Tensile Strain Effect on Thermoelectric Properties in Epitaxial CaMnO₃ Thin Films

Abstract

A deterministic platform for engineering epitaxial strain in CaMnO_3-δ (CMO) thermoelectric thin films is demonstrated using pulsed laser deposition, enabling precise control of the interplay between strain state and oxygen vacancy formation. High-quality epitaxial CMO films are grown on four different single crystalline substrates, which impose fully relaxed, partially relaxed, low tensile, and high tensile strain states, respectively. Increasing tensile strain induces a monotonic expansion of the unit cell volume and a systematic rise in oxygen vacancy concentration. Oxygen vacancies increase carrier concentration but decrease mobility due to enhanced scattering. Reducing tensile strain suppresses scattering of electrons by oxygen vacancies and increases both electrical conductivity (σ) and the Seebeck coefficient (S), mitigating the conventional inverse relationship between S and σ. Fully relaxed films exhibit σ approximately four orders of magnitude higher at room temperature than highly tensile strained films. These relaxed films also show the highest power factor (PF = S²·σ), exceeding strained films by up to six orders of magnitude. Strain-controlled oxygen vacancies thus provide a direct route to optimize charge transport and maximize the thermoelectric performance of CMO thin films.

1. Introduction

Thermoelectric (TE) materials convert heat directly into electricity, offering a pathway for waste-heat recovery and decentralized power generation [1,2,3]. The TE conversion efficiency is quantified by the dimensionless figure of merit, ZT = ${\displaystyle \frac{\sigma {\mathrm{S}}^{2}T}{\kappa }}$, where σ, S, κ, and T are the electrical conductivity, Seebeck coefficient, thermal conductivity, and absolute temperature, respectively [4,5,6]. State-of-the-art performance has traditionally been achieved by heavy-metal chalcogenides, such as bismuth telluride (Bi₂Te₃) and lead telluride (PbTe) [7]. However, these compounds rely on scarce and toxic elements and often exhibit chemical and thermal instability at elevated temperatures, particularly in oxidizing environments [8,9]. Transition metal oxides are compelling alternatives due to their earth abundance, environmental benignity, and robust chemical/thermal stability under high temperature, oxygen-rich conditions [10,11,12].

Among transition metal oxides, CaMnO_3-δ (CMO) has attracted increasing interest for n-type applications owing to its relatively large S and highly tunable electronic structure [9,13]. Despite these advantages, the overall TE efficiency of CMO remains modest due to its intrinsically low σ [9,14], which limits the power factor, PF = σS². While aliovalent cation substitution has been widely used to increase σ, optimizing the PF is challenging due to the strong interdependence between S and σ [15,16,17,18]. Increasing carrier concentration (n) typically reduces S, and vice versa, leading to a trade-off relationship [19,20,21].

In transition metal oxides, oxygen vacancies play a central role in this trade-off. In CMO, it is well established that oxygen vacancies introduce electron carriers and modify the Mn oxidation state, with neutral oxygen vacancies being charge-compensated by a reduction in neighboring Mn⁴⁺ → Mn³⁺ to maintain charge neutrality [22,23,24,25,26]. These vacancies also introduce scattering centers that degrade carrier mobility (μ) [22,23,24]. Thus, precise control of oxygen vacancy concentration is required for improving TE properties of oxides. Epitaxial strain has emerged as a powerful approach to tune oxygen vacancies, since strain can alter the concentration of oxygen vacancies [27,28,29,30,31,32]. Tensile strain, in particular, has been reported to lower the formation energy of oxygen vacancies, thereby increasing vacancy concentration and carrier density [23,33]. This strain–vacancy coupling offers a route to partially decouple S and σ, and thereby enhance PF.

Despite these insights, the explicit impact of strain-induced oxygen vacancies on the TE properties of CMO is not fully understood [34,35,36,37]. In this study, we investigate this effect by synthesizing high-quality epitaxial n-type CMO thin films via pulsed laser deposition (PLD). Epitaxial CMO films are deposited on single crystalline SrTiO₃ (STO), (LaAlO₃)_0.3(Sr₂TaAlO₆)_0.7 (LSAT), SrLaAlO₄ (SLAO), and LaAlO₃ (LAO) substrates, which impose different strain states ranging from fully relaxed (STO) to tensile-strained (LAO). We demonstrate that controlling epitaxial strain in CMO thin films provides a direct route to correlate strain state, oxygen vacancy concentration, and charge transport behavior, establishing a practical strain engineering pathway to maximize PF in oxide thin films.

