Analytical method for calculation of the potential profiles of nitride-based resonance tunneling structures

Abstract

Using the effective mass model for an electron and the dielectric continuum model, analytical solutions of the self-consistent Schrödinger-Poisson system of equations are obtained. Quantum mechanical theory of electronic stationary states, the oscillator strengths of quantum transitions and a method of potential profile calculation is developed for the experimentally constructed three-well resonance-tunneling structure -a separate cascade of quantum cascade detector. For the proposed method, a comparison with the results of other methods and with the results of the experiment was carried out. A good agreement between the calculated value of the detected energy and its experimental value has been obtained, the difference being no more than 2.5%.

Investigation of the electron-acoustic phonon interaction via the deformation and piezoelectric potentials in AlN/GaN resonant tunneling nanostructures

“…The physical notion of each of the terms (44) is described in details in the papers [30,31]. Δ ( ) = Δ ( , ) -is the energy scheme of the nanostructure for an electron in the model of rectangular potential wells and barriers, which is calculated according to the Varshni relation [30] for a given temperature value T ;…”

“…, where -is the Fermi level of the nanosystem material, obtained from the neutrality condition, -is the -th electronic level energy value; -is the exchange-correlation potential in the Hedin-Lundqvist representation, -is the potential, which is determined by contribution of the internal electric field = [8,9,30,31] arising in the -th separate nanostructure layer, caused by the total value of the piezoelectric and spontaneous polarizations ( ) = ( ) + ( ) [8,9]. Besides, in the Poisson equation from system (41), the value ( ) = +1 ( )…”

“…-specifies the surface charges arising at the boundaries of the nanosystem layers due to different values of the total polarization in them. The methodology for finding solutions of the system (41) is well known from [30,31] and similar papers. In this regard, we will not describe this issue in details, determining the solutions of the system (41) with the required accuracy, using the finite difference method [30] or the semi-analytical method [31].…”

“…The methodology for finding solutions of the system (41) is well known from [30,31] and similar papers. In this regard, we will not describe this issue in details, determining the solutions of the system (41) with the required accuracy, using the finite difference method [30] or the semi-analytical method [31]. Then we approximate the nanostructure effective potential for an electron (37), representing it as a piecewise continuous function:…”

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

“…Lately, considerable attention of researchers of multilayer nitride nanostructures has been paid to the study of internal electric fields arising in RTS layers due to significant values of spontaneous and piezoelectric polarizations [5,6], and due to the development of methods for calculating potential profiles of these nanosystems [7,8]. Besides, some theoretical and experimental papers deal with the study of excitons and interband transitions in the mentioned nanosystems [9,10].…”