Engineering thermoelectric and mechanical properties by nanoporosity in calcium cobaltate films from reactions of Ca(OH)₂/Co₃O₄ multilayers

Abstract

Controlling nanoporosity to favorably alter multiple properties in layered crystalline inorganic thin films is a challenge. Here, we demonstrate that the thermoelectric and mechanical properties of Ca₃Co₄O₉ films can be engineered through nanoporosity control by annealing multiple Ca(OH)₂/Co₃O₄ reactant bilayers with characteristic bilayer thicknesses (b_t). Our results show that doubling b_t, e.g., from 12 to 26 nm, more than triples the average pore size from ∼120 nm to ∼400 nm and increases the pore fraction from 3% to 17.1%. The higher porosity film exhibits not only a 50% higher electrical conductivity of σ ∼ 90 S cm⁻¹ and a high Seebeck coefficient of α ∼ 135 μV K⁻¹, but also a thermal conductivity as low as κ ∼ 0.87 W m⁻¹ K⁻¹. The nanoporous Ca₃Co₄O₉ films exhibit greater mechanical compliance and resilience to bending than the bulk. These results indicate that annealing reactant multilayers with controlled thicknesses is an attractive way to engineer nanoporosity and realize mechanically flexible oxide-based thermoelectric materials.

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1. Introduction

The rapid development of autonomous, portable and wearable devices and sensors has sparked a great deal of interest in self-sustaining energy sources to replace batteries that are typically limited by shape constraints, periodic recharging and replacement.^1,2 Harvesting electricity from heat using devices made from mechanically flexible thermoelectric materials is promising for such applications.^3–6 Besides a high thermoelectric figure of merit ZT = α²σT/κ (α is the Seebeck coefficient, σ and κ the electrical and thermal conductivities, respectively, and T the absolute temperature^7–9) for efficient energy conversion, properties such as high mechanical flexibility and toughness are key requirements.

Conducting polymer-based organic thermoelectric materials are mechanically flexible and exhibit ZT values as high as 0.42,^10–17 but are unsuitable for higher than near-room-temperature applications. Purely inorganic thermoelectrics¹⁸ are usually brittle. Integrating nanograined films or nanocrystal assemblies of inorganic thermoelectrics, e.g., Bi_2−xSb_xTe₃, on flexible substrates that can withstand moderately high temperatures addresses these challenges to some extent, and yield α²σ values up to 0.2 mW m⁻¹ K⁻² at ∼200 °C.^19,20 Semiconductors with extraordinary metal-like ductility, e.g., Ag₂S, and Ag₂Se also hold promise as free-standing thermoelectric materials that obviate flexible substrates.^21–23

Oxide-based thermoelectric films on layered substrates such as mica offer greater stability at even higher temperatures and can become viable alternatives if high α and σ, are achieved together with high mechanical flexibility.^24,25 Calcium cobaltate Ca₃Co₄O₉ is an attractive p-type thermoelectric that exhibits inherently high α and high σ due to its layered crystal structure.^26–30 The thermoelectric properties of layered cobaltates can be improved by nanostructuring, such as fabricating a high-quality single-phase,^31,32 nanostructuring approaches,³³ elemental doping,³⁴ growing textured films with c-axis orientation.³⁵ However, the thermal conductivity was normally increased with the improving electrical conductivity.^36,37 Introducing nanoscale with dimensions mainly in the ranges of phonon mean free paths is a possible approach to reduce thermal conductivity without inhibiting electrical conductivity due to phonon mean free paths are typically significantly higher than electronic mean free paths. The textured nanograins and faceted nanopores not only offer additional means to lower the κ,^38,39 but also alleviate the brittleness.^40,41 Flexible porous nanograined Ca₃Co₄O₉ films obtained by annealing CaO/CoO reactant multilayers exhibit power factors as high a 0.23 mW m⁻¹ K⁻² at room temperature.⁴⁰ To further increase the porosity of nanoporous Ca₃Co₄O₉ films retaining α and σ, it might be an effective way to further reduce κ and improve flexibility.

