Intrinsic asymmetric ferroelectricity induced giant electroresistance in ZnO/BaTiO3 superlattice

Here, we combine the piezoelectric wurtzite ZnO and the ferroelectric (111) BaTiO3 as a hexagonal closed-packed structure and report a systematic theoretical study on the ferroelectric behavior induced by the interface of ZnO/BaTiO3 films and the transport properties between the SrRuO3 electrodes. The parallel and antiparallel polarizations of ZnO and BaTiO3 can lead to intrinsic asymmetric ferroelectricity in the ZnO/BaTiO3 superlattice. Using first-principles calculations we demonstrate four different configurations for the ZnO/BaTiO3/ZnO superlattice with respective terminations and find one most favorable for the stable existence of asymmetric ferroelectricity in thin films with thickness less than 4 nm. Combining density functional theory calculations with non equilibrium Green's function formalism, we investigate the electron transport properties of SrRuO3/ZnO/BaTiO3/ZnO/SrRuO3 FTJ and SrRuO3/ZnO/BaTiO3/SrRuO3 FTJ, and reveal a high TER effect of 581% and 112% respectively. These findings provide an important insight into the understanding of how the interface affects the polarization in the ZnO/BaTiO3 superlattice and may suggest a controllable and unambiguous way to build ferroelectric and multiferroic tunnel junctions.


Introduction
The past decades have witnessed an explosion in the design of ferroelectric tunnel junctions (FTJs) with the aim of accelerating their commercial applications into nonvolatile information devices. [1][2][3][4][5][6][7][8][9][10][11][12][13] Switching the ferroelectric polarization gives rise to a dramatic change of the tunneling electroresistance (i.e., TER effect), 10 making it possible to nondestructively read out the polarization state that carries information. Incorporating ferroelectric and piezoelectric components could help to construct a ferroelectric tunnel junction and show a TER effect. [14][15][16][17] Coupling between the piezoelectric ZnO and the ferroelectric BaTiO 3 may cause bistable ferroelectric polarization orientation. [18][19][20][21][22] The piezoelectric ZnO has an inherent polarization which is difficult to reverse using an electric eld, but the polarization of ferroelectric BaTiO 3 can be reversed in experiments. The parallel or antiparallel polarizations of ZnO and BaTiO 3 may lead to intrinsic asymmetric ferroelectricity in the ZnO/BaTiO 3 superlattice which is similar to that found in tricolor superlattices. 23 However, there are few studies on the transport properties of ZnO/BaTiO 3 heterostructures both in theory and experiment. In addition, BaTiO 3 can be stacked along the [111] direction [24][25][26] and can provide corrugated honeycomb interfaces which can stack closely with wurtzite ZnO. This stacking may make FTJs based on ZnO/BaTiO 3 thinner than those currently available. The research of ZnO/ BaTiO 3 heterostructure which combined wurtzite ZnO and (111) BaTiO 3 is relatively few. 20,21 The theoretical research is needed to reveal its atomic scale of interfaces and transport properties.
In this paper, the piezoelectric wurtzite ZnO and the ferroelectric perovskite (111) BaTiO 3 are closed-packed with good match of the lattice constants in all the theoretical study. We consider four congurations with respective terminations and show a systematic research on the orientation of polarization induced by the interface of ZnO/BaTiO 3 /ZnO lms using rstprinciples calculations. Aer comparing the four congurations, we choose one conguration which is most favorable for the stable existence of asymmetric ferroelectricity in thin lms to study its transport properties. The thickness of this ZnO/ BaTiO 3 lm is less than 4 nm. Combining density functional theory calculations with non equilibrium Green's function formalism, we investigate the electron transport properties of SrRuO 3 /ZnO/BaTiO 3 /ZnO/SrRuO 3 and SrRuO 3 /ZnO/BaTiO 3 / SrRuO 3 with a giant TER effect of 581% and 112% respectively. Compared to the previous results, 27-31 the TER effect of 581% for the tunnel junction combined ZnO and (111) BaTiO 3 in this article is larger than the highest TER effect of 400% 31 for the previous BaTiO 3 -based tunnel junctions. The junctions combined ZnO and (111) BaTiO 3 may exhibit richer and more novel properties in the future. These ndings provide an

