By minimizing the free energy while constraining dopant density, a universal curve was derived which related the formation energy, Eform, of doping and the efficiency of defect passivation in terms of the segregation of dopants at defect sites. The universal curve took the simple form of a Fermi-Dirac distribution. The imposed constraint defined a chemical potential that played the role of a sort of Fermi energy which set a thermodynamic limit on the Eform required to overcome the effect of entropy such that dopant segregation at defects in semiconductors could occur. Using the Si edge dislocation as an example, it was shown using first-principles calculations how to map the experimentally measurable passivation efficiency to the calculated Eform by using the universal curve for typical n- and p-type substitutional dopants. It was shown that n-type dopants were ineffective. Among p-type dopants, B could satisfy the thermodynamic limit while improving the electronic properties.

Limits on Passivating Defects in Semiconductors: the Case of Si Edge Dislocations. T.L.Chan, D.West, S.B.Zhang: Physical Review Letters, 2011, 107[3], 035503