摘要
We consider a typical heterostructure "domain patterned ferroelectric film - ultra-thin dielectric layer - semiconductor," where the semiconductor can be an electrolyte, paraelectric or multi-layered graphene. Unexpectedly, we have found that the space charge modulation profile and amplitude in the semiconductor, that screens the spontaneous polarization of a 180-deg domain structure of ferroelectric, depends on the domain structure period, dielectric layer thickness and semiconductor screening radius in a rather non-trivial nonlinear way. Multiple size effects appearance and manifestation are defined by the relationship between these three parameters. In addition, we show that the concept of effective gap can be introduced in a simple way only for a single-domain limit. Obtained analytical results open the way for understanding of current-AFM maps of contaminated ferroelectric surfaces in ambient atmosphere as well as explore the possibilities of conductivity control in ultra-thin semiconductor layers. © 2014 AIP Publishing LLC.