Acoustic phonons in multilayer nitride-based AlN/GaN resonant tunneling structures

Abstract

The study of physical processes associated with acoustic phonons in nitride-based nanosystems is of great importance for the effective operation of modern nanoscale devices. In this paper, a consistent theory of acoustic phonons arising in multilayer nitride-based semiconductor resonant tunneling structures, that can function as a separate cascade of a quantum cascade laser or detector is proposed. Using the physical and geometric parameters of a typical nanostructure, the spectrum of various types of acoustic phonons and the corresponding normalized components of the elastic displacement vector are calculated. It has been established that the spectrum of acoustic phonons of a multilayer nanostructure consists of two groups of the shear phonons dependencies and three groups of dependencies for a mixed spectrum of flexural and dilatational phonons. The dependencies of the acoustic phonons spectrum of the nanostructure and the components of the elastic displacement vector on its geometric parameters are studied. It has been established that for the components of the displacement vector u 2 for shear phonons have a decrease in the absolute values of their maxima with increasing of energy level number. The components u 1 and u 3 of flexural and dilatational phonons behave respectively as symmetric and antisymmetric functions relatively the center of an separate selected layer of the nanostructure. The proposed theory can be further applied to study the interaction of electrons with acoustic phonons in multilayer resonant tunneling structures.

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

“…In figure 4 (a) It can be seen from figure 4 (a), (b), (c) that with an increase of the spectrum number of the branch 1 , and accordingly, the energy of acoustic phonons corresponding to these branches, dependences 1 ( ) and 3 ( ) tend to increase the number of maxima and minima that are formed by calculated dependences over the given range of . In addition, it should be noted that the effect, which consists of the simultaneous formation of maxima of function 1 ( ), accordingly, minima of function 3 ( ), as it was established in [19,20], is mainly observed for the dependences shown in figure 4 (a), (b), (c). However, in this case, the formation of these extrema occurs at arbitrary points inside separate the nanosystem layers and they are a little offset from each other, and are not formed in the middle of these layers, as established in [20],…”

“…Before analyzing the dependencies shown in figure 5, it should also be noted that the calculated acoustic phonon energies for wurtzite semiconductors AlN and GaN should correspond to the first Brillouin zone, that is, they are limited by maximum values of the order of 25-30 meV [19]. In this case, the conditions are fulfilled at 0 K:…”

“…we obtain the Hamiltonian of noninteracting electrons in the form: 19) where¯is determined by relation (2.8), and the fermionic creation (ˆ+¯) and annihilation (ˆ¯) operators of stationary electronic states satisfy the well-known anticommutative relations.…”

“…The theory of acoustic phonons modes arising in multilayer nitride resonant tunnelling structures and their calculations were performed recently for the first time in papers [19] and [20] for binary and ternary semiconductor alloys, respectively. The results obtained in these papers demonstrate a significant difference in the calculated dependences of the spectra of acoustic phonons and corresponding components of the displacement field which deal with the formation of an additional group of the spectrum of acoustic phonons dependences on the wave vector in the presence of a layer with a ternary AlGaN semiconductor being in the nanostructure.…”

“…the dispersion equation is obtained, from which the mixed spectrum Ω (FL,DL) ( ) of flexural (FL) and dilatational (DL) phonon modes is found. These acoustic phonon modes are determined using components 1(3) ( ) as: ( ) ( ) = ( ) ( ) 1 ( ), ( ) 3 ( ) and ( ) ( ) = ( ) ( ) 1 ( ), ( ) 3 ( ) , where the indices " " and " " are used to mark the symmetric and antisymmetric functions of , correspondingly [14,19,20].…”