Electron-optical Phonon Interaction Research Articles

Microscopic calculation of the electron-optical-phonon interaction in ultrathin GaAs/AlxGa1-xAs alloy quantum-well systems.

We have calculated electron--optical-phonon scattering rates in ultrathin GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As alloy quantum-well systems of finite depth, based on a fully microscopic lattice dynamics approach for the phonon spectra. A pseudo-unit-cell model is utilized to calculate the lattice-dynamical properties of the ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As alloy system together with the two-parameter Keating potential and the long-range Coulomb potential between ions. The polar interactions of quantum confined electrons with GaAs- and AlAs-like optical modes are presented for both intrasubband and intersubband transitions, and the comparison with other theoretical calculations made. Good agreement is obtained for the 1\ensuremath{\rightarrow}1 and 2\ensuremath{\rightarrow}1 transition rates between the microscopic pseuso-unit-cell model and a macroscopic two-pole dielectric continuum model.

The effect of Γ-X mixing on the direct excitonic photoluminescence in GaAs/AlGaAs quantum wells

We studied the pressure shift of direct PL lines in two different GaAs/AlGaAs quantum-well samples in the diamond anvil cell and in the gas cell. We found that up to the Γ-X crossover pressure the shift of the lines agrees with the effective-mass calculation and exhibits small dependence on the well parameters. When the X minima in the barriers become lower than the Γ level in the well, the pressure coefficient of the direct line is lowered. We attribute the Γ-X mixing to two factors: (i) boundary conditions at the interface and (ii) electron-optical phonon interaction. We believe that the first factor is more important than the second because the Γ-X resonant effects are much stronger in quantum wells than in the bulk. Our results imply that the pressure shift of the PL lines in quantum wells should not be fitted with a single linear or quadratic dependence below and above the crossover.

Effect of bulk dispersion on the electron-optical-phonon interaction in a single quantum well.

Effect of bulk dispersion on the electron-optical-phonon interaction in a single quantum well.

Hot-electron overcooling and intersubband population inversion in quantum wires

Monte Carlo simulation of hot photoexcited electron relaxation in rectangular quantum wires is carried out. Simulation shows that at the initial stage the electron cooling dynamics is defined by electron-optical phonon interaction and exhibits strong dependence on excitation energy. When electrons are excited above the optical phonon energy they cool down in a subpicosecond time-scale to the bottom of the first subband. Electrons may even occur below thermal equilibrium energy and then slowly (during tens of picoseconds) relax to equilibrium due to interaction with acoustic phonons. At certain excitation energies strong intersubband electron scattering by optical phonons leads to carrier redistribution and intersubband population inversion.

Phonon confinement effect observed in longitudinal magnetophonon resonance in Al0.3Ga0.7As/GaAs superlattices with/without AlAs thin barriers

Electron-optical phonon interaction is studied in longitudinal transport through a series of Al0.3Ga0.7As/GaAs superlattices by measuring longitudinal magnetophonon resonance (MPR). In addition to well resolved MPR peaks caused by GaAs phonons, peaks ascribable to AlAs interface phonons are observed when a thin AlAs barrier is inserted at each GaAs/Al0.3Ga0.7As heterointerface. A calculation based on the Huang-Zhu model describes the features of experimental spectra. When the well width is reduced in Al0.3Ga0.7As/GaAs superlattices with narrow quantum wells, the AlAs-like phonon mode also becomes important in miniband transport.

Carrier capture and relaxation in narrow quantum wells

In separate confined heterostructure (SCH) lasers, injected electrons and holes thermalize into a quantum well after diffusion through the outer cladding layers. The carriers move towards equilibrium by emitting optical phonons. In narrow quantum wells, as compared to the 1-2 ps required in bulk semiconductors, this phonon emission process can be considerably slowed down due to the 2-D density of states and the nature of the electron-optical phonon interaction. This process has been studied theoretically using a Monte Carlo program which allows us to see the carrier distribution as a function of time. Typical times for carrier relaxation are 10-15 ps for a 50 /spl Aring/ GaAs well with Al/sub 0.30/Ga/sub 0.70/As barriers and /spl sim/5 pS for a 200 /spl Aring/ well. These calculations have been complemented by time-resolved photoluminescence measurements on SCH structures where the relaxation time from a 3D distribution into In/sub 0.20/Ga/sub 0.80/As/GaAs wells is measured at T=200 K. Carrier relaxation times of 50, 41, 22, and 17 ps are obtained for wells of sizes 30, 40, 50, and 100 /spl Aring/, respectively. The results show clearly that the use of narrow quantum wells in low threshold lasers will pose a serious limitation to the efficiency and small-signal modulation bandwidth of these devices. >

