Phonon optical

MaxweU-Boltzmann distribution. At high electric fields, E > 10 kV/cm, no longer increases with electric field and approaches a limiting saturation speed, determined primarily by optical phonon emission. Eigure 3 shows the variation of drift speed with electric field for electrons and holes in various semiconductors. 

Momentum conservation implies that the wave vectors of the phonons, interacting with the electrons close to the Fermi surface, are either small (forward scattering) or close to 2kp=7i/a (backward scattering). In Eq. (3.10) forward scattering is neglected, as the electron interaction with the acoustic phonons is weak. Neglecting also the weak (/-dependence of the optical phonon frequency, the lattice energy reads ... 

The continuum model with the Hamiltonian equal to the sum of Eq. (3.10) and Eq. (3.12), describing the interaction of electrons close to the Fermi surface with the optical phonons, is called the Takayama-Lin-Liu-Maki (TLM) model [5, 6], The Hamiltonian of the continuum model retains the important symmetries of the discrete Hamiltonian Eq. (3.2). In particular, the spectrum of the single-particle states of the TLM model is a symmetric function of energy. 

Bulk phonon modes are absent in wave numbers near 357 cm , the center-frequency of the second band. According to electron energy loss studies done in a vacuum [52, 53], TMA-free TiO2(110) surfaces exhibit surface optical phonons at 370-353 cm . The 357-cm band is related to the surface optical phonons. 

Chang, Y. M., Xu, L. and Tom, H. W. K. (1997) Observation of coherent surface optical phonon oscillations by time-resolved surface second-harmonic generation. Phys. Rev. Lett., 78, 4649-4652. 

Chang, Y.-M., Lin, H. H., Chia, C. T. and Chen, Y. F. (2004) Observation of coherent interfacial optical phonons in GalnP/ GaAs/GalnP single quantum wells. Appl. Phys. Lett., 84, 2548-2550. 

Melnikov, A. V., Radu, I., Bovensiepen, U., Krupin, O., Starke, K., Matthias, F. and Wolf M. (2003) Coherent optical phonons and parametrically coupled magnons induced by femtosecond laser excitation of the Gd(OOOl) surface. Phys. Rev. Lett., 91, 227403. 

If optical phonons are responsible for the Raman processes, the Einstein model for the phonon spectrum is more appropriate. In this case, one finds... 

It is important to realize that even in the presence of traps, the measured Hall mobility refers to that in the higher conducting state (Munoz, 1991). Thus, a value of r significantly >1.0, and increasing with temperature in a certain interval, has been taken as an evidence in favor of traps in NP near the critical point (Munoz, 1988 Munoz and Ascarelli, 1983). Similarly, a nearly constant value of r near 1.0 in TMS over the temperature interval 22-164°C has been taken to indicate absence of trapping in that liquid. The scattering mechanism in TMS is consistent with that by optical phonons (Doldissen and Schmidt, 1979 Munoz and Holroyd, 1987). 

Summary. Coherent optical phonons are the lattice atoms vibrating in phase with each other over a macroscopic spatial region. With sub-10 fs laser pulses, one can impulsively excite the coherent phonons of a frequency up to 50THz, and detect them optically as a periodic modulation of electric susceptibility. The generation and relaxation processes depend critically on the coupling of the phonon mode to photoexcited electrons. Real-time observation of coherent phonons can thus offer crucial insight into the dynamic nature of the coupling, especially in extremely nonequilibrium conditions under intense photoexcitation. 

With development of ultrashort pulsed lasers, coherently generated lattice dynamics was found, first as the periodic modulation in the transient grating signal from perylene in 1985 by De Silvestri and coworkers [1], Shortly later, similar modulation was observed in the reflectivity of Bi and Sb [2] and of GaAs [3], as well as in the transmissivity of YBCO [4] by different groups. Since then, the coherent optical phonon spectroscopy has been a simple and powerful tool to probe femtosecond lattice dynamics in a wide range of solid... 

