Semiconductor, relaxation case

In a relaxation-case semiconductor a linear current-voltage characteristic can occur even though most of the applied voltage drops at the contact (van Roosbroeck and Casey (1972)). This situation can be detected by testing the scaling of resistance with electrode separation. 

When the NCS is sufficiently thick, the high field effects should be determined by the uniform field in the bulk. The independence of the current on the polarity of the applied voltage is usually taken as an experimental proof that conduction is not determined by nonuniform fields near the contact. This requirement is, however, not sufficient since most processes, discussed in the previous chapter, are insensitive to the parameters of the electrode material. The injection mechanisms are essentially controlled by the properties of the semiconductor too and Queisser et al (1971) showed that ohmic conduction can be space charge controlled over a wide voltage range in a relaxation case semiconductor. Moreover, the rectification ratio of NCS contacts are expected to be small even for blocking... 

The question whether amorphous semiconductors fulfil the condition for relaxation-case semiconductors was raised (Fagen (1972)) because the photoconductive decay time is found to be much longer than the lifetime assumed by van Roosbroeck and coworkers (about 10 sec). However, Ryvkin (1964) and also van Roosbroeck pointed out that in the relaxation regime the photoconductive decay is not governed by the lifetime but by the much longer relaxation time. 

However, most impurities and defects are Jalm-Teller unstable at high-symmetry sites or/and react covalently with the host crystal much more strongly than interstitial copper. The latter is obviously the case for substitutional impurities, but also for interstitials such as O (which sits at a relaxed, puckered bond-centred site in Si), H (which bridges a host atom-host atom bond in many semiconductors) or the self-interstitial (which often fonns more exotic stmctures such as the split-(l lO) configuration). Such point defects migrate by breaking and re-fonning bonds with their host, and phonons play an important role in such processes. 

Perhaps not surprisingly, the most thorough NMR studies of Knight shifts, Korringa relaxation, metal-insulator transitions, and the NMR of the dopant nuclei themselves have been carried out for doped silicon. Since few semiconductors other than PbTe, which presents a considerably more complicated case, have been studied in such detail, it is worthwhile here to summarize salient points from these studies. They conveniently illustrate a number of points, and can shed light on the behavior to be expected in more contemporary studies of compound semiconductors, which are often hindered by the lack of availability of a suite of samples of known and widely-varying carrier concentrations. 

The high conductivity observed at low frequencies would overlap the existence of another new relaxation (Fig. 2.78) what is very similar to that found for transfer complexes [243, 244] in which some of them have a pronounced semiconductor character. In this kind of compounds, the observation of dielectric relaxations over room temperature is inhibited by the high conductivity observed. To avoid this problem and to detect the conductivity effect, it is possible to use the complex polarizability a defined by equation [182], The transformation defined by equation (2.45), has been applied with good results in the case of dielectric relaxation peaks in terms of a" or tan 8 . 

The rate of the photobleaching relaxation of ultradispersed CdS, and hence the rate of the electron interfacial transfer from CdS to the surrounded media (finally, to protons yielding the hydrogen) appeared to depend on the size of the colloidal particles (see Fig. 2.10). The photobleaching relaxation rate increases as the size of the CdS semiconductor particles decreases. Such behavior may be caused by the increasing of reductive potential of photoexcited electron with decreasing size of semiconductor nanocolloids. In this case, according to the modern concepts of electron interfacial transfer reaction [19], the rate of electron transfer to the surrounded media should increase. 

Power law behaviour has also been observed by Dutoit et al. [73] and ascribed to more general relaxation processes within a narrow layer at the surface of the semiconductor. It is, of course, not possible to distinguish by a.c. techniques alone the model put forward by Dutoit et al. [73] and that described above since the mathematical development is the same and the differences may, in any case, be largely semantic. Nevertheless, Dutoit et al. s analysis is of considerable interest. An equivalent circuit of the form... 

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