Here, we demonstrate that nanoporosity characteristics in Ca₃Co₄O₉ films can be controlled by adjusting the reactant bilayer thickness in multilayer stacks. The porosities change from 11.2 to 17.1%. The nanoporous films show high σ with a narrow range from 80 to 95 S cm⁻¹ and high α of ∼130 to ∼135 μV K⁻¹, which are close to the values.^42–44 The film with the highest porosity 17.1% has the lowest κ (∼0.87 W m⁻¹ K⁻¹). The nanoporous Ca₃Co₄O₉ films exhibit greater mechanical compliance and resilience to bending than the bulk. Our findings showing pore engineering of layered-ceramics is attractive for realizing mechanically flexible thermoelectrics.

2. Experimental section

Nanoporous Ca₃Co₄O₉ thin films were synthesized by annealing Ca(OH)₂/Co₃O₄ multilayers on muscovite mica(00l) substrates. CaO/Co₃O₄ multilayers were deposited at 600 °C by reactive RF-magnetron sputtering from Ca and Co targets with a 2 mTorr plasma of a 0.5% O₂/99.5% Ar gas mixture⁴⁰. Ambient air-exposure of the CaO/Co₃O₄ multilayers for one month resulted in Ca(OH)₂/Co₃O₄ multilayers via CaO hydration into Ca(OH)₂.⁴⁵ Subsequent annealing Ca(OH)₂/Co₃O₄ multilayers at 700 °C for 2 hours in air led to nanoporous Ca₃Co₄O₉ formation. We prepared five sets of multilayers with different Ca(OH)₂/Co₃O₄ bilayer thicknesses, b_t. The deposition times for CaO and Co₃O₄ were varied while keeping the total nominal multilayer thickness constant at ∼140 nm. The individual thicknesses of Ca(OH)₂ and Co₃O₄ layers in each multilayer film were identical, i.e., b_t/2. Thus, altering the bilayer thickness in the 12 ≤ b_t ≤ 50 nm range is equivalent to varying the number of bilayers b_n in the 21 ≥ b_n ≥ 5 range.

Phase identification was carried out by X-ray diffractometry (XRD) using a PANalytical X'Pert PRO instrument with monochromatic Cu Kα radiation (λ = 1.5406 Å) and a Ni filter. X-ray reflectivity (XRR) measurements were carried out in a PANalytical Empyrean diffractometer equipped with a copper Cu Kα source with a hybrid mirror on the incidence beam path, a triple-axis Ge 220 analyzer on the diffracted beam path, and a PIXcel3D detector operated in open detection mode. The XRR data were fitted using the X'Pert reflectivity program.

Scanning electron microscopy (SEM) and energy dispersive X-ray (EDX) spectroscopy were carried out in a LEO Gemini 1550 Zeiss instrument operated at 10 kV to characterize film morphology and composition. The surface porosity fraction was determined by analyses of SEM micrographs using the Java version of image J software^46,47. Most of the nanopores were hexagonal in shape. The average nanopore sizes were estimated from the nanopore area with an uncertainty of 20%, by assuming all the pores to be regular hexagons. The average nanopore size is equal to L + 2L cos 60° where L is hexagon side length. Transmission electron microscopy (TEM) was carried out in a FEI Tecnai G2 TF20 UT instrument operated at 200 kV on multilayer cross-sections prepared by face-to-face gluing of two sample pieces and mounting them on a Ti grid. The samples were mechanically polished down to 50 μm and ion-milled in a Gatan system with 2–5 kV Ar⁺ beams incident at 5°.

Electrical conductivity σ was determined from the sheet resistance measured with a four-point probe Jandel RM3000 station and the film thickness determined from cross-sectional TEM images. Seebeck coefficient α was determined from the slope of the temperature gradient–voltage characteristics measured in a homemade Seebeck measurement setup system equipped with two K-type thermocouples placed at the same position as two Cu electrodes, a Keithley 2001 multimeter, two Peltier elements acting as temperature controller, and two thermometers^45,48.

