Efficient interlayer charge release for high-performance layered thermoelectrics

Abstract Many layered superlattice materials intrinsically possess large Seebeck coefficient and low lattice thermal conductivity, but poor electrical conductivity because of the interlayer transport barrier for charges, which has become a stumbling block for achieving high thermoelectric performance. Herein, taking BiCuSeO superlattice as an example, it is demonstrated that efficient interlayer charge release can increase carrier concentration, thereby activating multiple Fermi pockets through Bi/Cu dual vacancies and Pb codoping. Experimental results reveal that the extrinsic charges, which are introduced by Pb and initially trapped in the charge-reservoir [Bi2O2]2+ sublayers, are effectively released into [Cu2Se2]2− sublayers via the channels bridged by Bi/Cu dual vacancies. This efficient interlayer charge release endows dual-vacancy- and Pb-codoped BiCuSeO with increased carrier concentration and electrical conductivity. Moreover, with increasing carrier concentration, the Fermi level is pushed down, activating multiple converged valence bands, which helps to maintain a relatively high Seebeck coefficient and yield an enhanced power factor. As a result, a high ZT value of ∼1.4 is achieved at 823 K in codoped Bi0.90Pb0.06Cu0.96SeO, which is superior to that of pristine BiCuSeO and solely doped samples. The present findings provide prospective insights into the exploration of high-performance thermoelectric materials and the underlying transport physics.

Thermoelectric performance can be significantly improved in layered superlattice materials [16], arising mainly from an increase in Seebeck coefficient as a result of the peculiar electronic structure. Meanwhile, the comparatively weak bonding between the sublayers endows semiconductor superlattices with intrinsic low lattice thermal conductivity [17][18][19][20][21][22]. Unfortunately, the superlattice structure does not favor fine electrical conductivity in the bulk state, which has proved a stumbling block to achieve high thermoelectric figure of merit in two-dimensional superlattices [22][23][24][25][26]. Specifically, for a multi-layered superlattice with alternating stacked insulating sublayers and conductive sublayers, charges are mostly trapped in the insulating sublayers. The concentration of charges stored in the insulating charge-reservoir sublayers is extremely low. Furthermore, release of the dominant trapped charges into the conductive sublayers to become conduction carriers is difficult because they must surmount the interlayer energy barrier. As a result, intrinsically low carrier concentration is found in thermoelectric superlattices, accounting for the poor electrical conductivity. These issues urge us to find a novel strategy to tailor the trapping and conduction characteristics of charges in a superlattice system.
Generally, element or vacancy doping is the primary choice for regulating the carrier concentration toward an optimal range of 10 19 -10 21 cm −3 [3][4][5]. However, as discussed above, superlattice compounds suffer from both intrinsic low charge concentration and absence of charge-transport channels, implying that the single doping is overstretched. It is therefore urgently necessary to develop multiple doping for carrier concentration optimization in thermoelectric superlattices. On the other hand, it is well known that band convergence has been demonstrated to be a robust strategy for yielding high power factor (S 2 σ ) in thermoelectrics [3][4][5]11]. For compounds exhibiting multiple extrema with energy difference of no more than a few k B T in the energy bands, it is essential to move the Fermi level significantly in energy so that more Fermi pockets can be populated. However, in most cases, the intrinsic low carrier concentration is not sufficient to activate the multiple converged bands.
In view of the above situation, one may expect that if additional charges and interlayer chargetransport channels are provided simultaneously in thermoelectric superlattice, the carrier concentration would be significantly increased. Furthermore, the multiple converged bands could be expected to be activated as the increase in carrier concentration could regulate the position of Fermi level. We put forward the idea of efficient interlayer charge release via multiple-defect codoping, in which some defects construct channels for interlayer chargetransport process, while others provide plentiful extrinsic charges to diffuse along these channels (as shown in Scheme 1). It is expected that efficient interlayer charge release in superlattice will ensure high carrier concentration and activate multiple converged bands if there are multiple extrema in the energy band.
