Effect of In and Cd co-doping on the thermoelectric properties of Sn1−xPbxTe

Pristine tin telluride (SnTe) with a similar electronic structure to PbTe shows inferior thermoelectric performance owing to high p-type hole concentration (1021 cm−3), high lattice thermal conductivity, κlatt (∼2.8 W mK−1 at room temperature) and large energy gap between light and heavy hole valence bands. Interestingly, 30 mol% substitution of lead in SnTe decreases the excess hole carrier concentration and lattice thermal conductivity (∼0.67 W m−1K−1 at 300 K) significantly. Here, we report the promising thermoelectric performance in Sn0.70Pb0.30Te by enhancing the Seebeck coefficient via the co-adjuvant effect of resonant level formation and valence band convergence. We obtain a Seebeck coefficient value of ∼141 μV K−1 at 300 K, which further increases to ∼260 μV K−1 at 708 K for Sn0.70Pb0.30Te—3% Cd and 0.50% In sample. This is one of the highest S values for SnTe based system, to the best of our knowledge. In and Cd have discrete but complementary roles to augment the Seebeck coefficient value of Sn0.70Pb0.30Te where In acts as a resonant dopant and Cd serves as valence band convergent, respectively, as demonstrated by the well-known Pisarenko plot of SnTe. Finally, we have achieved a maximum thermoelectric figure of merit, zT, of ∼0.82 at 654 K for Sn0.70Pb0.30Te—3% Cd and 0.25% In sample.


Introduction
Thermoelectric (TE) technology has attracted attention recently as they are able to convert waste heat directly into electricity. The efficiency of TE materials is dependent upon the delicate concert of adversely interdependent parameters and is quantified in term of a dimensionless figure of merit (zT), defined as Where S is Seebeck coefficient, σ is electrical conductivity, κ el is electrical thermal conductivity, κ latt is lattice thermal conductivity and T is absolute temperature [1][2][3][4][5][6][7][8][9]. These three mutually interdependent parameters such as σ, S and κ el provide hindrance in the pursuit of higher zT in a single material [1,2]. The Last few decades have witnessed a significant enhancement of thermoelectric performance either by enhancing the Seebeck coefficient via manipulating the electronic band structure (band convergence or generation of the resonant level near Fermi level) [10][11][12][13][14] and/or reducing the thermal conductivity (lattice) by engineering phonon scattering sources [15][16][17][18].
PbTe is considered as an efficient thermoelectric material among IV-VI family for mid-temperature power generation applications [10,13,16]. However, pristine SnTe with a similar electronic structure to PbTe is not so popular as thermoelectric material because of its poor thermoelectric performance [5,19]. This can be attributed to its high carrier concentration (10 21 cm −3 ), resulting from intrinsic Sn vacancy and large energy separation between light and heavy hole valence bands (∼0.3-0.4 eV) than that of PbTe (∼0.18 eV) which inhibit the Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence.
Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. contribution of heavy hole valence band in the electrical transport and results low Seebeck coefficient [5,16,[19][20][21][22]. Manipulation of electronic structure is an effective approach to improve the thermoelectric performance of SnTe by enhancing the Seebeck coefficient [5,11,12,19,23,24]. Previously, Ren and coworkers revealed that indium (In) acts as a resonant dopant in SnTe and enhances the Seebeck coefficient significantly near room temperature [14]. Tan et al demonstrated that addition of Cd in SnTe decreases the energy gap between two valence bands and improves its Seebeck coefficient [23].
Moreover, pristine SnTe shows κ latt of ∼2.8 W m −1 K −1 which is notably higher compare to its theoretical limit of minimum lattice thermal conductivity (κ min ∼0.5 W m −1 K −1 ) at 300 K [18]. However, several approaches have been endeavored to reduce the κ latt of SnTe based alloys to enhance the thermoelectric performance such as entropy engineering via introduction of multi principle element alloying [25], addition of nanoprecipitates of CdSe/HgTe [23,26], encapsulation of layered intergrowth compound in matrix [18]. Recently, we have effectively reduced the κ latt to ∼0.67 W m −1 K −1 in Sn 1−x Ge x Te by introducing the ferroelectric instability concept in the system without degrading the electrical transport [27]. In our previous work, we have shown that substitution of 30 mol% of Pb in SnTe effectively reduced the excess hole carrier concentration of SnTe and lattice thermal conductivity to ∼0.67 W m −1 K −1 at 300 K due to the enhanced solid solution point defect scattering [28]. Motivated by all these results, here, we thought to study the effect of cosubstitution of In and Cd in Sn 0.70 Pb 0.30 Te sample, which may improve the S values over a broad temperature range through the co-adjuvant effect of the resonance level formation and valence band convergence.