Thermal conductivity of the annealed Ca₃Co₄O₉ film-on-mica samples was determined by non-contact scanning thermal microscopy (SThM) described elsewhere^49–52. This technique utilizes a Joule-heated 5 μm-diameter Wollaston wire probe, whose thermal resistance was measured in air at 100 nm above the sample surface based on temperature-induced changes in the electrical resistance of the probe and the dissipated Joule heating power. For each film, we measured thermal resistance at three different locations on the sample surface. Thermal conductivity was determined by fitting the thermal resistance data with a 3D finite element model (3DFEM) of the probe-to-sample surface heat transfer assuming isotropic thermal properties for the films and the substrate.

Mechanical flexibility was evaluated by estimating the elastic moduli of the films by surface Brillouin scattering (SBS) spectroscopy and measuring bending-induced relative changes in electrical resistance. SBS spectra were collected by using a JSR Scientific Instruments six-pass high-contrast Fabry–Perot interferometer equipped with a 532.18 nm Verdi V2 DPSS green laser probe. Surface Rayleigh and Sezawa wave velocities were obtained by using V = (λ₀Δf)/(2 sin θ_s), where λ₀ is the laser wavelength, Δf the Brillouin frequency shift, and θ_s the scattering angle.⁵³ For the bending tests, we measured the normalized electrical resistance change ΔR/R₀ for different bending radii and cycles, where the initial resistance R₀ includes contact resistances. A constant resistance during bending corresponds to ΔR/R₀ = 0 and indicates good mechanical flexibility and retention of electrical properties.

3. Results and discussion

X-ray diffractograms acquired immediately after deposition for all b_t values investigated show 111 and 222 Bragg reflections from CaO besides those from the mica substrate (Fig. 1a). The 400 diffraction peaks reflected from Co₃O₄ is overwhelmed by a stronger 00l reflection from the mica substrate (Fig. 1a) but is observable in diffractograms from as-deposited films on sapphire (Fig. 1b). Films on sapphire also show a weak 111 peak from CoO. The CaO and Co₃O₄ peaks intensities, normalized to that of the 004 mica substrate reflection and sapphire reflection, increase with increasing b_t (Fig. 1c).

Fig. 1 X-ray diffractograms from as-deposited CaO/Co₃O₄ multilayers with different bilayer thicknesses b_t, on (a) mica (00l), and (b) sapphire (006) substrates. (c) CaO and Co₃O₄ peak intensities normalized with the intensity of the corresponding substrate peak, plotted as a function of b_t.

Air-exposure of the as-deposited multilayers growing on mica and sapphire leads to the diminution and eventual disappearance of the CaO 111 and 222 peaks (see Fig. 2a and b). Multilayers on sapphire also show a similar behaviour besides revealing a concomitant emergence of the Ca(OH)₂ 001 peak. This peak is not observable in diffractograms from films on mica due to substrate peak overlap. These results are indicative of the conversion of CaO to Ca(OH)₂ through ambient moisture uptake.⁴⁵ We note that the intensities of the Ca(OH)₂ and Co₃O₄ peaks increase with increasing b_t, the intensity of Ca(OH)₂ is not the highest when the b_t is 50 nm (Fig. 2c).

Fig. 2 X-ray diffractograms from Ca(OH)₂/Co₃O₄ multilayers formed by air-exposure of CaO/Co₃O₄ multilayers with different bilayer thicknesses between 12 ≤ b_t ≤ 50 nm on (a) mica (00l) and (b) sapphire (006) substrates. (c) Ca(OH)₂ and Co₃O₄ peak intensities normalized to that of the 006 peak from the sapphire substrate, plotted as a function of b_t.

