Evidence for power-law frequency dependence of intrinsic dielectric response in the $\mathrm{Ca}{\mathrm{Cu}}_3{\mathrm{Ti}}_4{\mathrm{O}}_{12}$

We investigated the dielectric response of $\mathrm{Ca}{\mathrm{Cu}}_3{\mathrm{Ti}}_4{\mathrm{O}}_{12}$ (CCTO) thin films grown epitaxially on $\mathrm{La}\mathrm{Al}{\mathrm{O}}_3$ (001) substrates by pulsed laser deposition. The dielectric response of the films was found to be strongly dominated by a power law in frequency, typical of materials with localized hopping charge carriers, in contrast to the Debye-like response of the bulk material. The film conductivity decreases with annealing in oxygen, and it suggests that oxygen deficit is a cause of the relatively high film conductivity. With increase of the oxygen content, the room temperature frequency response of the CCTO thin films changes from the response indicating the presence of some relatively low conducting capacitive layers to purely power law, and then toward a frequency independent response with a relative dielectric constant ${\epsilon }^{\prime }\sim {10}^2$. The film conductance and dielectric response decrease upon decrease of the temperature, with dielectric response being dominated by the power-law frequency dependence. Below $\sim 80\mathrm{K}$, the dielectric response of the films is frequency independent with ${\epsilon }^{\prime }$ close to ${10}^2$. The results provide another piece of evidence for an extrinsic, Maxwell-Wagner type, origin of the colossal dielectric response of the bulk CCTO material, connected with electrical inhomogeneity of the bulk material.

Figure 1

Typical x-ray diffraction $\theta \text{‐}2\theta$ pattern of an epitaxial CCTO film on (001) $\mathrm{La}\mathrm{Al}{\mathrm{O}}_3$ substrate studied in the present work.

Figure 2

Layout of an interdigital capacitor used to measure the dielectric and conducting properties of CCTO films. Parameters are defined in the text.

Figure 3

(Color online) Room temperature frequency response of three IDE capacitors on the CCTO films listed in Table . Symbols are the experimental data, solid and dashed curves are fittings to the models shown in the lower right panel with ac conductance $G_{\mathrm{ac}}\left(f\right)=G_f{f}^s$ and capacitance $C\left(f\right)=C_{\infty }+{\left(2\pi \right)}^{-1}{G}_f\tan (\pi s∕2)f^{(s-1)}$ as follows from the universal dielectric response law (Ref. 14). $R_s$ is the parasitic resistance of the capacitor electrodes. Parameters of the fits are shown in corresponding panels. The diamonds show the dc conductance of the capacitors $G(f=0)$.

Figure 4

Temperature dependence of dielectric response for CCTO films listed in Table between $80\mathrm{K}$ and $300\mathrm{K}$. ${\epsilon }^{\prime }$ is the real part of the relative permittivity shown for four frequencies (open symbols) $100\mathrm{Hz}$, $1000\mathrm{Hz}$, $10\mathrm{kHz}$, and $100\mathrm{kHz}$. $\sigma$ is the film conductivity at a frequency of $100\mathrm{Hz}$.

Figure 5

The permittivity temperature dependence data of Fig. 4 are replotted here for the three most conducting samples after subtraction of ${\epsilon }_{80\mathrm{K}}^{\prime }$. Only data points with significant signal-to-noise ratio are shown. In the case of sample 1, the value of ${\epsilon }_{80\mathrm{K}}^{\prime }$ for $1000\mathrm{Hz}$ was used to plot the curve for $100\mathrm{Hz}$.

Figure 6

(a) Arrhenius plots for $100\mathrm{Hz}$ conductivity of the four most conducting samples listed in Table . Dashed lines show the parts of the curves that can be approximately linearized by the Arrhenius representation. The numbers are activation energies. (b) Conductivity at $100\mathrm{Hz}$ of the four most conducting samples of Table shown in the representation linearizing the law $\sigma \sim \exp (-B∕T^{1∕4})$. Piecewise, the conductivity data for samples 2–4 can be better linearized in this representation than in the Arrhenius representation. Numbers are the values of the parameter $B$ in units of ${\mathrm{K}}^{1∕4}$.

Figure 7

(a) Simulated electron diffraction pattern corresponding to ideal, twin-free CCTO lattice with symmetry group $Im\overline{3}$; the spot diameters are proportional to their intensity. (b) Small-area diffraction pattern taken from the CCTO film. (c) TEM dark field image of a cross section of a CCTO film on LAO; the image is taken using the (013) spot of the film pattern. (d) HRTEM image of the film-substrate interface of a sample annealed $15\mathrm{h}$ at $695°\mathrm{C}$.