Thermoelectric materials offer a viable and environmentally friendly approach toward clean electricity generation directly from waste heat.11. J. He and T. M. Tritt, “ Advances in thermoelectric materials research: Looking back and moving forward,” Science 357, eaak9997 (2017). https://doi.org/10.1126/science.aak9997 However, for their widespread use, it is important that the thermoelectric materials are both high performing and cost effective. The thermoelectric performance of a material is determined by a dimensionless figure of merit, zT = S2 σT/κ, where S, σ, and κ are respectively, the Seebeck coefficient, electrical conductivity, and thermal conductivity of the material at any temperature T measured in degree Kelvin. For near room-temperature thermoelectric applications, the Bi2Te3 based alloys are possibly the most dependable materials,22. Z. Han, J.-W. Li, F. Jiang, J. Xia, B.-P. Zhang, J.-F. Li, and W. Liu, “ Room-temperature thermoelectric materials: Challenges and a new paradigm,” J. Materiomics 8, 427–436 (2022). https://doi.org/10.1016/j.jmat.2021.07.004 with zT in some state-of-art n-type Bi2Te3 alloys reaching as high as 1.2.3,43. I. T. Witting, T. C. Chasapis, F. Ricci, M. Peters, N. A. Heinz, G. Hautier, and G. J. Snyder, “ The thermoelectric properties of bismuth telluride,” Adv. Electron. Mater. 5, 1800904 (2019). https://doi.org/10.1002/aelm.2018009044. B. Zhu, X. Liu, Q. Wang, Y. Qiu, Z. Shu, Z. Guo, Y. Tong, J. Cui, M. Gu, and J. He, “ Realizing record high performance in n-type Bi2Te3-based thermoelectric materials,” Energy Environ. Sci. 13, 2106–2114 (2020). https://doi.org/10.1039/D0EE01349H However, the acute scarcity of Te in the earth's crust escalates their cost, making it necessary to search for alternative materials.The compound Ag2Se is a narrow bandgap n-type semiconductor, offering a combination of high carrier mobility (∼103 cm2 V–1 s−1) and Seebeck coefficient (∼ −140 μV K–1), and an intrinsically low thermal conductivity (∼1 W m−1 K–1). The zT in Ag2Se1+δ materials has been reported to be as high as ∼1, making it a potential alternative to replace Bi2Te3.5–105. P. Jood, R. Chetty, and M. Ohta, “ Structural stability enables high thermoelectric performance in room temperature Ag2Se,” J. Mater. Chem. A 8, 13024–13037 (2020). https://doi.org/10.1039/D0TA02614J6. M. Jin, J. Liang, P. Qiu, H. Huang, Z. Yue, L. Zhou, R. Li, L. Chen, and X. Shi, “ Investigation on low-temperature thermoelectric properties of Ag2Se polycrystal fabricated by using zone-melting method,” J. Phys. Chem. Lett. 12, 8246–8255 (2021). https://doi.org/10.1021/acs.jpclett.1c021397. S. Huang, T.-R. Wei, H. Chen, J. Xiao, M. Zhu, K. Zhao, and X. Shi, “ Thermoelectric Ag2Se: Imperfection, homogeneity, and reproducibility,” ACS Appl. Mater. Interfaces 13, 60192–60199 (2021). https://doi.org/10.1021/acsami.1c184838. J. Chen, Q. Sun, D. Bao, T. Liu, W.-D. Liu, C. Liu, J. Tang, D. Zhou, L. Yang, and Z.-G. Chen, “ Hierarchical structures advance thermoelectric properties of porous n-type β-Ag2Se,” ACS Appl. Mater. Interfaces 12, 51523–51529 (2020). https://doi.org/10.1021/acsami.0c153419. P. Wang, J.-L. Chen, Q. Zhou, Y. T. Liao, Y. Peng, J. S. Liang, and L. Miao, “ Enhancing the thermoelectric performance of Ag2Se by non-stoichiometric defects,” Appl. Phys. Lett. 120, 193902 (2022). https://doi.org/10.1063/5.008555010. D. Yang, X. Su, F. Meng, S. Wang, Y. Yan, J. Yang, J. He, Q. Zhang, C. Uher, M. G. Kanatzidis et al., “ Facile room temperature solventless synthesis of high thermoelectric performance Ag2Se via a dissociative adsorption reaction,” J. Mater. Chem. A 5, 23243–23251 (2017). https://doi.org/10.1039/C7TA08726H Along with promising thermoelectric properties, Ag2Se also exhibits colossal, non-saturating linear magnetoresistance up to very high fields.11,1211. R. Xu, A. Husmann, T. Rosenbaum, M.