Structure and Tunneling Magnetodielectric Effects of Cobalt–(Barium Fluoride) Lateral Nanogranular Films

Abstract

Controlling the conductance of miniaturized electrical components via spin-dependent tunneling is a challenging step for nano-scale implementation. In this study, we demonstrate the fabrication of lateral nanogranular films with oblate magnetic metal nanoparticles and achieve variable out-of-plane intergranular gap. Changes in insulating layer thickness from 0.4 to 2.1 nm resulted in a marked increase of 10,000-fold for both in-plane and out-of-plane electrical resistivities. A 4% enhancement in permittivity, namely the magnetodielectric effect, was obtained under an in-plane magnetic field of 10 kOe. The frequency at which the maximum magnetodielectric effect is found shifts from 15 kHz to 880 kHz depending on the out-of-plane resistivity. We demonstrated frequency control of the magnetodielectric effect via electrical resistivity by structural modulation of the lateral nanogranular system.

1. Introduction

Nanogranular films, which consist of dispersed ferromagnetic nanogranules in a dielectric matrix, have attracted great interest because of their unique nano-scale electrical and magnetic interactions. Various magnetic field functionalities dependent on the spin-dependent tunneling probability in the films have been discovered in the past decades, including magnetoresistance,^1–3) magnetodielectric,^4–12) magneto-optic,¹³⁾ and Faraday effects.^14–17) In these functionalities, the tunneling magnetodielectric (TMD) effect has gained considerable attention because of its frequency selectivity above the MHz range^5–7,12) and electric bias field control.^9,12) For applications such as magnetic field sensors, high-frequency filters, and frequency-selective switches, achieving desirable electrical resistivity and controllable frequency response with improved magnetic properties of nanogranular films is essential. In the past, two approaches, which involve material improvement and suitable integration into the sensing device structure, have been explored to improve the electric and magnetic performance of isotropic nanogranular films. The first approach involves structural refinement, such as changing the packing density of nanogranules or post-annealing, to optimize tunneling electron transport and enhance multifunctionalities. However, this approach often involves a trade-off between high electrical resistivity (robustness against breakdown voltage) and magnetic low-field sensitivity. The second approach is device design using a microfabrication technique known as nanogranular-in-gap structure (GIGS).^18–20) In this design, although the magnetic sensitivity of the nanogranular films is low, nearby high-permeability magnetic poles suitably magnified the surrounding magnetic field, leading to improved sensitivity. Regarding GIGS’s thin film planar shape, the resistivity change in the film plane was used for sensing.

Although the approaches mentioned above are based on films with spherical and randomly dispersed magnetic nanogranules of similar intergranular gap, little attention has been paid to the anisotropic modulation of intergranular gap using oblate nanogranules. For lateral nanogranular systems, out-of-plane resistivity can also be used for sensing. Regarding the anisotropic advantage of the lateral nanogranular film, we aimed to control 1) the electrical resistivity along the out-of-plane direction of the film and 2) the frequency response of the magnetodielectric effect.

Cobalt–(barium fluoride) (Co–BaF₂) nanogranular films were selected because previous studies have shown that sputtered BaF₂ crystallizes and is an excellent potential energy barrier against ferromagnetic metal Co particles.⁷⁾ In addition to the sensitivity enhancement due to in-plane magnetic anisotropy, we developed an anisotropic nanogranular structure in which the direct and alternating tunneling currents are hybridized for the in-plane and out-of-plane directions, respectively, using the tandem sputtering method.²¹⁾ The hybridization of the direct and alternating tunneling current implies that the controllable tunneling probability is connected to the frequency response of the magnetodielectric effect in the laterally structured film.

This study covers two topics: optimizing intermediate structure between multilayer and granular by changing substrate rotation speed (Sections 3.1 and 3.2) and evaluating the role of tunneling conductance (out-of-plane electrical resistivity) in the magnetodielectric performance under various vertical intergranular gaps of nanogranular films (Sections 3.3 and 3.4).

