Introduction

Thermoelectric materials can directly convert thermal gradients to electricity, and vice versa. The performance of thermoelectric materials can be described by the figure of merit ZT, ZT=S2T/ρκ. Herein, S, T, ρ, and κ denote the Seebeck coefficient, absolute temperature, electrical resistivity, and total thermal conductivity (including the lattice and electronic components), respectively.1, 2, 3 The lattice thermal conductivity κL can typically be reduced via a low sound velocity,4 a large lattice anharmonicity,5, 6, 7, 8 rattling atoms in lattice voids,9, 10, 11 or even liquid-like sublattices,12, 13, 14, 15 and multi-scale microstructures.16, 17, 18, 19, 20 The electronic properties can be improved by band convergence,21, 22, 23, 24, 25, 26 dimensionality reduction,1, 27, 28, 29 and resonant levels.2, 30 By modulating the electronic and thermal terms, the figure of merit and energy conversion efficiency of thermoelectric materials can be optimized for widespread applications.

GeTe is a narrow band gap IV–VI compound,31 which exhibits rhombohedral and cubic crystal structures in low and high temperatures, respectively, due to a ferroelectric phase transition at ~370 °C.32 Due to high concentrations of Ge vacancies,33 GeTe shows p-type conduction behavior in both phases. The common strategies for the optimization of GeTe are reducing the hole concentrations and the thermal conductivity.34 Over the years, GeTe-based materials have been regarded as high-performance thermoelectric materials and components, especially GeTe-AgSbTe2 solid solutions (known as TAGS).35 In TAGS, a figure of merit ZT >1.5 can be achieved by controlling the Ag/Te ratio36 or doping rare earth Ce, Yb and Dy.37, 38 Recently, Pb dopants in GeTe were successfully used to optimize the carrier concentration and form sub-micron phase separation domains to reduce the thermal conductivity, which resulted in a ZT of ~2 for PbxGe1−xTe.39 Bi2Te3-doped PbxGe1−xTe has also been reported with an excellent ZT of ~1.9.40 SbxGe1−xTe compounds showed a similar ZT of ~1.85 and high mechanical stability.41 Therefore, GeTe can provide a versatile lead-free base material for thermoelectric applications.34

However, the influence of resonant levels on the thermoelectric response of GeTe warrants further exploration. Resonant levels can be introduced through interactions between the dopants and the host. The dopants normally have similar electronic configurations as the host atoms, and they are usually selected from the neighboring main group elements,42 such as doping Tl on the Pb-site of PbTe,2, 30 Sn on the Bi-site of Bi2Te3,43 Pb on the Bi-site of BiCuSeO,44 and In on the Sn-site of SnTe.45 The modified density of states (DOS) obtained by the resonant levels can have an important effect on the Seebeck coefficients of thermoelectric materials. The Mott relationship shows the fundamental expression of the Seebeck coefficient:46

Herein, kB and σ(E) are the Boltzmann constant and the energy-dependent electrical conductivity. Equation (1) indicates that the energy dependence of the carrier concentration p or mobility μ near the Fermi level determines the Seebeck coefficient. Critical scattering near phase transitions and charge-carrier relaxation can lead to an abrupt change of μ(E).47, 48 However, a large dp(E)/dE could also originate from an unconventional distortion of the DOS by the introduction of proper dopants, as aforementioned, which is another fundamental reason for the enhanced Seebeck coefficients.

