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Asep Ridwan Nugraha, [Shamim Sk](https://orcid.org/0000-0001-7644-7093), [Andrei Novitskii](https://orcid.org/0000-0002-7304-806X), Dedi, Fainan Failamani, Bambang Prijamboedi, [Takao Mori](https://orcid.org/0000-0003-2682-1846), Agustinus Agung Nugroho

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[High thermoelectric performance of BiCuSeO by optimized carrier concentration and point defect scattering through a Cr-induced compositing effect](https://mdr.nims.go.jp/datasets/59b4214e-1147-4507-8b38-5cd8ceb91fdc)

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Article    High-ZT from optimized carrier concentration and electron – phonon interaction in Cr-doped BiCuSeO oxyselenide Asep Ridwan Nugraha,*a,b,c Shaikh Shamim,b Andrei Novitskii,b Dedi,c Fainan Failamani,d Bambang Prijamboedi,d Takao Mori,b and Agustinus Agung Nugroho d a Physics Graduate Program, Institut Teknologi Bandung, Jl Ganesha 10, Bandung  40132, Indonesia.   b Research Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science (NIMS), Namiki 1-1, Tsukuba 305-0044, Japan.   c National Research and Innovation Agency (BRIN), Jl. Sangkuriang, Bandung 40135, Indonesia. d Faculty of Mathematics and Natural Sciences (FMIPA), Institut Teknologi Bandung (ITB), Jl Ganesha 10, Bandung  40132, Indonesia. *Email: asep051@brin.go.id  Abstract BiCuSeO has intrinsically low electrical conductivity, high Seebeck coefficient and low thermal conductivity. Therefore, the improvement of BiCuSeO thermoelectric performance focuses on enhancing its electrical conductivity. In this study, we report one of the strategies to optimize carrier concentration by Cr doped on Cu site. After doping with Cr, enhanced electrical conductivity coupled with a moderate Seebeck coefficient leads to power factor of ~0.4 – 0.6 mW/mK2 at 323 – 773 K. It is increased of ~4 – 6 times compared to pure BiCuSeO. Moreover, Cr doping reduces lattice thermal conductivity by ~21% as confirmed by both experimental result and Callaway model calculation. The analysis indicates that the lattice thermal conductivity can be reduced to 0.5 W m-1 K-1 at 773 K through the combined effect of point defect and phonon – electron scattering. The combination of optimized power factor and intrinsically low thermal conductivity result in high ZTmax and ZTaverage. The ZTmax and ZTaverage values were obtained in the BiCu0.96Cr0.04SeO sample of ~1.0 at 675 K and ~0.83 at 323 – 773 K, respectively. The high ZT of ~0.9 is realized over a broad temperature range from 473 to 773 K. This strategy makes BiCuSeO a promising candidate for medium temperature thermoelectric applications.  Keywords: BiCuSeO, point defect scattering, phonon – electron scattering, low lattice thermal conductivity, thermoelectric. 1. Introduction The first layered oxyselenide (BiO)Cu1-xSe was synthesized by T.Ohtani et al. in 1997 during the rapid development of superconducting material [1]. It was reported that (BiO)Cu1-xSe are degenerate semiconductor with holes as dominant charge carrier. Two decades later, in 2010, Zhao et al. reported the thermoelectric performance of Bi1-xSrxCuSeO in medium temperature range. The highest ZT of 0.76 at 873K was achieved from the sample of 7.5% Sr-doped on Bi site [2]. Since then, the development of BiCuSeO for thermoelectric applications are still going on. High performance thermoelectric materials can lead to efficient power generation by their modules [T. Hendricks, T. Caillat, and T. Mori, “Keynote Review of Latest Advances in Thermoelectric Generation Materials, Devices, and Technologies 2022”, Energies, 15, 7307 (2022).  doi:10.3390/en15197307]. Pristine BiCuSeO exhibits low electrical conductivity, high Seebeck coefficient and low thermal conductivity [3]. Considering the high Seebeck coefficient and low thermal conductivity, several researches have been conducted to improve the thermoelectric performance of BiCuSeO through charge carrier optimization. The single-doped materials with monovalent (Ag [4], Na [5], and Cs [6]) ions or divalent (Pb [7], Mg [8], Ca [9], Ba [10], Cd [11], and Sn [12]) ions are well observed for doping in the Bi site. The monovalent or divalent ions can optimize the charge carrier concentrations from 1019 cm-3 to 1021 cm-3 which improved the electrical conductivity. Additionally, they can reduce the thermal conductivity by point defect scattering. The point defect scattering depends on the mass and strain fluctuation between monovalent or divalent ions with the host lattice. The large mass difference between Bi and monovalent or divalent ions yields a huge mass fluctuation that predominately contribute to reduce lattice thermal conductivity. However, the enhancement of thermoelectric performance achieved by single doped material on the Bi site has limitation due to a dramatic decrease in carrier mobility.  Several attempts have been made to introduce dual doping on the Bi site by using Pb/In [13], Pb/Ca [14], Pb/Na [15],  Pb/Ba [16], Pb/In [17], on the Cu site by using Ba/Co [18], Pb/Ag [19], Ba/Ni [20], Pb/Fe [21], and on the Se sites by using 2  Ba/Te [22]. The majority of these materials utilized Pb as a dopant. It has been proven that doping on Bi site with Pb is very effective in increasing the carrier concentration of BiCuSeO. Since dopant Pb has electron configuration [Xe] 4f14 5d10 6s2 6p2, the substitution of Pb on Bi [Xe] 4f14 5d10 6s2 6p3 will produce more holes. Moreover, Pb doping introduces an additional peak near the Fermi level originated from delocalized lone-pair 6s orbital [7]. It can maintain moderate Seebeck coefficient by increasing the density of state effective mass. However, excessive use of heavy metal and toxic element such as Pb will cause environmental problems. Therefore, a new strategy is needed to improve the thermoelectric performance of BiCuSeO. To avoid the use of heavy and toxic metals, various transition metals have been used as dopants in Cu sites such as Mn [23], Fe [21], Co [24], Ni [20] and Zn [25]. The incorporation of Zn into the Cu site has been demonstrated to effectively enhance the carrier concentration by two orders of magnitude. Consequently, the maximum ZT of 0.9 was achieved at 873 K for BiCu0.9Zn0.1SeO, which is approximately 39% larger than that of the undoped BiCuSeO [25]. Similar to the enhancement observed in Zn doping, Ni doping in Bi0.875Ba0.125Cu1-xNixSeO has also led to an increase in electrical conductivity, attributed to an enhanced carrier concentration. Furthermore, in this system, the magnetic ion of Ni has significantly improved the Seebeck coefficient. The maximum ZT of 0.97 was achieved