2. Experimental Procedure

A series of films with various nanogranule shapes were prepared using the tandem sputtering method.²²⁾ Both φ76 mm-BaF₂ and φ50 mm-Co targets were alternately sputtered onto the substrate at various annular rotation speeds (v rpm). The experiment involved two steps to achieve a lateral nanogranular structure with a multidirectional tunneling magnetoelectric effect. First, the substrate rotation speed was varied from 1 to 5.5 rpm to obtain oblate-shaped nanogranules (Section 3.1). Second, the input power of the BaF₂ target (P_BaF2) was varied from 100 to 200 W to optimize the insulating BaF₂ layer thickness (t_BaF2) (Section 3.2). The base pressure was maintained below 8 × 10⁻⁵ Pa, and the Ar gas flow pressure during sputtering was set at 0.23 Pa. For structural analysis, electrical and magnetic measurements along different directions, Si(100), Pt/Ti/Si(100), and quartz substrates were used interchangeably. The in-plane and out-of-plane electrical resistivities were evaluated using the conventional four-probe method for films on quartz and the two-probe method for films on Pt/Ti/Si(100) with a φ0.5-mm top indium electrode. Transmission electron microscopy (TEM) and small-angle X-ray scattering analysis (SAXS) were performed using cross-sectional and in-plane incident beam configurations to determine the shape and alignment of the nanogranules. Film composition was determined by X-ray fluorescence analysis (XRF). Magnetization curves were measured using a vibrating sample magnetometer with a maximum applied field of 2 T, both in-plane and out-of-plane. The dielectric properties of the metal sandwiched films were characterized out-of-plane with an oscillation voltage of 0.5 V within a frequency range of 100 Hz to 100 MHz. The TMD effects were evaluated under an in-plane magnetic field of 1.2 T with the same frequency range. All measurements were performed at room temperature.

3. Results and Discussions

3.1 Structure optimization: Lateral nanogranular film with oblate nanogranules

To optimize the sputtering conditions and achieve the desired lateral structure, we investigated the effect of rotational v on the film structure (Fig. 1). At v = 2.5 rpm, the film exhibited a continuous multilayered stack of Co and BaF₂ (Fig. 1(a)), with both Co and BaF₂ crystallized. The diffraction pattern (top inset) exhibited vertically aligned spots, indicating the preferred orientation of polycrystalline BaF₂ crystal phases projected onto the layer ordering structure and the preferred orientation of the long axis of BaF₂. For v values higher than 4 rpm, Co transformed into spherical particles, but the shape and order of the Co particles differed significantly. At 4 rpm, oblate ellipsoidal particles with lateral ordering were successfully achieved, whereas at 5.5 rpm, randomly distributed spherical particles were observed. This v-dependent structural change indicates that Co growth on BaF₂ layers follows the Volmer–Weber mode when the sputtering interval between Co and BaF₂ targets is longer than the nucleation of Co in BaF₂. In addition, the (111) plane of the BaF₂ layer covered the Co surface, indicating that the film crystal plane with the lowest surface energy is enhanced when the surface energy of the underlayer exceeds that of the film.²³⁾ Simultaneously, a lateral discontinuous nanogranular structure was formed at 4 rpm. Because of the poor wettability of Co, which has a low surface free energy, on BaF₂, which has a high surface free energy, an intermediate state between layers and granules was realized as a result of mass-dependent nucleation and surface and surface-interface energy balance.^24,25) The shape of the nanoparticles changed from oblate to sphere when v was varied from 4 to 5.5 rpm. This shape change indicates a shift in the initial growth mode from a solid-like equilibrium state to a liquid-like nonequilibrium state.²¹⁾ In the former state, particle nucleation occurs at the surface, whereas in the latter state, particle nucleation occurs randomly in the film. Notably, the structural change from multilayer (Fig. 1(a)) to laterally ordered oblate granular (Fig. 1(b)) achieves a 10⁵-fold electrical resistivity increase up to 10⁷ µΩ cm. This significant increase in electrical resistivity can be explained by electron tunneling via a few nanometer-thick BaF₂ intergranular gaps, which hinder metallic conduction. We suggest that out-of-plane electron tunneling dominates in the case of lateral granular structures and can be controlled by changing the vertical intergranular gap.

Fig. 1

Cross-sectional TEM image of Co–BaF₂ films prepared at (a) 2.5, (b) 4, and (c) 5.5 rpm. The top inserted figures are diffraction patterns for low-magnification images.

