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Abstract
Our first principles studies predict that PbZnO3 will realize the phase transition from LiNbO3-type to perovskite-type and finally to post-post-perovskite-type with the gradual increase of pressure. Three types of PbZnO3 quantum dots are constructed based on such three phases, and their plasmon properties are investigated. It is found that the perovskite-type PbZnO3 can realize the regulation of optical absorption in near-infrared to ultraviolet regions, and the dipole oscillation mode of post-post-perovskite PbZnO3 plasmons can change from short range to long range. More accurately, we estimated the electric polarization of LiNbO3-type PbZnO3 to be 116µC/cm2. Our investigations confirm the excellent properties and great application prospect of PbZnO3 materials in different photoelectric fields.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent years, transition metal oxides including Perovskite (Pv)-type, post-Perovskite (pPv)-type and post-post-Perovskite (ppPv)-type oxides (general formula: ABO3) have attracted widespread interest in science and technology due to their various functional properties [1–3]. PbVO3, PbCrO3, BaVO3, Pb (Zn1/3Nb2/3)O3 and BaRuO3, as Pv-type transition metal oxides, are obtained under high pressure [4–9]. LiNbO3-type (LN-type) structure, such as PbNiO3, CdPbO3, GaFeO3, and ZnTiO3, can be described as a derivative of the Pv-type structure and its compounds are considered as quenchless Pv-type phases under high pressure [10–13]. The MgSiO3, NaMgF3 and CaTiO3 can be further transform from pPv-type phase to ppPv-type phase with gradual increase of pressure [14–16]. Furthermore, there are many methods to induce structural phase transition, among which the hydrostatic pressure, laser-induced [17] and temperature-induced [18] are the common ways to achieve novel properties due to its influence on crystal structure, electronic orbitals, chemical bonding, etc. Many neoteric materials have been formed by this means for recent years, such as 3D lead-halide, diamond like BC5, and hydrogen clathrate structures in rare earth hydrides [19–23]. Therefore, it is reasonable to conjecture that the phase state transition of perovskite is closely related to the increase or decrease of hydrostatic pressure. Lately, a novel LN-type lead zinc oxide, PbZnO3 (PZO), has successfully been synthesized under high pressure and high temperature [24]. Based on the recent findings about high-pressure-induced new structures in other perovskites, it is legitimate to wonder if LN-type PZO material can also come into being new phases when it subjects to high pressure.
All-inorganic perovskite quantum dots (QDs) are tiny semiconductor particles which have a few nanometres in size, and they have optical and electronic properties that differ from larger LED particles [25–27]. Because of their highly tunable properties, QDs have attracted a wide range of interest. Potential applications include transistors, solar cells, LEDs, diode lasers and second-harmonic generation, quantum computing, and medical imaging. Surface plasmons (SPs) are usually found in noble metal nanostructures and they have collective excitation [28,29]. It offers opportunities of breaking the diffraction limit at a nanoscale. Previous studies found that plasmon optoelectronic devices which is made of traditional metal nanometer materials have two main issues, one is severe attenuation during transmission and the other is non-modulation [30,31]. We artificial design a series of PZO quantum dots as the ideal candidate structures, and we dedicate to exploring effective modulation methods used on SPs. Moreover, LN-type PbZnO3, owning robust polar (typically above 50 µC/cm2), have attracted a lot of attention recently. The rhombohedral perovskite structure contains small A-site cations and crystallizes in noncentrosymmetric polar space group R3c [32–34]. The R3c structure is derived from the cubic aristotype accompanied by antiferrodistortive tilts of the BO6 octahedra and the polar displacement of A-site cations along the pseudocubic [111] axis (a−a−a− in Glazer notation [35–37]). Due to the new material synthesized in the experiment has a rough calculation and judgment on its electric polarization, we have made a more accurate judgment on the electric polarization and metallicity. The electric ploarization of LN-type PZO calculated by using Z* is along the c-axis with PBEC = 116µC/cm2.
Our paper is mainly devoted to the study the plasmons properties of PZO QDs. We predict that the LN-PZO firstly undergo a reconstructive phase transition to the pV-PZO, and then it experiences the phase transition to a novel stable crystal structure that belongs to the ppPv-type. This discovery of new phase states has enriched the variety of QDs. PZO QDs have obvious surface plasmons phenomenon which can be modulated effectively by the direction of impulse polarization and the size. During the modulation process, it was found that Pv-PZO has significant absorption effect on visible and ultraviolet region, and the strongest absorption peak could shift in different optical region through the change of polarization direction. The plasmons of ppPv-PZO QDs is obviously affected by size, and its dipole oscillation changes from short range to long range with the decrease of size. The electric polarization of LN-PZO is estimated to be 116 µC/cm2 along the c-axis through the calculation of density functional theory. In conclusion, PZO with three configurations all has a widely application, which can predict its huge potential as an optoelectronic material.