for x = 0.15 at 923 K [20]. The influence of transition metal doping resulted in a remarkable enhancement of electrical conductivity while increasing the Seebeck coefficient, resulting in an improved power factor. This strategy seems promising due to the intrinsically low thermal conductivity of BiCuSeO. However, the thermoelectric performance of BiCuSeO by transition metal doping with lead-free material leaves some room for improvement. In this report, we designed a single-doping at the single site-based experimental approach to produce high-performance BiCuSeO with lead-free material. We selected a transition metal element such as Cr as a dopant on the Cu site to improve the electronic transport properties. The Cr doping can modify the carrier concentration, which simultaneously increases the electrical conductivity while not deteriorating the Seebeck coefficient, leading to an enhanced power factor. The role of Cr doping is not only increasing the power factor but also decreasing lattice thermal conductivity. The decrease of lattice thermal conductivity is dominated by point defect and strong phonon – electron scattering. The ZTmax and ZTaverage have been achieved in BiCu0.96Cr0.04SeO around ~1.0 at 675 K and ~0.83 at 323 – 773 K, respectively. To the best of our knowledge, it is the highest ZTmax and ZTaverage for single doping in BiCuSeO system. 2. Experimental details Polycrystalline samples of BiCu1-xCrxSeO (x = 0, 0.02, 0.04, 0.06, and 0.08) were prepared by solid-state reaction followed with spark plasma sintering (SPS). The raw materials of nanopowder Bi2O3 (90 – 210 nm particle size, 2N, Sigma Aldrich), Bi (2N, Sigma Aldrich), Cu (2N, Sigma Aldrich), Cr (2N, Sigma Aldrich) and Se shot (2-6 mm, 5N, Alfa Aesar) were weighed according to stoichiometric ratio. The raw materials were mixed in agate pestle and mortar, then pressed into pellets under 20 MPa in a steel die. The pellets were sealed in quartz tubes under a vacuum (~10−3 Pa). Prior to use, the quartz tube had been baked in dry box for 1.5 h at 423 K to evaporate the volatile compounds such as alcohol and acetone. The ampoules were heated to 673 K at a rate of 2 K/min, then dwelled for 10 h to ensure that the reaction between chromium and other metals proceeded completely. Afterwards, the temperature slowly raised to 973 K at a rate of 1 K/min and held at this temperature for 20 h before cooling to room temperature naturally. The obtained ingots were hand-ground into fine powders and densified using SPS (SPS Syntax – 1080, Japan) at 973 K for 5 min under a uniaxial pressure of 50 MPa. Finally, the dense sintered pellets with a thickness of ~ 4 mm and a diameter of 10 mm were obtained.  The structural phases were identified using X-ray diffraction (XRD) Rigaku Mini-Flex, Japan, with Cu-Kα radiation (λ = 1.54060 Å). The obtained data were analyzed using GSAS [26]. The microstructure and compositional analysis of bulk sample were characterized by FE-SEM with EDS (SU-4800, Hitachi, Japan). Samples for EDS were embedded in a conductive resin and polished with standard metallographic procedures. The transport properties of electrical resistivity (ρ) and Seebeck coefficient (S) were measured in a low-pressure helium atmosphere on a commercial thermoelectric measurement system, ZEM-2 (Ulvac- Rico, Japan) from 323 K to 773 K. The typical dimensions of the electrical resistivity and Seebeck coefficient measurement are about 2 × 2 × 9 mm3. The thermal diffusivity coefficient (D) was measured using laser flash method (LFA427, Netzsch, Germany) in same temperature range. The total thermal conductivity (κ) was calculated from the equation 𝜅𝜅 = 𝐷𝐷𝐶𝐶𝑝𝑝𝑑𝑑, where Cp is the specific heat calculated using Debye model, and d is the density measured by the Archimedes method. The electronic thermal conductivity (κE) is estimated using the Wiedemann-Franz law (𝜅𝜅𝐸𝐸  =  𝐿𝐿𝐿𝐿𝐿𝐿), where L was estimated by single parabolic band (SPB) model and acoustic phonon scattering (APS) [27]. The pieces of 8.4 mm × 8.4 mm × 0.5 mm were used for Hall coefficient (𝑅𝑅𝐻𝐻) measurements under a reversible magnetic field of 0.52 T (ResiTest 8300DC, Tokyo, Japan). The Hall carrier concentration (𝑛𝑛𝐻𝐻 ) and mobility (𝜇𝜇𝐻𝐻 ) were calculated using 𝑛𝑛𝐻𝐻 =  1/(𝑒𝑒𝑅𝑅𝐻𝐻) and 𝜇𝜇𝐻𝐻  =  𝜎𝜎𝑅𝑅𝐻𝐻 , respectively. The estimation of extended uncertainty measurement of electrical resistivity, Seebeck coefficient, thermal diffusivity, total thermal conductivity, and density are 5%, 5%, 5%, 10% and 2%, respectively. The combined uncertainty for all measurement involved in ZT determination is below 20%. 3 3. Result and discussions 3.1. Phase and microstructure  Figure 1 (a) shows the normalized XRD patterns of the BiCu1-xCrxSeO (x = 0; 0.02; 0.04; 0.06; 0.08) samples at room temperature. All the diffraction patterns of obtained BiCu1-xCrxSeO samples well be indexed to tetragonal BiCuSeO (PDF Card #67-00327) with P4/nmm space group. There are no additional peaks due to secondary phase in all samples indicating the high purity of our samples. Since the Cr content is very low, the peaks derived from the Cr were not found in the XRD patterns. However, the peaks were slightly shifted to the higher angle 2θ with the increase of doping content as shown in the Fig. 1 (b). These results indicate that the Cr element was successfully incorporated into the BiCuSeO lattice. The weighted profile factor (RW), profile factor (RF), GoF, and lattice constants refined from XRD data using by GSAS-II are shown in Table I. The lattice constant and volume of the BiCu1-xCrxSeO samples decrease with increase of doping content. The decrease of the lattice constants is related to the fact that the ionic radius of Cr2+ (73 pm) or Cr3+ (61 pm) are lower than that of Cu+ (74 pm) assuming with Cr have a mixed valence in the system. The lattice constants agree with experimental data obtained in Ref. [24] when giving Co-doped in the Cu site of BiCuSeO. The substitution of Cu+ by Cr2+ modifies the electronic charge carrier between layers become (Bi2O2)(2-2x)+ and  ((Cu1-xCrx)2Se2)(2-2x)- using simple electron count, respectively. Table 1 shows the bond length and angle of dCu-Se, dBi-O, dBi-Se, αSe-Cu-Se and αBi-O-Bi, respectively. A slight increase of the Cu/Cr-Se bond length can be observed, simultaneously with a slight increase of the distortion of the CuSe4 tetrahedra. The massive change occurred at x = 0.04, where the Cr content influences the local environment of Cu in ((Cu1-xCrx)2Se2)(2-2x)- layer. Therefore, the angle of Se – Cu/Cr – Se decreases while the distances of Cu/Cr – Se and Bi – O increase. This effect leads to a reduction in the Coulombic attraction between layers and decrease the crystal volume. This is a similar mechanism with a decrease of the Bi – Se distance, which leads to a slight overlap of Bi and Se orbitals. This mechanism was also found in the Bi1-xSrxCuSeO [28] and Bi0.94Pb0.06Cu1-xFexSeO series [21].  