3.2 Structural variation: Vertical intergranular gap

To control the t_BaF2, the P_BaF2 was increased from 100 to 150 W, while the other sputtering conditions were unchanged (v = 4 rpm). For all P_BaF2, lateral-ordered oblate nanogranules were observed in the film. With increasing P_BaF2, the t_BaF2 linearly increased from 0.4 to 2.1 nm (Fig. 2(g)). In addition, the plan-view images (Figs. 2(e) and (f)) revealed that the projected shape of Co was spherical, with a similar diameter of approximately 5 nm, as estimated from the TEM cross-sectional image (Fig. 2(c)).

Fig. 2

Cross-sectional TEM image of Co–BaF₂ films prepared with (a) 100, (b) 125, (c) 140, and (d) 150 W. (e) and (f) TEM plan-view of the film prepared with 140 W. (g) BaF₂ thickness (t_BaF2) as a function of BaF₂ input power.

To obtain statistical structure information to account for the macroscopic magnetoelectric effect, we performed SAXS evaluation for a series of films with various P_BaF2 (Fig. 3(a)). Based on the in-plane X-ray projections of randomly distributed spherical particles, the small-angle scattered signal depends on the scattering vector |q|, (= 4π sin θ, θ: scattering angle) which is described as follows:

  

\begin{equation} I(q) = \varDelta\rho^{2}\int\nolimits_{0}^{\infty}V(r)N(r)S(q,r)F^{2}(q,r)dr \end{equation} (1)

where N indicates the number density of nanogranules, Δρ is the difference in density between the two phases, V(r) is the volume of nanogranules, N(r) is the volume-weighted size distribution given as a log-normal distribution, and F(q, r) is the form factor.²⁶⁾ The particle has some anisotropy in shape, i.e., it is elongated in the lateral direction. However, because the ratio between the lateral and thickness directions is less than 2 (Table A1), we use the form factor for spherical particles as a reasonable approximation. The characteristic length evaluated by SAXS is in the in-plane direction, and the determined average size of the sphere reflects the lateral size of the particles (b). While the high-q behavior may deviate from that of ideal spheres due to the shape difference, this effect is absorbed in the size distribution in this analysis. The SAXS profiles of a series of Co–BaF₂ films (solid lines) exhibit a clear peak around q_max, indicating the contribution of intergranular interference. Therefore, the structural factor S(q) is included in this analysis. We used a “local monodisperse hard-sphere model” with a structure factor based on the hard-sphere potential.^27,28) From q_max, we can also obtain the interparticle distance (L) value derived from Bragg’s equation.

  

\begin{equation} L = 2\pi/q_{\textit{max}} \end{equation} (2)

The SAXS profiles were fitted using eq. (1) to obtain the average size of the metal nanogranules (Fig. 3(b)). The lateral particle width increases with increasing amplitude of the P_BaF2. This trend is consistent with the estimation of the TEM cross-sectional image shown in Fig. 2. The increase in b with P_BaF2 suggests that Co aggregation occurs during film formation under high energy levels at high P_BaF2.

Fig. 3

(a) In-plane SAXS profiles of Co–BaF₂ films prepared at 100–150 W. (b) Input power dependence on the lateral width of oblate nanogranules from TEM cross-sectional image (red closed circle) and SAXS profiles (blue open circle).

3.3 Relationship between the electrical properties and structure of lateral nanogranular films

To understand the importance of the anisotropic configuration on the electric properties of the nanogranular films, the in-plane and out-of-plane electrical resistivities were summarized using the spacing parameter (Fig. 4). Figure 4(a) shows the electrical resistivity vs. the vertical BaF₂ thickness (t_BaF2) obtained from Fig. 2(g). Both in-plane and out-of-plane electrical resistivity tend to increase with increasing t_BaF2. In general, in nanogranular films, electrical resistivity increases with decreasing metal content,^29,30) including in the case of the Co–BaF₂ nanogranular system.⁷⁾ In this study, the Co content of the film decreased from 38 at% to 25 at% by changing the P_BaF2 from 100 to 200 W. There are two differences between the in-plane and out-of-plane electrical resistivities. First, the amplitude of the out-of-plane resistivity is 10–10⁴ times higher than that of the in-plane resistivity. Second, the rate of increase in ρ for in-plane and out-of-plane exhibits the opposite tendency. The in-plane electrical resistivity shows a steep increase with increasing t_BaF2 up to 1 nm, followed by a slow rise from 1 to 3 nm. However, the out-of-plane electrical resistivity exhibits a steep increase beyond 1 nm. This difference implies that the intergranular gap, where electron tunnels occur, differs depending on the measuring direction.

