2D α-In2Se3/semiconductor vdW heterostructures
The α-In2Se3 ferroelectric heterostructures and their electronic properties are calculated based on DFT as implemented in the Vienna ab initio simulation package (VASP) code46. The three-fold rotational symmetry of α-In2Se3 and considered 2D semiconductors (SnTe and PbSe) results in the same in-plane triangular cell shapes as shown in Fig. 1a-c. The optimized in-plane lattice constants of monolayers α-In2Se3, SnTe and PbSe (4.110, 4.172 and 4.096 Å, respectively) agree well with the existing results19, 44, 45, 47, 48, leading to tolerable lattice mismatches of 1.4% (In2Se3/SnTe) and 0.05% (In2Se3/PbSe). Band gaps of monolayer α-In2Se3, SnTe and PbSe are calculated to be 0.78, 1.87 and 1.83 eV, respectively, which are also in accordance with the existing results19, 44, 45, 47, 48 in Supplementary Fig. 1.
Both terminations of SnTe with Sn or Te atoms at the interface with In2Se3 are considered in the heterostructures. The two terminations of SnTe in conjunction with two different OOP polarization directions of α-In2Se3 make four types of In2Se3/SnTe heterostructures as shown in Fig. 1d-g. Each heterostructure is stacked with the top layer atoms of SnTe directly under the top layer In atoms of In2Se3 based on the structure optimizations. The total energies of the four heterostructures as shown in Fig. 1d-g are calculated to be 156, 0, 180 and 149 meV per unit cell, respectively (the energy of the most stable heterostructure is set to be 0). These results indicate that the In2Se3/SnTe heterostructures with Sn-Se interfaces (Fig. 1d, e) have lower energy than those with Te-Se interfaces (Fig. 1f, g) due to the Coulomb interaction. The Sn-Se interface heterostructures with the P↑ state (polarization of In2Se3 points away from SnTe) has 156 meV lower energy than the P↓ state (polarization of In2Se3 points into SnTe). For the Te-Se interface heterostructures, the energy of the P↑ state is only 31 meV lower than that of P↓ state. The atomic structures of In2Se3/PbSe heterostructures are similar to those of In2Se3/SnTe heterostructures with the total energies calculated to be 123, 0, 146 and 147 meV per unit cell, respectively.
Next, we investigate the band alignment in the In2Se3/SnTe heterostructures. Figure 2a-d plot the calculated band structures of the four heterostructures shown in Fig. 1d-g. For the P↓ state of the Sn-Se interface heterostructure, the valence band maximum (VBM) and the conduction band minimum (CBM) are contributed by SnTe and In2Se3, respectively, resulting an indirect band gap of 0.84 eV (Fig. 2a). If the polarization is reversed upward (P↑), the heterostructure becomes metallic (Fig. 2b) with the VBM (mainly contributed by SnTe) 0.39 eV higher than the CBM (mainly contributed by In2Se3). This transition to the metallic state is caused by the ferroelectric polarization charge at the In2Se3/SnTe interface lifting the electrostatic potential energy of SnTe up and resulting in the electron charge transfer from the SnTe valence band to the In2Se3 conduction band. This fact is evident from the atomic layer-resolved density of states (LDOS) and charge transfer at the interface as illustrated in Supplementary Figs. 2 and 3.
The predicted transition between insulating and metallic states for the Sn-Se interface heterostructure driven by polarization reversal from the P↓ to P↑ state is consistent with the type II to type III band alignment transition as defined in ref.32. However, the band tuning effect in the present study is much more pronounced than those found in the similar 2D α-In2Se3/semiconductor heterostructures31, 32, 49. The Te-Se interface heterostructure behaves differently. In this case, the P↓ state exhibits an indirect band gap of 1.08 eV (Fig. 2c) with both VBM and CBM derived from the In2Se3 layer, whereas the P↑ state reveals an indirect band gap of 0.28 eV (Fig. 2d) where the VBM and CBM are contributed by the SnTe and In2Se3, respectively. This transition is consistent with the type I to type II band alignment transition as defined in ref.32. The In2Se3/PbSe heterostructures show similar electronic properties to those of the In2Se3/SnTe heterostructures in Supplementary Fig. 4.
In-plane ferroelectric tunnel junctions
The significant polarization-induced band tuning effect and the resulting transition between insulating and metallic states, makes the α-In2Se3 ferroelectric heterostructures promising for application in memory and logical devices, such as ferroelectric field-effect transistors (FeFET) and FTJs. In this work, we design an IP FTJ based on the Sn-Se terminated interface In2Se3/SnTe heterostructure. The transport direction of the FTJ is set along the IP polarization direction of α-In2Se3 (see Fig. 1a, b), which allows the simultaneous switching of OOP and IP polarizations through the application of IP external electric field between the two electrodes. Figure 3 plots the atomic structures of the IP FTJs for the P↓ and P↑ states, respectively. The tunneling barrier in the FTJs consists of integer multiples (N) of the orthorhombic cells (denoted by the green rectangles in Fig. 1a and Fig. 3a) stacked along the transport direction. N is set to be ranging from 3 to 6. The lattice constant along the transport direction of each orthorhombic cell is 0.71 nm. Heavily electron-doped In2Se3/SnTe heterostructures ((In0.5Sn0.5)2Se3/(Sn0.5Sb0.5)Te) are used as electrodes in the FTJs. Their electronic structure is obtained using the virtual crystal approximation (VCA)50 by mixing 50% Sn on the In site and 50% Sb on the Sn site(see Supplementary Fig. 5).
