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.