Fig. 4

Electrical resistivity of Co–BaF₂ films assembled by (a) t_BaF2 and (b) neighboring particle gap. The measured direction is along the in-plane (red circle) and out-of-plane directions (blue square). The black dashed line represents an estimated ρ_tunnel with various V₀ values. (c) Schematic illustration of free electrons incident on a d-nm-thick simple barrier with a barrier height of V₀.

To understand the importance of the intergranular gap on the electric properties of the film, we estimated the effective tunneling among the intergranular gaps. For conventional nanogranular films with randomly dispersed spherical metal particles, a simple cubic lattice model has been applied to calculate the tunneling conductance.³¹⁾ In the case of our laterally elongated granular structure, plausible quasi-close-packed hexagonal arrangements were proposed for estimating the minimum intergranular gap (See appendix). Our plausible model provides a neighboring particle gap based on the following measured parameters: t_BaF2, granule size, and packing density. The electrical resistivity of the films was re-plotted with the neighboring particle gap (Fig. 4(b)). We added a 0.5-nm error bar to account for randomness in the neighboring particle gap estimation. A similar increase ratio in the neighboring particle was observed for both in-plane and out-of-plane electrical resistivity. In metal–vacuum–metal tunneling cases, the slope of the plot yields an effective barrier height, which represents the potential barrier height of the insulating layer (V₀) relative to the Fermi level of the metal (E).³²⁾ Assuming their theory applies to our granular case with favorable phase separation, the slope observed in Fig. 4(b) implies a particular effective band gap for a series of films with different Co assemblies.

The topological extension of single free-electron tunneling approximated the macroscopic tunneling probability of the nanogranular films. The tunneling probability (T) of a free-electron transmitting metal–insulator–metal tunneling junction (Fig. 4(c)) is expressed as follows:

  

\begin{equation} T = \left[1 + \frac{V_{0}^{2}}{4E \cdot |E - V_{0}|} \cdot \mathit{sin}^{2}\,\gamma \cdot d\right]^{-1} \end{equation} (3)

  

\begin{equation} \gamma^{2} = \frac{2m \cdot |E - V_{0}|}{(h/2\pi)^{2}} \end{equation} (4)

where V₀ is the barrier height of the insulator, E is the energy of electrons in a metal (typically the Fermi energy), d is the thickness of the insulating layer, m is the electron mass, and h is Planck’s constant. Tunneling probability and tunneling barrier thickness are inversely proportional in ultrathin crystal tunneling junctions.³³⁾ If the metal particle density is below the percolation threshold, the nanogranular system is a topologically equivalent circuit with several metal–insulator–metal junctions.³¹⁾ Suppose the conduction process exclusively occurs through electron tunneling and metallic conduction (given the Fermi level of Co metal is 7 eV). In that case, the measured electrical resistance can be regarded as the product of the metal conductivity (σ) and the electron’s tunneling probability (T). Therefore, the tunneling electrical resistivity (ρ_tunnel, ρ = 1/σ) is written as follows:

  

\begin{equation} \rho_{\textit{tunnel}} \cong \rho_{\textit{Cobalt}}\frac{1}{T} \end{equation} (5)

The t_BaF2 dependence of the measured electrical resistivity was fitted within a range of tunneling barrier height (V₀) of 7.5–9 eV, which is in the same order of magnitude as that of BaF₂ (∼9 eV).³⁴⁾ The estimated V₀ is lower because of the presence of impurities (metallic Co) in the matrix of the nanogranular film under the non-equilibrium state of the tandem sputtering process.

Based on the relationships between electrical properties and structure, we demonstrated that electrical resistivity can be controlled via tunneling gap modulation by changing t_BaF2. Compared to the magnetocapacitance effect observed in metal–insulator–metal tunneling junctions with a tunneling gap of approximately 2 nm,³⁵⁾ tandem sputtered nanogranular films offer robust advantages without the need for rigorous base pressure (often 10⁻⁷ Pa) to maintain a consistent interface in the tunneling junction. In addition, the film offers controllable t_BaF2 by simply changing the substrate rotation speed. The graded robustness of the electrical resistivity (Fig. 4(b)) originates from the controllable average tunneling gaps formed by numerous nanocapacitors.

