Mg-pressure-controlled annealing for tuning Mg content and thermoelectric properties of Mg2–δ (Si0.5Sn0.5)1–x Sb x

Highlights: • Mg-pressure-controlled annealing realizes precise Mg content control in Mg_2–δ(Si_0.5Sn_0.5)_1–xSb_x. • The maximum Δδ of 0.012 (0.037 ≤ δ ≤ 0.049) is obtained at x = 0.10. • Owing to the Δδ, carrier concentration varies from 0.2 × 10²⁰ to 3.7 × 10²⁰ cm⁻³. • High carrier concentration at the Mg-rich composition suppresses bipolar effect. • Precise Mg content control enables carrier concentration tuning for maximizing zT. -- Abstract: Control of the Mg content is essential for tuning the carrier concentration of Mg₂Si-based thermoelectric materials. In this study, we achieved precise control of the Mg content in Mg_2–δ(Si_0.5Sn_0.5)_1–xSb_x by Mg-pressure-controlled annealing via solid-gas equilibrium. The range of possible Mg deficiency δ, which is estimated under assumption that each Sb donates one electron and Mg vacancy compensates them, depends on the Sb content x. At x = 0.10, the widest range Δδ = 0.012 (0.037 ≤ δ ≤ 0.049) is obtained. Owing to Mg non-stoichiometry, Mg-rich Mg_2–δ(Si_0.5Sn_0.5)_0.90Sb_0.10 (δ = 0.037) shows a roughly 18 times higher carrier concentration (n = 3.7 × 10²⁰ cm⁻³) than the Mg-poor composition (δ = 0.049 and n = 0.2 × 10²⁰ cm⁻³). The Mg content of Mg_2–δ(Si_0.5Sn_0.5)_1–xSb_x shifts the Fermi level within the rigid band approximation, resulting in a consistent relationship between the Seebeck coefficient and carrier concentration in both experiment and DFT calculation. Mg-pressure-controlled annealing enables carrier concentration tuning for zT maximization and yields a zT_max of 1.0 at 773 K for Mg_2–δ(Si_0.5Sn_0.5)_0.90Sb_0.10 with an intermediate Mg content (δ = 0.042 and n = 2.2 × 10²⁰ cm⁻³ under P_Mg = 2 Pa) that is larger than those for Mg-rich and Mg-poor compositions (zT_max = 0.9 and 0.6 for δ = 0.037 and 0.049, respectively).