Discovery of high-performance low-cost n-type Mg3Sb2-based thermoelectric materials with multi-valley conduction bands

Widespread application of thermoelectric devices for waste heat recovery requires low-cost high-performance materials. The currently available n-type thermoelectric materials are limited either by their low efficiencies or by being based on expensive, scarce or toxic elements. Here we report a low-cost n-type material, Te-doped Mg3Sb1.5Bi0.5, that exhibits a very high figure of merit zT ranging from 0.56 to 1.65 at 300−725 K. Using combined theoretical prediction and experimental validation, we show that the high thermoelectric performance originates from the significantly enhanced power factor because of the multi-valley band behaviour dominated by a unique near-edge conduction band with a sixfold valley degeneracy. This makes Te-doped Mg3Sb1.5Bi0.5 a promising candidate for the low- and intermediate-temperature thermoelectric applications.

Thank you for the three referee reports. We are grateful for their constructive and helpful comments, and below we address the reports point by point.

Reviewer 1
Comment 1 'D. Statistic approach does not apply. The study was made on single sample.
E. Concerning the material composition reported in the manuscript I do not have doubts in the reliability of the results. The robustness and validity of the results cannot be judged in general and should be considered with the usual criterions for the thermoelectric measurements made on the single specimen.
F. The report is written quiet fragmentarily and is focused only on one specimen.'

Reply
We thank the referee for this comment. We agree that in general the robustness and validity of the results cannot be judged on a single sample. To address this concern, we have made more samples with nominal compositions Mg 3 Sb 1.5-0.5x Bi 0.5-0.5x Te x (x = 0.04, 0.05, 0.08, and 0.20), which have been characterized on our homebuilt systems. The high zT in the high-performance sample with x = 0.05, is measured both on the commercial ZEM-3 setup and the homebuilt system, and the two sets of data show very good agreement with each other (see Supplementary Fig. 9).
The manuscript has been rewritten to include the additional samples with more compositions. The major revision is summarized below: (a) Figures 1-4, Supplementary Figures 3-7, and their captions have been modified to include different compositions Mg 3 Sb 1.5-0.5x Bi 0.5-0.5x Te x (x = 0.04, 0.05, 0.08, and 0.20).
(b) One sentence is modified in line 5 of the second paragraph on page 3: "The TE performance of n-type Mg 3 Sb 1.5-0.5x Bi 0.5-0.5x Te x (x = 0.04, 0.05, and 0.08) is at least 2 times higher than that of p-type Mg 3 Sb 2 -based compounds including Na-doped Mg 3 Sb 2 (Supplementary Fig. 6b), a factor of at least 3.7 larger than the mobility 17,18 of the undoped Mg 3 Sb 2 ".
(f) In the beginning of the second paragraph several sentences have been modified as: "The total thermal conductivity values of n-type Mg 3 Sb 1.5-0.5x Bi 0.5-0.5x Te x (x = 0.04, 0.05, 0.08, and 0.20) samples are low and exhibit decreasing trends with increasing temperature (Fig. 4d). The lowest room-temperature thermal conductivity of 0.743 W m -1 K -1 is observed for the sample with x = 0.04. The total thermal conductivity, κ, value decreases to ~0.556 W m -1 K -1 at 725 K." (g) In sample synthesis of Methods on page 13: "The samples with nominal compositions Mg 3 Sb 1.5-0.5x Bi 0.5-0.5x Te x (x = 0.04, 0.05, 0.08, and 0.20) were synthesized by combining arc melting and SPS techniques." (h) In the first paragraph of page 15 one sentence is added: "The Seebeck coefficients of the pellets were then measured from the slope of the thermopower versus temperature gradient using chromel-niobium thermocouples on an in-house system, which is similar to the one reported by Iwanaga et al 30  The composition with Bi 0.5 was chosen as a proof-of-concept, because Mg 3 Sb 1.5 Bi 0.5 possesses a suitable band gap of 0.43 eV as well as ΔE K-ML = 0.12 eV with the ML band as the conduction band minimum. This is good for the electrical transport since the ML band with a high valley degeneracy of 6 can be reached with a low doping concentration. In addition, the formation energy of Te doping on the anion sites was calculated and shown in Supplementary Fig. 2, which indicates that Te doping on the anion sites of Mg 3 Sb 1.5 Bi 0.5 is easier than that of Mg 3 Sb 2 .
We agree that other compositions with x < 1 and x ≠ 0.5 might also show good performance. However, as a proof-of-concept paper, we have shown a progression to high zT in n-type Mg 3 Sb 1.5 Bi 0.5 samples with different Te compositions. It is an excellent idea to caary out a study of the full range of Bi compositions in a future study. Thanks.
(a) The energy gap E g versus x plot was added in Figure 3b.
(b) Two sentences are added in the beginning of page 9: "The obvious bipolar effect for Mg 3 Sb 2-x Bi x (x > 1) is confirmed in a previous experimental report 17 . Hence, n-type Mg 3 Sb 2-x Bi x (x ≤ 1) compounds are very promising TE candidates if properly doped on the anion sites." (c) Two sentences have been modified in the second paragraph of page 9: "Achieving n-type Mg 3 Sb 2 by doping tellurium on the anion sites has been attempted and found to be difficult, while it is easier in Mg 3 Sb 2- x Bi x solid solutions. This is probably due to the lower formation energy of tellurium doping on the anion sites of Mg 3 Sb 2-x Bi x solid solutions (see one example in Supplementary Fig. 2). From the above theoretical calculation, Mg 3 Sb 1.5 Bi 0.5 possesses a small band gap of 0.43 eV as well as ΔE K-ML = 0.12 eV with the ML band as the conduction band minimum (Fig. 3a), making it a potential candidate for n-type doping.
The experimental validation is successfully demonstrated in n-type doped Mg 3 Sb 1.5 Bi 0.5 solid solution using tellurium as an effective dopant." Comment 3 'Justification of the doping: why tellurium and not selenium or sulfur, why is 0.05 an optimum of the doping if it is).'

