Thermoelectric properties of Pb and Na dual doped BiCuSeO

BiCuSeO is a promising thermoelectric material not only because of its good thermoelectric properties, but also earth abundant constituents. In this report, Pb and Na have been simultaneously doped at the Bi site of BiCuSeO. Doping Pb is beneficial for the Seebeck coefficient whereas doping Na maintains the hole mobility. Both the dopants increase the carrier concentration and reduce the thermal conductivity by point-defect scattering. The samples with nominal composition Bi0.985-xNa0.015PbxCuSeO (x=0.00, 0.04, 0.06 and 0.08) were prepared using two-step solid-state synthesis. The X-ray diffraction pattern reveals a small amount of Bi2O2.5 phase (<1 vol. %) which is responsible for adversely affecting the electrical conductivity of all the samples. Both the Seebeck coefficient and electrical resistivity decrease with increasing doping fraction due to increasing hole concentration. The highest power factor of 530 μW/mK2 was obtained for Bi0.905Na0.015Pb0.08CuSeO sample at 773 K because of moderate Seebeck coefficient and low electrical resistivity. A low lattice thermal conductivity of 0.37 W/m-K at 773 K was obtained in the Bi0.905Na0.015Pb0.08CuSeO. Due to this low lattice thermal conductivity combined with the high power factor, a zT of 0.63 was obtained for the Bi0.905Na0.015Pb0.08CuSeO sample at 773 K. © 2019 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/1.5066296


I. INTRODUCTION
Thermoelectricity converts heat directly into electricity and vice-versa.The conversion efficiency of such system is governed by the dimensionless thermoelectric figure of merit (zT) of the material, which is given by- where S the Seebeck coefficient, ρ the electrical resistivity, κ the thermal conductivity and T is the temperature.The aim of the research in thermoelectricity is to increase the efficiency of the device by increasing the zT of TE material.Along with high zT, the oxidation resistance and the stability are the major issues for the thermoelectric materials in mid to high temperature (>600 K) applications.Bismuth oxy-selenide is a ptype thermoelectric material which has good stability at high temperatures and is fairly oxidation resistant up to 573 K. 1 It has favorable transport properties like moderately high S (350-425 µV/K in 300-923 K), and ultra-low κ (0.62-0.42 W/m-K in 300-923 K).However, the ρ is high (10-0.67mΩ-m in 300-923 K) due to a low charge carrier concentration of ∼10 18 /cm 3 , which limits the zT to 0.5 at 923 K. 2 High zTs (>1) have been obtained in BiCuSeO by doping Ba (1.1 at 923 K) 3 or Pb (1.14 at 823 K) 4 at the Bi site.The 6S 2 lone pair electrons of Pb introduces states near the Fermi level which is advantageous for the S.However, the optimally Pb-doped BiCe-SeO does not reach to the charge carrier concentration of 10 21 /cm 3 , since its solubility is limited to 6-8 at.%. 4 Hence, there is scope to further increase the charge carrier concentration of the Pb-doped BiCuSeO by dual doping.This can be accomplished by doping another element along with Pb.For example, simultaneous doping of Ca, Pb leads to a zT of 1.5 at 873 K which is the highest zT achieved till date in BiCuSeO. 5owever, dual doping can severely reduce the already low hole mobility of BiCuSeO (∼10 cm 2 /V-s) 4 by lattice distortion induced charge scattering.The similar atomic radii of Na + (0.96 Å) and Bi +3 (0.97 Å) results in lower lattice-distortion and hence higher hole-mobility in Na-doped BiCuSeO in comparison to the other dopants like Ba. 6 Thus, Na has been doped simultaneously with Pb at the Bi site in this study.Both the dopants increase the hole concentration.The mass difference between the host Bi atoms and the dopants (Pb and Na) can decrease the lattice thermal conductivity (κ L ).The doping fraction of Na was fixed to the optimized value of 1.5 at.%