Next, we explore the electron transport in In2Se3/SnTe IP FTJs. The electron transmission is calculated within the general scattering formalism51 implemented in Quantum ESPRESSO46, 52. Figure 4a shows the calculated transmission (T) as a function of electron energy (E) for the FTJs with N = 5. It is seen that, for the P↓ state, the transmission drops significantly when the electron energy increases from EF − 0.6 eV to EF − 0.3 eV, and stays low until the energy increases up to about EF + 0.2 eV (EF stands for the Fermi energy). Then the transmission rises again as the energy keeps increasing. On the contrary, for the P↑ state, the FTJ maintains a high transmission state under the considered electron energy range. The TER ratio (ON/OFF transmission ratio T(P↑)/T(P↓)) of the FTJ at E = EF is estimated to be 9.4 ⋅ 102. For E = EF − 0.3 eV, the ON/OFF ratio is found to be as large as 5.0 ⋅ 104.
Then the barrier width dependence of the transports is studied by calculating the transmission of FTJs at E = EF with the barrier layer width varying from 3 to 6 orthorhombic unit cells. It is seen from Fig. 4b, the transmission of the ON state (P↑ state) is almost unchanged when the barrier width increases. This is because, in the P↑ state, the heterostructure is metallic, allowing the FTJ behave as a conductor. On the contrary, for the OFF state (P↓ state), the calculated transmission decays exponentially with increasing the barrier width, exhibiting a typical tunnelling behavior. As a result, the ON/OFF transmission ratios are calculated to be 5.9 ⋅ 101, 1.4 ⋅ 102, 9.4 ⋅ 102, and 5.2 ⋅ 103 for the barrier layer width varying from 3 to 6 orthorhombic cells (Fig. 4b). We conclude, therefore, that the ferroelectric polarization induced TER effect of the designed In2Se3/SnTe IP FTJ can be enhanced exponentially by increasing the barrier width.
In order to understand the origin of the predicted transport behaviors, the electronic structures of the FTJ are analyzed. First, the layer-resolved density of states (LDOS) along the width direction are calculated as plotted in Fig. 5. Each layer of Fig. 5 shows the total DOS projected on half an orthorhombic cell in the electrode and barrier regions for P↓ (Fig. 5a) and P↑ (Fig. 5b) states, respectively. As seen from Fig. 5a, the barrier layer exhibits an obvious band gap from about − 0.6 eV to 0.2 eV relative to EF. This feature of the band structure well illustrates why the transmission of the P↓ state decreases and increases at the energy of EF − 0.6 eV and EF + 0.2 eV, respectively, as shown in Fig. 4a. On the contrary, for the P↑ state, as shown in Fig. 5b, there is no band gap across the barrier layer, leading to good conductivity under the entire considered energy range (see Fig. 4a). The band structure controlled tunneling and conducting properties of the barrier layer for the P↓ and P↑ states also explain the barrier width dependence of transport behaviors as shown in Fig. 4b.
To further clarify the transport mechanism of the designed IP FTJ, the partial charge densities in the real space are analyzed. Figure 6 visualizes the partial charge densities in the range of energies from EF − 0.1 eV to EF for P↓ and P↑ states, respectively. It is seen from Fig. 6a that, for the P↓ state, the partial charge density at EF only exists in the electrodes and a few atomic layers of the barrier near the interfaces, agreeing well with the LDOS of the FTJ at the Fermi energy in Fig. 5a. On the contrary, for the P↑ state, as seen from Fig. 6b, there is abundant charge distributed within the barrier region, corresponding to the LDOS in Fig. 5b. From the spatial distribution, the partial charge density is mainly concentrated on the SnTe layer and the In2Se3/SnTe interface in the barrier region, which indicates electron transport along these channels under the external bias as in a conductor.
In conclusion, we have designed vdW heterostructures with α-In2Se3 ferroelectric and hexagonal group IV-VI 2D semiconductor layers (SnTe and PbSe). Based on systematic first-principles studies, we demonstrated that these heterostructures exhibit a pronounced ferroelectric polarization-controlled band tuning property, which is interesting for electronic device applications. We predicted that the In2Se3/SnTe heterostructure with Sn-Se interface termination can be switched from insulating with a large band gap to metallic, when the OOP ferroelectric polarization of α-In2Se3 is reversed from pointing into to away from 2D semiconductor layer. Driven by the significant band tuning effect and the coupled IP and OOP ferroelectric polarizations of the designed In2Se3/SnTe heterostructures, we proposed a two-terminal IP 2D FTJ. We predicted that the designed FTJ has two distinct electron transport mechanisms − tunnelling and metallic for the OFF and ON, respectively, resulting a giant TER effect with the ON/OFF ratio exceeding 5 ⋅ 103. The predicted TER effect was shown to be exponentially amplified by increasing the barrier width of the FTJ. Our results may be useful for the design of 2D ferroelectric heterostructures and FTJ-based non-volatile memories. We hope therefore that they will stimulate experimental efforts to explore such kind of FTJs in practice and demonstrate the predicted properties.