-L. Saboungi, J. Enderby, and P. Littlewood, “ Large magnetoresistance in non-magnetic silver chalcogenides,” Nature 390, 57–60 (1997). https://doi.org/10.1038/3630612. F. Yang, S. Xiong, Z. Xia, F. Liu, C. Han, and D. Zhang, “ Two-step synthesis of silver selenide semiconductor with a linear magnetoresistance effect,” Semicond. Sci. Technol. 27, 125017 (2012). https://doi.org/10.1088/0268-1242/27/12/125017 Upon heating above ∼407 K, Ag2Se becomes superionic. In the superionic phase, the Se ions form a rigid bcc lattice and the Ag ions become mobile or liquid-like. It owes its n-type behavior to the presence of Ag interstitials (Ag∗), which easily ionize Ed≈2 meV to add 1 e−1/Ag∗ to the conduction band.1313. M. Jafarov, “ On the nature of charge carrier scattering in Ag2Se at low temperatures,” Semiconductors 44, 1280–1284 (2010). https://doi.org/10.1134/S1063782610100064 Controlling the density of Ag interstitials via excess anions helps optimize the carrier concentration, and hence, in obtaining high zT (∼1), as has been shown in several recent studies.5,9,10,145. P. Jood, R. Chetty, and M. Ohta, “ Structural stability enables high thermoelectric performance in room temperature Ag2Se,” J. Mater. Chem. A 8, 13024–13037 (2020). https://doi.org/10.1039/D0TA02614J9. P. Wang, J.-L. Chen, Q. Zhou, Y. T. Liao, Y. Peng, J. S. Liang, and L. Miao, “ Enhancing the thermoelectric performance of Ag2Se by non-stoichiometric defects,” Appl. Phys. Lett. 120, 193902 (2022). https://doi.org/10.1063/5.008555010. D. Yang, X. Su, F. Meng, S. Wang, Y. Yan, J. Yang, J. He, Q. Zhang, C. Uher, M. G. Kanatzidis et al., “ Facile room temperature solventless synthesis of high thermoelectric performance Ag2Se via a dissociative adsorption reaction,” J. Mater. Chem. A 5, 23243–23251 (2017). https://doi.org/10.1039/C7TA08726H14. W. Mi, P. Qiu, T. Zhang, Y. Lv, X. Shi, and L. Chen, “ Thermoelectric transport of Se-rich Ag2Se in normal phases and phase transitions,” Appl. Phys. Lett. 104, 133903 (2014). https://doi.org/10.1063/1.4870509The question then is whether Ag2Se is ready for the next step or even close to it? A recent study by Huang et al. finds that Ag2Se samples prepared by spark-plasma-sintering (SPS) or solid-state melting (SSM) exhibit significant compositional variations over small length scales. Consequently, they found that samples obtained from different parts of the same spark-plasma-sintered (SPS) ingot show variations up to ∼20% in their thermoelectric properties.77. S. Huang, T.-R. Wei, H. Chen, J. Xiao, M. Zhu, K. Zhao, and X. Shi, “ Thermoelectric Ag2Se: Imperfection, homogeneity, and reproducibility,” ACS Appl. Mater. Interfaces 13, 60192–60199 (2021). https://doi.org/10.1021/acsami.1c18483 The fact that in a superionic material, high temperature processing (temperatures exceeding the superionic transition temperature) results in metal-ion migration is a well-recognized problem.15–2015. T. P. Bailey and C. Uher, “ Potential for superionic conductors in thermoelectric applications,” Curr. Opin. Green Sustainable Chem. 4, 58–63 (2017). https://doi.org/10.1016/j.cogsc.2017.02.00716. K. Zhao, P. Qiu, X. Shi, and L. Chen, “ Recent advances in liquid-like thermoelectric materials,” Adv. Funct. Mater. 30, 1903867 (2020). https://doi.org/10.1002/adfm.20190386717. P. Qiu, X. Shi, and L. Chen, “ Cu-based thermoelectric materials,” Energy Storage Mater. 3, 85–97 (2016). https://doi.org/10.1016/j.ensm.2016.01.00918. P. Qiu, M. T. Agne, Y. Liu, Y. Zhu, H. Chen, T. Mao, J. Yang, W. Zhang, S. M. Haile, W. G. Zeier et al., “ Suppression of atom motion and metal deposition in mixed ionic electronic conductors,” Nat. Commun. 9, 2910 (2018). https://doi.org/10.1038/s41467-018-05248-819. T. Mao, P. Qiu, X. Du, P. Hu, K. Zhao, J. Xiao, X. Shi, and L. Chen, “ Enhanced thermoelectric performance and service stability of Cu2Se via tailoring chemical compositions at multiple atomic positions,” Adv. Funct. Mater. 