Boosting thermoelectric performance of ferroelectric monolayer α-In₂Se₃ via strongly enhanced phonon scattering induced by site-specific Te doping

Weinan Zheng^ab, Xinyang Li^b, Qiuyun Wang*^b and Anmin Chen*^c
aSchool of Electrical and Mechanical Engineering, Jilin University of Architecture and Technology, Changchun 130114, China
^bSchool of Physics, Changchun University of Science and Technology, Changchun 130022, China. E-mail: wangqiuyun@cust.edu.cn
^cInstitute of Atomic and Molecular Physics, Jilin University, Changchun 130012, China. E-mail: amchen@jlu.edu.cn

First published on 12th August 2025

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1. Introduction

The development of high-performance thermoelectric (TE) materials is crucial for efficient energy conversion, particularly in applications such as waste heat recovery and solid-state cooling.¹ The thermoelectric efficiency of a material is determined by the dimensionless figure of merit zT, defined as:

where S is the Seebeck coefficient, σ is the electrical conductivity, κ is the total thermal conductivity, and T is the absolute temperature.² To achieve high zT, materials must exhibit high power factor (S²σ) and low lattice thermal conductivity (κ_L), thereby enhancing thermoelectric performance.^3–5

In recent years, two-dimensional (2D) materials have attracted significant attention as promising thermoelectric candidates due to their unique quantum confinement effects, high electrical conductivity, and intrinsically low lattice thermal conductivity.^6–8 Among them, ferroelectric monolayer α-In₂Se₃ has gained interest for its spontaneous in-plane polarization and tunable electronic properties, making it a potential TE material.⁹ Nian et al. investigated the thermoelectric properties of monolayer α-In₂Se₃ and demonstrated that its excellent performance arises from a combination of high electrical conductivity and low lattice thermal conductivity, driven by its unique band structure and strong anharmonic phonon scattering.¹⁰ This makes α-In₂Se₃ a promising candidate for 2D thermoelectric applications. Rivera et al. conducted a first-principles study on monolayer α-In₂S₃ and α-In₂Se₃, revealing that their strong lattice anharmonicity—evidenced by low phonon group velocities, short lifetimes, and high Grüneisen parameters—leads to intrinsically low lattice thermal conductivity.¹¹ These features make both materials promising candidates for efficient thermoelectric applications. However, its relatively high lattice thermal conductivity (κ_L) limits its efficiency, necessitating strategies to suppress heat transport while preserving good electronic properties.¹²

One effective approach to reducing κ_L is through atomic substitution, which introduces phonon scattering mechanisms such as mass disorder, local structural distortions, and enhanced anharmonicity.^13,14 Chalcogen doping, in particular, has been widely explored in layered thermoelectric materials, as elements in the same group share similar chemical properties while inducing notable modifications in phonon transport.^15,16 Yan et al. investigated the phonon transport in monolayer MoSe₂ and found that W doping can enhance thermal conductivity by reducing the three-phonon scattering phase space.¹⁷ Bayikadi et al. demonstrated that Sb/W co-doping in GeTe leads to strong lattice strain and microstructural distortions—which introduce multiple phonon scattering mechanisms and reduce the lattice thermal conductivity to as low as ∼0.2 W m⁻¹ K⁻¹ at 825 K, resulting in a high zT of ∼2.93.¹⁸ Xu et al. investigated the thermoelectric properties of monolayer Sb₂Te_3−xSe_x and found that moderate Se doping (x = 1/12 or 1/36) significantly enhances zT, primarily through tuning of the band structure and Seebeck coefficient.¹⁹ Overall, the electronic contribution to zT shows a moderate improvement across the doping range. Radha et al. investigated the thermoelectric properties of Mn- and Te-co-doped Mg₃Sb₂-based compounds and demonstrated that while the power factor shows only a modest improvement,²⁰ the lattice thermal conductivity is significantly reduced due to enhanced phonon scattering, leading to a substantial increase in the zT value, reaching 0.69 at 673 K. These studies collectively suggest that lowering the lattice thermal conductivity is the most crucial factor in enhancing the zT value. Tellurium (Te) and selenium (Se) both belong to group VI, but Te has a larger atomic mass and lower electronegativity than Se, which can significantly influence phonon scattering when substituted into α-In₂Se₃.