The texture refinement was fitted using 10th order spherical harmonics in GSAS-II for all samples compared with non-texture sample from ICDD. Figure 2 shows the fitted model compared with the diffraction intensity of the BiCu1-xCrxSeO (x = 0; 0.04) in (003) and (102) planes, respectively. The degree of preferred orientation of different crystal planes can be determined using Harris’s analysis by calculating the texture coefficient as showed in eq (1)  𝑃𝑃(ℎ𝑖𝑖𝑘𝑘𝑖𝑖𝑙𝑙𝑖𝑖) =𝐼𝐼(ℎ𝑖𝑖𝑘𝑘𝑖𝑖𝑙𝑙𝑖𝑖)𝐼𝐼𝑜𝑜(ℎ𝑖𝑖𝑘𝑘𝑖𝑖𝑙𝑙𝑖𝑖)�1𝑁𝑁∑𝐼𝐼�ℎ𝑖𝑖𝑘𝑘𝑖𝑖𝑙𝑙𝑖𝑖�𝐼𝐼𝑜𝑜�ℎ𝑖𝑖𝑘𝑘𝑖𝑖𝑙𝑙𝑖𝑖�𝑁𝑁𝑖𝑖=1 �−1  (1) where 𝑃𝑃(ℎ𝑖𝑖𝑘𝑘𝑖𝑖𝑙𝑙𝑖𝑖)is the texture coefficient of the planes specified by Miller Indices (hkl), 𝐼𝐼(ℎ𝑖𝑖𝑘𝑘𝑖𝑖𝑙𝑙𝑖𝑖)is the integrated intensity of texture sample, 𝐼𝐼𝑜𝑜(ℎ𝑖𝑖𝑘𝑘𝑖𝑖𝑙𝑙𝑖𝑖)is the intensity of non-texture sample and N is the number of diffractions. 𝑃𝑃(ℎ𝑖𝑖𝑘𝑘𝑖𝑖𝑙𝑙𝑖𝑖) = 0 means that there is no orientation, 𝑃𝑃(ℎ𝑖𝑖𝑘𝑘𝑖𝑖𝑙𝑙𝑖𝑖) = 1 means that the sample has random orientation and 𝑃𝑃(ℎ𝑖𝑖𝑘𝑘𝑖𝑖𝑙𝑙𝑖𝑖) > 1 means that the sample is highly oriented. The increase of texture coefficient indicates that a higher degree of preferred orientation along a particular direction as compared with the non-texture sample. Figure 2 (inset) shows the degree of preferred orientation in (003) plane as a function of Cr doping. The texture analysis shows that the BiCu0.96Cr0.04SeO is highly textured along (003) plane which 10 times higher than non-textured sample.  Figure 3 (a-b) displays the SEM images on the fractured surface of BiCu1-xCrxSeO with x = 0.00 and 0.04, respectively. It can be observed that the SEM image of pristine BiCuSeO exhibits a variety of shapes and sizes of crystals, whereas the BiCu0.96Cr0.04SeO sample displays a lath-shaped crystal. The small dots on the images are identified as micropores, which are more prevalent in the pristine BiCuSeO sample than in the BiCu0.96Cr0.04SeO sample. The average grain size of the pristine BiCuSeO and BiCu0.96Cr0.04SeO samples is approximately 2.1 µm and 1.8 µm, respectively. Figure 4 (a-c) shows the SEM and EDX images on the polished surface of the BiCu1-xCrxSeO (x = 0.02;0.04; 0.08) samples. The Bi, Cu, and Se elements are homogeneously distributed in the BiCuSeO matrix. However, the BiCu1-xCrxSeO (x = 0.02; 0.04; 0.08) samples show an uneven distribution of Cr and O elements. The Cr and O elements are distributed randomly in the BiCuSeO matrix and some of them are agglomerated to form a chromium oxide. The point mapping on the Cr-rich area of the BiCu0.96Cr0.04SeO indicate the presence of chromium oxide phases, CrO. Furthermore, the chromium oxide forms a composite in the BiCuSeO matrix at high Cr doped. Based on the results of SEM and EDX measurements, we estimate that the reaction occurring in this system can be expressed as follows:  𝐵𝐵𝑖𝑖2𝑂𝑂3 + 𝐵𝐵𝐵𝐵 + 3𝑥𝑥𝑥𝑥𝑥𝑥 + 3𝑆𝑆𝑆𝑆 + 3(1 − 𝑥𝑥)𝐶𝐶𝐶𝐶 → 3𝐵𝐵𝐵𝐵𝐵𝐵𝑢𝑢1−𝑥𝑥𝑆𝑆𝑆𝑆𝑂𝑂1−𝑥𝑥 + 3𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥  (2) and  𝐵𝐵𝑖𝑖2𝑂𝑂3 + 𝐵𝐵𝐵𝐵 + 3𝑥𝑥𝑥𝑥𝑥𝑥 + 3𝑆𝑆𝑆𝑆 + 3(1 − 𝑥𝑥)𝐶𝐶𝐶𝐶 → 3𝐵𝐵𝐵𝐵𝐵𝐵𝑢𝑢1−𝑥𝑥𝐶𝐶𝑟𝑟𝑥𝑥𝑆𝑆𝑆𝑆𝑆𝑆 (3) Consistent with XRD measurement, it is also found that the CrO phases began to appear at x = 0.06, indicating that the solubility limit of Cr in the BiCuSeO matrix is less than x = 0.06. The solubility limit of BiCu1-xCrxSeO is lower than the Bi1−xLixCu1−xMnxSeO [23] and BiCu1-xCoxSeO [13], which are below 8% and 15%, respectively. The smaller solubility limit 4  of BiCu1-xCrxSeO is attributed to the larger ionic radius of Cr2+ (73 pm) in comparison to Mn2+ (67 pm) and Co2+ (65 pm), respectively.  3.2. Thermoelectric properties The electrical conductivity (𝜎𝜎) for the BiCu1-xCrxSeO (x = 0; 0.02; 0.04; 0.06; 0.08) samples as a function of temperature is shown in Fig. 5 (a). The pristine BiCuSeO has a very low electrical conductivity as reported in various papers [5,9,29]. It has a continuous increasing tendency as the temperature rises. It indicates the degenerate semiconductor behavior. In addition, the BiCu1-xCrxSeO (x = 0.02; 0.04; 0.06; 0.08) samples show a significant enhance in electrical conductivity (~6 – 17 times) compared with the pristine BiCuSeO. Specially, the electrical conductivity of pristine BiCuSeO is ~3.44 S cm-1 at 473 K, while this value increase to ~52.46 S cm-1 in BiCu0.94Cr0.06SeO. The primary factor contributing to the increased conductivity of BiCu1-xCrxSeO (x = 0.02; 0.04; 0.06; 0.08) samples is the increase in carrier concentration in the system. Table 2 illustrates the carrier concentration and mobility of the BiCu1-xCrxSeO (x = 0; 0.02; 0.04; 0.06; 0.08) at room temperature. The substitution of Cu+ by Cr2+ is theoretically expected to follow the equation, 𝐶𝐶𝑟𝑟2+ → 𝐶𝐶𝑟𝑟𝐶𝐶𝐶𝐶• + 𝑒𝑒′ . It was hypothesized that the substitution of Cu+ by Cr2+ should produce more electrons than holes, resulting in a decrease in electrical conductivity and an increase in the Seebeck coefficient due to the charge carrier. However, the observed mechanism in our system does not align with this hypothesis. The probable explanation for this discrepancy lies in the possibility that Cu+ is not fully substituted by Cr2+. When the Cr doping concentration is low, the Cr2+ tends to form nano- to microscale precipitates of CrO. The CrO precipitates will create additional holes in the oxide layer due to the presence of oxygen vacancies and in the conducting layer due to a deficiency of copper. The additional holes increase the carrier concentration in the system. Upon further increase in Cr doping, the Cr2+ partially substitutes the unoccupied Cu+, leading to the introduction of electrons. The CrO’s tendency to provide holes is suppressed, which slightly decreased the carrier concentration. The introduction of Cr2+ in BiCu1-xCrxSeO can be illustrated by Eq. 4:  2(𝐵𝐵𝐵𝐵𝐵𝐵𝑢𝑢1−𝑥𝑥𝐶𝐶𝑟𝑟𝑥𝑥𝑆𝑆𝑆𝑆𝑆𝑆) = �𝐵𝐵𝑖𝑖2𝑂𝑂2(1−𝑥𝑥)�2(1−𝑥𝑥)+ + 2𝑥𝑥ℎ+ + �𝐶𝐶𝑢𝑢2(1−𝑥𝑥)𝑆𝑆𝑒𝑒2�(2+𝑥𝑥)− + 𝑥𝑥𝑉𝑉𝐶𝐶𝐶𝐶− + 2𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥 + 2𝑥𝑥ℎ+ (4) where 𝑉𝑉𝐶𝐶𝐶𝐶−  and ℎ+ are the Cu vacancy and the produced holes introduced by Cr doping, respectively.  