Band Structure Engineering and Thermoelectric Properties of Charge-Compensated Filled Skutterudites

Thermoelectric properties of semiconductors are intimately related to their electronic band structure, which can be engineered via chemical doping. Dopant Ga in the cage-structured skutterudite Co4Sb12 substitutes Sb sites while occupying the void sites. Combining quantitative scanning transmission electron microscopy and first-principles calculations, we show that Ga dual-site occupancy breaks the symmetry of the Sb-Sb network, splits the deep triply-degenerate conduction bands, and drives them downward to the band edge. The charge-compensating nature of the dual occupancy Ga increases overall filling fraction limit. By imparting this unique band structure feature, and judiciously doping the materials by increasing the Yb content, we promote the Fermi level to a point where carriers are in energetic proximity to these features. Increased participation of these heavier bands in electronic transport leads to increased thermopower and effective mass. Further, the localized distortion from Ga/Sb substitution enhances the phonon scattering to reduce the thermal conductivity effectively.


Results
Lattice parameters and filling fractions. Figure 1 shows the lattice parameters (a) of the samples as a function of the Yb content determined by EPMA. The lattice parameters of this study were calculated from powder XRD data by Rietveld refinement. The detailed experimental data of lattice parameters and actual compositions can be found in supporting information -Supplementary Table 1 and Supplementary Figure 1. The lattice parameter of Ga 0.2 Co 4 Sb 11.9333 sample is 9.039 Å, which is larger than that of unfilled skutterudites Co 4 Sb 12 (~9.034 Å) 3 . The expansion of the lattice is due to partial Ga filling at the 2a site, consistent with the previous findings 25 . The lattice parameter of Yb, Ga-CCCD samples increases monotonically with increasing Yb content up to 38% of 2a site occupancy. It is important to notice that this filling fraction of Yb is much higher than the filling fraction limit from the previous experiment and the theoretical prediction on the Yb single filled Co 4 Sb 12 , which is around 22% of the cage filling fraction 27,28 . According to our EPMA data, the actual Yb chemical composition in the nominal Yb 0.40 Ga 0.15 Co 4 Sb 11.95 reaches as high as 0.38 without any tendency of saturation. We believe that the Ga-CCCD is responsible for the enhancement of filling fraction of Yb in the Co 4 Sb 12 . Yb acts as the second filler into the Ga charge-compensated matrix, and competes with filler site Ga thermodynamically. As such, the filler site Ga has a tendency to move partially to Sb site. The introduction of more electron deficient Ga onto Sb site boosts the ability of the compound to absorb more donated free charges from the second filler atom, Yb in this case, and hence increases carrier concentration and the filling fraction limit of Yb. A recent theoretical study indeed shows that the filler site Ga tends to partially move to Sb site at higher carrier concentrations 29 . Structurally, a lattice contraction would be expected if the Ga does move to the Sb site. As demonstrated in Fig. 1, the lattice parameter of Yb, Ga-CCCD Co 4 Sb 12 is smaller than that of Yb single filled Co 4 Sb 12 under the high Yb filling fraction, indicating a contracted lattice due to the Ga-CCCD. This finding is consistent with the systematic lattice contraction observed in Ga x Yb 0.20 Co 4 Sb 12-x/3 when varying the Ga content, shown in the inset of Fig. 1. The contraction of the lattice with assumed increasing Ga content on the Sb site reduces the lattice strain caused by the expansion imparted by increasing Yb content and is another reason for the increased solubility of Yb.

STEM structural characterizations.
