Introduction

Ferroelectric tunnel junctions (FTJs) have attracted significant attention due to the interesting physics controlling their properties, as well as the potential for application in random access memories. A typical ferroelectric tunnel junction (FTJ) is a heterostructure with a nanoscale-thick ferroelectric film sandwiched between electrodes, where reversal of the polarization of the ferroelectric film results in the switching of the tunneling electroresistance (TER) across the barrier between low resistance ON state and high resistance OFF state. A large enough magnitude of TER is crucial for the practical application of FTJs in electronic devices1,2,3,4,5. Among different microscopic processes, the TER effect usually arises from asymmetry in FTJs concerning its electronic and atomic structures. The asymmetry can be achieved by dissimilar electrodes6,7,8, interface engineering9,10,11,12,13, and composite barrier layer14,15,16,17. Because of asymmetry, reversal of the polarization leads to different barrier heights or widths between the ON and OFF states. To achieve a large TER ON/OFF ratio in FTJs, efforts are made to increase the asymmetry of the structure by increasing the resistance of the OFF state or reducing the resistance of the ON state. In reality, most of the efforts focus on improving the barrier height or width to increase the resistance of the of states, for example, by using composited dielectric layers14,15, semiconductor electrodes18,19, polarization induced phase transition20,21,22 on the interfaces etc. But too large asymmetry may lead to ferroelectric stability problems in the ferroelectric film23. Also, through practical applications, reducing the resistance-area product of the ON state is required to integrate FTJs devices with the complementary metal-oxide semiconductor electronics. To reduce the resistance of the ON state, however, a thinner ferroelectric barrier is needed which usually suppresses the ferroelectric polarization under critical thickness. From this point of view, a giant TER with low resistance-area product of ON state in an FTJ by reducing the thickness of the ferroelectric barrier while persisting the ferroelectric polarization is contradictory with each other.

When we consider the tunneling of carriers across an FTJ, the barrier height and width dominate the resistance and result in direct tunneling, which is extensively studied in experiments and theory3,24. Besides the direct tunneling, another mechanism that was not considered enough is the resonant tunneling effect, which could suddenly decrease the tunneling resistance. A quantum well in the scattering area is required to achieve resonant tunneling. Several previous studies have discussed the possibility and effect of introducing resonant tunneling into FTJs by an inserted metal layer, domain wall, or two-dimensional electron gas methods, which are a huge challenge to realize in experiments25,26,27. A practical way to introduce resonant quantum well into FTJs might be by resonant band engineering, where an atomic thickness of dielectric layer with a smaller bandgap is embedded into the ferroelectric barrier layer and leads to polarization controlled resonant tunneling28. The ferroelectric polarization held resonant tunneling solely could induce a TER ratio more than 103 as calculated in the previous studies. To further improve the functionalities of FTJs, in this study, we propose that the polarization controlled resonant band could be effectively integrated with the asymmetry, and a giant TER ratio with a low resistance of ON state could be realized in this way.

To demonstrate the integration of resonant tunneling and asymmetry in one FTJ, we theoretically studied a prototypical composite FTJ SrRuO3/BaTiO3/SrTiO3/SrRuO3, where the asymmetry is due to the inserted dielectric layer SrTiO3 at the interface. Using first-principles calculations and quantum-mechanical tunneling model, we show that the polarization controlled resonant band could be well integrated with the asymmetry in the elaborated FTJ SrRuO3/BaTiO3/BaSnO3/SrTiO3/SrRuO3 by introducing atomic thickness of the BaSnO3 layer. Our studies indicate that the ferroelectric polarization controlled resonant band and asymmetry work together and dramatically enhanced TER ON/OFF ratio. Furthermore, without reducing the effective thickness of the barrier, the tunneling resistance of the ON state is significantly reduced while the resistance of the OFF state is kept high. A giant TER with low-resistance-area product thus could be realized in such an elaborated FTJ.

