Rare-earth elements have unique structural characteristics and physical and chemical properties. After long-term research and accumulation of rare-earth ions, rare-earth-doped materials are widely used in photonic devices, flat panel displays, optical sensors, and other multifunctional optical devices. Rare-earth elements comprise Scandium (Sc), Yttrium (Y), and 15 lanthanides. The lanthanides include Lanthanum (La), Cerium (Ce), Praseodymium (Pr), Neodymium (Nd), Promethium (Pm), Samarium (Sm), Europium (Eu), Gadolinium (Gd), Terbium (Tb), Dysprosium (Dy), Holmium (Ho), Erbium (Er), Thulium (Tm), Ytterbium (Yb), and Lutetium (Lu). Lanthanide atoms have shell configurations of 1s²2s²2p⁶3s²3p⁶3d¹⁰4s²4p⁶4d¹⁰4f⁰⁻¹⁴5s²5p⁶5d⁰⁻¹6s². Rare-earth ions possess unique energy level structures and have attracted extensive research attention around the world. They are often doped in thin films, ceramics, single crystals, and other materials, which are used in lighting devices, displays, sensors, and other multifunctional devices ^[1][2][1,2]. Among them, rare-earth ions, as luminous centers (also known as activators), generate different radiative transitions under irradiation. When the activator shows a weak absorption cross-section, other kinds of impurity ions will be co-doped in the matrix material. Such other kinds of impurity ions are called sensitizers [3]. The sensitizer ion-absorbing photon transitions to the excited state, and during the process of returning to the ground state, the sensitizer ion will transfer energy to the activator ion. The doped lanthanide ions are often referred to as Ln³⁺. The 5d–4f level transition allowed by parity (such as Ce³⁺) and the 4f-4f level transition prohibited by parity occur in Ln³⁺ ions. Lanthanide ions characterized by partially filled 4f shells are shielded from the surrounding environment by filled 5s² and 5p⁶ orbitals, resulting in sharp and narrow emission lines of transitions within 4f structures. However, because 5d electrons are not shielded, the emission spectrum generated by the 5d-4f transition (such as Ce³⁺) generally has a broad band. Therefore, the surrounding environment of different energy levels has a great influence on the emission spectra generated by energy level transitions.

For the lifetime of emission photons, the lifetime of emission photons generated by 4f-4f transition is longer than that generated by 5d-4f transition. Due to the forbidden characteristic of f-f transition in 4f ions, the lifetime of emitted photons generated by 4f-4f transition is milliseconds [4]. At present, some Ln³⁺ ions (Er³⁺, Tm³⁺, Ho³⁺ and Pr³⁺) with rich energy levels have been widely studied as activators of luminescent materials. Rare earth ion-doped ferroelectric oxides exhibit excellent upconversion or downconversion luminescence in the ultraviolet (UV) and near-infrared (NIR) regions ^[5][6][7][5,6,7]. Upconversion and downconversion luminescence are both photoluminescence processes. This process is a luminescence phenomenon caused by the radiation transition of electrons from the ground state to the excited state under excitation. For upconversion luminescence, when the ground-state electron absorbs a photon, it transits from the ground state to a higher-level excited state, and then the excited-state electron transits to a relatively lower excited state through the nonradiative transition. Then, the electron in the excited state absorbs another photon, which transits to a higher excited state. Then, the photon through radiation transits back to the ground state, releasing a short-wavelength photon. For downconversion luminescence, when the ground-state electron absorbs the energy of a short-wavelength (high energy) photon, it transits from the ground state to a higher energy level excited state. Then, the excited-state electron transits to a relatively lower excited state through nonradiation. The lower excited state transits back to the ground state through radiative transition, which releases a long-wavelength photon at the same time.

Perovskite oxide ferroelectrics possess abundant fascinating physical functionalities. BaTiO₃ (BTO) and LiNbO₃ demonstrate superior electro-optic, acousto-optic, and nonlinear optical characteristics, which are very beneficial for photonic applications ^[8][9]. Ferroelectric oxides exhibit spontaneous polarization under the Curie temperature. This spontaneous polarization will change repeatedly upon the external electric field. Pristine ferroelectric oxides cannot emit efficient luminescence because of the indirect and wide bandgap nature. Perovskite oxides such as SrTiO₃(STO) can emit blue photoluminescence (PL) from band-to-band radiative recombination only under low temperature. Rare-earth ions have abundant energy levels, sharp emission bandwidths, and large Stokes shift, which are regarded as important for phosphor choices ^[9][10]. So, rare-earth-doped ferroelectric oxides are endowed with efficient luminescent properties ^[10][11]. Some high-functional ferroelectric oxides have solid crystal fields and low vibration frequencies. These Ln³⁺ ions provide a suitable matrix material. Ferroelectricity, piezoelectricity, and photoexcitation based on Ln³⁺-doped ferroelectrics have many applications in various aspects ^[11][12].

