Pyrite–bismuth telluride heterojunction for hybrid electromagnetic-to-thermoelectric energy harvesting

Abstract

The rapid proliferation of wireless networks and connected devices has led to the pervasive dissipation of electromagnetic (EM) energy into the environment—an underutilized resource for energy harvesting. Here, we demonstrate a pyrite (FeS₂)–bismuth telluride (Bi₂Te₃) heterostructure that enables hybrid electromagnetic-to-thermoelectric energy conversion. Fabricated via a simple cold-press compaction of powders, the heterostructure forms a Schottky interface at FeS₂, facilitating efficient RF absorption and localized heating. This heat is harvested by Bi₂Te₃ through thermoelectric conversion. Under 35 MHz RF irradiation at 1 W input power, the device achieved a local temperature rise of 46 °C and a thermal gradient of 5.5 K across the Bi₂Te₃, resulting in a peak power density of ∼13 mW cm⁻². Molecular dynamics (MD) simulations and density functional theory (DFT) calculations further elucidate the heat transport behaviour and interfacial thermoelectric performance. This work introduces a new class of heterostructures for RF-responsive energy harvesting, offering a scalable route toward self-powered IoT and wireless sensing systems.

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1. Introduction

Our living environment provides several natural energy sources, including solar, wind, heat, and vibrations, as well as artificial energy sources such as electromagnetic waves. These energy sources have been effectively utilized in the development of various energy harvesting technologies, including piezoelectric,¹ triboelectric,² thermoelectric,^3–5 photovoltaic,^6,7 magnetic field energy harvesting,^8,9 and radiofrequency (RF) energy harvesting.¹⁰

While piezoelectric and triboelectric energy harvesting rely on moving components, RF and thermoelectric energy harvesting operate without such mechanical dependencies, making them more durable. Additionally, with the rapid expansion of wireless technologies such as 5G, IoT devices, and wireless power transmission, there has been a significant rise in electromagnetic energy density in the environment.¹¹

Most studies on RF energy harvesting have focused on designing rectenna-based systems (integrating antennas and rectifiers to convert RF signals into DC power directly). However, relatively little attention has been given to RF-to-thermal energy conversion.¹² Electromagnetic waves, particularly in the radio frequency range, have low energy and long wavelengths, making them challenging to capture efficiently. Conventional rectennas require precise frequency tuning and often operate efficiently only within narrow frequency bands.¹³

An alternative and less-explored approach involves converting RF energy into localized thermal energy, which can then be harvested using thermoelectric materials to generate electricity. Thermoelectric materials are widely recognized for their ability to convert thermal energy into electricity, making them ideal for energy harvesting through waste heat recycling and renewable energy generation. Various material systems, including metal oxides,¹⁴ metal tellurides,¹⁵ and high entropy alloys,¹⁶ have demonstrated excellent thermoelectric properties. An ideal thermoelectric material is characterized by a high figure of merit (ZT), which depends on the optimal balance between thermal conductivity and electrical conductivity.^17,18

Significant progress has been made in enhancing the thermoelectric and functional properties of these materials. However, their interaction with electromagnetic waves remains relatively unexplored. The high thermal conductivity and electrical conductivity of thermoelectric materials typically result in lower electromagnetic energy absorption. While microwave-to-thermoelectric energy conversion has been demonstrated,¹⁹ harvesting lower-energy electromagnetic waves, such as radio waves, remains a significant challenge due to their longer wavelengths and lower photon energy. Efficient absorption of these waves requires semiconductors with extremely low band gaps to facilitate charge excitation.

Integrating such low bandgap semiconductors with thermoelectric materials offers a promising pathway to not only convert ambient RF energy into usable electrical power but also to mitigate electromagnetic interference (EMI). This synergistic approach addresses dual challenges—energy sustainability and electromagnetic pollution—making it highly relevant for next-generation wireless and IoT ecosystems.

To address the challenges outlined above, this work presents the development of a radio frequency-thermoelectric (RFTE) heterojunction comprising FeS₂–Bi₂Te₃, constructed using straightforward techniques such as cold pressing. Fig. 1 shows the fabrication of the FeS₂–Bi₂Te₃ heterojunction and a photograph of the resultant heterojunction pellet.

Fig. 1 Schematic of the fabrication of the FeS₂–Bi₂Te₃ heterostructure and photograph of the pellet.

Pyrite (FeS₂), an earth-abundant semiconducting material with a low band gap of 0.8–0.9 eV, serves as a key component as it can absorb RF energy in high-frequency regions.^20,21 The Ti/FeS₂ heterojunction functions as a Schottky junction, enabling the detection of radio waves (RF) and their conversion into thermal energy. Subsequently, Bi₂Te₃, a well-known thermoelectric material, efficiently converts this thermal energy into electrical energy.²²

The Schottky heterojunction generated a maximum temperature of 45.5 °C at 35 MHz RF, and the overall RF-TE composite delivered a peak power output density of 13 mW cm⁻². The integration of sustainable materials with thermoelectric materials for developing RF-TE devices positions FeS₂–Bi₂Te₃ as a promising candidate for the conversion of electromagnetic energy into electricity.

2. Experimental section

2.1. Fabrication of FeS₂–Bi₂Te₃ heterojunction

To fabricate the FeS₂–Bi₂Te₃ heterojunction, 3 g of Bi₂Te₃ powder was first placed into a 10 mm diameter stainless steel die and cold-pressed. Subsequently, 2 g of bulk FeS₂ pieces were added on top of the compacted Bi₂Te₃ layer. The stacked composite was then cold-pressed under a load of 1 ton for 5 minutes. This process yielded a robust pellet forming the FeS₂–Bi₂Te₃ heterojunction.