30, 1908315 (2020). https://doi.org/10.1002/adfm.20190831520. N. Jakhar, N. Bisht, A. Katre, and S. Singh, “ Synergistic approach toward a reproducible high zt in n-type and p-type superionic thermoelectric Ag2Te,” ACS Appl. Mater. Interfaces 14, 53916 (2022). https://doi.org/10.1021/acsami.2c17039 In the presence of temperature or electric potential gradients, the metal-ions in the superionic phase diffuse, leading to composition inhomogeneity. How high a gradient can a given superionic material withstand depends on the temperature: the higher the temperature, the smaller the threshold. In the case of Ag2Se, the problem of compositional inhomogeneity due to Ag migration is further compounded by the evaporation of Se at high temperatures. There is no guarantee then that two different samples prepared identically using these commonly employed techniques will have identical properties too. This is apparent from a review of the previous literature where wide variations in the electronic properties is commonplace.5–10,14,21–255. P. Jood, R. Chetty, and M. Ohta, “ Structural stability enables high thermoelectric performance in room temperature Ag2Se,” J. Mater. Chem. A 8, 13024–13037 (2020). https://doi.org/10.1039/D0TA02614J6. M. Jin, J. Liang, P. Qiu, H. Huang, Z. Yue, L. Zhou, R. Li, L. Chen, and X. Shi, “ Investigation on low-temperature thermoelectric properties of Ag2Se polycrystal fabricated by using zone-melting method,” J. Phys. Chem. Lett. 12, 8246–8255 (2021). https://doi.org/10.1021/acs.jpclett.1c021397. S. Huang, T.-R. Wei, H. Chen, J. Xiao, M. Zhu, K. Zhao, and X. Shi, “ Thermoelectric Ag2Se: Imperfection, homogeneity, and reproducibility,” ACS Appl. Mater. Interfaces 13, 60192–60199 (2021). https://doi.org/10.1021/acsami.1c184838. J. Chen, Q. Sun, D. Bao, T. Liu, W.-D. Liu, C. Liu, J. Tang, D. Zhou, L. Yang, and Z.-G. Chen, “ Hierarchical structures advance thermoelectric properties of porous n-type β-Ag2Se,” ACS Appl. Mater. Interfaces 12, 51523–51529 (2020). https://doi.org/10.1021/acsami.0c153419. P. Wang, J.-L. Chen, Q. Zhou, Y. T. Liao, Y. Peng, J. S. Liang, and L. Miao, “ Enhancing the thermoelectric performance of Ag2Se by non-stoichiometric defects,” Appl. Phys. Lett. 120, 193902 (2022). https://doi.org/10.1063/5.008555010. D. Yang, X. Su, F. Meng, S. Wang, Y. Yan, J. Yang, J. He, Q. Zhang, C. Uher, M. G. Kanatzidis et al., “ Facile room temperature solventless synthesis of high thermoelectric performance Ag2Se via a dissociative adsorption reaction,” J. Mater. Chem. A 5, 23243–23251 (2017). https://doi.org/10.1039/C7TA08726H14. W. Mi, P. Qiu, T. Zhang, Y. Lv, X. Shi, and L. Chen, “ Thermoelectric transport of Se-rich Ag2Se in normal phases and phase transitions,” Appl. Phys. Lett. 104, 133903 (2014). https://doi.org/10.1063/1.487050921. J. Conn and R. Taylor, “ Thermoelectric and crystallographic properties of Ag2Se,” J. Electrochem. Soc. 107, 977 (1960). https://doi.org/10.1149/1.242758422. M. Ferhat and J. Nagao, “ Thermoelectric and transport properties of β-Ag2Se compounds,” J. Appl. Phys. 88, 813–816 (2000). https://doi.org/10.1063/1.37374123. F. Aliev, M. Jafarov, and V. Eminova, “ Thermoelectric figure of merit of Ag2Se with Ag and Se excess,” Semiconductors 43, 977–979 (2009). https://doi.org/10.1134/S106378260908002824. H. Duan, Y. Li, K. Zhao, P. Qiu, X. Shi, and L. Chen, “ Ultra-fast synthesis for Ag2Se and CuAgSe thermoelectric materials,” JOM 68, 2659–2665 (2016). https://doi.org/10.1007/s11837-016-1980-425. K. H. Lim, K. W. Wong, Y. Liu, Y. Zhang, D. Cadavid, A. Cabot, and K. M. Ng, “ Critical role of nanoinclusions in silver selenide nanocomposites as a promising room temperature thermoelectric material,” J. Mater. Chem. C 7, 2646–2652 (2019). https://doi.org/10.1039/C9TC00163H Since Ag2Se achieves its high-zT near the room temperature, a synthesis method that does not involve high temperatures processing can solve this issue. The question, however, is how should one get high density, preferably nanostructured, without resorting to the SPS, hot-pressing, or melting techniques?Interestingly, Ag2Se also has some very unique properties, which, if exploited well, can help overcome the above-mentioned issue. First, the phase Ag2Se forms readily when Ag and Se powders are mechanically processed.1010. D. Yang, X. Su, F. Meng, S. Wang, Y. Yan, J. Yang, J. He, Q. Zhang, C. Uher, M. G. Kanatzidis et al., “ Facile room temperature solventless synthesis of high thermoelectric performance Ag2Se via a dissociative adsorption reaction,” J. Mater. Chem. A 5, 23243–23251 (2017). https://doi.org/10.1039/C7TA08726H In addition, second is the metal-like malleability and ductility of Ag2Se,26–2926. R. Simon, R. Bourke, and E. Lougher, “ Preparation and thermoelectric properties of β-Ag2Se,” Adv. Energy Convers. 3, 481–505 (1963). https://doi.org/10.1016/0365-1789(63)90064-X27. H. Hu, Y. Wang, C. Fu, X. Zhao, and T. Zhu, “ Achieving metal-like malleability and ductility in Ag2Te1-xSx inorganic thermoelectric semiconductors with high mobility,” Innovation 3, 100341 (2022). https://doi.org/10.1016/j.xinn.2022.10034128. H. Chen, T.-R. Wei, K. Zhao, P. Qiu, L. Chen, J. He, and X. Shi, “ Room-temperature plastic inorganic semiconductors for flexible and deformable electronics,” InfoMat 3, 22–35 (2021). https://doi.org/10.1002/inf2.1214929. X. Shi, H. Chen, F. Hao, R. Liu, T. Wang, P. Qiu, U. Burkhardt, Y. Grin, and L. Chen, “ Room-temperature ductile inorganic semiconductor,” Nat. Mater. 17, 421–426 (2018). https://doi.org/10.1038/s41563-018-0047-z which was pointed out as early as in 1963 by Simon et al.2626. R. Simon, R. Bourke, and E. Lougher, “ Preparation and thermoelectric properties of β-Ag2Se,” Adv. Energy Convers. 3, 481–505 (1963). https://doi.org/10.1016/0365-1789(63)90064-X Here, we combine these properties to fabricate highly dense and chemically homogeneous Ag2Se1+δ pellets. We investigate the effect of stoichiometry δ on the thermoelectric properties and establish the excellent reproducibility, thermal stability, and chemical homogeneity along with high zT in our samples.The Ag2Se1+δ samples studied here are listed in Table I. The samples, named AS1, AS2, …, AS6, were prepared by ball-milling under Ar atmosphere followed by cold-pressing under 55 MPa pressure using KBr press. The cold-pressed pellets were hard with densities reaching 100% of the theoretically calculated density. These pellets were glued to an aluminum platform using a cold mounting epoxy and cut into desired shapes using a low-speed diamond saw. No chipping-off or breaking could be observed. The cuts were neat, and the resulting bar shaped samples were dense and shiny. The density was estimated from the spatial dimensions and mass of the samples. The high density of our samples without SPS or SSM can be attributed to the metal-like ductility of Ag2Se, which allows the powder particles to pack closely under applied pressure in order to achieve 100% space filling. The phase purity was checked using the x-ray powder diffraction (XRD) technique (Bruker, D8 Advance). The microstructure was assessed using the field-effect scanning electron microscope (FESEM) (Ultra Zeiss plus) equipped with an energy dispersive x-ray (EDS) analysis attachment (Oxford Instruments). The high-resolution electron micrographs were obtained using a transmission electron microscope (JEOL JEM 2200FS 200 keV). The simultaneous Seebeck coefficient and resistivity measurements were done on bar shaped samples using an LSR3 setup (Linseis). The maximum uncertainty in these measurements is ≤ 5%. The temperature dependent Hall measurements were done on a home-built setup by sweeping the field between ±1 T. The thermal conductivity κ was estimated by measuring the thermal diffusivity using the laser flash method (LFA 1000, Linseis). The maximum uncertainty in our thermal conductivity measurement is less than 6%.

