Mechanically exfoliated low-layered [Ca₂CoO₃]_0.62[CoO₂]: A single-crystalline p-type transparent conducting oxide Open Access

Transparent conducting oxides (TCOs) show good electrical conductivity and optical transparency in the visible range and are widely adopted as components of optoelectronic devices, such as liquid crystal displays and touch screens.^1–3 Among such TCOs, n-type materials, including indium oxides,^4–8 zinc oxides,⁹ tin oxides,¹⁰ and titanium oxides,¹¹ are known as highly efficient TCOs and have been often used as those components. On the other hand, p-type TCOs are less used due to their low carrier mobility,^12,13 although various p-type TCOs, such as NiO,¹⁴ Cr₂O₃,¹⁵ SrCu₂O₂,¹⁶ LaCuOS,¹⁷ delafossite series CuMO₂,^18–23 V₂O₃,^24,25 and perovskite oxides,^26,27 have been studied so far. The development of p-type TCOs including computational approach²⁸ is, thus, expected for future optoelectronic applications such as the growing field of the transparent semiconductors in which the p–n junction is essential.^29–31 

Recently, misfit layered cobalt oxide [Ca₂CoO₃]_0.62[CoO₂] thin films have been proposed as a peculiar class of p-type efficient TCOs. As shown in Fig. 1(a), the crystal structure of this material is two-dimensional, consisting of alternating rock salt-type Ca₂CoO₃ block layers and CdI₂-type triangular-lattice CoO₂ conducting layers stacking along the c axis.^32–34 Interestingly, these two layers possess different lattice parameters along the b-axis direction to establish incommensurate nature as is also seen in layered chalcogenide materials.³⁵ Thus, $γ = 0.62$ in [Ca₂CoO₃] $γ$[CoO₂] is approximate value for the incommensurate structure, and this material is often called Ca₃Co₄O₉ as the approximate chemical formula. [Ca₂CoO₃]_0.62[CoO₂] has intensively been studied as an promising oxide thermoelectrics because of its large positive Seebeck coefficient of $S ≈ 130$ μV/K near room temperature owing to the entangled spin and orbital entropy of correlated Co 3d electrons, coexisting with the metallic resistivity.^36–40 

For the promising aspect of [Ca₂CoO₃]_0.62[CoO₂] for TCOs, Aksit et al. and Fu et al. have reported the optical transmittance and electrical transport measurements on the transparent polycrystalline⁴¹ and c-axis oriented⁴² thin films, respectively. The figure of merit (FOM) for TCOs has been evaluated as $− 1 / ( R sheet × ln T opt )$⁠, where $R sheet$ is the sheet resistance and $T opt$ is the transmittance averaged for the specific photon energies in the visible range.^27,43 Although the evaluated values of FOM (151 M $Ω − 1$ for the polycrystalline film⁴¹ and 988 M $Ω − 1$ for the c-axis oriented film⁴²) are still less efficient, these previous studies suggest a potential layered optoelectronic oxides for the p-type TCOs.

In this paper, we attempt to fabricate transparent low-layered [Ca₂CoO₃]_0.62[CoO₂] single crystals by utilizing a mechanical tape-peeling method. This simple peeling method may have a certain merit for the layered crystals to keep high carriers mobility.⁴⁴ In this method, we have fabricated the transparent low-layered single crystals on the glass substrate with typical thickness of several orders of hundred nanometers. Through the transmittance and sheet resistance measurements, we find that the FOM of the present low-layered crystals is higher than the values reported in the previous studies. These results indicate that the present low-layered [Ca₂CoO₃]_0.62[CoO₂] is not only a potential p-type TCO but also a unique class of transparent thermoelectric oxides with multi-functional properties.

We have first grown single-crystalline samples of [Ca₂CoO₃]_0.62[CoO₂] by using a flux method.^46–48 The low-layered single crystals were fabricated by utilizing a tape peeling method. The single crystal was first sandwiched by the peeling tapes to remove the irregular surfaces of the crystal. Then, as illustrated in Figs. 1(b) and 1(c), the cleaved crystal was fixed on the glass substrate by using a small amount of transparent adhesive bond and mechanically exfoliated by the tape peeling method. The transparent low-layered region was partly obtained in the single crystal as shown in Fig. 1(e). Figure 1(f) displays a side-view scanning-electron-microscope (SEM) image for small pieces of the exfoliated crystals, indicating that the crystal thickness is approximately less than 1 μm. The present fabrication of low-layered crystals is interesting because the layered coupling in [Ca₂CoO₃]_0.62[CoO₂] may have rather strong covalent nature in contrast to the weak interlayer coupling of van der Waals materials. Owing to the incommensurate layered structure of [Ca₂CoO₃]_0.62[CoO₂], the samples may become more exfoliative to realize such transparent low-layered crystals. Note that similar layered cobalt oxide Bi₂Sr₂Co₂O₈ could be exfoliated into nanosheets due to weak van der Waals interlayer coupling.^49–51 