2.2. Characterization techniques

X-ray diffraction (XRD) was carried out using a Bruker D8 Advance diffractometer equipped with a LynxEye detector and Cu-Kα radiation to determine the crystal structure and phase composition. Surface morphology and elemental composition were analyzed using scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (EDS) (ZEISS Sigma). Raman spectroscopy was performed using a WITec UHTS 300VIS system to probe the vibrational characteristics. X-ray photoelectron spectroscopy (XPS) (Thermo Fisher Scientific Nexsa base) was employed to determine the chemical oxidation states of the constituent elements.

Voltage–current characteristics of the Ti/FeS₂–Bi₂Te₃ heterojunction were measured using a Keithley 2450 SourceMeter, while dielectric measurements were conducted using a precision LCR meter (SM6026). Thermoelectric measurements, including the Seebeck coefficient and electrical conductivity, were performed in a Physical Property Measurement System (PPMS). RF heating experiments were carried out using a custom-built 1 W RF signal generator, and thermal imaging was conducted using an Optris PI640 infrared camera. Thermal voltage generated during RF heating was monitored using a Moku:Go voltage measurement instrument.

2.3. Computational details

2.3.1. Density functional theory (DFT) calculations. Spin-polarized ab initio calculations based on density functional theory (DFT) were carried out using the Vienna Ab initio Simulation Package (VASP),²³ employing the Projector Augmented-Wave (PAW) pseudopotential method.²⁴ The valence configurations used were: 3d⁷ 4s¹ for Fe, 3s² 3p⁴ for S, 6s² 6p³ for Bi, and 5s² 4p⁴ for Te. Kohn–Sham orbitals were expanded using a plane-wave basis set with a kinetic energy cutoff of 300 eV. Exchange and correlation interactions were approximated using the revised non-local Vydrov and Van Voorhis (rVV10) functional as implemented by Sabatini et al.²⁵ The DFT+U approach²⁶ was employed to account for the localized nature of Fe d electrons, with the Hubbard U parameter set to 2 eV, consistent with previous studies.²⁷ Although spin–orbit coupling effects are important to describe the topological insulator behavior of Bi₂Te₃,²⁸ these effects were not taken into account due to the size of the system (the FeS₂ @Bi₂Te₃ interface cell has 144 atoms). The Brillouin zone was sampled using a uniform Monkhorst–Pack grid;²⁹ the specific k-point mesh used for each structure is detailed in the following sections. The self-consistency threshold was set to 10⁻⁷ eV, and atomic forces were minimized below 10⁻² eV Å⁻¹. Electronic structure data were analyzed using the VASPKIT suite.³⁰ Thermoelectric properties of the FeS₂–Bi₂Te₃ heterojunction were evaluated using semiclassical Boltzmann transport theory under the Relaxation Time Approximation (RTA) as implemented in the BoltzTraP code.³¹ The Seebeck coefficient (S), electrical conductivity (σ), and the electronic contribution to the thermal conductivity (κ_e) were computed from the Kohn–Sham eigenvalues, which were interpolated to obtain analytic expressions as functions of chemical potential (μ), temperature (T), and relaxation time (τ₀). In this work, we adopted a time relaxation of 10⁻¹⁴ s, following previous works.³²

2.3.2. Molecular dynamics details. Molecular dynamics (MD) simulations are performed to gain insights into thermal transport in Bi₂Te₃. We only simulate Bi₂Te₃ instead of FeS₂/Bi₂Te₃ heterojunction due to differences in lattice structures and the absence of appropriate cross-interaction parameters in the literature. Bi₂Te₃ has a rhombohedral lattice structure with a hexagonal conventional cell with three quintuple layers. We define two orthogonal directions in the hexagonal plane as x and y directions (i.e., in-plane directions) and the cross-plane direction as the z direction, as shown in Fig. 7a. There are two types of Te atoms with two bonding environments. Te1 atoms have weaker interlayer van der Waals interactions with other atoms, while Te2 atoms form strong intralayer bonds. The short-range interactions within Bi₂Te₃ are described in the form of a Morse potential developed by Qiu and Ruan.³³

ϕ_s(r_ij) = D_e{[1 − exp − a(r_ij − r₀)]² − 1} (1)

where ϕ_s is the interatomic potential, r_ij is the distance between atoms i and j, and D_e, a, r₀ are parameters whose values can be found in ref. 34. The long-range Coulombic interactions are treated by the particle–particle particle-mesh (PPPM) method. The MD simulations are carried out using the large-scale atomic/molecular massively parallel simulator (LAMMPS) package.³⁵

A cubic simulation box with a dimension of 60 × 60 × 60 ų is created to calculate thermal conductivity. The system is minimized and equilibrated in the NPT and NVT ensembles for 2 ns. The temperature and pressure damping parameters are 0.1 and 1 ps, respectively. The lattice constants obtained from the equilibrated simulation box at 300 K are a = 4.343 Å and c = 30.443 Å, which agree well with previous experimental results.³⁶ We carry out a production run for 20 ns where heat fluxes are recorded in x, y, and z directions. We calculate the thermal conductivity using the Green–Kubo method³⁷ by integrating the heat flux autocorrelation function:

where V is volume, k_B is the Boltzmann constant, T is temperature, J is heat flux, t is the correlation time, and 〈 〉 is the average overall time of origins t₀. More specifically, J is calculated bywhere e_i, v_i and S_i are energy, velocity and stress of ith atom, respectively. The thermal conductivity κ is calculated as a function of correlation time t ranging from 0 to 100 ps. The production period is divided into 20 trajectories of 1 ns, and the thermal conductivity is averaged over 20 trajectories.