In order to directly determine the structural changes imparted by introducing Ga-CCCD into the skutterudite structure, high-resolution STEM images of Yb 0.26 Ga 0.2 Co 4 Sb 11.9333 were taken with a double aberration-corrected transmission electron microscope. Figure 2 shows a high-angle annular dark-field (HAADF) STEM image viewed along the [001] direction, where the frame elements (Co and Sb) as well as the fillers are clearly distinguishable, as shown in the structure model highlighted in Fig. 2a. The cage distortion combined with the off-center-cage filling behavior is identified by comparing the experimental line scan profiles with the simulation results, shown in Fig. 2b. The orange and green lines in Fig. 2b are from the orange and green scan lines in Fig. 2a which pass through the positions of Sb in the cage frame. In an ideal filled skutterudite, the two lines should overlap based on the structural symmetry. However, as shown in Fig. 2b, the peak positions shift between the orange and green lines, indicating the distortion of Sb atoms and the cage structure. As a matter of fact, we can clearly identify the distortion of the Sb cage as the atoms, indicated by two circles pointed by the yellow arrow in Fig. 2a, are not aligned vertically. Further, it is interesting to point out that the cage distortion is always associated with the off-center-cage filling behavior of the filler atoms. An ideal cage-center filling behavior, as seen in most filled skutterudites 10 , should produce perfectly symmetric double valleys in the profile intensity represented by the light blue simulated line scan shown in Fig. 2b. However, the experimental line scan profile (red dots in Fig. 2b) deviates from the light blue line (center-filling model) near the center filler position (0 nm position) relative to the 2a site in Fig. 2b. Instead, an off-center filling model, which is represented by the black line in Fig. 2b, fits the experimental results quite well. This off-center-cage feature was the result of a covalent bond between filler Ga and the host Sb cage that was partially substituted by Ga, in agreement with the first-principles calculations in ref. 26 and ref. 29. Here, STEM crystallographic data provides the first direct experimental evidence for the off-center-cage filling behavior of Ga filler atoms, that can be clearly identified in the longer range intensity line scan at the bottom of Fig. 2a. The variation of the image intensity of these Sb columns that indicates the partial replacement of Sb with Ga in Sb site is rather significant. Otherwise, the image intensity of the Sb columns in the line scan should be the same if they are fully occupied by Sb atoms, based on the crystal symmetry. The covalent bonding of Ga should be effective for scattering heat carrying phonons to further reduce the thermal conductivity of the material, which will be studied in the future.
Electronic band structure. First-principles band structure calculations have been carried out to shed light on the band variations caused by the introduction of Yb and Ga. Figure 3a shows the band structure of Co 4 Sb 12 around its conduction band bottom (CBB). The CBB is located at the Γ point, and is composed of three degenerated bands. The next bands at the Γ point, ~0.2 eV above the CBB (denoted as Δ in Fig. 3a), are also triply-degenerated. Figure 3b shows the band structure of Yb 0.25 Co 4 Sb 12 with zero energy point representing the Fermi level (E F ) of the system. The conduction band of Yb 0.25 Co 4 Sb 12 is similar to that of Co 4 Sb 12 , especially at the Γ point, the Δ is barely changed by the Yb filling (~0.19 eV), and the upper triple-degenerated bands are 0.03 eV higher than the E F , limiting their contribution to the electrical transport. The values of Δ are almost identical in all the n-type Co 4 Sb 12 -based skutterudites with alkali metal (Δ = 0.20 eV in K 0.25 Co 4 Sb 12 ), alkali earth (Δ = 0.20 eV in Ba 0.25 Co 4 Sb 12 ), or rare earth fillers, indicating that all the metallic fillers have negligible influence on the conduction band of Co 4 Sb 12 30 .
