Ferroelectric SnPz/In₂Se₃ as a Stable and Durable Non-Volatile 2D Ferroelectric Memory Material

Abstract

In ferroelectric memory, the repeated application of external electric fields can cause ferroelectric fatigue, limiting its stability and service life, especially as the storage unit size decreases. To address this issue, we conducted first-principles research on a SnPz/In₂Se₃ structure and examined its structure under different polarization directions. Our analysis revealed significant differences in the adsorption position of Sn atoms depending on the polarization direction, suggesting that SnPz/In₂Se₃ could be a highly stable ferroelectric storage material. Moreover, the polarization-induced changes in the electronic structure near the Fermi level, which allowed for the use of tunneling current and obtaining stored information without causing the ferroelectric fatigue effect during information readout. These findings highlight the potential of SnPz/In₂Se₃ to significantly extend the lifespan of ferroelectric materials, reduce energy consumption, and minimize the environmental impact of discarded electronic devices.

1. Introduction

Storage devices play a critical role in the information age and are of great significance for human production and daily life. To develop high-performance devices, researchers have explored various materials for storage electronics, including organic materials [1,2,3], quantum dots [4], 2D materials [5], metal oxides [6], hybrid composite materials [7], and ferroelectric [8] and ferromagnetic materials [9]. Ferroelectric memory has numerous advantages, such as low power consumption, long durability, and fast switching, and is considered one of the candidates for the next generation of data storage devices [10].

In ferroelectric memory, the polarization states of the storage unit, such as the positions of atoms, are utilized to store binary information, resulting in stable and reliable data storage. Ferroelectric materials have high polarization and dielectric constants, making them suitable for durable data storage [10,11,12]. Compared to traditional storage methods, ferroelectric memory can store more information in a smaller volume, making it widely used in modern electronic devices [13,14].

The information writing and reading processes in ferroelectric memory require applying an external electric field to the storage unit. In the information reading process, the external electric field is used to detect whether the core atoms have moved. If not, it indicates that the external electric field matches the originally stored information; otherwise, if the core atoms have moved, it means that the originally stored information is different from the information specified by the external electric field. It should be noted that the original information is destroyed in this case, and need to be restored by reapplying an external voltage [15]. After multiple reading and writing processes, the repeated movement of atoms can damage the crystal structure, leading to the gradual weakening or disappearance of polarization phenomena in ferroelectric materials, known as ferroelectric fatigue phenomenon [16]. With the decreasing size of storage devices, the problem of ferroelectric fatigue has become increasingly prominent [17,18,19]. Reducing ferroelectric fatigue can greatly extend the lifespan of memory and enhance its stability [16,20,21]. In addition, in the current context of energy conservation and extending the lifespan of devices, reducing ferroelectric fatigue to promote the development of ferroelectric memories will help reduce energy consumption and reduce the impact of discarded electronic devices on the environment. In particular, the reading process may change the original information; if so, it is necessary to rewrite the information, creating more damage to the storage materials. Designing different reading mechanisms is crucial to promoting the development of modern ferroelectric devices.

In recent years, there has been a surge of interest in two-dimensional ferroelectric materials (2D FEs) that have reversible electric polarization, which respond to external electric fields within an extremely thin atomic layer structure [22,23,24,25]. These materials have enormous potential for applications in nanoelectronics and intelligent devices [26,27,28,29,30,31,32,33,34]. Among various ferroelectric two-dimensional III₂VI₃ compounds, In₂Se₃ has been extensively studied in theoretical and experimental work due to its plane and perpendicular ferroelectricity, which has been proven in experiments [26,28]. Ferroelectricity allows materials to be polarized and maintain a stable charge distribution under the effect of an external electric field, thus promoting the application of photoelectric and electroacoustic conversion, memory [35,36], and sensors [37]. Moreover, the reversible electric polarization direction of In₂Se₃ can be switched by applying an external electric field, allowing for the formation of a special “switch”, thus regulating the properties of materials in a reversible manner [26,38,39,40]. In addition to its ferroelectricity, In₂Se₃ exhibits good photocatalytic properties, which have broad application prospects in the fields of photocatalysis, water decomposition, hydrogen energy preparation, etc. Compared with metal catalysts, In₂Se₃ has higher electrocatalytic activity and a longer life, making it an attractive alternative for photocatalytic applications [41,42].

