Near-Broken-Gap Alignment between FeWO4 and Fe2WO6 for Ohmic Direct p–n Junction Thermoelectrics

We report a near-broken-gap alignment between p-type FeWO4 and n-type Fe2WO6, a model pair for the realization of Ohmic direct junction thermoelectrics. Both undoped materials have a large Seebeck coefficient and high electrical conductivity at elevated temperatures, due to inherent electronic defects. A band-alignment diagram is proposed based on X-ray photoelectron and ultraviolet–visible light reflectance spectroscopy. Experimentally acquired nonrectifying I–V characteristics and the constructed band-alignment diagram support the proposed formation of a near-broken-gap junction. We have additionally performed computational modeling based on density functional theory (DFT) on bulk models of the individual compounds to rationalize the experimental band-alignment diagram and to provide deeper insight into the relevant band characteristics. The DFT calculations confirm an Fe-3d character of the involved band edges, which we suggest is a decisive feature for the unusual band overlap.


■ INTRODUCTION
A known problem of state-of-the-art thermoelectric generators (TEGs) is their low thermal stability and poor environmental friendliness, as they are built up from low melting point intermetallic alloys, containing toxic and scarce elements such as Pb, Te, and Bi. The use of oxide thermoelectrics (TEs) promises increased temperature stability, better environmental compatibility, and lower costs through the use of more abundant elements and is hence likely to expand the field of application of TEs. 1,2 TEGs, however, are not only limited by the TE material properties but also limited by the electric and thermal contacts between the materials and the metal interconnects, which pose additional challenges. 3,4 It is essential to establish good nonrectifying ("Ohmic") contacts between the TE material and the metal interconnect, while avoiding interdiffusion, melting, and oxidation of the contact materials. This often makes it unavoidable to use expensive noble metal interconnects. At the same time, it must be ensured that the thermal expansion coefficients of the individual components such as TE materials, interconnect, solder, and diffusion barrier do not differ too much from one another in order to avoid failure of the module during thermal cycling. 5 Many of these issues could be tackled by the approach of Shin et al. through the use of oxide TEs with a direct p−n junction, hereby omitting the metal interconnects at the hot side. 6−8 However, p−n junctions are usually not Ohmic but exhibit rectifying behavior, which represent large parasitic resistances in the device. A solution to the rectifying behavior is a broken-gap junction couple, well-known in the field of photovoltaics. 9−11 A broken-gap junction forms a charge accumulation region instead of a charge depletion zone, which leads to fully Ohmic characteristics.
In this work, we study the p−n junction of the TE couple ptype FeWO 4 and n-type Fe 2 WO 6 . The two phases show no reactivity toward each other and can be regarded as coexistent. We combine experimental studies with ab initio calculations on the individual materials to establish a model for the band alignment between the two materials. Our findings support a near-broken-gap junction alignment, with a nonrectifying junction behavior. The implementation of broken-gap junctions in direct junction TEGs could give them a significant advantage over their diode-like alternatives without the need of hightemperature thermionic emission. until a single-phase product was confirmed by powder XRD. A dense pellet of 87% relative density was fabricated by sintering at 1050°C for 4 h in air. FeWO 4 was synthesized by mixing Fe 2 O 3 (STREM chemicals 99.8%), Fe (Sigma-Aldrich ≤99.9%), and WO 3 stoichiometrically, thoroughly grinding in an agate mortar, sealing in an evacuated quartz tube, and reacting at 950°C for 48 h. The powder was reground and the procedure was repeated for a total of 200 h reaction time until a singlephase product was confirmed by powder XRD. A cylindrical pellet with a relative density of 85% was obtained by sintering a pressed powder pellet at 1150°C for 4 h in an argon atmosphere. In-house X-ray diffraction measurements were performed on a Bruker D8 Discover with Cu K-alpha-1 radiation, Ge(111) Johanssen monochromator, and Lynxeye detector. Structural refinement was carried out in a Rietveld refinement using the software TOPAS V5. Optical reflectance spectroscopy was performed on each material separately with an OceanOptics USB2000+ spectrometer and a halogen lamp light source at room temperature. The background was calibrated to the reflectance spectrum of a BaSO 4 reference sample.