This study aims to enhance the thermoelectric figure of merit of monolayer α-In₂Se₃ by suppressing κ_L through Te substitutional doping. Rather than targeting improvements in electronic properties such as the Seebeck coefficient or electrical conductivity, our strategy focuses on reducing phonon transport by introducing mass disorder and lattice distortions—two key mechanisms known to effectively lower κ_L without significantly degrading electronic transport. In this paper, we investigate the impact of Te doping on the thermal transport properties of ferroelectric monolayer α-In₂Se₃ using first-principles calculations combined with Boltzmann transport theory. By examining phonon dispersion, phonon lifetime, and lattice thermal conductivity, we provide insight into how Te substitution alters heat transport and its potential implications for enhancing thermoelectric performance.

2. Calculation methodology

First-principles calculations based on density functional theory (DFT) were performed using the Vienna ab initio simulation package (VASP) to investigate the structural, electronic, and phonon properties of Te-doped monolayer α-In₂Se₃. The exchange–correlation interactions were described by the Perdew–Burke–Ernzerhof (PBE) functional within the generalized gradient approximation (GGA).^5,21,22 A plane-wave energy cutoff of 360 eV and a Γ-centered 3 × 3 × 1 k-point mesh were used for Brillouin zone sampling. To avoid interactions between periodic images, a vacuum layer of 25 Å was added along the out-of-plane direction. Structural optimization was carried out until the residual atomic forces were below 0.01 eV Å⁻¹. Electronic transport properties were evaluated using the AMSET package,²³ which accounts for ionized impurity (IMP) scattering, acoustic deformation potential (ADP) scattering, and polar optical phonon (POP) scattering mechanisms.²⁴ Due to the large size of the doped supercells, the PBE functional was employed as a computationally efficient alternative to hybrid functionals, which are impractical for dense k-point sampling in large systems.²⁵ For phonon-related thermal transport calculations, a 2 × 2 × 1 supercell was constructed based on the previously generated 4 × 4 × 1 Te-doped models. To accurately capture anharmonic lattice dynamics while maintaining computational efficiency, on-the-fly machine learning molecular dynamics (ML-MD) simulations were carried out in VASP to generate high-quality interatomic potentials.²⁶ The trained potential was used to compute force constants for subsequent phonon analysis. The second- and third-order interatomic force constants were obtained using the on-the-fly machine-learning-assisted force constant method implemented in VASP, which enables efficient and accurate modeling of anharmonic phonon interactions with minimal prior input. Phonon dispersion relations were obtained using Phonopy,²⁷ and the κ_L was calculated using Phonon3py,²⁸ including three-phonon scattering processes. And, the calculated lattice thermal conductivity was normalized by the physical thickness of monolayer to eliminate the influence of vacuum spacing introduced in the simulation.

3. Results and discussion

3.1. Structural optimization and stability

To investigate the effect of Te doping on the thermal transport properties of ferroelectric monolayer α-In₂Se₃, a 4 × 4 × 1 supercell containing 32 In atoms and 48 Se atoms was constructed as the base structure. Te doping was introduced by substituting one Se atom with a Te atom, resulting in the composition In₃₂Se₄₇Te₁, corresponding to α-In₂Se_3−xTe_x with x = 1/16. To examine the influence of atomic position on phonon behavior, Te was substituted at different Se sites: one in the top layer (site 1) and two in the bottom layer (site 2). This allows for analysis of how the local bonding environment affects phonon scattering.²⁹ The optimized structures remain dynamically stable and preserve the layered configuration of monolayer α-In₂Se₃. The atomic configuration and doping sites are shown in Fig. 1. Te atoms were selectively substituted at two representative Se sites located near the top and bottom layers of the structure, denoted as site 1 and site 2, respectively. Site 1 is located near the upper surface of the monolayer, while site 2 resides closer to the bottom boundary. Both sites lie away from the structural center, but the degree of symmetry breaking and local distortion differs due to their vertical (out-of-plane) positions. The Te atom in the site 1-doped structure exhibits a vertical (z-direction) displacement of 0.247 Å from the original Se position, whereas the displacement increases to 0.291 Å in the site 2-doped structure. This larger out-of-plane deviation indicates that the local bonding environment at site 2 is more significantly distorted, which may enhance lattice anharmonicity. However, complementary analyses of the electron localization function (ELF), Bader charge distribution, and –COHP reveal minimal changes in bonding character across the three configurations (see Fig. S5–S7). These results suggest that despite the greater structural perturbation at site 2, the overall electronic structure and bond strength remain largely preserved. Therefore, the enhanced phonon scattering and reduced thermal conductivity in the site 2-doped structure are likely driven more by geometric and dynamic disorder than by direct changes in electronic bonding.

