Phonon mode frequency

FIGURE 6.12 First-principle calculations of the E2g phonon mode frequency as functions of (a) charge transfer and (b) in-plane lattice-constant change. (From Chan, C.T., et al., Phys. Rev. B, 36, 3499, 1987. With permission.)... 

In this chapter some of the presently known optical properties of zinc oxide are reviewed. In particular, the anisotropic dielectric functions (DFs) of ZnO and related compounds from the far-infrared (FIR) to the vacuum-ultraviolet (VUV) spectral range are studied. Thereupon, many fundamental physical parameters can be derived, such as the optical phonon-mode frequencies and their broadening values, the free-charge-carrier parameters, the static and high-frequency dielectric constants, the dispersion of the indices of refraction within the band-gap region, the fundamental and above-band-gap band-to-band transition energies and their excitonic contributions. 

By evaluation of the phonon-mode frequencies, information about strain [29] or about the incorporation of doping or alloying atoms can be derived. Besides the phonon-mode frequency, the phonon-mode broadening parameter provides information about crystal quality [30], because scattering due to a lower crystal quality or due to alloying makes the phonon-mode broadening parameter larger. 

Table 3.4 summarizes the phonon-mode frequencies of ZnO bulk samples and ZnO thin films, as obtained by Raman scattering spectroscopy, IR-reflection measurements, and IRSE. 

Fig. 3.9. Experimental (dotted lines) and best-model (solid lines) generalized IRSE spectra J ij of a (1120) ZnO thin film (d = 1455 5 nm) on (1102) sapphire [43,71]. Spectra are shifted for clarity. Vertical dashed lines indicate the ZnO phonon mode frequencies. Spectra in (a,d,g), (b,e,h), and (c,f,i) belong to different sample azimuth angles, respectively. The best-model values of the Euler angle 0znO, Sapphire, which describe the c-axis inclination with respect to the sample normal are 89.0° 1.0° and 54.9° 0.8°, respectively. Reprinted with permission from [71]...

Temperature-dependent Raman data were reported for the E -mode of flux-grown ZnO platelets in the temperature range from T 15 K to T 1050K [127], and for the T -mode, the E -mode, and the MP-mode at w 332 cm-1 of a ZnO bulk sample in the temperature range from T 300 K to T 700 K [43] In Fig. 3.11 the unpolarized Raman spectra and the temperature-dependence of the phonon-mode frequencies from [43] are... 

Fig. 3.10. Experimental (dotted lines) and best-fit model (solid lines) IRSE spectra of a PLD-grown (0001) ZnO thin film on (001) silicon (panel (a), film thickness d 670 nm), and magnetron-sputtered ZnO thin films on metallized polyimide foil (panel (b), d 500nm) and on metallized glass (panel (c), d 30nm) [43]. ZnO phonon-mode frequencies, as obtained by best-model analysis, are marked by vertical arrows...

A and B are model parameters representing the high-temperature linear slope (du>/8T t oo) and effective phonon-mode temperature (l>hui(Q) jfc >), respectively. w(0) is the phonon-mode frequency at T = OK. Table 3.5 summarizes the best-model parameters reported in [43]. In [127], a linear temperature-dependence with dw[E2 ]/ T = —1.85 x 10 2cm 1 K 1 was reported for temperatures above RT. 

The pressure-dependence of ZnO phonon-mode frequencies measured by Raman scattering was reported in [37, 130]. From that the Griineisen parameters 7j... 

ZnO bulk sample [43], Spectra are shifted for clarity, (b) Phonon-mode frequencies vs. temperature as determined from the Raman data in Fig. 3.11a. The solid lines are model approximations according to (3.22). Excitation with Nd YAG-laser line A = 532 nm and laser power P 60 mW... 

The phonon mode frequencies of wurtzite- and rocksalt-structure Mg Zni- O thin films vs. x, as obtained by combination of Raman scattering and IRSE, are plotted for 0 < x < 1 in Fig. 3.13. 

Fig. 3.13. Phonon-mode frequencies of wurtzite-structure PLD-grown Mg Zni- O thin films with Ai-symmetry (panel a, triangles) and Fi-symmetry (panel b, triangles), and of rocksalt-structure PLD-grown Mg Zni- O thin films (circles in both panels) vs. x [43,62,72,74], Open and solid symbols represent TO- and LO-modes, respectively. The dashed lines are linear approximations of the rocksalt-structure phonon modes from [74], the solid lines represent MREI calculations for the wurtzite-structure phonon modes redrawn from [132]. The shaded area, marks the composition range, where the phase transition occurs. Reprinted with permission from [74]...