Recently, phase-change materials have attracted significant attention for high-performance energy conversion.8, 12, 49 Searching for dopants in a phase-change material, which can induce resonant levels in both the low- and high-temperature phases, would be technically useful for thermoelectric applications. The energetic positions of resonant levels could be temperature dependent in IV–VI compounds due to the relative energy shifts of the host states and resonant levels when the temperature changes.2 The shifted Fermi level can also hinder the beneficial effect of resonant levels on the electrical properties. In this study, ab initio calculations and experiments are carried out to study the possible resonant levels in GeTe by doping the materials with group IIIA elements. Among them, indium dopants in GeTe are found to create strong resonant levels in both the rhombohedral and the cubic phases. In our experiments, In-doped GeTe compounds exhibit significantly enhanced Seebeck coefficients. The reduced hole concentration as the In content increases indicates that the dopants help to reduce the intrinsic Ge vacancies. The increased electrical resistivity, due to the lowering of the carrier concentration and mobility, reduces the total thermal conductivity and leads to a relatively high ZT of 1.3 near 355 °C in the In0.02Ge0.98Te compound. The average ZT is enhanced by ~70% across the entire temperature range. The resonant levels induced by indium doping make InxGe1−xTe attractive for further optimization.

Experimental procedures

Theoretical calculations

The DOS was obtained by first-principles calculations with the Vienna ab initio simulation package (VASP).50 Generalized gradient approximation51 and projected augmented wave methods52, 53 were adopted in the calculations. We adopted a 4 × 4 × 4 supercell of the formula unit GeTe for all the calculations in the rhombohedral and cubic phases, including the ones with vacancies or group IIIA dopants. Vacancies in Ge63Te64 were found to have no effect on the total DOS. All crystal structures were fully relaxed before the DOS calculations. The theoretical transport properties (the carrier concentration dependence of the Seebeck coefficient) were calculated by combining density functional theory (DFT) with the Boltzmann transport formula, based on the constant relaxation time approximation.54, 55 The spin-orbit coupling effect can have a strong influence on the band structure and DOS of GeTe,56 which was considered in all the first-principles calculations.

Synthesis of InxGe1−xTe samples

The InxGe1−xTe (x=0, 0.01, 0.02, 0.03, 0.04, 0.05, 0.06) compounds were synthesized by melting stoichiometric elements In, Ge, and Te (99.999%, Sigma-Aldrich, St Louis, MO, USA) in sealed quartz tubes. The mixtures were first kept at 1050 °C for 24 h, subsequently slowly cooled to ~500 °C and held for 70 h. The grown ingots were ground into fine powders in agate mortars. Powders were sintered into bulk materials in a spark plasma sintering (SPS) System using a graphite die with a diameter of 12.7 mm under a pressure of 45 MPa. The crystal structure is determined by X-ray diffraction (XRD) on a Rigaku D/max 2200 (Rigaku Corporation, Tokyo, Japan). The XRD patterns are shown in Supplementary Figure S1. The phase purity and compositions are examined using a Zeiss Supra 55 scanning electron microscope (SEM) with an Oxford energy dispersive spectrometer (EDS). SEM and EDS elemental mapping results are presented in Supplementary Figures S2–S4.

Measurements of thermoelectric properties

The Seebeck coefficient (S) and electrical resistivity (ρ) for InxGe1−xTe from room temperature to ~460 °C were measured on an ULVAC ZEM-3 system using bar samples (~2.5 × 2.5 × 8 mm3) cut from the sintered pellets. The total thermal conductivity of InxGe1−xTe was determined from the thermal diffusivity (α), density (D) and heat capacity (Cp) using the equation κ=Cp × D × α, where the thermal diffusivity (α) was measured by a Netzsch LFA 457. Archimedes’ method was used to determine the densities of the sintered samples, while the heat capacity was estimated by the Dulong-Petit law. The differences in the rhombohedral and cubic phases were considered. The uncertainties of the measured electric resistivity, Seebeck coefficient, and calculated thermal conductivity were estimated at approximately 5, 5, and 10%, respectively.

Hall effect measurements

Hall measurements were performed on thin bar samples (~2 × 7 × 0.6 mm3) in a physical property measurement system (PPMS) equipped with a 9-T magnet (up to±3T used in this work) to determine the room temperature carrier concentration and mobility. The Hall measurements were verified by comparing the results with those obtained from 125Te NMR methods.34 The Hall coefficients (RH) of InxGe1−xTe were calculated from the slopes of Hall voltage vs magnetic field curves. Then, the carrier concentration (p) and Hall mobility (μ) were calculated from the Hall coefficients and electrical resistivity using the relations, p=β/|eRH| and μ=|RH|/ρ, respectively, where β is approximately equal to unity for degenerate GeTe compounds.