Method of calculation
The geometry optimizations and electronic structure calculations of all models are performed within density functional theory (DFT) calculations by using the projector augmented wave (PAW) method as implemented in the Vienna ab initio simulation package (VASP). [32][33][34] The exchange-correlation potential is treated in the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE). 35 We use the energy cutoff of 500 eV for the plane wave expansion of the PAWs. A 6 Â 6 Â 1 G centered grid for k-point sampling is adopted for supercells in the self-consistent calculations. The Brillouin zone integrations are calculated using the tetrahedron method with Blöchl corrections. 36 In the structural relaxations, the atomic geometries were fully optimized until the Hellmann-Feynman forces were less than 1 meVÅ À1 .
The device properties of the FTJ are calculated by using density functional theory plus non equilibrium Green's function formalism (DFT + NEGF approach) 37,38 as implemented in the Atomistix ToolKit-Virtual NanoLab (ATK-VNL) soware package. 39 The double-z plus polarization basis set is employed, and a real-space mesh cutoff energy of 80 Hartree is used to guarantee the good convergence of the device conguration. The electron temperature is set at 300 K. The 5 Â 5 Â 101 k mesh is used for the self-consistent calculations to eliminate the mismatch of Fermi level between electrodes and the central region. The 35 Â 35 k mesh is adopted during the calculations of transmission spectra. The screening effect is considered by building screening region consist of electrode extension region and surface region.