ELECTRON-OPTICAL PHONON INTERACTIONS IN POLAR SEMICONDUCTOR QUANTUM WELLS

Electron-optical phonon interactions in polar semiconductor quantum wells are reviewed. Three macroscopic and one microscopic models for electron-optical phonon interactions are compared with experimental results in GaAs-AlAs polar semiconductor quantum wells recently obtained by picosecond time-resolved Raman spectroscopy. The macroscopic model of Huang and Zhu as well as the microscopic model of Rucker et al. are found to be in good agreement with the experimental data. Direct measurements of electron-optical phonon scattering rates in GaAs-AlAs polar semiconductor quantum wells carried out by subpicosecond time-resolved Raman scattering technique are also presented. These experimental results are explained with the model of Huang and Zhu.

Intersubband relaxation dynamics in ternary/binary quantum wells: Role of the electron-optical phonon interaction

Ensemble Monte Carlo calculations of the intersubband dynamics in binary-ternary double-heterostructure systems are presented. The presence of a ternary alloy has been explicitly incorporated to account for complexities arising from the multimode nature of phonons in real heterostructures. Electronic scattering rates are derived as a function of energy and quantum-well width for both confined and interface modes on the basis of a continuum model. Results of Monte Carlo simulations yield an intersubband time constant that is in reasonable agreement with the experimental value, but only when details of the phonon modes and their dispersion, spreading of the electronic wave functions due to poor confinement, and the phonon amplification effects are comprehensively included.

Picosecond time-resolved Raman studies of electron-optical phonon interactions in ultrathin GaAs-AlAs multiple quantum well structures

Electron-optical phonon interactions in ultrathin GaAs-AlAs multiple quantum well structures have been studied by using picosecond time-resolved Raman spectroscopy. The authors experimental results have shown that the electrons primarily relax through the emission of interface optical phonons and that the electrons interact not only with GaAs-like interface phonons but also with AlAs-like interface phonons. The interaction strength of electrons with AlAs-like interface phonons has been shown to be much stronger than that of electrons with GaAs-like interface phonons for ultrathin GaAs quantum wells. The strength of electron-AlAs-like interface phonon interaction has been demonstrated to decrease very rapidly as the thickness of the GaAs well increases.

Electron-optical-phonon interactions in ultrathin GaAs/AlAs multiple quantum wells.

Nonequilibrium populations of both confined and interface phonons generated by picosecond laser pulses in a series of GaAs/AlAs quantum wells have been studied by time-resolved picosecond Raman scattering as a function of well width. The dependence of the nonequilibrium phonon populations on well width is found to be sensitive to the theoretical model which is used to describe the electron-phonon interaction. Our data disagree with the macroscopic model of electron-phonon interaction, but they are in excellent agreement with the microscopic model proposed recently by Huang and Zhu.

The optical polaron model in one-dimensional systems

The author shows that, for a Hamiltonian describing the electron-optical phonon interaction in one spatial dimension, the electron dynamics is described by an electron gas interacting through an exactly determined effective potential. He argues in favour of a critical coupling above which this system becomes unstable as regards a transition to a superconducting state.

Dynamical screening of the electron-optical phonon interaction in two dimensions

Abstract We have included dynamical screening in a calculation of the interaction of LO phonons with electrons in a quantum well. The average phonon emission rate is reduced by a factor of about 2 for an electron areal density of 5×1011/cm2 and temperature in the range of 50–100K. The 2-dimensional plasmon enhances the interaction over a small range of wavevectors, which increases the importance of hot phonon effects and should cause a further reduction in cooling rates.

