Schematic configuration of the system adopted in the present calculations for a typical A-FTJs. The arrows denote the directions of the polarization , unscreened depolarization field , charge screening electric field and built-in electric field .
The relative Ti–O and Ba–O displacements along the bulk tetragonal soft mode -axis direction with the fully relaxed configurations (as shown in Fig. 1) as a function of the film thickness for different , 4, 6, 8, and 10, respectively. In order to compare, the data of relative Ti–O displacements in a two layers ferroelectric film with symmetric top and bottom Pt electrodes are also presented.
The polarization calculated as a function of FTF thickness (unit cells). The dotted line represents the calculated tetragonal bulk value.
(a) The macroscopic total (ionic plus electronic) charge density. (b) The macroscopic-averaged electrostatic potential [black line (bottom)], which include the contribution of the unscreened depolarizing field , charge screening electric field and built-in electric field (as shown in Fig. 1), for the fully relaxed (BTO) FTJ is shown. In order to show the existence of the built-in electric field caused by the dissimilar electrodes Pt and (SRO) with the different electronic environment of the two electrodes in the short-circuited conditions, the electrostatic potential of film (red dashed line) with the original paraelectric configurations is also presented. Moreover, the green line (top) represents the difference of electrostatic potential between the paraelectric (PE) and ferroelectric (FE) phases.
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