To evaluate the thermodynamic viability of Te doping, we calculated the formation energy by the next expression:

Eform = Edoped − Epristine + μSe − μTe	(1)

where μ_Se and μ_Te are the chemical potentials of Se and Te. The calculated formation energies are 0.985 eV and 1.088 eV for site 1 and site 2 configurations, respectively, under Se-poor and Te-rich conditions. While both values are moderately positive, they remain within the typical range reported for substitutional doping in 2D materials, suggesting thermodynamic feasibility.

To evaluate the mechanical stability and application potential of both pristine and Te-doped α-In₂Se₃ monolayers, we calculated their elastic constants, bulk modulus, and Young's modulus, as summarized in Table 1. These parameters confirm the mechanical stability of the doped configurations and indicate that Te substitution does not significantly compromise the mechanical integrity of material. All configurations satisfy the elastic stability criteria,³⁰ confirming their mechanical robustness.

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In the following analysis, the phonon-related thermal transport properties of these three structures are evaluated using a 2 × 2 × 1 supercell derived from the optimized 4 × 4 × 1 configurations. The resulting supercell contains 320 atoms, making the calculation of third-order force constants computationally intensive. To address this challenge, a machine-learning-based force field was employed to accelerate the subsequent phonon calculations. The accuracy of the trained interatomic potential was validated by comparing atomic forces and phonon dispersion relations with DFT results, as shown in Fig. S2.

3.2. Phonon dispersion

The vibrational properties of pristine and Te-doped monolayer α-In₂Se₃ are analyzed through their phonon dispersion relations and projected phonon density of states (PDOS), as presented in Fig. 2. In all three cases—pristine α-In₂Se₃ [Fig. 2(a)] and Te-doped configurations with substitution at site 1 and site 2 [Fig. 2(b) and (c)]—the phonon spectra contain no imaginary modes, confirming the dynamic stability of both the undoped and doped structures.³¹ In addition, ab initio molecular dynamics (AIMD) simulations at 600 K further verify their thermal stability, as shown in Fig. S1. The acoustic branches near the Γ point exhibit linear and quadratic dispersion, typical of two-dimensional layered systems.³² The corresponding PDOS plots in Fig. 2(d) reveal distinct vibrational characteristics of the Te atom depending on the substitution site. Compared to site 1, Te substitution at site 2 results in a stronger contribution to low-frequency phonon modes, suggesting enhanced coupling with long-wavelength acoustic phonons. This indicates that Te doping perturbs phonon transport in α-In₂Se₃, and that the specific substitution site plays a non-negligible role in modulating phonon behavior. Notably, Te doping at site 2 may lead to a greater reduction in lattice thermal conductivity compared to site 1.