In the rare-earth-doped ferroelectric oxide luminescence, some of the rare-earth ions as the luminescence center have rich trapezoidal energy levels. The ferroelectric oxide matrix provides a suitable crystal field and environmental energy for the luminescence center. The rare-earth-doped ferroelectric oxides exhibit upconversion or downconversion luminescence.

2. Ferroelectric Oxides

Ferroelectric oxides can be insulators, metals, and even topological ferroelectric metals ^[12][16]. The ferroelectric material has spontaneous polarization (P) that can be switched by the applied electric field (E), and the destruction of the symmetry of the spatial inversion allows the charge center unit separation, which is a prerequisite for the emergence of ferroelectric polarization ^[13][17]. The remaining magnetization is distributed among the oxygen ligands due to the itinerant spin-polarized electrons ^[14][18].

2.1. Crystal Field for The Luminescence Center

For rare-earth-doped ferroelectric oxides, we take the bismuth layer structure ferroelectrics (BLSFs) family is taken aas an example. BLSFs are expressed as Bi₂A_m-1B_mO_3m+3 = (Bi₂O₂)²⁺(A_m-1B_mO_3m+3)²⁻, where A is a large 12-coordinate cation, B is a small 6-coordinate cation, and the electronic configuration is d⁰. A can be monovalent, divalent, trivalent ions, or their mixtures; B represents tetravalent, pentavalent, or hexavalent ions; the subscript m and m-1 subtables are the number of sample octahedron and pseudoperovskite units. Peng et al. studied Er doping into CaBi₄Ti₄O₁₅ [5]. For CaBi₄Ti₄O₁₅, 1/2Bi³⁺ ions are located in the (Bi₂O₂)²⁺ layer, 1/2 Bi³⁺ ions and all Ca²⁺ ions are dispersed at site A, and Ti⁴⁺ ions occupy site B. Er³⁺ ions can enter the A position of the pseudoperovskite block, randomly replacing Bi³⁺ or Ca²⁺ ions. The radius of Er³⁺ (0.88 Å) ions is much smaller than that of Bi³⁺ (1.03Å) and Ca²⁺ (1.07Å) ions. According to the Judd–Ofelt (J-O) theory, PL emission is affected by the local crystal field around rare-earth ions, thus affecting the structural symmetry of the host body ^[15][19]. High structural symmetry will lead to weak PL emission. Lanthanide ion doping will preferentially replace the A position in the lattice and occupy the position with anti-center three-position symmetry. Because the radius of doped ions is smaller than that of the original position, the symmetry will be reduced. In principle, when the rare-earth ions are located in the low symmetry position, the electric dipole transition probability of doped rare-earth ions increases. In other words, the low symmetry host body usually imposes a crystal-field high-symmetry counterpart containing more heterogeneous components around the doped ions ^[16][20]. The inhomogeneous component enhances the electronic coupling between the 4f level and higher 4f5d configuration, and then increases the f-f transition probability of doped ions. Therefore, when the laser pump power is low, the corresponding light emission also has high intensity. In addition, compared with pure ferroelectric materials, the dielectric loss of ferroelectric materials doped with rare-earth ions increases with temperature, and the loss value after doping is lower than that of pure ferroelectric materials. In the hysteresis loop of Pr ions doped with (Ba_0.99Ca_0.01) (Ti_0.98Zr_0.02)O₃(BCZT) reported by Wang, it was found that Pr ions’ doping will affect the polarization and coercive field of BCZT ceramics ^[17][21]. The doped ferroelectric materials will obtain enhanced remanent polarization.

