Compound Semiconductor Dopability Assessed via the Maximum Carrier-to-Dopant Ratio and Facilitated by an Algorithmic Determination of the Fixed Doping Level Defect Equilibria

Kröger–Vink diagrams (KVD) are used to visualize the concentrations of defects across different thermodynamic conditions, such as temperature and chemical potential. For doped semiconductors, KVDs provide insights into the doping effect on changing the electronic charge carriers’ concentrations. Though KVDs with fixed doping levels are widely used, calculating the fraction of each charge state of the dopant is rarely discussed and is not straightforward in comparison to calculating the same fractions when the chemical potential is specified. Therefore, this paper presents an implementation of a self-consistent algorithm that finds the correct value of the dopant’s chemical potential corresponding to a specific doping concentration. Thus, the distribution of the dopant’s charge states is consequently calculated based on this chemical potential. This algorithm facilitates exploring the maximum electronic carrier-to-dopant ratio, which is a recently introduced metric to judge the dopant’s ability to inject excess electronic carriers in a semiconductor. The hematite phase of iron oxide (α-Fe2O3) was taken as a model system, and five different dopants at different temperatures (700–1300 K) and concentrations (0.25–1%) were analyzed. The analysis shows that higher temperatures and lower dopant’s concentrations maximize this ratio for both donors and acceptors. The origins of these observations were explained based on the equilibria of both native and dopant defects depicted by the KVDs. The implications of these results on doped hematite sample preparation conditions are discussed. The herein presented algorithm and analyses have broad applicability to compound semiconductors in the dilute limit of doping