Air-exposed CaO/Co₃O₄ multilayers specified by low b_t (e.g., ∼12 nm) consist of equiaxed grains of Ca(OH)₂ and Co₃O₄ without any discernible interfaces (Fig. 3a). EDX spectral maps of Ca and Co indicate that Ca(OH)₂ and Co₃O₄ are interspersed across individual layers (Fig. 3a inset). This result is consistent with Co₃O₄ layers comprised of discontinuous grains that facilitate moisture intake and transport, as suggested in our recent work.⁴⁵ Air-exposed multilayers with b_t = 16 nm exhibit more distinct Ca(OH)₂/Co₃O₄ interfaces (Fig. 3b). The Ca-containing layers that appear brighter due to a higher Z-contrast are about 81% thicker than the Co₃O₄ layers, consistent with a 95.2% unit cell volume expansion caused by the CaO → Ca(OH)₂ conversion during air-exposure. For b_t > 16 nm, TEM images show distinct Co- and Ca-containing layers, but with a greater interface roughness that increases with b_t. Such interface roughening is attributable to the higher volume Ca(OH)₂ grains encroaching into the nearly unchanged adjacent Co₃O₄ layers. For b_t = 50 nm, the thickness of Ca(OH)₂ layer in top larger than that in bottle near mica, which may be due to the low hydration reactions by preventing of thicker Co₃O₄ layers and lead to the low intensity of Ca(OH)₂ 001 in Fig. 2c. SAED patterns indicate increased in-plane grain texturing with increasing b_t (see Fig. 3c and d). EDX spectral maps from air-exposed films with higher b_t show distinct Co-containing layers, in contrast to the uniform distribution of Ca, indicating Ca diffusion (see ESI Fig. S1†). Our results indicate that the bilayer thickness needs to be greater than a critical value of b_t > 12 nm to form layers structure with sharp interfaces.

Fig. 3 (a and b) Cross-sectional bright-field TEM images and (c and d) selected-area electron diffraction (SAED) patterns from Ca(OH)₂/Co₃O₄ multilayers with different bilayer thicknesses b_t.

Otherwise, EDS maps from multilayers with b_t = 16 nm show clear Co layers and almost uniform distribution Ca elements in multilayers (see ESI Fig. S1a†).

X-ray diffractograms show that annealing the Ca(OH)₂/Co₃O₄ multilayers leads to Ca₃Co₄O₉ formation through a reaction between the Co₃O₄ and Ca(OH)₂ layers (Fig. 4a). The exclusive presence of multiple 00l peak reflections of Ca₃Co₄O₉ indicate textured basal planes oriented parallel to the substrate surface. The Ca₃Co₄O₉ grain size is largest for films specified by b_t = 22 nm, as indicated by the narrowest width of the Ca₃Co₄O₉ 002 reflection.

Fig. 4 (a) X-ray diffractograms showing Ca₃Co₄O₉ formation on mica (00l) substrate by annealing Ca(OH)₂/Co₃O₄ multilayers with different bilayer thicknesses in the 12 ≤ b_t ≤ 50 nm range. (b) Ca₃Co₄O₉ 001 and 002 peak intensities normalized with the intensity of the corresponding substrate peaks, plotted as a function of b_t.

Surfaces of the annealed films exhibit faceted intergranular nanopores (see Fig. 5). Films with the smallest b_t in our studies reveal a relatively rough surface, probably due to the edge-on orientation of some platelet-shaped grains on the surface (see Fig. 5a). In contrast, annealed films with b_t ≥ 16 nm exhibit smoother surfaces, with faceted nanopores between hexagonal terraces and plate-shaped grains (Fig. 5b–e). The average pore size increases monotonically from around 120 to 400 nm with increasing b_t from 12 nm to 50 nm (see Fig. 5f). The porosity fraction increases with b_t from 3.7% to 17.1% for 12 ≤ b_t ≤ 26 nm but drops to 13.4% for b_t = 50 nm (Fig. 5f).

Fig. 5 (a–e) SEM images from annealed Ca(OH)₂/Co₃O₄ multilayers with 12 ≤ b_t ≤ 50 nm grown on mica (00l) substrates. (f) Surface porosity fraction determined from SEM image analyses.

Cross-sectional TEM micrographs of films obtained by annealing Ca(OH)₂/Co₃O₄ multilayers with 12 ≤ b_t ≤ 50 nm created from CaO/Co₃O₄ multilayers (Fig. 6a–e) reveal a polycrystalline Ca₃Co₄O₉ layer separated from the substrate by an amorphous glass layer.⁴⁰ Lattice images for the Ca₃Co₄O₉ layer and SAED patterns (Fig. 6f–j) confirm that the (001) basal planes are oriented parallel to the film surface, corroborating our XRD and SEM results. The in-plane/out-of-plane aspect ratio of the pores is about four for the film with b_t = 50 nm (Fig. 6e). This observation is consistent with the SEM results and our recent work⁴⁵ indicating that oriented nanopore formation arises from basal plane removal driven by local densification of textured Ca₃Co₄O₉. For all b_t values except b_t = 50 nm, we observe nanopores spanning across the Ca₃Co₄O₉ layers and microporous gaps at the Ca₃Co₄O₉ – amorphous layer interface and interlayer nanoporosity (see Fig. 6a–e). No microporous gaps or interlayer porosity are discernible in the amorphous layers.

