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Nitride-based materials still offer opportunities for the development of new electronic and optoelectronic applications. From the seventies of the 20th century, GaAs was considered as mature family material for many electronic applications. In the beginning of the 21th century, GaAs is step by step replaced by GaN in many applications due to its high polarization, chemical and physical stability, and wide bandgap. In this work we study theoretically the electronic and optoelectronic properties of GaN, and we conceive its applications. We test the triangular quantum well model for the high electron mobility transistors. We discuss the use of GaN-based HEMTs for the design of chemical and biological sensors. The plasmon frequencies of the 2DEG in the HEMT are calculated. Optoelectronic characterizations of AlGaN/GaN structures with GaAs-Au grating are discussed using full vector diffraction software. In the context of the optical properties of GaN, we calculate the free-carrier absorption coefficient with strong longitudinal-optical (LO) phonon-plasmon interaction. We take several mechanisms into account, which assist in the photon absorption process.