Scattering coefficient: density mean free path

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... 

Above about 0.5 GHz, Brillouin scattering provides an elegant technique of measuring phonon mean free paths (which are inversely proportional to the sound attenuation coefficient) by evaluating the width of the Brillouin lines [53]. However, as a result of finite spectrometer resolution and contrast, this method is limited to aerogel densities above 180 kg/m. ... 

B. Density Coefficient A decrease in density decreases the macroscopic cross sections, which results in an increase of the mean free paths for absorption and scattering. The result is that the thermal diffusion length (L) and neutron age (t) increase. Because of the increase in L and T, the thermal and fast nonleakage probabilities are reduced. From Eq. (1) note that the reduced nonleakage probabilities decrease kg , which means that the reactivity effect is negative. A partial compensation for the effect of an increased L and t on the nonleakage if the core volume exp[Pg.193]

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