Majority flux limitations

The extent to which dark currents are limited by transport of majority carriers across the interface can be gauged by the following argument [91], The electron flux is given by 

If we make the assumption that the semiconductor behaves classically and there is an applied voltage V0 at which = 0 and n°s = Bexp(-e0 V0/kT) 

Although this is clearly an extreme case, and mobilities are commonly much higher than this and Debye lengths smaller, nevertheless, oxide semiconductors may well be limited in practical application by carrier transport. Naturally, if the bias is such that the semiconductor is not in depletion, there will be no restriction arising from transport indeed, the semiconductor will behave like a metal under these circumstances. 

In the previous section, we considered electron transfer processes involving only the majority carrier band. For semiconductors with lower band-gaps, either doped or intrinsic, both bands may be involved and we consider two current contributions arising from the two bands as shown in Fig. 41. In practice, it is found that the dominant contribution usually arises from only one of the two bands if the majority carrier band is involved, the treatment will reduce to that given above, but if the minority carrier band is the more significant, then the current may be limited by the rate of thermal generation and transport of the majority carriers to the surface. 

Let us consider the problems of an n-type semiconductor that is biased positive and which must sustain a faradaic reaction through hole transfer 

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The term numerical diffusion describes the effect of artificial diffusive fluxes which are induced by discretization errors. This effect becomes visible when the transport of quantities with small diffusivities [with the exact meaning of small yet to be specified in Eq. (42)] is considered. In macroscopic systems such small diffusivities are rarely found, at least when being looked at from a phenomenological point of view. The reason for the reduced importance of numerical diffusion in many macroscopic systems lies in the turbulent nature of most macro flows. The turbulent velocity fluctuations induce an effective diffusivity of comparatively large magnitude which includes transport effects due to turbulent eddies [1]. The effective diffusivity often dominates the numerical diffusivity. In contrast, micro flows are often laminar, and especially for liquid flows numerical diffusion can become the major effect limiting the accuracy of the model predictions. 

Heaters encounter four major design limitations heat flux, process pressure drop, TWT, and BWT. Heat flux limited heaters are usually characterized with high pressure AP (>20psi) and most general service heaters fall into this flux-limited category. Typically, the flux limit for single-fired heaters is around 10,000 Btu/ft h. 

The assessment first looked into the opportunities associated with design margin. By optimizing process conditions and pushing the equipment to the absolute limits, the plant could make majority of the spare capacity and push plant capacity by 10% with some minor modifications. However, beyond a 10% expansion, several major limitations were identified from detailed simulations, which included the feed heater flux limit before the main fractionator column, jet flooding limit in the main fractionation column, and reactor space velocity limit in the hydrocracking unit. 

INS is flux-limited technique. Thus major instrumental advances can only be expected when more-intense neutron sources become available. These will... 

In principle, Chen, given the flux relations there is no difficulty in constructing differencial equations to describe the behavior of a catalyst pellet in steady or unsteady states. In practice, however, this simple procedure is obstructed by the implicit nature of the flux relations, since an explicit solution of usefully compact form is obtainable only for binary mixtures- In steady states this impasse is avoided by using certain, relations between Che flux vectors which are associated with the stoichiometry of Che chemical reaction or reactions taking place in the pellet, and the major part of Chapter 11 is concerned with the derivation, application and limitations of these stoichiometric relations. Fortunately they permit practicable solution procedures to be constructed regardless of the number of substances in the reaction mixture, provided there are only one or two stoichiomeCrically independent chemical reactions. 

In the majority of methods described thus far, the interfacial kinetics are deduced by measuring concentration changes in the bulk of the solution rather than at the interface, where the reaction occurs. This introduces a time lag, limiting the resolution of the measurement in the determination of interfacial kinetics. A more direct approach is to identify the interfacial flux. This can be achieved in the electrolyte dropping electrode, via the current flow, but this method is only applicable to net charge-transfer processes at externally polarized interfaces. 

The number of naturally occurring radionuclides is limited and few are of analytical value. For the majority of purposes artificial radionuclides are manufactured. Bombardment reactions are generally used in their production. A suitable target material is exposed to an intense flux of the appropriate particles in a nuclear reactor or particle accelerator such as a cyclotron. Thermal neutrons in the reactor... 

Since nitrogen is a nutrient, which limits the productivity of almost all Boreal and Sub-Boreal Forest ecosystems, its biogeochemical cycling is relatively well understood at present. The major N transformations and fluxes are shown in Figure 3. 

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