Herein, we demonstrate the promising thermoelectric performance of Sn 0.70 Pb 0.30 Te sample by enhancing its Seebeck coefficient via the co-adjuvant effect of formation of the resonance level by In doping and valence band convergence enables by Cd doping. Co-doping of In and Cd increases the Seebeck coefficient of Sn 0.70 Pb 0.30 Te sample significantly throughout the measured temperature range (300-710 K) compared to that of singly doped (In and Cd) Sn 0.70 Pb 0.30 Te samples. We have attained a Seebeck coefficient value of ∼141 μV K −1 at 300 K, which further increases to 260 μV K −1 at 708 K for Sn 0.70 Pb 0.30 Te-3% Cd and 0.50% In sample. As a result, a maximum zT of ∼0.82 at 654 K for Sn 0.70 Pb 0.30 Te-3% Cd and 0.25% In sample which is higher compared to pristine SnTe and undoped Sn 0.70 Pb 0.30 Te samples.

Results and discussion
The balance between the resonant level and valence band convergence is necessary to optimize the thermoelectric performance of the Sn 0.70 Pb 0. 30 Te system. Band convergence always requires relative high doping concentration to manipulate band dispersion in k-space [29]. In this work, we select Cd as the valence band convergent. The effect of band convergence will be stronger if the concentration of Cd is high [29]. Previous results confirm that the solubility of Cd is only 3 mol% in SnTe [23,29]. Thus we fix the concentration of Cd is 3 mol% in the present work and then varies the concentration of resonant dopant, In. The resonant state is the deformation of the density of states (DOS) near Fermi level, and it reduces electrical conductivity significantly due to the reduction of carrier mobility at higher doping concentration [29]. Therefore, a lower concentration of resonant dopant and a higher concentration of band convergence dopant are always desired. Thus, the amount of In is varied from x=0 to x=0.50 mol%.
The temperature variations of electrical conductivity, σ, of Sn 0.70 Pb 0. 30 Te-x % Cd and y % In (x=0, y=0; x=3, y=0.05, 0.25, 0.50) samples are shown in figure 2(a). The σ values for all the samples decrease with increasing temperature, like a degenerate semiconductor. Substitution of 3 mol% Cd reduces the σ from ∼4260 S cm −1 for Sn 0.70 Pb 0.30 Te to ∼2500 S cm −1 for Sn 0.67 Cd 0.03 Pb 0.30 Te sample at 300 K (figures 2(a) and S2(a), SI). This confirms that the tendency of formation of Sn vacancy decreases with Cd substitution and reduces the hole carrier concentrations (table 1). Substitution of indium in Sn 0.70 Pb 0.30 Te-3% Cd sample further decreases the electrical conductivity owing to the significant reduction in carrier mobility due to resonant scattering, resulting from In doping (see table 1). Typically, σ of Sn 0.70 Pb 0.30 Te sample is to be ∼5471 S cm −1 at 300 K, which further decreases to ∼ 620 S cm −1 at ∼708 K. At room temperature, Sn 0.70 Pb 0.30 Te-3% Cd and 0.25% In sample exhibits a σ value of ∼773 S cm −1 and reduces to ∼264 S cm −1 at 708 K.
