Decomposed defect formation energy for analysis of doping process: The case of n-type and p-type doping of β-FeSi2

Defect formation energy governs the thermodynamics of a specific dopant within the host material. Here, we introduce an approach to decomposing the defect formation energy into intuitive components, each representing a distinct physical step in the process of defect formation. Through this approach, we illustrate that adhering solely to conventional criteria, such as ionic radius, may overlook potential dopants. Taking β-FeSi2, a promising high-temperature thermoelectric material, as an example, we demonstrate that non-intuitive chemical interactions can play a more significant role in lowering the defect formation energy. As a result, Ir on Fe site is found to exhibit unexpected low defect formation energy among the 26 candidate dopants and has been employed in experiment to enhance the thermoelectric figure of merit of n-type β-FeSi2. The understanding gained from this work could be of general interest for addressing the doping limit issue for other potential thermoelectric materials.