Nonequilibrium molecular dynamics (NEMD) simulations are carried out to simulate the heat transfer in the cross-plane direction under RF heating. We create a slab-shaped simulation box with dimensions of 60 Å, 60 Å and 600 Å in x, y, and z directions, respectively. The simulation box is divided into 100 bins in the z direction with equal width, and the leftmost and rightmost bins are fixed as walls. Periodic boundary conditions are applied in the x and y directions only. We consider the 10 bins nearest to the left wall an RF heat source (Fig. 7c). Since a continuous function of variable heating rate cannot be defined in LAMMPS, a stepwise heating rate ranging from 0.0016 to 0.01 kcal mol⁻¹ fs⁻¹ is applied to the heat source for 1 ns to emulate the sinusoidal heating by RF (Fig. S4). The spatial temperature distribution of the simulation box is recorded during the heating process.

3. Results and discussion

The structural and crystalline nature of the pellet was analyzed using X-ray diffraction (XRD), as shown in Fig. 2a. The XRD pattern reveals peaks corresponding to Bi₂Te₃, indexed to hexagonal Bi₂Te₃ (ICSD: 74348), and FeS₂, indexed to cubic FeS₂ (ICSD: 53529). A more detailed morphological analysis of the FeS₂–Bi₂Te₃ heterojunction was performed using scanning electron microscopy (SEM) and energy-dispersive spectroscopy (EDS), as illustrated in Fig. 2(b–f). The cross-sectional SEM image distinctly highlights the heterojunction between Bi₂Te₃ and FeS₂, while the EDS elemental maps show the elemental distribution across the heterojunction.

Fig. 2 (a) XRD pattern of FeS₂–Bi₂Te₃ pellet, (b) FESEM cross sectional image of FeS₂–Bi₂Te₃ heterojunction, (c)–(f) EDS colour map showing elemental distribution of Bi, Te, Fe and S across the heterojunction, (g) Raman spectra of FeS₂–Bi₂Te₃ heterojunction (h) XPS survey plot of FeS₂–Bi₂Te₃ pellet, (i)–(k) binding energy plots of Fe 2p, Bi 4f, S 2p and Te 3d.

The vibrational nature of the heterojunction was analyzed using Raman spectroscopy, as shown in Fig. 2g. The peaks at 105.2 cm⁻¹, 122.6 cm⁻¹, and 140 cm⁻¹ correspond to the E_2g, A_1u, and A_2g modes in Bi₂Te₃,^38,39 and the peaks at 342 cm⁻¹, 376 cm⁻¹, and 428 cm⁻¹ correspond to A_g, E_g, and T_g modes in FeS₂.^40–42

The chemical oxidation states of the pellet were analyzed using X-ray photoelectron spectroscopy (XPS). Fig. 2h shows the XPS survey spectrum, indicating the presence of Bi 4p, Te 3d, Fe 2s, Fe 2p, and S 2p core levels. The Fe 2p binding energy spectrum (Fig. 2i) exhibits peaks at 708.4 eV, 711.6 eV, 721.2 eV, and 730.2 eV. The prominent peaks at 708.4 eV and 721.2 eV correspond to Fe²⁺ states, confirming the formation of Fe(II)–S,^20,43 while the 711.6 eV peak is attributed to Fe³⁺–O surface oxidation states.

Due to their close binding energies, the S 2p and Bi 4f spectra are presented together in Fig. 2j. For S 2p, the peak at 162 eV corresponds to S²⁻, indicating the formation of FeS₂, and a weaker peak at 168.8 eV is associated with SO₄²⁻, likely due to surface oxidation. For Bi₂Te₃, the Bi 4f spectrum exhibits peaks at 157.2 eV and 162.5 eV, characteristic of the Bi³⁺ oxidation state. The Te 3d spectrum (Fig. 2k) shows peaks at 572.2 eV and 582.5 eV corresponding to Te²⁻ states, and a minor peak at 574 eV attributed to TeO₂, resulting from surface oxidation.^44,45 These studies confirm the structural integrity and chemical stability of the FeS₂–Bi₂Te₃ heterojunction. Table 1 summarize the results of XRD, Raman spectroscopy and XPS for clarity.

Table 1 Summary of structural, vibrational, and chemical analysis of the FeS₂–Bi₂Te₃ heterojunction

Technique	Feature/peak position	Assignment/interpretation	Fig. ref.
XRD	Peaks matching hexagonal Bi2Te3 (ICSD: 74348)	Confirms crystalline Bi2Te3 phase	Fig. 2a
	Peaks matching cubic FeS2 (ICSD: 53529)	Confirms crystalline FeS2 phase	Fig. 2a
Raman	105.2 cm^−1 (E2g), 122.6 cm^−1 (A1u), 140 cm^−1 (A2g)	Vibrational modes of Bi2Te3	Fig. 2g
	342 cm^−1 (Ag), 376 cm^−1 (Eg), 428 cm^−1 (Tg)	Vibrational modes of FeS2	Fig. 2g
XPS – survey	Bi 4p, Te 3d, Fe 2s/2p, S 2p	Elements present in pellet	Fig. 2h
XPS – Fe 2p	708.4 eV, 721.2 eV	Fe^2+ in FeS2	Fig. 2i
	711.6 eV	Fe^3+ (surface oxide)	Fig. 2i
XPS – S 2p	162.0 eV	S^2− in FeS2	Fig. 2j
	168.8 eV (weak)	SO4^2− (surface oxidation)	Fig. 2j
XPS – Bi 4f	157.2 eV, 162.5 eV	Bi^3+ in Bi2Te3	Fig. 2j
XPS – Te 3d	572.2 eV, 582.5 eV	Te^2− in Bi2Te3	Fig. 2k
	574.0 eV (minor)	TeO2 (surface oxidation)	Fig. 2k