Figure 5 (b) shows the temperature dependence of the Seebeck coefficient (S) of the BiCu1-xCrxSeO (x = 0; 0.02; 0.04; 0.06; 0.08) samples. The positive value of the Seebeck coefficient indicate the whole samples are p-type semiconductor. The pristine BiCuSeO has a high value of Seebeck coefficient of around 425 – 500 µV/K for a temperature range of 325 – 773 K. This value is higher than pristine BiCuSeO reported in the earlier studies [5,9,29]. The Seebeck coefficient decrease from ~ 484.5 µV/K in pristine BiCuSeO to ~ 305.4 µV/K in BiCu0.94Cr0.06SeO at 473 K. The reduction in Seebeck coefficient consistent with the enhancement in electrical conductivity as the Cr doping increases. The Seebeck coefficient in doped sample decrease with raising temperature and reach a minimum value at 473 K. When T > 473 K it slightly increases monotonically, owing to the thermal activation of secondary phase of chromium oxide. In the context of non-degenerate semiconductors, the effective mass (m*) can be calculated by the following equation (5-7) based on experimental carrier concentration (n) and Seebeck coefficient (S), with the assumption of single parabolic band (SPB) model and acoustic phonon scattering (APS).   𝑚𝑚∗ = ℎ22𝑘𝑘𝐵𝐵𝑇𝑇� 𝑛𝑛4𝜋𝜋𝐹𝐹1/2(𝜂𝜂)�2/3   (5)  𝑆𝑆 = ± 𝑘𝑘𝐵𝐵𝑒𝑒�(𝑟𝑟+5/2)𝐹𝐹𝑟𝑟+3/2(𝜂𝜂)(𝑟𝑟+3/2)𝐹𝐹𝑟𝑟+1/2(𝜂𝜂)− 𝜂𝜂� (6)  𝐹𝐹𝑖𝑖(𝜂𝜂) = ∫ 𝑥𝑥𝑖𝑖1+𝑒𝑒𝑥𝑥−𝜂𝜂𝑑𝑑𝑑𝑑∞0  (7) Where 𝐹𝐹𝑖𝑖(𝜂𝜂) is the i-th order Fermi integral, 𝜂𝜂 = 𝐸𝐸𝐹𝐹/𝑘𝑘𝐵𝐵𝑇𝑇 is the reduce Fermi energy, S is the Seebeck coefficient, 𝑘𝑘𝐵𝐵 is the Boltzmann constant, e is the charge carrier, h is the reduces Plack constant, m* is the carrier effective mass, n is the carrier concentration, and r is the scattering parameter which assumed as −1/2 for the acoustic phonon scattering near room temperature. The estimated of effective mass is presented in Table 2. The effective mass of BiCu1-xCrxSeO varies from ~3.9m0 (m0 is the free electron mass) to ~8.9m0, indicating the multi-band behaviour in these doped samples. It is clear from Fig.5 (c) that the Seebeck coefficient decrease simultaneously with reduction of effective mass from ~4.7m0 for x = 0 to ~4.1m0 for x = 0.08 and increasing the carrier concentration from ~5.9×1018 for x = 0 to ~1.8 × 1019 for x = 0.08. The Pisarenko relationship of the Seebeck coefficient for non-degenerate semiconductors is fitted by equation (8). The results demonstrated that the dependence of S on n and m* for the BiCu1-xCrxSeO (x = 0; 0.02; 0.04; 0.06; 0.08) samples is in fair agreement with the theoretical description of the single parabolic band (SPB) model and acoustic phonon scattering (APS). 5  𝑆𝑆 = ± 𝑘𝑘𝐵𝐵𝑒𝑒�52+ 𝑟𝑟 + 𝑙𝑙𝑙𝑙 �2(2𝜋𝜋𝑚𝑚∗𝑘𝑘𝐵𝐵𝑇𝑇)32ℎ3𝑛𝑛�� (8) The electronic transport properties of material are well explained by the weighted mobility. The weighted mobility calculated by equation 9 using the experimental data electrical conductivity and Seebeck coefficient proposed by J. Snyder which expressed as:[30]  𝜇𝜇𝑤𝑤 = 3ℎ3𝜎𝜎8𝜋𝜋𝜋𝜋(2𝑚𝑚𝑒𝑒𝑘𝑘𝐵𝐵𝑇𝑇)3/2 �𝑒𝑒� |𝑆𝑆|𝑘𝑘𝐵𝐵/𝑒𝑒−2�1+𝑒𝑒�−5� |𝑆𝑆|𝑘𝑘𝐵𝐵/𝑒𝑒−1��+3𝜋𝜋2|𝑆𝑆|𝑘𝑘𝐵𝐵/𝑒𝑒1+𝑒𝑒�5� |𝑆𝑆|𝑘𝑘𝐵𝐵/𝑒𝑒−1��  �   (9) where h, e, 𝜌𝜌, 𝑘𝑘𝐵𝐵, 𝑚𝑚𝑒𝑒, S, and T represent the Planck constant, the charge carrier, the experimental electrical resistivity in 𝑚𝑚Ω cm, the Boltzmann constant, the mass of electron, the experimental Seebeck coefficient, and the absolute temperature, respectively. Figure 5 (d) shows the weighted mobility of the BiCu1-xCrxSeO (x = 0, 0.02; 0.04; 0.06; 0.08) as a function of temperature.  The µw of doped samples follow the ~𝑇𝑇−1.5 tendency, indicates the domination of acoustic – phonon scattering in whole temperature region.  Figure 5 (e) shows the power factor of the BiCu1-xCrxSeO (x = 0; 0.02; 0.04; 0.06; 0.08) samples. The BiCu0.96Cr0.04SeO sample shows the high electrical conductivity, while maintaining its Seebeck coefficient of around 350 – 425 µV/K in the whole temperature range. This makes the power factor (PF) of the BiCu0.96Cr0.04SeO sample is the highest compared to all samples over the entire temperature range. The power factor of the BiCu0.96Cr0.04SeO is around ~0.60 mWm-1K-2 at 473 K. This value is higher than that of Mg [29], Ca [9], Fe [23], Sb [31], La [32] and Pr [33] doped BiCuSeO. The power factor (PF) of the BiCu1-xCrxSeO decreases as the doping level increase further more than 0.04, which is attributed to the presence of secondary phase confirmed by SEM.  The total thermal conductivity of the pristine BiCuSeO sample decreases with increasing temperature, from ~1.09 Wm-1K-1 at 300 K to ~0.55 Wm-1K-1 at 773 K, as shown in Fig. 5 (f). The total thermal conductivity decreases with increased Cr doping fractions caused by multiple scattering factors. The maximum reduction in the total thermal conductivity is observed at x = 0.08, with a decrease of approximately 21.02%. In order to investigate the electronic and phonon contributions, we calculate the electronic thermal conductivity using Wiedermann – Franz relation, 𝑘𝑘𝐸𝐸 = 𝐿𝐿𝐿𝐿𝐿𝐿, where L was derived by equation 10 expressed as:  𝐿𝐿 = �𝑘𝑘𝐵𝐵𝑒𝑒�2�(𝑟𝑟+72)𝐹𝐹𝑟𝑟+52(𝜂𝜂)(𝑟𝑟+32)𝐹𝐹𝑟𝑟+12(𝜂𝜂)− �(𝑟𝑟+52)𝐹𝐹𝑟𝑟+32(𝜂𝜂)(𝑟𝑟+32)𝐹𝐹𝑟𝑟+12(𝜂𝜂)�2� (10) with assumption of a single parabolic band (SPB) and acoustic phonon scattering (APS). Figure S5 (a-b) shows the Lorenz number and electronic thermal conductivity as a function of temperature. Based on the calculation, the electronic thermal conductivity of the BiCu1-xCrxSeO samples maintains a very low value over the temperature range. The maximum contribution of the electronic part to the total thermal conductivity is less than 2% for all samples. The lattice thermal conductivity decreases as the temperature decreases as shown in Fig.6 (a). It is hypothesized that the lattice thermal conductivity is reduced by point defect scattering through Cr doping. To understand the role of point defect in decreasing the lattice thermal conductivity, theoretical calculations are conducted using the Callaway model, which is defined as the ratio of the lattice thermal conductivity of a material containing a defect to that of the parent material [34,35] (see Supplementary Information).   𝜅𝜅𝑙𝑙𝑙𝑙𝑙𝑙𝜅𝜅𝑙𝑙𝑙𝑙𝑙𝑙,𝑝𝑝= 𝑡𝑡𝑡𝑡𝑡𝑡−1(𝑢𝑢)𝑢𝑢         (11) where 𝜅𝜅𝑙𝑙𝑙𝑙𝑙𝑙 , 𝜅𝜅𝑙𝑙𝑙𝑙𝑙𝑙,𝑝𝑝 are the lattice thermal conductivities of the defected and parent materials, respectively, and the parameter u is defined by:   𝑢𝑢 = �𝜋𝜋2𝜃𝜃𝐷𝐷𝛺𝛺ℎ𝑣𝑣𝑎𝑎2𝜅𝜅𝑙𝑙𝑙𝑙𝑙𝑙,𝑝𝑝𝛤𝛤�12         (12) where h, Ω, va and θD stand for the Planck constant, average volume per atom, lattice sound velocity (𝑣𝑣𝑎𝑎 = 2107 m/s) [9], and the Debye temperature (𝜃𝜃𝐷𝐷 = 243 K) [36]. The disorder parameter Γ = ΓM + 𝜀𝜀Γ𝑆𝑆𝑆𝑆 is calculated by Abeles and Slack model which includes both mass fluctuation (ΓM) and strain field fluctuation between Cr – Cu atom (ΓSF) [37,38]. In our system, the adjustable parameter 𝜀𝜀 is approximately 170, obtained from the fitting between the model and experimental data. The disorder parameter Γ varies depending on the fractional occupation of the Cr on the Cu site. The disorder parameter and the difference between the calculated and measured values are listed in Table S2, respectively. The result reveals that the calculated lattice thermal conductivity at room temperature agrees with the measured