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

Abstract

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.

Figures (20)

• Figure 1: (a) (top) MoS$_2$ supercell used in DFT calculations, showing biaxial and uniaxial bending with the darker shades denote higher $z$ values. (bottom) Schematic of biaxially bent ML MoS$_2$ lattice with increasing $h$. Variation of (b) % induced strain with $h$, (c) Mo-S bond lengths, (d) S-S distance and (e) S-Mo-S bond angle with central height of the deformation.
• Figure 2: (a) Evolution of electronic density of states with $h$ (the arrows indicate additional band edge states due to bending), (b) variation of band gap energy ($E_g$) with $h$ and (c) variation of $E_g$ with height and temperature.
• Figure 3: (a) Variation of calculated dc in-plane $\varepsilon_r$ of ML MoS$_2$ with deformation $h$ under biaxial and uniaxial bending. (b) Energy dependence of in-plane $\varepsilon_r$ for flat and biaxially and uniaxially bent ML. Inset shows a zoomed view of $\varepsilon_r$ close to zero energy. (c) Energy dependence of in-plane $\varepsilon_i$ for flat and biaxially and uniaxially bent ML, zoomed view of the marked area has shown in the inset
• Figure 4: Steps for generating the DOS map, and followed by generating band gap map of ML MoS$_2$ on a patterned substrate (a) AFM topography of ML MoS$_2$ flake draped over gold pillars on Si, (b) Strain map, calculated from AFM topography for the selected region. Prediction map: (c) conduction band minima (CBM), (d) valence band maxima (VBM), (e) bandgap energy
• Figure 5: Spatial maps of frequency for (a) $E_{2g}^{1}$ ($\Gamma$) and (b)$A_{1g}$ ($\Gamma$) Raman modes of the ML MoS$_2$ flake on patterned substrate (Fig. \ref{['fig:pred_map']}) (c) strain map calculated from Raman spectral shifts and (d) strain map from AFM topography (white dashed line denote flake boundary)