X-ray photoelectron spectroscopy (XPS) was performed on a ThermoFisher Scientific Thetaprobe, with carefully calibrated energy scale to the Ag 3d 5/2 peak of 368.21 eV binding energy with the stage polarized to −16 V during the experiments. XPS experiments were carried out on freshly broken surfaces of the respective sintered pellets of FeWO 4 and Fe 2 WO 6 . Electrical conductivity and Seebeck coefficient at high temperatures were measured in a custom-built assemblymounted ProboStat (NORECS, Oslo, Norway) measurement cell, described in detail elsewhere. 12 The disc-shaped pellets were placed on an alumina plate with an integrated S-type thermocouple. Two thermocouples and four platinum electrodes for the van der Pauw measurements were pressed on top of the surface of the pellet by springload. A resistive heater on one side of the sample allowed us to apply a temperature difference in-plane of the sample. The setup allows us to measure in-plane Seebeck and conductivity under identical experimental conditions. FeWO 4 was measured under a protective Ar atmosphere to avoid decomposition of the compound above 540°C. To establish the direct p−n junction, individual pellet surfaces were thoroughly ground to 1.5 mm height, polished, and one side of each pellet was painted with platinum ink. The n-type and p-type pellets were sandwiched between platinum net and flat platinum electrodes and pressed together by springload to ensure good electrical contact. After an initial "as-prepared" characterization, the stack was annealed at 900°C for 24 h in a protective atmosphere to ensure good surface contact. I−V characteristics of the p−n junction were measured using a Gamry Reference 3000 potentiostat in the three-wire mode.
Density functional theory (DFT) calculations are performed with the Vienna Ab initio Simulation Package (VASP), 13−15 using the projector augmented wave (PAW) method for computational efficiency. 16 An initial optimization of the structural models is performed, starting from experimental outputs, within the general gradient approximation (GGA) for the exchange and correlation functionals, following the implementation proposed by Perdew, Burke, and Ernzerhof (PBE). 17 The Hubbard parameter U is introduced to account for the strong on-site Coulombic interaction of localized d electrons, not correctly described within the GGA approach, using the rotational invariant method, introduced by Dudarev and co-workers, 18 with an effective U value of 4 eV for both Fe and W. The energy cutoff for the expansion in plane waves is set to a 500 eV, while reciprocal space is sampled using a Monkhorst−Pack (MP) grid 19 with a 0.1 Å −1 spacing between adjacent points. Integrals over the Brillouin zone are computed using the tetrahedron method with Blochl corrections. 20 These parameters ensure a convergence of the total energies within 5 meV. The nonlocal part of the pseudopotential is evaluated using the real-space projection scheme to improve the computational efficiency. 21 The energy convergence thresholds of the self-consistent field and of the structural optimization calculations are set to 10 −5 eV and 10 −3 eV, respectively. Each calculation is repeated for distinct magnetic orderings of the Fe sublattice, considering ferromagnetic and antiferromagnetic configurations. The properties of the energetically most favorable systems are then recalculated using the screened hybrid functional originally developed by Heyd, Scuseria, and Ernzerhof (HSE). 22,23 We follow both the well-established recipes known in the literature, HSE03 and HSE06, for the ratio between the screened Hartree-Fock and the standard PBE exchange. We find better agreement with experimental data for the HSE03 approach. Due to the large computational cost of these calculations, we have reduced the density of the sampled points in the reciprocal space to 0.5 Å −1 , while the other parameters are unmodified with respect to the GGA calculations. A test calculation with a 0.3 Å −1 density, performed only for the FeWO 4 system because of its smaller unit cell, revealed a convergence within 5 meV and 30 meV for the total and the band gap energy, respectively, indicating a good accuracy level. , as seen in Figure 1a. The p-type conductivity is maintained over the entire temperature range, which is evident from the positive Seebeck coefficient plotted in Figure 1b. The p-type charge carriers have been described as small polaron holes, localized on Fe sites, representing oxidized Fe 3+ species. 24−26 Bharati et al. 27 proposed the change at 500°C to stem from a transition from small to large polarons; however, we find this as untypical and suggest a relation to defect chemistry. 