Investigating the Effects of Defect Energetics on Phase Boundaries Shapes

Thermoelectric (TE) devices which offer a route for energy recovery/production often need to be optimized by doping with other elements to improve the thermoelectric figure of merit (zT), which qualifies the device's efficiency. The solubility of these elements in the bulk system is usually in such dilute concentrations that they can best be described as 0-D defects in an otherwise essentially uniform crystal. Though dilute, the defects can nevertheless be visualized on a phase diagram as providing some width to nominally single-phase regions or so-called line compounds. The width of these phases is known to be set directly by the defect energy of the defects, however, little attention is paid to the shape of these regions despite the fact that the shape of the region directly sets the solubility limits and thus the maximum concentration of defects in addition to providing an understanding of the dominant defects in that system. We discuss the thermodynamic factors that impact the shape of the phase diagrams and show how they can provide a guide to the optimal doping of semiconductors.