Electron–Electron Interaction and Isotope Effects in Superconducting Metal–Hydrogen (Deuterium) Systems Like PdHx(Dx)

AbstractUsing various experimental and theoretical data the origin of the inverse isotope effect (IIE) for the superconducting transition temperature Tc of the PdH(D) system is analyzed on the basis of a solution of the Berk‐Schrieffer equations. It is found that the IIE can be described at weak or intermediate anharmonicity of the electron–optical phonon interaction β = (λ/ −1≈︁to 0.14, standard or slightly enhanced values of Coulomb pseudopotential μ', and weak spin fluctuations λsp ≈︁ 0.05 to 0.1. The importance of the electron‐electron interaction in determining the superconducting properties of non‐stoichiometric PdHx(Dx) and some other hydrides (deuterides) is emphasized.

Surface polarons in Voigt configuration

Surface polarons are observed in Voigt configuration cyclotron resonance in inversion layers on InSb. From the experiments we can deduce, that only the form of the electron wave function is important for the surface polaron effect. Screening of the electron-optical phonon interaction and influence of interface or two-dimentional optical phonons are not found.

On the Role of the Nonlocal Hartree-Fock (HF) Exchange in Narrow-Band Materials

The influence of the nonlocal Hartree-Fock (HF) exchange in narrow-band materials with finite band gaps is analyzed. The mean-field Hamiltonian in the crystal orbital (CO) basis contains two k-dependent matrix elements responsible for the dispersion of the one-electron levels: the classical tight-binding integrals (kinetic energy of the electrons) that decay exponentially as well as the (non)local exchange. The asymptotic behavior of the two-electron potential is determined by the fall-off of the intercell bond-order matrices; their range exceeds significantly the spatial extension of the k-dependent one-electron integrals. The analytic structure of the HF dispersions of narrow-band systems (weak intercell interactions) is largely influenced by the magnitude of the Fermi-correlation beyond the direct neighbors. The associated ε(k) curves differ strongly from idealized tight-binding relations. The bands are broadened and show enhanced energy gradients in certain domains of k-space. Nonlinearities in the ε(k) relations are a direct consequence of finite neighbor's approximations adopted for the evaluation of the lattice sums. The analytic structures of such HF bands are intermediate between idealized tight-binding relations of covalent solids, on one side, and HF dispersions of metals in (nearly-)free electron-gas approximations, on the other, that show divergent ε(k) gradients at the Fermi level. The exchange influence in insulating narrow-band materials is restricted to the filled one-particle space; this is demonstrated by a perturbational analysis. The crucial importance of reliable numerical integration procedures for the determination of the intercell bond-order matrices is pointed out. Standard techniques may lead to artificial periodicities pretending unphysical decay properties of the electronic exchange. Dispersion patterns of a simple one-orbital model are analyzed as a function of the mutual strength of the kinetic hopping integrals and the HF exchange as well as the spatial extension of the k-dependent two-electron potential. The validity of the theoretical expectations deduced from simple model calculations is studied for two complex polymers. Important one-electron properties of one-dimensional (1 D) porphyrinato nickel(II) derivatives (2 and 3) are investigated by means of semiempirical SCF (self-consistent-field) HF INDO (intermediate neglect of differential overlap) CO calculations. The lattice spacings of 2 and 3 differ by 0.31 Å. This geometrical distinction allows for an inversion of the relative importance of the k-dependent one- and two-electron contributions to the mean-field operator. The exchange influence on the width of the HF dispersion in 3 exceeds the one-electron part by nearly one order of magnitude. It is shown that band structure properties of narrow-band systems are neither properly described by one-electron models of the Wolfsberg-Helmholtz-type nor by bare (unscreened) HF dispersions. The width of a mean-field band calculated within a nonlocal exchange approximation has to be corrected for quasi-particle (QP) interactions beyond the HF scheme (i.e., long-range and short-range correlations and relaxations) as well as for electron (optical) phonon interactions. The phononic coupling leads to a narrowing of the band width via Franck-Condon-like vibrational overlaps; this part is independent of the theoretical details of the electronic structure investigation. Important physical consequences of the exchange-control in narrow-band solids are shortly discussed.