3.3. Lattice thermal conductivity

Following the phonon dispersion and PDOS analysis in Fig. 2, we further investigate the thermal transport behavior by evaluating the lattice thermal conductivity κ_L and phonon–phonon scattering characteristics, as shown in Fig. 3. The in-plane lattice thermal conductivity was calculated along both the x- and y-directions, and the results show negligible difference between the two, confirming that the system exhibits in-plane isotropic thermal transport. In Fig. 3(a), the pristine structure exhibits the highest κ_L across the entire temperature range, while Te doping at both site 1 and site 2 significantly reduces the κ_L. Notably, the site 2 doped structure shows the lowest κ_L, dropping below 0.1 W m⁻¹ K⁻¹ at high temperatures, indicating a stronger suppression of phonon transport. Fig. 3(b) presents the phonon–phonon scattering rates as a function of frequency. Compared to the pristine and site 1 cases, the site 2 doped structure exhibits significantly enhanced scattering rates, especially in the low-frequency acoustic region, which plays a dominant role in thermal transport. This enhanced scattering explains the markedly reduced κ_L in the site 2 doped structure, highlighting the critical role of dopant position in modulating phonon transport. To further resolve the origin of κ_L suppression, Fig. 3(c) and (d) illustrate the mode-resolved contributions to κ_L at 300 K and 600 K, respectively. In the pristine structure, low-frequency phonon modes (below ∼2 THz) contribute significantly to thermal conductivity, forming the dominant heat-carrying channels. Upon Te doping—particularly at site 2—these low-frequency contributions are drastically diminished, consistent with the observed increase in scattering rates. The suppressed κ_L in the doped systems thus primarily arises from the reduced participation of long-wavelength acoustic phonons, which are most sensitive to mass fluctuation and local structural disorder introduced by Te substitution.

The stronger phonon scattering observed in the site 2-doped structure can be attributed to a combination of structural and dynamical factors. First, the large mass contrast between Te and the substituted Se introduces significant mass disorder, which enhances phonon scattering—particularly for low-frequency acoustic modes (0–2 THz) that dominate lattice thermal transport in 2D materials. This is evidenced by the suppressed phonon group velocities and lifetimes across the spectrum, as shown in Fig. 5. Additionally, Fig. 3(d) reveals a strong suppression of these low-frequency modes in the site 2 configuration, further confirming their disruption. Second, although electron localization function (ELF), Bader charge, and –COHP analyses indicate that the local bonding environment is largely preserved (see Fig. S5–S7), Te substitution at site 2 leads to a significantly larger out-of-plane displacement and increased local structural asymmetry. These geometric perturbations introduce bond-angle distortions and strain in the vibrational network,^33,34 thereby enhancing lattice anharmonicity. Furthermore, the Te atom at site 2 is embedded deeper into the lattice framework, resulting in stronger interaction with neighboring atoms and potentially activating additional phonon–phonon scattering channels.^35–37 These effects are further reflected in Fig. 3(c) and (d), which show mode-resolved κ_L contributions at 300 K and 600 K. In the pristine structure, low-frequency modes contribute significantly to the overall κ_L. However, for the site 2-doped system, these contributions are drastically suppressed across the frequency range, especially below 2 THz. This confirms that the reduced κ_L originates primarily from the suppression of acoustic phonon transport due to combined mass and structural perturbations induced by Te doping at site 2.

The top- and bottom-layer doping configurations can be associated with opposite ferroelectric polarization states, allowing us to examine how spontaneous polarization direction influences thermoelectric behavior. Our results suggest that polarization switching alters the phonon symmetry and scattering characteristics, leading to a measurable impact on lattice thermal conductivity.

3.4. Phonon transport

To further evaluate the anharmonic nature of the lattice vibrations, we calculated the mode-resolved Grüneisen parameters for pristine and Te-doped monolayer α-In₂Se₃, as shown in Fig. 4. The Grüneisen parameter characterizes the sensitivity of phonon frequencies to lattice strain and thus serves as a key indicator of lattice anharmonicity. Across all configurations, the Grüneisen parameters exhibit large values at low frequencies, particularly below 2 THz, where acoustic modes dominate. Notably, the site 2-doped structure shows a significant enhancement in the Grüneisen parameters in this region, compared to both the pristine and site 1-doped cases. This trend indicates that Te doping at site 2 leads to stronger lattice anharmonicity, which enhances phonon–phonon scattering, especially for low-frequency modes that are critical to thermal transport. These results are consistent with the shortened phonon lifetimes and suppressed thermal conductivity observed in the site 2 configuration, indicating the critical role of local structural perturbations in modulating phonon dynamics.

