Raman modes and dielectric relaxation properties of epitaxial BaBiO₃ thin films

Our main interest towards BaBiO₃ epitaxial thin films is how their physical properties would differ as orientation as well as strain vary. For this purpose, we first resorted to light scattering measurements of the thin films because the Raman modes of BaBiO₃ would be sensitive to strain variation. Structural distortion, which connects the ideal cubic structure to the observed distorted structure, can be identified as a symmetry breaking element of displacive nature, either polar or non-polar, leading to distinct electromagnetic responses. For BaBiO₃ the most distorted structure is monoclinic with symmetry group P2₁/n; for the transition from ideal cubic $Fm\bar{3}m$ to monoclinic P2₁/n, two symmetry modes, ${{\rm{\Gamma }}}^{4+}$ and ${X}^{3+},$ are involved [9]. ${{\rm{\Gamma }}}^{4+}$ corresponds to out-of-phase tilting along the pseudo-cubic [110] axis while ${X}^{3+}$ is the mode responsible for in-phase tilting along the pseudo-cubic [010] axis. Both of these modes are non-polar, and the distortion can be understood in terms of the octahedral tilting only. At room temperature BaBiO₃ belongs to another monoclinic I2/m (a⁻a⁻c⁰) with out-of-phase tilting along the [110] direction; in the monoclinic phase, Raman active optical phonon modes are ${{\rm{\Gamma }}}_{{\rm{Raman}}}=7{{\rm{A}}}_{{\rm{g}}}\oplus 5{{\rm{B}}}_{{\rm{g}}}$ [18, 19].

Figure 3 shows Raman scattering spectra for the films on MgO (100) and SrTiO₃ (001) substrates. With the help of the reported optical data [20], we are able to assign the peaks in the Raman spectra as the OT modes (Bi–O bending and Bi–O stretching) and the OB (BiO₆ breathing) mode from low to high energy values. Specifically, the strongest Raman peak at 565 cm⁻¹ is due to the BiO₆ breathing with A_g symmetry [21], the peak at 492 cm⁻¹ is assigned to the Bi–O stretching mode, and the one around 300 cm⁻¹ is the superposition of the multiple Bi–O bending modes as designated in figure 3(a). 2nd order peak also appears around 1130 cm⁻¹. For the multiply superposed bond bending peak in the vicinity of 300 cm⁻¹ whose details are displayed in figures 3(b) and (c), the spectral line at 298 cm⁻¹ would be due to the out-of-phase Bi–O bending with A_g symmetry while the mode at wave number 314 cm⁻¹ may be assigned to the A_g symmetric in-plane mixed vibrations of Bi and O atoms. The peaks at 342 cm⁻¹ and 347 cm⁻¹ are due to the out-of-phase bond bending with B_g symmetry. From figure 3(b) for the relaxed film on SrTiO₃ (001), it is of interest to note that the A_g symmetric in-plane vibrational mode at 314 cm⁻¹ has a higher intensity and a narrower width than the out-of-phase bending mode at 298cm⁻¹. In addition, a broad spectral line with B_g symmetry appears at 342 cm⁻¹. It is also noted from figure 3(c) that the strained film on MgO (100) gives rise to a narrower linewidth and a higher intensity at 299 cm⁻¹ than at 314 cm⁻¹ and only a very small B_g mode at 347cm⁻¹ is seen. These results would imply that in-plane bond bending is restricted in strained films and thus a shortened phonon lifetime and a broader linewidth would follow. Again it is recalled that BaBiO₃ with lattice constant a = 0.4338 nm has 3% lattice mismatch with MgO (a = 0.421 nm) whereas 10% with SrTiO₃ (a = 0.395 nm). In particular, a large mismatch between BaBiO₃ and SrTiO₃ would cause relaxation; indeed, BaBiO₃ films grown on SrTiO₃ (001) are fully relaxed while the films on MgO (100) are strained. It is mentioned in passing that Inumaru et al claimed a partial suppression of the OT modes for BaBiO₃ films grown on MgO substrates [13], and, in contrast, local breathing and tilting distortions were reported even for superconducting Ba_1−xK_xBiO₃ and BaPb_1−xBi_xO₃ films on SrTiO₃ substrates [22].

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To monitor the changes in the tilt pattern of BaBiO₃ in association with the structural tranistion around 140 K, Raman scattering measurements were performed, as a function of temperature ranging from 50 K to 300 K, on the films on SrTiO₃ substrates with (001) and (110) orientations. The broad peak in the vicinity of 300 cm⁻¹ is analyzed in terms of the superposition of multiple Lorentzian lines and the results are displayed at various temperatures in figures 4(a) and (b). As can be seen from the figures, there is a significant change in the superposition contents of the modes below and above the transition temperature. The structural transition from monoclinic P2₁/n (a⁻a⁻c⁺) to monoclinic I2/m (a⁻a⁻c⁰) occurring at temperature 140 K upon raising temperature is known to be an octahedral tilt-driven continuous transition [7]. From figures 4(a) and (b), it is immediately obvious that the vibrational modes of A_g symmetric 306 cm⁻¹ and B_g symmetric 352 cm⁻¹ appear only in the low temperature phase; in-phase rotation of the BiO₆ octahedra around the c-axis would induce such modes. In figure 4(c), there is not too much change in the energy shift for the observed Raman modes except for A_g symmetric in-plane vibrational mode at 314 cm⁻¹ which shows hardening on cooling. The peak intensity of the A_g symmetric 306 cm⁻¹ mode increases with lowering temperature for the film grown on SrTiO₃ (110) substrate as can be seen from figure 4(d). The intensity of all other modes decreases with decreasing temperature. The spectral width of a line in the Raman spectrum is a measure of the phonon lifetime. With the in-phase rotation around c-axis at transition temperature 140 K, the width of the B_g modes at 342 cm⁻¹ and 352 cm⁻¹ broadens with decreasing temperature. It is also seen from figure 4(d) that there is a difference in the spectral features depending on the orientation; the film with (001) orientation shows low scattering intensity for the 314 cm⁻¹ mode compared to the film with (110) orientation in the low temperature phase. It may be recalled that a BaBiO₃ film grown with (001) orientation was reported to have a tetragonal structure [14]; an elongation in the c-axis would release the out-of-phase octahedral tilting along the [110] axis, corresponding to the in-plane vibrational mode at 314 cm⁻¹, and this could be a reason for the lower intensity of the 314 cm⁻¹ mode for the film on SrTiO₃ (001) compare to the film with (110) orientation.

