Limits on Passivating Defects in Semiconductors: The Case of Si Edge Dislocations

By minimizing the free energy while constraining dopant density, we derive a universal curve that relates the formation energy (E-form) of doping and the efficiency of defect passivation in terms of segregation of dopants at defect sites. The universal curve takes the simple form of a Fermi-Dirac distribution. Our imposed constraint defines a chemical potential that assumes the role of Fermi energy, which sets the thermodynamic limit on the E-form required to overcome the effect of entropy such that dopant segregation at defects in semiconductors can occur. Using Si edge dislocation as an example, we show by first-principles calculations how to map the experimentally measurable passivation efficiency to our calculated E-form by using the universal curve for typical n- and p-type substitutional dopants. We show that n-type dopants are ineffective. Among p-type dopants, B can satisfy the thermodynamic limit while improving electronic properties.