Results

Electronic structures of FTJs

For comparison, we consider three FTJs: The diagram on the top of Fig. 1a shows FTJ-1 with only asymmetry induced TER; The diagram on the top of Fig. 1b shows FTJ-2 with only resonant band induced TER; The diagram on the top of Fig. 1c shows elaborated FTJ-3 including both the features of FTJ-1 and FTJ-2. In detail, FTJ-1 is the parent structure of a prototypical FTJ SrRuO3/BaTiO3/SrTiO3/SrRuO3, which is constructed of 6.5 unit-cells of BaTiO3 and two unit-cells of SrTiO3 sandwiched by 6.5 unit-cells of SrRuO3 electrodes. The total thickness of the barrier is 8.5 unit-cells (about 3.5 nanometers of the total barrier). The dielectric layer SrTiO3 has almost the same bandgap as BaTiO3. Similar FTJs have been extensively studied both in experiment and theory, which exhibit asymmetry-inducedd TER ON/OFF ratio15. In this FTJ, the asymmetry is from the composite SrTiO3 layer. Due to the existence of the SrTiO3 at the right interface, the state with polarization pointing to the left is the OFF state which has an efficient barrier higher than that of the ON state with polarization pointing to the right. FTJ-2 is a structure of SrRuO3/BaTiO3/SrRuO3 with two BaSnO3 atomic layers embedded in the BaTiO3 barrier. The total thickness of the barrier is also 8.5 unit-cells (about 3.5 nanometers of the total barrier). The BaSnO3 has a relatively smaller band gap than BaTiO3. Depending on the polarization orientations, the ferroelectric polarization of BaTiO3 shifts the conduction-band minimums of the BaSnO3 layer above or below the Fermi energy and results in switching between direct tunneling and resonant tunneling, which leads to TER effect28. FTJ-3 is an elaborated FTJ structure with 4.5 unit-cells of BaTiO3, two unit cells of BaSnO3, and two unit-cells of SrTiO3 (about 3.5 nanometers of the total barrier).

Fig. 1: Calculated relative polar displacement between cation (M) and anion (O) on each AO (A = Ba or Sr) and BO2 (B = Ti, Sn or Ru) layers.
figure 1

a FTJ-1: SRO/BTO/STO/SRO, b FTJ-2: SRO/BTO/BSO/SRO, and c FTJ-3: SRO/BTO/BSO/STO/SRO. Positive (negative) values of the displacement shown in red (blue) correspond to polarization pointing to the right (left). Open and solid symbols denote Ti–O, Sn–O, Ru–O, and Ba–O, Sr–O displacements, respectively.

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We find that the ferroelectric polarization is switchable in each of the three FTJs as shown in Fig. 1a–c by the relative cation–anion displacements for polarization pointing to the left (blue curves) and right (red curves). By studying the electronic structures and transport properties, we will demonstrate that, the asymmetry mechanism responsible for the TER effect in FTJ-1 and the polarization-controlled resonant tunneling mechanism responsible for the TER effect in FTJ-2 could be well integrated in the elaborated FTJ-3 to work together and result in a giant TER with low resistance of ON state.

Fig. 2a–f show the local density of states (LDOS) of the three FTJs projected on each atomic layer of the barrier with polarization pointing to the right and left as indicated by the red and blue arrows. Over all, we could see bands bending across the barrier in all structures due to the depolarizing field whose direction depends on the polarization orientations. The positions of the conduction band minimum (CBM) reflect the shape of the tunneling barrier. In FTJ-1, the OFF state as shown in Fig. 2b with polarization pointing to the left, performs larger effective barrier height than the ON state with polarization pointing to the right as shown in Fig. 2a. At the BaTiO3/SrTiO3 interface, since there are insufficient screening charges, the potential in SrTiO3 pinned to that at the interface with BaTiO3, thus forms an additional flat efficient potential barrier which reverses with ferroelectric polarization orientations and leads to larger effective barrier height of the OFF state15. In FTJ-2 for the OFF state as shown in Fig. 2d with polarization pointing to the left, the CBM of each layer is above the Fermi level. For the ON state as shown in Fig. 2c with polarization pointing to the right, the CBM of the BaSnO3 atomic layers bends below the Fermi level and serves as an effective quantum well which would provide resonant states and result in resonant tunneling28. In FTJ-3, for the OFF state as shown in Fig. 2f with polarization pointing to the left, the whole electronic structure is similar as the OFF state of FTJ-1 as shown in Fig. 2b. Specifically, the SrTiO3 and BaSnO3 layers form additional flat efficient potential barrier. In this case, the asymmetry dominates the shape of the potential barrier for direct tunneling. For the ON state as shown in Fig. 2e with polarization pointing to the right, the electronic structure is similar as the ON state of FTJ-2 as shown in Fig. 2c with the CBM of BaSnO3 layers below the Fermi level.

Fig. 2: Local densities of states (LDOS) as a function of energy E on each BO2 (B = Ti, Sn) atomic layer.
figure 2

a, b FTJ-1, c, d FTJ-2, and e, f FTJ-3 with the opposite polarization directions. Arrows indicate the directions of the polarization.

