Dynamic Conductivity of Electrons and Electron-Phonon Interaction in Open Three-Well Nanostructures

Abstract

The theoretical description of electronic tunneling transport through the three-well nanostructure (In0.53Ga0.47As/In0.52Al0.48As), being an expanded active region of quantum cascade detector, is presented. Using the solution of the Schrödinger equation, the dynamic conductivity caused by quantum transitions due to the interaction of electrons with electromagnetic eld and phonons is calculated. Within the Green functions approach, the electron spectrum, renormalized due to the interaction with conned optical and interface phonons is obtained at cryogenic and room temperatures. The role of dierent mechanisms of electronphonon interaction in the formation of temperature shifts, decay rates of electron states and electromagnetic eld absorption bands is investigated. It is shown that independently of the temperature, the contribution produced by interface phonons into renormalized electron spectrum is several times bigger than that of conned phonons. However, the experimentally observed long-wave shift and broadening of absorption band at higher temperatures is, mainly, caused by the decreasing heights of resonant tunneling structure potential barriers.

Influence of the Space Charge on Tunneling of Electrons and Their Conductivity by the Resonance Tunneling Structures in the Constant Electric Field

“…is variable in space electrons concentration. It is seen from the equations (3) and 5, taking into account Hamiltonian (4) and relation (7), that they form self-consistent system. 3with Hamiltonian (4) in the weak signal approximation is found as:…”

“…The effect of electron-electron interaction on electron tunneling was investigated in the paper [4]. The electron-phonon interaction and the influence of phonons on the electronic spectrum were studied in the works [5][6][7]. The effect of static and dynamic charge fields generated by electrons on the electron transport in open RTS is studied poorly.…”

Photon- and phonon-assisted transport of electrons in resonant tunneling structures

“…Combining the system of Maxwell equations for the potential of polarization field of RTS in the dielectric continuum model, the equation ε(ω)∆Φ(r) = 0, ω = Ω/ is obtained [45,46]. Due to invariantness in the plane xoy,…”

“…For the investigation of electron spectrum renormalized due to the interaction with phonons using the method of Green's functions, the Hamiltonian of electron-phonon system is written in the representation of the second quantization over all variables [45,46]…”

The Spectrum of Transverse Acoustic Phonons in Planar Multilayer Semiconductor Nanostructures

“…Actually, the study of electron tunneling processes in planar semiconductor multilayer resonant tunneling structures (RTS) occupies an important place for an effective work of modern quantum cascade lasers (QCL) [1][2][3] and detectors (QCD). Much attention is paid to the theoretical study of interaction of electrons with optical phonons [4], constant electric [5,6] and magnetic field [7] with the electron beam and its static and dynamic spatial charge [8,9], but the acoustic phonons influence on the resonant tunneling is still practically unexplored. Also the value of contribution of electrons interaction with acoustic phonons in multilayer RTS is not been studied yet.…”