Enhanced thermoelectric performance of β-Zn4Sb3 based nanocomposites through combined effects of density of states resonance and carrier energy filtering

It is a major challenge to elevate the thermoelectric figure of merit ZT of materials through enhancing their power factor (PF) and reducing the thermal conductivity at the same time. Experience has shown that engineering of the electronic density of states (eDOS) and the energy filtering mechanism (EFM) are two different effective approaches to improve the PF. However, the successful combination of these two methods is elusive. Here we show that the PF of β-Zn4Sb3 can greatly benefit from both effects. Simultaneous resonant distortion in eDOS via Pb-doping and energy filtering via introduction of interface potentials result in a ~40% increase of PF and an approximately twofold reduction of the lattice thermal conductivity due to interface scattering. Accordingly, the ZT of β-Pb0.02Zn3.98Sb3 with 3 vol.% of Cu3SbSe4 nanoinclusions reaches a value of 1.4 at 648 K. The combination of eDOS engineering and EFM would potentially facilitate the development of high-performance thermoelectric materials.

ter λ , which corresponds to the energy filtering mechanism (EFM) 14 . Heremans et al. showed that after Tl-doping of PbTe, its ZT is doubled due to the enhancement of the thermopower 17 . This is attributed to the resonant distortion of the eDOS. Accordingly, the recently observed enhanced thermopower of Pr and Sm doped β -Zn 4 Sb 3 can also be ascribed to the eDOS distortion of the host 18,19 .
On the other hand, Heremans et al. also observed an enhanced thermopower in PbTe-based nanocomposites containing Pb and Ag nanoparticles. This can be referred to the EFM 20,21 revealed by the increase of the scattering parameter λ . Only recently, Zou et al. experimentally proved that the introduction of Cu 3 SbSe 4 nanoinclusions increases the thermopower S of β -Zn 4 Sb 3 by EFM 22 . Theoretical studies indicate that the resulting interface potentials of semiconductor-based nanocomposites with semiconducting 23 or metallic 24 nanoinclusions stimulate the EFM. Although both resonant eDOS distortion and EFM have been used separately to enhance the thermopower S of a specific material, a successful application of both effects at the same time has not been reported so far.
In this study, we show that the two approaches can be combined to improve the thermoelectric performance of β -Zn 4 Sb 3 . As it is known, β -Zn 4 Sb 3 is one of the most promising thermoelectric materials on account of its low glasslike thermal conductivity and good electrical properties at moderate temperatures [25][26][27][28][29] ; Cu 3 SbSe 4 is another important thermoelectric material with a narrow band gap 9,[30][31][32] . In order to induce resonant distortion of the eDOS, we substituted Pb for Zn in β -Zn 4 Sb 3 forming β -(Zn 1-x Pb x ) 4 Sb 3 (x = 0, 0.01, 0.02, and 0.03). On the other hand, we synthesized β -(Zn 1-x Pb x ) 4 Sb 3 -based composites with Cu 3 SbSe 4 nanoinclusions to enhance energy filtering by creating interface potentials. Our results show that appropriate Pb-doping and Cu 3 SbSe 4 nanoinclusions both increase PF owing to an increased thermopower and significantly reduce (approx. 2-fold) the thermal conductivity of β -Zn 4 Sb 3 . This results in a large ZT of up to 1.4 at 648K of the nanocomposite f(Cu 3 SbSe 4 )/β -Pb 0.02 Zn 3.98 Sb 3 with f = 3 vol.% (where f is the volumetric percentage of Cu 3 SbSe 4 ).
