Electronic conduction theory semiconductors

Note that the above model is for a simple system in which there is only one defect and one type of mobile charge carrier. In semiconductors both holes and electrons contribute to the conductivity. In materials where this analysis applies, both holes and electrons contribute to the value of the Seebeck coefficient. If there are equal numbers of mobile electrons and holes, the value of the Seebeck coefficient will be zero (or close to it). Derivation of formulas for the Seebeck coefficient for band theory semiconductors such as Si and Ge, or metals, takes us beyond the scope of this book. 

For many years, during and after the development of the modem band theory of electronic conduction in crystalline solids, it was not considered that amorphous materials could behave as semiconductors. The occurrence of bands of allowed electronic energy states, separated by forbidden ranges of energy, to become firmly identified with the interaction of an electronic waveform with a periodic lattice. Thus, it proved difficult for physicists to contemplate the existence of similar features in materials lacking such long-range order. 

Theory (1) The effective energy barrier between the two harmonic oscillators, AE (oo IT), which determines the probability of electron transfer along the conjugated chain decreases with increasing temperature thus, conductivity is semiconductor-like. (2) The spin susceptibility is due only to the unpaired Ji-electrons from TTF (all the 7i-electrons on TCNQ are in the paired state). Thus, the susceptibility is weak. (3) The spin-paired n-electrons on TCNQ resonate between the two harmonic oscillator states at frequency, . Such oscillation can perturb the g-factor of (TTF)+. As the increases with the temperature rise, the perturbation becomes greater, and the g-factor deviates more from that of the pure (TTF)+. 

Nov. 21, 1931, Tbilisi, Georgia, USSR - May 13, 1985) Dogonadze was one of the founders of the new science - electrochemical physics [i]. The main scientific interests of Dogonadze were focused on condensed-phase reactions. His pioneering works of 1958-59 have laid the foundations of the modern quantum-mechanical theory of elementary chemical processes in electrolyte solutions. He developed a comprehensive quantum-mechanical theory of the elementary act of electrochemical reactions of -> electron and -> proton transfer at metal and - semiconductor electrodes [ii—v]. He was the first to obtain, by a quantum-mechanical calculation, the expression for the electron transfer probability, which was published in 1959 in his work with -> Levich. He conducted a number of studies on the theory of low-velocity electrons in disordered systems, theory of solvated electrons, and theory of photochemical processes in solutions. He made an impressive contribution to the theory of elementary biochemical processes [vi]. His work in this area has led to the foundation of the theory of low-temperature -> charge-transfer processes cov-... 

To determine forbidden energy gaps in a semiconductor, one can investigate how its electronic conductivity (a) varies with temperature. Semiconductor theory indicates that the logarithm of the conductivity varies linearly with the inverse temperature. The value of the energy gap, Eg, is given by the slope of the In a Vs. 1/T line. Table 5A.4 contains the values of nine runs performed in duplicate with a germanium intrinsic semiconductor. The data were obtained at the Modern Physics Laboratory of the Physics Department of the Londrina State University, under the supervision of Prof. J. Scarminio. 

Electrolytical production of metals from chalcogenide (in particular, sulphide) compounds was, in fact, the first problem where the researchers faced the essential effect of mixed conductivity in electrochemical practice. Owing to the studies of Velikanov and his team [1-7], we had got the term polyfunctional conductor (PFC) and the main ideas about physico-chemical properties of this object. According to his theory, the electronic conductance of PFC can undergo the semiconductor to metal transformation (Mott transition), which can be detected from the ccaiductivity-temperature dependency. The possibihty had been found for the enhancement of ionic conductivity and, thus, for the improvement of electrochemical behaviour of the melt. It was achieved by means of so-called heteropolar additives— compounds with ionic chemical bond. 

According to the developed classification (see Chap. 1), this film system belongs to the category of the ion-semiconductor ones with very low total conductivity— that is, to dielectric type of systems. Its low conductivity constitutes of electronic (semiconductive) and ionic (migrative) parts. The electronic band theory prescribes the exponential temperature dependence of the electronic conductivity. Then, the electronic current can be written as... 