BiCuSeO provides an ideal platform for the above strategy. As a typical superlattice material, BiCuSeO consists of [Bi 2 O 2 ] 2+ and [Cu 2 Se 2 ] 2− sublayers [27][28][29][30][31] stacking alternately along the c axis of the tetragonal cell. In BiCuSeO, the insulating [Bi 2 O 2 ] 2+ sublayers act as a charge reservoir, while conduction takes place in the conductive [Cu 2 Se 2 ] 2− sublayers [27,28]. Intrinsically low electrical conductivity is found in pristine BiCuSeO [32][33][34][35][36][37][38], arising from the extremely low carrier concentration. BiCuSeO has a complex electronic structure with multiple extrema in the valence bands [27], but the intrinsically low carrier concentration is insufficient to allow holes to populate those multiple converged valence bands. In the present study, for the purpose of achieving efficient interlayer charge release and thereby activating multiple Fermi pockets in BiCuSeO, we demonstrate an integrated strategy through Bi/Cu dual vacancies and Pb codoping. Specifically, Bi/Cu dual vacancies construct channels for interlayer charge-transport process, and Pb-doping introduces plentiful extrinsic charges, which are initially trapped in [Bi 2 O 2 ] 2+ sublayers. As expected, our studies show that charge concentration gradient drives release of these confined charges, enabling the charges to almost completely diffuse into [Cu 2 Se 2 ] 2− sublayers along the interlayer transport channels and thus become conduction carriers. As a result, the concentration of conduction holes is remarkably increased in vacancies/Pb codoped BiCuSeO, reaching the theoretical limiting value. This efficient interlayer charge release in Bi 1-x-y Pb y Cu 1-x SeO results in significant enhancement in carrier concentration and thus electrical conductivity. Meanwhile, the substantial increase in carrier concentration pushes the Fermi level into the valence band, activating multiple converged valence bands, which enables a relatively high Seebeck coefficient and yields an increased power factor for Bi 1-x-y Pb y Cu 1-x SeO. As a consequence, a maximum ZT value of ∼1.4 for Bi 0.90 Pb 0.06 Cu 0.96 SeO is derived at 823 K, which is superior to that of (i) the pristine Bi-CuSeO, (ii) BiCuSeO solely doped with Bi/Cu dual vacancies, and (iii) BiCuSeO solely doped with Pb. The present results open up a promising avenue for regulating transport properties in thermoelectrics.

RESULTS AND DISCUSSION
The powder X-ray diffraction (PXRD) patterns of Bi 1-x-y Pb y Cu 1-x SeO are shown in Supplementary  Figure 1 plots the temperature-dependent electrical transport properties of Bi 1-x-y Pb y Cu 1-x SeO samples. With increasing doping fraction of Bi/Cu dual vacancies, the electrical conductivity increases from ∼1.3 S cm −1 for pristine BiCuSeO to ∼1.8 S cm −1 for Bi 0.98 Cu 0.98 SeO, and then to ∼3.1 S cm −1 for Bi 0.96 Cu 0.96 SeO at room temperature (Fig. 1a). An analogous relationship between the electrical conductivity and concentration of dual vacancies is also observed in dual-vacancyand Pb-codoped samples (Fig. 1b). Meanwhile, for Pb-doped BiCuSeO, the electrical conductivity gradually decreases with rising temperature, exhibiting characteristics of metallic conduction and a heavily doped state. In addition, the electrical conductivity of Pb-doped samples is significantly increased compared to that of the Bi 1-x Cu 1-x SeO without Pb doping over the entire test temperature range. Consequently, the dual-vacancy-and Pbcodoped sample (that is, Bi 0.90 Pb 0.06 Cu 0.96 SeO) features a maximum electrical conductivity of ∼629.9 S cm −1 at room temperature, which is higher than that of the solely Pb-doped samples (∼483.7 S cm −1 for Bi 0.94 Pb 0.06 CuSeO at room temperature) and far higher than that of the solely dual-vacancy-doped samples (∼3.1 S cm −1 for Bi 0.96 Cu 0.96 SeO at room temperature). The transport properties for the Bi 1-x-y Pb y Cu 1-x SeO samples are listed in Supplementary Table S1, and it can be concluded that the enhancement in electrical conductivity of dual-vacancy-and Pb-codoped samples is mainly a result of the significantly increased carrier concentration. Figure 1c depicts the Seebeck coefficients as a function of temperature for Bi 1-x-y Pb y Cu 1-x SeO samples. The positive Seebeck coefficient for all samples in the entire temperature range reflects p-type conduction, which is consistent with the conclusion given by the Hall measurement. The room-temperature Seebeck coefficient reduces from 576.  Table S1). The temperature-dependent power factors for all Bi 1-x-y Pb y Cu 1-x SeO compounds are plotted in Fig. 1d. Pristine BiCuSeO displays the lowest power factor among all samples mainly stemming from its extremely low electrical conductivity. For solely dual-vacancy-doped samples, the power factor is slightly improved relative to pristine BiCuSeO. Compared with solely Pb-doped samples, the power factors of dual-vacancy-and Pb-codoped samples are improved in the medium to high temperature range, originating from the  increased electrical conductivity together with the considerable Seebeck coefficients. Details of the cause of this phenomenon will be discussed below.