Elastic constants depend on pressure and temperature because of the anharmonicity of the interatomic potentials. From the dependence of bulk and shear moduli on hydrostatic and uniaxial pressure, third order elastic constants and Griineisen parameters may be determined. Griineisen parameter shows the effect of changing volume, V, on the phonon mode frequencies, co. 

In parallel with these experimental studies of PL for SQD suspensions, the role of the observed linewidth broadening has been examined. In particular, the linewidth broadening due to acoustic-phonon-assisted transitions is expected [1] to contribute to satellite lines in PL spectra that are downshifted by the acoustic phonon energies. Within the elastic continuum approach [6], the phonon mode frequencies sensitive to the boundary conditions at the SQD surface were calculated. The lowest-order spherical acoustic mode frequency for CdS for different matrix materials differ by as much as a factor of three for a given SQD radius. 

Fig. 24. Various phonon mode frequencies of RB compounds as a function of the lattice parameter.

Fig. 40. (a) Temperature dependence of the longitudinal acoustic-phonon frequencies of Smo Y jsS in the [111] direction for four different values of the wavevector q (see Mook et al. 1981). (b) Temperature dependence of the bulk modulus Cg of Sm Y 25S measured by Bril-iouin scattering. Cg continues to soften upon cooling below 200 K, uniike the behavior of the phonon mode frequencies for qaO.l (flg. 40a). (c) Temperature dependence of the charge relaxation rate derived from the experimental data in figs. 40a and 40b (open circles) and calculated from theory (Schmidt and Miiller-Hartmann 1985) (solid line). The theoretical curve has been matched at 300 K to the experimental value. 

In case of p-type Cdo.2 Hgo.sTe alloy the main TO - phonon mode frequency of HgTe -like sub-band increases from 118 cm-i at 30K to approximately 122 cmi at 300 K. 

We can see a considerably larger number of lines for p-type sample in comparison with n-type sample but the temperature shift of the phonon mode frequencies is similar. These results obtained for the n- and p-Hgo.sCdo.2Te at 30 K agree generally with data presented in (Rath et al., 1995) but in this work was not performed a comparison for n- and p-type... 

Fig. 8. The temperature dependencies of the phonon mode frequencies for the p- typ>e The Hgo.8Cdo.2Te, shown in Fig. 2 and 3 as well as in Table 11 and 111. To, Ti and T2 are tetrahedra generated the corresponding CPM modes. The T v are tetrahedra generated by the corresponding APM modes.

Fig. 9. The temperature dependencies of the phonon mode frequencies for the n- type Hg0.sCd0.2Te.

Fig.4.5-TI (CH3NHCH2C00H)3 CaCl2. vq versus T. Vo is the phonon mode frequency. Triangles measured by millimeter spectroscopy. Brown circles measured from far-infrared spectra. Gray circles measured from electric-field-induced Raman spectra. In the paraelectric phase T > 0f), Vo decreases as the temperature decreases toward 0f, that is, the phonon mode softens...

Xii(o>) = magnetic susceptibility x(q, a>) = electronic susceptibility XzziQ ") = longitudinal susceptibility 1/ (2) = trigamma function ip z) = digamma function o) = Matsubara frequencies op(fl) = dispersion of optical phonons oj(q) = dispersion of magnetic excitons phonon mode frequencies = antisymmetric part of deformation tensor... 

These EPPs may reproduce the static crystal structures as the high site symmetries may preclude the formation of (low order) induced moments. Once the site symmetry is broken (i.e. at finite temperature) a description of ion polarization effects is required to reproduce key dynamic properties such as phonon mode frequencies. The inclusion of ion polarization is also required to reproduce key liquid static structural and dynamic properties [37],... 

In noncubic sohds, the phonon mode frequencies of the polar lattice vibrations depend, in general, on the phonon mode propagation direction. Likewise, directionally dependent free-chargescattering rates and the anisotropic inverse effective freecarrier mass tensor will produce nonscalar free-charge-carrier contributions. The infrared dielectric function is then represented by a complex-valued second-rank tensor s, which can be expressed in Cartesian coordinates (x,y,z) as ... 

A correlation between phonon mode frequencies and strain components in films with different strains can, in principle, allow determination of the isotropic deformation potentials, a and b (see Equations 9 and 8). a-Plane GaN films offer a unique opportunity to obtain the Ai(TO) phonon deformation potentials by GIRSE. This is particularly important in view of the existing discrepancy in the literature between the values of the Ai(TO) phonon deformation potentials determined by Raman scattering [54] and theory [14]. Further, the aEi(io) and fcii(LO) have not been experimentally determined yet. 

Table1.9 Phonon mode frequencies (in units ofcm ) ofwurtzite ZnO at the center of the Brillouin zone obtained from infrared spectroscopic ellipsometry (IRSE) and Raman scattering measurements in comparison with theoretical predictions.

---