Metal porphyrazine molecule is a complex composed of metal ions and porphyrazine molecules which are tightly bound together through coordination bonds. Porphyrazine is a large cyclic molecule composed of four pyrrole rings and four nitrogen atoms, not four benzene rings. Its structure is similar to that of porphyrin, but its chemical properties are different due to the presence of more nitrogen atoms [43,44,45,46]. Porphyrazine molecules themselves have excellent electron transfer and photocatalytic properties, and can absorb visible and near-ultraviolet light, making them widely used in photoelectric conversion and catalytic reactions [47,48,49,50,51,52]. The coordination of metal ions with porphyrazine molecules can enhance the properties of porphyrazine and endow them with new functions [49,50,52]. For example, copper porphyrazine molecules can serve as effective oxidants and act as catalysts in organic synthesis reactions; cobalt porphyrazine molecules are an important artificial photosynthetic catalyst that can decompose water into hydrogen and oxygen [50,53,54]; and the electron transfer and oxygenation properties of manganese porphyrazine molecules make them a potential biomedical research tool [49,55,56]. Furthermore, research has revealed that Sn-doped phthalocyanines possess tunable geometric and electronic structures on surfaces in the presence of the Sn atom [57,58].

This study investigates the potential of using a combination of a low-toxicity and low-melting-point metal Sn atom with SnPz to form a SnPz/In₂Se₃ structure with ferroelectricity material In₂Se₃. Using a first principles research method, the study examines and determines the structure of SnPz/In₂Se₃ under different polarization directions and analyzes the resulting geometric structure and electronic properties. The research findings demonstrate that the position of the Sn atom in adsorbed SnPz molecules varies significantly depending on the polarization direction, while remaining stable under a specific polarization direction. This indicates that SnPz/In₂Se₃ could serve as a highly stable ferroelectric memory material. Moreover, due to different charge transfer methods in different polarization states, the electronic structure of SnPz/In₂Se₃ exhibits a significant difference around the Fermi level, making it possible to detect stored information in SnPz/In₂Se₃ through measuring the tunneling current. Such a process is demonstrated by simulating the STM images under different polarizations. This approach avoids the impact of ferroelectric fatigue on the storage unit caused by the repeated application of external voltage during the information reading process. Overall, the results of this study suggest that SnPz/In₂Se₃ is a promising non-volatile ferroelectric storage material that has the potential to significantly extend the service life of ferroelectric materials, reduce energy consumption, and decrease the environmental impact of discarded electronic devices.

2. Materials and Methods

First-principles calculations based on density functional theory were carried out with the Vienna ab initio simulation package (VASP) at the level of spin-polarized generalized-gradient approximation (GGA) in the form of the Perdew–Burke–Ernzerhof (PBE) functional [59,60]. The interaction between the valence electrons and ionic cores was described within the projector-augmented wave (PAW) framework [61]. The Grimme’s method (DFT-D2) was employed to incorporate the effects of van der Waals interactions [62]. An energy cutoff of 400 eV was adopted for the plane-wave basis. The electron step convergence standard was set to 1.0 × 10⁻⁴ eV, and the ion step convergence limits were set to 0.02 eV/Å force convergence standard. To minimize the interaction between adjacent SnPz molecules, a 4 × 4 × 1 supercell was constructed where the distance of adjacent molecules was more than 6 Å. A vacuum space of at least 15 Å perpendicular to the layer was added to avoid spurious interactions between two neighboring sheets. The Brillouin zone was sampled by 4 × 4 × 1 k-points using the Gamma centered mesh. Additionally, the k-mesh was increased to 9 × 9 × 1 to obtain the density of states.

The structural stability was characterized by the binding energy ($E_b$), defined as $E_b=E_{SnPz}+E_{I{n}_{2}S{e}_3}-E_{SnPz/I{n}_{2}S{e}_3}$, here, where $E_{SnPz}$, $E_{I{n}_{2}S{e}_3}$, and $E_{SnPz/I{n}_{2}S{e}_3}$ are the total energies of the freestanding SnPz molecules, monolayer α-In₂Se₃ supercell, and SnPz/In₂Se₃ system, respectively.

