Plasmon-phonon Modes Research Articles

Electron-phonon interaction, dynamical screening and collective excitations in heterostructures: III. Coupled intra- and intersubband plasmon-phonons

The complete spectrum of elementary excitations for the quasi two-dimensional electron gas interacting with the optical phonons of semiconductor heterostructures is calculated within the random-phase approximation. The dispersion curves of the coupled intra- and intersubband plasmon-phonons are plotted in graphical form for various cases. Considering the intersubband mixing we found that this yields only a very weak contribution to the dispersion curves of the plasmon-phonon modes. The theoretical results for the dispersion curve of the (0-0) intrasubband plasmons obtained, including exchange and correlation effects, coupling to the long-wavelength optical phonons, intersubband mixing and screening effects of the grating on top of the sample agree very well with experimental results from far-infrared transmission spectroscopy.

Raman scattering from coupled plasmon-phonon modes in HgTe.

An inelastic-light-scattering experiment from the (100) face of p-type HgTe, a zero-band-gap semiconductor, is reported. The spectral features, which involve coupling of the longitudinal phonon mode with the multicomponent plasma comprised of light electrons in the ${\mathrm{\ensuremath{\Gamma}}}_{8}^{\mathit{c}}$ conduction band and heavy holes in the ${\mathrm{\ensuremath{\Gamma}}}_{8}^{\mathit{v}}$ valence band, are analyzed by calculating Im[${\mathrm{\ensuremath{\epsilon}}}^{\mathrm{\ensuremath{-}}1}$(q,\ensuremath{\omega})], where \ensuremath{\epsilon}(q,\ensuremath{\omega}) is the frequency- and wave-vector-dependent dielectric function of the medium. The sharp peak at 138 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ is ascribed to ``forbidden'' LO-phonon scattering. The partially screened allowed LO phonon appears as a broad peak around 127 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, which is higher than the TO-phonon frequency (\ensuremath{\sim}118 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$). The hole carriers give rise to additional features in the spectrum around 160 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. The results of infrared-reflectivity measurements by Grynberg et al. are also discussed in light of Raman data. While the ir spectra can be analyzed using \ensuremath{\epsilon}(\ensuremath{\omega}), it is seen that a finite wave vector involved in the light-scattering experiment modifies the phonon-plasmon spectrum profoundly.

Doping density dependence of intersubband transitions in GaAs/AlxGa1−xAs quantum-well structures

Intersubband transitions in GaAs/AlxGa1−xAs quantum wells have been studied as a function of the doping level by Raman scattering and infrared absorption. The n-type dopant concentration placed in the well was varied between 1×1018 and 8×1018 cm−3. With increasing doping level Raman scattering reveals a frequency down-shift of the single-particle intersubband transition and a shift to higher frequencies of the collective intersubband plasmon-phonon mode. The resonance in infrared absorption follows closely the collective mode observed in Raman scattering, demonstrating clearly that the doping-dependent depolarization shift of the absorption peak is an important parameter that must be taken into account in device design. Possible models for the frequency down-shift of the single-particle transition are also discussed.

Subband structure and plasmon-phonon coupled excitations in the accumulation layer of ZnO.

Calculations of electronic subbands and collective excitations are presented for strong accumulation layers in ZnO. Our model for this system is that of a free-electron gas with an effective mass embedded in a dielectric medium that supports lattice vibrations. Allowance is made for the conduction electrons to tunnel into the surface barrier. The effects of a position-dependent effective mass and of exchange and correlation are also considered. Using a nonlocal dielectric response formalism based on the random-phase approximation, we obtain the dispersion and line shapes of both intrasubband and intersubband plasmons. Evidence is found for two-dimensional intrasubband plasmons, as well as intersubband and ``acoustic'' plasmons; the latter have a nearly linear dispersion relation. When lattice vibrations are included, coupled plasmon-phonon modes or ``plasmarons'' are obtained. Some of these modes have been observed in earlier high-resolution electron-energy-loss spectroscopy experiments.

Inelastic scattering in a doped polar semiconductor.