TABLE I. Details of Ag2Se1+δ samples studied in this work.

Nameδρm (%)Extra phaseAS10∼100NilAS20.005∼100NilAS30.025∼100Minor SeAS40.025∼100Minor SeAS50.05∼100SeAS6−0.01∼100AgThe powder x-ray diffraction (XRD) patterns are shown in Fig. 1. All samples formed in the previously reported orthorhombic structure (space group P212121).3030. R. Dalven and R. Gill, “ Energy gap in β-Ag2Se,” Phys. Rev. 159, 645 (1967). https://doi.org/10.1103/PhysRev.159.645 The stoichiometric (AS1) and 0.5% Se-excess samples (AS2) are found to be phase pure. However, in Ag-excess sample (AS6) and in the higher Se-excess (δ≥0.025) samples, small extra peaks are observed. These are due to unreacted Ag in the Ag-excess and unreacted Se in the Se-excess samples. The Rietveld refinement for a representative sample (AS1) is shown in Fig. S1. The lattice parameters (see the supplementary material) are in good agreement with the previous literature.22,31,3222. M. Ferhat and J. Nagao, “ Thermoelectric and transport properties of β-Ag2Se compounds,” J. Appl. Phys. 88, 813–816 (2000). https://doi.org/10.1063/1.37374131. J. Yu and H. Yun, “ Reinvestigation of the low-temperature form of Ag2Se (naumannite) based on single-crystal data,” Acta Crystallogr. E 67, i45 (2011). https://doi.org/10.1107/S160053681102853432. H. Billetter and U. Ruschewitz, “ Structural phase transitions in Ag2Se (naumannite),” Z. Anorg. Allg. Chem. 634, 241–246 (2008). https://doi.org/10.1002/zaac.200700452 The Se off-stoichiometry did not show any appreciable effect on the lattice parameters.The chemical maps for our samples are shown in Fig. S2 of the supplementary material. In stoichiometric (AS1) and 0.5% Se-excess (AS2) samples, a uniform distribution of Ag and Se is seen. In AS6, Ag metal precipitates are visible, and in AS5, Se precipitation is observed. In AS3 and AS4, small Se precipitation is seen occasionally. These observations corroborate the XRD results. This suggests that the homogeneity field δ is extremely narrow in the Ag-rich side (δ≪ −0.01), but in the Se-rich side, the solubility limit is higher than 0.005 but less than 0.025. These observations are in agreement with previous studies where δ in the Se-rich side was estimated to be ∼0.01,5,265. P. Jood, R. Chetty, and M. Ohta, “ Structural stability enables high thermoelectric performance in room temperature Ag2Se,” J. Mater. Chem. A 8, 13024–13037 (2020). https://doi.org/10.1039/D0TA02614J26. R. Simon, R. Bourke, and E. Lougher, “ Preparation and thermoelectric properties of β-Ag2Se,” Adv. Energy Convers. 3, 481–505 (1963). https://doi.org/10.1016/0365-1789(63)90064-X and, in the Ag-rich side, the solubility limit is reported to be practically nil.3333. F. Grønvold, S. Stølen, and Y. Semenov, “ Heat capacity and thermodynamic properties of silver (I) selenide, oP-Ag2Se from 300 to 406 K and of cI-Ag2Se from 406 to 900 K: Transitional behavior and formation properties,” Thermochim. Acta 399, 213–224 (2003). https://doi.org/10.1016/S0040-6031(02)00470-7In Fig. 2(a), the FESEM micrographs for a representative cold-pressed sample (AS1) is shown. For comparison, the corresponding microstructure for a SSM sample is shown in Fig. 2(b). While both the methods yield ∼100% sample density, in SSM, the grains are macroscopic with lateral dimensions exceeding 1 μm, but in AS1, large number grains varying in size from a few nanometers to several hundreds of nanometers can be seen. This is also depicted in the inset. The AS1 sample was reexamined after heating it up to 380 K, but this has no detectable effect