Fig. 5 presents the mode-resolved phonon properties of pristine, site 1-doped, and site 2-doped monolayer α-In₂Se₃. As shown in Fig. 5(a), the phonon heat capacity at 300 K shows negligible differences among the three configurations, indicating that doping has little effect on the vibrational density of states near thermal equilibrium. This is expected, as the phonon heat capacity is primarily governed by the phonon frequency spectrum and not strongly affected by localized perturbations introduced by single-atom substitutions. In contrast, Fig. 5(b) reveals a substantial reduction in phonon group velocity, especially in the low-frequency acoustic region for the site 2-doped structure. Since the lattice thermal conductivity (κ_L) is proportional to both group velocity and phonon lifetime, the suppression of group velocity directly limits the ability of phonons to transport heat. The pronounced reduction in group velocity suggests enhanced phonon scattering and localization effects, possibly arising from increased mass contrast and structural asymmetry near the dopant site. Fig. 5(c) and (d) show the phonon lifetimes at 300 K and 600 K, respectively. A systematic reduction in lifetime is observed upon doping, with the most dramatic decrease seen in the site 2-doped system. This reflects stronger anharmonic interactions and impurity-induced phonon scattering. The lifetime suppression is particularly significant for low-frequency modes (<2 THz), which typically dominate heat conduction in 2D materials. The combined effects of lower group velocity and shorter lifetime effectively reduce phonon mean free paths, thereby explaining the sharp drop in (κ_L) for the site 2 configuration. These results indicate that while the heat capacity remains relatively unaltered, phonon transport is strongly degraded due to both dynamical (reduced velocity and lifetime) and structural (mass disorder, symmetry breaking) factors, making dopant site selection a critical parameter for tuning thermal conductivity in low-dimensional materials.

3.5. Electronic structure

Fig. 6 presents the partial density of states (PDOS) and element-projected band structures of monolayer α-In₂Se₃ for three configurations: (a), (d) pristine, (b), (e) Te substitution at site 1, and (c), (f) Te substitution at site 2. The PDOS plots (a)–(c) indicate that Te doping does not introduce significant in-gap states, and the states near the band edges remain dominated by Se and In atoms. The corresponding element-projected band structures (d)–(f) further demonstrate that both the band dispersion and the bandgap are only weakly perturbed by Te substitution. These results suggest that the semiconducting nature of α-In₂Se₃ is well preserved upon Te doping, with negligible impact on its electronic transport characteristics. The corresponding calculated band gaps and carrier effective masses are summarized in Table 2.

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Table 2 summarizes the calculated electronic properties of pristine, site 1-doped, and site 2-doped monolayer α-In₂Se₃, including the indirect and direct band gaps, as well as the effective masses of electrons and holes. Compared to the pristine structure, the site 2-doped configuration exhibits a slightly larger band gap, while the band gap of the site 1-doped structure is slightly reduced. Given the relatively low electron effective masses in all configurations (0.162m₀ for pristine, 0.163m₀ for site 1-doped, and 0.142m₀ for site 2-doped), electrons are expected to exhibit high mobility. In contrast, the hole effective masses are significantly larger, especially in the doped systems. Therefore, the electronic transport properties discussed in this work focus on n-type conduction.

3.6. Thermoelectric properties

Among the considered scattering mechanisms, only ADP scattering shows a noticeable enhancement upon Te doping, while IMP and POP scattering remain nearly unchanged (see Fig. 7). This can be attributed to the fact that Te substitution introduces neither additional charged centers nor significant alterations to the dielectric environment, thus having minimal influence on IMP and POP scattering. The incorporation of Te induces mass disorder and bond stiffness fluctuations, especially near the dopant site, which modifies the acoustic phonon polarization and enhances ADP scattering by increasing local variations in lattice potential gradients. In the case of site 2 doping, these effects are more pronounced due to strong local symmetry breaking and distortion of the acoustic phonon polarization directions (see Fig. S3). Although the elastic constants exhibit only slight changes, these eigenmode-level distortions contribute more significantly to ADP scattering. As a result, the difference in ADP scattering between site 1 and site 2 can explain the slight variation in carrier mobility, while the overall electronic transport remains nearly unaffected due to the dominance of IMP and POP scattering mechanisms. This indicates that while ADP scattering is modulated by local structural perturbations, its influence on thermoelectric performance is more pronounced through phonon scattering and lattice thermal conductivity suppression, rather than through a drastic reduction in electrical transport.