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3.1. Electrical characterization and Schottky barrier analysis

To understand the electronic nature of the Bi₂Te₃–FeS₂ heterojunction, voltage–current (V–I) characteristics were studied. The V–I curves for Bi₂Te₃ and FeS₂ individually showed ohmic behavior, as evidenced by the linear relationship in Fig. 3a. This ohmic nature is attributed to the similar work functions of Bi₂Te₃ (5.1 eV)⁴⁶ and FeS₂ (5.2 eV).⁴⁷

Fig. 3 (a) Voltage–current characteristics of FeS₂–Bi₂Te₃, (b) temperature-dependent voltage–current characteristics of Ti-FeS₂, (c) temperature-dependent forward voltage–current characteristics of Ti-FeS₂ showing turn-on voltage at 0.18 V, (d) ln(j₀)–V plot for extracting saturation current, (e) Richardson plot, and (f) temperature-dependent Schottky barrier height plot of Ti/FeS₂ junction.

To make the pellet sensitive to radio frequencies (RF), a Schottky junction was engineered at the FeS₂ surface using a Ti metal tip of 1 mm diameter. Fig. 3b shows the temperature-dependent Schottky diode characteristics of the Ti/FeS₂ junction, and Fig. 3c displays the forward bias behavior, revealing a turn-on voltage of 0.18 V.

The Schottky barrier height (SBH) was calculated using the Richardson equation:

where Φ_B is the Schottky barrier height, k is the Boltzmann constant, T is the absolute temperature, q is the elementary charge, A* is the Richardson constant, A is the contact area, and I₀ is the reverse saturation current obtained from Fig. 3d.⁴⁸ The Richardson constant was determined from the slope of the plot shown in Fig. 3e. The temperature-dependent variation of the SBH is presented in Fig. 3f.

A low SBH of 0.28 eV was observed at room temperature for the Ti/FeS₂ junction. As temperature increases, the SBH also increases due to the influence of inhomogeneities at the metal-semiconductor interface, which can cause Fermi-level pinning. With rising temperature, more thermally activated electrons contribute to current flow through thermionic emission. This leads to dominant conduction through higher barrier regions, resulting in an apparent increase in SBH.^49–51

For RF detector applications, an ideal diode should exhibit a low forward voltage drop and a low SBH to effectively detect weak RF signals. The electrical characteristics of the Ti/FeS₂ junction satisfy these conditions, making it a promising candidate for RF detection applications.

3.2. Electronic structure and thermoelectric properties from first-principles calculations

First-principles calculations based on Density Functional Theory (DFT) were carried out to understand the electronic structure and thermoelectric properties of the FeS₂–Bi₂Te₃ heterojunction. The heterojunction was modelled based on experimental characterization data consisting of Bi₂Te₃ on top of the FeS₂ (001) surface. We emphasize that the theoretical model employed in our simulations was conceived to investigate the electronic and thermoelectric properties of the interface. Some approximations were made to ensure convergence due to the size of the system and the necessary modifications to ensure commensurability, as discussed in the following. However, both FeS₂ and Bi₂Te₃ have different crystal symmetries: the former is orthorhombic, while the latter is rhombohedral. Thus, to ensure commensurability, we built a model based on the modification of Bi₂Te₃ symmetry to an orthorhombic-like one. The model is shown in Fig. 4a, beginning with a slab of FeS₂ (001) surface with 2 layers. We take an orthorhombic piece of Bi₂Te₃ supercell that minimizes the lattice mismatch with FeS₂ (001) surface. The sublattice taken from bulk Bi₂Te₃ has the following lattice parameters: a = 7.67, b = 4.43 Å. When a 3 × 1 × 1 (with lattice parameters of a = 23.749 Å, b = 4.43 Å) supercell of modified Bi₂Te₃ is placed on top of a 7 × 1 × 1 (a = 23.509 Å, b = 4.440 Å) supercell of FeS₂ (001) slab (Fig. 4a), the lattice mismatch is minimized within 2%. In this system, Bi₂Te₃ slab is strained (tensile strain of 7% on the x-axis and 0.22% on the y direction), which has been previously shown to improve the out-of-plane thermoelectric properties of this material, enhancing its figure of merit (ZT).³² Then, both structures are assembled with an initial separation (height h) of 2.5 Å. Atoms on the first two layers of FeS₂ (001) and the top layer of Bi₂Te₃ are frozen to mimic bulk conditions, while the atoms at the heterojunction are allowed to relax according to the computational details discussed earlier. In this work, despite not including spin–orbit coupling (SOC) due to the large system considered, we prioritized a high-fidelity interface model that enables well-converged calculations of the electronic and thermoelectric response of FeS₂–Bi₂Te₃. This methodological choice is also supported by prior results showing that including SOC generally diminishes the thermoelectric performance of Bi₂Te₃.⁵² The computed interfacial electronic structure is metallic, in line with experimental measurements, which lends confidence to our theoretical description. It is worth mentioning that the modified Bi₂Te₃ is not stable when considered as a free-standing structure, as our optimization calculations show a massive shrinking of the cell. On the other hand, we stress that these structures are only considered to enable a feasible computational cost on DFT simulations.