on the morphology (see Fig. S3 of the supplementary material). A representative high-resolution TEM micrograph of sample AS1 showing highly crystalline grains with well-resolved atomic planes is shown in Fig. 2(c). The inverse fast Fourier transform (IFFT) image of the area enclosed within the white box is shown in panel (d). The interplanar spacing for the 112 family of planes is also shown.The thermoelectric properties of our samples are shown in Fig. 3. The highest temperature was kept low (∼380 K), well below the superionic transition temperature to prevent possible changes in the microstructure due to Ag migration in the superionic phase. Also, the zT of Ag2Se decreases significantly in the superionic phase; the normal phase around room temperature is, therefore, of primary interest. As shown in Fig. 3(a), in all the studied samples, σ shows an increasing trend upon heating but significant variations are observed due to Se excess. Depending on the slope dσ/dT, we can group our samples as X = (i.e., stoichiometric and slightly Ag excess) and Y = (Se-excess samples). For group X, both σ and dσ/dT are higher than for Y. In AS1, for example, σ ranges from ∼1600 S cm− 1 at 310 K to ∼2850 S cm− 1 at 370 K, whereas in AS2, the corresponding values are ∼1000 S cm− 1 (310 K) and ∼1300 S cm− 1 (380 K). The same behavior, i.e., higher σ, dσ/dT for stoichiometric and slightly Ag doped samples compared to the anion excess sample, has been found in some previous studies (see, for example, Ref. 55. P. Jood, R. Chetty, and M. Ohta, “ Structural stability enables high thermoelectric performance in room temperature Ag2Se,” J. Mater. Chem. A 8, 13024–13037 (2020). https://doi.org/10.1039/D0TA02614J). This is due to the presence of a larger concentration of Ag interstitials in samples of group X as compared to Y. Upon Se doping, Ag interstitials (Ag∗) decrease, resulting in a decrease in the carrier concentration, and hence, σ decreases.2626. R. Simon, R. Bourke, and E. Lougher, “ Preparation and thermoelectric properties of β-Ag2Se,” Adv. Energy Convers. 3, 481–505 (1963). https://doi.org/10.1016/0365-1789(63)90064-X The increasing behavior of σ is due to the minority carrier excitations. Fits using the Arrhenius relation, σ∝e−Δ/2kBT, where kB is Boltzmann constant and Δ is the activation energy, yields Δ≈0.19 eV for AS1 (representing X) and 0.05 eV for AS2 (representing Y). These values are in good agreement with previous reports.5,345. P. Jood, R. Chetty, and M. Ohta, “ Structural stability enables high thermoelectric performance in room temperature Ag2Se,” J. Mater. Chem. A 8, 13024–13037 (2020). https://doi.org/10.1039/D0TA02614J34. A. Epstein, S. Kulifay, and R. Stearns, “ Energy gap of β silver selenide,” Nature 203, 856–856 (1964). https://doi.org/10.1038/203856b0 Due to a small bandgap (Eg ≈ 0.025 eV66. M. Jin, J. Liang, P. Qiu, H. Huang, Z. Yue, L. Zhou, R. Li, L. Chen, and X. Shi, “ Investigation on low-temperature thermoelectric properties of Ag2Se polycrystal fabricated by using zone-melting method,” J. Phys. Chem. Lett. 12, 8246–8255 (2021). https://doi.org/10.1021/acs.jpclett.1c02139) and high self-doping (∼1018 cm3), the activation energy Δ in these samples is essentially Δ=Eg+εF, where εF is the Fermi energy measured from the bottom of the conduction band. The number density of Ag∗ determines εF. εF (hence Δ) is accordingly higher for the samples in group X compared to the samples in Y, which explains why dσ/dT is higher for X compared to Y. A naive estimation of εF using the free electron model, εF=(3πℏ2n)2/3/2m∗ (where symbols have their usual meaning), gives the correct order of magnitude by taking the experimentally observed carrier densities and m∗=0.18me (vide infra). Before moving on, we note that σ of our two different 2.5% Se-excess samples (AS3 and AS4) exhibit a good overlap