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We next turn to dielectric measurements of BaBiO₃ films. BaBiO₃ is considered to be a semiconducting material because it has a band gap arising from the CDW [10, 23]; using the 2-probe method, we measured the surface resistance of a BaBiO₃ film and found it to be 16 MΩ at 300 K. In general, disorder inevitable even in crystalline samples causes the occurrence of localized states, and electrons could be trapped in the localized states. Random thermal fluctuations would then give electrons enough energy to get out of a localized state and move to a near one by hopping, that is, electrons move, for a brief amount of time, before relaxing into another localized state. For BaBiO₃, conduction would be possible due to hopping of 6 s electrons on the localized states and this behavior could lead to relaxation phenomena. Furthermore, charge disproportionation in two adjacent B-site Bi ions in distorted BaBiO₃ might give rise to a local electric dipole that can absorb electromagnetic energy depending on measuring field frequency and temperature.

We grew BaBiO₃ films on conducting substrates, 5 wt% Niobium doped SrTiO₃ in (001) and (110) orientations, and out-of-plane dielectric measurements were taken in a vertical capacitor arrangement as sketched in figure 5(a). Top electrodes were deposited with gold in a thermal evaporation chamber. For quantitative analyses with regard to the orientation dependence, we covert the raw data to complex dielectric constant of intrinsic nature without geometric dependence of measuring devices. In the vertical configuration as in the present case, it is straightforward to obtain ε'; real part and ε''; imaginary part of the complex dielectric constant from the raw data [24]:

$$\begin{eqnarray*}&&\varepsilon ^{\prime} =\displaystyle \frac{{C}_{x}d}{{\varepsilon }_{o}A}\end{eqnarray*}$$

$$\begin{eqnarray*}&&\varepsilon ^{\prime\prime} =\,\varepsilon ^{\prime} \tan \,\delta \end{eqnarray*}$$

where C_x is the measured capacitance value for material, $\tan \,\delta$ is the loss tangent, d is the thickness of a film, A is the area of the electrode, and ${\varepsilon }_{o}$ is the permittivity of free space.

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For 200 nm thick BaBiO₃ films on Nb-doped SrTiO₃ (001) and (110), ε' and ε'', obtained from the data measured at applied signal frequencies of 50 and 500 Hz, are plotted against temperature in figures 5(b)–(e). The structural transition of BaBiO₃ from monoclinic-I (P2₁/n) to monoclinic-II (I2/m), occurring around 140 K on increasing temperature, is associated with a large abrupt change in dielectric constant ε' from a low value to a large value [7].

In figures 6(a) and (c) imaginary part of dielectric constant ε'' is plotted against temperature for BaBiO₃ film on Nb-doped SrTiO₃ (001) measured at frequencies of 50 and 500 Hz, respectively, with a fitting curve. Only one broad relaxation peak is observed here, and the fitting curve is from a Gaussian distribution of relaxation times. In contrast, for a 200 nm thick film on Nb-doped SrTiO₃ (110), ε'' again obtained at measuring frequencies of 50 and 500 Hz, behave quite differently from the case of the (001) orientation as can be seen from figures 6(b) and (d). The imaginary part ε'' in particular can be considered to consist of two broad relaxation peaks, one peak around 140 K and another one around 180 K. The fitting curves in figures 6(b) and (d) are again from the Gaussian distribution of relaxation times. In BaBiO₃, Bi 6s and O 2p orbitals form an electronic band near the Fermi level, i.e., the conduction band. Lattice distortions in the perovskite structure would modify the conduction properties of BaBiO₃; the breathing distortion opens the charge gap while the tilting distortion causes an overall band narrowing [25]. To hybridize with Bi 6s orbitals, only O 2p_δ orbitals with A_1g symmetry are allowed. For low energy electronic excitations in BaBiO₃, Khazraie et al estimated effective hopping integrals for nearest neighbor and next nearest neighbor using a single orbital tight binding model [26]. They showed that with the breathing distortion of $0.1\dot{\,A}$ and no external electric field, the size of the hopping integral t₁ between nearest neighbors involving oxygen atoms with A_1g symmetry is four times larger than that of the next nearest neighbor hopping integral t₂ between two Bi ions sit at a distance $\sqrt{2}a$ as shown in figure 6(e). The difference in the relaxation behaviors of BaBiO₃ films with orientations (001) and (110) may be due to the difference in the relative contributions of hopping integrals, i.e., t₁ alone vs both t₁ and t₂ depending on the direction of an applied electric field. When an applied electric field is parallel to the [001] axis, only t₁ contributes whereas both hopping integrals, t₁ and t₂, contribute when E // [110], leading to two relaxation peaks as observed experimentally. It is also noted that the relaxation peak height due to t₂ in figures 6(b) and (d) is about 1/4 less than that due to nearest neighbor hoping t₁; in fact, this quantitative difference was already demonstrated by the calculation in 26.

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