3.4 Tunneling magneto dielectric effects on various intergranular gaps

Figure 5 presents the frequency profiles of (a) permittivity (ε′), (b) D (= ε′′/ε′), and (c) TMD change ratio of Co–BaF₂ films for various t_BaF2. At low frequency, ε′ varies from 200 to 500, which is higher than that of pure BaF₂ and similar to metal–insulator nanogranular films.⁷⁾ All samples ε′ decreases with increasing frequencies, indicating relaxation of interfacial polarization in metal–dielectric composite systems.³⁶⁾ The dielectric relaxation frequency (f_Relax) decreased from 1.2 MHz to 26 kHz with increasing t_BaF2 (Fig. 5(b)). This f_Relax shift is specific to the metal–insulator nanogranular system films and can be attributed to the intergranular gap expansion,^7,10,12) which correlates with the increase in t_BaF2 in the lateral nanogranular films. Although an increase in frequency-dependent permittivity has also been observed in semiconductor ferrite materials,^37,38) our case differs regarding the contribution of spin-dependent tunneling electrons³⁹⁾ to the ε′ enhancement.

Fig. 5

Frequency profiles of (a) ε′, (b) D, and (c) TMD ratios of Co–BaF₂ films for various P_BaF2 and t_BaF2. The frequency is indicated by a black arrow, where maximum-D (b) and maximum-TMD ratio (c) are indicated as f_relax and f_TMD, respectively.

When an external magnetic field is applied in the film plane, the ε′-frequency curves shift to a higher frequency range because of an increase in the spin-dependent tunneling probability resulting from the parallel configuration of magnetic moments in neighboring nanogranules.^5,7) The mechanism for increasing the tunneling probability with magnetic field application has been discussed in Ref. 4). These shifts in ε′-frequency curves have TMD effects, i.e., the slight increments of ε′ observed around f_Relax in Fig. 5(b). The TMD ratio exhibits maximum values of up to 4% around the frequency, which we defined as f_TMD (Fig. 4(c)). As t_BaF2 increased from 0.4 to 1.5 nm, f_TMD shifted to a lower frequency range from 435 kHz to 15 kHz, corresponding to f_Relax. These shifts in f_TMD result from changes in relaxation due to the spin-dependent tunneling effect, including changes in ρ. The maximum values of TMD were approximately 4% when t_BaF2 changed from 0.77 to 1.53 nm, indicating that the total conversion efficiency of spin-dependent charge transport did not depend on the degree of conductance but rather on the magnetization and spin polarization ratio for Co content ranging from 30.7 at% to 36.1 at%.

Figure 6 presents the relationships among f_relax, f_TMD, and ρ_⊥ which were measured perpendicularly to the film. Both f_relax and f_TMD appeared in similar frequency ranges because the highest increase in admittance resulted in a decrease in the dielectric constant at f_Relax due to shifts in the frequency profile under the application of a magnetic field. Both f_Relax and f_TMD decreased proportionally with increasing ρ_⊥. A similar relaxation of the macroscopic magnetocapacitance effect has been reported in ferromagnetic metal–insulator tunneling junctions.⁴⁰⁾ However, the dependence of tunneling probabilities on the thickness of the insulating layer has never been discussed because of the difficulty in fabricating high-quality tunneling junctions. The averaged dielectric performance of the nanogranular film is equivalent to that of a three-dimensional network of capacitors in the electric circuit.⁴¹⁾ The merit of lateral nanogranular structures is that minor conducting paths do not significantly affect the overall dielectric performance (including nanogranules between the electrodes). It is possible to convert the electrode gap of the capacitors’ average intergranular gap. Therefore, we have achieved vertically uniform intergranular gap by lateral nanogranular films in Section 3.1. We found the nano-scale spin-dependent tunneling probability controllability as a function of the vertical intergranular distance t_BaF2 (Sections 3.2, a-3). The dielectric properties in Section 3.4 reveal that the f_TMD was coupled with ρ_⊥ dominated by the probability of spin-dependent tunneling via t_BaF2 as well.

Fig. 6

f_Relax and f_TMD of Co–BaF₂ films assembled by ρ_⊥.

4. Conclusion

To reveal the magnetodielectric performance in the lateral nanogranular film, the anisotropic electrical properties and the frequency response of the magnetodielectric effect were investigated as a function of the vertical intergranular gap. The following conclusions were obtained.