The band structure changes remarkably with IIIA elements, as shown in Fig. 3c for Co 4 Sb 12 with both Yb filling and Ga-CCCD, in which the ratio of Ga at the filler sites and the Sb sites is 2:1. The degeneracy of the CBB is broken by the Ga at the Sb sites. The most distinct variation relating with the electrical transport is the upper three degenerated bands split and shift downwards. The Δ , calculated from the averaged values of the upper three bands and those at CBB, decreases to 0.10 eV. The E F (zero energy point) therefore crosses these upper bands and enhances the density of states around the E F , which is beneficial to the thermopower. We also calculated the band structure of Ga 0.25 Co 4 Sb 12 and In 0.25 Co 4 Sb 12 to justify the origin of the effect as shown in Supplementary Figure 2. In these calculations we assume the IIIA atoms are all at filler sites. The Δ values are 0.11 eV and 0.12 eV for the Ga-and In-filled, respectively. This result indicates that the downwards shifting of the upper three bands is caused by the filler Ga rather than the Ga substituting at the 24 g site. The change in the energy positions of bands in Co 4 Sb 12 with Ga or In incorporation onto the 2a site is probably due to their differing filler-host bonding interactions. In contrast to more electropositive fillers, IIIA elements form polar-covalent bonds with the Co 4 Sb 12 host, according to our first-principles study as well as ref. 29. The covalent character of the bond causes the off-center filling shown in the STEM results, and energetically lowers some of the anti-bonding bands of the host. In the perspective of transport, these shifted bands can contribute to the electronic states around E F s. Electrical transport properties. For simplicity of presentation, we label our specimens based on their nominal Yb and Ga content in the form of Yb A Ga B for Ga-CCCD samples and Yb C for Yb single  Figure 4a shows electrical resistivity (ρ) of all the samples as a function of temperature. A transition from semiconducting behavior to metallic behavior is observed with increasing Yb content. Due to the charge-compensation between the void-filling Ga (nominally Ga 1+ ) and Sb-substitutional Ga (nominally Ga 2− ), the Ga 0.20 sample exhibits intrinsic semiconducting behavior and has the lowest carrier concentration (n), as shown in Fig. 4c. This behavior agrees quite well with the result reported previously and indicates invariance of this result with different sample preparation methods 26 . The electrical resistivity decreases with increasing Yb content, mainly due to the increased filling fraction of Yb and a concomitant increase in carrier concentration. Correspondingly, the absolute value of thermopower decreases with increasing Yb content. It is important to point out that Yb 0.26 sample has a similar carrier concentration to that of Yb 0.26 Ga 0.20 sample, as shown in Fig. 4c. However, Yb 0.26 Ga 0.20 sample exhibits a significantly higher absolute thermopower value than that of Yb 0.26 sample at all temperatures (Fig. 4b).
Thermopower is related to the charge carrier density of states near Fermi level as expressed by the Mott relation 31 : Here, k B is the Boltzmann's constant, q the electronic charge, and μ(E) the carrier mobility.
is the charge density of states and f(E) is the Fermi function. E F is the Fermi level. As shown in Eq. 1, thermopower S is proportional to the energy dependence of charge density-n(E), which is determined by the electronic band structure of the materials. The enhanced thermopower of Yb 0.26 Ga 0.20 as compared to Yb 0.26 sample is attributed to the change of electronic band structure that we have shown in Fig. 3. The heavy bands, which are shifted down in energy by the introduction of Ga-CCCD, start to contribute to the density of states and thermopower in the high carrier concentration region.
The carrier concentration is tunable in these Ga-containing charge-compensated compounds in the same way that carrier concentration can be modified by controlling the filling fraction in Ga-free material, as shown in Fig. 4c. The Ga 0.20 sample has the lowest carrier concentration of ~3 × 10 19 cm −3 at 300 K, while Yb 0.40 Ga 0.15 sample has the highest carrier concentration level ~9 × 10 20 cm −3 at 300 K in this study. We conclude, based on the monotonic increase in both the lattice parameters and carrier concentration with increasing Yb content, that we can reach a filling fraction of 0.38 for Yb. This is higher than the filling fraction limit calculated for Yb x Co 4 Sb 12 and is believed to be the result of the charge-compensating nature of the Ga 28,29 .
We have also calculated the low temperature carrier mobility (μ H ) of all the samples and plotted their temperature dependence in Fig. 4d. For typical n-type filled skutterudites with moderate to high n, acoustic phonon scattering dominates near room temperature 32 , leading to a µ ∝ − / T H 3 2 , as the trend line highlights in Fig. 4d. Ga 0.20 and Yb 0.05 Ga 0.20 samples show positive temperature dependence of carrier mobility, indicating the presence of more than one dominant scattering mechanism, most likely a mixture of acoustical phonon and ionized impurity scattering (a purely ionized impurity scattering has a µ ∝ / T H 3 2 relation). In low carrier concentration samples, ionized impurity scattering makes the dominant contribution to the transport, while acoustic phonon scattering becomes dominant when increasing carrier concentrations. The Ga-CCCD is responsible for the ionized impurity scattering as the Sb-substitutional Ga introduces ionized impurity centers, which greatly influence the carrier mobility, especially at low temperatures. It is known that the Sb-rings provide conduction paths in the skutterudites, and substitution of Sb with Ga will distort the conduction framework and hence affect the electrical transport properties greatly.