Fig. 4 (a) The FeS₂–Bi₂Te₃ heterojunction is constructed by combining 2 monolayers of a (3 × 1 × 1) supercell of modified Bi₂Te₃ (taken as a sublattice of bulk Bi₂Te₃), on top of a (7 × 1 × 1) supercell of 2L FeS₂ (001) slab, (b) the charge density difference analysis for the FeS₂–Bi₂Te₃ heterojunction. The yellow (cyan) regions represent charge accumulation (depletion). Isosurface was set to 0.003 e A⁻³, (c) the electronic band structure of the heterojunction projected into the FeS₂ and Bi₂Te₃ counterparts.

To probe the interfacial interactions, we performed differential charge density analysis, shown in Fig. 4b. This revealed charge depletion from Te atoms and accumulation near S atoms at the interface, indicating strong electronic coupling between the two layers.

The electronic band structure of the heterojunction, presented in Fig. 4c, displays partially filled valence bands, suggesting metallic character. This is consistent with the experimentally observed ohmic behavior of the FeS₂–Bi₂Te₃ interface (see Fig. 3a). Band projections indicate that the states near the Fermi level are primarily contributed by the FeS₂ (001) slab, further confirming its metallic nature.

Interestingly, no significant band dispersion is observed along the Γ → Z direction in reciprocal space, with all bands appearing flat in this region. A small band gap of approximately 0.06 eV was observed along this path, indicating limited electronic conduction in that crystallographic direction at the heterojunction.

We now discuss the thermoelectric properties of Bi₂Te₃, FeS₂, and the FeS₂–Bi₂Te₃ heterojunction. Bulk Bi₂Te₃ crystallizes in a rhombohedral symmetry (space group R3̄m). The optimized lattice parameters are a = b = 4.439 Å and c = 30.661 AA with α = β = 90° and γ = 120°. From the electronic perspective, bulk Bi₂Te₃ is a semiconductor with a narrow direct band gap of 0.18 eV (Fig. S1a), in agreement with previous results.^53,54

Fig. S1b in the SI shows the temperature dependence of the Seebeck coefficient (S) along the x, y, and z crystallographic directions. It can be observed that the narrow band gap results in nearly vanishing Seebeck coefficients along the x and y directions. The z component shows a small value of 20 μV K⁻¹, which decreases with increasing temperature.

The same calculations were performed for FeS₂ (pyrite), with optimized lattice parameters of a = 3.402 Å, b = 4.443 Å, and c = 5.421 Å with α = β = γ = 90°. The obtained electronic structure shows a semiconductor with an indirect bandgap of 1.16 eV (Fig. S2a), which is larger than values reported in previous studies (0.95 eV).^55,56

Bulk FeS₂ has a high Seebeck coefficient reaching 1600 μV K⁻¹ with a distinct behavior: all the components vanish below 300 K with a discontinuous drop at approximately 307 K for the z component, 305 K for the y component, and 290 K for the x component. Above 315 K, all the components decrease with increasing temperature (Fig. S2b). The anisotropic behavior among the x, y, and z components is attributed to the low symmetry of the orthorhombic crystal lattice.

In contrast with bulk FeS₂ and Bi₂Te₃, the electronic structure of the heterojunction, shown in Fig. 4c, has partially filled valence bands, evidencing its metallic behaviour. This observation agrees with electrical measurements of FeS₂–Bi₂Te₃ showing an ohmic behaviour indicating a metallic nature (Fig. 3a). To gain further insights, we have projected these bands into the FeS₂ (001) slab and Bi₂Te₃ counterparts as represented by the colour map. It is noticeable how the states near the Fermi level are dominated by FeS₂ (001), which is metallic as shown in Fig. 4c. Interestingly, no dispersion relation is observed at the path Γ → Z in the reciprocal space, since all the bands are flat within the range of energies investigated. Moreover, in this direction, there is a bandgap of roughly 0.06 eV indicating the smaller electronic conduction at the heterojunction. To explore the interactions on the heterojunction, we performed differential charge analysis (Fig. 4b) revealing charge depletion from the Te atoms and its rearrangement near the S atoms at the heterojunction showcasing the significant interaction between both structures. As shown in Fig. 5a, the y component of the Seebeck coefficient (S) is very low (5 μV K⁻¹) and increases linearly with temperature, reaching 10 μV K⁻¹ at 425 K. The S_x component has a negative value (approximately −20 μV K⁻¹), indicating that electrons dominate the charge carrier character.⁵⁷ The asymmetry compared to the x component is related to the significant difference in lattice parameters in the plane. The Seebeck coefficient in the xy plane is larger compared to the bulk, the origin for this result could be attributed to the strain on the heterostructure: there is a 7% tensile strain on the x direction and a 0.22%, observing Fig. 5a, one can confirm that S_x is larger than S_y in agreement with the observed results. This also corroborates previous studies that shown the effectiveness of tensile strain in modulating the thermoelectric properties of Bi₂Te₃.³²

Fig. 5 Thermoelectric properties of the FeS₂–Bi₂Te₃ heterojunction: (a) Seebeck coefficient components (b) the electronic conductivity components and (c) power factor as a function of the temperature.

On the other hand, the z component is larger (in absolute value), reaching −95 μV K⁻¹ at 325 K. This difference compared to the xy plane is attributed to the almost zero electronic conductivity (σ) in the z direction, as observed in Fig. 5b. It can be seen that the conductivity decreases to zero from the y, x, and z components. Therefore, the larger Seebeck coefficient in the z direction is a combination of zero electronic conductivity in this direction (an indication of a bandgap, in agreement with the previous discussion) and the electron concentration at the heterojunction, as shown by the charge density difference plot (Fig. 4b).

