together with the strain‑induced band‑gap reduction, leads to higher free‑carrier density, improved screening of charged impurities, and consequently a substantial boost in carrier mobility (reported in literature as 10‑ to 10³‑fold).

Overall, the work demonstrates that out‑of‑plane biaxial bending is a far more effective tool than in‑plane strain for engineering electronic, optical, and dielectric properties of 2D semiconductors. The DFT‑RNN framework provides a computationally efficient pathway to predict and exploit strain effects in MoS₂ and can be readily extended to other transition‑metal dichalcogenides, heterostructures, and more complex deformation modes, opening new avenues for strain‑adaptive, high‑performance flexible electronics and optoelectronics.