Grain boundary scattering

AP-CVD ZnO Hu and Gordon [10,28] observed an increase of electron mobility p with increasing film thickness d, both for boron-doped and for gallium-doped AP-CVD ZnO films, with a more pronounced slope for small thickness. They attributed this behavior to the influence of the grain boundary scattering effect, which is dominant for thinner films that are composed of smaller crystallites. 

The reduction in <5 corresponds to the reduction in p and in the haze factor as observed in Figs. 6.28b and 6.29b, respectively. As the carrier density N does not vary with H2O/DEZ, we can safely assume that the density of ionized impurities within the ZnO films also remains constant when the H2O/DEZ ratio is increased. The observed decrease in p would therefore be induced here solely by an increase in grain boundary scattering, i.e., by an increase in the density of grain boundaries. This increase of grain boundary density evidently occurs when the grains become smaller (i.e., when <5 is reduced). 

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... 

Fig. 100. The temperature dependence of ic for a single crystal of TmV04 at H = 0 and 70 kOc, H c (Daudin et al. 1984). The dashed line gives the calculated ic due to grain boundary scattering.

The increase in resistivity at narrow fine widths has been attributed to surface scattering and grain-boundary scattering. The Fuchs and Sondheimer (FS) model attributes the resistivity increase in thin and narrow fines to diffuse scattering of electrons at the exterior surfaces with a probability of 1 — p, where p is the specular scattering coefficient. The length scales in the FS model are the thickness and line width of the conductor and the mean free path A. The simplified expression for resistivity as a function of thickness (T) and linewidth (W) of the conductor is given by ... 

Even though deviations from Matthiessen s rule are known to occur in the presence of grain-boundary scattering, this expression can be used as a good approximation to understand the relative importance of the various effects that influence the resistivity in narrow Cu lines. Figure 2.3 shows the variation of the resistivity as a function of Unewidth for the various components and pxotal-... 

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