From the available data, the thermoelectric conversion capacity of the FeS₂–Bi₂Te₃ heterojunction can be evaluated by calculating the power factor (PF), expressed as:

where S is the Seebeck coefficient, σ is the electrical conductivity, and τ₀ is the relaxation time (Fig. 5c). Analysis reveals that the z-component of the power factor in the FeS₂–Bi₂Te₃ system is limited primarily by its relatively low electronic conductivity in that direction.

In this context, maximum thermoelectric performance along the z-axis can be achieved through an optimal combination of intermediate Seebeck values and improved electronic transport. Importantly, introducing a localized heating source—as in the case of RF-induced heating of FeS₂—can induce a significant thermal gradient across the interface, enhancing the Seebeck voltage across the Bi₂Te₃ layer. This enhancement arises from the non-uniform temperature distribution at the interface, which promotes directional charge carrier diffusion and improves thermoelectric output.

Thus, localized heating via RF absorption not only initiates the energy conversion process but also strategically enhances thermoelectric response by leveraging the anisotropic transport properties of the heterojunction components.

3.3. RF heating-induced thermoelectric effect at Bi₂Te₃ heterojunction

To investigate the localized RF heating-induced thermoelectric effect at the Bi₂Te₃–FeS₂ heterojunction, a series of controlled RF heating experiments were performed. Fig. 6a presents the schematic of the electrode configuration employed during the measurements, with a corresponding experimental setup digital photograph included in the SI (Fig. S3). A custom-built RF generator was developed for this study, capable of producing RF signals in the 35–40 MHz range with a maximum output power of 1 W. The RF signal was delivered via a 2-meter coaxial cable to a monopole antenna. The Ti–FeS₂ side of the heterojunction was exposed to these RF signals by placing the antenna approximately 10 cm from the device. Resulting temperature distributions were captured using thermal imaging, as shown in Fig. 6b, and the corresponding frequency-dependent maximum temperature plot is shown in Fig. 6c.

Fig. 6 (a) Schematic representation of the experimental setup used to study the RF heating-induced thermoelectric effect in the FeS₂–Bi₂Te₃ heterojunction; (b) thermal images showing RF-induced heating in the heterojunction; (c) frequency-dependent maximum temperature plot; (d) frequency-dependent output voltage and current generated across the Bi₂Te₃ layer; (e) frequency-dependent output power plot; (f) frequency-dependent power density plot; (g) comparison of power output from various RF energy harvesting approaches: (α) receiving antenna (Wi-Fi, GSM 900, 1800 MHz), (β) textile antenna (Wi-Fi), (γ) patch antenna (Wi-Fi, GSM), (δ) multi-resonator antenna (915 MHz), (Φ) rectenna (Wi-Fi, GSM), (Ψ) RF–thermoelectric composite (HF 35–38 MHz, this work).

Experimental observations indicate that the maximum recorded temperature was 46 °C at 35 MHz, which exhibited a gradual decrease with an increased frequency up to 38 MHz. Simultaneously, the output voltage and current across Bi₂Te₃ (Fig. 6d) were measured to evaluate the power generated by RF heating. The maximum recorded voltage output from the device was 7.5 mV at 35 MHz, with a gradual decline in voltage observed at higher frequencies. This behaviour suggests that 35 MHz corresponds to the resonant frequency of the transmitting antenna system, which includes the 2-meter coaxial feed and the 75 cm monopole antenna. At resonance, efficient impedance matching and strong electromagnetic coupling occur, leading to enhanced RF absorption by the device and localized heating, which translates into a higher thermoelectric voltage. The observed peak temperature and voltage at this frequency further support this hypothesis. However, to conclusively attribute this effect to resonance, systematic experiments involving variations in antenna geometry, cable length, and impedance matching conditions are necessary. These investigations will be carried out in future studies to establish a robust understanding of the resonance-driven energy conversion mechanism.

Finally, the overall power generated and power density by RF heating are shown in Fig. 6e and f, calculated by taking the product of output voltage with current and current density. The heterojunction pellet delivered a maximum power output of 100 μW and a power density of 13 mW cm⁻². To evaluate the electromagnetic-to-thermoelectric (EM–TE) performance, both overall conversion efficiency and power output normalized to device mass and volume were considered. In our experiments, the RF source delivered 1 W to the transmitting antenna at 35 MHz, yielding a maximum electrical output of ≈100 μW from the FeS₂–Bi₂Te₃ heterojunction. Taking the transmitter output as the reference, the global conversion efficiency is therefore ≈0.01%. The actual RF power absorbed by the device is much lower than the transmitted power. Using a conservative geometric upper bound based on isotropic spreading at a 10 cm distance and a pellet cross-sectional area of 0.785 cm² the maximum incident RF power on the pellet is estimated at ≈0.625 mW. Relative to this upper-bound value, the local conversion efficiency is ≈16%. This local value provides a more realistic measure of the material/device's ability to convert intercepted RF energy into electrical power. For comparison with other reported materials and devices, the power output was normalized by the pellet's active mass (≈5 g) and volume (≈0.275 cm³), resulting in a mass-normalized power density of ≈20 μW g⁻¹ and a volume-normalized power density of ≈364 μW cm⁻³. These metrics, along with the efficiency values, establish a baseline for future optimization through improved RF coupling, impedance matching, and thermal management strategies. Multiple such heterojunctions can be cascaded, and when integrated with an appropriate network matching circuit, the overall power performance can be significantly enhanced. Multiple such heterojunctions can be cascaded, and when integrated with an appropriate network matching circuit, the overall power performance can be significantly enhanced. A comparison of the output power from previously reported RF energy harvesting methods is shown in Fig. 6g. Most studies focus on designing specific antennas and rectifiers (rectenna) to capture RF signals at various frequencies.^58–62 The collected RF signal is then fed into rectifiers to generate a DC voltage. In contrast, our work engineers the material itself to convert RF energy into heat, which is subsequently converted into electricity by a thermoelectric material.