Thermal transport properties. The temperature dependence of the total thermal conductivity of all the samples is plotted in Fig. 5a. In order to show clearly the effect of Ga-CCCD to the thermal conductivity, only the low temperature (5 K-300 K) lattice thermal conductivity of Yb x Ga 0.2 Co 4 Sb 11.9333 (x = 0, 0.05, 0.10, 0.15, 0.26) is shown in Fig. 5b. And the data of Yb 0.26 sample is also included for comparison. The lattice thermal conductivity is obtained by subtracting the electronic component (κ e ) from total thermal conductivity, where κ e is determined by Wiedemann-Franz law (κ e = L 0 T/ρ). L 0 is the Lorenz number. A constant Lorenz number L 0 = 2.0 × 10 −8 V 2 K −2 is applied to calculate all κ e values. Besides benefitting the electrical performance by improving thermopowers, the introduction of Ga-CCCD into filled skutterudites also has positive effects by reducing the thermal conductivity of the materials. As shown in Fig. 5, both κ and κ L of Ga 0.20 are significantly reduced compared to binary Co 4 Sb 12 , with the values of 4.3 Wm −1 K −1 at 300 K for Ga 0.2 as compared to Co 4 Sb 12 whose room temperature value is 10 Wm −1 K −1 1 . The reduction in κ could be explained by the dual-character phonon scattering mechanism proposed previously 25 , in that both resonant scattering from void-filled Ga and point defect scattering from Sb-substitutional Ga combine to more strongly reduce κ L compared to void filling alone. We found a lower κ L for Yb 0.26 Ga 0.20 sample as compared to that of Yb 0.26 in Fig. 5b, further supporting the role of Ga plays in reducing κ and κ L . The detailed study of thermal conductivity will be reported elsewhere. Suffice it to say that we conclude that the κ L reduction is attributed to both the point defects from Ga/Sb substitution as well as a different localized vibration frequency as fillers from Ga in addition to Yb filled skutterudites.
Thermoelectric figure of merit zT. Figure 6 shows the calculated zT values for all the Yb, Ga-CCCD skutterudites. The zT value is enhanced at higher Yb content and the highest zT reaches 1.25 at 780 K in the sample Yb 0.35 Ga 0.15 , comparable to the best performing Yb single filled skutterudites. The inset of Fig. 6 shows the zT value greatly enhanced by introducing Ga-CCCD with the same Yb filling fraction. The thermoelectric performance improvement is mainly attributed to its unique electronic band structure as well as mixed phonon scattering mechanism produced by Ga-CCCD. The thermoelectric performance of Ga-containing CCCD materials can be optimized by adjusting filling fraction of the secondary filler atoms, like Yb in this study.

Discussion
The influence to the thermoelectric properties from electronic band structure change could be better understood by investigating thermopower at different carrier concentration. Figure 7 shows the carrier concentration dependence of thermopower for all samples at 300 K. The general trend line was drawn by fitting thermopower of n-type single filled-Co 4 Sb 12 from literature data 25 . We highlighted the Yb single filled Co 4 Sb 12 data from ref. 7 with the solid star symbols, and in order to distinguish our experimental result from the literature data, the thermopower values of single filled samples Yb 0.20 and Yb 0.26 from this study were plotted using hollow star symbols in the figure. The Yb single filled samples follow the general trend line relatively well. However, the Ga-containing samples behave very differently, especially for the samples with high carrier concentrations. A solid blue trend line was drawn based on the thermopower values of Yb, Ga-CCCD samples and that of the Ga-CCCD Co 4 Sb 12 from ref. 25. A crossover between the Ga-free filled skutterudites trend line and the Ga-containing CCCD samples trend line is shown in Fig. 7.
