Localization and percolation in semiconductor alloys: GaAsN vs GaAsP

Tradition has it that in the absence of structural phase transition, or direct-to-indirect band-gap crossover, the properties of semiconductor alloys (bond lengths, band gaps, elastic constants, etc.) have simple and smooth (often parabolic) dependence on composition. We illustrate two types of violations of this almost universally expected behavior. First, at the percolation composition threshold where a continuous, wall-to-wall chain of given bonds (e.g., Ga-N-Ga-N...) first forms in the alloy (e.g., $\mathrm{Ga}{\mathrm{As}}_{1-x}{\mathrm{N}}_x$), we find an anomalous behavior in the corresponding bond length (e.g., Ga-N). Second, we show that if the dilute alloy (e.g., $\mathrm{Ga}{\mathrm{As}}_{1-x}{\mathrm{N}}_x$ for $x\to 1$) shows a localized deep impurity level in the gap, then there will be a composition domain in the concentrated alloy where its electronic properties (e.g., optical bowing coefficient) become irregular: unusually large and composition dependent. We contrast $\mathrm{Ga}{\mathrm{As}}_{1-x}{\mathrm{N}}_x$ with the weakly perturbed alloy system $\mathrm{Ga}{\mathrm{As}}_{1-x}{\mathrm{P}}_x$ having no deep gap levels in the impurity limits, and find that the concentrated $\mathrm{Ga}{\mathrm{As}}_{1-x}{\mathrm{P}}_x$ alloy behaves normally in this case.