Fig. 6 (a–e) Cross-sectional bright-field TEM images from Ca₃Co₄O₉ films obtained by annealing Ca(OH)₂/Co₃O₄ multilayers with 12 ≤ b_t ≤ 50 nm created from CaO/Co₃O₄ multilayers. (f–j) The corresponding high-resolution TEM images and SAED patterns capturing the layered atomic structure of Ca₃Co₄O₉.

TEM micrographs reveal that for all our films, the Ca₃Co₄O₉ layer thickness is around twice the amorphous layer thickness (Fig. 7). Increasing the b_t from 12 nm to 26 nm increased the Ca₃Co₄O₉ layer thickness from 170 ± 10 nm to 193 ± 10 nm but decreased the amorphous layer thickness from 103 nm to 73 nm. EDX analyses of the amorphous layer revealed O, Al, Si and Ca (ESI Fig. S2†), but no traces of Co above the EDX detection limit. These results suggest that the amorphous layer is formed due to preferential Ca diffusion and incorporation into the mica substrate. This inference is supported by the inverse correlation between amorphous layer thickness and b_t and the higher Ca/Co ratio of 55 : 45 in multilayer than that in the Ca₃Co₄O₉ layer. The anomalously low Ca₃Co₄O₉ layer thickness of 159 ± 10 nm for b_t = 50 nm is likely an outlier due to a very low surface porosity fraction of 13.4% and no microporous gaps at the Ca₃Co₄O₉ – amorphous layer interface and needs further study.

Fig. 7 The thicknesses of crystalline Ca₃Co₄O₉ and amorphous layers in porous films obtained by annealing Ca(OH)₂/Co₃O₄ multilayers created from CaO/Co₃O₄ multilayers with 12 ≤ b_t ≤ 50 nm.

Thermoelectric properties

Considering that amorphous materials normally have lower electrical conductivity σ than corresponding crystalline materials and the amorphous layer has a low thermal conductivity κ, the amorphous oxide layer is assumed as an insulator. The electrical conductivity σ of Ca₃Co₄O₉ films slightly increases with b_t (Fig. 8a) and peaks around 13% porosity (Fig. 8b). For example, σ ∼ 90 S cm⁻¹ for the film with higher porosity (13.8%) is 50% higher than for the film with lowest porosity (3.7%). But σ for the film with different porosities from 11.2 to 17.1% shows a narrow range from 80 to 95 S cm⁻¹. The reason may be that the rough morphology and lowest quality layered structure of annealed film with b_t = 12 nm cause lower carrier mobility and the high-quality layered structure of the annealed films with b_t ≥ 16 nm led to high carrier mobility as shown in Fig. 4 and the size range of nanopores mainly from 120 nm to 400 nm has a slight effect for the electrical conductivity.

Fig. 8 (a) The electrical conductivity σ and the Seebeck coefficient α and (b) power factor α²σ of nanoporous Ca₃Co₄O₉ films as function of surface porosity fraction at room temperature.

The Seebeck coefficient α increases sightly with nanoporosity fraction, e.g., from α = 128 μV K⁻¹ observed for porosity = 3.7% to α = 136 μV K⁻¹ for porosity = 17.1%. The power factor increases from 0.96 to 1.53 μW cm⁻¹ K⁻² with increasing porosity (Fig. 8b). The highest power factor is α²σ = 1.63 μW cm⁻¹ K⁻² for the film with b_t = 50 nm with highest σ.