Conducting polymers are unusual in that they do not conduct electrons via the same mechanisms used to describe classical semiconductors and hence their electronic properties cannot be explained well by standard band theory. The electronic conductivity of conducting polymers results from mobile charge carriers introduced into the conjugated -system... 

The proposed model for the so-called sodium-potassium pump should be regarded as a first tentative attempt to stimulate the well-informed specialists in that field to investigate the details, i.e., the exact form of the sodium and potassium current-voltage curves at the inner and outer membrane surfaces to demonstrate the excitability (e.g. N, S or Z shaped) connected with changes in the conductance and ion fluxes with this model. To date, the latter is explained by the theory of Hodgkin and Huxley U1) which does not take into account the possibility of solid-state conduction and the fact that a fraction of Na+ in nerves is complexed as indicated by NMR-studies 124). As shown by Iljuschenko and Mirkin 106), the stationary-state approach also considers electron transfer reactions at semiconductors like those of ionselective membranes. It is hoped that this article may facilitate the translation of concepts from the domain of electrodes in corrosion research to membrane research. 

The high electrical conductivity of metals as well as the high electron (and hole) mobility of inorganic covalently bound semiconductors have both been clarified by the band theory [I9, which slates that the discrele energy levels of individual atoms widen in the solid stale into alternatively allowed and forbidden bands. The... 

According to the electronic theory, a particle chemisorbed on the surface of a semiconductor has a definite affinity for a free electron or, depending on its nature, for a free hole in the lattice. In the first case the chemisorbed particle is presented in the energy spectrum of the lattice as an acceptor and in the second as a donor surface local level situated in the forbidden zone between the valency band and the conduction band. In the general case, one and the same particle may possess an affinity both for an electron and a hole. In this case two alternative local levels, an acceptor and a donor, will correspond to it. 

The Schottky-Mott theory predicts a current / = (4 7t e m kB2/h3) T2 exp (—e A/kB 7) exp (e n V/kB T)— 1], where e is the electronic charge, m is the effective mass of the carrier, kB is Boltzmann s constant, T is the absolute temperature, n is a filling factor, A is the Schottky barrier height (see Fig. 1), and V is the applied voltage [31]. In Schottky-Mott theory, A should be the difference between the Fermi level of the metal and the conduction band minimum (for an n-type semiconductor-to-metal interface) or the valence band maximum (for a p-type semiconductor-metal interface) [32, 33]. Certain experimentally observed variations of A were for decades ascribed to pinning of states, but can now be attributed to local inhomogeneities of the interface, so the Schottky-Mott theory is secure. The opposite of a Schottky barrier is an ohmic contact, where there is only an added electrical resistance at the junction, typically between two metals. 

It is important to realize that each of the electronic-structure methods discussed above displays certain shortcomings in reproducing the correct band structure of the host crystal and consequently the positions of defect levels. Hartree-Fock methods severely overestimate the semiconductor band gap, sometimes by several electron volts (Estreicher, 1988). In semi-empirical methods, the situation is usually even worse, and the band structure may not be reliably represented (Deak and Snyder, 1987 Besson et al., 1988). Density-functional theory, on the other hand, provides a quite accurate description of the band structure, except for an underestimation of the band gap (by up to 50%). Indeed, density-functional theory predicts conduction bands and hence conduction-band-derived energy levels to be too low. This problem has been studied in great detail, and its origins are well understood (see, e.g., Hybertsen and Louie, 1986). To solve it, however, requires techniques of many-body theory and carrying out a quasi-particle calculation. Such calculational schemes are presently prohibitively complex and too computationally demanding to apply to defect calculations. 

In the case of elemental semiconductors such as Si, which are also well described in band theory terms, the equation for the conductivity is composed of an electron and hole component so that ... 

As described in the preceding sections, fundamental studies of heterogeneous catalysis at the surface of catalysts are important for understanding reaction pathways and for the development of new or improved catalysts and processes. There have been earlier hypotheses proposed for selective oxidation catalysis for example, the multiplet theory which suggests that the activity depends upon correctly spaced groups (multiplets) of atoms to accommodate the reactant molecule (Balandin, 1969) and electronic theory based on the nature of adsorption on semiconductors and empirical correlations between activity, work function and electrical conductivity (Wolkenstein 1960). The importance... 

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