Reply
In this work we choose tellurium for n-type doping, because tellurium is the close neighbor of antimony in the Periodic Table. It means that tellurium has a similar ion radius and electronegativity relative to antimony and bismuth, which will possibly make it easier for tellurium to be doped on the Sb or Bi sites. In addition, tellurium has been widely used as an effective n-type dopant in thermoelectric research. We agree that selenium or sulfur doping might also be very interesting due to the abundance of Se and S elements and we believe that it could be a nice future work. Thanks for this comment.
To address the second part of the comment, we have made more samples with nominal compositions Mg 3 Sb 1.5-0.5x Bi 0.5-0.5x Te x (x = 0.04, 0.05, 0.08, and 0.20). As shown in the updated Fig. 1a, x = 0.04 is an optimum of Te doping, and the sample with x = 0.05 shows a comparable performance. Please see the reply to comment 1 for details.

Reply
We are sorry for the confusion about this point. In Figures 3 and 2a,b, the DFT model is for n-type Mg 3 Sb 2 , which has the ML band and the K band converged. But our experimental data is on Te-doped Mg 3 Sb 1.5 Bi 0.5 which has an energy difference of 0.12 eV between the ML band and K band. This is why the DFT curve looks overestimated.
Unfortunately, it is impossible for semi-classical Boltzman theory to calculate Seebeck coefficient from the spectral-weight representation of the band structure of Mg 3 Sb 1.5 Bi 0.5 . The spectral-weight representation of the band structure of Mg 3 Sb 1.5 Bi 0.5 was used to understand that the ML band moves downward 0.12 eV below the K band and becomes the conduction band minimum. Since the ML band with a high valley degeneracy of 6 is highly desirable for electrical transport, moving the ML band to the conduction band minimum is good and it can be reached with a low doping level.
In order to make the multiple band behavior of Mg 3 Sb 1.5 Bi 0.5 clear, the following revision has been applied: (a) The second paragraph of page 8: "The results prove that multiple band behavior including the ML band with a six-fold valley degeneracy is indeed preserved in Mg 3 Sb 1.5 Bi 0.5 solid solution and the dispersions and effective masses of the K band and ML band are very similar to those of Mg 3 Sb 2 . The main difference, however, is that the ML band in Mg 3 Sb 1.5 Bi 0.5 is shifted downward 0.12 eV below the K band and therefore becomes the conduction band minimum. This is good for the TE performance of Mg 3 Sb 1.5 Bi 0.5 since the ML band with a high val-ley degeneracy of 6 can be easily reached with a relatively low doping level." (b) The reason of DFT overestimation is explained in the third paragraph of page 9: "The experimental Seebeck coefficients of n-type Mg 3 Sb 1.5-0.5x Bi 0.5-0.5x Te x samples at 300 K or 725 K are larger than the Seebeck value calculated by a single band model using the DOS effective mass of the ML band ( See Figs 2a and 3c). This result not only confirms the theoretical calculation that the ML band dominates the conduction band minimum of Mg 3 Sb 1.5 Bi 0.5 , but also reveals that the K band located 0.12 eV above the conduction band minimum makes a contribution to both the room-temperature and high-temperature electrical transports. Since there is an energy difference of 0.12 eV between the ML band and the K band in n-type Mg 3 Sb 1.5 Bi 0.5 , the experimental Seebeck coefficients of n-type Mg 3 Sb 1.5-0.5x Bi 0.5-0.5x Te x are smaller than the calculated value by DFT for n-type Mg 3 Sb 2 with the effective convergence of the two bands (see Figs 3a,b and 2c)." (c) The second paragraph of page 