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Here, we need to point out that even though the CBM of the interfacial SrTiO3 atomic layers are also below the Fermi level with polarization pointing to the right as shown in Fig. 2e, the different orbital features between the Sn-2s orbital of BaSnO3 and the Ti-3d orbital of SrTiO3 atomic layers make the interfacial SrTiO3 layer serves as effective barrier for the BaSnO3 layer. It is notable that the quantum-well states in the BaSnO3 layer reveal themselves as peaks in the LDOS near the CBM due to the confinement. To illustrate it, we calculated the spectral density of states (SD) around the \({{{\bar{\mathrm {\Gamma}}}}}\) point projected in the 2-dimensional (2D) Brillouin Zone (BZ) near the Fermi level at −0.12 eV, which corresponds to the peak of LDOS below the Fermi level as shown in Fig. 2e for each of the two BaSnO3 atomic layers. The SD of the two BaSnO3 atomic layers are shown in Fig. 3a, b while the SD of the two SrTiO3 atomic layers are shown in Fig. 3c, d. The ring-like high SD of the BaSnO3 atomic layers around \({{{\bar{\mathrm {\Gamma}}}}}\) point indicates the presence of a 2D free-electron-like band within the SnO2 layers and is largely composed of the Sn-2s orbital. In the adjacent interfacial SrTiO3 atomic layers at the right interface, we could see obvious vanishing of SD in the area around \({{{\bar{\mathrm {\Gamma}}}}}\) point where the SD is sizable for the BaSnO3 atomic layers. This is because of the nonoverlapping between Ti-3d and Sn-2s states in the reciprocal space. Therefore, the SrTiO3 layer provide an effective barrier for tunneling electrons with transverse wave vector k|| corresponding to the quantum-well states of the BaSnO3 layer. Qualitatively, from the electronic structures, we could predict that the FTJ-3 has both the advantage of FTJ-1 with asymmetry-induced additional efficient barrier height for direct tunneling of the OFF state and the advantage of FTJ-2 with an effective quantum well responsible for resonant tunneling to reduce the resistance of the ON state.

Fig. 3: Spectral density of states around the \({{{\bar{\mathrm {\Gamma}}}}}\) point (k|| = 0) at −0.12 eV below the Fermi level.
figure 3

Projecting onto the left SnO2 layer (a), the right SnO2 (b), the right adjacent TiO2 layer (c), and the right interface TiO2 layer (d) for FTJ-3 with ferroelectric polarization pointing to the right.

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To quantitatively understand the improvement of transport properties by the integration of resonant band with asymmetry, we calculated the distribution of the k||-resolved transmission in the 2D BZ perpendicular to the transport z direction as shown in Fig. 4a, b for polarization pointing the right and left, respectively. We could see a ring “hot spot” around the \({{{\bar{\mathrm {\Gamma}}}}}\) point for the ON state. This ring “hot spot” corresponds to the ring-like area of the SD of the BaSnO3 atomic layers as shown in Fig. 3a, b, which is due to the resonant tunneling effect contributed by the quantum well states in the BaSnO3 layer. For the OFF state with polarization pointing to the left, the asymmetry dominates the direct tunneling with large effective barrier height, and the transmission in this area is very small, 10−4 orders less than the ON state.

Fig. 4: k||-resolved transmission across FTJ-3.
figure 4

For polarization pointing right (a) and left (b) at −0.12 eV below the Fermi level.

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TER effects of FTJs

Figure 5a shows the calculated TER ON/OFF ratio of each FTJ near the Fermi level. For both FTJ-1 and FTJ-2, the TER ratios are around 102–104 as shown by the green and orange curves, respectively. However, we could see that the TER ratio of FTJ-3 has much larger average value of about 106 around the Fermi level as shown by the black curve. To further understand the improvement of the TER ratio in FTJ-3, we calculated the conductance of each structure and each polarization state. The results are shown in Fig. 5b. Compared with FTJ-1 (solid green curve for ON state and dotted green curve for the OFF state) and FTJ-2 (solid orange curve for ON state and dotted orange curve for the OFF state), the average conductance of FTJ-3 of OFF state (black dotted curve) is as low as the conductance of the OFF state of FTJ-1 which is due to the additional efficient barrier of the SrTiO3 layers, while the average conductance of FTJ-3 of ON state (black solid curve) has the highest conductance value. Therefore, the giant TER ratio of FTJ-3 shown in Fig. 5a results from both the asymmetry-induced additional efficient barrier height of the OFF state with polarization pointing to the left and the effective quantum well induced resonant tunneling of the ON state with polarization pointing to the right.

Fig. 5: TER and conductance G calculated by first-principles.
figure 5

a TER of the FTJs as a function of energy E around Fermi level. b G per lateral area of FTJs as a function of energy E for polarization pointing right (solid arrow) and left (dotted arrow). The Fermi energy is at zero. Green, orange, black lines represent FTJ 1–3, respectively.