2. Computational details
The density functional theory (DFT) [38] calculations are performed by using the Vienna abinitio Simulation Package (VASP [39,40]) within the generalized gradient approximation. We use the projected augmented wave (PAW) method within the the Perdew, Burke, and Ernzerhof (PBE) [41,42] parametrization scheme. The plane wave energy cutoff is chosen here to be 550 eV. The following states were described as valence electrons: 5d, 6s and 6p for Pb; 3d and 4s for Zn and 2s and 2p for O. The enthalpy (H = E + PV, where E is the total internal energy, P is the hydrostatic pressure, and V is the volume) is computed.
Section 3.2 calculations were performed using the real-space and real-time time-dependent density functional thetheory (TDDFT) approach, as employed in the OCTOPUS code [43]. Those atoms were described by Troullier-Martins pseudopotentials [44]. The generalized gradient approximation (GGA) expressed by the Perdew-Burke-Ernzerhof (PBE) functional for the exchange-correlation is used in both the ground-state and excited-state calculations [45]. The program has been successfully used to calculate linear absorption spectra and the fourierinduced-charge-density distributions [46,47]. The simulation zone was a sphere around each atom with a radius of 6 Å and a uniform mesh grid of 0.2 Å. In a real-time propagation, the Kohn-Sham wave functions are evolved for typically 6000 steps with a time step of ∆t = 0.003 ħ/eV.
Moreover, the space groups of the different equilibrium structures determined in the present study are performed with the FINDSYM [48] programs and the nuclear structures were drawn by VESTA. Electric polarization is calculated using the Point-charge-model method. The total electric polarization [49] for the R3c structure was derived from the approximate expression as follows:
where e is the elementary charge, V is the unit-cell volume, is Born Effective Charges (BECs), and u is the displacement of atomic i in the direction of .3. Results and discussion
3.1 Structural phase transition
Crystallographer Glazer et al. studied the torsion of oxygen octahedron systematically [35]. By calculateing PZO corresponding to 15 Glazer torsion modes, we find that the system corresponding to Pnma group has the lowest energy. Recently, after a large number of ABO3 and A2O3 (A, B is different atoms, X = O or F) configurational compounds were searched, it was found that many compounds had pPv or even ppPv structures under high pressure [50]. Based on the above two analyses, it is reasonable to suspect that PZO has other configurations (Pv, pPv and ppPv-type) besides the LN-type.
We first studied on PZO bulk. By allowing the cell shape and volume of the supercells mimicking three phases LN (R3c), Pv (Pnma) and ppPv (Pnma) to be fully relaxed. Figure 1 shows the predicted enthalpy of LN (R3c), Pv (Pnma) and ppPv (Pnma) phases in PZO bulk are respectively represented by red, black and blue lines. Compared to the Pnma phase, R3c phase has a slightly lower energy. we confirm that the rhombohedral R3c phase is the ground state for PZO when the pressure is lower than 16.5GPa. With the pressure keeps increasing, it was found that the enthalpy of Pv (pnma) phase was lower than that of LN (R3c) phase (Fig. 1(a)). When the pressure continues increase to 140GPa, the ppPv (Pnma) phase with the lowest enthalpy appears (Fig. 1(b)). This means that Pv-type PZO could be synthesized under the pressure of 16.5 GPa and ppPv-type PZO could be synthesized under the pressure of 140 GPa.
According to the calculation of enthalpy, the structure corresponding to the above three phase states is given as shown in the Figs. 2(a)-2(c). Figure 2(a) is a hexagonal polar LN-type structure with an acentric space group R3c (No. 161); Fig. 2(b) is a Pv-type structure with a centrosymmetric space group Pnma (No. 62), and Fig. 2(c) is a ppPv-type structure also with the same space group Pnma. Pv-type (Fig. 2(b)) is a three-dimensional grid structure connected by the vertices of oxygen octahedron. The ppPv-type (Fig. 2(c)) structure is a chain structure of the one-dimensional octahedron extending along the b-axis. Two one-dimensional-chains make a group, forming a double chain state. And any adjacent octahedron in this chain is connected by the same edge (namely, shared two O ions).
The refined structural parameters by the analysis for the LN-PZO (0GPa), the Pv-PZO (16.5GPa), and ppPv-PZO (140GPa) are summarized in Table 1. By comparing the experimental values [24] of the lattice parameter of LN-PZO configuration, it is not difficult to determine that the error between the theoretical value of lattice parameter and the experimental value is within 2% range (a and c are 1.3% and 1.9% respectively). This shows that our theoretical calculation results are in good agreement with the experimental results, which directly explains the rationality of our theoretical calculation methods, and also confirms the reliability of the other two phase structures.
Table 1. Structural Lattice Parameters for a LN-type, Pv-type and ppPv-type PZO under given pressure.
