Mathematical Modeling of the Acoustic Phonons Spectra Arising in Multilayer Nanostructures

Based on a modification of the elastic continuum model, a mathematical model describing the processes of the emergence and propagation of acoustic phonons in multilayer planar semiconductor nanostructures was constructed. Using the obtained mathematical model, supplemented by the boundary conditions for medium displacements and components of the elastic tensor at the boundaries of the studied nanostructure, the theory of the spectrum was developed and the phonon modes were normalized. Using the geometric and physical parameters of a typical nanostructure, we calculated and simulated the spectral characteristics of acoustic phonons. The obtained results can be used for further research and mathematical modeling of the electron-phonon interaction subsidence in complex semiconductor nanoheterosystems, which are the basic elements of quantum cascade lasers and detectors.