Surface effects on converse piezoelectricity of crystals

The contribution of surface units to bulk properties are often neglected in theoretical and computational studies of crystalline systems. We demonstrate that this assumption has to be made with caution in the case of (electric field) polarization. As a generalization of an earlier work on quasi-one-dimensional systems [Springborg, et al., Phys. Rev. B: Condens. Matter Mater. Phys., 2010, 82, 165442], it is shown that the polarization for 2D and 3D systems contains a surface contribution that can, in principle, take any value (within physical limits) and has consequences for converse piezoelectric responses. Subsequently, we determine the surface effects quantitatively for a group of ferroelectric perovskite structures. Our results indicate that such contributions can be substantial.