10: "The carrier concentration of Mg 3 Sb 1.5-0.5x Bi 0.5-0.5x Te x increases with increasing temperature and reaches 4.83 × 10 19 cm -3 at 725 K in the high-performance sample with x = 0.04 ( Supplementary Fig. 6a), suggesting that the Fermi level will move upward approaching the K band with rising temperature. Additionally, the broadening of the Fermi distribution makes the Fermi level easier to reach the K band at high temperatures. The temperaturedependent DOS effective mass in Te-doped Mg 3 Sb 1.5 Bi 0.5 are illustrated in Fig. 3d. As shown in Fig. 3d, the DOS effective mass of Mg 3 Sb 1.5-0.5x Bi 0.5-0.5x Te x (x=0.04 and 0.05) derived from the experimental Seebeck coefficient increases with increasing temperature at 400-725 K, ruling out the single band behavior at high temperatures. The above results again prove that the multiple band behavior, including the effects from both the ML band and the K band, makes a contribution to the high temperature transport properties." (d) One sentence is added to the caption of Figure 2 to explain the overestimation of DFT modelling: "Our experimental data lie below the curve by DFT for Mg 3 Sb 2 , which is because there is an energy difference of 0.12 eV between the ML band and K band in n-type Mg 3 Sb 1.5 Bi 0.5 while these two bands are nearly converged in Mg 3 Sb 2 (see Fig. 3a)." (e) Two sentences are added to the caption of Figure 3: "The band structure of Mg 3 Sb 1.5 Bi 0.5 depicts a multiple band behavior similar to that of Mg 3 Sb 2 (Fig. 2c), where the ML band possesses a six-fold valley degeneracy and the K band has a two-fold valley degeneracy. However, the ML band in Mg 3 Sb 1.5 Bi0.5 becomes the conduction band minimum, which is about 0.12 eV below the K band." The same impression makes also the summary. Here, the multi-valley approach is presented as a basis for the materials design, which was not the issue in the presented manuscript.'

Reply
In the revised manuscript, the overestimation of theoretical calculation is explained. Six-fold valley degeneracy, which is another expression of a valley degeneracy of 6, is added in the caption of Figure 3. Please see the reply to Comment 4 for details.
Multi-valley band behavior was explained in detail for n-type Mg 3 Sb 2 . Several methods, including ab initio band structure, Fermi surface, and the dependence of Seebeck coefficient and power factor on carrier concentration, have been used to demonstrate the multiple band behavior in n-type Mg 3 Sb 2 . The multiple conduction band feature of Mg 3 Sb 1.5 Bi 0.5 is similar to that of Mg 3 Sb 2 . They have the ML band with a six-fold valley degeneracy and the K band with a two-fold valley degeneracy. The only difference, however, is in Mg 3 Sb 1.5 Bi 0.5 the ML band moves downwards 0.12 eV below the K band, which makes the ML band easier to reach at a low doping level. To make the multiple band behavior clearer, a few modifications are applied. Please see the reply to Comment 4 for details. Thanks.

assume that the authors are in the process of preparing more samples for a more complete paper and a communication is warranted with the combination of the theoretical support.'
Reply Thanks for the suggestion. We agree and that is why we originally submitted the paper based on a single sample. However, we also acknowledge that the study is more definitive when based on multiple samples and as explained above we have in the revised manuscript added data for more samples with different compositions. The progression to high zT can be seen in Fig. 1a in the revised manuscript. Please see the reply to the Comment 1 of the first reviewer for details.

