Plasmon-phonon mode

A new experimental result is the observation of a broad and weak signal in the gap between the acoustic and optic branches and marked in fig. 23 with triangles. Such a mode has been observed before in IV chemically collapsed SmS by Mook et al. (1978). These modes are probably connected with bound heavy-electron plasmon-phonon modes where the f-like quasiparticles in the narrow bands below (described in section 4.1.1.2 and shown in figs. 2d and 14) couple to the phonons and perform collective oscillations. We recall that we have two plasrria oscillations, one for normal mass electrons and one for heavy mass electrons in the far infrared. It is the latter plasmon modes which are expected to couple to acoustic phonons in an out of phase motion as first proposed by Varma (1976). This idea has been quantitatively expanded in papers by Entel et al. (1979), Sinha and Varma (1983) and Stiisser et al. (1982). Further investigation of these modes seems necessary, however, they are only rarely observed (see also section 4.3.1.2). 

Fig, 74. (a) LA phonon dispersion in the [111] direction for intermediate-valent TmSe. An electronic plasmon mode is shown as the dashed horizontal line. Mixed electronic plasmon-phonon modes are shown with dotted lines. The heavy dashed line is the phonon mode without interaction, (b) Phonon density of states with (solid curve) and without (dashed curve) plasmon interaction. (After Treindl and Wachter 1980.)... 

Ions in the lattice of a solid can also partake in a collective oscillation which, when quantized, is called a phonon. Again, as with plasmons, the presence of a boundary can modify the characteristics of such lattice vibrations. Thus, the infrared surface modes that we discussed previously are sometimes called surface phonons. Such surface phonons in ionic crystals have been clearly discussed in a landmark paper by Ruppin and Englman (1970), who distinguish between polariton and pure phonon modes. In the classical language of Chapter 4 a polariton mode is merely a normal mode where no restriction is made on the size of the sphere pure phonon modes come about when the sphere is sufficiently small that retardation effects can be neglected. In the language of elementary excitations a polariton is a kind of hybrid excitation that exhibits mixed photon and phonon behavior. 

Therefore the dispersion of the LO plasmon-phonon states is formally equivalent to the dispersion of the TO photon-phonon states, with 4irne2/m replacing k2 c2. When the plasmon-phonon frequency to is plotted against fn instead of k, dispersion curves for the LO modes are obtained which are similar to the polariton dispersion curves, the TO phonons showing no dispersion with /n. 

FIGURE 1 Phonon, plasmon and phonon-plasmon coupled modes in Raman and infrared reflection spectroscopy as a function of free electron density (+ data from [25], see also [3]) [24],... 

Infrared absorption in typically highly n-type bulk GaN is mainly controlled by free carrier absorption [37,38], Infrared reflection of phonons and phonon-plasmon coupled modes in GaN in the range of the reststrahl band has been reported [1,8,9,37], Similarly to the interpretation of coupled modes in Raman... 

The first investigation of the phonon modes in binary InN was an extrapolation of the Gai-xInxN (0 < x < 1) alloy modes in reflection towards the binary compound [1], A typically high free carrier concentration in the mid 1020 cm 3 range controls the absorption (Drude absorption) in the infrared and must also account for the broadened Reststrahlen band in pure InN films (e.g. in [1]). In this case infrared active phonons couple to the plasma of the free electrons forming phonon-plasmon coupled modes [10,11], However, layers of low carrier concentration have been achieved and pure LO phonon energies have been derived in Raman spectroscopy. Resonant Raman spectroscopy at 514 nm has been performed, assigning five of the six Raman allowed zone centre phonon modes [8,9] (TABLE 1). 

Despite resonant excitation conditions (Egmp(InN) 1.9 eV) the Raman spectrum of InN strongly resembles that of GaN although shifted to softer modes. Note, however, that the sequence of E2(LO) and Ai(LO) appears to be inverted compared to GaN. The Ei symmetry assignment of the reflection modes [1] was performed in [7] and by the present authors after a re-evaluation of the data. In addition, the large value of 694 cm 1 indicates an E1(LO)-plasmon coupled mode. It may be assumed that phonon frequencies in heteroepitaxial InN are subject to stress conditions in a similar way to that in heteroepitaxial GaN. 

The free carrier concentration at room temperature was determined by Raman experiments using the Ai(LO) phonon-plasmon coupled mode and by the reflectance in the mid-infrared and the optical absorption in the near-infrared range. Each experiment for the GaN layer of 60 pm thickness showed a free carrier concentration in the order of 1017 cm 3. 

The plasma frequency corresponds to an oscillation as a whole of the electronic charge density with respect to the fixed ionic charge. By analogy with the phonon excitation, the corresponding excitation is called plasmon and it can be considered as the quantization of classical plasma oscillation. The plasmon oscillation is longitudinal with respect to its propagation and is comparable to the TO phonon mode. The macroscopic electric field associated... 