At low carrier concentrations, the absolute values of thermopower of the Yb, Ga-CCCD samples are slightly smaller than the extrapolated values of Ga-free single filled skutterudites. By increasing carrier concentration above 1.0 × 0 20 cm −3 , the absolute thermopower value exceeds that of Ga-free single filled skutterudites. At high carrier concentrations (> 3 × 10 20 cm −3 ), the absolute thermopower value of Yb, Ga sample is nearly 20% larger than that of the normal single filled skutterudites at the same carrier concentration. This special thermopower trend of Ga-containing samples can be explained by the electronic band structure result shown in Fig. 3. Due to the band split and reduced degeneracy at the conduction band edge, our Ga-containing samples exhibit smaller absolute S value compared with that of Ga-free filled skutterudites at low carrier concentrations. By gradually increasing Yb content, the Fermi level is pushed deeper into the conduction bands and goes across the three bands near conduction band edge. Thus, the absolute S gradually increases to the value comparable to that of Ga-free filled skutterudites. By further increasing the Yb filling fraction, we were able to tune the Fermi level to merge with the heavier  bands whose energy has been decreased. On the other hand, the Yb filling fraction limit is increased by introducing Ga-CCCD, enabling us to tune the carrier concentration/Fermi level to much higher range. The enhanced electronic density of states from these heavier bands, which are normally inaccessible in Ga-free filled skutterudites, contributes additionally to the absolute thermopower value at high carrier concentrations, resulting in significantly enhanced thermopower compared with that of Ga-free filled skutterudites.
The change of the effective mass as a function of carrier concentration can also be understood from the calculated band structures. Assuming acoustic phonon scattering and a single parabolic band, the effective mass is obtained from the measured thermopower and carrier concentration, by using the following equations: Here h is the Planck constant and ⁎ m is the density of states effective mass. η ( ) F j are the Fermi integrals of order j, ξ is the reduced carrier energy (E/k B T), and η represents the reduced Fermi energy (E F /k B T). The value of η is obtained from experimental values of S from Equation 2. However, for skutterudites, a two-band Kane model, well-accepted for explaining the relation between S, n and ⁎ m is applied here to understand the effective mass increase with the increase of n using the relationship 33,34 : where ⁎ m is the effective mass of the compound, m b is the effective mass at the bottom of the band and ω = / E k T g B is the reduced band gap energy. Figure 8 shows the carrier concentration dependence of the effective mass, where we applied the Kane model to the Yb single filled skutterudites data, from both our samples and the data from ref. 7, and obtained fitting parameters m b = 2.2 m e and E g = 0.19 eV. The fitting result for effective mass and the band gap agree with prior measurements and theoretical calculations 15,35,36 . As shown in Fig. 8, there is a substantial increase of effective mass in the Yb, Ga-CCCD samples with high level Yb filling fraction while the effective mass of low carrier concentration samples is quite similar as that of Yb single filled skutterudites. This is further experimental evidence to support the first-principles calculation results and shows the influence of the electronic band structure change on the transport properties introduced by Ga-CCCD.
In summary, our findings shed the light on the nature of the dual-site occupancy of Ga on the electronic band structure and the thermoelectric properties of the Yb, Ga filled skutterudites. The cage distortion and off-cage-center filling behavior has been directly observed through the analysis of atomic imaging. The carrier concentration of the charge-compensated skutterudites is tunable by adding the second filler. Ga/Sb substitution creates ionized impurity defects, resulting in a mixed electron scattering mechanisms in the materials. A distinct deviation of thermopower from the normal filled skutterudites trend, coupled with sharp increase of effective mass, has been observed in the Yb, Ga filled compounds with high carrier concentration. This is attributable to the electronic band structure change after introducing Ga-CCCD. We found the Yb, Ga-CCCD samples show lower thermal conductivity compared with that of Yb single filled samples with the same Yb filling fractions. The cage site Ga plays a role in providing additional vibration modes for the Yb filler atoms, combined with the Ga-substitutional point defects. The optimized high temperature zT reaches 1.25 at 780 K in the sample Yb 0.35 Ga 0.15 Co 4 Sb 11.95 . Our study points to the possibility of electronic band structure engineering and thermal conductivity engineering in the filled skutterudites by introducing Ga-containing or similar charge-compensated defects. The present study can be extended to a broad range of thermoelectric materials for optimizing their electrical and thermal properties simultaneously.