Reviewer 3
Comment 1 '1. There are a variety of zT values depending on the method of sample preparation. In this sense, the authors need to show their own data on pristine Mg 3 Sb 2 and Mg 3 Sb 1.5 Bi 0.5 samples, which need to be compared with their own theoretical results for p type cases.'

Reply
Thank you for the suggestion. We agree that the zT value depends on the method of sample preparation, and this is why we carefully chose the reported data (RSC Adv. 3, 8504-8516 (2013); Acta Mater. 93, 187-193 (2015)) using the similar synthesis method (i.e. Mechanical milling followed by SPS press) for comparison. However, to additionally address the concern, we have prepared one Mg 3 Sb 2 sample using our synthesis method. The obtained zT value by our synthesis method is very similar to the reported data cited in the manuscript (see Figure A).
We would like to stress that the focus of this work is on n-type Mg 3 Sb 2based materials rather than p-type. Therefore, we think using the previous reported data is reasonable and does not affect the present work.   Supplementary Fig. 2. As shown in the figure, doping tellurium on the anion sites (Sb or Bi sites) in Mg 3 Sb 1.5 Bi 0.5 has lower formation energy than that in Mg 3 Sb 2 . We prepared our samples with the nominal compositions Mg 3 Sb 1.5-0.5x Bi 0.5-0.5x Te x (x=0.04, 0.05, 0.08, 0.20) since initially we do not know if Te will prefer to substitute Sb atoms or Bi atoms. In addition, quantitative elemental analysis of the high-performance pellet with x = 0.05 was carried out by SEM-EDS (see Supplementary Table 1). We find that the actual composition is close to the nominal composition, and the actual composition shows slightly less Bi and more Sb relative to the nominal composition. This can be explained by the assumption that more Te has been doped on the Bi sites than on the Sb sites due to the lower formation energy of Te Bi . The above result indicates that in the future we could try synthesis of n-type Mg 3 Sb 1.5 Bi 0.5-x Te x , which might be more effective. We have made the following revisions to address this comment: (a) A few sentences are added in the beginning of second paragraph on page 9: "Achieving n-type Mg 3 Sb 2 by doping tellurium on the anion sites has been attempted and found to be difficult, while it is easier in Mg 3 Sb 2-x Bi x solid solutions. This is probably due to the lower formation energy of tellurium doping on the anion sites of Mg 3 Sb 2-x Bi x solid solutions (see one example in Supplementary Fig. 2)." (b) A few sentences are added in the second paragraph on page 14: "Quantitative elemental analysis of the high-performance pellet with x = 0.05 was carried out on FEI Nova Nano SEM 600 equipped with an element EDS X-ray detector. The result shown in Supplementary Table  1 was the average value from five randomly selected areas of the pellet." (c) Supplementary Fig. 2  The actual composition estimated by SEM-EDS analysis for the high-performance Mg 3 Sb 1.5-0.5x Bi 0.5-0.5x Te x sample with x = 0.05. The actual composition by SEM-EDX is close to the nominal composition. The actual composition shows less Bi and more Sb relative to the nominal composition. This is possibly because that more Te has been doped on the Bi sites than on the Sb sites due to the lower formation energy of Te Bi (see Supplementary Fig. 2)." '4. I believe that the authors did not consider temperature effect in their DFT calculations. Nevertheless, they compare the theoretical data of ntype Mg 3 Sb 2 with the experimental data taken at 300 K (see Figs. 2a and 2b), and the theoretical data of n-type Mg 3 Sb 1.5 Bi 0.5 with the experimental data taken at 725 K (see Fig. 3d). If one considers different temperature, for example, 300 K in Fig. 3d and 725 K in Figs. 2a and 2b, the experimental data do not agree with the simulated curves.'

