Plasmon-phonon Modes Research Articles

Study of the dielectric function of PbSnTe epitaxial film by far-infrared reflectivity

Far-infrared reflectivity measurements have been carried out from \ensuremath{\sim}40 to 320 ${\mathrm{cm}}^{\ensuremath{-}1}$ on a ${\mathrm{Pb}}_{0.88}$${\mathrm{Sn}}_{0.12}$$\mathrm{Te}$ epitaxial film of low carrier concentration ($p\ensuremath{\sim}{10}^{16}$ ${\mathrm{cm}}^{\ensuremath{-}3}$) on a high-carrier-density ($p\ensuremath{\sim}{10}^{18}$ ${\mathrm{cm}}^{\ensuremath{-}3}$) ${\mathrm{Pb}}_{0.78}$${\mathrm{Sn}}_{0.22}$Te substrate. The reflectivity data were analyzed using a two-oscillator dielectric function including free-carrier and phonon linewidths. An upper bound for the LO-phonon frequency was determined to be 115.7 ${\mathrm{cm}}^{\ensuremath{-}1}$ at room temperature and 113.5 ${\mathrm{cm}}^{\ensuremath{-}1}$ at liquid-${\mathrm{N}}_{2}$ temperature. Other parameters obtained were the phonon linewidth $\ensuremath{\gamma}=19$ ${\mathrm{cm}}^{\ensuremath{-}1}$ at room temperature and 12 ${\mathrm{cm}}^{\ensuremath{-}1}$ at liquid-${\mathrm{N}}_{2}$ temperature, and the substrate free-carrier linewidth $\ensuremath{\nu}=81$ ${\mathrm{cm}}^{\ensuremath{-}1}$ at room temperature and \ensuremath{\sim}70 ${\mathrm{cm}}^{\ensuremath{-}1}$ at liquid-${\mathrm{N}}_{2}$ temperature. An analysis of the oscillatory behavior of the reflectivity at frequencies above the highest plasmon-phonon mode permitted the determination of the spatial variation of carrier concentration in the region of the film-substrate interface.

Free carriers, coupled modes, and the generalized dielectric function in PbTe

The reflectivity of $n$-PbTe has been measured at 300\ifmmode^\circ\else\textdegree\fi{}K in the range 16-235 ${\mathrm{cm}}^{\ensuremath{-}1}$ for samples with carrier concentrations between 2 \ifmmode\times\else\texttimes\fi{} ${10}^{17}$ and 2 \ifmmode\times\else\texttimes\fi{} ${10}^{19}$ ${\mathrm{cm}}^{\ensuremath{-}3}$. Both the conventional two-oscillator dielectric function and the generalized function ${\ensuremath{\epsilon}}_{K}$ proposed by Kukharskii were used to fit the data with equally valid results. Unlike previous low-temperature measurements there was no serious difference between the dc and optical values for the free-carrier scattering time $\ensuremath{\tau}$ except at the highest concentration where $\frac{{\ensuremath{\tau}}_{\mathrm{dc}}}{{\ensuremath{\tau}}_{\mathrm{opt}}}=3$. This discrepancy may be related to screening effects. Kukharskii's extended Lyddane-Sachs-Teller relation was found to hold despite the relatively heavy damping. ${\ensuremath{\epsilon}}_{K}$ was used to analyze the damped plasmon-phonon modes and indicated the presence of an overdamped mode at very low frequencies. The lattice damping constant was found to be 21\ifmmode\pm\else\textpm\fi{}5 ${\mathrm{cm}}^{\ensuremath{-}1}$, a value comparable to that measured in PbSe but much larger than is typical for other semiconductors.

Enhanced interband recombination in Pb1−xSnxTe

Photoconductive measurements have been performed on Pb1−xSnxTe in the small-energy-gap region. Experimentally observed shortening of the photoconductive lifetime is inferred to occur as a result of strong coupling of photoexcited carriers to some elementary excitations (phonon and phonon-plasmon modes) in the material. Applications to fast infrared detectors are discussed.

Generalized dielectric function and the plasmon-phonon coupling in GaAs and CdTe

Far infrared (12–235 cm -1 reflectivity data for GaAs and CdTe have been fitted equally well with the usual two-oscillator dielectric function and Kukharskii's generalized form ϵ K . Kukharskii's extended Lyddane—Sachs—Teller relation was confirmed and the quantities appearing in ϵ K agreed fairly well with other determinations. ϵ K was used to analyze the damped plasmon-phonon modes.

Dispersion of plasmon-phonon modes in semiconductors: Raman scattering and infrared spectra

In n-InP and n-GaAs the Raman scattering spectra from plasmon-phonon modes (PPM) with wave vector q ⋍ 10 6 cm -1 have been measured. The frequencies of PPM thus obtained are different from plasmon-phonon frequencies at q ⋍ 10 3 cm -1 evaluated from infrared reflectivity spectra. This difference is explained in terms of the spatial dispersion of PPM. Good agreement between observed and calculated frequencies is obtained. Additional broadening in Raman scattering spectra due to Landau damping has been observed. The observed shift of the bands in Raman spectra with different polarization of the scattered light relative to each other has been explained by taking into account the frequency dependence of the phonon contribution into the scattering, cross-section.