The carrier concentrations determined by Hall coefficient measurements are given in Table 1. It can be seen that with x increasing from 0 to 0.01 and 0.02, the hole concentration of β -(Zn 1-x Pb x ) 4 Sb 3 increases from 12.1 to 13.6 and 16.9 × 10 19 cm −3 , respectively (see Table 1). With further increase of x to 0.03, the hole concentration slightly decreases to 15 19 cm −3 as the Cu 3 SbSe 4 content increases from 2 to 3 and 4 vol.%, respectively. In addition, the mobility μ decreases moderately from 17.4 cm 2 /Vs to 15.1 cm 2 /Vs as f increases from 2 to 4 vol.%. These results indicate that the decrease of the resistivity with increasing inclusion content (see Fig.1 (a)) originates from the increased carrier concentration. Besides, the increase of the carrier concentration significantly exceeds the decrease of the mobility. The carrier concentration of f(Cu 3 Sb-Se 4 )/β -Pb x Zn 1-x Sb 3 for various values of x and f agrees with the resistivity trend in Fig.1 (a)     that the decrease of the resistivity with increasing doping and inclusion content originates from the changes of carrier concentration. Figure 1(b) shows the temperature dependences of thermopower of β -Zn 4 Sb 3 , β -(Zn 1-x Pb x ) 4 Sb 3 (x = 0.01, 0.02, and 0.03) and f(Cu 3 SbSe 4 )/β -Pb 0.02 Zn 3.98 Sb 3 (f = 2, 3 and 4 vol.%) nanocomposite samples. Two points are particularly interesting: (1) Unlike the resistivity ( Fig. 1(a)), the thermopower of all nanocomposite samples is nearly independent of the Pb and Cu 3 SbSe 4 content; (2) From the observed increased carrier concentration ( Fig.1(a)), a lower thermopower S of the Pb-doped samples and nanocomposite samples compared to pristine β -Zn 4 Sb 3 would be expected. Instead, we find that the thermopower of these samples obviously increases in the whole temperature range implying an increase of N(E) or/and λ (energy filtering effect) according to Eq. 2 (see below).
Enhanced S by the resonant distortion of eDOS in Pb-doped β-(Zn 1-x Pb x ) 4 Sb 3 . From these results we assume that the anomalously enhanced thermopower [ Fig. 1(b)] of the nanocomposite samples is due to resonant distortion of the eDOS and the EFM, respectively. Evidence of the resonant distortion of the eDOS will be provided by means of the Pb-doped samples. Based on the measured values of carrier concentration p and thermopower S, the effective mass m d * is calculated. In the single parabolic band model, m d * and S can be approximated by 33,34 : where h is the Planck constant, ξ F is the reduced Fermi level F f /(k B T) and λ is the scattering parameter. As mentioned by Heremans et al., the scattering parameter λ of doped systems without inclusions (or secondary phase) is dominated by the acoustic modes and can be zeroed 17 . Table 1  for a free-electron gas) 35 .
Using formulae (3) and (4) and m d * = 1.51 m e for the un-doped β -Zn 4 Sb 3 , we can plot the dependence of S on carrier concentration at 300K (black solid line in Fig. 2). Without resonant distortion of the eDOS Pb-doping, the thermopower S would be the same irrespective of the Pb-content and result in the same line. However, we find that S of β -(Zn 1-x Pb x ) 4 Sb 3 with x = 0.01, 0.02, and 0.03 is ~23, 31 and 29 μ V/K higher than the values of the black line, respectively (at 300K in Fig. 1(b)), indicating strong eDOS resonant distortion effects.
The origin of the resonant eDOS distortion caused by Pb substitution is determined by first principle calculations of the energy bands of pristine β -Zn 4 Sb 3 and Pb-doped β -Zn 4 Sb 3 (Fig. 3). The calculated result indicates that Pb-doping induces a strong sharp resonant peak near the Fermi level, which is mainly dominated by the Pb s orbitals (bottom of Fig. 3). The Pb p orbitals contribute little to the peak, which is due to the transfer of the outmost p electrons from Pb to Sb. The sharp peak indicates a larger effective mass (m d *) and thermopower (S) of the Pb-doped system compared to pristine β -Zn 4 Sb 3 .