For the STM calculations, we used the Tersoff–Hamann method available in the VASP code, which is a simple model of an s-wave STM tip [63,64,65]:

$$n(r,E)=\sum _{\mu }{|{\psi }_{\mu }(r)|}^2\delta ({\epsilon }_{\mu }-E)$$

(1)

$$\begin{array}{c}I\left(r,V\right)\propto \underset{E_F}{\overset{E_F+eV}{{\displaystyle \int }}}dEn\left(r,E\right)\end{array}$$

(2)

In this method, the tunneling current $I$, which is depends on the tip position $r$ and the applied voltage ${\psi }_{\mu }$, is proportional to the integrated local density of states (ILDOS). The ILDOS is calculated from the Kohn—Sham eigenvectors, ${\psi }_{\mu }$, and eigenvalues, ${\epsilon }_{\mu }$, where $\mu$ labels different states. $E_F$ is the Fermi energy. In this study, a constant-height mode with an external potential of 0.5 V was applied, and the STM images were calculated within the range of 0.1 to 0.5 Å on the material surface. It should be noted that plane wave codes such as VASP may not accurately describe the exponential decay of wave functions far from atoms, and may require the extrapolation of wave functions to display physical results at large heights (such as 7 Å), otherwise non-physical effects may be displayed [66]. All the STM images were made at least 31.8 Å long in the xy plane by repeating the primitive SnPz/In₂Se₃ unit cell.

3. Results and Discussion

The tin porphyrazine molecule consists of four pyridine rings and a central tin atom, as shown in Figure 1a. From a top view, the Sn atom is located at the center of the plane. However, from a side view, the Sn atom is significantly raised relative to the porphyrazine plane, with a distance of 1.16 Å in the direction perpendicular to the macro ring from the nearest N atom. This is due to its larger atomic radius, which results in a stronger repulsion with surrounding atoms and “pushes” the Sn atom out of the porphyrazine plane. At the same time, the Sn atom also has a certain influence on the porphyrazine, ultimately causing the whole tin porphyrazine molecule to present a certain curved state.

In₂Se₃ has a strong out-of-plane ferroelectricity, with its most stable phase being the α phase. In a single layer of In₂Se₃, Se and In atoms are arranged in alternating layers through covalent bonds. We optimized the unit cell of α-In₂Se₃ and calculated its lattice constant to be 4.1 Å, which was very close to previous research results [26,28]. The calculated single-layer structure of In₂Se₃ with ferroelectric polarization upward (FE_up) and ferroelectric polarization downward (FE_dn) is shown in Figure 1b.

To investigate the most stable adsorption configuration of SnPz on the surface of In₂Se₃ in different polarization states, as depicted in Figure 2a,b, by considering the relative position of the central Sn atom of SnPz to In₂Se₃, we tested eight different adsorption configurations for each case. In these configurations, the raised up (Sn-up) or sunken downward Sn atom in SnPz was located above the top layer In atom (Top1 site), above the top layer Se atom (Top2 site), above the bridge position between two adjacent top layer In atoms (Bridge site), or above the center of the triangle region in the lower right corner of the In₂Se₃ unit cell (Hollow site), respectively. The calculation results are shown in Figure 2c,d and Figure 3a, where the most stable adsorption configuration of SnPz in both FE_up and FE_dn states was with the Sn atom located above the Hollow site, corresponding to a large adsorption energy of 1.30 eV and 1.41 eV, respectively, indicating that these two adsorption structures are very stable at room temperature. Interestingly, there were significant differences in the relative positions of the Sn atom in the two polarization directions. When the system was in the FE_up state, the central Sn atom was in the Sn-up configuration, and the distance between the porphyrazine molecule and In₂Se₃ was 3.34 Å. When in the FE_dn state, the Sn atom configuration was Sn-dn, meaning that the Sn atom was located at the interface between the porphyrazine molecule and In₂Se₃. At this time, although the porphyrazine molecule was still far from the substrate (3.33 Å), the distance between the Sn atom and In₂Se₃ was only 2.13 Å, which means that the Sn atom may serve as a medium to enhance the interaction between SnPz and In₂Se₃. In summary, in the most stable structure of SnPz/In₂Se₃, the relative position of the Sn atom exhibited a significant ferroelectric dependence.