While the FeS₂–Bi₂Te₃ heterojunction offers a compelling route for RF energy harvesting by combining an earth-abundant sulfide with a high-performance thermoelectric material, it is important to weigh its merits, potential, and challenges for real-world use. Key merits include the synergistic RF-to-heat and thermoelectric conversion within a single heterojunction, the use of scalable pellet pressing and sintering fabrication, and the stable structural/chemical integrity observed after RF exposure in our tests. The approach shows strong potential for further optimization through multiple strategies: interfacial engineering between FeS₂ and Bi₂Te₃ could reduce thermal boundary resistance (TBR) and thereby improve phonon transport; incorporating highly RF-absorptive materials such as graphene, CNTs, or MXenes could increase localized heating; tuning the Schottky barrier at the Ti/FeS₂ interface via work function engineering or alternative metal contacts (Pt, Pd) could enhance charge transport and thermionic emission; nanostructuring, defect engineering, or high-entropy alloying in Bi₂Te₃ could boost the thermoelectric figure of merit (ZT); and optimizing the RF frequency response and device geometry could enable broader spectral absorption across multiple frequency bands.

Interfacial thermal resistance between FeS₂ and Bi₂Te₃ is a critical factor that can strongly influence the effective temperature gradient and, consequently, the overall thermoelectric performance of the heterojunction. This resistance, often referred to as thermal boundary resistance (TBR) or Kapitza resistance, originates from several physical causes: (i) lattice mismatch between the cubic pyrite structure of FeS₂ and the rhombohedral Bi₂Te₃, which creates structural discontinuities at the atomic level; (ii) differences in bonding character, as FeS₂ exhibits predominantly covalent–ionic bonding while Bi₂Te₃ is a layered van der Waals solid, leading to different stiffness and vibrational coupling at the interface; and (iii) mismatch in phonon spectra, where the dominant phonon modes and group velocities differ between the two materials, reducing the probability of phonon transmission across the interface.⁶³ These factors cause partial reflection and scattering of heat-carrying phonons at the junction, creating a temperature discontinuity that effectively reduces the portion of the RF-induced heat reaching the thermoelectric legs. In the present device, where RF absorption in FeS₂ produces localized heating that must be efficiently transferred to Bi₂Te₃ for thermoelectric conversion, any additional temperature drops across the interface directly diminishes the usable ΔT and therefore lowers the achievable power output. The magnitude of this effect depends on the intrinsic TBR, the interfacial quality from the fabrication process, and the contact pressure in the pellet assembly. In practical terms, minimizing TBR is essential for maximizing conversion efficiency, particularly in compact devices where the available ΔT is already limited. Potential strategies to address this include atomic-level surface cleaning or functionalization of FeS₂ prior to Bi₂Te₃ deposition to improve bonding,⁶⁴ introducing graded intermediate layers (e.g., Fe–Te or Bi–S compounds) that gradually bridge lattice and vibrational mismatches,⁶⁵ and nanostructuring the interface to increase the effective contact area while preserving good phonon coupling.⁶⁶ These approaches, widely studied in thermoelectric superlattices and heterostructures, could be adapted to the FeS₂–Bi₂Te₃ system to reduce TBR and unlock higher performance in RF-to-thermoelectric energy harvesting applications.

The current device performance was evaluated under controlled RF excitation at a frequency matched to the antenna's resonance, ensuring maximum coupling and heating efficiency. While this demonstrates proof-of-concept under optimal conditions, the heterojunction can also operate under ambient RF fields if the antenna and matching network are designed for broadband or multi-resonant operation. Such designs could improve energy harvesting efficiency in real-world scenarios where the available RF spectrum varies with time and location. At the same time, challenges for practical deployment remain: the current output of ≈13 mW cm⁻² is insufficient for medium or high-power electronics without supplemental storage or amplification; long-term stability under continuous or cyclic RF exposure is yet to be established; and efficient RF coupling in realistic environments will require tailored antenna–device integration. Notably, the RF power levels and operating temperatures used in our experiments were relatively low—well below thresholds typically associated with thermomechanical degradation—making significant stability issues unlikely in the short term. Nonetheless, future studies will perform systematic cycling and reusability tests to quantify any potential degradation in electrical output, interfacial quality, or thermoelectric performance. Scaling up device area while maintaining low contact resistance and interfacial quality will also demand careful process control. Addressing these points through targeted materials, interface, antenna, and device-level improvements could enable the FeS₂–Bi₂Te₃ heterojunction to evolve into a viable RF-to-thermoelectric energy conversion technology for self-powered IoT sensors, wireless communication systems, and other low-power applications.

