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The theory of the interaction of electrons with acoustic phonons inmultilayer nitride-based AlN/GaN nanostructures was developed for the firsttime at $T\geqslant 0$ using the method of finite-temperature Green's functionsand Dyson equation. Components of the Hamiltonian describing the system ofelectrons with acoustic phonons and the magnitudes of the electron spectrumshifts due to the electron-phonon interaction were obtained. Dependences of theelectronic spectrum levels and spectrum of the acoustic phonons were founddepending on the position of the internal potential barrier in the studiednanostructure. The temperature shifts of the electronic spectrum and decayrates were calculated for various values of temperature $T$.

Interaction of electrons with acoustic phonons in AlN/GaN resonant tunnelling nanostructures at different temperatures