The effect of Mg doping on the dielectric and tunable properties of Pb 0 . 3 Sr 0 . 7 TiO 3 thin ﬁlms prepared by sol–gel method

Mg doped Pb 0 . 3 Sr 0 . 7 TiO 3 (PST) thin ﬁlms were fabricated by the sol–gel method on a Pt/Ti/SiO 2 /Si sub-strate. The microstructure, surface morphology, dielectric and tunable properties of PST thin ﬁlms were investigated as a function of Mg concentration. It is found that proper Mg doping dramatically improves the dielectric loss (0.0088 @ 1 MHz), furthermore, the crystallinity, dielectric constant, and tunability of ﬁlms simultaneously decrease with the increase of Mg content. The 2 mol% Mg doped PST thin ﬁlm shows the highest ﬁgure of merit (FOM) value of 36.8 for its the smallest dielectric loss and upper tunability. The dependence of Rayleigh coefﬁcient on the doping concentration was examined, which indicated that the reduction of dielectric constant and tunability of ﬁlms should be related to the Mg (cid:2)(cid:2) Ti –V •• O defect dipoles pinning the domain wall motion of residual polar clusters in PST.


Introduction
Solid solutions of Pb x Sr 1−x TiO 3 (PST) thin films have drawn great attention in recent years. Its Curie temperature can be adjusted linearly from 490 to −230 • C with increasing Sr content and the process temperature of PST films is relatively low. It is considered as one of the most potential candidate materials for the future tunable microwave device components, such as phase shifters, filters, varactors, delay lines, etc. [1][2][3][4]. However, significant reductions in loss at high frequencies together with the improved dielectric tunability are needed for their realization in devices.
In order to further improve the performance of PST films, many efforts have been tried in various ways. The effects of buffer layers [5], epitaxial or oriented growth [6,7], compositionally graded films [8] and multilayered films structures [9] on the dielectric and ferroelectric properties of PST films were investigated. Besides, it has been identified that proper acceptor doping is another effective way to optimize the ferroelectric and dielectric properties of perovskite ferroelectric films. In fact, doping may be able to change the defect concentration even of defect types. Furthermore, the different defect concentration and defect types have an important effect on the electric properties of thin films. Miao et al. controlled defects in (Ba 0.8 Sr 0.2 )(Zr 0.2 Ti 0.8 )O 3 films through Co acceptor doping to depress the leakage current and increase tunable properties of films [10]. In PST system, though some researches [11,12] about acceptor doping have been carried out, most of them mainly focus on the effect of acceptor dopant on the dielectric loss, and the related physics mechanisms behind the element doping adjusting defect concentration and types and then changing polarization and dielectric properties still need to be explored.
In this study, Mg doped PST thin films with dopant content from 0-6 mol% were prepared on Pt/Ti/SiO 2 /Si sub-strates by the sol-gel method. The microstructure and surface morphology of the Mg doped PST films were characterized by XRD and AFM. The Rayleigh law was used to characterize the effect of Mg as an acceptor dopant on the defects, polarization and dielectric properties of films.  4 ] as source materials. Glacial acetic acid, deionized water and 2-methoxyethanol were selected as solvents. Formamide, acetylacetone, and ethylene glycol were added to stabilize phase, adjust the viscosity and surface tension. The concentration of the precursor solution was adjusted to 0.5 mol/L. The precursor solution was coated on the Pt/TiO 2 /SiO 2 /Si substrates via a spin coating at a rate of 4000 rpm for 25 s and then to pyrolyzed at 400 • C for 10 min and 480 • C for 5 min. The spin-coating and heattreatment procedure was repeated several times to obtain desired thickness. Finally, all films were annealed at 700 • C for 30 min for crystallization.