II. EXPERIMENTAL DETAILS
Bi 2 O 3 , Cu, Se, Bi, NaNO 2 powders and finely cut Pb sheet were taken in a stoichiometric ratio according to the composition Bi 0.985-x Na 0.015 Pb x CuSeO (x=0, 0.04, 0.06 and 0.08).The samples were synthesized using standard two-step solid-state synthesis involving furnace reaction and hot press (the details can be found elsewhere 7 ).The density of the pressed pellets was more than 95% of the theoretical density as measured by the Archimedes principle.The X-ray diffraction (XRD) was carried out in a Rigaku Smartlab diffraction system having a Cu Kα source (λ = 1.54187Å).The Fullprof software was used for the Rietveld refinement of the diffraction patterns. 8A FEI ESEM-Quanta 200 scanning electron microscope was used for surface morphology studies.Electron probe microanalysis (EPMA) was performed in JEOL JXA8230 instrument.The Hall measurement was performed using a home-grown setup using an electromagnet with 0.7 T field strength.Keithley 6221 was used as a current source and Keithley 2182 nanovoltmeter was used to measure the voltage.Delta configuration was used to cancel out the thermal voltages.The S and the ρ of the bar-shaped samples (∼11.8×1.8×1.1 mm 3 ) were simultaneously measured in the Linseis LSR-3 system from 373K to 773 K.The thermal diffusivity (D) and the specific heat capacity (C p ) of the cylindrical samples (diameter =10 mm, thickness ∼1 mm) were measured using the laser flash apparatus LFA 457 MicroFlash.The κ was calculated using the formula κ = DdC p where d is the density of the samples.The errors in the measurement of the S, ρ, and the κ are 7%, 10%, and 6% respectively.

III. COMPUTATIONAL DETAILS
The density functional theory (DFT) calculation was performed using the Quantum Espresso (QE) software package. 9alculations were done in a 3×3×1 super cell (72 atoms), containing one Bi atom replaced by one Na atom.The planewave energy cutoff was 60 Ry and the electronic energy convergence was set at 10 −8 eV.The exchange-correlation energy was approximated using Perdew-Burke-Ernzerhof (PBE) functional and generalized gradient approximation (GGA) with projector augmented wave (PAW) method. 10The Brillouin zone was sampled by Monkhorst-Pack (MP) special k-point scheme (Γ-centered) with 4×4×3 k-point meshes.The force convergence for ions was set to 10 −3 eV/Å for variable-cell structure relaxation.

A. X-ray diffraction pattern
The X-ray diffraction patterns of the samples is shown in Figure 1.The major peaks were matched to the standard data of BiCuSeO (ICDD card no.04-007-6446) which confirmed the crystal structure (tetragonal, space group P4/nmm) of BiCuSeO.A trace amount of Bi 2 O 2.5 phase (ICDD card no.04-005-5135) was found for all the samples.Rietveld refinement was performed to retrieve the crystallographic and phase information.Figure 2 shows the Rietveld refinement result for the Bi 0.925 Na 0.015 Pb 0.06 CuSeO, comparing the experimental and simulated curves.The volume percentage of the Bi 2 O 2.5 phase, from the refinement is 0.62, 0.66, 0.85 and 0.67 for x=0.0, 0.04, 0.06 and 0.08 respectively.Repeated synthesis of the material was carefully performed to eliminate the secondary phase, but it the Bi 2 O 2.5 could not be completely removed.The lattice parameters, as a function of doping percentage, obtained from Rietveld refinement is shown in the inset of Figure 2.Both the 'a' and 'c' increases with increasing Pb content.The ionic radius of Pb +2 (1.19 Å) is more than that of the Bi +3 (0.97 Å) hence, the 'a' axis increases with increasing doping percentage. 10Since the (Bi 2 O 2 ) +2 and the (Cu 2 Se 2 ) -2 have opposite charges on the layers, the two layers are coupled by coulomb force.The doping of Pb at the Bi site produces hole which is transferred to the (Cu 2 Se 2 ) -2 layer.The Coulomb coupling gets weaker as the charge on both the layers decreases due to hole transfer.This weaker Coulomb coupling manifests in increased 'c' parameter.

B. Scanning electron microscopy and compositional analysis
The back scattered electron (BSE) image and the corresponding secondary electron (SE) image of the polished surface of the samples is shown in Figure 3.The black spots in the images corresponds to surface pits, and no phase contrast for the Bi 2 O 2.5 phase was observed, probably because of its low volume fraction.The SE image of the fractured surface of the samples is shown in Figure 4.The size of the particles in the microstructure varied from below 1 µm to few µm in sizes.The densely packed particle is indicative of high density of the sample (>95% of the theoretical density).The Bi, Cu, Pb and Na content of the sample obtained from EPMA is shown in Table I.All the samples show a slightly lower Bi content than the nominal composition, which is due to the formation of Bi 2 O 2.5 secondary phase.The Na content of the samples is underestimated because of lack of standard as well as low atomic number of Na.The Pb content in the Bi 0.905 Pb 0.08 Na 0.015 CuSeO sample is lower than the nominal composition which because of the onset of solubility limit of Pb at the Bi site.