value, which is significantly lower than the uncertainty measurement, as shown in the Fig.6 (a)(inset). However, the reduction in lattice thermal conductivity in Cr-doped samples as a function of temperature remains to be investigated. Several factors may contribute to decrease in lattice 6  thermal conductivity, such as Umklapp process, point defect, grain boundary and phonon – electron scattering. To elucidate the contribution of each scattering mechanisms as a function of temperature, the Callaway model was employed to evaluate the lattice thermal conductivity [39]. Here, 𝜅𝜅𝐿𝐿 can be calculated from the following equation (13-14):  𝜅𝜅𝐿𝐿 = 𝑘𝑘𝐵𝐵2𝜋𝜋2𝑣𝑣𝑠𝑠�𝑘𝑘𝐵𝐵𝑇𝑇ℏ�3∫ 𝜏𝜏𝑡𝑡𝑡𝑡𝑡𝑡𝑥𝑥4𝑒𝑒𝑥𝑥𝑒𝑒𝑥𝑥−1𝑑𝑑𝑑𝑑𝜃𝜃𝐷𝐷0  (13)  𝜏𝜏𝑡𝑡𝑡𝑡𝑡𝑡 = 𝜏𝜏𝑈𝑈 + 𝜏𝜏𝑃𝑃𝑃𝑃 + 𝜏𝜏𝐺𝐺𝐺𝐺 + 𝜏𝜏𝑃𝑃𝑃𝑃 (14) where 𝜏𝜏𝑡𝑡𝑡𝑡𝑡𝑡 is the total relaxation time. The detailed calculations and fitting parameters for this model are provided in the Supplementary Information. The analysis was restricted to data below 600 K to minimize the bipolar effect. As depicted in Fig. 6(b), the calculation of the lattice thermal conductivity (𝜅𝜅𝐿𝐿) using the Callaway model shows good agreement with the measured values. This model underscores the significant role of various scattering mechanisms in enhancing phonon scattering. The contributions of each scattering mechanism to the reduction of lattice thermal conductivity are illustrated in Fig. 6(c). The solid light blue line, dashed red line, dashed blue line, and dashed green line represent the contributions from the Umklapp process (U), Umklapp process and point defect scattering (U+PD), Umklapp process, point defect and phonon-electron scattering (U+PD+PE), and Umklapp process, point defect, phonon-electron, and grain boundary scattering (U+PD+PE+GB), respectively. As expected from the fractured samples observed in SEM measurements, grain boundary scattering (GB) does not significantly reduce lattice thermal conductivity due to the large grain size in both pristine and doped samples. Large grain sizes are less effective in scattering low – frequency phonons compared to nano grain size. Figure 6 (c) further compares the model excluding phonon-electron scattering (U+PD) with the model including it (U+PD+PE). The analysis indicates that the Umklapp process and point defect scattering contribute only ~7.24% to the reduction of lattice thermal conductivity. When phonon – electron scattering is included, the calculated 𝜅𝜅𝐿𝐿  decreases by approximately 20.39%, achieving a good match between theoretical and experimental data. Phonon – electron scattering significantly contributes (~13.15%) to phonon scattering across a wide frequency range. Phonon – electron scattering disrupts the coherent propagation of phonons. Each scattering event can change the direction and energy of phonons, effectively hindering their ability to carry heat in a straight line through the lattice, resulting in a lower lattice thermal conductivity. The figure of merit (ZT) of the BiCu1-xCrxSeO (x = 0.02; 0.04; 0.06; 0.08) samples as a function of temperature are shown in Fig 8 (a). The BiCu0.96Cr0.04SeO and BiCu0.94Cr0.06SeO samples have a ZT of about ~0.9 in the temperature range of 473 – 773 K. This value increases by about ~ 130 – 150 % as compared to pristine BiCuSeO. The ZTmax was obtained in the BiCu0.96Cr0.04SeO sample with a value of ~1.0 at 675 K. If we compare with several doping elements by single-doped method such as Pb [7], Ba [10], Cd [11], Ca [9], Sm [40], Sr [41], Na [42], La [32], Mg [29] and dual-doped method such as Pb/Fe [21] and Pb/Ca [14], our result show a moderate value among the BiCuSeO system. The achieved ZTmax is obtained in the low temperature region. It is lower than the other results which usually obtain the ZTmax above 800 K. The highest ZTmax is observed for the BiCuSeO system with the Pb/Fe double doping method at the Bi/Cu site with a value of ~1.5 at 873 K [21]. Furthermore, Cr doping can significantly increase the ZTaverage, which plays an important role in the applications. The calculated ZTaverage of the BiCu0.96Cr0.04SeO sample is approximately 0.83 in the temperature range of 323 – 773 K. It is the highest value among the single-doped system. This value can compete with the Pb/Fe and Pb/Ca dual-doped systems, where both systems use heavy metals and toxic materials. In contrast, our method only uses Cr single-doped, which is more environmentally friendly.   Conclusions In conclusion, the synthesis of BiCu1-xCrxSeO compounds with x = 0, 0.02, 0.04, 0.06, and 0.08 was successfully accomplished using the SSR+SPS method. The BiCu0.96Cr0.04SeO sample exhibited maximum and average figure of merit, ZTmax and ZTaverage, of approximately 1.0 at 675 K and 0.83 over the temperature range of 323–773 K, respectively. These values represent enhancements of about 150% and 330%, respectively, compared to the pristine BiCuSeO. The observed improvement in ZT is attributed to two main factors. Firstly, the increased charge carrier concentration improved electrical conductivity, as the substitution of Cr atoms generated additional holes in the oxide layer due to oxygen vacancies and in the conducting layer due to copper deficiency. Secondly, the reduction in lattice thermal conductivity was achieved through point defect scattering and phonon-electron scattering. The disparity in mass and strain fields between Cr and Cu atoms led to increased point defect scattering, while phonon-electron interactions significantly enhanced phonon scattering across a wide frequency range, thereby reducing lattice thermal conductivity. Our results demonstrate a remarkable improvement in both ZTmax and ZTaverage through single doping, achieving a ZT of approximately 0.9 in the low-temperature region of 473–773 K. This strategy makes BiCu1-xCrxSeO a promising candidate for medium-temperature thermoelectric applications. 7 Acknowledgements This work was supported by The Indonesia Endowment Fund for Education (LPDP), Indonesia and International Cooperative Graduate Program (ICGP), NIMS- Japan. The authors also gratefully acknowledge the facilities, scientific and technical support of Advanced Characterization Laboratories, National Research and Innovation Agency (BRIN), E-Layanan Sains, Bandung, Indonesia.  References [1] T. Ohtani, Y. Tachibana, Y. Fujii, Electrical properties of layered copper oxyselenides (BiO)Cu1 − xSe and (Bi1 − xSrx)OCuSe, J Alloys Compd 262–263 (1997) 175–179. https://doi.org/10.1016/S0925-8388(97)00375-7. [2] L.D. Zhao, D. Berardan, Y.L. Pei, C. Byl, L. Pinsard-Gaudart, N. Dragoe, Bi1−xSrxCuSeO oxyselenides as promising thermoelectric materials, Appl Phys Lett 97 (2010) 092118. https://doi.org/10.1063/1.3485050. [3] L.D. Zhao, J. He, D. Berardan, Y. Lin, J.F. Li, C.W. 