Furthermore, the resonant distortion of the eDOS of β -(Zn 1-x Pb x ) 4 Sb 3 can also be quantified using the low-temperature heat capacity C p of the samples. However, there are two temperature-dependent Zn 4 Sb 3 modifications, i.e. β -Zn 4 Sb 3 (T > 260 K) and α -Zn 4 Sb 3 (T < 260 K), meaning that below ~260 K the β phase will transform to the α -phase. As a result, one can only measure low-temperature heat capacity C p of α -Zn 4 Sb 3 . Nevertheless, previous work 36 showed that the eDOS patterns of the two Zn 4 Sb 3 modifications (β and α ) are similar. Thus, it is appropriate to deduce the heat capacity (eDOS) of β -Zn 4 Sb 3 from the α -Zn 4 Sb 3 measurements. The temperature dependence of the low temperature (< 4 K) heat capacity Scientific RepoRts | 5:17803 | DOI: 10.1038/srep17803 C p of a solid is expressed by C p = γT + bT 3 , where the term bT 3 stands for the lattice contribution and γT for the charge carrier contribution with γ being related to N(E f ) (eDOS at the Fermi level) 37 : Hence, the slope of a C p /T 3 vs. 1/T 2 plot gives γ , which is directly proportional to the eDOS at the Fermi level. Figure 4 shows the C p /T 3 vs. 1/T 2 plots of un-doped Zn 4 Sb 3 (α phase) and a typical doped compound (Zn 1-x Pb x ) 4 Sb 3 (x = 0.02) (α phase). The slope (γ ) of the plot of doped (Zn 1-x Pb x ) 4 Sb 3 is substantially larger than that of un-doped Zn 4 Sb 3 . Linear fitting in the low temperature regime yields the ratio γ dop /γ un-dop = N(E f ) dop /N(E f ) 0un-dop ~3.5 (see Fig. 4) revealing that Pb-doping indeed significantly increases the eDOS at Fermi level. This is in agreement with the first principle calculation result shown in Fig. 3. We calculated the scattering parameters λ (Table 1) of the nanocomposites using the effective mass   Table 1) suggesting a higher thermopower of the nanocomposite samples. The carrier concentration dependence of the thermopower S of β -Pb 0.02 Zn 3.98 Sb 3 (λ = 0) at 300 K can be evaluated using formulae (3) and (4)  The above results indicate that the incorporation of nanophase Cu 3 SbSe 4 in the Pb-doped β -Zn 4 Sb 3 contributes to the large enhancement of S through the EFM. Microstructure analysis using high-resolution transmission electron microscopy (HRTEM) reveals the underlying mechanism. As shown in Fig.5(b), the Pb-doped β -Zn 4 Sb 3 matrix and the dispersed Cu 3 SbSe 4 particles are incoherently jointed at the phase boundary. Moreover, at room temperature the band gaps E g of Cu 3 SbSe 4 and Pb-doped β -Zn 4 Sb 3 are 0.3-0.4 eV 31,38 and 0.26 eV 39 , respectively, leading to a valence band offset and the formation of p-p-type heterojunction barriers at the phase boundary. It is reasonable to assume that these potential barriers act as scattering centers giving rise to the EFM 23 . Hence, the enhanced thermopower of f(Cu 3 Sb-Se 4 )/β -Pb 0.02 Zn 3.98 Sb 3 results from the two effects: the resonant distortion of the eDOS in the Pb-doped β -Pb 0.02 Zn 3.98 Sb 3 matrix and the energy filtering effect at the phase boundaries confirming that it is feasible to combine both effects in one system.
