Electron scattering on acoustic phonons in plane semiconductor GaN/AlN nanostructures

Using the effective mass model for an electron within the layers of a nanosystem and rectangular potential wells and barriers for the effective potential of a GaN/AlN resonant tunneling structure, analytical solutions of the Schrödinger equation are obtained. The theory of a stationary electronic spectrum and wave functions of an electron is developed. Using the elastic continuum model, exact solutions of the equations describing the elastic displacement of the semiconductor medium of the studied nanostructure are obtained. Using these solutions, the theory of acoustic modes of the nanosystem has been developed. Using the Hamiltonian of acoustic phonons and electrons in the representation of secondary quantization, the quantummechanical theory of electron scattering on acoustic phonons is developed. Using the parameters of the nanosystem under study, based on the analysis of the poles of the Green's function, the displacements of the electronic spectrum associated with acoustic phonons at T = 0 К are obtained.