2. Materials and Methods

2.1. Synthesis and Characterization of Thin Films

Epitaxial CMO thin films with a film thickness of ~200 nm were grown on (001)-oriented substrates: SLAO (a = 3.756 Å), LAO (a = 3.79 Å), LSAT (a = 3.865 Å), and STO (a = 3.905 Å). These substrates impose different strain states on CMO (a = 3.72 Å); tensile strain (LAO, SLAO), partial relaxation (LSAT), and complete relaxation (STO) through lattice mismatch. Prior to deposition, substrates were mounted on the PLD substrate holder using silver paste (Leitsilber 200, Ted Pella, Redding, CA, USA), heated for 15 min, and fixed into the chamber. High-quality CMO films were deposited using PLD with a KrF excimer laser (λ = 248 nm) at a repetition rate of 5 Hz and pulse energy of 4 J/cm², under an oxygen partial pressure (pO₂) of 25 mTorr at 700 °C. Following deposition, the films were cooled to room temperature at 10 °C/min under a pO₂ of 100 mTorr for ~1 h.

High-resolution X-ray diffraction (HRXRD) with a four-circle diffractometer was used to examine the crystallography and phase purity of all thin films at room temperature in both in-plane and out-of-plane configurations. XRD measurements were performed in both normal and off-normal configurations. The in-plane lattice parameter of CMO was determined from the off-normal (202)_pc reflection (where “pc” denotes pseudocubic notation), and the out-of-plane lattice parameter, normal to the film surface, was determined from the (002)_pc reflection. The in-plane strain was then calculated as

$$\epsilon \left(\%\right)={\displaystyle \frac{a_{\mathit{film}}-a_{\mathit{bulk}}}{a_{\mathit{bulk}}}}\times 100\%,$$

(1)

where a_film is the in-plane pseudocubic lattice parameter and a_bulk is the pseudocubic lattice parameter of bulk CMO. Film thicknesses were confirmed by X-ray reflectivity (XRR). Strain states were analyzed by XRD reciprocal space mapping (RSM) around the substrates’ 103 Bragg reflections.

2.2. Evaluation of Thermoelectric Properties

S was measured from 20 to 350 °C using a home-built measurement system based on the differential method of S = ${\displaystyle \frac{\Delta V}{\Delta T}}$, where ΔV is the electric potential induced by an applied temperature difference (ΔT) [38]. Two thermocouples were attached to the film ends using high temperature resistant clips to ensure stable contacts. One end was heated, and both ΔV and ΔT were recorded and the resulting slope was taken as S.

σ was measured in the same temperature range using a van der Pauw electrode configuration with a DC voltage/current source/monitor (Keithley 2450 Sourcemeter, Keithley Instruments, Cleveland, OH, USA). Both S and σ were first measured during heating (20 °C to 350 °C) and then repeated during cooling (350 °C to 20 °C) to confirm reproducibility. Following this procedure, the S measurements were accurate to within ±2 µV·K⁻¹, while the σ values were accurate to within ±10 S∙cm⁻¹.

2.3. Evaluation of Carrier Properties

Carrier properties were further investigated through analysis of n and µ. Since Hall measurements are challenging for oxide thin films at elevated temperatures [39], the weighted mobility (µ_w) approach was employed. This method is well established and widely used in TE transport studies, providing reliable mobility trends when direct Hall data are impractical [39]. From µ_w, the weighted carrier concentration (n_w) was extracted [40]. µ_w quantifies electron mobility while considering the density of electronic states [39,41] and can be evaluated in a manner similar to Hall mobility, using measured S and σ [39]. The following equation is a simple analytic form for µ_w [39]:

$${\mu }_w={\displaystyle \frac{3h^3\sigma }{8\pi e{\left(2m_e{k}_{B}T\right)}^{3/2}}}\left[{\displaystyle \frac{exp\left(\frac{\left|S\right|}{k_B/e}-2\right)}{1+exp\left(-5\left(\frac{\left|S\right|}{k_B/e}-1\right)\right)}}+{\displaystyle \frac{\frac{3}{{\pi }^2}\frac{\left|S\right|}{k_B/e}}{1+exp\left(5\left(\frac{\left|S\right|}{k_B/e}-1\right)\right)}}\right]$$

