On the relevance of point defects for the selection of contacting electrodes: Ag as an example for Mg2(Si,Sn)-based thermoelectric generators
Graphical abstract
Introduction
Thermoelectric (TE) materials are used in several industrial fields such as aerospace, automotive, and industry; and research to develop more environmental-friendly TE generators is continuously expanding [[1], [2], [3], [4]]. In order to have a highly efficient TE device, contacting the TE legs is as important as optimizing the TE material [5,6]. In fact, this step adds contact resistances and potential chemical interactions between the contact materials and the TE material, and both can be detrimental to the TE device if not controlled. The electrical contact resistances Rc, as well as the thermal contact resistances, have to be kept as low as possible, and the electrodes should be chemically and physically stable metals or conductive intermetallics that (mechanically) adhere well to the TE material [7,8]. There should also preferably be very limited diffusion between the metal and the semiconductor that would result in reactions forming new phases. All the mentioned conditions should remain stable in the long term under working temperature and thermal stress [9]. That is also why the electrode and the TE material should have similar coefficients of thermal expansion (CTE), which would guarantee a stable behavior free of failure under temperature cycling.
Several studies on developing contacting solutions were conducted, studying different material systems for thermoelectric applications. In fact, finding suitable contacts is a material specific problem, as the outcome will depend on the TE material, the metallic electrode and the potential interactions between them (CTE, adhesion, diffusion, reaction …). Among others, Ni [10,11] and Fe [12] were studied with PbTe showing good bonding results thin interface layers and low electrical contact resistances, Ti [13] and Fe–Ni [14] were successfully tested for skutterudites materials, and Mo [15] and Ag [16] were used with half-heusler systems.
One of the also frequently studied TE materials are Mg2Si1-xSnx solid solutions as they consist of abundant elements, are environmentally friendly, and have improved thermoelectric properties compared to their binaries [[17], [18], [19], [20], [21]]. Contacting of Mg2Si1-xSnx materials was tested using Ag [22] Ni [[22], [23], [24]] and Cu [7,25,26] electrodes, and electrical contact resistances and microstructure of the reaction layers were reported.
In this work and for the first time, contacting Mg2Si1-xSnx based-TEGs is studied from a point defect perspective. We discuss here experimental results of contacting for the binaries Mg2Si and Mg2Sn as well as the Mg2Si1-xSnx solid solutions with Ag as a suitable example for the importance of point defects in the thermoelectric material in the selection of joining electrodes.
The issue was first observed while contacting n- and p-type Mg2Si1-xSnx (with x = 0.4 and x = 0.3, respectively) with Ag, where the results showed different behaviors of the TE materials after joining [22]. In fact, not only the electrical contact resistances were very different (rc ∼ 400 ± 38 μΩ cm2 for n-type vs. ∼9 ± 1 μΩ cm2 for p-type, both joined at 450 °C), but also a change in the Seebeck values of the n-type samples was measured after joining (from ∼ - 110 μV K−1 to ∼ - 200 μV K−1 at room temperature), while they remained unchanged for p-type samples (∼100 μV K−1).
A similar behavior was also observed after contacting n- and p-type Mg2Si0.3Sn0.7 with Cu [25]. Seebeck values of n-type samples also changed during contacting (from ∼ - 110 μV K−1 to ∼ - 160 μV K−1) and annealing (to ∼ - 230 μV K−1), while no change was observed for p-type samples. In this study, only Ag will be considered because it showed a less complex reaction layer and much less diffusion than what was observed with Cu as reported in Refs. [22] and in Ref. [25].