28 The Seebeck coefficient below 500°C is nearly constant (see Figure 1b). In the Hubbard model for correlated systems, 29 this indicates a region of constant charge carrier concentration, which can be attributed either to a specific doping level or to a frozen-in defect concentration. Activation energies are obtained from a ln(σT) versus 1/T plot, as these materials conduct in a polaron hopping manner with a diffusion-like mechanism. The conductivity activation energy of 0.18(2) eV in the constant charge carrier region is thus equal to the polaron mobility migration barrier. The experimental value of 0.18 (2) eV is close to the theoretically predicted minimum migration barrier of 0.14 eV. 30 Above 500°C, a decrease in the Seebeck coefficient can be identified, which indicates an increase in the charge carrier concentration. The conductivity activation energy now reflects both concentration (formation) and mobility (migration) of the charge carriers. Assuming that the mobility migration barrier of 0.18(2) eV remains unchanged, the total conductivity activation energy of 0.52(3) eV results in a charge carrier formation energy of 0.34 eV, which is again close to the theoretically predicted formation energy of 0.48 eV. 30 As this energy is too small to be half the band gap and to reflect intrinsic ionization, it may rather be attributed to a charge carrier formation reaction in the form of oxygen interstitials or cation vacancies. This would result in a standard enthalpy of the formation of the point defect and two hole charge carriers of 0.34 eV × 3 ≈ 1 eV, which is a typical value for the formation of oxygen excess or cation deficiency defects from O 2 (g). According to DFT calculations, Fe vacancies are the most stable intrinsic defects, 30 and if formed alone (without simultaneous formation of W vacancies), they must be accompanied by exsolution of an iron-rich phase, such as a binary iron oxide. The leveling out below 500°C in both conductivity and Seebeck coefficientas indicated aboveis accordingly interpreted as a region of the frozen-in defect formation reaction or an overtaking of a slight nonstoichiometry in the cation ratio inherent to the synthesis. Band gap measurements for FeWO 4 are quite consistently around 2 eV in the literature 26,30,31 and supported by our DFT calculations, which will be discussed in a later section. Optical reflectance measurements, analyzed in a Kubelka−Munk plot, revealed a major indirect absorption edge at 1.48(2) eV, which is too low to be in the region of the band gap (shown in the Supporting Information Figure S11). DFT calculations suggest major parallels in the density of states (DOS) near the band gap between FeWO 4 and FeO; 32 we thus compare the two briefly in the following. Balberg et al. reported an absorption feature at ∼1.3 eV, 33 assigned to the 5 T 2g → 5 E g transition, 34 which effectively "blackens-out" higher absorption edges. Although they could observe the hint of an absorption edge at 2 eV, representing the band gap, this was not possible for FeWO 4 . For the construction of the band-alignment diagram (see below), we assume a band gap of 2.00 eV for FeWO 4 .

■ RESULTS AND DISCUSSION
Fe 2 WO 6 . Likewise, thermally activated conductivity is observable in an Arrhenius plot for Fe 2 WO 6 , with two straight lines and a transition at 650°C. The negative Seebeck coefficient indicates n-type conductivity over the accessible temperature range. A decrease in the absolute Seebeck coefficient coincides with the transition in the Arrhenius plot at 650°C. The conductivity is of small polaron hopping nature with electrons localized on Fe sites, representing reduced Fe 2+ states. 35 In an earlier publication, we have investigated the electrical transport and oxygen nonstoichiometry of Fe 2 WO 6 in detail, based on a defect chemical description. 36 Band gap estimates for Fe 2 WO 6 are not straightforward and several energies have been reported in the literature. Optically measured band gaps are often reported to be of 1.5−1.7 eV, 37 which is close to, but smaller than the absorption edge visible for our sample in the Kubelka−Munk-plot occurring at 1.84(2) eV (see Supporting Information Figure S11). A band gap smaller than 1.66 eV would indicate a degenerate semiconductor with the Fermi level in the valence band (as this corresponds to the valence band off-set (VBO) determined for our sample by XPS), contradicting the nondegenerate semiconductor properties from conductivity measurements. Our DFT calculations (see Figure 6) predict a band gap of 2.3 eV, which is much larger than the experimentally obtained values. However, it should be noted that the calculations do not include any defects or mixed valence states in the structure, and it is possible that the presence of oxygen vacancies and reduced iron species lowers the band gap significantly. We take the band gap estimate of 1.84 eV as a realistic assumption for the construction of the band diagram. As indicated above, the two tungstates show related yet opposite characteristics. The charge-carrying species of one of the tungstates represents the matrix component of second tungstates, and vice versaspecifically: In the divalent iron matrix of FeWO 4 , Fe 3+ represents an electron hole, whereas in Fe 2 WO 6 , the opposite situation is given, with Fe 2+ representing an extra electron in the trivalent iron, the host structure. FeWO 4 and Fe 2 WO 6 are the only ternary compounds in the phase diagram of the Fe−W−O system and have been shown to coexist as separate phases. 38−40 The lattice constants of FeWO 4 and Fe 2 WO 6 prior and after being in contact with each other at high temperatures for an extended period of time did not change significantly and there is no indication for the formation of other phases. For comparison, in the solid solutions of Fe 1−x Mn x WO 4 , the a-axis lattice parameter shows a high sensitivity on the Mn content, varying by more than 0.1 Å. 41 We therefore expect FeWO 4 and Fe 2 WO 6 to be separated by a large miscibility gap in a quasi-binary-phase diagram.