Having analyzed the phonon-related thermal transport properties, we next turn to the electronic transport behavior of pristine and Te-doped α-In₂Se₃. Since the electron effective mass is significantly smaller than that of holes (see Table 1), the n-type transport behavior is primarily considered in the following analysis.³⁸ The electronic transport properties of pristine and Te-doped α-In₂Se₃ were further evaluated as functions of carrier concentration and temperature, as illustrated in Fig. 8. Fig. 8(a)–(c) show the power factor (PF) for the three configurations. In all cases, PF increases with carrier concentration and temperature, reaching a maximum near 10¹² cm⁻². Compared to the pristine structure, the PF in both site 1 and site 2 doped systems exhibits a slight reduction, especially at high carrier concentrations. However, the decrease is relatively minor, indicating that the introduced Te doping has a limited impact on electronic transport and does not significantly degrade the PF performance.³⁹ Fig. 8(d)–(f) present the electronic thermal conductivity (κ_e), which shows a monotonic increase with carrier concentration due to its proportionality to electrical conductivity via the Wiedemann–Franz law.⁴⁰ κ_e exhibits only minor differences among the three structures, further confirming that Te doping minimally affects the electronic heat transport. The combined effect of PF and reduced lattice thermal conductivity is reflected in the zT values shown in Fig. 8(g)–(i), where the total thermal conductivity is the sum of the κ_e and κ_L contributions. While the pristine and site 1 doped systems yield moderate zT values (typically < 0.5), a substantial enhancement is achieved in the site 2 doped configuration. Notably, the zT exceeds 2.0 at 600 K and reaches a peak near 2.5 under optimal carrier concentration, highlighting the effectiveness of site-specific Te doping in boosting thermoelectric performance through phonon engineering.⁴¹ This improvement is consistent with the stronger phonon scattering observed in site 2, as discussed in Fig. 3(b), where enhanced scattering rates and reduced lattice thermal conductivity were evident.

Since the electronic band structure remains largely preserved upon Te doping (Fig. 6), and the Seebeck coefficient and carrier mobilities are not significantly altered (Fig. S8), the improvement in zT primarily stems from the pronounced reduction in lattice thermal conductivity, as shown in Fig. 3(a). This indicates the effectiveness of phonon engineering strategies for enhancing thermoelectric performance in 2D systems. Furthermore, since the two doping configurations correspond to opposite ferroelectric polarization states, this also suggests the possibility of switching thermoelectric properties via polarization reversal.

4. Conclusions

This study systematically explores the thermoelectric performance of monolayer α-In₂Se₃ with site-specific Te doping using first-principles calculations and on-the-fly machine-learning-assisted phonon transport simulations. The pristine structure exhibits a moderate figure of merit (zT ≈ 0.4 at 600 K), whereas Te substitution—especially at the bottom-layer site—significantly enhances phonon scattering and reduces lattice thermal conductivity, resulting in a zT value approaching 2.5 under optimal carrier concentration. Although a slight reduction in power factor is observed, the overall thermoelectric performance is substantially improved due to the pronounced suppression of thermal transport. These findings demonstrate that selective doping at structurally sensitive sites enables effective phonon engineering without severely compromising electronic transport, offering a practical strategy to optimize zT in two-dimensional ferroelectric materials. In addition, since the top- and bottom-layer doping configurations correspond to opposite ferroelectric polarization states, this system provides a model case for exploring polarization-dependent control of thermoelectric behavior.

Conflicts of interest

There are no conflicts to declare.

Data availability

Data used in this work will be available on request.

Supplementary information available: Additional results including AIMD stability tests, phonon eigenmodes, electronic structure, and transport properties for pristine and Te-doped α-In₂Se₃ are presented. See DOI: https://doi.org/10.1039/d5cp01969a

Acknowledgements

We acknowledge the support by the Education Department of Jilin Province of China (Grant No. JJKH20241490KJ).

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