Dynamical Screening, Collective Excitations, and Electron–Phonon Interaction in Heterostructures and Semiconductor Quantum Wells. General Theory

Abstract

A theory of dynamical screening in heterostructures and semiconductor quantum wells is developed which contains electron-electron interaction and electron-phonon interaction. I n this theory both the types of long-wave optical phonons, LO phonons and interface phonons, which occur in those layered structures are included. An expression is derived for the longitudinal screened interaction of subband electrons in heterostructures and quantum-wells. The obtained screened interaction potential allows the derivation of the total 1 ongitudinal dielectric function and the dispersion relation of the coupled intra-and intersubband plasmon-phonon modes. This screened interaction potential is used t o develope a dynamically screened and finite-temperature theory of the electronphonon interaction in heterostructures and quantum wells. The leading-order electron self-energy is disscnssed. An analytic expression of the polarization function of the quasi-two-dimensional electron gas is calculated within the random-phase approximation. Further approximations, t h e plasmon pole approximation and the long-wave approximation are discussed and the resulting analytic expressions of the polarization function are given. E s wird e k e Theorie der dynamischen Abschirmung in Heterostrukturen und Quanten-Wells entwickelt. Die dynamische Abschirmnng beinhaltet sowohl die Elektron-Elektron-als auch die Elektron-Phonon-Wechselwirkung, wobei in letzterer die zwei Typen von langwellig-optischen Phononen (LO Phononen und Grenzflachen-Phononen), die in solchen schichtftirmigen Strukturen auftreten, explizit beriicksichtigt werden. Das longitudinal abgeschirmte Wechelwirkungspotential der Subband-Elektronen in Heterostrmkturen und Qnanten-Wells wird berechnet. Ausgehend von diesem Potentmid wird ein Ausdruck fur die totale longitudinale dielektrische Funktion und fiir die Dispersionsrelntion der gekoppelten Tntra-und Intersubband-Plasmon-Phonon-RIoden abgeleitet. Weiterhin wird aus diesem Potential eine Theorie der dynamisch abgeschirmten Elektron-Phonon-Wechselwirkung bei endlichen Temperaturen in Heterostrukturen und Quanten-Wells abgeleitet. Die aus dieser Wechselwirkung resultierende Selbstenergie der Elektronen wird diskutiert. Es wird ein anulytischer Aosdruck fur die Polarisationsfunktion des quasi-zweidimensionalen Elektronengases in der Random-Phase Spproximation abgeleitet. Weitere Naherungen, die Plasmon-Pol-Naherung und die langwellige Niherung werden diskutiert und analytische Ausdrucke fur die Polarisationsfunktion abgeleitet.

Scattering of plasmons in a quasi-two-dimensional electron gas containing a fixed-point charge

“…2 The carrier density propagator is defined as a time-ordered densitydensity correlation function. The lowest-order term in the perturbation expansion of its irreducible part is given by FIG.…”

“…5 In the case of a semiconductor quantum well with a finite electron or hole density, there are both intrasubband plasmons which are associated with a single-carrier subband and also intersubband plasmons which are associated with carrier transitions between two subbands. 2 The energy of the intersubband plasmons has a positive lower bound. We have shown in an earlier study that this feature contributes to the existence of the bound state of the intersubband plasmon.…”

“…In particular the effects of confinement on plasmon dispersion have been well studied. 1,2 In addition, recently the interaction of quantum-well plasmons with impurities such as ionized acceptors 3 and neutral donors 4 have been of interest. An electron plasma interacting with a single ionized donor or acceptor can be represented by an electron gas containing a fixed-point charge.…”

Calculation of the dark current in a quantum well infrared photodetector

“…The electron density therefore oscillates in order to cancel the electric field created from the polarized medium. The collective excitations of the electron density give rise to plasma modes [24]. As the wave vector increases, the plasmon energy increases up to a cut-off wave vector above which the collective excitations start transferring into single-particle excitations in the Landau damping region.…”

Solitary excitations of a two-dimensional electron gas

“…This interest has been driven both by the challenge to fabricate and probe devices based on these low-dimensional structures, and by the search for novel behavior and/or modified behavior from bulk semiconductor systems. The dispersion relation for the plasmons, [1][2][3][4][5][6][7][8][9][10][11] as well as the coupling of these modes to phonons and photons, 8,[12][13][14][15][16][17][18][19][20] in these low-dimensional systems has been studied extensively both experimentally and theoretically, using linearized hydrodynamic models, 10,11,20,21 and quantum many-body formulations. 1,3,18 The results from these models yield similar behavior in the low , k regime, where kϽk F , the Fermi wave vector.…”