The temperature dependence of κ of β -Zn 4 Sb 3 , β -(Zn 1-x Pb x ) 4 Sb 3 (x = 0.01, 0.02, and 0.03) and f(Cu 3 SbSe 4 )/β -Pb 0.02 Zn 3.98 Sb 3 (f = 2, 3 and 4 vol.%) nanocomposite samples is shown in Fig.1(d). It can be seen that in the range of 300K to 500-550K, κ decreases with increasing temperature and then gradually increases as the temperature is further increased. κ includes the lattice thermal conductivity κ L and the carrier contribution κ c : κ = κ L + κ c . Thus, κ L can be obtained by subtracting κ c evaluated by the Wiedemann-Franz relation: κ c = LT/ρ, where L is the Lorenz number. It is known that for heavily doped semiconductors, L is far below the Sommerfeld value L 0 = 2.45 × 10 −8 Ω WK −2 , but depends on the reduced chemical potential ξ F , the band structure and the scattering process. In the single parabolic band model the Lorenz number is expressed as 33 :  where ξ F is obtained by fitting the measured S data using Eq. (4). The evaluated L(T) curve is plotted in Fig.S4 (Supplementary Information). Due to phonon scattering at both the doped sites and the boundaries, κ L of all β -(Zn 1-x Pb x ) 4 Sb 3 (x = 0.01, 0.02, and 0.03) and f(Cu 3 SbSe 4 )/β -Pb 0.02 Zn 3.98 Sb 3 (f = 2, 3 and 4 vol.%) samples is lower than that of the pristine β -Zn 4 Sb 3 ( Fig. 1(e)). For instance, at 300K κ L of the doped composite sample f(Cu 3 SbSe 4 )/β -Pb 0.02 Zn 3.98 Sb 3 with f = 3 vol.% is only 0.58 W/Km, which is approx. 40% smaller than that of the β -Zn 4 Sb 3 matrix. Because of the simultaneous increase of PF and decrease of κ, the ZT values of all composite samples are enhanced compared to β -Zn 4 Sb 3 , as it is shown in Fig. 1(f). Specifically, 3 vol.% (Cu 3 SbSe 4 )/β -Pb 0.02 Zn 3.98 Sb 3 reached ZT = 1.4 at 648 K, which is about twice as large as that of β -Zn 4 Sb 3 studied here. This is the largest ZT value ever reported for a β -Zn 4 Sb 3 -based systems at 648 K 34,[40][41][42] .

Conclusions
We have demonstrated the enhancement of the thermoelectric properties as a result of two simultaneous effects: drastic reduction of the thermal conductivity and significant improvement of power factor. A figure of merit ZT = 1.4 at 648K could be achieved with f(Cu 3 SbSe 4 )/β -Pb 0.02 Zn 3.98 Sb 3 with f = 3 vol.%, which is the largest ZT value ever reported in a β -Zn 4 Sb 3 -based systems at 648 K. The enhanced thermopower of β -Pb 0.02 Zn 3.98 Sb 3 -based composites with Cu 3 SbSe 4 nanoinclusions results from the combination of resonant distortion of the eDOS in the Pb-doped matrix and intensified energy filtering at the heterojunction potential barriers. These findings provide a comprehensive way to design high-performance thermoelectric materials.
X-ray diffraction (Philips-X PERT PRO) with Cu K α radiation was used to check the phase constitutions. Scanning electron microscopy (SEM)(Hitachi S4800) equipped with an energy dispersive X-ray spectroscope (EDS) was used to analyze the microstructures of the composite samples. Moreover, microstructure investigations were also carried out using high-resolution transmission electron microscopy (HRTEM; JEOL JEM-2010) operating at a 200 kV accelerating voltage. Hall coefficients were measured by using a physical property measurement system (PPMS, Quantum Design). Low temperature heat capacity measurements were performed on the same instrument in the range of 2 K to 4 K. Electrical resistivity and thermopower were measured simultaneously by the standard four-probe method (ULVAC-RIKO: ZEM-3) in helium atmosphere from 300 K to 650 K. The thermal diffusivity α was measured with a NETZSCH LFA-457 instrument in the temperature range of 300 K to 650 K. The thermal conductivity κ was calculated according to κ = DC p α , where C p is the specific thermal capacity obtained by differential scanning calorimetry (DSC, perkin-Elmer) and D is the sample density measured by the Archimedes method.
DFT calculations were performed using the Vienna Ab Initio Simulation Package (VASP) with the projector augmented wave (PAW) scheme and the generalized gradient approximation of Perdew, Burke and Ernzerhof (GGA-PBE) for the electronic exchange-correlation functional. The energy cutoff for the plane wave expansion was 450 eV. The Brillouin zones were sampled by Monkhorst-Pack k-point meshes (3 × 3 × 2). Atomic positions and unit cell vectors were relaxed until all forces and components of the stress tensor were below 0.01 eV/Å and 0.2 kbar, respectively.