Results and Discussion

Possible distortions of the DOS due to group IIIA elements (Ga, In, Tl) in GeTe were first determined by ab initio calculations. Figure 1a shows the DOS of GeTe (Ge64Te64) and In0.016Ge0.984Te (InGe63Te64) in their room temperature rhombohedral phases. For stoichiometric GeTe, the Fermi level is located in the middle of the band gap. However, due to large amounts of intrinsic Ge vacancies, binary GeTe compounds in the experiments usually have high hole concentrations. The Fermi level falls deeply into the valence band (VB), which leads to the p-type transport behavior of GeTe. When the indium dopants are introduced, the total DOS is distorted near the VB maximum (VBM). The ab initio calculations for In0.016Ge0.984Te exhibit two states induced by the In: the hyper-deep states at −5~−6 eV below the VBM (not shown here) and the deep defect states (DDSs) right above the VBM, which pin the Fermi level (Figure 1a). The DDS is caused by the hybridization between In and the host, with 5p1 from In instead of 5s2. As shown in Figure 1a, 20% of the DDS are composed of In, 10% from Ge, 50% from Te, and the rest are interstitial states. The DDS is originally a fully filled bulk band in GeTe, and it is pulled upwards and becomes half-filled due to the In dopant, which implies that each In supplies one hole when it substitutes Ge in GeTe (forming the defect InGe). At high temperatures, GeTe transforms into a face-centered cubic structure. The transition temperature is ~370 °C, depending on the alloying contents. By considering the working temperature range of GeTe-based thermoelectric materials, which is across the phase transition point, the mechanism by which In-doping alters the DOS of the cubic phase is another important question. Figure 1b shows GeTe and the In-doped compound in their face-centered cubic phases. Compared with the undoped GeTe, the In-doped GeTe shows very similar resonant levels to those in the rhombohedral phase. The energy differences between the VBM and resonant levels are relatively small in both phases. The enhanced total DOS in both phases originates from the interaction between hosts and dopants, which do not depend on the actual crystal structure or temperature. Because the DDSs are around the Fermi levels, the DOS changes should contribute to a sizeable Seebeck enhancement.

Figure 1
figure 1

The calculated density of states (DOS) for (a) room temperature rhombohedral phase GeTe (Ge64Te64) and In0.016Ge0.984Te (InGe63Te64); (b) high-temperature cubic phase Ge64Te64 and InGe63Te64; (c) rhombohedral GaGe63Te64; and (d) rhombohedral TlGe63Te64. The In, Ga, and Tl projected DOS and the Fermi levels in InGe63Te64 are included. InGe63Te64 shows an abrupt change of DOS at EF, i.e., the resonant level, in both phases.

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Figures 1c and d show the calculated DOS for Ga-doped and Tl-doped GeTe in the rhombohedral phases. Similar to In, Ga can form a resonant level around the VBM, which changes the total DOS accordingly. The additional energy level leads to a narrow plateau near the VBM in GaGe63Te64. The difference between Ga- and In-doped GeTe is that the DOS peak in the former is hybridized with the VBM, which is probably due to the different energy level of its valent p states with respect to the VBM of GeTe. By contrast, Tl has almost no effect on the total DOS near the VBM. This non-monotonic trend from Ga, In to Tl has also been observed in PbTe, which is attributed to the relativistic effects in Tl.57 Thus, compared with other group IIIA elements, indium contributes a much more distinct resonant level to the electronic bands of GeTe, which may lead to high thermoelectric response, according to our ab initio analysis. Thus, InxGe1−xTe (x=0, 0.01, 0.02, 0.03, 0.04, 0.05, and 0.06) compounds were synthesized to experimentally determine the influence of the resonant levels on thermoelectric properties. The phase purity and compositions were analyzed by XRD and EDS (Supplementary Figures S1–S4). No obvious indium-containing impurity phases were found.