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Yang, Ultra-fast synthesis and high thermoelectric properties of heavy sodium doped BiCuSeO, J Alloys Compd 708 (2017) 955–960. https://doi.org/10.1016/J.JALLCOM.2017.02.290.     10  Table captions Table 1: Lattice parameters, local structures (bond distance and angle), and atomic positions obtained from Rietveld analysis using GSAS-II ......................................................................................................................................................................... 11 Table 2. Carrier concentration, carrier mobility, effective mass, and density of the BiCu1-xCrxSeO (x = 0; 0.02; 0.04; 0.06; 0.08) samples at room temperature. ......................................................................................................................................... 12   11 Table 1: Lattice parameters, local structures (bond distance and angle), and atomic positions obtained from Rietveld analysis using GSAS-II x a (Å) c (Å) Vol. (Å)3 GoF RW RF d (Cu-Se) (Å) d (Bi-O) (Å) d (Bi-Se) (Å) Angle (°) (Se-Cu-Se) Angle (°) (Bi-O-Bi) 0.00 3.9296(3)* 8.9296(7) 137.89(3) 1.17 5.68 4.55 2.516(0) 2.331(0) 3.226(0) 102.66(0) 114.87(0) 0.02 3.9295(2) 8.9299(7) 137.89(3) 1.36 6.42 2.49 2.517(0) 2.331(0) 3.226(0) 102.62(0) 114.93(0) 0.04 3.9293(4) 8.9297(1) 137.87(3) 1.58 6.97 4.11 2.519(0) 2.332(0) 3.222(0) 102.50(0) 114.78(0) 0.06 3.9287(2) 8.9279(7) 137.80(3) 1.34 6.38 3.82 2.517(0) 2.331(0) 3.224(0) 102.57(0) 114.88(0) 0.08 3.9288(6) 8.9299(5) 137.84(3) 1.31 6.24 2.55 2.515(0) 2.330(0) 3.227(0) 102.72(0) 114.94(0) Phase BiCuSeO BiCu0.98Cr0.02SeO BiCu0.96Cr0.04SeO BiCu0.94Cr0.06SeO BiCu0.92Cr0.08SeO Atomic Positions      Bi      x 0.25 0.25 0.25 0.25 0.25 y 0.25 0.25 0.25 0.25 0.25 z 0.140478 0.139951 0.140776 0.140472 0.140161 Cu      X 0.75 0.75 0.75 0.75 0.75 Y 0.25 0.25 0.25 0.25 0.25 Z 0.5 0.5 0.5 0.5 0.5 Se      X 0.25 0.25 0.25 0.25 0.25 Y 0.25 0.25 0.25 0.25 0.25 Z 0.676039 0.675982 0.676661 0.676678 0.675802 O      X 0.75 0.75 0.75 0.75 0.75 Y 0.25 0.25 0.25 0.25 0.25 Z 0 0 0 0 0 Cr      x - 0.75 0.75 0.75 0.75 y - 0.25 0.25 0.25 0.25 z - 0.5 0.5 0.5 0.5 *Standard deviations are given in parentheses and refer to the estimated errors in the least significant units.             12  Table 2. Carrier concentration, carrier mobility, effective mass, and density of the BiCu1-xCrxSeO (x = 0; 0.02; 0.04; 0.06; 0.08) samples at room temperature. samples n (1019 cm-3) µ (cm2 V-1 S-1) m*(m0) 𝝆𝝆 (g/cm3) x = 0 0.596 4.979 4.726 8.453 x = 0.02 1.298 1.412 3.909 8.454 x = 0.04 5.683 0.223 8.905 8.459 x = 0.06 2.128 0.293 4.420 8.673 x = 0.08 1.846 0.338 4.174 8.421    13 Figure captions Figure 1. (a). The XRD patterns of the BiCu1-xCrxSeO (x = 0; 0.02; 0.04; 0.06; 0.08) samples at room temperature (b). The enlarged peaks at 2θ between 29° - 31° ................................................................................................................................... 14 Figure 2. Texture refinement using spherical harmonic in GSAS-II.  Degree of preferred orientation in 003 plane (inset) ... 14 Figure 3. The SEM images of the fractured sample of BiCu1-xCrxSeO (a) x = 0 (b) x = 0.04 samples .................................... 15 Figure 4. The elemental mapping of polished surface of the BiCu1-xCrxSeO (a) x = 0.02, (b) x = 0.04, and (c) x = 0.08 ....... 15 Figure 5. Thermoelectric properties as a function of temperature of the BiCu1-xCrxSeO (x = 0; 0.02; 0.04; 0.06; 0.08) samples, (a) Electrical conductivity, (b) Seebeck coefficient, (c) Pisarenko plot for non-degenerate semiconductor at 300 K, (d) The weighted mobility (the dash-line represent the trend of µw ∝ T-n), (e) Power factor (PF), and (f) Total thermal conductivity. ............................................................................................................................................................................ 16 Figure 6. (a). The temperature dependent of 𝜅𝜅𝜅𝜅 for the BiCu1-xCrxSeO samples (symbols). (inset) A comparison of the experimental and the calculated lattice thermal conductivity at 300 K. (b) The dash line showing the prediction of 𝜅𝜅𝜅𝜅 using the Callaway model with different scattering mechanism. (b). The contribution of Umklapp process scattering (U), point defect scattering (PD), phonon – electron scattering (PE) and grain boundary scattering (GB) for the BiCu1-xCrxSeO ( x = 0.08) samples. .......................................................................................................................................................................... 17 Figure 7. (a) The ZT as a function of temperature, (b) The comparison of ZTmax at 675 K, (c) The comparison of ZTaverage in the temperature range of 323 – 773 K compared with several doping elements from earlier studies ..................................... 18    14   Figure 1. (a). The XRD patterns of the BiCu1-xCrxSeO (x = 0; 0.02; 0.04; 0.06; 0.08) samples at room temperature (b). The enlarged peaks at 2θ between 29° - 31°  Figure 2. Texture refinement using spherical harmonic in GSAS-II.  Degree of preferred orientation in 003 plane (inset)  15  Figure 3. The SEM images of the fractured sample of BiCu1-xCrxSeO (a) x = 0 (b) x = 0.04 samples   Figure 4. The elemental mapping of polished surface of the BiCu1-xCrxSeO (a) x = 0.02, (b) x = 0.04, and (c) x = 0.08 16     Figure 5. Thermoelectric properties as a function of temperature of the BiCu1-xCrxSeO (x = 0; 0.02; 0.04; 0.06; 0.08) samples, (a) Electrical conductivity, (b) Seebeck coefficient, (c) Pisarenko plot for non-degenerate semiconductor at 300 K, (d) The weighted mobility (the dash-line represent the trend of µw ∝ T-n), (e) Power factor (PF), and (f) Total thermal conductivity.     17  Figure 6. (a). The temperature dependent of 𝜅𝜅𝐿𝐿 for the BiCu1-xCrxSeO samples (symbols). (inset) A comparison of the experimental and the calculated lattice thermal conductivity at 300 K. (b) The dash line showing the prediction of 𝜅𝜅𝐿𝐿 using the Callaway model with different scattering mechanism. (c). The contribution of Umklapp process scattering (U), point defect scattering (PD), phonon – electron scattering (PE) and grain boundary scattering (GB) for the BiCu1-xCrxSeO ( x = 0.08) samples.     18   Figure 7. (a) The ZT as a function of temperature, (b) The comparison of ZTmax at 675 K, (c) The comparison of ZTaverage in the temperature range of 323 – 773 K compared with several doping elements from earlier studies                19 Supporting information: High-ZT from optimized carrier concentration and electron – phonon interaction of Cr-doped BiCuSeO oxyselenide Asep Ridwan Nugraha,*a,b,c Shaikh Shamim,b Andrei Novitskii,b Dedi,c Fainan Failamani,d Bambang Prijamboedi,d Takao Mori,b and Agustinus Agung Nugroho d a Physics Graduate Program, Institut Teknologi Bandung, Jl Ganesha 10, Bandung  40132, Indonesia.   