Methods
Sample preparation. High-purity elements Co (99.999%, shot), Sb (99.999%, shot), Yb (99.98% ingot), and Ga (99.999% ingot) were used as the starting materials and were weighted to achieve Yb x Ga 0.2 Co 4 Sb 11.9333 (x = 0, 0.05, 0.10, 0.15, 0.20, 0.26), Yb y Ga 0.15 Co 4 Sb 11.95 (y = 0, 0.25, 0.30, 0.35, 0.40) and Yb 0.20 Ga z Co 4 Sb 12-z/3 (z = 0, 0.10, 0.15), respectively. The stoichiometric quantities of the elements were loaded into carbon-coated quartz tubes and sealed under vacuum. The sealed ampoules were induction heated and melted twice. The obtained ingots were put into quartz crucible with a 0.5 mm diameter nozzle, induction melted and ejected under a pressure of 0.02 MPa of argon gas onto the high-speed rotating copper wheel with the linear speed of 20 m/s. The melt-spun ribbons were sintered using both hot press and spark plasma sintering (SPS) methods. The hot press sintering was carried out at 620 °C under 50 MPa pressure while the SPS samples were sintered at 625 °C under a uniaxial load of 50 MPa. For both of the hot press and SPS processing the pressure and temperature were held for 20 min before allowing the sample to cool to room temperature naturally with the load removed. The density of all the samples was above 95% of the theoretical value. The resulting billets were cut into bars for transport property measurements. TEM specimens were prepared by mechanical slicing, polishing, and dimpling, and followed by ion-milling until electron transparency was achieved.
Structural characterization. Identification of the crystalline phase was determined by powder X-ray diffraction (XRD) at room temperature, which was carried out on a Philips 3100E diffractometer (Cu K radiation, λ = 0.15418 nm, 40 kV/30 mA). The phase purity and quantitative elemental analysis of the sintered bulk samples were determined by using Electron Probe Micro-Analysis (EPMA) by averaging the measurements at eight randomly selected spots on polished sample surfaces. EPMA was performed using a Cameca SX100 Electron Probe Micro Analyzer at an accelerating voltage of 20 kV. The STEM-HAADF images were taken with double aberration-corrected JEOL-ARM200F with convergent angle of 21 mrad and collection angle from 67 to 275 mrad. The STEM image calculations were carried out with computer codes, written at BNL, running on Graphics Processing Unit (GPU) based on the multislice method with the frozen phonon approach.
First-principles calculations. First principles calculations were performed with the Vienna ab initio simulation package (VASP) 37 . We adopt generalized gradient approximation (GGA) functional of Perdew-Burke-Ernzerhof (PBE) form and projected augmented wave (PAW) method [38][39][40] . In order to simulate the compositions close to our experiments, 2*2*2 supercells of the primitive unit Co 4 Sb 12 , which contains 128 framework atoms and 8 filler sites, were constructed and used throughout all the calculations. For skutterudites with fillers and/or CCCDs, several atomic configurations are tested, and the most stable configurations are adopted. The supercells are fully relaxed before band structure calculations.
Thermoelectric transport properties measurements. The low-temperature (5 K to 300 K) thermoelectric property measurements (electrical resistivity, ρ, thermopower, S, thermal conductivity, κ, and Hall coefficient, R H ) were carried out in the sintered samples with a Physical Property Measurement System (PPMS, Quantum Design). The Hall coefficients were measured by sweeping the magnetic field up to 5T in both positive and negative directions. The Hall carrier concentration, n, was calculated by using 1/R H e, where e is elementary charge. The Hall carrier mobility, μ H , was obtained according to the relation μ H = R H /ρ. The high temperature transport property measurements were carried out in the SPS samples. The thermopower and electrical resistivity was measured from 330 K to 770 K using a Linseis LSR-3 system. Thermal conductivity from room temperature to 770 K was assessed by measurement of the diffusivity, λ (Anter Flashline 3050 diffusivity analyzer), specific heat, C p (Netzsch 404 c differential scanning calorimeter), and density, ρ (as assessed by mass and dimension of a polished SPS' d billet) of the samples using the equation κ = λ·C p ·ρ and taking the product of these values as a function of temperature.