Space charge mechanism

Figure 20.1. Schematic of electric, ionic, molecular and space-charge mechanisms.

The results of several studies were interpreted by the Poole-Erenkel mechanism of field-assisted release of electrons from traps in the bulk of the oxide. In other studies, the Schottky mechanism of electron flow controlled by a thermionic emission over a field-lowered barrier at the counter electrode oxide interface was used to explain the conduction process. Some results suggested a space charge-limited conduction mechanism operates. The general lack of agreement between the results of various studies has been summari2ed (57). 

Semiconductor-electrolyte interface, photo generation and loss mechanism, 458 Semiconductor-oxide junctions, 472 Semiconductor-solution interface, and the space charge region, 484 Sensitivity, of electrodes, under photo irradiation, 491 Silicon, n-type... 

The lattice gas has been used as a model for a variety of physical and chemical systems. Its application to simple mixtures is routinely treated in textbooks on statistical mechanics, so it is natural to use it as a starting point for the modeling of liquid-liquid interfaces. In the simplest case the system contains two kinds of solvent particles that occupy positions on a lattice, and with an appropriate choice of the interaction parameters it separates into two phases. This simple version is mainly of didactical value [1], since molecular dynamics allows the study of much more realistic models of the interface between two pure liquids [2,3]. However, even with the fastest computers available today, molecular dynamics is limited to comparatively small ensembles, too small to contain more than a few ions, so that the space-charge regions cannot be included. In contrast, Monte Carlo simulations for the lattice gas can be performed with 10 to 10 particles, so that modeling of the space charge poses no problem. In addition, analytical methods such as the quasichemical approximation allow the treatment of infinite ensembles. 

In the lattice-gas model, as treated in Section IV.D above, ion transfer is viewed as an activated process. In an alternative view it is considered as a transport governed by the Nernst-Planck or the Langevin equation. These two models are not necessarily contra-dictive for high ionic concentrations the space-charge regions and the interface have similar widths, and then the barrier for ion transfer may vanish. So the activated mechanism may operate at low and the transport mechanism at high ionic concentrations. 

Dewald58 has introduced a mechanism in which space charge generation in the anodic oxide results from the difference between activation energies at the oxide surface and in the bulk. Winkel et... 

This equation presumes that each photon absorbed creates an electron-hole pair if there are other absorption mechanisms, the right-hand side must be multiplied by a quantum efficiency. The total rate of minority carrier generation is obtained by integrating over the space-charge region ... 

Important electrical informations about OLEDs, such as charge transport, charge injection, carrier mobility, etc., can be obtained from bias-dependent impedance spectroscopy, which in turn provides insight into the operating mechanisms of the OLED [14,15,73,75 78]. Campbell et al. reported electrical measurements of a PLED with a 50-nm-thick emissive layer [75], Marai et al. studied electrical measurement of capacitance-voltage and impedance frequency of ITO/l,4-Mv-(9-anthrylvinyl)-benzene/Al OLED under different bias voltage conditions [76], They found that the current is space-charge limited with traps and the conductivity exhibits power-law frequency dependence. 

There are five possible physical phases in the current path in which the current conduction mechanisms are different as illustrated in Figure 19. They are substrate, space charge layer, Helmholtz layer, surface oxide film, and electrolyte. The overall change in the applied potential due to a change of current density in the current path is the sum of the potential drops in these phases ... 

Similar analysis can be made for other types of materials. Thus, as a generalization, the curvature of a surface causes field intensification, which results in a higher current than that on a flat surface. Although the detailed current flow mechanism can be different for different types of materials under different potentials and illumination conditions, the effect of surface curvature on the field intensification at local areas is the same. The important point is that the order of magnitude for the radius of curvature that can cause a significant effect on field intensification is different for the substrates of different widths of the space charge layer. This is a principle factor that determines the dimensions of the pores. 

The fundamental reason for the uneven distribution of reactions is that the rate of electrochemical reactions on a semiconductor is sensitive to the radius of curvature of the surface. This sensitivity can either be associated with the thickness of the space charge layer or the resistance of the substrate. Thus, when the rate of the dissolution reactions depends on the thickness of the space charge layer, formation of pores can in principle occur on a semiconductor electrode. The specific porous structures are determined by the spatial and temporal distributions of reactions and their rates which are affected by the geometric elements in the system. Because of the intricate relations among the kinetic factors and geometric elements, the detail features of PS morphology and the mechanisms for their formation are complex and greatly vary with experimental conditions. 

This form of an isotherm is characteristic for a chemisorption process on an n-type catalyst forming a boundary layer with a space charge. It is evident that this mechanism is quite different from the mechanism of physical or van der Waals adsorption, which is represented by the Langmuir equation. 

After having described the mechanism of electron interchange between the catalyst and the reactive gas molecules, we will show in the following chapters how the electron disorder and the space-charge effects are expected to influence the rate of reaction. The electron interchange between the catalyst and the different species of molecules involves a different mechanism of potentially higher reaction rates than is the case in the homogeneous gas phase reactions. 

---