Electronic Junction between FeWO 4 and Fe 2 WO 6 . The I−V characteristics of the p−n junction are shown in Figure 2a.
Already, the as-assembled junction of polished separate pellets showed fully Ohmic behavior at room temperature in a bias window from −5 to +5 V, with no sign of rectification. Annealing of the junction at 900°C for 24 h decreased the absolute resistance as the two pellets grew together, increasing the effective contact area. Ohmic behavior did, however, not change and was observable at temperatures from −196°C to 1000°C.
The course of the area-specific resistance (ASR) as a function of temperature is depicted in Figure 2b (low-temperature I−V characteristics are available in the Supporting Information).
Above 500°C, the ASR levels out, becoming seemingly temperature-independent at approximately 1.2 Ω cm 2 . We attribute this to the collective resistances of setup wiring and current collectors, which cannot be fully eliminated in the twoelectrode three-wire measurements. The individual material resistances are by 1 order of magnitude lower compared to the measured total junction resistance, indicating that the majority of voltage drops across the junction and not in the individual materials.
The Ohmic behavior of the p−n junction points toward the band alignment of a broken-gap junction. A broken-gap junction forms between materials with a large difference in electron affinities, where the respective band gaps do not overlap.
Bringing such two materials into contact results in a flow of electrons from the p-type to the n-type, as the Fermi level of the p-type lies above the Fermi level of the n-type.
This leads to a charge accumulation region at the junction in contrast to a charge depletion zone in classic staggered junctions.
With the Fermi level aligned in equilibrium, charge transfer takes place directly between the p-type valence band and the ntype conduction band. A schematic illustration of the broken band junction is shown in Figure 3.
Nonrectifying, low contact resistance is also typical for tunnel junctions at low biases. 10 These tunnel junctions however usually depend highly on the applied bias and show a characteristic breakdown region of negative differential resistance in forward bias, due to a bias-driven misalignment between the n-type conduction band and p-type valence band, when crossing a critical transition point. At further increased forward bias, beyond the negative resistance region, the tunnel junctions behave like typical rectifying p−n junctions with exponential current increase. For the iron tungstate junction, the tunneling junction explanation can be ruled out, due to the absence of a breakdown region and of an exponential growth region.
Below temperatures of 500°C, the junction shows an activation energy of 0.42(2) eV in an Arrhenius plot. The activation energy has to be attributed to the potential barrier arising from the charge accumulation layer forming at the junction.
X-ray Photoelectron Spectroscopy. To confirm the validity of this type of band alignment, X-ray photoelectron spectroscopy (XPS) measurements were carried out. XPS provides insight on the Fermi level position via the work function (Φ) with respect to the vacuum level, and VBO with respect to the Fermi level, and allows calculation of the electron affinity (χ). From the primary electron onset, the VBO with respect to the Fermi level can be obtained, whereas the secondary electron cutoff gives the work function (Φ), which is the position of the Fermi energy with respect to the vacuum level. Intensity onsets can, in most cases, be extracted from linear fit intersects, between the baseline and leading edge of the onset slope.
Following this practice, VBOs with respect to the Fermi energy were determined to be 1.66 eV and 0.17 eV for Fe 2 WO 6 and FeWO 4 , respectively (see Figure 4b,d). The primary electron onset for FeWO 4 shows a peculiar double onset, shifted by 1.2 eV to which we will return in a later section. Secondary electron cutoff for Fe 2 WO 6 produced a work function of 4.51 eV. The cutoff for FeWO 4 , however, is not accessible by this method as the onset is smeared out, which is likely to stem from tail states, surface space charge, or surface roughness. An exclusion principle based on the confidence interval of the baseline was used to determine the real onset in FeWO 4 (described in the Supporting Information). Applying this method resulted in a work function of 4.32 eV for FeWO 4 . For comparison, applying this method to the cutoff in Fe 2 WO 6   produces the same work function as the linear extrapolation method. Junction Band Alignment. From work function (Φ), VBO, and band gap (E g ), a simple band-alignment diagram can be constructed and the electron affinity (χ) can be calculated. Electron affinities χ p = 2.49 eV and χ n = 4.33 eV were calculated for FeWO 4 and Fe 2 WO 6 , respectively, from the relation The schematic energy band diagram is shown in Figure 5. The vacuum level is taken as the reference point. The Fermi level of the p-type FeWO 4 lies 0.19 eV higher in energy than E f for the ntype Fe 2 WO 6 , fulfilling the condition Φ p < Φ n for nonrectifying p−n junctions. 42 It becomes clear that the alignment is not a fully broken one but rather a near-broken-gap junction, as the CBM of Fe 2 WO 6 still lies 0.16 eV above the VBM of FeWO 4 . Near-broken-gap junctions, however, can still exhibit the Ohmic behavior of full-broken-gap junctions, assuming band tails to enable the crossing between the conduction and valence band. 11 We thus suggest a band bending, as described in Figure 3b, where the n-type conduction band bends downward and the ptype valence band bends upward, forming an s-shape-like alignment.