C. Hall measurement
The Hall measurement was performed for the Bi 0.985 Na 0.015 CuSeO, Bi 0.945 Na 0.015 Pb 0.04 CuSeO and Bi 0.925 Na 0.015 Pb 0.06 CuSeO samples.Hall measurement of the Bi 0.905 Na 0.015 Pb 0.08 CuSeO sample could not be performed because of low signal to noise ratio owing to its high carrier concentration.This is evident from the fact that it has lower Seebeck coefficient and electrical resistivity than the pristine BiCuSeO (∼2×10 18 /cm 3 ) 12 as the Na + acts as an acceptor defect.The carrier concentration increases with increasing Pb doping fraction as Pb +2 also acts as an acceptor defect at the Bi site.The mobility of the Bi 0.985 Na 0.015 CuSeO, Bi 0.945 Na 0.015 Pb 0.04 CuSeO and Bi 0.925 Na 0.015 Pb 0.06 CuSeO are 10.28 cm 2 /V-s, 10.21 cm 2 /V-s and 5.78 cm 2 /V-s respectively.Since this is a multi-phase system the mobility of the sample has contribution from both the secondary phase (Bi 2 O 2.5 ) and main phase (Bi 0.985-x Na 0.015 Pb x CuSeO).As a result, the mobility calculated from the usual formula µ = 1/(neρ) does not reflect the true mobility of the main phase (Bi 0.985-x Na 0.015 Pb x CuSeO).

Seebeck coefficient (S)
The Seebeck coefficient (S) of the samples is shown in Figure 5.The positive S of the samples indicates that the holes are the majority charge carriers.The S decreases with increasing doping fraction indicating that holes are getting liberated in the system with Na and Pb doping.Lan et al. 4 have shown that the 6s 2 lone pair electrons of Pb introduce states near the Fermi level.This enhancement of the density of states increases the effective mass of the holes, and in turn, positively affects the S, according to the Mott's formula. 13Li et al. observed a higher S for the Na-doped BiCuSeO in comparison to the other dopants for the same carrier concentration. 6They attributed this to the modification in the electronic structure due to Na doping.We did not observe a significant contribution of Na to the density of states (DOS) near the Fermi level from density functional theory as shown in Figure 6.lattice distortion caused by the dopants at the Bi site may disrupt the linear geometry of the Cu 2 Se 4 chain through the Bi 6p Se 4p orbital interaction, and thus the sharp feature in the DOS is lost.The similar ionic radii of Na and Bi maintains the structure of the Cu 2 Se 4 chain, and thus the S of Na-doped samples is higher than the other dopants for the same carrier concentration.The S of Bi 0.985 Na 0.015 CuSeO varies from 287 µV/K to 323 µV/K, throughout the temperature range (373-773 K), which is similar to the reported value of 270 µV/K to 309 µV/K in the same temperature range and same composition. 6This is because of similar carrier concentration of both the samples.The S of the sample with 0.06, and 0.08 varies linearly with temperature, showing metallic characteristics, as the doping of Pb and Na shifts the Fermi level inside the valence band.

Electrical resistivity (ρ)
The electrical resistivity (ρ) of the samples is shown in Figure 7.The ρ of the samples decrease with increasing in doping fraction of Pb, liberate holes into the system since they act as acceptor defects at the Bi site.Although the charge reservoir in Bi 2 O 2 layer is separated from the conduction channel of Cu 2 Se 2 , dopants at Bi site sharply reduces the hole mobility.For example, the hole-mobility of pristine BiCuSeO is ∼10 cm 2 /V-s, whereas the mobility of Bi 0.875 Ba 0.125 CuSeO is ∼2 cm 2 /V-s. 3,4The ionic nature of Na does not affect the charge carrier mobility as the bonding between Na-O may not affect the conduction channel.Pb doping is also advantageous for the hole mobility because of the delocalized 6s 2 lone pair electrons. 4The ρ of the Bi 0.985 Na 0.015 CuSeO sample varies from 0.24-0.34mΩ-m throughout the temperature range which is twice that of the reported value by Li et al.Cu x Se phase which can readily occur in BiCuSeO system, 13 the bismuth oxide phase has high resistivity, and hence, it can adversely affect the ρ of the samples. 15The ρ of the samples decreases with increasing doping concentration, as Pb and Na act as acceptor defects.The samples with x=0.04,0.06 and 0.08 vary linearly with temperature showing a metallic characteristic, in agreement with the S. The lowest ρ has been achieved for the x=0.08 sample which varies from 0.022 -0.046 mΩ-m in the measured temperature range.