3.4. Molecular dynamics calculations

To explain the mechanisms of thermal transport in RF-heated Bi₂Te₃, we performed a series of molecular dynamics calculations. Fig. 7a shows the structure of Bi₂Te₃ used for MD simulations. The thermal conductivities of Bi₂Te₃ in three directions calculated by MD simulations are presented in Fig. 7b. The thermal conductivity generally decreases within a temperature range of 300 to 425 K. This can be attributed to multiple factors, such as defects (e.g., grain boundaries and vacancies) in Bi₂Te₃ crystal at higher temperatures; an additional reason could be heterogeneities at bulk scale as compared to an ideal system considered for MD simulations. Interestingly, different trends of thermal conductivity as a function of temperature are reported in the literature. Huang and Kaviany⁶⁷ show that the thermal conductivity of Bi₂Te₃ decreases with temperature using MD simulations, which agrees with the experimental results by Satterthwaite and Ure.⁶⁸ However, Zhang et al.⁶⁹ report an increase in thermal conductivity of nanostructured Bi₂Te₃ with temperature. Our MD simulations also reveal the anisotropy in Bi₂Te₃, where the thermal conductivity is higher in the x and y directions (in-plane directions) than z direction (cross-plane direction) due to different governing interactions between atoms. The same anisotropic behaviour is reported in previous studies.^70–72Fig. 7(d–f) presents the spatial temperature distributions of the simulation box at different stages of simulated RF heating. Temperature is evenly distributed at the early stage (0 to 0.1 ns) since the heating rate is low and little thermal energy is added to the system (Fig. 7d). When the system is heated at a higher rate, thermal energy starts to accumulate in the heat source and propagates through the system, creating a significant thermal gradient (Fig. 7e). At 0.9 to 1 ns, the gradient becomes more pronounced and a temperature difference up to 200 K is observed due to the low thermal conductivity of Bi₂Te₃ in the z-direction (Fig. 7f).

Fig. 7 Molecular dynamics simulations of Bi₂Te₃. (a) The hexagonal conventional cell of Bi₂Te₃, (b) calculated thermal conductivities in three directions as a function of temperature, (c) NEMD setup to simulate RF heating where the heat source is the region coloured in red, (d)–(f) temperature distributions in the system at different stages during RF heating.

With the thermal gradient induced by RF heating in Bi₂Te₃ confirmed through molecular dynamics (MD) simulations, the RF-induced thermoelectric effect in FeS₂–Bi₂Te₃ is further discussed below. When an RF signal is applied to the metal-semiconductor junction, in this case, the Ti-FeS₂ heterojunction, the incident electromagnetic energy interacts with the charge carriers at the junction. These carriers gain sufficient energy from the RF field to overcome the Schottky barrier at the heterojunction, allowing for the flow of charge across the junction. This process, known as the Schottky barrier lowering, results in an increased carrier concentration and the excitation of electrons in the metal (Ti) and semiconductor (FeS₂) regions.⁷³ The RF energy also generates localized heating at the Ti–FeS₂ junction due to the interaction of the RF signal with the material's free electrons, which causes them to vibrate and collide with atoms, thus raising the temperature in this localized region. This localized heating leads to the establishment of a thermal gradient across the heterojunction. Bi₂Te₃, which is near this heated junction, benefits from this thermal gradient. Due to the thermoelectric properties of Bi₂Te₃, this temperature difference causes charge carriers in the material to diffuse from the hot region to the cooler region, creating a voltage gradient across the Bi₂Te₃ layer. The above concept is depicted schematically as shown in Fig. 8. The generated thermoelectric voltage is a direct result of the Seebeck effect, wherein the heat energy is converted into electrical energy. In this case, the localized heat at the Ti–FeS₂ heterojunction essentially drives the thermoelectric effect in Bi₂Te₃, thereby enabling the conversion of the thermal energy generated by the RF signal into usable electrical power. This localized heating not only enhances the efficiency of the thermoelectric effect but also demonstrates a unique coupling between RF energy absorption and thermoelectric energy harvesting.

Fig. 8 Schematic representation of localized RF heating-induced thermoelectric effect in FeS₂–Bi₂Te₃ heterojunction.

4. Conclusion

In this study, we present a novel FeS–2–Bi₂Te₃ heterojunction-based device for radiofrequency (RF) thermoelectric energy harvesting. The system leverages a Schottky junction formed at the Ti/FeS₂ interface to convert incident RF energy into localized heating, which is subsequently harnessed by Bi₂Te₃ to generate electricity via the Seebeck effect. RF heating experiments demonstrated efficient electromagnetic absorption, with a peak temperature of 45.5 °C achieved at 35 MHz under 1 W input power. A thermal gradient of 5.5 K across the heterojunction produced a maximum power output of 100 μW, underscoring the device's potential for practical energy harvesting applications.

Complementary density functional theory (DFT) and molecular dynamics (MD) simulations elucidated the underlying charge and heat transport mechanisms. These simulations confirmed electron accumulation at the Ti/FeS₂ interface and revealed anisotropic thermal conductivity in Bi₂Te₃, which plays a critical role in the development of the thermal gradient. The integrated computational–experimental approach offers new insights into the coupling between RF energy absorption and thermoelectric conversion.

This work establishes a promising alternative to conventional rectenna-based RF energy harvesting systems. Future efforts will focus on optimizing interfacial design, incorporating nanostructured thermoelectric materials, and enhancing RF absorption to advance the development of efficient, self-powered platforms for Internet-of-Things (IoT) devices and wireless sensor networks.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request. All other relevant data are included within the article and its SI. Supplementary information: The band structure of Bi₂Te₃ projected onto Bi-6p and Te-5p shows a narrow direct gap, and the Seebeck coefficient versus temperature highlights low planar values. For FeS₂, the band structure projected onto Fe-3d and S-3p shows an indirect gap, and the Seebeck coefficient versus temperature reveals anisotropy from low crystal symmetry. A digital photo shows electrode connections on the FeS₂–Bi₂Te₃ pellet, and MD simulations present the heating rate as a function of time. See DOI: https://doi.org/10.1039/d5tc02617b

Acknowledgements

CST acknowledges the Core research grant of SERB, India, STARS projects by MHRD-India, DAE Young Scientist Research Award (DAEYSRA), and AOARD (Asian Office of Aerospace Research and Development) grant no. FA2386-21-1-4014, and the Naval Research Board for funding support.

Notes and references

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