Doping boundaries

In order to obtain appreciable conductivities, semiconductors must be doped witli small amounts of selected impurities. It is possible to switch tire doping type from n to p type, or vice versa, eitlier during tire growtli of a crystal or by tire selective introduction of impurities after tire growtli. The boundary region between tire p type and n type regions is... 

To answer questions regarding dislocation multiplication in Mg-doped LiF single crystals, Vorthman and Duvall [19] describe soft-recovery experiments on <100)-oriented crystals shock loaded above the critical shear stress necessary for rapid precursor decay. Postshock analysis of the samples indicate that the dislocation density in recovered samples is not significantly greater than the preshock value. The predicted dislocation density (using precursor-decay analysis) is not observed. It is found, however, that the critical shear stress, above which the precursor amplitude decays rapidly, corresponds to the shear stress required to disturb grown-in dislocations which make up subgrain boundaries. 

This kind of microstructure also influences other kinds of conductors, especially those with positive (PTC) or negative (NTC) temperature coefficients of resistivity. For instance, PTC materials (Kulwicki 1981) have to be impurity-doped polycrystalline ferroelectrics, usually barium titanate (single crystals do not work) and depend on a ferroelectric-to-paraelectric transition in the dopant-rich grain boundaries, which lead to enormous increases in resistivity. Such a ceramic can be used to prevent temperature excursions (surges) in electronic devices. 

Ag-doped Cu. In all the boundaries examined by Bruley et al. (1999), Ag segregation did not lead to any observable effect on the Cu L2>3 edge, either in the as-recorded spectra or the difference spectra. Ag segregation does not embrittle Cu, and so the absence of a detectable effect is consistent with the suggestion that electronic factors are responsible for grain boundary weakness. 

As a final remark it must be mentioned that theoretical and experimental works have been dedicated to investigating the effect of the finite size of the chains [65]. In fact, as grows exponentially, at low temperatures it can become comparable with the distance between two consecutive defects (e.g. impurities and vacancies) which are always present in real systems and hardly separated by more than 103 -104 elementary units. In case of Z < , the nucleation of the DW is energetically favoured if occurring at the boundaries, because the energy cost is halved. However the probability to have a boundary spin is inversely proportional to L thus the pre-exponential factor becomes linearly dependent on L, as experimentally found in doped SCMs. As doping occurs at random positions on the chain, a distribution of lengths is observed in a real system. However, as the relaxation time is only linearly dependent on L, a relatively narrow distribution is expected. 

Under what conditions can experiments yield data relevant to the goal we have just described Two conditions have to be fulfilled the various dissolved hydrogen species have to have had time to get equilibrated with each other before the surface boundary conditions have changed appreciably, and the surface chemical potential /x must be, if not known, at least reproducible in experiments involving different bulk dopings. At the present writing, there have been no experiments that are entirely beyond question in either of these respects, but several experiments, which we shall presently discuss, can plausibly be argued to satisfy both criteria. 

When a semiconducting electrode is brought into contact with an electrolyte solution, a potential difference is established at the interface. The conductivity even of doped semiconductors is usually well below that of an electrolyte solution so practically all of the potential drop occurs in the boundary layer of the electrode, and very little on the solution side of the interface (see Fig. 7.3). The situation is opposite to that on metal electrodes, but very similar to that at the interface between a semiconductor and a metal. 

FIGURE1.9 The grain boundary and bulk conductivities at 300°C for 8YSZ ceramics doped with ZnO with reference to the undoped YSZ sintered at the same temperature as a function of ZnO content [52]. 

FIGURE 1.35 Contribution of the grain-boundary resistance (Rgb) to the total resistance (Rt) for samaria-doped ceria [115]. 

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