The transmittance spectra were measured by using a USB module of a complementary metal-oxide semiconductor (CMOS) spectrometer equipped with an optical microscope. We evaluated the transmittance $T ( ω )$ as $T ( ω ) = I sample ( ω ) / I ref ( ω )$⁠, where $I sample ( ω )$ is the intensity spectrum for the low-layered crystal on the glass substrate and $I ref ( ω )$ is the reference spectrum for the glass substrate without samples. To consider the reflection at the interfaces, the absorbance was obtained as follows: The measured intensity $I sample$ is given as $I sample = I 0 ( 1 − R 1 ) ( 1 − R 2 ) e − α d$⁠, where I₀ is the intensity of incident light, R₁ and R₂ are the reflectance at the crystal–glass and the crystal–air interfaces, respectively, and α is the absorption coefficient of the crystal. Note that the multiple reflection is negligibly small. Also, the reference intensity $I ref$ is given as $I ref = I 0 ( 1 − R 3 )$⁠, where R₃ is the reflectance at the glass–air interface. The measured transmittance T is then given as $T = I sample / I ref = e − α d / γ$⁠, where $γ = 1 − R 3 ( 1 − R 1 ) ( 1 − R 2 )$⁠. According to Fresnel's equation, the interface reflection between the media α and β is calculated as $| ( n ̃ α − n ̃ β ) / ( n ̃ α + n ̃ β ) | 2$⁠, where $n ̃ α$ and $n ̃ β$ are the complex refraction indices of the media α and β, respectively. We used $n ̃ air = 1.0$ and $n ̃ glass = 1.5$⁠. The complex refraction index of the crystal $n ̃ crystal = n ( ω ) + i κ ( ω )$ is obtained from the Kramers–Kronig (KK) analysis,⁵² where $n ( ω )$ is the refractive index and $κ ( ω )$ is the extinction coefficient. The absorbance of the crystal is then calculated from the measured transmittance T as $A exp = α d log 10 e = − log 10 ( γ T )$⁠.

The sheet resistance $R sheet$ of the low-layered crystals was measured by using a conventional van der Pauw method. The excitation current of I = 10 μA was applied by a Keithley 6221 current source and the voltage was measured with a synchronized Keithley 2182A nanovoltmeter. These two instruments were operated in a built-in Delta mode to cancel the offset voltage. We used a closed refrigerator to evaluate the temperature dependence of the sheet resistance below room temperature.

Figure 2(a) depicts the transmittance spectra $T ( ω )$ of the low-layered [Ca₂CoO₃]_0.62[CoO₂] single crystals in the visible range. The inset of Fig. 2(a) shows the optical image of the measured sample and the measured area is indicated by the red rectangular. The measured low-layered region is yellow-colored transparent and the averaged transmittance in the visible range is about 0.3, indicating that thin low-layered crystal is fabricated in the present peeling process using single crystals.

To examine the sheet resistance of the low-layered transparent single crystals, we have prepared a rectangular-shaped low-layered sample by cutting the exfoliated crystal and made four electrical contacts at the corners by using a silver paint as shown in the inset of Fig. 3(a). The sheet resistance $R sheet$ is then measured by the conventional van der Pauw (vdP) method, and the obtained temperature dependence of $R sheet$ and the resistivity $ρ = R sheet × d$ are shown in Figs. 3(a) and 3(b), respectively. Note that the measured resistivity in the vdP configuration is given as the geometric mean of $ρ = ρ a ρ b$⁠, where ρ_i $( i = a , b )$ is the resistivity measured along i direction,⁵³ since this material exhibits slight in-plane transport anisotropy.⁵⁴ 

Overall behavior of the temperature dependence of the resistivity in the present low-layered crystals agrees well with the previous data;^55,56 near room temperature, a metallic resistivity of $ρ ≈ 4$ mΩ cm is achieved and a semiconducting temperature dependence is observed below 100 K owing to the carrier localization effect⁵⁷ or a pseudo-gap formation associated with the spin-density-wave ordering.⁵⁸ Thus, these results indicate that a single-crystalline transparent conducting oxide is well fabricated in the layered [Ca₂CoO₃]_0.62[CoO₂] with no significant damage in the peeling process. Note that the low-temperature behavior seems sample-dependent, which probably comes from extrinsic effects such as the oxygen defects.

