Introduction

In view of excellent ferroelectric properties, high dielectric constant and great dielectric tunability, ferroelectric (Pb, Sr)TiO₃ (PST) films possess considerable potential applications in a variety of microelectronic-devices, including dynamic random access memories (DRAMs), ferroelectric random access memories (FeRAMs) and microwave tunable devices, etc ^{[1,2,3,4,5,6,7]}. Apart from these excellent electrical properties, (Pb, Sr)TiO₃ films unfold outstanding electro-optical and photoluminescence features as well. For instance, nonlinear optical response, i.e., the intensive second harmonic generation effect has been found in PST/(001)MgO epitaxial films ^[8]. Ambika et al. also investigated the optical nonlinearity of PST films in the visible region using the open aperture z-scan technique ^[9]. The evidence that the third order nonlinear absorption is dependent on ferroelectric polarization was observed. And the value of third order nonlinear absorption (β) was obtained to be 10^-7m/W. Utilizing ferroelectric PST film based tunable co-planar waveguide, second and third harmonics generation were produced for a fundamental at centimeter wavelengths ^[10]. Pyroelectric coefficient p of PST ceramics were evaluated to be 10^-3C/m²K and showed good infrared sensitiveness ^[11]. In addition, nano-crystalline PST films and PST nanotubes exhibited the room temperature tunable blue-green photoluminescence under UV excitation with intense emission bands centered at the range from 350-450 nm, and emission centers can be tuned by changing the Pb content^[12,13]. The above mentioned nonlinear optical, infrared response and photoluminescence of PST can be regarded as a candidate for the related photoelectric devices, such as photoelectric modulator, infrared sensors at room temperature, flat panel display devices, the integrated light emission devices, co-planar waveguide and so on.

In general, the proper element doping at A, B sites in ferroelectrics is an effective method to further optimize ferroelectric, dielectric and optical properties. In our previous work, it is found that the ferroelectric and dielectric properties of PST films can be greatly improve by Mn doping ^[14,15]. However, the issue that Mn composition dependence of optical characteristics of Mn:PST film is still an open topic. Understanding the Mn doping effects on optical properties, especially fundamental and band tail absorption behaviors is in favor of design and optimization of integrated optics, but also provides physics nature about doping modulated electronic energy band structure and localized band tail states. In this study, the transmittance spectroscopy of a series of Mn doped Pb_0.5Sr_0.5TiO₃ films at room temperature are presented. And Mn composition dependence of interband electronic transition and band tail absorption behaviors are investigated.

1 Experimental details

A series of 1, 2.5, 5, 10 mol% Mn doped Pb_0.5Sr_0.5TiO₃ (PSMT1, PSMT2.5, PSMT5, PSMT10) films with 300 nm thickness were prepared on sapphire substrate by chemical solution deposition ^{[14,15,16,17]}. The precursor solution was spin-coated on sapphire substrates. Then it was dried at 200 ℃ for 3min, heated at 400 ℃ for 3min, annealed at 650 ℃ for 5 min by a RTA furnace in air. The x-ray diffraction (XRD) was preformed for phase identification by a Rigaku-D/MAX3C diffractometer with Cu-Kα radiation at 40 kV. The XRD results show that the present films were pure perovskite structure polycrystalline ^{[14,15,16,17]}. The transmittance spectroscopy was measured with a double beam spectrophotometer (Perkin Elmer UV/VIS Lambda 2S) at the range from 1 to 5 eV.

2 Results and Discussions

Figure1 shows the transmittance spectroscopy of PSMT films at the range from 1 to 5 eV. In general, from low energy to high energy range, the spectrum is composed of three regions: (I) a transparent oscillating region, (II) a low transmittance region and (III) a fundamental absorption region. In transparent region, due to the multi-reflectance between the film and substrate, the Fabry-Pérot interference patterns are observed in low energy region (<3 eV). It can be seen that the number of Fabry-Pérot interference patterns decreases with Mn doping amount increasing, owing to less transparent in heavily doped PSMT samples. Similar phenomenon was also be reported in Co:BaTiO₃ films ^[18]. Low transmittance region is usually attributed to band tail absorption. The transmittance becomes sharper with the decrease of Mn dopant, which implies the density of localized band tail states rise with introducing Mn into PST lattices. In fundamental absorption region, the interband electronic transition between conduction and valence bands occurs. Therefore, the incidence photons were absorbed by the films totally, leading the transmittance to be zero. As the insets of Fig.1 shown, the edge of fundamental absorption shift to low energy end, i.e. a red shift comes to being with the increasing of Mn doping. It suggests that Mn doping has influence on the energy band structure and form localized band tail in band gap.

