Space charge distribution

Fig. 6. An abmpt p—n junction in thermal equiUbiium (a) space—charge distribution where (-) indicate majority carrier distribution tails and the charge...

The details of modeling the space charge distribution in oxides are presented elsewhere.249 Figure 36 presents the resulting space charge distribution in as-formed (curve 1) and aging oxides (curves... 

The general method for the determination of the flat band potential is based on the Mott-Schottky linear plot based on ca-pacitance/voltage relation. Starting from Eq. (9) the space charge distribution was calculated, and its potential dependence lead to the derivation of a model equivalent to a capacitance, given by ... 

A similar procedure can be used to determine the space charge distribution in n-type Si in the dark with a positive bias polarization so as to generate a depletion layer within the semiconductor substrate. In this case, the situation is somewhat different because the positive polarization in HF results in an anodic etching of the sample with a nonnegligible current density near 7 pA cm . Nevertheless, similar results were obtained, the components of the equivalent circuit were a capacitance of a few 10 F cm , and a resistance term ranging from 1 to 10Mf2cm for a bias potential varying from —0.1 to -1-0.9 V vs. SCE. 

Essentially the only source of flow in a solid ion-exchange membrane (ion-exchanger) is electro-osmosis. This is a flow induced by the interaction of the electric field with the space charge distributed in the fluid present in the solid. In this respect, electro-osmosis may be regarded as a relative of electro-convection in a hydrodynamically free solution. 

The presence of a space charge distributed in the fluid gives rise to a volume force ... 

A uniform electric field distribution across the sample is extremely important for achieving device quality materials. Unfortunately, real chromophore materials do not always behave as uniform insulator materials. We have already demonstrated that ionic impurities can dramatically reduce the effective electric field felt by chromophores. The presence of spatially and temporally varying nonuniform space charge distributions leads to nonuniform poling fields. The resulting nonuniform chromophore order can lead to light scattering. 

Redecker and Bossier (1996) described a method for determining mobilities that involves measuring the optical absorption of a packet of carriers. The technique also allows the determination of the space-charge distribution within a polymer layer. The technique requires that the free carrier absorption coefficient be known from an independent measurement. Related techniques have been described by Ziemelis el al. (1991) and Harrison et al. (1993). 

The photorefractive effect used in rewritable 3D optical data storage is based on nonuniform space-charge distribution produced by interfering beams... 

The dashed curve in Figure 6 includes the effect of mobile ions. The initial current is greater due to the ionic contribution, but the steady current is not affected. A comparison of Figs. 7 and 8 shows the differences in space charge distribution due to mobile ions migrating to the cathode. 

Figure 7. Calculated space-charge distributions at various times with fixed ions. Normalized times correspond to the time axis of Figure 1. (Reproduced with permission from Ref. 10. Copyright 1989 M.I.T.)...

Model. The comparison of theory and experiment in Figure 9 indicates that the simplified model can be used to calculate transients which agree with experiment in gross trends. The model permits quantitative analysis of bulk and contact space-charge effects in PI transient current measurements. In particular, this model is sufficient to calculate measurement-history effects due to mobile ions and bulk electronic space-charge (9). The relaxation of space-charge upon removal of the bias is intrinsically slower than its accumulation. Thus, the sample history is stored in the space-charge distributions. These results will be demonstrated in a future publication. 

Figure 1. Space-charge distribution of the excited current carriers p along z-coordinate within one period of superlattice structures (a) No. 4 and (b) No. Ai as a function of the quasi-Fermi level difference AF at 20 K.

Electrically driven convection in nematic liquid crystals [6,7,16] represents an alternative system with particular features listed in the Introduction. At onset, EC represents typically a regular array of convection rolls associated with a spatially periodic modulation of the director and the space charge distribution. Depending on the experimental conditions, the nature of the roll patterns changes, which is particularly reflected in the wide range of possible wavelengths A found. In many cases A scales with the thickness d of the nematic layer, and therefore, it is convenient to introduce a dimensionless wavenumber as q = that will be used throughout the paper. Most of the patterns can be understood in terms of the Carr-Helfrich (CH) mechanism [17, 18] to be discussed below, from which the standard model (SM) has been derived... 

As possible explanations, several ideas have been proposed a hand-waving argument based on destabilization of twist fluctuations" [52], a possibility of an isotropic mechanism based on the non-uniform space charge distribution along the field [53] and the flexoelectric effect [55-57]. 

Combining (11.85-11.87), we get the periodic space charge distribution over x ... 

The Poisson equation, Eq. (8), identifies the space charge density in an electrolyte solution, pe = ZiCi, as the source of the electric field. Thus, whenever the electric field changes with position, there is a space charge distribution over the system. 

Space charge distributions are then expected to exist over regions of thickness Lp, which is of the order of 10 cm for a 100 mM aqueous solution. A practical consequence of this comment is that the behavior of electrochemical systems comprising microgeometries is affected by space charge layers [80-82]. 

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