The structural and dielectric properties of Mg doped PST thin films were characterized by various techniques. X-ray diffraction (XRD) was performed for phase identification using a Ultima IV X-ray diffractometer with Cu K α radiation. The surface and roughness were observed by the SPM-9500J3 atomic force microscope (AFM). The cross section and thickness of the films were examined with a JSM-7500F field emission scanning electron microscope (FE-SEM). Dielectric measurements were carried out using the metalinsulator-metal (MIM) capacitor configuration. A gold top electrode with 0.3 mm diameter was deposited on the film by direct current magnetron sputtering system (JGP-560). The dielectric properties were measured using Agilent 4294A precision impedance analyzer. Ferroelectric hysteresis loops (P-E) of PST thin films were characterized by a ferroelectric tester (Precision Premier Workstation, Radiant Technology, USA).  phase with no evidence of secondary phase formation and show no preferred orientation. Furthermore, the diffraction peaks shifted towards low angle gradually with the increase in x, which implies that the dopants have entered the unitcell maintaining the perovskite structure of solid solution. The change in the peak position should be ascribed to the substitution of Ti 4+ by Mg 2+ ions. The ionic radius of Mg 2+ (0.720 Å) in the 6-fold coordination is larger than that of Ti 4+ (0.605 Å) in the 6-fold coordination [13], which leads to expansion of the crystal cells. In addition, the intensity of Pb 0.3 Sr 0.7 (Ti 1−x Mg x )O 3 thin films reduced slightly with increasing Mg content, which demonstrates that the crystallinity and/or grain size of Mg doped samples decreases. The shift of peak position and the reduction in crystallization and/or grain size by Mg dopant are in agreement with the results reported in other literature [14][15][16]. Figure 2 shows the surface morphology of Pb 0.3 Sr 0.7 (Ti 1−x Mg x )O 3 thin films analyzed by AFM. As shown in Fig. 2, all the AFM images show granular microstructure. The surface root-mean-square (RMS) roughness values of Pb 0.3 Sr 0.7 (Ti 1−x Mg x )O 3 thin films are 8.07-5.95 nm and the average grain sizes of films estimated using the linear intercept method are 52-62 nm. It can be seen that the reduction of grain sizes for Pb 0.3 Sr 0.7 (Ti 1−x Mg x )O 3 thin films is unobtrusive, combining with the XRD analysis, which implies that Mg dopant is likely to mainly decrease the crystallinity of the PST films. The incorporation of foreign ions in thin films can lead to the lattice distortion of the perovskite phase [14] and the phase formation ability is therefore decreased with increasing dopant content, which usually results in the reduction of the crystallinity of perovskite thin films. Ming-Chieh Chiu [15], X.T. Li [14] and Sea-Fue Wang [17] et al. also reported that the Mg or MgO doping retards the crystallization of the perovskite thin films due to an increase in activation energy barrier. In addition, the crosssectional SEM images of the PST thin films are also pre- It is reported that the dielectric properties of ferroelectric thin films are greatly influenced by microstructure, orientation, grain size and crystallization, etc. [20][21][22]. We know that the reduction of crystallinity and grain size of thin films all can depress the dielectric polarization and then decreases the permittivity since the volume of dielectric polarization is proportional to the crystallinity and grain size [23]. Quantitative dielectric polarization information can be obtained from the P-E hysteresis loops of Pb 0.3 Sr 0.7 (Ti 1−x Mg x )O 3 thin films (as shown in Fig. 4). As we can see, undoped PST thin film shows weak ferroelectricity, which should be mainly due to the presence of residual polar clusters in the paraelectric phase at temperature close to T C [24][25][26]. The similar phenomenon was also re-  [27,28]. With the increase of Mg content, the hysteresis loops of Pb 0.3 Sr 0.7 (Ti 1−x Mg x )O 3 films become slim and the polarization obviously decreases, which indicates the domains' reorienting or motion of residual polar clusters are gradually locked or pinned. And the remnant polarization (2P r ) decreases from 3.3 µC/cm 2 to 0.4 µC/cm 2 , which is similar to the change tendency of permittivity. According to the definition of polarization in dielectric physics (P = ε 0 (ε r − 1)E, where ε 0 , ε r , and E are the permittivity of vacuum, the relative dielectric permittivity of film, and the applied electrical  field, respectively), we know that the weaker the polarization is, the lower the dielectric permittivity.

Results and discussion
The dielectric property modifications produced by dopants are largely coupled to changes in the domain wall mobility. The domain wall motion contributions to the dielectric nonlinearity and polarization in subswitching fields can be described by the Rayleigh law [10,29], where E is the applied AC field; ε init is the sum of the intrinsic lattice and reversible domain wall responses; α is the Rayleigh coefficient due to the irreversible displacement of domain wall. The reciprocal of Rayleigh coefficient is proportional to the concentration of defect pinning domain wall motion. Figure 5 shows As we know, it is inevitable to engender some oxygen vacancies, a kind of point defect, in preparing ferroelectric thin films especially with the sol-gel method. However, oxygen vacancy should not be the defect penning domain wall motion in here. Because the concentration of oxygen vacancy cannot increase with proper increasing Mg content (no more than the Mg content required for charge balance of the intrinsic oxygen vacancy). We know from Fig. 1 [36] and showed the alignment of defect dipoles along the direction of the spontaneous polarization by means of electron paramagnetic resonance (EPR) spectroscopy in some perovskite oxides. As is described elsewhere, dipoles may produce local electric fields and reduce the irreversible domain wall motion [36,38]. Furthermore, the electric dipoles could be ordered under external electric field. It will, in turn, form a lower net internal field and reduce the polarization of polar clusters and then decrease the permittivity [39]. These phenomena are all consistent with the relationship of Mg content with the Rayleigh coefficient (α), the average remnant polarization (2P r ), and the dielectric constant (ε r ) (as shown in Fig. 6). So, these defect dipoles Mg Ti -V •• O are thought of as defects pinning domain wall motion.