In a heavily N-doped 6H sample (6xlOl9cm 3) Klein et al [34] observed an asymmetric broadening and a shift of the A,(LO) phonon which were attributed to the overdamped coupling between LO phonon and plasmon modes [35]. The interaction between these two excitations occurs via their macroscopic electric fields when the frequency of oscillation of a free-carrier plasma is close to that of the LO phonon. The dependence of the LO phonon-overdamped plasmon coupled modes on carrier concentration was reported by Yugami et al [36] in 3C-SiC films, where the carrier concentrations varied from 6.9 x 1016 to 2xl0,scm 3. They verified that the carrier concentrations obtained from RS were in fairly good agreement with the Hall measurement values, and that the Faust-Henry coefficient [35] for the 3C-SiC (C = + 0.35) was close to the value reported for 6H-SiC (C = + 0.39) [34]. 

Doping EuO has no strong influence on the TO mode, for EuO+ 1.26% Gd it shifts to shorter wavelengths by about 10% (Giintherodt and Wachter, 1973c). However, as new effect one observes now a coupling between plasmons and LO phonon modes, resulting in a more phonon like mode and a more plasmon like u- mode. 

Figure 5 Raman spectra of annealed Al-doped n-ZnSe recorded with parallel and crossed polarizations of incident and scattered light. In addition to the ZnSe TO and weak LO phonons, peaks of the upper (co ) and the lower branch (a> ) of the LO-plasmon coupled mode can be observed at parallel polarization. (Reproduced from Ref. 31.)... 

To study the carrier and vibrational relaxation dynamics, mode-locked laser systems, which provide femtosecond pulses and fast and sensitive detection systems are necessary. For detection, streak cameras are used for measurements with time resolution in the subpicosecond range or CCD cameras for time-integrated measurements. For the latter, time resolution can be achieved by using optical Kerr gates or upconversion [266,268]. In general, the two mainly used optical detection mechanisms for coherent phonons (optical, acoustical, or LO-plasmon coupled modes) are the pump/probe [280-285] and the four-... 

M Ichimura, A Usami, T Wada, Sz Fujita, Sg Fujita. Observation of phonon-plasmon coupled modes at the interface between ZnSe and semiinsulating GaAs by micro-Raman spectroscopy. Appl Phys Lett 62 1800-1802, 1993. 

The specific character of properties, demonstrated by nanoccmiposites is determined by the small size (units of nanometers) of filler partides, comparable with the wavelength of electron, which leads to the so called quantum size effects and the essential ratio of surface to volume in such systems, which increases the role of particle surface and interfaces between particle and polymer media (e.g., in a SO A CdS partide, about 15% of the atoms are on the surface). The latter fact is the reason for the higher chemical activity of nanoparticles and the increase in the role of such surface excitations as surface plasmons in small metal particles and spedfic surface phonon modes both as the increadng role surface states, espedally surface traps in semiconductor nanopartides. 

Free-charge carriers in semiconductors form collective excitation modes, the so-called plasma mode (plasmon). The plasma modes will couple to the LO lattice modes and form the so-called coupled LO plasmon-phonon (LPP) modes. Depending on the strength of the coupling, the free carriers thereby influence the dielectric function. A possible contribution from free carriers to the dielectric functions is also accounted for by virtue of the classical Drude model [38] ... 

Free carriers from plasmons in semiconductors, which interact with LO phonon modes and form LO phonon-plasmon coupled modes. Figure 15 shows the Raman peak positions for the TO and LO modes as a function of carrier concentration in 3C-SiC epilayers. The frequency of the LO band increases with increasing free carrier density, which shows that the LO-phonon band is coupled with the overdamped plasmon. Yugami et al. (78) have obtained the carrier concentrations by line shape fitting of the coupled modes and compared them with the values derived from Hall measurements. They found good agreement between the values derived by... 

In photoexcited polar semiconductors, the coherent LO phonons couple with photocarriers to form coherent LO phonon-plasmon coupled (LOPC) modes, which exhibit fundamentally different properties from those of bare phonons. Huber and coworkers revealed the ultrafast transition of an optical... 

The wide spread of studied material has led to some uncertainty in phonon frequencies, especially of the LO modes. Recently, however, the coupling to plasmons in doped material and stress induced effects due to lattice mismatch with the substrate have been separated. Aj(LO) lies close to Eg in sapphire and has been confused in Raman experiments. In 2 pm GaN/sapphire (0001) [9] modes are within 1 cm 1 of values in bulk GaN (TABLE 1). 

Infrared active modes couple to the free carrier plasma and the energy of the coupled phonon-plasmon mode is sensitive to the electron density [3,20-22], In the range 1 x 1017 cm 3 < n < 1019 cm 3 the following approximation can be used for the free electron density as a function of the Ai(LO) mode frequency vmax [21] ... 

Free carriers change Raman spectra, either by single particle contribution to the spectrum, or by phonon- plasmon interaction. In addition, interference of electronic transition continua with single phonon excitations may lead to Fano line shapes, as mentioned in the introduction. The Fano effect is encountered in p-doped Si crystals, as shown in Fig. 4.8-19. The shown lines correspond to the respective Raman active mode at 520 cm for crystals with 4 different carrier concentrations, excited with a red laser. The continuous line is calculated according to Eq. 4.8-6. Antiresonance on the low frequency side and line enhancement on the high frequency side are a consequence of the positive value of Q. A reverse type of behavior is possible in the case of a negative Q. 

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