over the whole temperature range.The temperature variation of Hall carrier concentration (nH) is shown in Fig. 3(b). The sign of Hall coefficient is negative in all cases, indicating n-type behavior. For samples in group X, nH and dnH/dT are higher than for the samples in group Y. In AS2, for example, nH at 370 K is ∼6 ×1018 cm−3, but it is as high as ∼14 ×1018 cm−3 for AS1. Due to its small bandgap, the intrinsic regime (i.e., carrier excitation across the bandgap) in Ag2Se sets in well below 300 K,66. M. Jin, J. Liang, P. Qiu, H. Huang, Z. Yue, L. Zhou, R. Li, L. Chen, and X. Shi, “ Investigation on low-temperature thermoelectric properties of Ag2Se polycrystal fabricated by using zone-melting method,” J. Phys. Chem. Lett. 12, 8246–8255 (2021). https://doi.org/10.1021/acs.jpclett.1c02139 resulting in an increasing nH(T) above room temperature. To confirm this, we measured σ for two representative samples, AS1 (higher Δ) and AS3 (lower Δ), down to 77 K. The results are shown in Fig. S4 of the supplementary material. Upon heating above 77 K, for AS1, σ remains nearly constant up to about 100 K, above which it increases slowly due to the onset of intrinsic regime. On the other hand, in AS3, due to its low activation energy, σ starts increasing upon heating above 77 K itself.The temperature dependence of Hall mobility (μH) is shown in Fig. 3(c). AS1 has a mobility of ∼1690 cm2 V−1 s−1 at 310 K, which is the highest among all the cold-pressed samples investigated here. Upon heating, μH decreases following approximately a T−α dependence with α ≈ 1.5, suggesting that the electron–phonon scattering is dominant in the pristine Ag2Se. This temperature dependence, however, gradually weakens as the off-stoichiometric increases with α → 0.6 in AS5, indicating the role of increasing defect scattering contribution. Interestingly, while nH is highest for the sample AS6, μH is highest for AS1. The decrease in μH on both sides of δ = 0 suggests that Ag or Se doping introduces additional scattering centers (point defects) leading to a mixed scattering decreasing α below the electron– phonon limit. In a recent paper by Jood et al., a similar behavior is reported but with μH peaking at 1% Se doping and nH at 0%.55. P. Jood, R. Chetty, and M. Ohta, “ Structural stability enables high thermoelectric performance in room temperature Ag2Se,” J. Mater. Chem. A 8, 13024–13037 (2020). https://doi.org/10.1039/D0TA02614J They argued that the lower mobility of their stoichiometric sample is due to the presence of a minor metastable monoclinic phase which coexists with the main orthorhombic phase and contributes to the electron scattering. They further claimed that the metastable phase can be completely suppressed by 1% Se doping, which, therefore, has the highest mobility. In our samples, however, we do not evidence any metastable phase. This may be due to the different synthesis procedures used in the two studies.The temperature variation of S is shown in Fig. 3(d). Near 300 K, S varies from −108 μV K–1 (AS6) to −144 μV K–1 (AS2). With further increase in Se doping, S decreases to −132 μV K–1 in AS5. This decrease can be attributed to the presence of Se precipitates in the higher doped sample. The elemental Se is a p-type semiconductor with very low mobility (0.12 cm2 V–1 s−1) and high value of S (∼103μV K–1 at 300 K).3535. H. W. Henkels, “ Thermoelectric power and mobility of carriers in selenium,” Phys. Rev. 77, 734 (1950). https://doi.org/10.1103/PhysRev.77.734 The thermal excitation of minority holes may also contribute to decrease in S upon heating above 300 K. Overall, the temperature variation of S follows the expected inverse correlation with the temperature variation of nH. The plot S vs nH is shown in Fig. S5 of the supplementary material. The data from several previous studies are also included. The Pisarenko plots (shown in SI) fits the (nH, S) data points for m∗ (effective mass) between 0.18me and 0.23me, where me is the free electron mass in good agreement with the literature.99. P. Wang, J.