Nanoscale physics

The theory of the interaction of electrons with acoustic phonons in AlN / GaN nanostructures at T=0 К
Boyko I.V., Petryk M.R., Zayats V.B.
Mathematical Modeling of Mass Transfer Laboratory, Ternopil Ivan Puluj National Technical University. Ruska str., 46001, Ternopil, Ukraine. 
E-mail: boyko.i.v.theory@gmail.com

Modern quantum cascade lasers and detectors of the near and middle infrared waves use plane multilayer nanostructures based on double  and triple  nitride semiconductor materials as active elements [1]. A feature of the mentioned materials is the possibility operating of nano-devices in a wide temperature range and the generation of a constant electric field associated with the piezoelectric effect in the layers of nanostructures [2]. For nanostructures based on such semiconductors, phonon processes, especially those associated with acoustic phonons and electron scattering on them, are rather poorly studied.
In the proposed work, the electronic problem was investigated by solving the Schrödinger equation for the effective potential  of the nanosystem using the effective mass and rectangular potential barriers model - the wave functions  and the electron spectrum  in the nanosystem were determined. The components of the displacement field , spectrum and modes of shear, flexural, and dilatational phonons are obtained by solving the equation of motion for an elastic continuum using the boundary conditions for the components  and components of the stress tensor  at the all nanosystem heteroboundaries.Using the Hamiltonians of acoustic phonons and electrons in the representation of the secondary quantization, the quantum-mechanical theory of electron scattering on acoustic phonons is developed. Based on the analysis of the poles of the Green function, we obtained the displacements of the electronic spectrum associated with acoustic phonons at .

1.	Mirzaei B., Rostami A., Baghban H. Terahertz dual-wavelength quantum cascade laser based on GaN active region // Opt. Laser Technol.- 2012.44, N 2.-P. 378-383.
2.	Boyko I. Analytical method for calculation of the potential profiles of nitride-based resonance tunneling structures // Condensed Matter Physics.-2018.-21, N 4.-P. 43701-1 – 43701-11.