DFT Calculations. The DOS obtained from ab initio density functional calculations are shown in Figure 6 and provide additional insight into the dominant character of the crucial bands involved. Hybrid functional HSE potentials are capable of providing an accurate description of complex structures. 43,44 We present results from HSE03 calculations, which shows better correspondence to experiments than HSE06. The DOS is spinaveraged for clarity and limited to the section that is relevant for the band gaps. A more detailed spin-resolved DOS plot in an extended range is available in the Supporting Information in Figure S13. The calculations assume perfect crystallinity at 0 K without the presence of defects, mixed valencies, or surface effects. Thus, no interband gap states occur and the Fermi level is put to the valence band edge at zero energy. In Figure 6, the DOS plot of Fe 2 WO 6 is shifted downward to represent the band alignment and the dashed line indicates the common Fermi level, as proposed by our XPS results.
Our DFT calculations predict a band gap of 2.00 eV for FeWO 4 in good accordance with previously reported DOS of FeWO 4 using a hybrid functional. 30,45 The main band gap is followed by a second band gap of 1.1 eV, between the localized Fe-3d state and lower-lying filled O-2p bands. This second band gap is indeed observable in Figure 4d, as a second onset shifted by 1.2 eV in the XPS primary electron onset. GGA+U calculations are not able to reproduce the isolated Fe-3d band above the O-2p valence bands. It should be emphasized that the VBM of FeWO 4 is a cationic state, in contrast to an anionic state that is usually the case for binary/ternary semiconductors (e.g., from the common anion rule).
The calculations predict a band gap of 2.3 eV for Fe 2 WO 6 , which is experimentally estimated at 1.84 eV. Intraband gap states from oxygen vacancies and reduced Fe species are not considered in the calculations and would expectedly reduce the calculated band gap. 46 The VBM of Fe 2 WO 6 is mainly composed of O-2p, and the CBM is dominated by Fe-3d bands. Since the VBM of FeWO 4 and the CBM of Fe 2 WO 6 are both of the Fe-3d character, the band alignment, as proposed above, conclusively takes place between bands of the same character. To date, the band alignment between semiconducting transition-metal oxides in heterojunctions is not well-investigated. We would like to emphasize that several other transition-metal oxides, containing, for example, Co or Mn, show cationic states at the VBM. It remains open whether the presence of a low-lying cation band is generally beneficial for the formation of Ohmic p−n junctions and can be exploited. Mentionable here is the p−n junction between Ca 3 Co 4 O 9 and CaMnO 3 , reported by Kanas et al., showing nonrectifying behavior. 47 The p-type Ca 3 Co 4 O 9 does indeed show a cationic Co-3d band at the valence edge. 48    Despite the small band discontinuity that junction exhibits rectifying behavior. For comparison, the FeWO 4 /Fe 2 WO 6 heterojunction in thermal equilibrium results in a band discontinuity of CB Fe 2 WO 6 − VB FeWO 4 = 0.35 eV.

■ CONCLUSIONS
We have investigated FeWO 4 and Fe 2 WO 6 as a model p−n couple for high-temperature direct junction TEs. In contact, these materials stay p-type/n-type, show no reactivity toward each other, and remain coexistent phases. Assembled p−n junctions show nonrectification over a large temperature range from −196 to 1000°C. This is consistent with the model of a near-broken-gap junction, forming a charge accumulation zone and a band alignment between the p-type VB and the n-type CB, in contrast to a depletion zone and a VB−VB/CB−CB alignment in a common staggered-gap junction. Based on XPS and UV/VIS reflectance measurements, we schematically describe the band-alignment diagram for the p−n couple. Our findings are supported by ab initio calculations, showing that both FeWO 4 VBM and Fe 2 WO 6 CBM are of Fe-3d character. These observations may have a wider validity. However, further investigations are needed to clarify whether the presence of dbands at the VBM represents a good criterion for designing broken-gap junctions in transition-metal oxide p−n couples. As FeWO 4 is not stable in air above 500°C, air-stable alternatives should be investigated in the future. We have demonstrated the first near-broken-gap junction to the field of TEs, which presents a promising approach to direct junction p−n junction TEs. They circumvent the rectifying diode behavior of classic staggered-gap junctions and their large parasitic resistance.