Tensile Strain Effect on Thermoelectric Properties in Epitaxial CaMnO₃ 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 = (σS² T)/κ, 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. As intrinsic point defects in ABO₃ systems, they increase n through Mn⁴⁺ → Mn³⁺ reduction, yet they 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 [25,26,27,28,29,30]. Tensile strain, in particular, has been reported to lower the formation energy of oxygen vacancies, thereby increasing vacancy concentration and carrier density [23,31]. 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 [32,33,34,35]. 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). This platform enables direct correlation between strain state, oxygen-vacancy concentration, and charge-transport metrics, revealing a pathway to suppress vacancy scattering, mitigate the S-σ trade-off, and maximize PF for oxide TE devices.

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, 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. 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 TE and Carrier Properties

S was measured from 20–350 °C using a home-built measurement system based on the differential method of S = ΔV/ΔT, where ΔV is the electric potential induced by an applied temperature difference (ΔT) [36]. 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). 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. Carrier properties were further investigated through analysis of n and µ. Since Hall measurements are challenging for oxide thin films at elevated temperatures [37], 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 [37]. From µ_w, weighted carrier properties, including n_w, were extracted [38]. Calculation details are included in the Supporting Information.

3. Results and Discussion

XRD θ-2θ scans at room temperature clearly show only 00l peaks from the CMO thin films, confirming (001)-oriented epitaxial growth on all substrates (Figure 1a). As shown in Figure 1b, the in-plane strain state varies with substrate: STO (fully relaxed, ε = 0.0%), LSAT (partially relaxed, ε = 0.39%), SLAO (low tensile strain, ε = ~ 0.47%), and LAO (high tensile strain, ε = ~ 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.

To investigate how in-plane tensile strain affects oxygen vacancy concentration, we evaluated the unit cell volume of CMO from HRXRD since changes in δ in ABO₃ perovskites can modify the unit cell volume [25,27,39,40]. 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). This monotonic volume expansion is consistent with an increased oxygen vacancy concentration at larger tensile strain [22,26,31]. First-principles studies reported that tensile strain lowers the oxygen vacancy formation energy across perovskites, favoring vacancy formation and concomitant lattice expansion [23,41,42].

Figure 2. Unit cell volume change as a function of strain state of the CMO thin films calculated from HRXRD measured at room temperature.

Figure 2. Unit cell volume change as a function of strain state of the CMO thin films calculated from HRXRD measured at room temperature.

The temperature-dependent S and σ of the CMO thin films, measured from 0 °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) [33,35]. 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 [43] 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 [44,45]. 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 [45,46,47,48].

In contrast, σ decreased as tensile strain increased (Figure 3b). σ depends on both n and μ based on σ = neμ, with e the electrical charge of carrier [49,50]. While oxygen vacancies induced by tensile strain increase n, they also act as scattering centers that reduce μ [51], 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.

To study the influence of strain-induced oxygen vacancies on the carrier properties of the CMO thin films, we evaluated μ and n extracted from the measured S and σ over the entire temperature range (calculation details in the Supporting Information). Figure 4a shows the calculated weighted carrier concentration (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 [43]. At room temperature, the tensile-strained CMO/LAO exhibited 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 [37,52]. 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]. As shown in Figure 4b, decreasing tensile strain increased μ_w by approximately six orders of magnitude for the unstrained CMO/STO at room temperature. This large μ_w enhancement outweighed the reduction in n and resulted in a substantial increase in σ for the unstrained film.

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 [53]. 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.

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 led 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.