DFTB Predictions of Twist Angle-Dependent Piezoelectricity in Heterobilayer Systems with 1000-2000 Atoms

Recent experimental findings suggest that twist angle is a critical factor in tailoring the piezoelectric properties of van der Waals heterostructures. In this study, we have expanded the DFTB method to predict piezoelectric coefficients of twisted and corrugated 2D heterostructures with 1000 – 2000 atoms. All DFTB parameters, including compression radii, exponents, and on-site energies, as well as internuclear repulsion energies, were tuned to accurately reproduce electronic structures and piezoelectric coefficients of hybrid DFT calculations. This approach is exemplified with twisted hBN/hBP and h-BN/MoS2 heterobilayer systems. Our results confirm that reliable simulations require supercell sizes of a minimum of 1000 atoms, to avoid the periodic boundaries influence the predictions. We observed a periodic relationship between in-plane piezoelectric coefficients and twist angles, with deviations from analytical models due to factors like charge transfer, symmetry breaking, corrugations, and nonlinear twist angle dependencies. In contrast, the out-of-plane piezoelectric response remains largely unaffected by twist angles and shows an exponential dependence on interlayer distance. Corrugation strongly influences the out-of-plane piezoelectric coefficients.