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

Abstract

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.

Figure 1. Lattice parameter (a) as a function of Yb content.

Blue triangles are Yb single filled Co₄Sb₁₂ and red circles represent Yb, Ga CCCD samples: Yb_xGa_0.2Co₄Sb_11.9333 (x = 0, 0.05, 0.10, 0.15, 0.20, 0.26) and Yb_yGa_0.15Co₄Sb_11.95 (y = 0.25, 0.30, 0.35, 0.40). The data of Yb single filled Co₄Sb₁₂ are from this study and taken from the literatures. The dashed lines are the trend for eye guidance. The inserted figure plots the lattice parameters of Yb_0.20Ga_zCo₄Sb_12-z/3 (z = 0, 0.10, 0.15) as a function of Ga content.

Figure 2. STEM analysis and structural modeling.

(a) STEM-HAADF image (convergent angle: 21 mrad, collection angle: 67–275 mrad). The structure model (red, green and blue spheres represent Co, Sb and Ga/Yb atoms, respectively) and calculated image (inset with white outline) are embedded in the image. A line scan intensity profile from the yellow dashed line is shown at the bottom. The green circles pointed by the yellow arrow illustrate the misalignment of the Sb atoms, indicating the distortion of the Sb cage that is associated with the off-center-cage filling behavior of the filler atoms. (b) Intensity line profiles from the experimental image and simulations. The red circles are from the red scan line shown in (a), the light blue and black lines are from the calculations based on the structure models of Yb_0.26Ga_0.2Co₄Sb_11.9333 with filled Ga/Yb at center (light blue) and deviated 0.027 nm away from the center (black), respectively. The orange and green lines are from the orange and green scan lines in (a).

Figure 3. Theoretical calculation of electronic band structures.

First-principles band structure calculations for (a) Co₄Sb₁₂, (b) Yb_0.25Co₄Sb₁₂, and (c) Yb_0.25Ga_0.25Co₄Sb_11.875Ga_0.125. The zero energy points in (b,c) represent the Fermi levels (E_Fs) of the two compounds.

Figure 4. Electrical properties as a function of temperature.

(a) Electrical resistivity, (b) thermopower, (c) carrier concentration and (d) carrier mobility of Yb_xGa_0.2Co₄Sb_11.9333 (x = 0, 0.05, 0.10, 0.15, 0.20, 0.26), Yb_yGa_0.15Co₄Sb_11.95 (y = 0.25, 0.30, 0.35, 0.40), Yb_0.20Ga_zCo₄Sb_12-z/3 (z = 0, 0.10, 0.15) and Yb_0.26Co₄Sb_12. The dashed line in (d) represents the temperature dependence of T^−3/2, indicating an acoustic phonon scattering trend line for eye guidance.

Figure 5. Thermal conductivity as a function of temperature.

(a) Total thermal conductivity of all the samples and (b) lattice thermal conductivity of Yb_xGa_0.2Co₄Sb_11.9333 (x = 0, 0.05, 0.10, 0.15, 0.26) and Yb_0.26Co₄Sb₁₂.

Figure 6. Thermoelectric figure of merit zT as a function of temperature for all the samples.

Temperature dependence of zT of Yb_0.20Ga_zCo₄Sb_12-z/3 (z = 0, 0.10, 0.15) was plotted in the inserted figure separately to show the influence from Ga-CCCD to the thermoelectric performance.

Figure 7. Thermopower values at different carrier concentration levels at 300 K.

The dashed line represents the general trend of thermopower taken from the literature for n-type filled skutterudites with different single fillers. The red circle symbols are Yb_xGa_0.2Co₄Sb_11.9333 (x = 0, 0.05, 0.10, 0.15, 0.20, 0.26) and the blue triangles are Yb_yGa_0.15Co₄Sb_11.95 (y = 0.20, 0.25, 0.30, 0.35, 0.40) from this study. The data of Ga-CCCD samples Ga_δCo₄Sb_12-δ/3 from ref. is also plotted in the figure. The solid blue line represents the data trend for all the Ga-containing charge-compensated compounds.

Figure 8. Carrier concentration dependence of effective mass at 300 K.

The dashed line is a fit of the Yb_yCo₄Sb₁₂ data using the Kane model with m_b= 2.2 m_e, and E_g= 0.19 eV. The solid blue line represents the trend for eye guidance.