Phonon temperature

Using the calculated phonon modes of a SWCNT, the Raman intensities of the modes are calculated within the non-resonant bond polarisation theory, in which empirical bond polarisation parameters are used [18]. The bond parameters that we used in this chapter are an - aj = 0.04 A, aji + 2a = 4.7 A and an - a = 4.0 A, where a and a are the polarisability parameters and their derivatives with respect to bond length, respectively [12]. The Raman intensities for the various Raman-active modes in CNTs are calculated at a phonon temperature of 300K which appears in the formula for the Bose distribution function for phonons. The eigenfunctions for the various vibrational modes are calculated numerically at the T point k=Q). 

A priori, when the phonon relaxation is faster than the tunneling rates, thermodynamic equilibrium should hold at the temperature of the host reservoir. However, for the nano-junctions the local surface temperature may differ from the bulk equilibrium temperature. This is due to the Anderson orthogonality catastrophe (AOC)3 associated with interplay between the van der Waals and the electrostatic forces. The electron tunneling affects the overlap between differently shifted phonon ground states of the surface. The faster the tunneling rate, the closer is the phononic overlap to zero, and that hinders relaxation of the surface temperature. AOC presents the mechanism also affecting the thermal state of the electronic reservoir due to electron-phonon coupling. In Sec. 3, from comparison of our theoretical I-V curves at different electron-phonon temperatures and the experimental data [Park 2000] we infer that AOC exists. 

Figure 2. Intensity-voltage (/ - V) curve of "dot + leads" system at the equilibrium electron temperature fcuTe = 0.4 meV, but at a different effective phonon temperature...

This condition pertains to most solar conditions and corresponds to picosecond time scales for electron distributions with 1 eV (< 10 carriers cm ) of excess energy to fully reach equilibrium with the lattice phonon temperature (3-10 ps for GaAs)... 

The effect of device temperature on the electrical behavior of the device occurs due to the lattice temperature dependence of the electron scattering rate. When the LO phonon and acoustic phonon temperatures rise, the electron scattering rate increases, thus increasing the electrical resistance or decreasing the carrier mobility. The coupling of electrical and thermal characteristics suggest that these must be analyzed concurrently. 

The general topic of surface analysis has already generated several books and some hundreds of review articles, so it is clearly outside the scope of this chapter to provide a comprehensive discussion of all of the techniques presently available for the study of clean surfaces and adsorption/desorption processes. Instead, we shall consider a few of the methods most relevant to semiconductors which have perhaps been treated less extensively elsewhere. We shall also concentrate on the type of information available rather than the details of its production. In Fig. 1, we have attempted to illustrate the complete range of surface evaluation techniques, from which we see that a surface can be probed by electrons, ions, photons, neutral particles and phonons (temperature programming), and the products of the resulting interactions analysed in various ways. 

The measurements of the electron-phonon coupling constant in SOI films have been done at the substrate temperature between 100 - 500 mK. The heating current was swept slowly and the electron and phonon temperatures were measured simultaneously. The electron and phonon temperatures as functions of the heating power for the sample with = 1210 cm are plotted in Fig. 1. 

The difference of the measured electron and phonon temperatures in the b power, i.e. T -Tph) was plotted against applied power density (see inset in Fig. 2) and from the slope of the graph we obtain the electron-phonon coupling constant 27. The dependence is linear in this scale and it indicates that the heat flow between the electron and phonon systems has a 7 -dependence. This corresponds to Te.ph °c 1 for the electron-phonon interaction relaxation time. 

FIGURE 3.16. Temporal evolution of a Ru(OOOl) surface covered by coadsorbed O + CO after irradiation with an IR pulse of 130 fs duration. Variation of the electronic and phonon temperatures, Tei and Tph, respectively, with time leading to CO desorption and CO2 evolution [52]. 

The local phonon temperature, Tp], can then be evaluated from Eq. (16) for equilibrium (To), extended (Tj), and compressed (T ) excited bonds. Calculations are shown in Fig. 7 Tj = 1000 K, T 100 K, whereas To = 300 K. These results prove that the regions containing the stretched dilated bonds are created by energy fluctuations rather than by mechanical stress, because the phonon temperature of the overstressed regions in solids must be equal to the thermodynamic temperature of the sample. 

To elucidate the difference between variously elongated excited bonds, their local temperatures, Ta, were evaluated. Figure IS provK that the phonon temperature of excited bonds depends on 6a an increase in Ca causes an increase in Ta at Ea = e, Ta = 2000 K. Perhaps, these strongly heated bonds are the first of all to be dissociated... 

Fig. 15. Phonon temperature, Tp, vs deformation of the excited bonds, for PP at 300 K Applied stress (GPa) (1), 0, (2), 04, and (3), 0.55. The dispersion of the excited bonds (------) IS also shown...

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