b Research Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science (NIMS), Namiki 1-1, Tsukuba 305-0044, Japan.   c National Research and Innovation Agency (BRIN), Jl. Sangkuriang, Bandung 40135, Indonesia. d Faculty of Mathematics and Natural Sciences (FMIPA), Institut Teknologi Bandung (ITB), Jl Ganesha 10, Bandung  40132, Indonesia. *Email: asep051@brin.go.id   Figure S 1. Rietveld refinement plots of BiCu1-xCrxSeO (x = 0, 0.02, 0.04, 0.06 & 0.08) with observed intensity in blue symbol, calculated pattern in green, background in red, differences in black, and reference BiCuSeO as a solid line at the bottom of the figure  20  . Figure S 2. Calculated grind size from SEM images  • The average grind size of pristine BiCuSeO and 4% Cr doped sample are 2.101 µm  and 1.778 µm, respectively. • The percentage of crystal size are 56% (below 2 µm), 35% (2-4 µm ) and 9% (>4 µm ) for Pristine BiCuSeO • The percentage of crystal size are 69% (below 2 µm), 23% (2-4 µm ) and 8% (>4 µm ) for 4%Cr doped sample.  Reproducibility of the sample  Figure S 3. The reproducibility of BiCu0.96Cr0.04SeO These samples (sample 1 and 2) of the BiCu0.96Cr0.04SeO were synthesized using the same method, and the results demonstrate good reproducibility among the samples.  Specific Heat Calculation & Thermal Diffusivity: The temperature dependence of specific heat capacity is calculated using Debye model when 𝑇𝑇 > 𝜃𝜃𝐷𝐷  with following equation  21  𝐶𝐶𝑝𝑝 = 𝛾𝛾𝛾𝛾 + 9𝑅𝑅𝑅𝑅𝑀𝑀∙ � 𝑇𝑇𝜃𝜃𝐷𝐷�3∙ ∫ 𝑥𝑥4𝑒𝑒𝑥𝑥(𝑒𝑒𝑥𝑥−1)2 𝑑𝑑𝑑𝑑𝜃𝜃𝐷𝐷/𝑇𝑇0   (S1) where γ is the Sommerfeld coefficient, γ = 3.075·10-7 J g-1 K-2 [1], R is the ideal gas constant, n is the number of atoms, M is the molar mass, θD is the Debye temperature, θD = 243 K [2], and x = hν/kBT. The Debye temperature and the Sommerfeld coefficient were assumed to be independent of the doping level. According to equation (S1), the calculated specific heat capacity of the BiCu1-xCrxSeO samples is slightly higher than pristine BiCuSeO due to the atomic mass difference between Cr (51.9961) and Cu (63.546) atoms. The thermal diffusivity is measured by laser flash method using LFA427, Netzsch, Germany. The typical dimension that used in thermal diffusivity measurement is 10 mm in diameter with a thickness of approximately ~1.7 mm.  Figure S 4. Thermal properties as a function of temperature of the BiCu1-xCrxSeO (x = 0; 0.02; 0.04; 0.06; 0.08) (a). Specific heat capacity, (b). Thermal diffusivity.  Reference: [1]. C. Barreteau, D. Bérardan, E. Amzallag, L.D. Zhao, N. Dragoe, Structural and electronic transport properties in Sr-doped BiCuSeO, Chemistry of Materials 24 (2012) 3168–3178. https://doi.org/10.1021/cm301492z [2]. L. Pan, D. Bérardan, L. Zhao, C. Barreteau, N. Dragoe, Influence of Pb doping on the electrical transport properties of BiCuSeO, Appl Phys Lett 102 (2013). https://doi.org/10.1063/1.4775593/975500.  Lorenz number calculation & electronic thermal conductivity:    The total thermal conductivity (κtot) is defined as a sum of the electronic (κele) and lattice thermal conductivity (κlat). The electronic part κele is directly proportional to the electrical conductivity σ through the Wiedemann-Franz relation, κe = LσT, where L is the Lorenz number [3]. The Lorenz number depends on the scattering parameter r and will decrease as the reduced Fermi energy η decreases with increasing temperature. The Lorenz number can be given as: [4]         𝐿𝐿 = �𝑘𝑘𝐵𝐵𝑒𝑒�2�(𝑟𝑟+72)𝐹𝐹𝑟𝑟+52(𝜂𝜂)(𝑟𝑟+32)𝐹𝐹𝑟𝑟+12(𝜂𝜂)− �(𝑟𝑟+52)𝐹𝐹𝑟𝑟+32(𝜂𝜂)(𝑟𝑟+32)𝐹𝐹𝑟𝑟+12(𝜂𝜂)�2�   (S2) For the Lorenz number calculation, we should get reduced Fermi energy η firstly; the calculation of η can be derived from the measured Seebeck coefficients by using the following relationship:  https://doi.org/10.1063/1.4775593/97550022                  𝑆𝑆 = ± 𝑘𝑘𝐵𝐵𝑒𝑒�(𝑟𝑟+52)𝐹𝐹𝑟𝑟+32(𝜂𝜂)(𝑟𝑟+32)𝐹𝐹𝑟𝑟+12(𝜂𝜂)− 𝜂𝜂�            (S3) where Fn(η) is the n−th order Fermi integral,               𝐹𝐹𝑛𝑛(𝜂𝜂) = ∫ 𝜒𝜒𝑛𝑛1+𝑒𝑒𝜒𝜒−𝜂𝜂∞0 𝑑𝑑𝑑𝑑                  (S4)                         𝜂𝜂 = 𝐸𝐸𝑓𝑓𝑘𝑘𝐵𝐵𝑇𝑇                        (S5) where, kB, e, and Ef are the Boltzmann constant, the electron charge, and the Fermi energy. By assuming that the acoustic phonon scattering (r = −1/2) is the main scattering mechanism, the Lorenz number can be obtained by applying the calculated reduced Fermi energy η and scattering parameter r into Eq. (S2). Table S1 shows the calculated Lorenz number based on SPB and APS model at room temperature. Figures S4 (a-b) show the Lorenz number and electronic thermal conductivity of the BiCu1-xCrxSeO as a function of temperature.  Table S1. The Lorenz number estimated by single parabolic band (SPB) and acoustic phonon scattering (APS) T Sexp S(SPB-APS) 𝜼𝜼 F0 F1 F2 L K (μVK-1) (μVK-1)     (WΩK-2) × 10-8 306 497.9700 497.970046 -3.759310 0.02303261 0.023166 0.04646502 1.49349976 322 491.7153 491.715306 -3.685950 0.02476414 0.024918 0.04999062 1.49382208 369 488.6485 488.648496 -3.649959 0.02566011 0.025825 0.05181673 1.49398886 417 488.1436 488.143586 -3.644032 0.0258107 0.025978 0.05212376 1.49401689 464 484.5475 484.547548 -3.601806 0.02690907 0.027091 0.0543643 1.49422135 512 467.7214 467.721412 -3.403896 0.03270285 0.032971 0.06621334 1.49529983 561 446.4189 446.419684 -3.152419 0.04186006 0.0423 0.08504593 1.49700436 610 428.9862 428.986208 -2.945652 0.05123263 0.051893 0.10445513 1.49874892 659 418.8106 418.810662 -2.824485 0.05764527 0.058481 0.11781312 1.49994249 707 411.2923 411.292365 -2.734698 0.06289362 0.063889 0.12879337 1.50091933 756 404.3442 404.344212 -2.651502 0.06816796 0.069338 0.13987131 1.50190099  23  Figure S 5. (a) Lorenz number, (b) electronic thermal conductivity of the BiCu1-xCrxSeO (x = 0; 0.02; 0.04; 0.06; 0.08) as a function of temperature.  [3] Fitsul, V. I. Heavily Doped Semiconductors; Plenum Press: New York, 1969. [4] Zhao, L.-D.; Lo, S.-H.; He, J. Q.; Li, H.; Biswas, K.; Androulakis, J.; Wu, C.-I.; Hogan, T. P.; Chung, D.-Y.; Dravid, V. P.; Kanatzidis, M. G. J. Am. Chem. Soc. 2011, 133, 20476.    Callaway model calculation:    In a solid solution system, point defects scattering originates from both the mass difference (mass fluctuations) and the size and the interatomic coupling force differences (strain field fluctuations) between the impurity atom and the host lattice. Callaway model has been applied to describe the influence of point defects on the lattice thermal conductivity [5−7]. We present a phonon scattering model based on the above theory and try to describe the effect of Cr doping on the lattice thermal conductivity of BiCuSeO system.     