1. (1)    Lateral nanogranular films with oblate magnetic metal nanoparticles were fabricated by the tandem sputtering method with optimized v.
2. (2)    The vertical intergranular gap was controlled by adjusting the t_BaF2 through changes in the P_BaF2 while maintaining a moderate substrate rotation speed. The in-plane and out-of-plane electrical resistivities drastically changed by several orders of magnitude by varying t_BaF2.
   • •    When t_BaF2 was below 1 nm, out-of-plane conduction or polarization was dominant because of the obliquely close neighboring particles.
   • •    When t_BaF2 was beyond 1 nm, in-plane conduction or polarization was dominant because the lateral neighbor was closer.
3. (3)    Out-of-plane magnetodielectric measurements revealed a 4% TMD ratio in films with t_BaF2 beyond 0.8 nm. The f_TMD corresponding to the peak dielectric constant enhancement was increased with increasing ρ_⊥.

We demonstrate the ability to manipulate nano-scale spin-dependent tunneling probability and the magnetodielectric frequency response based on the out-of-plane intergranular gap of lateral nanogranular films.

Acknowledgments

The authors are grateful to Dr. T. Kawai (Yokohama National Univ.) for the fruitful discussion. This work was partly supported by a grant-in-aid for frontier research from The Japan Institute of Metals and Materials, Toyota Riken Scholar from Toyota Physical and Chemical Research Institute, the Murata Science Foundation, Casio Foundation, and JSPS-KAKENHI under Grant-in-aid 21K14482 and 23H01678.

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Appendix

When the metal granule density is lower than the percolation threshold, tunneling occurs at the nearest neighboring granules. To obtain the distance between neighboring ellipsoidal granules, we assume that the granules in the insulating matrix were located on the quasi-hexagonal close-packed lattice (Fig. A1(a)). The upper-level oblate nanogranules (label “1”) tend not to overlap vertically, just one level lower layer (label “2”). The vertical lattice constant is the sum of the vertical granule thickness (a) and t_BaF2 (Fig. A1(b)). The lateral lattice constant was defined by the lateral granule diameter (b) and the gap between the horizontal nearest granules (l). Because the volume fractions of cobalt (ν_Co) and barium fluoride (ν_BaF2) in each periodic lattice are constant, l can be described as follows:

  

\begin{equation} l = \left[\left(\cfrac{4\pi \cdot a/2 \cdot (b/2)^{2}}{\cfrac{v_{\textit{Co}}}{v_{\textit{BaF}2}}} + 4\pi \cdot a/2 \cdot (b/2)^{2}\right)\left(\frac{3\sqrt{3}}{2}(t + a)\right)^{-1}\right]^{\frac{1}{2}}{} - b \end{equation} (A1)

As shown in Fig. 6(b), the center-to-center distance of the nearest neighboring granules (s) can be described as follows:

  

\begin{equation} s = \sqrt{\frac{(b + l)^{2}}{3} + (t + a)^{2}} - \sqrt{\frac{a^{2} \cdot b^{2}}{a^{2} \cdot \mathit{cos}^{2}\,\theta + b^{2} \cdot \mathit{sin}^{2}\,\theta}} \end{equation} (A2)

  

\begin{equation} \mathit{cos}^{2}\,\theta = \frac{(b + l)^{2}}{(b + l)^{2} + 3(a + t)^{2}},\ \mathit{sin}^{2}\,\theta = \frac{3(a + t)^{2}}{(b + l)^{2} + 3(a + t)^{2}} \end{equation} (A3,A4)

Using the measured volume fraction from XRF and the granule dimensions from TEM, l, and s were calculated as shown in Table A1. When t_BaF2 is below 1 nm, the s value is smaller than l, indicating that tilt-vertical tunneling favorably occurs. When t_BaF2 is beyond 1 nm, the l value is smaller than s, and horizontal tunneling favorably occurs. Thus, the tendency shift of the t_BaF2 dependence of ρ at 1 nm is attributed to this neighboring particle correlation shift.

Fig. A1

(a) Top and (b) cross-sectional view of schematic lateral nanogranular model wherein the nanogranule confined at the quasi-hexagonal close-packed lattice.

Table A1 The structural parameters and characteristics of films produced with different P_BaF2.