Study of the Dispersion Relations of the Coupled Phonon-Damped Plasmon Mode inn-GaAs by Light Scattering

Recent developments of the study on the coupled LO phonon-electron system are described. A special attention is paid to the behavior of a coupled mode in the Landau damping region in n·GaAs. Capability of the light scattering is also discussed for getting information about the semiconductor surfaces as well as the dispersion and damping of the mode. The study of electron and phonon interactions is of fundamental im­ portance in polar semiconductors. The longitudinal optical (LO) phonons interact with carriers through longitudinal polarization field, causing the well known polaron effects!) as well as a shift of the LO phonon frequency. 2>•3> The existence of the coupled LO phonon-plasmon modes was first predicted by Yokota in the long wavelength limit. 4> Gurevich et al. independently discussed the dispersion of the coupled modes in connection with the possibility of superconductivity in semiconductors. 5) The LO phonon-plasmon system was further studied theoretically for the degenerate polar semiconductors, G),7) where the usual self consistent field method is reliable. 8) Such a treatment is closely related to the theory of the coupled electron-ion system in simple metals. 9>• 10> Fallowing the invention of the laser sources, the opening of the Renaissance was notified in the light scattering spectroscopy which had been a valuable tool in the investigation of vibrational and rotational energy levels of molecules as well as the determination of phonon frequencies in crystalline solids.11> Accordingly theoretical aspects of light scattering also entered upon a new phase. Many exciting effects have been discovered in the field of light scatter­ ing in this decade. Elementary excitations such as phonons, plasmons, magnons and polaritons as well as single particle excitations have been studied extensively_l2)~ 15) Experimental researches on LO phonon and high density

Phonon-plasmon modes in small GaN crystals

The absorption of i.r. radiation in GaN crystallites about 3 μ in size has been measured. Variations in the spectra of different samples have been explained in terms of differing free carrier concentrations. Absorption bands due to surface and bulk phonon-plasmon modes have been identified by comparison with theoretical spectra calculated for small GaN spheres.

Optical properties and electronic structure of europium chalcogenides

The normal incidence reflectivity of europium chalcogenide single crystals and of Gd doped EuO has been measured at room temperature in the spectral region from 250 μm to 12 eV and has been analyzed in terms of the optical constants. In addition, in a reduced spectral region from 0.5 to 6 eV, the optical constants have been evaluated by means of a polarimetric method, as well above as below the magnetic ordering temperature. To enhance the resolution of the magneto-optical transitions, a modulation technique has been applied with a magnetic field as modulating parameter. The Kramers-Kronig relation has been used to analyze the normal incidence reflectivity and the magnetoreflectance spectra in terms of, respectively, the optical constants and the changes in the real and imaginary part of the dielectric response function. For Gd doped EuO the Kramers-Kronig analysis has revealed plasmon and coupled plasmon-phonon modes. The interband transitions of the europium chalcogenides are discussed within the framework of recent APW and OPW energy band calculations. On the other hand we have derived an energy level scheme of the europium chalcogenides from our optical data.

Surface effects on optical phonons and on phonon-plasmon modes

The size and shape dependence of the properties of long wave optical phonons in polar crystals is discussed. The main effect occurring due to the presence of surfaces is the appearance of a surface optical phonon band in the frequency region between the frequencies ω t and ω l of the long wave transverse and longitudinal bulk modes. The surface modes give rise to strong absorption peaks in the infrared absorption spectra of small samples. For very small crystallites the surface mode absorption is dominant, and as the size of the specimens is increased, the ratio of surface to bulk mode absorption decreases. It is shown that the large spread in particle sizes usually encountered in experimental work and the increased damping of the phonon modes in small samples both tend to obscure the fine structure of the absorption spectrum. The surface phonon-plasmon modes in polar crystals containing free carriers are treated in an analogous manner.

Surface plasmon-phonon interaction in n-InSb

The mixed plasmon-phonon surface modes (SM) in n-InSb have been investigated by the modified attenuated total reflection method. The concentration dependence of SM has been found in the concentration range 1.5 × 10 16 − 1.1 × 10 18 cm −3. The dispersion curves of mixed SM have been obtained. The effect of repulsion of surface phonon and plasmon modes near their crossing point has been observed. The experimental results are compared with the theoretical calculations. Possible reasons of additional damping of SM are discussed.

Size effects on plasmon-phonon modes in polar semiconductors

The coupled plasmon-optical phonon modes in a finite sample of a degenerate polar semiconductor are studied in the long wavelength limit. The novel feature resulting from the finiteness of the crystal is the existence of surface modes. The manifestation of these modes in the infrared absorption spectra of small samples is disucssed. The effects of the application of a magnetic field are also investigated.

Size effects on plasmon-phonon modes in polar semiconductors

Size effects on plasmon-phonon modes in polar semiconductors