At temperature above the Debye temperature, the ratio of the lattice thermal conductivities of a material containing defects to that of the parent material can be written as: [5−7]  𝜅𝜅𝑙𝑙𝑙𝑙𝑙𝑙𝜅𝜅𝑙𝑙𝑙𝑙𝑙𝑙,𝑝𝑝= 𝑡𝑡𝑡𝑡𝑡𝑡−1(𝑢𝑢)𝑢𝑢         (S6) where 𝜅𝜅𝑙𝑙𝑙𝑙𝑙𝑙 , 𝜅𝜅𝑙𝑙𝑙𝑙𝑙𝑙,𝑝𝑝 are the lattice thermal conductivities of the defected and parent materials, respectively, and the parameter u is defined by:   𝑢𝑢 = �𝜋𝜋2𝜃𝜃𝐷𝐷𝛺𝛺ℎ𝑣𝑣𝑎𝑎2𝜅𝜅𝐿𝐿,𝑝𝑝𝛤𝛤�12         (S7) where h, Ω, va and θD stand for the Planck constant, average volume per atom, lattice sound velocity, and the Debye temperature.   𝑣𝑣𝑎𝑎 = �13� 1𝑣𝑣𝑙𝑙3 + 2𝑣𝑣𝑠𝑠3��−13    (S8) Here, the longitudinal (vl, 3290m/s) and transverse (vs,1900m/s) sound velocities have been obtained from previous research which gives va about 2107 m/s. Debye temperature θD is defined by: [8] 24   𝜃𝜃𝐷𝐷 = ℎ𝑘𝑘𝐵𝐵� 3𝑁𝑁4𝜋𝜋𝜋𝜋�13 𝑣𝑣𝑎𝑎   (S9)     where the V is the unit−cell volume, N is the number of atoms in a unit cell, kB is Boltzmann parameter, and h presents the Planck constant. Eq. (S9) gives θD about 243 K.  The disorder scattering parameter Γ in Eq. (S7) represents the strength of point defects phonon scattering, which includes two components, the scattering parameter due to mass fluctuations ΓM and the scattering parameter due to strain field fluctuations ΓS. A phenomenological adjustable parameter ε is always included because of uncertainty of ΓS, one writes Γ = ΓM + εΓS. In this paper, ε is directly estimated by following relationship: [9]  𝜀𝜀 = 29�(7+6.4)×𝛾𝛾(1+𝜐𝜐𝑝𝑝)�1−𝜐𝜐𝑝𝑝��2      (S10) where υp the Poisson ratio, which can be derived from the longitudinal (vl) and transverse (vs) sound velocities by the relationship as: [5-7, 9]  𝜐𝜐𝑝𝑝 =1−2�𝑣𝑣𝑠𝑠𝑣𝑣𝑙𝑙�22−2�𝑣𝑣𝑠𝑠𝑣𝑣𝑙𝑙�2         (S11) Eq. (6) gives υp about 0.25. Gruneisen parameter (γ) has been calculated using Poisson ratio (υp) as: [5-7, 9]  𝛾𝛾 = 32� 1+𝜐𝜐𝑝𝑝2−3𝜐𝜐𝑝𝑝�           (S12) Gruneisen parameter (γ) was calculated to be ~1.5 for BiCuSeO. Combination of Eq. (S10), (S11) and (S12), gives phenomenological adjustable parameter ε about 170.    There is no change on the sites of Bi, Se and O when the substitution between Cu and Cr occurs, ΓBi = ΓSe = ΓO = 0, which gives:  𝛤𝛤𝐵𝐵𝐵𝐵𝐵𝐵𝑢𝑢1−𝑥𝑥𝐶𝐶𝑟𝑟𝑥𝑥𝑆𝑆𝑆𝑆𝑆𝑆 = 14�𝑀𝑀(𝐶𝐶𝐶𝐶,𝐶𝐶𝐶𝐶)𝑀̄𝑀�2𝛤𝛤(𝐶𝐶𝐶𝐶,𝐶𝐶𝐶𝐶)         (S13)  𝛤𝛤 = 𝛤𝛤𝑀𝑀 + 𝛤𝛤𝑆𝑆                           (S14)  𝛤𝛤(𝐶𝐶𝐶𝐶,𝐶𝐶𝐶𝐶) = 𝛤𝛤𝑀𝑀,(𝐶𝐶𝐶𝐶,𝐶𝐶𝐶𝐶) + 𝛤𝛤𝑆𝑆,(𝐶𝐶𝐶𝐶,𝐶𝐶𝐶𝐶)               (S15)  𝛤𝛤𝑀𝑀,(𝐶𝐶𝐶𝐶,𝐶𝐶𝐶𝐶) = 𝑥𝑥(1 − 𝑥𝑥) � 𝛥𝛥𝛥𝛥𝑀𝑀(𝐶𝐶𝐶𝐶,𝐶𝐶𝐶𝐶)�2            (S16) where 𝛥𝛥𝛥𝛥 = 𝑀𝑀𝐶𝐶𝐶𝐶 − 𝑀𝑀𝐶𝐶𝐶𝐶, and 𝑀𝑀(𝐶𝐶𝐶𝐶,𝐶𝐶𝐶𝐶) = (1 − 𝑥𝑥)𝑀𝑀𝐶𝐶𝐶𝐶 + 𝑥𝑥𝑀𝑀𝐶𝐶𝐶𝐶  𝛤𝛤𝑆𝑆,(𝐶𝐶𝐶𝐶,𝐶𝐶𝐶𝐶) = 𝑥𝑥(1 − 𝑥𝑥) � 𝛥𝛥𝛥𝛥𝑟𝑟(𝐶𝐶𝐶𝐶,𝐶𝐶𝐶𝐶)�2,                            (S17) where 𝛥𝛥𝛥𝛥 = 𝑟𝑟𝐶𝐶𝐶𝐶 − 𝑟𝑟𝐶𝐶𝐶𝐶 , and 𝑟𝑟(𝐶𝐶𝐶𝐶,𝐶𝐶𝐶𝐶) = (1 − 𝑥𝑥)𝑟𝑟𝐶𝐶𝐶𝐶 + 𝑥𝑥𝑟𝑟𝐶𝐶𝐶𝐶  25 then,   𝛤𝛤(𝐶𝐶𝐶𝐶,𝐶𝐶𝐶𝐶) = 𝑥𝑥(1 − 𝑥𝑥) �� 𝛥𝛥𝛥𝛥𝑀𝑀(𝐶𝐶𝐶𝐶,𝐶𝐶𝐶𝐶)�2+ 𝜀𝜀 � 𝛥𝛥𝑟𝑟𝑟𝑟(𝐶𝐶𝐶𝐶,𝐶𝐶𝐶𝐶)�2�                (S18) and then,  𝛤𝛤𝐵𝐵𝐵𝐵𝐵𝐵𝑢𝑢1−𝑥𝑥𝐶𝐶𝑟𝑟𝑥𝑥𝑆𝑆𝑆𝑆𝑆𝑆 = 14�𝑀𝑀(𝐶𝐶𝐶𝐶,𝐶𝐶𝐶𝐶)𝑀̄𝑀�2𝑥𝑥(1 − 𝑥𝑥) �� 𝛥𝛥𝛥𝛥𝑀𝑀(𝐶𝐶𝐶𝐶,𝐶𝐶𝐶𝐶)�2+ 𝜀𝜀 � 𝛥𝛥𝑟𝑟𝑟𝑟(𝐶𝐶𝐶𝐶,𝐶𝐶𝐶𝐶)�2�  (S19)    After the calculation of point defects scattering on phonon for Γ from those relative physical properties, we obtained perfect agreement between the calculated and measured values. Table S2. The disorder parameters, measured 𝜅𝜅𝐿𝐿, calculated 𝜅𝜅𝐿𝐿 and the difference between measured and calculated 𝜅𝜅𝐿𝐿 x Γ 𝜿𝜿𝑳𝑳 (exp) 𝜿𝜿𝑳𝑳 (calc) diff   (Wm-1K-1) (Wm-1K-1) (%) 0 0 1.09293 1.092884 0.004198 0.02 6.71678E-04 0.96804 1.015331 4.885215 0.04 1.29746E-03 0.95454 0.958083 0.371167 0.06 1.87889E-03 0.88892 0.91386 2.805652 0.08 2.41747E-03 0.9091 0.878624 3.352301   The theoretical calculation of lattice thermal conductivity is performed according to the Callaway model [10].  𝜅𝜅𝐿𝐿 = 𝑘𝑘𝐵𝐵2𝜋𝜋2𝑣𝑣𝑠𝑠�𝑘𝑘𝐵𝐵𝑇𝑇ℏ�3∫ 𝜏𝜏𝑡𝑡𝑡𝑡𝑡𝑡𝑥𝑥4𝑒𝑒𝑥𝑥𝑒𝑒𝑥𝑥−1𝑑𝑑𝑑𝑑𝜃𝜃𝐷𝐷0  (S20) where x is the reduced frequency (x = ħω/kBT), ω the phonon angular frequency, kB the Boltzmann constant, vs the average sound speed, ħ the reduced Planck constant, θD the Debye temperature, and τtot the combined phonon relaxation time. Assuming scattering channels are independent of each other, the τtot can be evaluated by Matthiessen’s rule:  𝜏𝜏𝑡𝑡𝑡𝑡𝑡𝑡 = 𝜏𝜏𝑈𝑈 + 𝜏𝜏𝑃𝑃𝑃𝑃 + 𝜏𝜏𝐺𝐺𝐺𝐺 + 𝜏𝜏𝑃𝑃𝑃𝑃 (S21) where 𝜏𝜏𝑈𝑈, 𝜏𝜏𝑃𝑃𝑃𝑃, 𝜏𝜏𝐺𝐺𝐺𝐺, 𝜏𝜏𝑃𝑃𝑃𝑃 are the relaxation time for Umklapp process (U), point defect scattering (PD), phonon – electron scattering (PE), and grain boundary scattering (GB), respectively.  The relaxation time for point defect scattering is showed as follows: [11]  1𝜏𝜏𝑃𝑃𝑃𝑃= 𝐴𝐴𝜔𝜔4;𝐴𝐴 = 𝑉𝑉𝑎𝑎4𝜋𝜋𝑣𝑣𝑠𝑠3𝛤𝛤 (S22)  where A is the fitting parameter, ω the phonon angular frequency, vS is the average sound speed, Va the atomic volume of the compound, Γ the disorder scattering parameter that characterizes the phonon scattering cross section of point defects. If we only consider Cr doping on Cu-site in BiCuSeO, Γ can be calculated by following equation S13 – S19 [12,13].   26  The relaxation time for Umklapp scattering at high temperature is [11]:  1𝜏𝜏𝑈𝑈= 𝐵𝐵𝜔𝜔2𝑇𝑇 (S23) where B is a constant, ω the phonon angular frequency,and θD the Debye temperature.  The relaxation time for the grain boundary scattering is:  1𝜏𝜏𝐺𝐺𝐺𝐺= 𝑣𝑣𝑆𝑆𝑑𝑑 (S24) where vs the average sound speed and d is the average grain size.  The relaxation time for the phonon – electron scattering is:  1𝜏𝜏𝑃𝑃𝑃𝑃= 𝐶𝐶𝐶𝐶𝐶𝐶 (S25) where C is a fitting parameter and ω the phonon angular frequency. Since the value of B depends solely on the crystal structure of BiCuSeO, we determined its precise value by fitting Eq. S20-25 to the lattice thermal conductivity of pure BiCuSeO. Table S3 presents the obtained value of B alongside the calculated value of A. Consequently, the only adjustable parameter, C, for various levels of Cr-doping can be derived by fitting Eq. S20-35 to the measured lattice thermal conductivity data.  Table S3. Fitting parameters of calculated lattice thermal conductivity κL using Callaway model. x A (10-42 s3) B (10-17 sK-1) C (10-4) 0 0.0012 3.0955 0.0001 0.02 2.3206 3.0955 37.41 0.04 4.4819 3.0955 19.23 0.06 6.4892 3.0955 17.56 0.08 8.3478 3.0955 0.33  [5] Callaway, J.; Von Baeyer, H. C. Phys. Rev. 1960, 120, 1149;  [6] Dey, T. K.; Chaudhuri, K. D. J. Low. Temp. Phys. 1976, 23, 419;  [7] Yang, J.; Meisner, G. P.; Chen, L. Appl. Phys. Lett. 2004, 85, 1140.  [8] K. Kurosaki, A. Kosuga, H. Muta, M. Uno, S. Yamanaka, Appl. Phys. Lett. 2005, 87, 061919. [9] C. L. Wan, W. Pan, Q. Xu, Y. X. Qin, J. D. Wang, Z. X. Qu, M. H. Fang, Phys. Rev. B 2006, 74, 144109. [10]. Callaway, J.; Phys. Rev. 1959, 113, 1046–1051.  [11]. P. G. Klemens, Proc. Phys. Soc. Lond. A., 1955, 68, 1113-1128. [12]. B. Abeles, Phys. Rev., 1963, 131, 1906. [13].  G. A. Slack, Phys. Rev., 1962, 126, 427   27