Space charge factor

In electroluminescence devices (LEDs) ionized traps form space charges, which govern the charge carrier injection from metal electrodes into the active material [21]. The same states that trap charge carriers may also act as a recombination center for the non-radiative decay of excitons. Therefore, the luminescence efficiency as well as charge earner transport in LEDs are influenced by traps. Both factors determine the quantum efficiency of LEDs. 

Satisfactory agreement of experiments with kinetic laws, described by Eqs. (44) and (45), are observed only for tantalum and niobium, when the current efficiency approaches 100%. Even for these metals, certain deviations occur which could be attributed to space charge effects,82 electronic leakage currents,83 or other factors. In the case of aluminum, these deviations are relatively large, as, even in barrier-forming electrolytes, some oxide dissolution takes place from the very beginning of voltage supply to an anodized sample.32... 

When all these factors contribute, the situation becomes almost hopelessly complicated. The simplest realistic case is that in which the photocarriers are generated in the space-charge region and migrate to the surface, where they are immediately consumed by an electrochemical reaction. We consider this case in greater detail. Suppose that light of frequency i/, with hu > Eg, is incident on a semiconducting electrode with unit surface area under depletion conditions (see Fig. 8.8). Let Iq be the incident photon flux, and a the absorption coefficient of the semiconductor at frequency v. At a distance x from the surface, the photon flux has decreased to Iq exp(—ax), of which a fraction a is... 

Because of the different potential distributions for different sets of conditions the apparent value of Tafel slope, about 60 mV, may have contributions from the various processes. The exact value may vary due to several factors which have different effects on the current-potential relationship 1) relative potential drops in the space charge layer and the Helmholtz layer 2) increase in surface area during the course of anodization due to formation of PS 3) change of the dissolution valence with potential 4) electron injection into the conduction band and 5) potential drops in the bulk semiconductor and electrolyte. 

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. 

For moderately doped substrates, when the surface is free of oxide the change of potential is mostly dropped in the space charge layer and in the Helmholtz double layer. The reactions are very sensitive to geometric factors. The reaction that is kinetically limited by the processes in the space charge layer is sensitive to radius of curvature, while that limited by the processes in the Helmholtz layer is sensitive to the orientation of the surface. Depending on the relative effect of each layer the curvature effect versus anisotropic effect can vary. 

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. 

A similar problem of calculating iph by a somewhat different method is considered in the paper by Reichman (1980), who makes additional model assumptions to take into account, apart from other factors, such as recombination of carriers in the space-charge region in this connection, see also the paper by Kireev et al. (1981). 

---