However, Mg2Si1-xSnx solid solutions are known to suffer from demixing under certain conditions [[27], [28], [29]] and indeed demixing into Si-rich and Sn-rich phases was observed for both Cu and Ag contacted samples, potentially also influencing the Seebeck coefficient. In order to reduce the chemical complexity and identify the origin of the observed alteration of the Seebeck coefficient, we contacted n-type Mg2Si and Mg2Sn with Ag at different temperatures. To further understand the observed Seebeck behavior, an investigation of the intrinsic and extrinsic point defects of the studied binaries is required. This does not come as a surprise, as point defects are known to play a crucial role in determining semiconductors’ conduction types [[30], [31], [32], [33]]. In fact, for materials like Bi2Te3, references [34,35] reported that, under anion-rich conditions, the antisite defect Te on Bi (TeBi) account for the n-type conduction, while, under cation-rich conditions, the negatively charged antisite defects such as Bi on Te sites (BiTe) account for the p-type conduction. As for the case of Bi2Se3, the n-type conduction was related to the Se on Bi antisite defect (SeBi) under anion-rich conditions, while it was related to the Se vacancies (VSe) under cation-rich growth conditions.
Defect studies and computation of their formation energies can be easier done for binaries than for solid solutions, and an interpolation to the intermediate ternary compositions can be achieved from the results of the binaries. This explains why almost all respective research focuses on the binary Mg2X (X = Si, Sn, Ge) rather than to their solid solutions.
In the case of Mg2X materials, Kato et al. [36] used density-functional theory (DFT) calculations to evaluate point defect formation energies in Mg2Si and to understand the origin of the previously reported intrinsic n-type conduction of this material [37,38] Their results showed that the n-type conduction comes from the positively charged (q = 2+) Mg ions at interstitial sites (IMg), which are the most energetically stable point defects under both Mg-rich and Mg-poor (Si-rich) conditions.
Jund et al. [39] studied the relative stabilities of Mg2Si and Mg2Ge using first principles calculations with different functionals. They showed that the stability of the point defects strongly depends on the growth conditions. In case of Mg2Si, under stoichiometric and Mg rich conditions, Mg interstitials (IMg) is the most stable defect, while under Mg poor conditions, SiMg is more stable. This contradicts what was reported by Kato [36], but Kato et al. considered charged defects and dependence of the formation energies on chemical potentials, while Jund et al. considered neutral defects.
Another work by Liu et al. [40] stated that Mg vacancies VMg and Mg interstitials IMg are the dominant defects in Mg2Si and Mg2Sn, independently of the chemical environment (Mg-rich or Si/Sn-rich). The concentration of these defects is what determines the conduction type in each material. VMg is an acceptor (q = 2-) more favorable under Mg-depleted conditions, and IMg is a donor more favorable under Mg-rich conditions. Si/Sn related defects are less likely to occur in the binaries, partly because their ionic radii (2.72 Å/2.94 Å) are larger than that of Mg (0.66 Å), so the local disorder and strain due to these defects are much larger than the strain caused by Mg related defects.
Meanwhile, there have been few studies on intrinsic defects in Mg2Sn mitigated by the band gap underestimation in conventional DFT calculations, i.e. using the local density approximation or generalized gradient approximation. While Liu et al. [40] reported a quantitative analysis of the possible intrinsic defects in Mg2Si, Mg2Ge, and Mg2Sn, their quantitative analysis of the defect densities suffers from a severe band gap underestimation: most of the major carriers are compensated by the minority carriers due to the small band gap calculated by DFT. This underestimation of the band gap persists with other works using conventional DFT, including the works of Kato et al. [36] and Jund et al. [39] mentioned above. In agreement with this, our conventional DFT calculations also showed that the band gap is obtained negative for Mg2Sn. Such band gap underestimations affect the electronic chemical potential, which in turn affects defect stabilities. To overcome this issue, advanced computational methods such as hybrid-DFT [41] and quasi-particle calculations [42] were found to be important. Our recent hybrid functional study on intrinsic defects in Mg2Si and Mg2Sn finally quantitatively describes the intrinsic defect properties of these material systems [43].
Besides intrinsic defects, extrinsic defects (e.g. due to doping) are used to tune the carrier concentration of TE materials as the most common way to improve zT [[44], [45], [46], [47]]. As these “added” defects can be more stable than the intrinsic defects of the material and influence the charge carrier concentrations in the chemical potential region of interest, both defect types need to be taken into consideration in order to have a full picture and predict the materials’ behavior [48].