We calculate, within a many-body theory, the inelastic-scattering rate for hot electrons injected into doped GaAs as a function of electron energy and doping density by treating Coulomb and Fr\"ohlich interactions on an equal footing. Our theory, which includes effects of quantum degeneracy, dynamical screening, plasmon-phonon mode coupling, and phonon self-energy correction, is in excellent quantitative agreement with recent experimental findings, and resolves a puzzle about why a recent observation of single-optical-phonon emission in highly doped GaAs can be quantitatively explained by unscreened theoretical results.

Raman and IR spectroscopies: a useful combination to study semiconductor interfaces

We report on the lattice-matched semiconductor combination InSb/CdTe. Raman scattering by vibrational modes was used to identify chemical phases (In 2Te 3, Sb) at the interface formed in the molecular beam epitaxial growth of InSb/CdTe heterostructures. Far-IR spectroscopy, in particular, revealed the presence of a free electron gas at the interface and allowed a quantitative description of its properties. As a consequence coupled longitudinal optical phonon-plasmon modes were also observed by Raman scattering. It was thus possible to probe the chemical nature as well as the electronic properties at the semiconductor interface as a function of growth conditions by a combination of both Raman and far-IR spectroscopic techniques.

Collective excitations in the accumulation layer of InAs(110): Nonlocal response theory.

We discuss plasmon and phonon modes in the accumulation layer of a model semiconductor with the aid of calculations based on a nonlocal description of dielectric response in the random-phase approximation. The first model we consider is that of a polarizable jellium slab at finite temperature with surface charges that bend the bands downward; lattice vibrations are ignored. Choosing model parameters appropriate to lightly doped InAs(110) at room temperature, we obtain intersubband as well as intrasubband plasmons and discuss their dispersion relations, localization, and line shapes. Evidence for two-dimensional and ``acoustic'' plasmons is presented: dispersion relations that have square-root and linear behavior at long wavelengths, respectively. All plasmon modes are strongly damped when their dispersion curves enter the single-particle continua. When the dynamical response of the lattice is included in the model, we obtain coupled plasmon-phonon modes or ``plasmarons'' and study their dispersion and line shapes. Our results confirm and extend the interpretation of high-resolution electron-energy-loss spectroscopy data reported recently for InAs(110) exposed to atomic hydrogen.

Quasiparticle properties of a coupled two-dimensional electron-phonon system.

We calculate quasiparticle properties of a weakly polar two-dimensional electron gas by taking into account both electron-electron Coulomb and electron--optical-phonon Fr\ohlich interactions. Electronic self-energy is calculated exactly in the leading order of the total effective dynamical interaction. The total effective dynamical interaction is obtained within the random-phase approximation (RPA) by starting from the total bare interaction, which includes both Coulomb and Fr\ohlich interactions and then by screening it with all the bubble diagrams. Our theory thus treats Coulomb and Fr\ohlich interactions on an equal footing and includes all effects (within the RPA) of Fermi statistics, Landau damping, plasmon-phonon mode coupling, phonon self-energy correction, and dynamical screening. We include finite-thickness effects in actual GaAs-based semiconductor microstructures by considering electron- and phonon- (``slab modes'') confinement effects. Some of our interesting results are (1) Coulomb and Fr\ohlich interaction effects are nonmultiplicative, and the actual many-body correction for an electron gas is substantially different from the one-polaron result; (2) there are interesting and observable plasmon- and phonon-induced satellite structures in the low-energy side of the electronic spectral function and the density of states; (3) at low electron densities phonons tend to screen Coulomb interaction, whereas at large electron densities electrons screen the Fr\ohlich interactions; (4) our calculated effective mass and inelastic-scattering length are consistent with the available experimental results.

Analysis of Raman Spectra from Heavily Dopedp-GaAs

A theory of Raman scattering by both coupled LO phonon-plasmon (LO-PL) modes and surface “unscreened” LO phonons in a doped semiconductor is presented with a simple two-layer (surface depletion layer-bulk substrate) model. Effects of the optical penetration depth and the depletion layer thickness on the line shape are examined. The theory is applied to an analysis of Raman spectra from a (100) surface of p -GaAs, and reproduces experimental profiles very well. An analysis suggests that the observed broad band near the transverse optical phonon frequency is ascribed to the lower branch of the coupled LO-PL modes.