Interelectronic collisions and electron-optical phonon interactions in polar semiconductors: A criterion for the electron temperature model

In this letter a new criterion for the electron temperature model in polar semiconductors is proposed. This criterion accounts for the low energy e-e interaction which replenishes the depletion of electrons caused by intense optical phonon emission above the phonon energy h ̵ ω . It shows that a maxwellian distribution can hardly be achieved at all in the presence of polar optical phonon scattering and non-equilibrium conditions.

Effect of the electron-phonon interaction on the subband structure of inversion layers in compound semiconductors

Recently electron inversion layers have been fabricated on a number of compound (principally III–V) semiconductors. Because of the polar nature of these materials, the effect of the electron-optical phonon interaction is expected to be significant. This has certainly been true in recent calculations of the ground state energy and equilibrium density of electron-hole liquids in a number of compound semiconductors [1]. We have calculated the subband structure of inversion layers in polar semiconductors. The starting point of our many-body calculation is the Hartree subband structure determined using a variational method described in ref. [2]. Using the Hartree wavefunctions as basis functions we have calculated the self-energy of the ground and first excited subbands to lowest order in the effective interaction. This interaction is the sum of Coulomb (direct and image) and electron-phonon terms which are screened by a dielectric function that includes both e-e and e-ph effects. The screening by inversion layer electrons has been treated in the plasmon-pole approximation. We have obtained the electron self-energy, the quasi-particle energy, and the subband separations as a function of inversion layer concentration for parameters corresponding to GaAs. The coupling of electrons to bulk phonons is considered. Our results are compared to those obtained using the simpler ϵ 0 ∗ approximation [1]. Here, explicit phonon terms are neglected, but the bare band mass is replaced by the polaron mass, and the high frequency dielectric constant (ϵ ∞) is replaced by the static dielectric constant (ϵ 0). This approximation has been applied to the electron-hole liquid for situations in which the optical phonon frequency is larger than the electron plasma frequency. The idea behind the ϵ 0 ∗ approximation is to account in a very rough way for vertex corrections to the electron-phonon interaction. A principal criticism of our dynamic RPA calculations is the neglect of vertex corrections in the effective interaction. In three-dimensional metallic systems (high density), Migdal's theorem applies and vertex corrections are small. However, it is not clear that we may neglect such corrections in inversion layers. This point will be discussed further.

Electron- and phonon-polaron effects in TCNQ

Abstract The effects of electron correlation and electron-optical phonon interaction were investigated in the case of the valence- and conduction bands of pure TCNQ crystals using the electron-polaron model of Toyozawa and the Frohlich electron-phonon interaction Hamiltonian. The original Hartree-Fock bandwidths were reduced by a factor of ∼3–5 to 0.034 and 0.090 eV, respectively, and the forbidden gap decreased to ∼2.7 eV due to polaron formation.

Quantum theory of electron-optical phonon interaction in ionic crystal films

A quantum-mechanical treatment is developed for the interaction of an electron with optical phonons of an ionic crystal film. When applied to the case of a fast electron, the electron energy loss and gain spectra are obtained and agree well with the experimental data on LiF. The gain spectrum is obtained for the first time and shows the observed strong temperature-dependence. Losses through multi-phonon processes occur in the LO phonon energy range.

The influence of dielectric properties on the emission of a metal-dielectric-metal system: Traps, discussion of the transfer ratio

Under the assumption that the Fowler-Nordheim equation holds for the leakage current the influence of traps on the emission current from the sandwich cathodes is investigated. A simple model, describing the capture of electrons at the localized states in the forbidden band of the dielectric, their liberation by a thermal emission or by a field, the transmission of these electrons through the top metal electrode and the transfer into vacuum, has been proposed for this purpose. The expression obtained for the transfer ratio α is then discussed and compared with the other expressions derived in a preceding paper for ideal dielectrics, for dielectrics containing an elastic scattering mechanism and for electron-optical phonon interactions. It is shown that at the same intensity of various scattering processes the traps reduce the emission current to the highest degree.