Theory of electronic structure evolution in GaAsN and GaPN alloys

Using the empirical pseudopotential method and large atomistically relaxed supercells, we have systematically studied the evolution of the electronic structure of ${\mathrm{GaP}}_{1-x}{\mathrm{N}}_x$ and ${\mathrm{GaAs}}_{1-x}{\mathrm{N}}_x,$ from the dilute nitrogen impurity regime to the nascent nitride alloy. We show how substitutional nitrogen forms perturbed host states (PHS) inside the conduction band, whereas small nitrogen aggregates form localized cluster states (CS) in the band gap. By following the evolution of these states and the “perturbed host states” with increasing nitrogen composition, we propose a new model for low-nitrogen-content ${\mathrm{GaAs}}_{1-x}{\mathrm{N}}_x$ and ${\mathrm{GaP}}_{1-x}{\mathrm{N}}_x$ alloys: As the nitrogen composition increases, the energy of the CS is pinned while the energy of the PHS plunges down as the nitrogen composition increases. The impurity limit (PHS above CS) is characterized by strongly localized wave functions, low pressure coefficients, and sharp emission lines from the CS. The amalgamation limit (PHS overtake the CS) is characterized by a coexistence of localized states (leading to high effective mass, exciton localization, Stokes shift in emission versus absorption) overlapping delocalized PHS (leading to asymmetrically broadened states, low temperature coefficeint, delocalized $E_{+}$ band at higher energies). The alloy limit (PHS well below CS) may not have been reached experimentally, but is predicted to be characterized by conventional extended states. Our theory shows that these alloy systems require a polymorphous description, permitting the coexistence of many different local environments, rather than an isomorphous model that focuses on few impurity-host motifs.