Fig. 1 The transmittance spectroscopy of PSMT films with Mn content 1%, 2.5%, 5% and 10% at photon energy range from 1 to 5 eV. The inset is enlarging scale of transmittance spectroscopy in absorption region

图1 掺杂Mn含量为1%、2.5%、5%和10%的PSMT薄膜在1-5 eV光子能量范围内的透射光谱.插图是放大的吸收区透射光谱

In transparent region, a three-layered structure (air/film/substrate) was used to fit the transmittance spectroscopy for refraction index of PSMT films ^[18]. The dielectric function of dielectric layer is descried by Cauchy dispersion relation ^[19]:

where n is the refraction index, a, b, c are fitting parameters, λ is incident wavelength. Figure 2(a), (b) and (c) show that the measured data are in consistent with the model fitting results in PSMT1, PSMT2.5 and PSMT5 films. And obtained refraction index of PSMT films is present in Fig.2 (d), (e) and (f). However, because of less transparency, the fitting with Cauchy dispersion relation can not applied in PSMT10. Refraction index of the present films is increasing, when the incidence photon energy becomes stronger. This is a typical dispersion relation of ferroelectric films in transparent region. Generally, in transparent region, the dispersion behavior can be depicted by single oscillator Sellmeier model ^[20],

Fig. 2 Experimental (symbols) and calculated (solid lines) data of PSMT films with Mn content (a) 1%, (b) 2.5% and (c )5% in transparent region. The refractive index (n) and of PSMT films with Mn content (d) 1%, (e) 2.5% and (f )5% as a function of the photon energy. 1/(n²-1) vs. 1/λ² plots of of PSMT films with Mn content (g) 1%, (h) 2.5% and (i )5%. The solid line is the fitting of the experimental data with a single oscillator model

图2 Mn掺杂量为(a) 1%、(b) 2.5%和(c) 5%的PSMT薄膜在透明区域透射光谱的实验值（符号）和计算值（实线）数据；Mn含量为(d) 1%、(e) 2.5%和(f) 5%的PSMT薄膜的折射率(n)与光子能量的函数关系；Mn含量为(g) 1%，(h) 2.5%和(i) 5% PSMT薄膜中1/(n2-1)与1/λ2的关系图

Where λ₀ is an average oscillator position and oscillator energy E₀ =hc/eλ₀ , S₀ is an average oscillator strength. 1/(n²-1) vs. 1/λ₂ plots with linear fittings of Sellmeier model are displayed in Fig. 2(g), (h)and (i). And E₀ is obtained to be 5.43, 4.76 and 4.27 eV, S₀ is 0.67, 0.50 and 0.33 ×10¹⁴ m^-2 for PSMT1, PSMT2.5 and PSMT5 films, respectively, which are accord with those value in (Bi,La)₄Ti₃O₁₂ films^[21] and SrTiO₃ ^[20]. The transitions between critical points (CP) in high energy region are usually regarded as a single oscillator, which contribute to dielectric dispersion in transparent region ^[18]. In Ti based perovskite oxides, the higher CP transitions of (A₁-A₂) are scribed to the transition between X_5’- X₅ energy levels and the value of transition energy is 4-5eV^[22]，which is in agreement with this case and the origin of dielectric dispersion. It can be found that the oscillator energy and strength become weaker with Mn doping, which reveals that high energy CP transition energy decreases and Mn doping alters PST electronic energy band structure. It is in consistent with the above mentioned results about transmittance spectroscopy.

In absorption region, absorption coefficient α is are derived form α=ln(1/T)/d (T is transmittance and d is film thickness) to determine the optical band gap of the PMST films^[23]. Usually, in fundamental absorption region (E >E_g ^opt ), Tauc’s power law can describe the incident photon energy E dependence of the absorption coefficient. There are two case: (1) for the direct interband transition between the valence and conduction bands , α ∝ (E-E_g ^opt)^1/2/E, and (2) for the indirect interband transition, α ∝ (E-E_g ^opt)²/E, where E_g ^opt is optical band gap (OBG)^[24]. Good linear fittings of the relations between E and (αE)² can be shown in Fig. 3(a), (b), (c) and (d), which indicates direct interband transition between the conduction and valence bands in Mn doped PST films. The E_g ^opt is evaluated to be about 3.89, 3.86, 3.77 and 3.66 eV for PSMT1, PSMT2.5, PSMT5 and PSMT10 films, respectively, which is litter less than that of pure PST films^[16]. The Mn composition dependence of optical band gap is shown in Fig.4. Similar to the decrease of high energy CP transitions as the above mentioned, it is found that optical band gap undergoes shrinkage when Mn content increases, which follows the red-shift of the fundamental absorption edge in transmittance spectroscopy. Moreover, the relation of optical band gap and Mn dopant amount is approximately linear, just as the description of Vegard’s law^[25]. In PbTiO₃-based perovskite ferroelectrics, the upper structure of valence bands mainly comes from O 2p orbitals, while the lower laying of conduction bands origins from Ti 3d orbitals. Because of crystalline field effect in Ti-O octahedra, Ti 3d conduction bands split into lower energy threefold degenerate t _2g and higher energy two-fold degenerate Ti 3d e_g subbands. Therefore, the lowest laying of conduction bands arises from Ti 3d t _2g orbitals. The gap of O 2p and Ti 3d t _2g states would be optical band gap and the value of the gap is near 4 eV^[26]. Therefore, the optical band gap comes from the interband transition between upper laying of O 2p orbitals and lower laying of Ti 3d t _2g orbitals. Introducing Mn ions into B site of PST lattices, lower enengy Mn 3d orbitals partly replace Ti 3d t _2g orbitals, which can lead to the gradual decline of the lowest laying in conduction bands and the shrinkage of OBG^[25], but also influences the hybridization strength between the Ti 3d-O 2p orbitals and Mn 3d-O 2p orbitals, and therefore decreases the high energy CP transition. On the other hand, the lattice constant is also a critical cause for OBG. Basing on Harrison model ^[27], OBG can be determined by

