Coupling of Piezo/Flexoelectricity and Its Effect on the Band Structure of Wrinkled ZnO Monolayers

Abstract Wrinkles are used in manufacturing stretchable electronics, soft materials, smart displays, and microstructures. The emerging 2D materials enable the investigation of the intertwined piezoelectric and flexoelectric coupling effect in wrinkled structures and their energy, sensing, and other applications. However, current studies of the electromechanical coupling effect often consider it one effect or even overlook one of the two effects. This oversimplification leads to inaccuracies in the analysis. Here, a theoretical model is proposed to separate the piezoelectric and flexoelectric coefficients by fitting polarization formulas with discrete polarization values calculated using density functional theory. Wrinkled ZnO monolayers are built to mimic the realistic situation, where six nonzero coefficients are successfully isolated, revealing that the coupling of piezo/flexoelectricity and the contribution of piezoelectric and flexoelectric polarizations to the total polarization vary in different directions. Combined with the dipole moment analysis, the relationship between the polarization, piezoelectric coefficient, flexoelectric coefficient, and wrinkle amplitude is established. This study demonstrates that increasing the wrinkle amplitude significantly decreases the energy gap of 560 meV. The separation and quantification of piezoelectric and flexoelectric effects advance the understanding of wrinkles' mechanical and electromechanical properties and lay the foundation for their future applications.