Zener effect

Figure 1 The schematic representation of various electronic excitation mechanisms due to ac or dc external electric fields (a) the tuneling electrons from the valence band (VB) to the conduction band (CB) and ionization of an acceptor state (-o-) (Zener effect) followed by electron-hole recombination, indicated by horizontal and vertical arrows, respectively (b) excitation or ionization by electron impact (c) recombination of electrons ( ) and (o) holes at a semiconductor p-n junction and (d) bulk recombination of electrons and holes injected from electrodes. Adapted from Ref. 2...

A. Thiel, The Landau-Zener effect in nuclear molecules, J. Phys. G 16 867 (1990). 

EFFECT OF SECOND-PHASE PARTICLES ON GRAIN GROWTH ZENER EFFECT... 

Figure 6.3. Dragging of grain boundary movement by second-phase particles the Zener effect.

In addition to the Poole-Frenkel effect and the field-induced tunneling from traps to conduction band states, the Zener effect (field-induced transitions from valence band to conduction band) and various forms of avalanche breakdown effects, can give a bulk conductivity rising sharply with field. These effects are difficult to assess in the present systems, because little is known about the electronic states in amorphous oxides, the electronic transport process, or the lattice vibration spectrum. 

The Zener effect will require very large fields with wide band semiconductors. In p-n junctions in silicon, avalanche rather than Zener breakdown normally occurs except in very thin junctions. ... 

Unlike the Zener effect in which the breakdown voltage is engineered into the design of the dielectric, many of the above mechanisms are unpredictable and time-dependent, so the chances of breakdown increases with age. 

The physical description of strongly pressure dependent magnetic properties is the object of considerable study. Edwards and Bartel [74E01] have performed the more recent physical evaluation of strong pressure and composition dependence of magnetization in their work on cobalt and manganese substituted invars. Their work contrasts models based on a localized-electron model with a modified Zener model in which both localized- and itinerant-electron effects are incorporated in a unified model. Their work favors the latter model. 

Exact solutions to the electronic Schrodinger equation are not possible for many-electron atoms, but atomic HF calculations have been done both numerically and within the LCAO model. In approximate work, and for molecular applications, it is desirable to use basis functions that are simple in form. A polyelectron atom is quite different from a one-electron atom because of the phenomenon of shielding", for a particular electron, the other electrons partially screen the effect of the positively charged nucleus. Both Zener (1930) and Slater (1930) used very simple hydrogen-like orbitals of the form... 

The height of the potential barrier is lower than that for nonadiabatic reactions and depends on the interaction between the acceptor and the metal. However, at not too large values of the effective eiectrochemical Landau-Zener parameter the difference in the activation barriers is insignihcant. Taking into account the fact that the effective eiectron transmission coefficient is 1 here, one concludes that the rate of the adiabatic outer-sphere electron transfer reaction is practically independent of the electronic properties of the metal electrode. 

FIGURE 34.7 Dependence of the effective electron transmission coefficient on the electrochemical Landau-Zener parameter. 

The study of the effect of electric fields on the properties of solids dates back to Zener s (1934) investigation of electrical breakdown in solid dielectrics. Further pioneering work was carried out by Houston (1940) and Slater... 

This mixed classical/quantum expression is valid for classical nuclear behavior and, strictly speaking, for the case of direct two-site interaction rather than superexchange, as the Landau-Zener expression was derived from the time-dependent Schrodinger equation assuming a two-state (reactant/product) electronic system with direct coupling. Nevertheless, it becomes clear on physical grounds that the form of Eqs. 4-5 can serve to define an effective A in the superexchange case in terms of the Rabi precession frequency characteristic of the two trap sites embedded in the complex system wherein 2A/h would be computed from this net effective Rabi precession frequency. 

The earliest derivation of was made by Zener (1955) who postulated that the effect of an alloying element was proportional to its effect on Tc. With the assumption that 6Tc/6x is a constant, it is then possible to write ... 

We have examined the proton transfer reaction AH-B A -H+B in liquid methyl chloride, where the AH-B complex corresponds to phenol-amine. The intermolecular and the complex-solvent potentials have a Lennard-Jones and a Coulomb component as described in detail in the original papers. There have been other quantum studies of this system. Azzouz and Borgis performed two calculations one based on centroid theory and another on the Landau-Zener theory. The two methods gave similar results. Hammes-Schiffer and Tully used a mixed quantum-classical method and predicted a rate that is one order of magnitude larger and a kinetic isotope effect that is one order of magnitude smaller than the Azzouz-Borgis results. 

An interesting class of exact self-similar solutions (H2) can be deduced for the case where the newly formed phase density is a function of temperature only. The method involves a transformation to Lagrangian coordinates, based upon the principle of conservation of mass within the new phase. A similarity variable akin to that employed by Zener (Z2) is then introduced which immobilizes the moving boundary in the transformed space. A particular case which has been studied in detail is that of a column of liquid, initially at the saturation temperature T , in contact with a flat, horizontal plate whose temperature is suddenly increased to a large value, Tw T . Suppose that the density of nucleation sites is so great that individual bubbles coalesce immediately upon formation into a continuous vapor film of uniform thickness, which increases with time. Eventually the liquid-vapor interface becomes severely distorted, in part due to Taylor instability but the vapor film growth, before such effects become important, can be treated as a one-dimensional problem. This problem is closely related to reactor safety problems associated with fast power transients. The assumptions made are ... 

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