Figure 2 shows the Seebeck coefficient S as function of the carrier concentration p (the Pisarenko relation). The measured carrier concentrations of InxGe1−xTe (x=0, 0.01, 0.02, 0.03, 0.04, 0.05, and 0.06) compounds are 7.2, 6.5, 5.5, 5.1, 4.6, 3.8, and 3.4 × 1020 cm−3, respectively. The corresponding Seebeck coefficients are 33, 54, 68, 84, 95, 116, and 137 μV K−1. A trend line (the dotted line) calculated by the single parabolic band (SPB) model is also obtained by considering a carrier effective mass of 1.28 me, with me as the free electron mass. An acoustic-phonon scattering is assumed (scattering parameter r=−0.5). The experimental Seebeck coefficients are much higher than the SPB results. We then calculate the Seebeck coefficient based on the real band structure of GeTe, as shown by the dashed line in Figure 2, and the theoretical Seebeck coefficients are not consistent with the high experimental ones in most InxGe1−xTe compounds (x>0.02). Only the Seebeck coefficients of In2Te3-GeTe solid solution reported by Sun et al.58 are consistent with the results herein, which indicates the uniqueness of the In dopants in the GeTe host.

Figure 2
figure 2

The room temperature Seebeck coefficient S as a function of the carrier concentration p (the Pisarenko relation). The experimental results of In-doped GeTe and theoretical calculations by the SPB model and density functional theory (DFT) are from the work presented here. Experimental results from the references are shown for comparison, including In2Te3-GeTe solid solution reported by Sun58 and undoped GeTe or GeTe with other dopants reported by Levin,34, 60 Kolomoets,61 and Lubell,62 and Gelbstein.63, 64

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The experimental data for undoped GeTe or GeTe with other dopants are collected for comparison.34, 59, 60, 61, 62, 63, 64 The Seebeck coefficients in In-doped GeTe are considerably higher than those of samples with no dopant or with other dopants. For instance, the carrier concentration of In0.06Ge0.94Te is similar to those of Pb0.05Ge0.95Te and (GeTe)0.97(BiTe)0.03.63, 64 However, the Seebeck coefficient of In0.06Ge0.94Te is three times as high as those of the Pb- or Bi-doped samples. Similarly, the Seebeck coefficient of In0.01Ge0.99Te is twice the S value of an undoped GeTe,63 which has a comparable carrier concentration of 6.3 × 1020 cm−3. Considering the sizable difference in Seebeck coefficients between indium and other dopants, the resonant levels in In-doped GeTe should be responsible for the enhancement of the Seebeck coefficient. The greater Seebeck coefficient enhancements observed for samples with lower carrier concentrations can be rationalized by considering that the Fermi levels move closer to the resonant levels, which are above the VBM of the GeTe host.

Figure 3 shows the indium content x-dependent carrier concentration p and carrier mobility μ in InxGe1−xTe (x=0, 0.01, 0.02, 0.03, 0.04, 0.05, and 0.06) compounds. The decrease in the hole concentration as the In content increases indicates that the In dopants may fill the germanium vacancies,

Figure 3
figure 3

The indium content x-dependent room temperature (a) carrier concentration p and (b) carrier mobility μ in InxGe1−xTe (x=0, 0.01, 0.02, 0.03, 0.04, 0.05, and 0.06) compounds.

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In most conventional thermoelectric materials, the carrier mobility increases as the carrier concentration decreases. However, the carrier mobility values μ in InxGe1−xTe compounds have an opposite dependence on the carrier concentration, and they reduce significantly as the In content x increases. For instance, when the In content changes from x=0 to x=0.06, the carrier concentration and mobility reduce by ~53% and 80%, respectively. Moreover, the mobility reduction phenomenon is commonly observed in materials with resonant dopants.45 The reduction in the carrier mobility should be mainly due to the increased density of ionized impurities as the dopant content becomes higher.