Theoretical and experimental study of Raman scattering and infrared reflectivity in indium phosphide.

Room-temperature Raman and infrared-reflectivity measurements are performed on semi-insulating InP doped with Fe and on n-type InP doped with Sn and S in the concentration range from 6.8\ifmmode\times\else\texttimes\fi{}${10}^{17}$ to 1\ifmmode\times\else\texttimes\fi{}${10}^{19}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$. In the Raman spectra low(${\ensuremath{\omega}}_{\mathrm{\ensuremath{-}}}$)- and high(${\ensuremath{\omega}}_{+}$)-frequency coupled plasmon--LO (\ensuremath{\Gamma})-phonon modes are observed. The ${\ensuremath{\omega}}_{\mathrm{\ensuremath{-}}}$-mode linewidth shows a definite concentration dependence with the lines narrowing as the concentration is increased. A broad minimum due to the coupled plasmon-phonon modes of the infrared-reflectivity spectrum shifts towards high photon energies with increasing carrier concentration. The spectra are calculated by using the same semiclassical model of permittivity as in the interpretation of the Raman spectra. From the best fit to the experiment, energy values and damping constants of the ${\ensuremath{\omega}}_{\mathrm{\ensuremath{-}}}$ and ${\ensuremath{\omega}}_{+}$ modes are obtained. The carrier concentrations also determined from the infrared spectra with the aid of the model are in good agreement with those obtained from the Raman spectra.

Electron plasma in a non-parabolic conduction band

The electron plasma in highly n-doped GaAs and InP is significantly influenced by the nonparabolicity of the conduction band. Its properties for densities up to 2·10 19cm −3 have been studied experimentally by Raman scattering of coupled plasmon-LO-phonon modes. The Raman spectra and the dispersion of the plasmon-phonon modes were described by evaluating the Lindhard-Mermin dielectric function including the nonparabolicity of the band structure with the carrier concentration and the electron collision time as the only free parameters. It turns out, that this procedure is a very sensitive method to determine the carrier concentration of a sample.

Free-carrier density determination in p-type GaAs using Raman scattering from coupled plasmon-phonon modes

A nondestructive optical means of determining the activated hole concentration in p-type polar semiconductors is described. The Raman spectra from coupled plasmon-longitudinal-optical-phonon modes in five samples of Be-doped GaAs are measured and fitted using a theory which takes into account the degenerate light- and heavy-hole valence bands. The results indicate that coupled plasmon-longitudinal-optical-phonon modes in p-type material differ both quantitatively and qualitatively from those in n-type semiconductors.

The effect of hot phonons and coupled phonon-plasmon modes on scattering-induced NDR in quantum wells

We have extended our Monte Carlo simulation of scattering-induced NDR in Al. 8Ga 2As/GaAs quantum wells by including (a) the effect of hot phonons (b) coupled phonon-plasmon modes (c) degeneracy. Hot phonons were modelled using a phenomenological lifetime which we ranged from 3ps to 10ps. Coupled modes were modelled in the antiscreening approximation. Bulk-like modes were assumed in both cases. NDR is quenched if the phonon lifetime exceeds 7ps, but is little affected if the lifetime is 3ps. The effect of coupled modes is appreciable at a doping density of 10 18cm −3, virtually eliminating NDR, but at 10 17cm −3 the effect is much smaller. Including degeneracy has only a small effect on the results. We conclude that NDR is still possible at electron densities around 10 17cm −3.

Phonon, plasmon and gap behavior in superconducting high-T c Y 1Ba 2Cu 3O 7 and Gd 1.5Ba 1.5Cu 3O 7

Infrared and Raman spectra (50 – 600 cm -1 of superconducting Y 1Ba 2Cu 3O 7 and Gd 1.5Ba 1.5Cu 3O 7 (T c(onset) = 91 − 95K) show strong phonon modes nearly independent of the rare earth (at 93–100, 158, 198–201, 270–275 and 298–311 cm -1) and low plasma frequencies ( ω p = 450 − 1220 cm -1 ; 0.06 − 0.15 eV). Data below T c are fitted in detail with 2Δ kT c = 3.6 ± 0.2 using a minority of superconducting carriers. Temperature-dependent longitudinal plasmon-phonon modes at 233 cm -1 (near the gap) and at 140–155 cm -1 may be associated with plasmon-mediated superconducting processes.

