Debye temperature semiconductors

The behavior of covalent semiconductors is quite different below and above the Debye temperature of a crystal. This was first shown by Trehlov and his colleagues (Gridneva, Mil man and Trehlov, 1972). Figure 5.12 illustrates the... 

Since there is no good physical framework in which the measured hardness versus temperature data can be discussed, descriptions of it are mostly empirical in the opinion of the present author. Partial exceptions are the elemental semiconductors (Sn, Ge, Si, SIC, and C). At temperatures above their Debye temperatures, they soften and the behavior can be described, in part, in terms of thermal activation. The reason is that the chemical bonding is atomically localized in these cases so that localized kinks form along dislocation lines. These kinks are quasi-particles and are affected by local atomic vibrations. 

Diamond has the highest Debye temperature of 1860 K. The semiconductors silicon and germanium have 625 and 290 K, respectively. For metals, the Debye temperature ranged from 100 K for potassium to 470 K for iron. 

Table 4.1-8 Heat capacities and Debye temperatures of Group IV semiconductors and IV-IV compounds...

Phonon surface bands of some insulators and semiconductors are given in Figs. 5.2-56-5.2-58. Surface phonon energies of alkali halide crytals are summarized in Table 5.2-23. Since insulators and semiconductors have in general more than one atom per unit cell, they display both acoustical and optical branches. Surface Debye temperatures of some semiconductors are given in Table 5.2-22. 

Table 5.2-22 Surface Debye temperatures of semiconductors. References to the original articles are given in [2.4,6]...

Figure 27.12 presents the T-BOLS reproduction of the size and temperature-dependent Raman shift of II-Vl semiconductors. Table 27.3 features information of the atomic cohesive energy (Fcoh). Debye temperature (0d), and reference frequencies (o(l) derived from the reproduction, with comparison of the documented 0D-... 

The Debye characteristic temperature of isotropic bodies is directly associated with the bulk modulus and therefore with all the other properties of matter dependent, to a certain degree, on the atomization energy, the surface energy u, the elasticity moduli, the expansion coefficients, the width of the forbidden band in semiconductors, etc. 

Total thermal conductivity is a sum of the lattice and electronic parts, K = Ki + Ke- The lattice part of the thermal conductivity describes the scattering of phonons on the vibrations of atoms, whereas the electronic part describes thermal conductivity appearing due to conduction electrons and is related to the electrical conductivity Wiedemann-Franz equation, = a T Lo, where T is the absolute temperature and Lq is the ideal Lorenz number, 2.45 X 10 Wf2K [64]. The electronic part of the thermal conductivity is typically low for low-gap semiconductors. For the tin-based cationic clathrates it was calculated to contribute less than 1% to the total thermal conductivity. The lattice part of the thermal conductivity can be estimated based on the Debye equation /Cl = 1 /3(CvAvj), where C is the volumetric heat capacity, X is the mean free path of phonons and is the velocity of sound [64]. The latter is related to the Debye characteristic temperature 6 as Vs = [67t (7V/F)] . Extracting the... 

Here x is the distance from a reference plane, corresponding to the distance of closest approach of hydrated ions z. and C are the charge number and unperturbed concentration of the i" ionic species is the local electric potential and R, F, and T are the gas constant, Faraday s constant, and the absolute temperature. The situation is quite analogous to the junction between a semiconductor and a metal, except that, in an electrolyte, the density of ionic states close to the interface is large compared with the electronic density of states, and therefore an ionic rather than an electronic space charge forms. This perturbation in concentration extends into the electrolyte for a characteristic distance known as the Debye length ... 

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