We used 3DFEM model fitting⁴⁹ to determine the effective thermal conductivity κ_film of the Ca₃Co₄O₉ films (see Fig. 9) by using a mica substrate thermal conductivity value of κ_sub = 0.421 W m⁻¹ K⁻¹, determined by SThM probe measurements. Since κ_film depends on the thermal conductivities of the amorphous (κ_amorphous) and nanoporous crystalline (κ_nanoporous) layers, both of which are unknown, we computed κ_nanoporous by using a one-dimensional cross-plane thermal resistance network model for the crystalline-amorphous bilayer described by . We selected three possible κ_amorphous values of 0.6, 0.8, and 1 (0.8 ± 0.2) W m⁻¹ K⁻¹, which are comparable to the thermal conductivity of amorphous silica.⁵⁴ We assumed κ_amorphous to be identical in all the five samples with 50 ≥ b_t ≥ 12 nm and used the measured amorphous layer thickness for each sample, i.e., 73 nm ≤ t_amorphous ≤ 103 nm. This model is apt because both the amorphous and the nanoporous regions are much thinner than the ∼5 μm probe-sample heat transfer radius and have low values of fitted thermal conductivities.

Fig. 9 (a) Effective thermal conductivity κ film of Ca₃Co₄O₉ films as a function of surface porosity fraction, and (b) thermal conductivity of the nanoporous crystalline Ca₃Co₄O₉ layer κ_nanoporous, assuming κ_amorphous = 0.8 W m⁻¹ K⁻¹ with a ±0.2 W m⁻¹ K⁻¹ uncertainty captured by error bars.

Plotting the effective κ_film and the values extracted for κ_nanoporous of the nanoporous layer as a function of porosity (see Fig. 9a and b) reveal peaks in both κ_film and κ_nanoporous around 13% porosity, at which σ also peaks, as shown earlier. We note that decreasing assumed κ_amorphous yields a higher κ_nanoporous. Both the κ_film and σ are low for the lowest porosity film due to the relatively higher surface roughness compared to the other films. The film with the highest porosity 17.1% (i.e., with b_t = 26 nm) has the lowest κ (∼0.87 W m⁻¹ K⁻¹) in annealed films with b_t ≥ 16 nm. The annealed film with b_t = 12 nm shows low κ (∼0.8 W m⁻¹ K⁻¹) due to the rough morphology.

Mechanical flexibility

Surface Brillouin scattering (SBS) spectra from Ca₃Co₄O₉ films (Fig. 10a) reveal stiffness values that are significantly lower than that of bulk Ca₃Co₄O₉. Rayleigh peaks are seen around ± 8.5 GHz at scattering angles θ_s ≥ 70°. At lower scattering angles, the Rayleigh peaks merge into the central elastic peak, and we observe Sezawa peaks around ±11.5 GHz. Sezawa peaks are typical of soft films on hard substrates,⁵⁵ as is our case for Ca₃Co₄O₉ on sapphire. The invariance of the surface Rayleigh velocity with k‖d (Fig. 10b) within experimental uncertainties is indicative of the elastic properties of the Ca₃Co₄O₉ film with negligible influence of the sapphire substrate. In contrast, the Sezawa velocity increases substantially with decreasing k‖d due to the hard sapphire substrate. We calculated the shear modulus G of the nanoporous Ca₃Co₄O₉ film from where ρ is the density and β = 0.94.^56,57 Assuming isotropy, invoking E = 2G(1 + ν), using the bulk Ca₃Co₄O₉ Poisson's ratio ν = 0.31,⁵⁸ and a density ρ ∼ 3.0 g cm⁻³ for the nanoporous Ca₃Co₄O₉ film determined from X-ray reflectivity measurements (ESI Fig. S3†), we get Young's and shear moduli values of G = 18.92 ± 1.14 GP, and E = 49.62 ± 2.99 GPa, respectively. Both these values for nanoporous Ca₃Co₄O₉ film are 52.7% lower than the predicted values of G = 39.98 GPa and E = 104.86 for bulk Ca₃Co₄O₉.⁵⁸ The 21% lower density of the nanoporous Ca₃Co₄O₉ film compared to bulk Ca₃Co₄O₉ (3.8 g cm⁻³) partially explains the lower moduli. We propose that the low atomic bond density near the nanopore walls in the film also contribute to the increased mechanical compliance.