Discrete coupled plasmon-phonon modes in finite semiconductor multi-layers

The coupled intra subband-phonon dispersion in N equally spaced quasi two-dimensional electron gas layers embedded in a polar semiconductor is analysed. The interactions of the Giuliani-Quinn surface plamon excitations with surface and bulk phonons are also investigated.

Effect of rapid thermal annealing on ion-implanted and neutron transmutation-doped GaAs

Raman spectroscopy with optical multichannel detection was used to study Se+ implanted and neutron-transmutation doped GaAs, both before and after rapid thermal annealing. Samples implanted at room temperature showed an amorphous surface layer, whereas those implanted at 320 °C exhibited Raman features of both amorphous and crystalline GaAs. After rapid thermal annealing, the material implanted at elevated temperatures showed a better structural recovery, as indicated by a lower intensity of forbidden phonon scattering. Using resonance Raman effects, we were able to discriminate between amorphous and crystalline features in the spectra. For the neutron-transmutation doped GaAs, the as-irradiated material showed a Raman spectrum similar to the one of undoped crystalline GaAs. The increase in electrical activation with increasing annealing temperature was monitored by Raman scattering from coupled plasmon-phonon modes, giving a carrier concentration comparable to the one obtained from Hall measurements.

Picosecond Raman scattering from photoexcited plasmas in InP with spatial and temporal resolution.

Picosecond, time-resolved Raman scattering spectra from photoexcited plasmon-phonon modes in semi-insulating InP are presented. Spectra of plasmas ranging in density from 0.1\ifmmode\times\else\texttimes\fi{}${10}^{17}$ to 5.0\ifmmode\times\else\texttimes\fi{}${10}^{17}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ are quantitatively fitted by extending equilibrium n-type plasmon-phonon scattering theories to include contributions from free holes. A novel application of time-resolved Raman scattering to measure the ambipolar diffusion coefficient and surface recombination velocity of nonequilibrium semiconductor plasmas is demonstrated.

Surface and interface phonon and plasmon excitations in iii-v semiconductor materials

The long range nature of dipolar scattering in HREELS of III-V materials gives the technique the ability to probe into the solid over a variable length range up to about 1000Å. This allows us to investigate the layer profile of heterostructures via excitation of surface and interface phonon modes. In doped materials, beam energy dependence of the intensity of coupled plasmonphonon modes provides information about carrier distribution close to the surface. We present examples of the application of HREELS to GaAs/Ga 1-XAl XAs heterostructures and both n- and p-type GaAs(100). Procedures needed to avoid carrier depletion at the surface of the samples are described.

Noncontact electrical characterization of epitaxial HgCdTe

It is important to be able to nondestructively characterize (‘‘screen’’) the electrical properties of those areas of HgCdTe epitaxial material that will later be made into devices. This paper compares several noncontact techniques for measuring resistivity, carrier concentration, and mobility with the standard Hall-effect technique. The noncontact techniques examined are far-infrared reflection, Raman scattering, eddy–current absorption, and electroreflectance. Of these techniques, far-infrared reflection was found to be the best noncontact technique for measuring resistivity, carrier concentration, and mobility. Resistivity values were within a factor of 2 of Hall-effect values, while carrier concentration and mobility values that depend on an assumed effective mass were within a factor of 3. In Raman scattering, interference between the free-carrier plasmon–phonon mode and other modes makes it an inaccurate method for estimating carrier concentration. Eddy–current absorption is useful for quickly measuring epitaxial layer resistivities to within a factor of 3 of Hall-effect values, while electroreflectance gives a relative value for the surface doping density, which is useful in layer profiling.

Raman scattering by coupled plasmon-phonon modes in n-type Ga1−xAlxAs epitaxial layers

Raman scattering by coupled plasmon-phonon modes in Ga0.75Al0.25As epitaxial layers grown by molecular beam epitaxy and metalorganic chemical vapor deposition was studied. Good agreement between predicted and observed behavior was found. It was concluded that Raman scattering can be conveniently used for nondestructive and fast evaluation of free electron concentration in these materials.