Reply
This appears to be a misunderstanding. The temperature effect is included in the electrical transport calculation by semi-classical Boltzman transport theory under the constant scattering time approximation (CSTA). Under CSTA, it is assumed that the carrier scattering time τ determining the electrical conductivity will not vary strongly with temperature and doping level. This approach has been successfully applied to predict the Seebeck coefficient and the trend of the electrical conductivity or power factor for a variety of thermoelectric materials (J. Concerning the reason why the DFT curve looks overestimated. This is because the DFT curve is simulated for n-type Mg 3 Sb 2 with nearly converged ML band and K band, while the experimental data is for n-type Mg 3 Sb 1.5 Bi 0.5 , which has the ML band lies 0.12 eV below the K band. Please see the reply to Comment 4 of the first reviewer for details. Thanks.
Comment 5 '5. According to their n_H and mu_H data; when simple looking, n_H is almost 2 times increased with temperature and mu_H is almost 3 times decreased with temperature, the resistivity should be increased about 1.5 times, which seems to be inconsistent with Fig. 4c.'

Reply
The inconsistency is caused by different resistivity measurement methods between our homebuilt setup and the commercial ZEM-3 setup. The mobility was calculated from the Hall coefficient and resistivity measured on the full pellet using four-point Van der Pauw method in our home built setup (Rev. Sci. Instrum. 2012, 83, 123902.). The resistivity shown in Fig.  4c  (a) Figures 1-4 in the main text are modified using the data measured by our homebuilt setups on the same pellet. (e) One sentence is added in line 13 of page 15: "The thermoelectric zT, obtained on the high-performance sample with x = 0.05 by the homebuilt system and ZEM-3 setup, shows good consistency between each other ( Supplementary Fig. 9)." Comment 6 '6. Also, the Seebeck coefficient at 725 K in Fig. 4b seems to be about 280 microV/K, but the data point in Fig. 3d is about 300 microV/K. They are not consistent each other.'

Reply
We have checked the Seebeck coefficients at 725 K in Fig. 4b and Fig. 3d in the initial version of manuscript and confirmed that they are consistent with each other (282 microV/K). Please note that the scales of Fig. 4b and Fig. 3d are not the same.
As explained above in the revised manuscript, we have used the electrical transport data measured on our homebuilt setups in the main text. The ZEM-3 data have been put in the Supplementary Information for comparison (see the reply to Comment 5).
Comment 7 '7. The authors need to explain the reason on thermal hysteresis of Seebeck coefficient and electrical resistivity (Figs. S7a and S7b). If it originates from annealing effect and/or slight oxidation, the hysteresis may not be reversible.'

Reply
Although the transport properties show hysteresis, the hysteresis can be repeated very well in two different cycles (see Supplementary Fig. 8). Moreover, the thermoelectric zT obtained on the high-performance sample with x = 0.05 by the home-built system and the commercial ZEM-3 setup shows excellent consistency between each other ( Supplementary  Fig. 9). The good repeatability and reproducibility of the high zT observed in two different setups indicate that the hysteresis in the sample is likely caused by reversible processes, and that it is not due to an annealing effect or oxidation. If the hysteresis is caused by annealing or oxidation, the transport properties curves will not be repeated in two different cycles and the high zT will not be reproduced by two different setups.
We stress that the focus of the present work is proof-of-concept of multivalley conduction bands in n-type Mg 3 Sb 2 -based compounds. We have demonstrated that the hysteresis does not affect the high performance in the n-type sample, and exploring the exact the reason of thermal hysteresis is beyond the scope of the present work. We are planning to perform in-situ X-ray diffraction on n-type samples for a comprehensive study of structure-property relation, which might explain the hysteresis in the future.
(a) The comparison of zT values measured on ZEM-3 and homebuilt setup is plotted in Supplementary Fig. 9. Supplementary Fig. 9 is added in the Supplementary Information. (b) A few sentences are added to the Supplementary Note 2: "The transport properties of the two cycles are consistent upon the repeated heating and cooling measurements. In addition, the thermoelectric zT, obtained on the high-performance sample with x = 0.05 by the home-built system and ZEM-3 setup, shows excellent consistency between each other ( Supplementary Fig. 9). The good repeatability and reproducibility observed in different setups indicate that the hysteresis in the sample is more likely caused by reversible processes."

Summary of the changes (marked in red in the revised manuscript)
23. A few sentences are modified in the end of page 12 and in the beginning of page 13. 33. One reference is added on page 19. 34. Figures 1, 2a,b, 3b,c,d, and 4 are modified. The order of Figure 3c and 3d is changed.  Once again we would like to thank the reviewers for the time they have devoted to our manuscript. Their very insightful comments have significantly improved our manuscript and we look much forward to your decision.