On the flexoelectric-like effect of Nb-doped SrTiO₃ single crystals

The enhanced flexoelectric-like effect in oxide semiconductors has outstanding properties that compare favorably with those of high-K materials, and this finding has stimulated research aimed at enhancing flexoelectricity of such materials. However, the effective flexoelectric coefficient approaches limits under different doping methods, which implies that there are still some fundamental questions that need to be addressed. In this context, we revisit the origin of the flexoelectric-like effect in oxide semiconductors, which differs significantly from flexoelectricity in dielectrics. The effective flexoelectric coefficient of Nb-doped SrTiO₃ single crystals increases with a larger doping concentration of Nb and is linearly proportional to the reciprocal of the depletion layer width, which is consistent with the theoretical model. More interestingly, due to the doping with Nb, the sign of the flexoelectric-like effect is reversed, which emphasizes the distinction from intrinsic flexoelectricity. Despite the contribution of electrons, frequency-scan measurements indicate that the presence of oxygen vacancies has a crucial impact on flexoelectricity at low frequencies. These results provide insights into semiconductor flexoelectricity and provide a strategy for enhancing the flexoelectric-like effect by optimizing the depletion layer.