To clarify the underlying reasons of the improvement in carrier concentration and electrical conductivity, we calculated the three-dimensional charge density distribution (Fig. 2a) and charge density difference (Fig. 2b-d) for BiCuSeO compounds, respectively. Figure 2a shows the electron charge density distribution of pristine BiCuSeO, where the charges feature a typical localized behavior along the in-plane direction. The three-dimensional charge density differences for the solely Pb-doped BiCuSeO, solely dualvacancy-doped BiCuSeO, as well as dual-vacancyand Pb-codoped BiCuSeO are shown in Fig. 2b- (Fig. 2b). Interestingly, for solely Bi/Cu dual-vacancy-doped compound (Fig. 2c), there is a distinct accumulation of holes between the adjacent Bi vacancy and Cu vacancy, signifying noteworthy charge delocalization behavior from [Bi 2 O 2 ] 2+ sublayers to [Cu 2 Se 2 ] 2− sublayers. The same interlayer delocalization feature of charges is also observed in dual-vacancy-and Pb-codoped material (Fig. 2d), which means that Pb-doping does not destroy the above delocalization behavior. From the above results, it can be concluded that the presence of Bi/Cu dual vacancies is essential for charge delocalization character along the out-of-plane direction. The interlayer charge delocalization character arising from Bi/Cu dual vacancies indicates the existence of interlayer charge-transport channels, which would motivate interlayer charge release. Once there is a charge concentration gradient between the two sublayers, it could be expected that charges trapped in [Bi 2 O 2 ] 2+ sublayers would diffuse into [Cu 2 Se 2 ] 2− sublayers along the interlayer charge-transport channels bridged by Bi/Cu dual vacancies.
In fact, dual vacancies and Pb play different but complementary roles in tailoring the electrical transport performance of BiCuSeO. Specifically, Bi/Cu dual vacancies give rise to delocalized distribution of charges between [Bi 2 O 2 ] 2+ sublayers and [Cu 2 Se 2 ] 2− sublayers, which offers channels for interlayer charge release. However, although the interlayer delocalization of charges is favorable for the interlayer charge transfer, Bi 1-x Cu 1-x SeO material without external dopant lacks sufficient charges for diffusion. Therefore, the increase in the observed carrier concentration is not significant in the solely dual-vacancy-doped samples compared with the pristine BiCuSeO (Supplementary Table S1). On the other hand, upon solely doping external dopant (such as Pb, Ba, Sr and Ca) [32][33][34]38] at the Bi site, the external dopant can indeed introduce plenty of charges into the charge-reservoir [Bi 2 O 2 ] 2+ sublayers of BiCuSeO material. However, because of the absence of interlayer transport channels, these extrinsic charges are still partially confined within the insulating [Bi 2 O 2 ] 2+ sublayers. The weak interlayer bonding blocks trapped charges from completely diffusing into the conductive [Cu 2 Se 2 ] 2− sublayers, thereby preventing the trapped charges from becoming conduction carriers. The theoretical hole concentration as a function of Pb content is plotted in Fig. 3a, assuming that each Pb atom (that is acceptor atom) contributes one hole to the effective hole concentration. The experimental carrier concentrations for solely Pb-doped BiCuSeO [38]   thus become conduction carriers. As a result, the carrier concentration is remarkably increased in vacancies/Pb codoped BiCuSeO. As shown in Fig. 3a, the experimental carrier concentrations of vacancies/Pb codoped BiCuSeO deviate strongly from that of the solely Pb-doped BiCuSeO and a theoretical limiting value of ∼8.69 × 10 20 cm −3 is reached, suggesting efficient interlayer charge release in codoped BiCuSeO.
To understand the influence of efficient interlayer charge release on the Seebeck coefficient and power factor for Bi 1-x-y Pb y Cu 1-x SeO, it is necessary to examine the relationship between the Seebeck coefficient and carrier concentration (the so-called Pisarenko plot) at room temperature. Using the single parabolic band (SPB) model [39,40], we calculated Pisarenko curves for different effective masses (Fig. 3c and d; details in the Supplementary data). For pristine BiCuSeO and solely dual-vacancy-doped BiCuSeO (carrier concentration ranges from 1.22 × 10 18 to 5.32 × 10 18 cm −3 ), the experimentally observed Seebeck coefficients are mainly located on the solid royal blue line, which indicates an effective mass of 3.01 m 0 (Fig. 3c). For solely Pb-doped sample (Bi 0.94 Pb 0.06 CuSeO, carrier concentration ∼384 × 10 18 cm −3 ), the measured Seebeck coefficient falls on the theoretical Pisarenko curve with effective mass of 3.86 m 0 . For dual-vacancy-and Pb-codoped samples (carrier concentration ranging from 789 × 10 18 to 946 × 10 18 cm −3 ), it is remarkable that the experimental Seebeck coefficients gradually deviate to the Pisarenko curve with higher effective mass of 5.95 m 0 (Fig. 3c). Specifically, as can be seen from Fig. 3d, the experimental points of Bi 0.92 Pb 0.06 Cu 0.98 SeO and Bi 0.90 Pb 0.06 Cu 0.96 