(2)

where h is Planck’s constant (J∙s), σ is the electrical conductivity (S∙cm⁻¹), e is the electron charge (C), k_B the Boltzmann constant (J∙K⁻¹), T is the operating temperature (K), and S is the Seebeck coefficient (µV∙K⁻¹).

n_w can be then calculated from µ_w using the formula stated below [40]:

$$n_w={\displaystyle \frac{\sigma }{{\mu }_{w}e}}$$

(3)

with µ_w (cm²∙v⁻¹∙s⁻¹) and n_w (cm⁻³).

In complex oxides, such as CMO, oxygen vacancy related defect states and the correlated electronic structure can violate the simple single parabolic band assumption of the weighted mobility model. In this context, µ_w and n_w extracted from S and σ are appropriately treated as effective, model-based descriptors rather than exact microscopic mobilities and carrier densities.

3. Results

3.1. Structural Characterization of CMO Thin Films

XRD θ-2θ scans at room temperature clearly show only 00l peaks from the CMO thin films, confirming (00l)-oriented epitaxial growth on all substrates (Figure 1a). In epitaxial oxide thin films, strain is initially introduced by the lattice mismatch between the film and the substrate [32]. However, when the lattice mismatch and/or film thickness become sufficiently large, the interface can change from coherent to incoherent as misfit dislocations form and partially relieve this strain [42]. Appropriate combinations of lattice mismatch and film thickness (typically yielding residual strain levels of ~±3%) are thus essential for obtaining well-defined strain states that enable elucidation of interfacial strain effects on the physical properties of oxide thin films. As shown in Figure 1b, the in-plane strain state varies with substrate: STO (fully relaxed, 0.0% strain), LSAT (partially relaxed, ~0.39%), SLAO (low tensile strain, ~0.47%), and LAO (high tensile strain, ~0.84%). CMO films were coherently strained on LAO and SLAO, as indicated by the alignment of the film and substrate peaks along the in-plane (q_x) direction in RSM. By contrast, the large lattice mismatch on LSAT (~3.9%) and on STO (~4.79%) led to partial and complete relaxation, respectively. Accordingly, the CMO film peaks did not align with the LSAT and STO substrate peaks.

3.2. Strain-Dependent Oxygen Vacancies in CMO Films

To investigate how in-plane tensile strain affects oxygen vacancy concentration, we evaluated the unit cell volume of CMO from HRXRD since changes in oxygen nonstoichiometry (δ) in ABO₃ perovskites can modify the unit cell volume [27,29,43,44]. In nanoscale thin films, resolving small deviations from full stoichiometry directly is challenging, and observation of an increase in unit cell volume is therefore widely used as an indirect indicator of δ in perovskite oxide thin films [27,29,45,46]. In epitaxial thin films, the unit cell volume–δ relationship can be influenced by strain–vacancy coupling, such as anisotropic chemical expansion and/or non-uniform vacancy distributions [47,48,49]. Accordingly, the unit cell volume is used here as a relative indicator of δ, not to determine an absolute δ. As shown in Figure 2, the unit cell volume increased gradually from ~51.79 ų (relaxed, STO) to ~52.32 ų at ~0.84% tensile strain (LAO). The measured increase in unit cell volume with increasing tensile strain indicates that films under larger tensile strain contain a higher concentration of oxygen vacancies, because chemical expansion in ABO₃ perovskites arises primarily from vacancy induced lattice expansion [22,28,33]. Our observation agrees well with first principles studies, which report that biaxial tensile strain lowers the oxygen vacancy formation energy in perovskites and thus promotes vacancy formation and the associated lattice expansion [23,50,51].