Figure 4 shows the temperature dependence of the Seebeck coefficient S, electrical resistivity ρ, and power factor (PF=S2/ρ) for all InxGe1−xTe (x=0, 0.01, 0.02, 0.03, 0.04, 0.05, and 0.06) compounds. The room temperature Seebeck coefficients in indium-doped samples are enhanced by a factor of between ~1.6 to 4.2, compared with that of the undoped GeTe. The advantages of a high Seebeck coefficient obtained by indium doping can be maintained across the measured temperatures. In the high-T cubic phases, the enhancement gradually reduces with increasing T, and the S values become close to that of the pristine sample at~460 °C. However, In-doping severely increases the electrical resistivity, as both the carrier concentration and mobility become much smaller than those of the pristine sample.

Figure 4
figure 4

Temperature dependence of the (a) Seebeck coefficient S, (b) electrical resistivity ρ, and (c) power factor PF for InxGe1−xTe (x=0, 0.01, 0.02, 0.03, 0.04, 0.05, and 0.06) compounds.

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Fundamentally, the transport characteristics of GeTe exhibit two stages, that is, a stage below and above the phase transition point. In addition, the transition point decreases as the dopant concentration increases. When the carrier concentration is high enough (for example, 7.2 × 1020 cm−3 for the undoped GeTe), the Seebeck coefficient S and resistivity ρ in both the rhombohedral and the cubic phase continue increasing as the temperature increases. The slopes of the S-T or ρ-T curves have two stages due to the phase transition. The curves are sharper in the low-temperature rhombohedral phase.34 As shown in Figure 4, the undoped sample clearly displays such two-stage transport properties. S and ρ in the rhombohedral phase (below ~370 °C) both behave similar to those of degenerate semiconductors. The S-T and ρ-T slopes clearly decrease in the high-T phase. However, as the carrier concentration decreases, the S-T or ρ-T curves can exhibit different evolutions in the two phases. One difference is that the rhombohedral phase may experience both extrinsic and intrinsic transport,64 as shown in the x=0.05 and x=0.06 doped samples. Below the phase transition point (which is already shifted to ~300 °C), the resistivity first increases, but then it decreases as the temperature increases, which indicates the intrinsic conduction behavior. Correspondingly, the Seebeck coefficient curves gradually become flat as the temperature approaches the transition point. The other difference is that the slopes of the S-T and ρ-T curves become negative in the high-T cubic phase in the In-doped samples, which is possibly due to the thermal activation of electrons. The mixed conduction may start to influence the transport properties in the cubic phase. The Seebeck coefficient and resistivity then gradually reduce as the temperature increases.

Due to the trade-off between the enhanced Seebeck coefficient S and electrical resistivity ρ, the PF undergoes an increase in the lower temperature range but a decrease in the higher temperature range. The largest PF of 1.5 × 10−3 W m−1 K−2 at room temperature appears in the x=0.02 sample, which is~80% higher than that of the pristine GeTe. The maximum PF in the x=0.02 sample is 4.2 × 10−3 W m−1 K−2 at 385 °C, which is close to the largest value obtained for the cubic phase undoped GeTe. Above 400 °C, the PF values in the indium-doped samples reduce, which is possibly due to the mixed conduction, as the enhancement of the Seebeck coefficient cannot compensate for the loss in resistivity.