SeO fall on the Pisarenko plot with different effective masses of 5.36 m 0 (olive line) and 5.95 m 0 (red line), respectively. It can be seen that the effective masses of dual-vacancyand Pb-codoped BiCuSeO compounds are significantly larger than those of pristine, solely dualvacancy-doped or solely Pb-doped samples. The increase in effective mass of holes is closely related to the multiple valence bands of BiCuSeO [15,41,42]. As shown in Fig. 3b, the first-principles simulations for the electronic band structure of Bi-CuSeO indicate complex multiband valence states that lie near each other in energy. The efficient interlayer charge release from [Bi 2 O 2 ] 2+ sublayers into [Cu 2 Se 2 ] 2− sublayers in real space endows dual-vacancy-and Pb-codoped BiCuSeO with drastically increased carrier concentration. Bi1-x-yPbyCu1-xSeO x=0%, y=0% x=2%, y=0% x=4%, y=0% x=0%, y=6% x=2%, y=6% x=4%, y=6%  Correspondingly, with increasing carrier concentration, in reciprocal space [7] the Fermi level is pushed into the valence band and more hole pockets are populated with hole carriers [3] for the p-type dualvacancy-and Pb-codoped BiCuSeO (see Fig. 4). The activated multiple converged valence bands account for the increase in effective mass, which is thought to be responsible for the increase in the Seebeck coefficient and the associated power factor at the similar carrier concentration. The total thermal conductivities κ tot , the electronic thermal conductivities κ ele and the lattice thermal conductivities κ lat as a function of temperature for Bi 1-x-y Pb y Cu 1-x SeO samples are plotted in Fig. 5a-c, respectively. The electronic thermal conductivity κ ele is calculated by the Wiedemann-Franz law κ ele = Lσ T, where L is the Lorenz number, σ is the electrical conductivity, and T is the absolute temperature [43]. Herein, the L value was estimated from the SPB model with acoustic phonon scattering [44][45][46][47] (details in the Supplementary data). The lattice part of thermal conductivity κ lat was obtained by subtracting the electronic part from the total thermal conductivity. For samples solely doped with Bi/Cu dual vacancies, the electronic thermal conductivity accounts for a very low percentage of the total thermal conductivity because of the low electrical conductivity (Fig. 5b). Meanwhile, both the total thermal conductivity and the lattice thermal conductivity decrease with increasing concentration of Bi/Cu dual vacancies. This is because vacancies have the capacity to enhance phonon scattering, which reduces the mean free path of low-frequency heatcarrying phonons [47]. Upon doping with Pb for the samples containing Bi/Cu dual vacancies, as a result of the much increased carrier concentration and enhanced electrical conductivity, the electronic thermal conductivity of dual-vacancy-and Pb-codoped BiCuSeO samples is obviously increased in comparison with that of solely dual-vacancy-doped or Pb-doped samples (Fig. 5b). Where the content of point defects in Bi 1-x-y Pb y Cu 1-x SeO is gradually increased after doping dual vacancies and Pb, the lattice thermal conductivity for codoped BiCuSeO is significantly reduced arising from the enhancement in phonon scattering. The minimum lattice thermal conductivity of 0.2 W m −1 K −1 is obtained for the Bi 0.90 Pb 0.06 Cu 0.96 SeO compound at 823 K (Fig. 5c), which compensates for the increase in electronic thermal conductivity, and ensures a very low total thermal conductivity in the codoped BiCuSeO.
Combining the electrical and thermal transport properties, the figure of merit ZT as a function of temperature for Bi 1-x-y Pb y Cu 1-x SeO samples are plotted in Fig. 5d. The dual-vacancy-and Pbcodoped BiCuSeO combines the merits of solely dual-vacancy-doping and solely Pb-doping, that is the figure of merit ZT values are enhanced over the entire test temperature range. Because of the high power factor of ∼8.1 μW cm −1 K −2 coupling with the low total thermal conductivity of

CONCLUSION
In conclusion, we present a promising strategy for activating multiple Fermi pockets and optimizing the thermoelectric properties in the BiCuSeO system by means of efficient interlayer charge release. This type of efficient charge release is realized by constructing channels for interlayer charge-transport process and providing plenty of extrinsic charges to diffuse along these channels. The efficient interlayer charge release produces substantial enhancement of carrier concentration while maintaining a considerable Seebeck coefficient as the released carriers activate multiple converged valence bands. Benefiting from the combination of improved power factor and low thermal conductivity, a significant enhanced ZT value of ∼1.4 is achieved in Bi 0.90 Pb 0.06 Cu 0.96 SeO at 823 K. The present strategy could be applied to other materials with layered structures and could inject fresh energy into the field of thermoelectric studies.

METHODS
The experimental details are given in the Supplementary data.

SUPPLEMENTARY DATA
Supplementary data are available at NSR online.