We study thermal conductivity and electronic ballistic coherent transport via perturbed 2D nanostructure because these areas have potential applications in quantum physics and microelectronic devices, among other fields. The term "inhomogeneous 2D nanostructure" refers to the electronic scattering caused by an integrated defect in domain boundaries. Localized electronic states and the scattering of an incident electronic wave result from the translation symmetry breaking caused by scattering in a perturbed system structure. The distinctive electronic characteristics of atomic sites that make up a comprehensive representation of defect domain boundaries are computed using the matching technique related to the Tight Binding technique. Relationship spectrum variations corresponding to hopping integral changes in the domain boundary were computed. It was demonstrated that the spectra's physical characteristics are sensitive to change of thephysical parameters at the neighbord of the defect.

Electronic properties; Matching method, quantic 2D system Green functions, Scattering phenomena,EDOS, Tight Binding method, Landaueur-Büttiker formalism