Polaron size

Fig. 9.1 Illustration of polaron size. The periodic potential, V(x), is plotted with the range of conduction band potentials (energies) depicted in gray. The wavefunctions, ij/, of a small (solid line), intermediate (dashed line), and large (dotted line) polaron are plotted as a function of a single spatial dimension, x. Illustration is based on [5]...

However we have not yet been able to accomplish differentiation for EDG = Me2N. Thus by controlling the size of the oligomeric segment we predetermine the delocalization length of the polaronic or bipolaronic domain as well as the absorption characteristics of the polymer in either pristine or oxidized form. 

For the size determination of spin polarons from the field-dependent magnetization data (SQUID results in Fig. 6) we first employed a fitting based on the Brillouin function /3(./), which is justified since the respective temperatures around T]T are sufficiently above the ferromagnetic transition. The paramagnetic magnetization as a function of field is given by... 

One can say that the obtained by us experimental results upon 2D exciton localization (taking place due to the growth of the crystal dielectric permeability anisotropy parameter) with o are very close to [27] where the behaviour of polaron excitons in parabolic quantum dots were considered and shown that the dot size decrease results in increasing the exciton binding energy. 

The size of the soliton pair as on Fig. 6a is determined by the so-called confinement parameter y = Ae/(2XAo) [27,29]. Its meaning is qualitatively quite clear If the energy difference AE between the two structures increases, the extension of the high-energy one decreases and the pair is more confined. For very small y (i.e., Ae 0), the soliton pair or the bipolaron will tend to dissociate into independent solitons or polarons. 

An increase in the extent of valence d electron localization is expected for smaller principal quantum numbers and as one moves to the right in a period because of a contraction in the size of the d orbitals. For example, with compounds of the late 3d metals, a mixture of 4s bands, and more-or-less localized 3d atomic orbitals may coexist, in which case, it becomes possible for cubic crystal fields to split the degenerate d orbitals and give rise to a localized JT distortion (e.g. a single octahedra), or small polaron in physics terminology. High concentrations of JT ions, where the polyhedra share stmctural elements, are subject to a cooperative JT effect, which can cause distortion to a lower crystalline symmetry. 

Conductivity sufficiently far down the band tails is by hopping and goes to zero at T = 0 K. The hopping may or may not have a polaron behavior depending on the size of the phonon interaction. 

Because of the small size of polarons in molecular crystals, the conduction channel in organic transistors extends in the transverse direction for only a few molecular layers [20-22]. For the same reason, polarons interact strongly with chemical impurities and structural defects. As a result, polaronic transport in organic OFETs is very sensitive to the morphology of the semiconductor surface and to the presence... 

Still there is no chance to find some experimental criterion for checking each of the described theories. It should be stressed that the polaron model of the cavity with the localized electron is definitely proved by the volume expansion of ammonia when adding the alkali metal to it (38). Besides, on the basis of any of the cavity theories it becomes comparatively easy to explain the results of investigation of e tr photoannealing—i.e., the dispersion of the trap depths, and temperature dependence of ExmaX of the electrons. In this connection it is rather desirable to find some approach to determining the sizes of the cavities for the electrons in the irradiated polar systems, as it has been done for the metal-ammonia solutions. 

An additional complication arises from the fact that the probability of an electron (or hole) being self-trapped due to the electron - phonon interaction increases strongly as the electronic wave function shrinks in size to the order of atomic dimensions (Emin, 1982). A consequence of this is that electrons in disorder-induced localized states are believed to be more susceptible to small polaron formation and self-trapping than are ordinary extended-state electrons (Emin, 1984 Cohen et al, 1983). Thus, not only does the disordered structure of amorphous semiconductors introduce new physical phenomena, namely, the mobility edge, but also the effect of known phenomena, such as the electron - phonon interaction, can be qualitatively different. 

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