3.2 Multiple regulation on plasmon properties of PZO in three configurations
Compared with bulk materials, QDs have unique quantum size effect, which makes QDs have better optical performance. In order to further explore the optical response characteristics of PZO, we designed three QDs of PZO. We must note that the number of atoms has a direct impact on optical absorption. Therefore, the number of atoms should be kept close when three kinds of QDs are manufactured artificially. The dimensions of PZO QDs in three configurations have been given in detail, as shown in Fig. 3. L, w and h respectively correspond to length, width and height.
Figure 4(a) illustrates the optical absorption spectrum for PZO QDs with three configurations (LN-PZO (black), Pv-PZO (red), and ppPv-PZO (blue)). The direction of impluse polarization is along the X-axis. We find that all three types have a certain degree of absorption. Pv-PZO configuration has a slightly better linear response than the others in the visible region. In ultraviolet region, we notice that Pv-PZO has an obvious absorption peak at 5.72eV, that is significantly better than the other two. For this quasi-two-dimensional rectangular plane structure with three configurations of PZO, we have calculated the induced-charge-density distribution at the resonant frequency. As shown in Figs. 4(b)-4(d), Due to the coupling of electrons and directional field, induced electron density and induced hole density are separated in space. Along the polarization direction, electrons and holes appear in pairs and left-right symmetry, which is the phenomenon of SPs. Through the above analysis, it can be found that Pv-PZO has a strong optical absorption, especially in the ultraviolet region. It means that this configuration has great potential application in high-frequency photoelectric devices, ultraviolet detectors and other aspects. PpPv-PZO has the most obvious SPs effect and has a great application prospect in photoelectric signal transmission devices.
Fig. 4 (a) Optical absorption of PZO QDs, LN-PZO (black), Pv-PZO (red), and ppPv-PZO (blue); (b-d)The fourier induced-charge-density distributions of PZO. The polarization direction is along the X-axis at the energy resonance points 1.74 eV of LN-PZO (b), 5.72 eV of Pv-PZO (c), 5.09 eV of ppPv-PZO (d).
3.2.1 Plasmons of PZO QDs are regulated by the polarized direction
It has been reported that anisotropic materials are subject to the regulation of induced direction [51,52], which has distinct influence on the effect of optical absorption. We have noticed the anisotropy of the quantum dots in the three configurations of PZO at the nanoscale, so we try to change the polarized direction to regulate the plasmons of PZO.
Figures 5(a)-5(c) show the dipole response (optical absorption) of the PZO quantum dots when the impulse polarized direction along X-axis (red) and Y-axis (black). For LN-PZO and ppPv-PZO, we find that the distribution of fourier induced-charge-density changes significantly, but the change of pulse direction has little influence on the intensity and position of light absorption. As shown in Figs. 5(d)-5(f), the local dipole oscillation still exists, and the resonance mode is changed from transverse to longitudinal by the direction of impulse. For Pv-PZO, both the intensity of optical absorption and the position of absorption peak are regulated by the excitation direction. As can be seen from Fig. 5(b), with the change of the incident direction, the distance of the two absorption peaks from the ultraviolet region increases. When the incident field is excited along the Y-axis, the position of one of the optical absorption peaks is 3.5eV. In other words, with the change of the incident direction, the light absorption peak appears redshift, and the absorption region expands from the ultraviolet region to the visible region. Similarly, its vibration mode changes from transverse to longitudinal, as shown in Fig. 5(e). Optical absorption spectrum is related to the projection position of atoms in the Z-plane. The higher the symmetry is, the less the influence of polarized direction to absorption spectrum will be. On the contrary, the adjustment of the absorption spectrum by the excitation direction is more and more obvious with the decrease of the atomic position's symmetry.
Fig. 5 (a-c) Optical absorption spectra of PZO QDs excited along the X-axis (red) and Y-axis (black); (d-f)The fourier induced-charge-density distributions of PZO. The polarized direction is along the Y-axis at the energy resonance points 1.28 eV of LN-PZO (d), 1.25 eV of Pv-PZO (e), 1.28 eV of ppPv-PZO (f).
In short, the vibration mode is changed by the change of excitation direction for the three configurations of PZO. Among them, the Pv-PZO optical absorption can achieve the transition from ultraviolet region to near-infrared region, so this structure has a great prospect and potential in the application of ultraviolet detectors and other photoelectric devices.
3.2.2 Plasmons of PZO QDs are regulated by the size
Many types of QDs, when excited by electricity or light that can be precisely tuned by changing the size of dots, enabling myriad applications. Given the quantum confinement effects and the highly tunable properties with nanometer size, we have designed three smaller QDs corresponding to the PZO, and the specific size is given in detail in Figs. 6(h)-6(g). Figures 6(a)-6(c) show the optical absorption spectrum (black) corresponding to the new QDs, with the direction of pulse polarization along the X-axis.
