AbstractIn a previous study, puzzling experimental results regarding the neutralization of N effects on the bandgap energy in the hydrogenated In0.21Ga0.79As0.975N0.025 alloy were explained by theoretical investigations revealing the occurrence of a novel phenomenon: thermal annealing changes the InGaAs host‐matrix by making it able to exert a selection of the N–H complexes responsible of the N neutralization. In view of technological applications of this effect, the underlying selective host‐matrix model was carefully checked here by theoretically investigating InGaAsN alloys of different compositions ranging from Ga‐rich to In‐rich. As a most important result, such an extensive investigation inspired a comprehensive explanation of the origin of the host‐matrix effect which clarifies how the effect works, firmly establishes its occurrence, gives indications for a bandgap tuning based on a matrix design, sets conditions for its extension to other III‐V‐N alloys and suggests ways to induce fine changes of the alloy mechanical behavior.