-L. Chen, Q. Zhou, Y. T. Liao, Y. Peng, J. S. Liang, and L. Miao, “ Enhancing the thermoelectric performance of Ag2Se by non-stoichiometric defects,” Appl. Phys. Lett. 120, 193902 (2022). https://doi.org/10.1063/5.0085550 This shows that excess Se does not affect either the band structure or the carrier effective mass significantly, confirming that the higher activation energy for samples AS1 and AS6 is not due to the bandgap widening but rather due to self-doping from interstitial Ag. Noteworthy is the fact that m* for Ag2Se is considerably low compared to, for example, Bi2Te3 (m* = 1.8me).44. B. Zhu, X. Liu, Q. Wang, Y. Qiu, Z. Shu, Z. Guo, Y. Tong, J. Cui, M. Gu, and J. He, “ Realizing record high performance in n-type Bi2Te3-based thermoelectric materials,” Energy Environ. Sci. 13, 2106–2114 (2020). https://doi.org/10.1039/D0EE01349H This, in turn, explains the relatively high carrier mobility of Ag2Se as compared to the other well-investigated thermoelectrics.4,36–384. B. Zhu, X. Liu, Q. Wang, Y. Qiu, Z. Shu, Z. Guo, Y. Tong, J. Cui, M. Gu, and J. He, “ Realizing record high performance in n-type Bi2Te3-based thermoelectric materials,” Energy Environ. Sci. 13, 2106–2114 (2020). https://doi.org/10.1039/D0EE01349H36. M. Saleemi, M. S. Toprak, S. Li, M. Johnsson, and M. Muhammed, “ Synthesis, processing, and thermoelectric properties of bulk nanostructured bismuth telluride (Bi2Te3),” J. Mater. Chem. 22, 725–730 (2012). https://doi.org/10.1039/C1JM13880D37. S. Roychowdhury, T. Ghosh, R. Arora, M. Samanta, L. Xie, N. K. Singh, A. Soni, J. He, U. V. Waghmare, and K. Biswas, “ Enhanced atomic ordering leads to high thermoelectric performance in AgSbTe2,” Science 371, 722–727 (2021). https://doi.org/10.1126/science.abb351738. K. Biswas, J. He, I. D. Blum, C.-I. Wu, T. P. Hogan, D. N. Seidman, V. P. Dravid, and M. G. Kanatzidis, “ High-performance bulk thermoelectrics with all-scale hierarchical architectures,” Nature 489, 414–418 (2012). https://doi.org/10.1038/nature11439 The combination of high σ and S results in high power factor (PF). The highest PF is recorded for AS2. The PF for this sample ranges from 22.2 μW cm−1 K–2 (310 K) to 24.3 μW cm−1 K–2 (370 K) (see Fig. S6 of the supplementary material). Comparable values of PF are reported in previous studies: for example, 26.6 μW cm−1 K–2 at 380 K was reported in a recent study on a very well characterized, zone-melted Ag2Se sample.66. M. Jin, J. Liang, P. Qiu, H. Huang, Z. Yue, L. Zhou, R. Li, L. Chen, and X. Shi, “ Investigation on low-temperature thermoelectric properties of Ag2Se polycrystal fabricated by using zone-melting method,” J. Phys. Chem. Lett. 12, 8246–8255 (2021). https://doi.org/10.1021/acs.jpclett.1c02139Temperature dependence of κ is shown in Fig. 4(a). κ near 300 K decreases from ∼1.4 W m−1 K–1 (AS1) to 0.8 W m−1 K–1 (AS3 and AS4). Overall, a good agreement is seen with the previous literature.5,7,10,14,405. P. Jood, R. Chetty, and M. Ohta, “ Structural stability enables high thermoelectric performance in room temperature Ag2Se,” J. Mater. Chem. A 8, 13024–13037 (2020). https://doi.org/10.1039/D0TA02614J7. S. Huang, T.-R. Wei, H. Chen, J. Xiao, M. Zhu, K. Zhao, and X. Shi, “ Thermoelectric Ag2Se: Imperfection, homogeneity, and reproducibility,” ACS Appl. Mater. Interfaces 13, 60192–60199 (2021). https://doi.org/10.1021/acsami.1c1848310. D. Yang, X. Su, F. Meng, S. Wang, Y. Yan, J. Yang, J. He, Q. Zhang, C. Uher, M. G. Kanatzidis et al., “ Facile room temperature solventless synthesis of high thermoelectric performance Ag2Se via a dissociative adsorption reaction,” J. Mater. Chem. 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