3.3. Thermoelectric Properties of CMO Thin Films

The temperature-dependent S and σ of the CMO thin films, measured from 20 °C to 350 °C, are shown in Figure 3. For all samples, S remains negative over the entire range, confirming that CMO is an n-type semiconductor with electrons as the majority carriers (Figure 3a) [35,37]. The magnitude of S increases as the strain state decreases, from fully tensile strained CMO/LAO to fully relaxed CMO/STO. As shown in Figure 2, tensile strain promotes oxygen vacancy formation, which increases n [49] in CMO through Mn⁴⁺ → Mn³⁺ reduction [22,24]. Accordingly, reducing tensile strain lowers the degree of electron doping. For degenerate semiconductors, S is inversely proportional to n, with S ∝ n^−2/3 [52,53]. Therefore, a decrease in n results in an increase in S, consistent with the trend observed in Figure 3a. At room temperature, the magnitude of S increases by nearly a factor of three when comparing the tensile-strained CMO/LAO with the fully relaxed CMO/STO. This observation agrees well with previous studies, showing that S decreases as n increases [53,54,55,56].

In contrast, σ decreases as tensile strain increases (Figure 3b). σ depends on both n and μ based on σ = neμ, where e the electrical charge of carrier [57,58]. While oxygen vacancies induced by tensile strain increase n, they also act as scattering centers that reduce μ [59], resulting in lower σ. Consequently, the unstrained CMO/STO film exhibits the highest σ, while the tensile-strained CMO/LAO shows the lowest. At room temperature, σ increases by nearly four orders of magnitude from the tensile-strained CMO/LAO to the fully relaxed CMO/STO.

3.4. Carrier Properties of CMO Thin Films

To study the influence of strain-induced oxygen vacancies on the carrier properties of the CMO thin films, we evaluated μ_w and n_w extracted from the measured S and σ over the entire temperature range. Figure 4a shows n_w as a function of temperature. n increased with increasing tensile strain, as expected, since tensile strain promotes oxygen vacancy formation and concomitant electron doping in CMO [49]. At room temperature, the tensile-strained CMO/LAO exhibits an n_w roughly one order of magnitude higher than that of the fully relaxed CMO/STO. This observation is consistent with the reduction in S with increasing tensile strain, shown in Figure 3a.

μ_w is a practical probe of charge transport, analogous to Hall mobility, and is widely used in TE studies owing to its robustness at elevated temperatures and suitability for low-mobility materials [39,60]. μ_w shows the opposite trend to n_w, decreasing with increasing tensile strain (Figure 4b). This behavior is attributed to strain-induced oxygen vacancies that act as scattering sites in the strained films [23]. Decreasing tensile strain increases μ_w by approximately six orders of magnitude for the unstrained CMO/STO at room temperature.

In Figure 1, the XRD data showed sharp, well-defined peaks consistent with high-quality single crystal films epitaxially grown on all substrates, with no indication of impurities or secondary phases, which implies that scattering from secondary phases or grain boundaries is negligible. This observation is consistent with reports on epitaxial transparent conducting oxides, where grain boundary scattering is negligible in epitaxial films but plays a major role in polycrystalline counterparts [61,62]. Several studies on perovskite oxides have attributed changes in carrier mobility to scattering by oxygen vacancies and their associated defect fields [62,63,64,65]. At low temperatures, phonon (lattice vibration) scattering is insignificant, and electron transport is dominated by static defects [61]. In our films, the dominant defects are oxygen vacancies, and these vacancy-related defect centers act as strong, static scattering sites that impede carrier motion. The large enhancement of the μ_w in relaxed film primarily results from a reduction in the density of oxygen vacancy-related scattering centers as the film relaxes. This large μ_w enhancement outweighs the reduction in n and leads to a substantial increase in σ for the unstrained film.

3.5. Power Factor of CMO Thin Films

We further evaluated the PF of the CMO thin films (Figure 5). PF increased with decreasing tensile strain over the entire temperature range (Figure 5a). At room temperature, the CMO/STO exhibited a PF more than six orders of magnitude higher than that of the tensile-strained CMO/LAO. This trend follows from the combination of higher σ and larger S in the unstrained films. A similar unusual trend has been reported for La_0.7Ca_0.2Ni_0.25Ti_0.75O_3-δ, where PF increased by eight orders of magnitude owing to a synergistic rise in both S and σ [66]. These results indicate that modulating oxygen vacancies by tuning epitaxial strain can be an effective strategy to mitigate the conventional S-σ trade-off and improve TE performance.

