Mean free path phonons/electrons

This competition between electrons and the heat carriers in the lattice (phonons) is the key factor in determining not only whether a material is a good heat conductor or not, but also the temperature dependence of thermal conductivity. In fact, Eq. (4.40) can be written for either thermal conduction via electrons, k, or thermal conduction via phonons, kp, where the mean free path corresponds to either electrons or phonons, respectively. For pure metals, kg/kp 30, so that electronic conduction dominates. This is because the mean free path for electrons is 10 to 100 times higher than that of phonons, which more than compensates for the fact that C <, is only 10% of the total heat capacity at normal temperatures. In disordered metallic mixtures, such as alloys, the disorder limits the mean free path of both the electrons and the phonons, such that the two modes of thermal conductivity are more similar, and kg/kp 3. Similarly, in semiconductors, the density of free electrons is so low that heat transport by phonon conduction dominates. 

As the temperature is increased, electron-phonon scattering becomes dominant. The mean free path for such scattering varies as 71"" with n larger than unity. The mean free path of electrons at room temperature is typically on the order of 100 A. The mean free path depends on the material but is independent of the sample, since electron-phonon scattering is an intrinsic process. As a result of electron-phonon scattering, thermal conductivity of metals decreases at higher temperatures. 

Static defects scatter elastically the charge carriers. Electrons do not loose memory of the phase contained in their wave function and thus propagate through the sample in a coherent way. By contrast, electron-phonon or electron-electron collisions are inelastic and generally destroy the phase coherence. The resulting inelastic mean free path, Li , which is the distance that an electron travels between two inelastic collisions, is generally equal to the phase coherence length, the distance that an electron travels before its initial phase is destroyed ... 

Since the number of phonons increases with temperature, the electron-phonon and phonon-phonon scattering are temperature dependent. The number of defects is temperature independent and correspondingly, the mean free path for phonon defect and electron defect scattering does not depend on temperature. 

The thermal conductivity of bulk silicon (148 W K m ) is dominated by phonons electronic contributions are negligible. Due to restrictions of the mean free path of phonons in the porous network the thermal conductivity of micro PS is reduced by two or three orders of magnitude at RT, compared to the bulk value. Because of the larger dimensions of its network, meso PS shows a thermal conductivity several times larger than that of micro PS, for the same value of porosity. Thermal oxidation at low temperatures (300°C) is found to decrease the thermal conductivity of meso PS by a factor of about 0.5 [Pe9]. In contrast to bulk Si the thermal conductivity of PS is found to decrease with decreasing temperature [Be21, La4, Ge9, Lyl]. 

The discussion of the previous section would also lead us to believe that since most ceramics are poor electrical conductors (with a few notable exceptions) due to a lack of free electrons, electronic conduction would be negligible compared to lattice, or phonon, conduction. This is indeed the case, and we will see that structural effects such as complexity, defects, and impurity atoms have a profound effect on thermal conductivity due to phonon mean free path, even if heat capacity is relatively unchanged. 

Materials whose dimensions (typically in the 20-80 A range for semiconductor particles) are comparable to the length of the Broglie electron, the wavelength of the Broglie electron, the wavelength of phonons, and the mean free paths of excitons. Size quantization can occur in one, two, or three dimensions and manifests in altered optical, electronic, and chemical properties. 

It is clear from Equation 11.3 that resistivity should approach within 10% of the bulk value when the film thickness exceeds about four times the mean free path. The better the conductor, the smaller the mean free path. Thus, the resistivity approaches the bulk value as the film thickness reaches typical values of 100-200 nm for metallic conductors, or perhaps as much as several micrometers for semiconductors, depending on the intrinsic or doped carrier density. For sufficiently thick metallic films with K 1, the temperature coefficient of resistivity becomes positive, as bulk electron-phonon scattering becomes the primary contribution to resistivity [5]. Conduction in semiconductor films remains activation-limited, and retains a negative temperature coefficient. Figure 11.1 illustrates the dependence of resistivity on film thickness for sputtered... 

The phonon structure in the PC spectra of MgB2 can be revealed by i) the inelastic backscattering current, like for ordinary PCS, and ii) by the energy dependence of the excess current. They can be discriminated after destroying the superconductivity by magnetic field and/or temperature, and by varying the electron mean free path. 

Abstract In strong-coupling superconductors with a short electron mean free path the self-energy effects in the superconducting order parameter play a major role in the phonon manifestation of the point-contact spectra at above-gap energies. We compare the expressions for the nonlinear conductivity of tunnel, ballistic, and diffusive point-contacts and show that these expression are similar and correspond to the measurements of the phonon structure in the point-contact spectra for the 7r-band of MgB2. 

The inelastic point-contact spectra of phonons in metals are based on expansion of the nonlinear I — V characteristic in terms proportional to d/l , where d is the characteristic size of metallic nanoconstriction connecting two bulk metal half-spaces and Zt is the inelastic electron mean free path [1, 2]. 

In addition to mechanical properties, other physical properties of polycrystaUine materials, such as electrical and thermal conduction, are also affected by microstmcture. Although polycrystals are mechanicaUy superior to single crystals, they have inferior transport properties. Point defects (vacancies, impurities) and extended defects (grain boundaries) scatter electrons and phonons, shortening their mean free paths. Owing to... 

Equation 6.22 predicts that electronic conductivity is dependent on the electron relaxation time. However, it suggests no physical mechanisms responsible for controlling this parameter. Since electrons exhibit wave-particle duahty, scattering events could be suspected to play a part. In a perfect crystal, the atoms of the lattice scatter electrons coherently so that the mean-free path of an electron is infinite. However, in real crystals there exist different types of electron scattering processes that can limit the electron mean-free path and, hence, conductivity. These include the collision of an electron with other electrons (electron-electron scattering), lattice vibrations, or phonons (electron-phonon scattering), and impurities (electron-impurity scattering). 

Photoelectron spectroscopy of valence and core electrons in solids has been useful in the study of the surface properties of transition metals and other solid-phase materials. When photoelectron spectroscopy is performed on a solid sample, an additional step that must be considered is the escape of the resultant photoelectron from the bulk. The analysis can only be performed as deep as the electrons can escape from the bulk and then be detected. The escape depth is dependent upon the inelastic mean free path of the electrons, determined by electron-electron and electron-phonon collisions, which varies with photoelectron kinetic energy. The depth that can be probed is on the order of about 5-50 A, which makes this spectroscopy actually a surface-sensitive technique rather than a probe of the bulk properties of a material. Because photoelectron spectroscopy only probes such a thin layer, analysis of bulk materials, absorbed molecules, or thin films must be performed in ultrahigh vacuum (<10 torr) to prevent interference from contaminants that may adhere to the surface. 

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