Generally, the resistivity of metallic films depends on the thickness due to the surface scattering as discussed in the Fuchs–Sondheimer model.⁵⁹ In such case, the resistivity may show a linear dependence of $ρ = ρ 0 ( 1 + Λ / d )$⁠, where ρ₀ and Λ are the bulk-crystal resistivity and a characteristic length, respectively. The characteristic length Λ is comparable to a mean free path of carriers near surfaces. We then plot the resistivity measured at 300 K as a function of the inverse of the thickness, $1 / d$⁠, for the low-layered crystals in the inset of Fig. 3(b) and find no significant thickness dependence. This result is consistent with the fact that the mean free path of [Ca₂CoO₃]_0.62[CoO₂] is about 1 nm,⁵⁸ which is much smaller than the thickness of the low-layered crystals and indicates that the surface scattering is not dominant in the present case. On the other hand, a thickness-dependent metal–insulator transition has been observed in the nanosheets Bi₂Sr₂Co₂O_8,⁵⁰ implying a strong thickness dependence of the resistivity in the layered oxides. Also, interesting spin-related surface transport⁶⁰ and two-dimensional quantum confinement effect⁶¹ have been suggested for the resistive behavior in the metallic films. A more detailed consideration may be required as a future study along with further magneto-transport experiments on the thinner low-layered crystals.

Table I summarizes the optoelectronic properties and the FOM of transparent [Ca₂CoO₃]_0.62[CoO₂] in the present study and previous reports.^41,42 Owing to the single-crystalline nature, the resistivity is lower than those in the previous reports,^41,42,62 leading to large values of FOM. Note that the resistivity of the high-quality epitaxial films is comparable to that in the low-layered crystals⁵⁵ while the transmittance of the epitaxial films has not been evaluated. We also note that the FOM values slightly decrease with decreasing thickness: As mentioned previously, the measured transmittance is $T = e − α d / γ$⁠. Thus, using the conductivity $σ = 1 / ( R sheet d )$⁠, the FOM is given as $FOM = σ / ( α + 1 d ln γ )$⁠. Since σ and α are thickness-independent parameters, in principle, and γ is larger than unity, this equation may indicate that the FOM value decreases with decreasing d owing to the reflectance at the interfaces in the present devices. Nonetheless, the FOM value in the present study is the same order of those in high-performance p-type TCOs, such as CuCr_1−xMg_xO₂ (FOM $∼ 5000$ M $Ω − 1$⁠)²⁰ and La_2/3Sr_1/3VO₃ (FOM $∼ 7000$ M $Ω − 1$⁠).²⁷ We note that a doping effect, such as Bi substitution,⁵⁸ may be promising to further enhance the FOM in the low-layered [Ca₂CoO₃]_0.62[CoO₂]. Figure 4 represents the single logarithmic plot of the sheet conductance $1 / R sheet$ as a function of $T opt$⁠. In Fig. 4, we plot the room-temperature data for four low-layered single crystals as well as the data from an earlier study of the polycrystalline and the c-axis oriented films,^41,42 along with the calculated curves for several values of FOM. Indeed, the present low-layered crystals exhibit higher value of FOM compared to those in the previous study, indicating that the present peeling technique using single crystals is efficient certainly to realize high-performance TCOs.

To summarize, we have fabricated the transparent low-layered [Ca₂CoO₃]_0.62[CoO₂] single crystals on the glass substrate by utilizing the mechanical peeling method. From the results of the optical and transport measurements, we find that the figure of merit in the present crystals is higher than the values reported in the previous studies on the polycrystalline and c-axis oriented films owing to the lower resistivity in the single-crystalline samples. Since [Ca₂CoO₃]_0.62[CoO₂] has been studied as a potential oxide thermoelectrics, the present study offers a unique class of transparent thermoelectric oxides with multi-functional properties.^63,64 Also, the present low-layered crystals belonging to the strongly correlated electrons system may provide a fascinating playground to investigate the nature of correlated electrons confined in low dimension.

We appreciate K. Tanabe for providing us with the reflectivity data of [Ca₂CoO₃]_0.62[CoO₂] single crystals. This work was supported by JSPS KAKENHI (Grant No. 22H01166) and Research Foundation for the Electrotechnology of Chubu (REFEC, No. R-04102).

The authors have no conflicts to disclose.

Reiji Okada: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal); Writing – review & editing (equal). Hiroto Isomura: Data curation (equal); Formal analysis (equal); Methodology (equal). Yoshiki J. Sato: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Project administration (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal). Ryuji Okazaki: Conceptualization (equal); Funding acquisition (equal); Investigation (equal); Project administration (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Masayuki Inoue: Data curation (equal); Formal analysis (equal); Methodology (equal). Shinya Yoshioka: Data curation (equal); Formal analysis (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author (R. Okazaki) upon reasonable request.