The aim of this paper is to understand the unexpected behavior of Ag contacted n-type Mg2Si1-xSnx using first principle calculations of point defect formation energies. In order to model the experimental situation (doped Mg2X in contact with Ag), we investigate the simultaneous presence of intrinsic and extrinsic defects in n- and p-type Mg2Si and Mg2Sn employing hybrid DFT calculations [41].
An understanding for the solid solutions can then be extrapolated. The considered dopants for n- and p-type conductions are respectively Bi and Li, and both Mg-rich (for n-type) and Mg-poor (for p-type) conditions are discussed.
Our findings show that the extrinsic defects generated after joining Ag with Mg2Si1-xSnx, namely AgMg, are behind the experimentally observed Seebeck changes in n-type materials. AgMg acts as an electron trap for the conduction electrons provided by Bi (BiSi for Mg2Si and BiSn for Mg2Sn), leading to a decrease in the majority charge carrier density. In case of p-type materials, Ag related defects have higher formation energies than Li defects, which makes the influence of AgMg or IAg not as visible as in n-type materials.
This example highlights that, in thermoelectricity, defect calculations are not just important for TE material development and dopant selection, but they also need to be taken into consideration when selecting contacting electrodes.
Section snippets
Sample preparation and characterization
Mg2Si and Mg2Sn were prepared from ball milled powder as reported in Ref. [18] with the respective nominal stoichiometries Mg2.06Si0.97Bi0.03 and Mg2.15Sn0.97Bi0.03. The powders from each material were pressed into three 15 mm diameter pellets for 10 min, at 800 °C for Mg2Si and at 600 °C for Mg2Sn [49] in a direct sinter press and then joined with Ag foil. The contacting experiments were also done through current assisted joining in the same direct sinter press. Each pellet was joined at a
Mg2Si/Sn with Ag
Seebeck scan lines by the PSM at room temperature of n-Mg 2Si and n-Mg2Sn joined with Ag at 3 different temperatures, (450 °C, 500 °C, 550 °C) and (400 °C, 450 °C, 500 °C) respectively, are presented in Fig. 1. All the samples displayed an interesting Seebeck profile where the S values peak near the interfaces and then return back to the bulk value beyond a certain depth. The portions of the samples where S changed are marked with yellow rectangles on Fig. 1. As no significant local variation
Discussion
The observed behavior might in principle and qualitatively be explained by Ag-induced point defects in the thermoelectric material. The formation energy of charged defects is a function of the Fermi level and will thus differ between n and p-type counterparts of the “same” composition, potentially leading to different abundance of defects in the n and p-type materials. The lattice diffusion process is governed by the diffusion barrier of the relevant defect, which is the sum of its formation
Conclusion
In this work, we re-assess the selection of Ag as a contacting solution for Mg2Si1-xSnx-based thermoelectric generators by describing the Ag diffusion mechanism and correlating unexpected experimental results with hybrid-DFT defect calculations. The observed change in Seebeck values of n-type binaries Mg2Si, Mg2Sn and their solid solutions is explained by AgMg defects which have low enough formation energy to counteract Bi-related defects and cause a diminution in charge carrier concentration.
CRediT authorship contribution statement
Sahar Ayachi: Methodology, Validation, Formal analysis, Investigation, Writing - original draft, Visualization. Radhika Deshpande: Validation, Investigation. Prasanna Ponnusamy: Software, Validation. Sungjin Park: Software, Validation, Formal analysis, Investigation. Jaywan Chung: Software. Sudong Park: Software, Validation, Writing - review & editing, Supervision, Funding acquisition. Byungki Ryu: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Writing -
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
The authors would like to gratefully acknowledge the endorsement for the DLR executive Board Members for Space Research and Technology, as well as the financial support from the Young Research Group Leader Program. We would also like to thank Pawel Ziolkowski and Przemyslaw Blaschkewitz for their help and assistance with the thermoelectric measurements.
This work was also supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) funded by the Ministry of Trade,
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