Effect of Surface Ionic Screening on Polarization Reversal and Phase Diagrams in Thin Antiferroelectric Films for Information and Energy Storage

Emergent behaviors in antiferroelectric thin films due to a coupling between surface electrochemistry and intrinsic polar instabilities are explored within the framework of the modified 2-4-6 Landau-Ginzburg-Devonshire (LGD) thermodynamic approach. By using phenomenological parameters of the LGD potential for a bulk antiferroelectric and a Stephenson-Highland (SH) approach, we study the role of surface ions with a charge density proportional to the relative partial oxygen pressure on the dipole states and their reversal mechanisms in antiferroelectric thin films. The combined LGDSH approach allows the boundaries of antiferroelectric, ferroelectriclike antiferroionic, and electretlike paraelectric states as a function of temperature, oxygen pressure, surface-ion formation energy and concentration, and film thickness to be delineated. This approach also allows the characterization of the polar and antipolar orderings dependence on the voltage applied to the antiferroelectric film, as well as the analysis of their static and dynamic hysteresis loops. The applications of the antiferroelectric films covered with a surface-ion layer for energy and information storage are explored and discussed.

Figure 1

(a) Layout of the considered system, consisting of an electron-conducting bottom electrode, an AFE film of thickness h, a layer of surface ions with charge density $\sigma (\varphi )$, an ultrathin gap separating the film surface, and a top electrode (from bottom to the top). Film thickness is h; gap thickness is λ. Adapted from Ref. [31]. (b) Schematics of the transition from an AFE-type polarization hysteresis to a FE-type AFI hysteresis loop induced by electric coupling with the charge of surface ions.

Figure 2

Phase diagram of an AFE film (a). Contour maps of the free-energy dependence on polarization (P) and antipolarization (A) for temperature values of T = 200 (b), 450 (c), and 500 K (d), and $E=0$. Relative units are used for the energy color scale. Dependences of A (dashed and dotted blue loops) and P (dashed red and dark-red loops) on the static external electric field, $E$_, calculated for $T=200$ (e), 450 (f), and 500 K (g). Polarization hysteresis, $P(E)$, calculated for dimensionless frequencies $w=0.3$ (black loops), 3 (red loops), 10 (magenta loops), 30 (blue loops), and 100 (green loops), and temperatures $T=200$ (h), 450 (i), and 500 K (j). For plots (h)–(j), external electric field is $E=(U_0/h)\sin (\omega t)$ and dimensionless frequency is $w=(\omega {\mathrm{\Gamma }}_P/2|{\alpha }_p|)$. surface charges from ambient medium are absent. Gap thickness, $\lambda <0.1\mathrm{nm}$; film thickness, h > 500 nm. Other parameters are listed in Table C1 [35].

Figure 3

Free energy as a function of polarization (P) and antipolarization (A) calculated for T = 200 (a), 300 (b), 400 (c), and 500 K (d), and relative partial oxygen pressures $\rho ={10}^4\mathrm{, }1\mathrm{, }{10}^{-4}\mathrm{,\; and }{10}^{-6}$; values are listed for each column or row. Relative units are used for the energy color scale. External electric field is absent, $E=0$. Thickness of AFE film, h = 50 nm; gap thickness, $\lambda =2\mathrm{nm}$; and ion-formation energies, $\mathrm{\Delta }{G}_1^{00}=\mathrm{\Delta }{G}_2^{00}=0.2\mathrm{eV}$.

Figure 4

Static dependences of order parameters (OPs)$A$ (solid blue curves) and P (solid red and dark-red curves), on external electric field E calculated for T = 200 (a), 300 (b), 400 (c), and 500 K (d) and relative partial oxygen pressures $\rho =1\mathrm{, }{10}^{-4}\mathrm{,\; and }{10}^{-6}$; values are listed for each column or row. Dotted vertical lines show thermodynamic transitions between different polar and antipolar states; yellow rectangles mark two or three stable polarization states. External electric field is $E=(U/h)$. Other parameters are the same as those in Fig. 3.

Figure 5

Polarization hysteresis loops, $P(E)$, calculated for dimensionless frequencies $w=0.3$ (black loops), 3 (red loops), 10 (magenta loops), 30 (blue loops), and 100 (green loops) at temperatures $T=200$ (a), 300 (b), 400 (c), and 500 K (d), and relative partial oxygen pressures, $\rho =1\mathrm{, }{10}^{-4}\mathrm{,\; and }{10}^{-6}$; values are listed for each column or row. External electric field is $E=(U_0/h)\sin (\omega t)$ and $w=(\omega {\mathrm{\Gamma }}_P/2|{\alpha }_p|)$. Other parameters are the same as those in Fig. 3.

Figure 6

Typical phase diagrams of thin AFE films with thicknesses $h=50\mathrm{nm}$ (a) and $h=5\mathrm{nm}$ (b), depending on temperature, $T$_, and relative partial oxygen pressure, $\rho$. There is an AFE phase coexisting with a weak FE phase, a FE-like AFI phase, and an electretlike PE phase. Typical free-energy maps at $E=0$ (b)–(d), and polarization hysteresis loops, $P(E)$ (e)–(g). Description of the insets is the same as those in Figs. 3 and 5. Other parameters are the same as those in Fig. 3.

Figure 7

Polarization field dependence, $P(E)$, calculated for a very low dimensionless frequency, $w={10}^{-3}$; $T=300$ (a),(b) and 550 K (c),(d); relative partial oxygen pressure, $\rho ={10}^{-6}$ (black curves), ${10}^{-5}$ (red curves), ${10}^{-4}$ (green curves), ${10}^{-3}$ (blue curves), ${10}^{-2}$ (magenta curves), ${10}^{-1}$ (purple curves), and 1 (brown curves). Film thickness, h = 5 (a),(b) and 50 nm (c),(d). External electric field is $E=(U_0/h)\sin (\omega t)$ and $w=(\omega {\mathrm{\Gamma }}_P/2|{\alpha }_p|)$. Other parameters are the same as those in Fig. 3.

Figure 8

(a) Schematic diagram relating loop shape, information, and energy-storage abilities to relative pressure, $\rho$, and temperature, T. Roman letters I–V indicate the five regions described in the text. Color maps of $W_{\mathrm{store}}$ (b) and $W_{\mathrm{loss}}$ (c) of the $P(E)$ dependences. Hysteresis loops (black curves) are superimposed on color maps. Film thickness, $h=5\mathrm{nm}$. Other parameters are the same as those in Fig. 3.