Fig. 2.2. Two generation models of coherent optical phonons, (a), (c), (e) impulsive stimulated Raman scattering (ISRS). (b), (d), (f) displacive excitation of coherent phonons (DECP). Graphs (e) and (f) display the time evolution of the driving force (grey areas) and that of the displacement (solid, curves) for ISRS and DECP, respectively...

Semimetals bismuth (Bi) and antimony (Sb) have been model systems for coherent phonon studies. They both have an A7 crystalline structure and sustain two Raman active optical phonon modes of A g and Eg symmetries (Fig. 2.4). Their pump-induced reflectivity change, shown in Fig. 2.7, consists of oscillatory (ARosc) and non-oscillatory (ARnonosc) components. ARosc is dominated by the coherent nuclear motion of the A g and Eg symmetries, while Af nonosc is attributed to the modification in the electronic and the lattice temperatures. 

Silicon is a model for the fundamental electronic and mechanical properties of Group IV crystals and the basic material for electronic device technology. Coherent optical phonons in Si revealed the ultrafast formation of renormalized quasiparticles in time-frequency space [47]. The anisotropic transient reflectivity of n-doped Si(001) featured the coherent optical phonon oscillation with a frequency of 15.3 THz, when the [110] crystalline axis was parallel to the pump polarization (Fig. 2.11). Rotation of the sample by 45° led to disappearance of the coherent oscillation, which confirmed the ISRS generation,... 

Fig. 2.12. Left transient anisotropic reflectivity change of the (001) surface of single crystal type Ha diamond. Inset shows the FT spectrum of the oscillation, demonstrating a narrow peak of the optical phonon at 40THz. Right pump and probe polarizations to detect the optical phonon. Adapted from [50]...

Isotope superlattices of nonpolar semiconductors gave an insight on how the coherent optical phonon wavepackets are created [49]. High-order coherent confined optical phonons were observed in 70Ge/74Ge isotope superlattices. Comparison with the calculated spectrum based on a planar force-constant model and a bond polarizability approach indicated that the coherent phonon amplitudes are determined solely by the degree of the atomic displacement, and that only the Raman active odd-number-order modes are observable. 

Coherent optical phonons can couple with localized excitations such as excitons and defect centers. For example, strong exciton-phonon coupling was demonstrated for lead phtalocyanine (PbPc) [79] and Cul [80] as an intense enhancement of the coherent phonon amplitude at the excitonic resonances. In alkali halides [81-83], nuclear wave-packets localized near F centers were observed as periodic modulations of the luminescence spectra. 

In a heavy fermion compound Yb MnSbn, the dephasing rate of the coherent optical phonons decreased with lowering temperature above Curie temperature Tc, but increased below Tc- The results were attributed to the coupling between an optical phonon mode and the Kondo effect [100]. 

In this chapter, we have reviewed the recent experimental researches on the coherent optical phonons using optical detection technique. Optical detection has great advantages in its experimental simplicity, higher time-resolution... 

TRXRD detects the propagation of coherent acoustic phonons as a transient change in the diffraction angles. In contrast, the atomic motions associated with coherent optical phonons modify only the Bragg peak intensity, because they do not change the barycentric positions of the crystal lattice. The Bragg peak intensity is proportional to the squared modulus of the structure factor [1,3,4] ... 

The earliest control experiments were performed in double- (or multiple-) pump and probe scheme on optical phonons generated via ISRS in transparent materials by Nelson and coworkers [24,25], Shortly later, similar experiments were carried out on coherent phonons generated in semiconductors via TDFS by Dekorsy and coworkers [26], and on those generated in semimetals via DECP by Hase and coworkers [27] (Fig. 2.1 in the previous chapter). These experiments demonstrated that the amplitude of the coherent oscillation can be controlled by varying the temporal separation At between the two pump pulses. At = nT leads to the maximum enhancement of the amplitude with an integer n and the phonon period T, while At = (n + 1/2)T results in complete cancelation. 

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