4. Discussion

Our results establish a coherent link between epitaxial strain, oxygen vacancy concentration, and charge transport in CMO thin films. Increasing tensile strain lowers the formation energy of oxygen vacancies in perovskites [22,23,33,50,51], and the monotonic unit cell expansion in Figure 2 indicates that more highly strained films contain a higher concentration of oxygen vacancies. In CMO, these vacancies act as electron donors via Mn⁴⁺ → Mn³⁺ reduction, which explains the higher n_w observed in the tensile strained CMO/LAO film compared with the relaxed CMO/STO film (Figure 4a).

At the same time, oxygen vacancies act as strong static scattering centers that reduce μ. This is reflected in the pronounced decrease of µ_w with increasing tensile strain (Figure 4b), despite the increase in n_w. XRD data (Figure 1) confirm that the films are high quality epitaxial single crystals without detectable secondary phases, and prior studies on epitaxial transparent conducting oxides reported that grain boundary scattering is negligible in such films [61,62]. Together with the relatively low measurement temperatures, where phonon scattering is still moderate, these observations indicate that vacancy related defect scattering is the primary factor controlling µ_w in these CMO films [62,63,64,65].

For the relaxed CMO/STO film, vacancy-related scattering centers are substantially reduced, yet the concentration of oxygen vacancies continues to provide electron carriers. Consequently, the enhancement in µ_w dominates over the decrease in n and produces a pronounced increase in σ compared with the highly strained films. At the same time, the lower carrier concentration in the relaxed film gives a larger magnitude of S, consistent with the inverse dependence of S on n in degenerate semiconductors (S ∝ n^−2/3) [52,53]. The concurrent increase in both σ and S yields the very large enhancement in PF observed for the relaxed CMO/STO film (Figure 3 and Figure 5). Although the systematic correlations with unit cell volume (Figure 2) and the extracted carrier descriptors (Figure 4) support a primary role of vacancy-related mechanisms in this work, further studies are needed to disentangle strain-induced electronic-structure contributions, which may also influence both S and σ.

These trends suggest a practical design guideline for oxide thermoelectrics based on CMO and related perovskites. Substrate and growth conditions that produce relaxed or weakly tensile strain states can suppress vacancy induced scattering while maintaining a moderate level of oxygen vacancy doping, thereby enabling simultaneous enhancement of σ and S without aliovalent cation substitution. More generally, strain-controlled oxygen vacancy engineering offers a route to mitigate the conventional S-σ trade-off in oxide thermoelectrics. The same strategy should be applicable to other perovskites and layered oxides in which strain modifies vacancy energetics and carrier scattering, although materials with strongly strain sensitive band edges may exhibit additional band structure effects that either reinforce or counteract the vacancy scattering trends identified here.

In the context of the full thermoelectric figure of merit, we note that the total thermal conductivity (κ), which is the sum of the electronic thermal conductivity (κ_e) and the lattice thermal conductivity (κ_L), can also be influenced by oxygen vacancies. Oxygen vacancies are expected to decrease κ_L by introducing point-defect disorder and local lattice distortions that enhance phonon scattering [67,68], whereas increased electrical conductivity can increase κ_e via the Wiedemann–Franz relation [69]. Epitaxial strain may further influence κ_L by modifying bonding geometry and phonon properties [70,71], and indirectly by changing the oxygen vacancy concentration, which enhances phonon scattering [22,72].

5. Conclusions

In this study, we examined how strain-induced oxygen vacancies influenced the TE properties of CMO thin films. Lattice mismatch between CMO and the substrates was used to impose different epitaxial strain states. Epitaxial CMO films grown on LAO, SLAO, LSAT, and STO resulted in tensile-strained films on LAO and SLAO and partially or fully relaxed films on LSAT and STO, respectively. The TE properties improved as tensile strain decreased. This improvement is attributed to a reduction in strain-induced oxygen vacancies, which simultaneously leads to increases in both σ and S. The combined enhancement of σ and S produced a substantial increase in PF, with an increase of approximately six orders of magnitude at room temperature. These findings demonstrate that modulation of oxygen vacancies through epitaxial strain is a promising strategy to improve the TE performance of oxide thin films and to mitigate the conventional S-σ trade-off.