Figure 5a shows the total thermal conductivity of InxGe1−xTe (x=0, 0.01, 0.02, 0.03, 0.04, 0.05, and 0.06) compounds. κ is monotonically reduced by In-doping. The undoped GeTe has a large κ mainly because of its high carrier concentration and thus low electrical resistivity. Near the ferroelectric phase transition, the thermal conductivity reaches its lowest point. Upon In doping, the κ-T slopes are lowered in the rhombohedral phase, and the κ-T curves become almost flat at high indium contents. The total thermal conductivity κ in thermoelectric materials generally can be divided into two components, electronic and lattice thermal conductivity, if the bipolar thermal conductivity is neglected.65 Thus, we have the fundamental relation, κ=κe+κL, where κe and κL are the electronic and lattice thermal conductivity, respectively. The Wiedemann-Franz law κe=LT/ρ directly connects the carrier contributions to the electrical and heat conduction, where L is the Lorenz number. L is dependent on the carrier concentration or Fermi level in the SPB model. The Lorenz numbers for InxGe1−xTe compounds were calculated for each temperature point using the previously discussed theoretical method.66 The Lorenz numbers decrease as the temperature or indium content increases, as shown in Supplementary Figure S5. Using these Lorenz numbers, the lattice thermal conductivity κL can be separated from the total thermal conductivity κ. As shown in Figure 5b, the lattice thermal conductivity κL of the doped samples becomes larger than that of the pristine GeTe above room temperature. The In-doped samples suffer from significantly reduced carrier concentrations and thus enhanced bipolar effects. Both the Seebeck coefficient and resistivity curves at high temperatures exhibit the mixed electron-hole conduction behavior. Therefore, the κL here should also include the bipolar term,65 which potentially makes the calculated values of the doped samples larger.

Figure 5
figure 5

Temperature dependence of the (a) total thermal conductivity κ, (b) lattice thermal conductivity κL, and (c) figure of merit ZT for InxGe1−xTe (x=0, 0.01, 0.02, 0.03, 0.04, 0.05, and 0.06) compounds.

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Figure 5c shows the figure of merit ZT for all InxGe1−xTe (x=0, 0.01, 0.02, 0.03, 0.04, 0.05, and 0.06) compounds. The undoped sample shows ZT values of 0.03 and 1.0 at room temperature and 460 °C, respectively. The highest ZT can be improved to ~1.3 in the In0.02Ge0.98Te compound at 355 °C. The best room temperature ZT is 0.2 in the In0.06Ge0.94Te compound. The electrical terms (S2p) and scattering terms (μ/κ) are calculated to determine the main contribution. At room temperature, the electrical terms are 0.76, 1.9, 2.5, 3.6, 4.1, 5.0 and 6.3 × 1024 V2 K−2 m−3 for x=0 to x=0.06 samples, while the respective scattering terms are 9.4, 8.5, 10.0, 8.1, 7.3, 6.8 and 7.1 × 10−4 S2 mK V−1 kg−1. The mobility loss has been compensated by the reduction in thermal conductivity, which results in similar scattering terms. Apparently, the enhanced ZT in indium-doped GeTe originates from the optimization of the electrical terms, due to the high thermoelectric response induced by the resonant levels. The average ZT is also important for thermoelectric applications in power generation and solid-state cooling, which is expressed as the integral of ZT over the working temperature range. The average ZT of the In0.02Ge0.98Te compound is ~0.7 over the entire measured temperature range, which represents an ~70% enhancement on that of the undoped GeTe.

Conclusions

The indium dopants create resonant levels in both the rhombohedral and cubic phase GeTe, which contribute to a significantly enhanced thermoelectric response. Though the electrical resistivity is increased due to the reduced carrier concentration and mobility, the Seebeck enhancement compensates for such a loss in performance and leads to a higher power factor in most of the temperature ranges. The total thermal conductivity is remarkably reduced, which is primarily due to the decreased electronic contribution. Due to the Seebeck enhancement and thermal conductivity reduction, the figure of merit ZT has been improved to ~1.3 in the In0.02Ge0.98Te compound. The corresponding average ZT is enhanced by ~70% over the entire temperature range. By screening other group IIIA dopants, we observe that resonant levels closer to the VBM are formed in Ga-doped GeTe, while no resonant level is found in Tl-doped GeTe. The strong resonant levels in In-doped GeTe may make it a promising base material in the search for an even higher thermoelectric performance.