Concentration ambipolar

Fuchs (F4, pp. 102-105) also points out that, for a unipolar aerosol, the rate of concentration change, as given by Eq. (9) or (10), is an intrinsic property of the aerosol, depending on neither size nor shape of cloud. Some of the other relationships [Eqs. (8) and (11)], however, are subject to the cloud symmetry specified above. Fuchs also points out that in an ambipolar cloud the particles of minority sign tend to be driven toward the center or core where the cloud approaches neutrality asymptotically. The outer edge of the cloud tends to become unipolar with the sign of the initially most prevalent charge. 

With ambipolar ions, a net charging can still take place. The charging rate for this case can be approximated by letting the term (/ ,- j) in Eq. (64) be equal to the difference between the corresponding terms for ions of each charge. Actually significant ambipolar ion concentrations may be short-lived because of ion recombination. 

From the formation reaction of protonic defects in oxides (eq 23), it is evident that protonic defects coexist with oxide ion vacancies, where the ratio of their concentrations is dependent on temperature and water partial pressure. The formation of protonic defects actually requires the uptake of water from the environment and the transport of water within the oxide lattice. Of course, water does not diffuse as such, but rather, as a result of the ambipolar diffusion of protonic defects (OH and oxide ion vacancies (V ). Assuming ideal behavior of the involved defects (an activity coefficient of unity) the chemical (Tick s) diffusion coefficient of water is... 

Equation (1.57a) implies that in the locally electro-neutral ambipolar diffusion concentration of both ions evolves according to a single linear diffusion equation with an effective diffusivity given by (1.57b). Physically, the role of the electric field, determined from the elliptic current continuity equation... 

Fig. 5.5. Luminescence quenching (bullets, right hand, axis) and short-circuit current Ac (black squares, left hand axis) vs. molar fullerene concentration in a bulk hetero junction composite. The different onsets for percolation for the two phenomena (exciton diffusion versus ambipolar carrier transport) can be clearly seen...

Similar approaches are used for most steady-state measurement techniques developed for mixed ionic-electronic conductors (see -> conductors and -> conducting solids). These include the measurements of concentration-cell - electromotive force, experiments with ion- or electron-blocking electrodes, determination of - electrolytic permeability, and various combined techniques [ii-vii]. In all cases, the results may be affected by electrode polarization this influence should be avoided optimizing experimental procedures and/or taken into account via appropriate modeling. See also -> Wagner equation, -> Hebb-Wagner method, and -> ambipolar conductivity. 

Wagner enhancement factor — describes usually the relationships between the classical - diffusion coefficient (- self-diffusion coefficient) of charged species i and the ambipolar - diffusion coefficient. The latter quantity is the proportionality coefficient between the - concentration gradient and the - steady-state flux of these species under zero-current conditions, when the - charge transfer is compensated by the fluxes of other species (- electrons or other sort(s) of -> ions). The enhancement factors show an increasing diffusion rate with respect to that expected from a mechanistic use of -> Ficks laws, due to an internal -> electrical field accelerating transfer of less mobile species [i, ii]. 

Another important case relates to ambipolar - diffusion, when a flux of neutral species is driven by a chemical potential gradient In this case, the thermodynamic factor is usually written in similar form (e.g., d[iB/dcB or d In aB/dlncB), and may comprise additional multipliers depending on particular formulae the concentration... 

Here ct, ce and cp are the concentrations of the positive ions, electrons and the positron probability density at a point r measured from the center of the blob at time t. Dp is the diffusion coefficient of the positron, Di = De = Damb 0 is the ambipolar diffusion coefficient of the blob, a2 o2 ss a2 is the dispersion of the intrablob species, and a2 is the dispersion of the positron space distribution by the end of its thermalization. Decay rate Te-1 = 1/t + kescs is the sum of the electron solvation rate and possible capture by solute molecules t 2 = 1 /t2 + l/r + kpscs accounts for the free e+ annihilation, solvation and reaction with S. Similarly, t 1 = l/rjmr + hscs, where T r is the rate of the ion-molecule reaction. 

The chemical diffusion coefficient includes, as we know from the formal treatment in Section VI..3iv., both an effective ambipolar conductivity and an effective ambipolar concentration. The latter parameter is determined by the thermodynamic factor which is large for the components but close to unity for the defects. 

In this work we have chosen the combination of hole-conducting copper-phthalocyanine (CuPc) and the n-conducting fullerene C o, which are both known from organic photovoltaic cells either as heterolayer structures or bulk-heterojunctions [18-21]. They can be considered as model systems for ambipolar transport where the asymmetry of the electron and hole mobilities is adjustable by the concentration of both materials in the mixture. 

Although Eqs. (12.4) to (12.6) elucidate the nature of the driving force operative during creep, they do not shed any light on how the process occurs at the atomic level. To do that, one has to go one step further and explore the effect of applied stresses on vacancy concentrations. For the sake of simplicity, the following discussion assumes creep is occurring in a pure elemental solid. The complications that arise from ambipolar diffusion in ionic compounds are discussed later. The equilibrium concentration of vacancies Cq under a flat and stress-free surface is given by (Chap. 6)... 

It has already been remarked that when the hole concentration approaches the electron concentration as in a near-intrinsic semiconductor or a photo-conductive insulator, the diffusion length is no longer the minority-carrier dilfusion length Lp = ylDpXp, but rather an ambipolar or effective L. In this section we wish to show the relationship of the measured Lq to the minority-carrier diffusion length Lp in the context of a material with the photocon-ductive properties of undoped a-Si H. 

We note that the molecular flux is proportional to the difference in hydrogen pressure (as in gas phase transport through a piorous membrane), whereas atomic transport has a square root dependence, and as such would behave similarly to ambipolar transport of protons and electrons limited by the conductivity of a minority concentration of protons. 

In cases where a continuous and coherent layer of oxide film is present, further reaction can proceed only by diffusion of some of the reactants across the film. There are several possible mechanisms for this transport of material. In many solids, the passage of neutral atoms is less likely than the transport of charged particles, ions and electrons. In such cases, called ambipolar diffusion, the concentration gradient is not the only constraint on the system. In addition, and at all times, overall charge neutrality needs to be maintained. 

This chapter concentrates on organic bipolar transistors, including details about the basic operation principles, device configurations, and processing methods, and describing the various strategies that have been applied to achieve ambipolar transport. Touching upon small molecule-based FETs and the hybrid approach, the main focus will be on polymer-based bipolar transistors since they can provide one of the ultimate solutions for simple, low-cost fabrication of flexible bipolar FETs. 

The ambipolar diffusion coefficient is the coefficient of the concentration gradient in Eq. (3). 

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