Understanding the Intrinsic P-Type Behavior and Phase Stability of Thermoelectric α-Mg₃Sb₂

α-Mg₃Sb₂ is an excellent thermoelectric material through excess-Mg addition and n-type impurity doping to overcome its persistent p-type behavior. It is generally believed that the role of excess-Mg is to compensate the single Mg vacancy to realize n-type carrier conduction. In contrary to this belief, the present work indicates that the role of excess-Mg is to compensate the electronic charge of defect complex (V_Mg(2) + Mg_I)^1-. The Mg solubility in α-Mg_3+xSb₂ is quite small when only considering a single defect, but it enlarged up to x = 0.011 with the defect complex (V_Mg(2) + Mg_I)^1-, which is more reasonable as supported by experiments. Under Mg-poor conditions, V_Mg(1)^2- and V_Mg(2)^2- are the dominant defects, and their concentrations can reach (1.05-1.18) × 10¹⁹ cm^-3 at 1200 K. Under Mg-rich conditions, (V_Mg(2) + Mg_I)^1- is found to be the dominant reason for strong p-type behavior, and their concentrations can reach as high as 3.5 × 10²⁰ cm^-3, which shifts the Fermi level closer to the valence band maximum. The predicted carrier concentrations in the range 10¹⁷-10²⁰ cm^-3 are in the same range found experimentally for pure p-type α-Mg₃Sb₂.