Fig. 10 (a) Representative Brillouin spectra from a ∼185 nm-thick nanoporous Ca₃Co₄O₉ film (corresponding to b_t = 26 nm) on sapphire for different scattering angles θ_s showing Rayleigh (R) and Sezawa (S) peaks. (b) Surface Rayleigh and Sezawa velocities plotted a of k‖d, where k‖ = (4π sin θ_s)/λ₀ is the surface acoustic wave vector, and d the film thickness.

Mechanical bending of the film-substrate composite showed a high retention of the electrical properties, consistent with high mechanical compliance indicated by the SBS results. Two-point resistance of the film measured as a function of bending radius r_b (see Fig. 11a) showed negligible changes in the normalized resistance (ΔR/R₀ ∼ 0) for r_b ≥ 4 cm, where R₀ is the initial resistance for each film, indicating good mechanical flexibility and low electromechanical coupling. Films synthesized from multilayers specified by b_t = 12 nm and b_t = 26 nm show a greater resilience to bending and bend cycling than the film corresponding to b_t = 50 nm (Fig. 11b and c). While further studies are needed to understand correlations between nanoporosity, bend cycling, and mechanical compliance, our results clearly indicate that the nanoporous films are mechanically flexible and have a low electromechanical coupling for a large range of b_t and bending.

Fig. 11 The normalized resistance changing ΔR/R₀ of the Ca₃Co₄O₉ films on mica (00l) substrates obtained by reactions of multiple stacks of Ca(OH)₂/Co₃O₄ bilayers with 12 ≤ b_t ≤ 50 nm as a function of (a) bending radius r_b and (b) the number of bending cycles at a bending radius of 2 cm, and (c) after restoration to non-bent geometry.

Conclusions

We have synthesized Ca₃Co₄O₉ films with different porosities by annealing multilayers of calcium and cobalt oxide bilayers specified by Ca(OH)₂/Co₃O₄ bilayer thicknesses b_t. Increasing b_t increases the nanoporosity fraction and average nanopore size in the Ca₃Co₄O₉ film formed during annealing. The higher porosity films exhibit a 50% higher electrical conductivity as well as a high Seebeck coefficient, together with a low thermal conductivity. The nanoporous Ca₃Co₄O₉ films show a higher mechanical compliance than the bulk Ca₃Co₄O₉ and are resilient to mechanical bending and bend cycling. These results indicate that engineering nanoporosity in layered oxides through reactions of multilayer stacks of component oxides could be attractive for achieving mechanically-flexible high-figure-of-merit thermoelectric nanomaterials for emergent applications.

Author contributions

Binbin Xin: performed experiments, data collection and analysis, writing – original draft, and writing – review & editing; Erik Ekström: magnetron sputtering; Jun Lu and Anna Elsukova: TEM data; Yueh-Ting Shih and Liping Huang: surface Brillouin scattering (SBS) spectroscopy; Yun Zhang, Wenkai Zhu, and Theodorian Borca-Tasciuc: thermal conductivity; Biplab Paul and Per Eklund: experiment design and supervision; Erik Ekström, Yueh-Ting Shih, Liping Huang, Jun Lu, Anna Elsukova, Yun Zhang, Wenkai Zhu, Theodorian Borca-Tasciuc, Ganpati Ramanath, Arnaud Le Febvrier, Biplab Paul and Per Eklund: writing – review & editing.

Conflicts of interest

The authors declare no conflicts of interest.

Acknowledgements

The authors acknowledge support from the Knut and Alice Wallenberg Foundation through the Wallenberg Academy Fellows program (grant no. KAW 2020.0196), the Swedish Research Council under project grant no 2021-03826, the Swedish Government Strategic Research Area in Materials Science on Functional Materials at Linköping University (Faculty Grant SFO-Mat-LiU No. 2009 00971), and the Swedish Energy Agency under project 46519-1. B. X. also acknowledges financial support from the China Scholarship Council. GR acknowledges funding from the grant CMMI 2135725 from the National Science Foundation.

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Footnote

† Electronic supplementary information (ESI) available. See https://doi.org/10.1039/d2na00278g

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