Thermal conductivity (κ)
The total thermal conductivity (κ) of the samples which is the sum of the lattice part κ L and the electronic part (κ e ) of thermal conductivity is shown in Figure 8.The κ e was calculated by the Wiedemann-Franz relation- where L is the Lorenz number.The Lorenz number was calculated assuming acoustic phonon scattering and single parabolic band conduction 16 using the following formula- .08 can be explained by the formation of nanoprecipitates in the system at the onset of solubility limit of Pb.Nano-precipitation of CuSe with sizes 5-10 nm has been observed in high-resolution transmission electron microscope at high doping fraction (≥6 at.%) by Lan et al. 4 as well as Ren et al. 18 Nano precipitations scatter the phonons through boundary scattering.Above Debye temperature (θ D ), the Umklapp scattering is more significant than the boundary scattering.However, particles below 10 nm can impede the phonons even at higher temperatures because of the significant contribution from the phonons which have mean free path more than 10 nm even at high temperatures. 19Thus, the κ L of x=0.08 is far less than the rest of the samples throughout the temperature range which could be due to nano-precipitation inside the BiCuSeO matrix.

E. Power factor (S 2 /ρ) and dimensionless figure of merit (zT)
The power factor (S 2 /ρ) is shown in Figure 10.Due to low ρ and moderate S, the highest power factor of 530 µW/m-K 2 was obtained for x=0.08 at 773 K.While this S 2 /ρ is more than Mg-doped BiCuSeO (∼200 µW/m-K 2 at 773 K) 20 it is less than the Ca and Pb dually doped BiCuSeO (∼800 µW/m-K 2 at 773 K). 5 Notably, the variation of S 2 /ρ for the Bi 0.905 Na 0.015 Pb 0.08 CuSeO sample is small ranging from 480 to 530 µW/m-K 2 throughout the temperature range which is beneficial for having a high average zT.This high average zT can enhance the device efficiency, as the device efficiency depends on the average zT between the hot and the cold side temperature.The zT of the samples is shown in Figure 11.The highest zT of 0.63 at 773 K was obtained for Bi 0.905 Na 0.015 Pb 0.08 CuSeO due to high S 2 /ρ and low κ L .The nanoparticles reduce the lattice thermal conductivity.Doping on the other hand, reduces the electrical resistivity, and the electrical resistivity of the sample with x=0.08 has the lowest electrical resistivity among all other sample (0.022 -0.046 mΩ-m in the measured temperature).As a result, the highest power factor of the was achieved sample with x=0.08 (530 µW/m-K 2 at 773 K).This lowest electrical resistivity and the highest power factor is achieved because of doping at the Bi site (both Na and Pb).This zT is higher than quite a few singly doped BiCuSeO like Mg-doped BiCuSeO (∼0.5 at 773 K), 19 Mn-doped BiCuSeO (∼0.4 at 773 K) 21 or Ag-doped BiCuSeO (∼0.55 at 773 K). 22 However, it is lower than many of the dually-doped BiCuSeO for example-Ca and Pb dually doped BiCuSeO (∼1.2 at 773 K), 5 Pb/Te co-doped BiCuSeO (∼1 at 773 K) 23 and Fe/Pb dually doped BiCuSeO (∼1.3 at 773 K). 24 In comparison to the other dually doped BiCuSeO, the zT is lower in this report because of the presence of impurity phase of bismuth oxide which increases the electrical resistivity and adversely affects the zT.

V. CONCLUSIONS
In summary, the thermoelectric properties of Na and Pb dually doped BiCuSeO with composition Bi 0.985-x Na 0.015 Pb x CuSeO (x=0.00,0.04, 0.06 and 0.08) were studied.Na was doped along with Pb at the Bi site to increase the hole concentration without deteriorating the mobility of holes.An impurity phase of Bi 2 O 2.5 was found for all the samples, which adversely affects the ρ. S and ρ decreased with increasing doping fraction due to the generation of holes.Although Na does not introduce states near the Fermi level, the similarity in the ionic radii of Bi and Na can be favorable for increasing the S. A sharp fall in the κ L was observed for x=0.08.Due to the low κ L of 0.37 W/m-K and a high power factor of 530 µW/m-K 2 at 773 K, a maximum zT of 0.63 was obtained for x=0.08 at the same temperature.The zT can be further improved by eliminating the impurity phase.

FIG. 6 .
FIG. 6. Projected density of states of Na doped BiCuSeO.The projected density of states of Na is shown in the inset.
6and the doping fraction of Pb was varied according to the composition Bi 0.985-x Na 0.015 Pb x CuSeO (x=0, 0.04, 0.06 and 0.08).Due to low ρ, and moderate S, a high power factor of 530 µW/m-K 2 was achieved in Bi 0.905 Na 0.015 Pb 0.08 CuSeO sample at 773 K.The improved power factor and the reduced κ L resulted in a maximum zT of 0.63 at 773 K.