Moreover, this ferroelectric dependence was also observed in other metastable adsorption configurations. As illustrated in Figure 3a, when the system was in the FE_up state (black line), the Sn atom tended to form a Sn-up structure at all adsorption sites, whereas in the FE_dn state (red line), Sn tended to form a Sn-dn structure at all adsorption sites except for the Top1 site. Furthermore, the calculation results presented in Figure 3a indicate that, in the FE_dn state, the adsorption energy of SnPz on In₂Se₃ in each adsorption configuration was more stable than that in the FE_up state. To shed light on this phenomenon, we analyzed the PDOS of In₂Se₃, as illustrated in Figure 3b. In the original single layer In₂Se₃, when it was in the FE_up state, the p orbital of the Se atoms of top layer had an obvious occupied state at the −2.7 eV level. However, when it was in the FE_dn state, the p orbital significantly shifted upward to around −1 eV. This phenomenon prompts us to consider In₂Se₃’s adsorption capacity for SnPz molecules from the perspective of the p-band center theory. According to the calculation of the p-band center, when In₂Se₃ was in the FE_up state the p-band center of the top Se atoms was situated at −2.2 eV, whereas in the FE_dn state, the p-band center significantly increased to −1.69 eV. This implies that, when In₂Se₃ and SnPz molecules are in the FE_dn state, a stronger bond can be formed between them, which is consistent with the calculation of the adsorption energy. In addition, the difference in adsorption energy is also related to the distribution of electrostatic potential. As shown in Figure 3c, the negative potential in SnPz molecules only existed near the Sn atom, while the Pz ring mainly exhibited positive electrostatic potential. For In₂Se₃, as shown in Figure 3d, the surface electrostatic potential in the FE_dn state was more positive than that in the FE_up state. Therefore, according to the complementary principle, when in the FE_dn state, the Sn atoms were more likely to adsorb on the surface of In₂Se₃.

We also utilized the NEB method to further verify the stability of the Sn atom position in different polarization states. The energy barrier for the Sn atom to migrate from its stable position to the other side of the SnPz molecule under both polarization states was calculated and the results are presented in Figure 3e and 3f. The Sn atom required 3.2 eV and 1.7 eV to complete the migration process under the FE_up and FE_dn states, respectively, which exceeded the thermal fluctuations at room temperature, indicating that the Sn atom position was stable under environmental conditions. More importantly, this suggests that the polarization direction can stably regulate the structure of the adsorbed SnPz, specifically the relative position of the Sn atom. By applying a specific external electric field, the position of the Sn atom can be specified and, after the external electric field has been removed, the Sn atom cannot move to the other side of the porphyrazine molecule due to the large migration energy barrier. During this process, SnPz/In₂Se₃ stores the information left by the external electric field in the structure; that is, it completes a certain information writing process, and the written information can be stably stored even without an external electric field. This means that SnPz/In₂Se₃ is a good information carrier and has the potential to be used as a non-volatile storage unit for ferroelectric memories.

To comprehend the electronic properties of the two adsorption structures under different polarization directions, an analysis of their electronic structures was conducted. As illustrated in Figure 4a,b, the differential charge analysis revealed that in the FE_up state, the distance between the SnPz molecule and In₂Se₃ was large, resulting in a weak charge exchange between the porphyrazine and In₂Se₃. Conversely, in the FE_dn state, the Sn atom concaved downwards, significantly reducing the distance between SnPz and In₂Sn₃ (from 3.34 Å in the FE_up state to 2.13 Å), thereby facilitating the transfer of charges between them. As shown in Figure 4b, a charge transfer channel was formed between the Sn atom and In₂Sn₃. Both Sn and porphyrazine were evidently in a state of electron loss, and transferred electrons to three nearby Se atoms through the Sn atom. This was further corroborated through Bader charge analysis, as presented in Figure 4c. When the system was in the FE_up state, In₂Se₃ transferred 0.03 electrons to SnPz through the porphyrazine molecule. Conversely, in the FE_dn state, due to the significant electronegativity difference between Se and Sn atom (Se: 2.55, Sn: 1.96), SnPz lost 0.26 electrons to In₂Se₃ through the Sn atom. Correspondingly, in the PDOS diagram in Figure 4d, compared to the free state, a significant relative displacement of the density of states of adsorbed SnPz near the Fermi level occurred in the occupied state. In the FE_up state, the occupied state near the Fermi level moved downwards due to electron gain. Conversely, in the FE_dn state, the occupied state moved upward due to electron loss, and even produced a significant electron state occupancy at the Fermi level. In summary, by adjusting the geometric structure and charge transfer, the ferroelectric polarization can result in significantly different electronic structure of SnPz/In₂Se₃ near the Fermi level in different polarization states.

The difference in occupation states near the Fermi level induced by ferroelectricity has an impact on the space charge distribution. As depicted in Figure 5a,b, the charge density was calculated in the range of −0.5 to 0 eV, and the results are presented under the same charge density isosurface. When the system was in the FE_up state, there was almost no charge distribution in the structure, especially at the interface. However, when the system was in the FE_dn state, the charge localization on the In₂Se₃ surface and SnPz molecule was clearly observable. The significant difference in charge distribution induced by ferroelectricity near the Fermi level makes it more suitable for interesting applications.