Fig. 6 (a-c) Optical absorption spectra of PZO quantum dots excited along the X-axis (red) and Y-axis (black); (d-f)The fourier induced-charge-density distributions of PZO. The polarization direction is along the Y-axis at the energy resonance points 1.28 eV of LN-PZO (d), 1.25 eV of Pv-PZO (e), 1.28 eV of ppPv-PZO (f).
For comparison, the optical absorption spectrum (red) of the previous three QDs are also given. On the one hand, due to the decrease of quantum dot size, the strength of the optical absorption is obviously weakened, and the position of the strongest peak of the three shows an overall blue shift. This provides the feasibility for the regulation of PZO in visible and ultraviolet regions; On the other hand, the Fourier induced charge-density distributions (Figs. 6(d)-6(f)) depicts that the electron-hole still appears in pairs, but the dipole oscillation is more intense, and the phenomenon of plasmons is more obvious. Especially for the configuration of ppPv-PZO, the coupling oscillation mode changes from short range to long range. This phenomenon is comparable to the collective excitation of electrons in metal nanostructures. In addition to its advantages of effective modulation, ppPv-PZO can become a new material to meet the requirements of functional diversification of optoelectronic devices.
On the whole, the optical properties of PZO in low and high energy regions can be regulated by size. Nanoscale semiconductor materials tightly confine either electrons or electron holes. Quantum dots optoelectronic properties change as a function of size. The smaller the QDs are, the stronger the quantum effects obtained.
3.3 Estimation of electric polarization
LN-PZO, as a unique polar material, was found that it contains 6s0 and d10 cations and dose not contain d0 transition metal, which induce polarization without second-order Jahn-Teller (SOJT) effect driven by cation-anion orbital overlop or covalency [37]. We used the simple eleven-atom cells on purpose to isolate A-site cation (Pb) and B-site (Zn) cation.This reduces the impact fromdisplacements of other ABO3 distortions. The obvious structural feature of space group R3c is that A-site and B-site cations with respect to the surrounding oxide ions have displacement along the C axis (see Fig. 7). Understanding the role of A-site cation and B-site cation in the whole structure is also conducive to further analysis of the cause of strong polarization. It is feasible to estimate the electric polarization via considered the relative displacements of the constituent ions away from their centrosymmetric positions [37,53]. For a more detailed discussion, we estimated the Born effective charges, Z*, and the electric polarization, PBEC, using DFT calculations. The electric ploarization of LN-PZO has been calculated with PBEC = 116µC/cm2along the c-axis.LN-PZO shares a feature is that the large displacement of the cations and the high charge are significant for the sizable polarization. The space group of Pv-PZO and ppPv-PZO is pnma which is non-polarized. So we do not consider the polarization of the two.
The strong polarization of the rhombohedral perovskite is largely preserved by its tetragonal counterpart. Here, the BO6 octahedral distortions induced by the B-site displacements have a strong effect. In case of LN-PZO, the cations are compressed, which will cause A-site cation to be closer to B-site cation. The reaction of the overall structure shows that the cell volume is compressed. The blue arrow (Fig. 7) represents the direction which the structure is compressed. It can be seen from the calculation formula of electrical polarization that the size of volume directly affects the calculation result of P value. The V in the denominator decreases, providing a strong explanation for the strong polarization. In addition, we also noticed that Pb and Zn are the 130th and 65th elements of the periodic table, respectively. They have large atomic radius, especially Pb. The size of the atomic radius has no effect on the overall structure, but locally the bonding distance decreases. Although this effect is small, we cannot ignore the fact that it will cause structure compression.
4. Conclusion
In this paper, we gain three innovative conclusions. The first is that we obtain two new phases under high-pressure, a Pv-type PZO and a ppPv-type PZO. PZO presents LN-type with r3c space group when pressure is under 16.5GPa, Pv-type with pnma space group when pressure is during 16.5GPa-140GPa, and ppPv-type still with pnma space group when the pressure is above 140Gpa. The second is that optical responses and SPs in PZO can be modulated effectively. This anisotropic structure were sensitively dependent on the polarized direction and the size.The absorption peak of Pv-PZO can move freely in NIR-UV regions.The SPs of ppPv-PZO can transform short range modes to long. The last is that the electric polarization of LN-PZO is estimated more accurately to be 116 (µC/cm2) through the calculation of Born Effective Charge. These innovative findings provide a valuable reference for the experimental synthesis of PZO in diverse phase states. Moreover, it has great potential in the application in solar cell, fuel cells, steam electrolysis, and resistance switching applications.
Funding
National Key R&D Program of China (Grant 2017YFA0303600), National Natural Science Foundation of China (Grant No. 11474207), and National Natural Science Foundation of China (Grant No. 11774248).
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