To determine the carrier concentration of Sn  figure 2(b) and S2(b), SI, respectively. Seebeck coefficient values for all the samples are positive which are consistent with our Hall coefficient data. Interestingly, for In and Cd co-doped Sn 0.70 Pb 0.30 Te samples exhibit higher Seebeck coefficient value throughout the measured temperature range (300-710 K) compared to that of controlled In or Cd single doped Sn 0.70 Pb 0.30 Te samples ( figure S2(b), SI). Typically, the Seebeck coefficient value of Sn 0.70 Pb 0.30 Te-3% Cd and 0.50% In sample is ∼140 μV K −1 at 300 K and further increases to ∼260 μV K −1 at 708 K (figures 2(b), S3, SI). Thus, the synergistic effect of In and Cd co-doping in Sn 0.70 Pb 0.30 Te is responsible for the observed notable augmentation in the Seebeck coefficient. At room temperature, highest Seebeck coefficient value is achieved in the present Sn 0.70 Pb 0.30 Te-3% Cd and 0.50% In sample which is higher than that of state-of-art SnTe based materials, to the best of our awareness [11, 12, 23-29, 31, 32].
To gain further insight into the origin of high Seebeck coefficient, we have plotted S values of Sn 0.70 Pb 0.30 Te-x% Cd and y % In (x=0, y=0; x=3, y=0.05, 0.25, 0.50) samples as a function of p and compared with the renowned Pisarenko line of SnTe (figure 2(c)) at 300 K [14]. Controlled In doped sample exhibits higher S value compared to theoretical Pisarenko line due to the formation of resonance level near the valence band of Sn 0.70 Pb 0. 30 figure 2(d). Typically, the Sn 0.70 Pb 0.30 Te-3% Cd and 0.25% In sample exhibits an S 2 σ value of ∼9.8 μWcm −1 K −2 at 300 K, which increases further to ∼ 15.9 μWcm −1 K −2 at 654 K. Co-substitution of In and Cd increases the Seebeck value in Sn 0.70 Pb 0.30 Te but no improvement in S 2 σ value is observed owing to the significant decrease in electrical conductivity and mobility.
The temperature variations of total thermal conductivity, κ total , of Sn 0.70 Pb 0.30 Te-x% Cd and y % In  The noteworthy reduction in κ total can be ascribed to the decrease in electrical thermal conductivity (κ el ) ( figure 3(b)). The κ el values for Sn 0.70 Pb 0.30 Te-3% Cd and y % In (y=0.05, 0.25 and 0.50) samples are significantly lower compared to that of undoped Sn 0.70 Pb 0.30 Te, which is due to the considerably lower electrical conductivity for co-doped samples than that of undoped Sn 0.70 Pb 0.30 Te sample ( figure 2(a)). The κ el values were calculated by using Wiedemann-Franz relation, κ el =LσT, where σ is measured electrical conductivity and L is calculated Lorenz number from reduced Fermi energy, which is acquired from the fitting of the temperature dependent S value [11,12]. Typically, Sn 0.70 Pb 0.30 Te-3% Cd and 0.25% In sample exhibits κ el value of ∼0.43 W m −1 K −1 at 300 K and further reduces to ∼0.30 W m −1 K −1 at 708 K. The lattice thermal conductivity,

Conclusions
We have prepared crystalline ingots of In and Cd codoped Sn 0.70 Pb 0.30 Te samples via vacuum-sealed tube melting reaction. Sn 0.70 Pb 0.30 Te sample exhibits κ latt of ∼0.67 W m −1 K −1 at 300 which is close to the κ min of SnTe (∼0.50 W m −1 K −1 ) due to the enhanced solid solution point defect scattering. Co-substitution of In and Cd increases the Seebeck coefficient of Sn 0.70 Pb 0.30 Te sample significantly over a wide range of temperatures (300-710 K) compared to that of singly doped (In and Cd) Sn 0.70 Pb 0.30 Te samples due to the co-adjuvant effect of resonance level formation near Fermi level and effective valence band convergence. At room temperature, highest Seebeck coefficient value has been realized in the present Sn 0.70 Pb 0.30 Te-3% Cd and 0.50% In sample (∼141 μV K −1 ) which is higher compared to that of state-of-the-art SnTe based materials. A maximum zT of  ∼0.82 is observed for Sn 0.70 Pb 0.30 Te-3% Cd and 0.25% In sample at 654 K which is higher than that of pristine SnTe and controlled Sn 0.70 Pb 0.30 Te samples. Thermoelectric performance of Sn 0.70 Pb 0.30 Te sample can be further improved by engineering phonon scattering centers via nanostructuring or all-scale hierarchical architecture.