Fig. 3 Variations of (αE) ² changing with the photon energy are used to determine the optical band gap of the PSMT films with Mn content (a) 1%, (b) 2.5%, (c )5% and (d) 10%. The insets are the exponential absorption coefficient as a function of the photon energy below the band gap energy

图3 (αE)2随光子能量变化而发生的变化，其中Mn含量(a) 1%、(b) 2.5%、(c) 5%和(d) 10%.插图是低于带隙能量区域内吸收系数的自然指数函数与光子能量的关系

Fig. 4 Mn composition dependence of optical band gap and Urbach band tail energy of PSMT film. The solid line is the linear fitting of the experimental data

图4 PSMT薄膜的光学带隙和Urbach带尾能量与Mn组分的依赖关系，实线是实验数据的线性拟合

where ɛ_c is lowest laying of conduction band, ɛ_V is top of conduction band, V_ppσ and V_ppπ is σ and π bonding energies of O 2p orbital, respectively. The last term varies with interatomic distance (t), in terms of

where η_ppσ , η_ppπ and f are dimensionless coefficients, m is the electron mass and h is Planck constant. As reported by Yang et al, the lattice parameter of PST films decreases after the Mn doping ^[15]. The decrease of interatomic distance can enhance the value of V_ppσ + V_ppπ and in turn contribute to the decrease of OGB.

Note that the absorption coefficient increases gradually when the incidence photon energy is increasing below OGB (~3.4-3.8eV), as the above motioned band tail absorption in a low transmittance region. This weak band tail absorption can be suggested as the electronic transition among the extended bands and the localized band tail states. Usually, this weak band tails absorption behavior obeys Urbach rule, which is described by α∝exp(E /E_U ) ^[28], where Urbach band tail energy ( E_U ) is the width of band tails of local states. The inset of Fig.3 (a), (b), (c) and (d) show that the band tail absorption yields Urbach law well and Urbach band tail energy is obtained to be 309, 347, 420 and 574 meV for PSMT1, PSMT2.5, PSMT5 and PSMT10 films (in Fig.4), respectively, which are larger than that of pure PST films (245 meV )^[16]. Urbach band tail energy increases with more Mn amount doping into PST films, which means the width of band tails of local states increasing. The localized states of Urbach tail are usually resulted from the thermal fluctuation disorder (electron-phonon interaction) or/and the structural disorder in lattices ^[16,29]. Obviously, doping induced Urbach tail states can be interpreted as the structural disorder, which is resulted from the impurities, defects e.g., oxygen vacancy or Pb vacancy and grain boundaries ^[16].In present case, firstly, Mn dopant ions occupy B site Ti ions randomly, which leads to the disorder of the lattices. Moreover, as an acceptor doping, with the Mn²⁺ dopant amount increasingly entering into Ti⁴⁺ site, the more concentration of oxygen vacancy with two positive charges will generate to keep electrical neutral of the whole film system ^[14,15]. This process can be described by

MnO→Mn_Ti ^’’+ 1/2O₂+ V_o ^¨　　　.　（5）

The increase of oxygen vacancy further deteriorates the structural disorder. Therefore, random occupation of Mn ion and the increase of oxygen vacancy after Mn doping are the main causes for the expansion of localized states in band tails.

3 Conclusions

In summary, Mn doping induced the decrease of interband transition energy and the expansions of the band tail states were observed. Lowering the bottom of conduction bands by Mn 3d orbitals and the decrease of lattice constant in Mn doped PST films contribute to the shrinkage of optical band gap. And the random occupation of Mn ion and the increase of oxygen vacancy after Mn doping are the main causes for the expansion of localized states in band tails.

References