Results and discussion
The cubic BaTiO 3 stacking along the [111] direction has a hexagonal-like structure, where the transition metal Ti ions form the graphene-like buckled honeycomb lattice (see Fig. 1). The [111] direction in the bulk structures corresponds to the z direction. The theoretical lattice constant we calculated for the cubic phase of BaTiO 3 is 4.036Å with PBE method, and the distance between two adjacent Ti atoms in one atomic layer in the (111)-plane is 5.707Å. The wurtzite ZnO has a hexagonal structure with theoretical in-plane lattice constant of 3.299Å, and the distance between two adjacent Zn atoms of the honeycomb in ffiffiffi 3 p Â ffiffiffi 3 p Â 1 superlattice is 5.714Å. Hence, the (111) BaTiO 3 and wurtzite ZnO have a very good match of the lattice constants (a mismatch is only about 0.1%) that allows layer-by-layer epitaxial growth of ZnO/BaTiO 3 (111) multilayers with no mist dislocation.
We calculated ZnO/BaTiO 3 /ZnO supercell composed of two layers of ZnO and three layers of BaTiO 3 (BTO). Four different congurations of the ZnO/BaTiO 3 /ZnO heterostructure were considered, with the respective terminations of Ti-O ( Fig. 2(a)), Ti-Zn ( Fig. 2(b)), BaO-O ( Fig. 2(c)) and BaO-Zn ( Fig. 2(d)). The direction of polarization of BaTiO 3 was adjusted to the [111] direction under the inuence of the interface and can be obtained by analyzing the relative Ti-O displacements along the [111] direction, see Fig. 2(e). The three O atoms at the top of the octahedron are on the same plane, and their vertical distance from Ti atom is d 1 . Similarly, d 2 is the vertical distance from three O atoms at the bottom of the octahedron to Ti atom. Therefore, the ferroelectric polarization is up when d 1 < d 2 , and is down when d 1 > d 2 . Using this way, the polarization P in the four different congurations were determined, as indicated by the red arrows in Fig. 2(a-d). As shown in Fig. 2(a), the rst kind of terminations of the interfaces is Ti-O, means the atomic layer of Ti in (111) BaTiO 3 contact with O layer in ZnO. This conguration make BaTiO 3 has a polarization pointing from top to bottom, and the polarization is very robust. The single well potential in Fig. 2(f) denotes the polarization is almost  impossible to reverse. The second conguration is Ti-Zn, means the Ti layer in (111) BaTiO 3 contact with Zn layer in ZnO. This kind of conguration make the interior polar displacements of BaTiO 3 near the top interface have opposite orientation with that near the bottom interface, and the net polarization is pointing up. The naming rules for the other two congurations are the same as above. When we increase the thickness of BaTiO 3 and decrease the thickness of ZnO for the Ti-Zn conguration, a double-well prole is observed in Fig. 2 Fig. 3(a). In the top interface, the O atoms is directly above the nearest neighbour Ti atoms, and the bond length is about 1.93Å. However, in the bottom interface, the O atoms lies diagonally below the Ti atoms, so the vertical distance between Ti and O atoms is small although the bond length is 1.85Å. The difference of Ti-O bonding between top interface and bottom interface can be claried in Fig. 4 In Fig. 5(a), three layers of SrRuO 3 (SRO) were interfaced to the ZnO/BTO/ZnO overlayers to form the SRO/ZnO/BTO/ZnO/ SRO and SRO/ZnO/BTO/SRO heterostructures. We dene the state which has polarization from bottom interface to top interface as the 'up' state and the opposite direction as the 'down' state. From the rumpling of the 'up' and 'down' states in junction structures as shown in Fig. 5(b), we can see that the ferroelectric displacements of both supercells are signicantly asymmetric. For the average polarization displacements, the difference between 'up' and 'down' states are dramatic. Our calculations have found two inequivalent energy minima in each system, as clearly shown in Fig. 5(c). This is the signature  of asymmetric ferroelectricity. Note that here the energy proles are obtained by simulating the so mode distortion of the BaTiO 3 layer (characterized by the parameter l), where we choose states with l ¼ +1 to be the lowest energy states ('up' states) and states with l ¼ À1 to be the metastable energy states ('down' states) for both two supercells. The coordinates of other l states are linear interpolations (|l| < 1) or extrapolations (|l| > 1) between the coordinates of 'up' and 'down' states according to their values. Here, the thickness of ZnO/BaTiO 3 superlattice is less than 4 nm, which is thinner than those currently available in experiment. [18][19][20][21][22] Essentially speaking, the asymmetric ferroelectricity of ZnO/ BaTiO 3 superlattice comes from the relative orientations of polarizations of ZnO and BaTiO 3 in supercells. When the orientations of the polarization of ZnO and BaTiO 3 are opposite, the counteraction of the intensity of total polarization is appeared. This will result in a low conductance. The high conductance comes from the enhancement of total polarization resulting from the same orientations of the polarization of ZnO and BaTiO 3 . Fig. 6 shows schematically the two conductance levels indicating the possibility of switching between them by electric (E) elds.
To evaluate the performance of SRO/ZnO/BTO/ZnO/SRO and SRO/ZnO/BTO/SRO FTJs, density functional theory plus non equilibrium Green's function formalism is used to study the electrical conductance and TER effect. In our calculations, the transmission coefficients and reection matrices are determined by matching the wave functions of the scattering region with linear combinations of propagating Bloch states in the electrodes. Because the electronic states at the EF dominate the transport properties, the zero-bias electrical conductance within the LandauerÀBüttiker formula can be evaluated as where G 0 ¼ 2 Â 10 2 /ħ is the conductance quantum, e is the electron charge, ħ is the Planck's constant, and T(E F ,k k ) is the transmission coefficient at the Fermi energy for a given Bloch wave vector k k ¼ (k x ,k y ) in the 2D Brillouin zone. By integrating the transmission probability for states at the Fermi energy over the 2D Brillouin zone, we can calculate the total conductance (G). In the up state of SRO/ZnO/BTO/ZnO/SRO FTJ, G up ¼ 1.122 Â 10 À7 S; by contrast, in the down state, G dn ¼ 1.647 Â 10 À8 S. For SRO/ZnO/BTO/SRO FTJ, G up ¼ 1.771 Â 10 À7 S, G dn ¼ 8.336 Â 10 À8 S. Following the conventional denition in previous study, 40 the TER ratio in our study is dened as As a result, the reversal of ferroelectric polarization in the SRO/ZnO/BTO/ZnO/SRO FTJ leads to a signicantly enhanced TER effect at zero bias, which is approximately about 581%. The TER effect for SRO/ZnO/BTO/SRO FTJ is 112%, which is also tremendous.
To understand the change in the conductance ratio during the polarization reversal, the k k -resolved transmissions at E F are   shown in Fig. 7. In the up state of SRO/ZnO/BTO/ZnO/SRO FTJ, the transmission coming from the rhombus regions of the 2D Brillouin zone are largest, indicating the feature of resonant tunneling. We nd the transmission eigenstates around this region show much smaller decay rate than those around G point, which is responsible for the signicant transmission. The reason is that the amplitude of transmission eigenstates for this region is much larger than that for G point, which indicates greater transmission probability. Compared to the up state, the transmission in the down state is largely reduced, leading to lower conductance than the up state. This explains the observed giant TER effect in the SRO/ZnO/BTO/ZnO/SRO and SRO/ZnO/ BTO/SRO FTJ.

Conclusions
In conclusion, the four stacking congurations of ZnO/BTO/ ZnO supercell with two layers of ZnO and three layers of (111) BTO have been studied using DFT calculations. The mechanism of polarization direction in (111) BTO inuenced by the interfaces are investigated. Combining density functional theory calculations with non equilibrium Green's function formalism, two giant TER effects of 581% and 112% are observed in our newly designed SRO/ZnO/BTO/ZnO/SRO and SRO/ZnO/BTO/ SRO FTJ heterostructure. The thickness of ZnO/BTO in this heterostructure is less than 4 nm. The proposed strategy in our study is applicable to design higher performance FTJs. We hope this work will stimulate the experimental endeavors of fabricating FTJs with a giant TER effect to accelerate their commercial applications into ultralow-power, high-speed, and nonvolatile nanoscale memory devices.

Conflicts of interest
There are no conicts to declare.