This charge redistribution induced by ferroelectricity reminds us that one can obtain the polarization state of the substrate directly by measuring the states of the molecule. Additionally, the states of the molecule can be measured by the tunneling current as is realized in a scanning tunneling microscope (STM). Because below the Fermi level as far as 0.5 eV, the FE_dn polarization generates a state on the macro-ring while the FE_up does not, which indicates that in bias voltage of −0.5 V, the FE_dn can generate tunneling current while the FE_up cannot. To be more specific, the STM images of structures under different polarization states were simulated, and the tunneling currents were detected at distances of 0.1 Å, 0.2 Å, 0.3 Å, 0.4 Å, and 0.5 Å on the surface of the material at a constant height mode with a bias voltage of −0.5 V. The results are displayed in Figure 6. The brightness areas suggest that significant tunneling currents were detected in the range of 0.1–0.5 Å on the surface of SnPz/In₂Se₃ in the FE_dn state, while no tunneling current was observed at all in the FE_up state. This characteristic makes the SnPz/In₂Se₃ system highly promising for ferroelectric memories. In SnPz/In₂Se₃, the presence of a tunneling current at a bias voltage of −0.5 V could be detected to obtain the stored information in the structure, thereby avoiding the repeated application of external voltage to the structure during information readout, which greatly extends the life of the memory by reduce ferroelectric fatigue.

There are many examples of porphyrazine-type molecules on various kinds of surface substrate. For example, in 1998 it was reported that zinc porphyrazine (ZnPz) could be successfully adsorbed onto Y-zeolite by stirring calcinated zeolite in freshly distilled pyridine [67]. In 2017, two rounds of ultrasonic treatment in THF were used to fix zinc pyrene-porphyrazine conjugate (ZnPzPy) and ZnPz onto a graphene substrate [68]. Additionally, CoPz has also been successfully immobilized on the oxygen vacancy-containing SnO₂ surface [54]. In addition, various metal porphyrazine derivatives have been successfully immobilized on Au (111) surface [69,70,71] and ZnO surface [72]. In recent years, there has been increasing theoretical research on anchoring metal porphyrazine onto various two-dimensional materials for use as catalysts, magnetic storage devices, sensors, and optoelectronic devices [38,50]. Based on the above research work, there might be two methods for obtaining porphyrazine adsorbed on a substrate. One is via synthesizing the porphyrazine molecules in solution and evaporating them in some vacuum environment and letting them deposit on the substrate. The other is via depositing pyrrole-derivation molecules and using some annealing techniques to make them take offside chains to form porphyrazine. Considering that the stability of 2D materials are usually low, maybe the first one is suitable for our case.

4. Conclusions

In this work, we used cheap and low toxicity SnPz molecules and the classic ferroelectric material In₂Se₃ to construct SnPz/In₂Se₃ structures. We fully considered various configurations of SnPz molecules adsorbed on the In₂Se₃ substrate in different polarization states. The results showed that when In₂Se₃ was in the FE_dn state, the p-band center of the top layer Se atom was obviously closer to the Fermi energy level than that in FE_up state, which enhanced the adsorption capacity for SnPz. Moreover, the placement of the Sn atom within SnPz molecules significantly affected the adsorption energy. In the FE_up state, Sn atoms are inclined towards being situated above the porphyrazine molecules, whereas in the FE_dn state they are more likely to be between the porphyrazine molecules and In₂Se₃. The ferroelectric dependence of the relative position of the Sn atom indicates the potential of SnPz/In₂Se₃ as a ferroelectric memory. Simultaneously, due to the diverse relative positions of the Sn atom in various polarization directions, there exists a substantial variation in charge transfer between SnPz and In₂Se₃. This variation results in the occupied state position near the Fermi level of the SnPz molecule moving in the opposite direction in FE_up and FE_dn states, leading to a significant difference in the electronic structure near the Fermi energy level. Further calculations confirm that this difference in the occupation state of SnPz results in significant differences in the charge density and tunneling current of SnPz/In₂Se₃ in different electric polarization states. Consequently, it is feasible to read stored information from the structure by detecting tunneling current. In conclusion, our calculations show that the structural changes and the differences in electronic structures of SnPz/In₂Se₃ induced by ferroelectricity make it not only a novel, non-volatile ferroelectric memory material, but also allow for the utilization of tunnel current to extract information from the structure and reduce ferroelectric fatigue caused by the repeated application of external voltage to storage cells. These characteristics are expected to greatly enhance the stability and durability of ferroelectric memories in practical use.