In addition, because the movement of domain wall in the remanent ferroelectric clusters would produce certain loss, the dielectric loss tangent of thin films should reduce while the domain-wall movements are constrained by the defect dipoles Mg Ti -V •• O . The reduction in dielectric loss due to As is known, acceptor-type dopants can prevent the reduction of Ti 4+ to Ti 3+ by neutralizing the donor action of the oxygen vacancies in perovskite materials. The similar result has been reported by Yanhua Fan et al. by means of the X-ray photoelectron spectra (XPS) analysis [41]. Because the electrons resulting from the generation of oxygen vacancy can hop between different titanium ions and provide a mechanism for dielectric losses, the compensation for oxygen vacancy with the correct amount of acceptor dopants such as Mg 2+ should, in theory, help to lower the loss tangent [42]. But if the acceptor doping ions are heavy, the oxygen vacancy required for charge balance may exceed the intrinsic oxygen vacancy, which induces the increase of dielectric loss [43]. So, before the Mg doping the content does not exceed the content of the intrinsic oxygen vacancy required for charge balance, the dielectric loss tangent of Mg doped PST thin films will dramatically decrease due to the corporate effect of proper acceptor doping and defect dipoles Mg Ti -V •• O pinning domain wall motion, reducing dielectric loss. The low dielectric loss of 2 mol % Mg doped PST thin film should belong to this situation. While the Mg doping exceeds the correct content, the superfluous Mg dopant induces the increase of dielectric loss which may surpass the reduce of dielectric loss for defect dipoles Mg Ti -V •• O pinning domain wall motions, which makes the dielectric loss tangent of Mg doped thin films slightly increase. Now we explore the possible applications of these materials in tunable microwave applications. The potential of the PST material system to be used in voltage tunable devices depends on the ability to change the dielectric constant by means of an applied electric field. The evolution of the dielectric constant (ε r ) and dielectric loss (tan δ) of PST thin films with different Mg content as a function of applied DC electric fields is shown in Fig. 7. The curves were measured at room temperature and 1 MHz. As shown in Fig. 7, the relative dielectric constant and dielectric loss of the PMST thin films nonlinearly decreases with increasing applied DC field. The nonlinearity of permittivity with electric field at the paraelectric phase of the material results from anharmonic interaction of titanium ions in perovskite   [44]. A phenomenological equation proposed by Johnson [45] can describe the dielectric constant under the DC field which could be represented as where ε r(0) and ε r(E) are the permittivity under zero electric field and applied electric field E, respectively. α is the anharmonic coefficient. The tunability, dielectric loss, and figure of merit (FOM) of PSMT films as a function of Mg content are shown in Fig. 8. The tunability is defined as (ε r(0) − ε r(E) )/ε r(0) . The tunability of Mg doped PST films calculated from Fig. 7 decreases with increasing Mg content, which shows the similar change trend with that of dielectric constant dependence Mg content. The values of tunability for the Pb 0.3 Sr 0.7 (Ti 1−x Mg x )O 3 thin films with x = 0, 2 %, 4 % and 6 % are 56.5 %, 40.7 %, 32.6 % and 20.9 %, respectively. Combining Eq. (2) and definition of tunability, we can deduce that tunability = 1 − 1/(1 + αε 3 r(0) E 2 ) 1/3 . As we can see, the tunability is a function of α · ε 3 r(0) , at given application electric field and temperature, furthermore, the ε r(0) plays a leading role for tunability. It can be predicted that tunability of the Pb 0.3 Sr 0.7 (Ti 1−x Mg x )O 3 thin films will decrease due to the obviously reduction of dielectric constant with increasing Mg content.
A tunable microwave circuit should take advantage of a high tunability together with a low loss factor (tan δ). A useful figure of merit is given by FOM, tunability/tan δ, which is desired to be as high as possible. As shown in Fig. 8, the FOM of the Mg doped PST thin films firstly increased and then decreased with increasing Mg content. The highest FOM value found for 2 mol % Mg doped PST was 36.8, which resulted from the upper tunability and the lowest loss among four samples.

Conclusion
PST thin films doped by Mg from 0 to 6 mol% were fabricated by the sol-gel method on Pt/Ti/SiO 2 /Si substrates. The microstructure, surface morphology, dielectric and tunable properties of thin films were investigated as a function of Mg concentration. It is found that the Mg concentration in doped PST thin films has a strong influence on the material properties. The increase of Mg content leads to simultaneous decrease of crystallinity, dielectric constant, and tunability of films. But the dielectric loss of Mg doped PST decreases firstly and then increases with the increase of Mg dopant. The 2 mol% Mg doped PST thin film with the smallest dielectric loss and upper tunability is the best choice for tunable device applications for its highest FOM value of 36.8. The reduction of dielectric constant and tunability is mainly due to crystallinity decrease and electric dipoles Mg Ti -V •• O pinning domain wall motion of residual polar clusters.