2.2. Physical Properties of The Rare-Earth-Doped Ferroelectrics

Ferroelectrics have P-E hysteresis loops, which are caused by domain polarization conversion and domain wall movement. The hysteresis loop will contain information such as maximum polarization, residual polarization, and coercive field (E_C), which also reflects the characteristics of ferroelectrics. The loop area of the hysteresis loop represents the energy consumed in the process of polarization switching. In Yao’s research on BiFeO₃(BFO), the Fe³⁺ and Bi³⁺ ions are shifted along the pseudocubic (111) direction from the center of the oxygen octahedron and the ideal position between the two octahedrons, respectively ^[18][22]. These shifts contribute to the enhancement in the spontaneous polarization of rare-earth-doped BFO. Indeed, the shifts in Bi³⁺ were shown to have a stronger influence on the ferroelectric properties of BFO. Secondly, counterrotations of the oxygen octahedra around the pseudocubic (111) axis will lead to rhombohedral symmetry (space group rare-earth ions) with a unit cell doubling compared with the perovskite primitive unit cell. Raman spectra indicated that the rare-earth ions’ dopant occupied the Bi-sites in the BFO unit cell. Consequently, the rare-earth ions’ dopant might also affect the shift of Bi³⁺ ions along the polar (111) axis, and this dominantly determines the ferroelectric properties of BFO. Therefore, the ferroelectric behaviors of rare earth ions-doped BFO are modified. Compared with pure BCZT ceramics, the Curie temperature (T_C) of Pr-ion-doped BCZT ceramics increased slightly. The T_C (118 °C) of (Pr_0.002Ba_0.988Ca_0.01) (Ti_0.98Zr_0.02)O₃(BCZT-A) ceramics is negligibly affected by doping with Pr ions, while the T_O-T expands and shifts to lower temperature. The doping of Pr ions influences the polarization as well as the coercive field of the BCZT ceramics. When Pr ions are doped in BCZT ceramics, Pr³⁺ /Pr⁴⁺ ions occupy the Ba²⁺/Ca²⁺ sites in the BCZT lattice and act as donors, thus enhanced remanent polarization is obtained.

2.3. Influence of Domain Wall and Oxygen Vacancies

In order to reduce the electrostatic energy, ferroelectrics tend to split into domains separated by domain walls and are polarized in different directions. In ferroelectric thin films, defects such as oxygen vacancies near the domain walls lead to domain wall pinning, which decreases the mobility of the domain walls and ultimately reduces the residual polarization value and increases leakage current density ^[19][23]. Furthermore, A-site vacancies will benefit the domain wall motion, which will lead to the low coercive field and slanted P–E loops. Therefore, the enhancement of residual polarization values can be attributed to the increased domain wall mobility through doping. The existence of oxygen vacancies also affects the ferroelectric properties. Rare-earth-doping bismuth ferrites reported by Verma showed that doping a small amount of Sm³⁺ at the Bi³⁺ site would stabilize the perovskite structure of BFO, thereby reducing the number of oxygen vacancies and subsequently increasing the dielectric constant ^[20][24]. The decrement in dielectric constant is related with the hopping of the electrons from Fe²⁺ to Fe³⁺ ions. At low frequency, the electric field does not provide enough energy to the electron for hopping, but as with the increase of the frequency of electric field, it then provides sufficient energy and a point is reached when hopping of the electron is started from Fe²⁺ to Fe³⁺ ions. Therefore, the conductivity of the dielectric increases as frequency is increased. Hence, a decrement occurs in ε’. The dielectric constant of doped BFO is larger than that of undoped BFO. This dielectric behavior of doped BFO might be connected in terms of oxygen vacancy and displacement of Fe³⁺ ions. There are always some oxygen vacancies in undoped BFO, which result in relatively high conductivity and a lower dielectric constant. The doping of rare-earth ions on the A site reduces the generation of oxygen vacancies ^[18][20][22,24]. Meanwhile, fewer oxygen vacancies lead to low leakage current density. Due to the reduction in the leakage current component, better P-E loops can be obtained. The squareness of the P-E loops is increased by adding rare-earth dopants. In addition, the improved piezoelectric properties and luminescence properties are due to the particular structure of BCZT-A ceramics: the coexistence of the O-T phase at room temperature, the asymmetric local environment, and the homogeneous microstructure. The asymmetric structure, coexistence of orthorhombic and tetragonal phases at room temperature, and fewer oxygen vacancies may be the reasons for the excellent luminescence properties of the BCZT-A ceramics ^[17][21].