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Besides the improved TER value, another important advantage of the elaborated FTJ-3 is its low resistance of the ON state which could be reflected by the calculated conduction values as shown in Fig. 5b. The low resistance of the ON state in FTJ-3 is due to the resonant assistant tunneling contributed by the resonant states in the effective quantum well of BaSnO3 layer when polarization is pointing to the right, as shown by the peaks of LDOS near the Fermi level in Fig. 2e. From Fig. 5b as shown by the solid black curve, we could see that the highest conductance of the ON state of FTJ-3 is more than 0.5 × 10−4 Ω−1 μm−2, which corresponds to a resistance about 5 MΩ μm2, with a ON/OFF ratio more than 10−7. In asymmetric ferroelectric tunnel junctions with BaTiO3/SrTiO3 composite barrier (about 4 nm thickness, almost the same thickness as the structure in our calculations), it was reported that the ON state resistance is 50–200 MΩ μm2 with 103–104 ON/OFF ratio29. Obviously, the integration of resonant band with asymmetry dramatically increases the TER ON/OFF ratio more than three orders while reduces the resistance of the ON state more than one order. The resistance of the ON state might be further reduced by larger resonant barrier or by introducing other asymmetry like different electrodes.

The calculated TER effect from first-principles calculations could be well explained by a quantum-mechanical tunneling model. Schematic diagrams of FTJs structures of the modeling corresponding to the FTJs calculated by first-principles calculations are shown in Fig. 6. The details of the parameters used in the model could be found in the Supplementary Information. Figure 7a, b show the TER ON/OFF ratio and the conductance of each FTJs as a function of energy near the Fermi level. Compared with the results of first-principles calculations as shown in Fig. 5a, b, we see that the results of the quantum-mechanical tunneling model qualitatively match the results calculated by first-principles calculations.

Fig. 6: Schematic diagrams of FTJs corresponding to the FTJs calculated by first-principles calculations.
figure 6

a FTJ-1′, b FTJ-2′, and c FTJ-3′. Gray layer: metal; Yellow layer: ferroelectric; Green layer: dielectric layer; Orange layer: dielectric layer with smaller bands gap. The four interfaces between the layers are at 0, a, b, and c with the left interface is set to be zero.

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Fig. 7: TER and conductance G calculated by quantum-mechanical tunneling model.
figure 7

a TER of the FTJ 1′–3′ as a function of E. The curves of insets show the corresponding tunneling potential profiles, blue for polarization pointing to the left and red for polarization pointing to the right. The arrows indicate the directions of the polarization. b Conductance G per lateral area of FTJs as a function of energy E for polarization pointing right (solid) and left (dotted). The Fermi energy is at zero. Green, orange, black lines represent FTJ 1′–3′, respectively.

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The resonant bands could also be integrated with other asymmetries in FTJs, for example with difference electrodes. In FTJs with different electrodes, the reversal of polarization tunes the effective tunneling barrier height and leads to TER effects due to the different screening length or work functions of the electrodes. To avoid the amounts of first-principles calculations, we just studied this case by quantum-mechanical tunneling model. The results are shown in Supplementary Information.

Discussion

In summary, using both first-principles calculations and quantum-mechanical tunneling model, we demonstrate that the resonant band could be integrated with the asymmetries of the extensively studied FTJs with different interfaces or electrodes. To illustrate the advantages the integration of polarization controlled resonant band with asymmetry, we focus on a prototypical FTJ where the asymmetry is due to the composite dielectric layer. By bands engineering, the polarization controlled resonant tunneling could dramatically reduce the tunneling resistance of the ON state while keep the tunneling resistance of OFF state large and leads to giant TER with low resistance-area product. The proposed integration of resonant tunneling by bands engineering with asymmetry is based on the band alignment and electronic structures of materials. The resonant quantum well is polarization dependent and the quantum well could be fully controlled by the polarization to be on or closed. This may provide a more efficient and applicable way to introduce resonant quantum well into FTJs rather than by introducing metal layer which could not be fully controlled by the polarization. We hope our theoretical predictions will stimulate experimental studies of FTJs and related functional oxide heterostructures with enhanced performance driven by the designed electronic bands.

Methods

First-principles calculations

First-principles density functional theory (DFT) calculations were performed using plane-wave pseudopotential code by Quantum Espresso30. The exchange and correlation effects are treated within the generalized gradient approximation (GGA). The electronic wave functions are expanded in a plane-wave basis set limited by a cut-off energy of 550 eV. The atomic position is relaxed until the force converges to <1 meV Å−1 in all supercells. The Brillouin zone is sampled with 8 × 8 × 1 Monkhorst–Pack k-point mesh for all supercells. For all structures, the in-plain lattice constants are fixed to be a = 3.94 Å, which is the ab initio calculated value of lattice parameter of cubic SrTiO3. Under this constrain, the calculated direct band gaps are 2.5 and 1.2 eV for BaTiO3 and BaSnO3 compounds, respectively.