Concentration profiles, charge carriers

Essential changes in the concentrations of charge carriers and accordingly in the potential profile and emission spectra are observed when the quasi-Fermi level difference AF exceeds, e.g., for the superlattice No. 4 the value of 0.9 eV. Then, the chemical potential for electrons in the n-type layers becomes positive and the degeneration begins. For superlattice No. 4i it occurs at a smaller value of AF. 

Fig ures 5-43 and 5—44 illustrate the band bending and the concentration profile of charge carriers in these four types of space charge layers. 

Figure 2. Decay constant of the photocurrent as a function of the normalized charge carrier concentration n at t 0 which Is proportional to the relative light Intensity I. Closed circles Indicate data obtained from field-dependent decay profiles of Figure 1.

We can treat them through a variant of the Henderson equation, (2.3.39), which was introduced earlier in Section 2.3.4. The usual form of this equation is derived from (2.3.36) by neglecting activity effects and assuming linear concentration profiles through the junction. Here, we are interested only in univalent positive charge carriers hence we can specialize (2.3.39) for the interface between m and m as... 

A schematic of the concentration profiles of various charge carriers within membranes is shown in Eig. 2.9. The protonic and electronic conductivity are presented as empirical functions of H2 partial pressure to substitute into Eq. (2.7). 

When the surface is taken as ideal, that is, flat and homogeneous, the physical quantities depend only on the distance a from the surface. The surface imposes boundary conditions on the polymer order parameter fix) and electrostatic potential fix). In thermodynamic equihhrium, all charge carriers in solution should exactly balance the surface charges (charge neutrality). The Poisson-Boltzmann Equation (55), the self-consistent field Equation (56), and the boundary conditions uniquely determine the polymer concentration profile and the electrostatic potential. In most cases, these two coupled nonlinear equations can only he solved numerically. 

The solid solution KCl-RbCl differs basically from the solid solution NiO-MgO in two ways. Firstly, the system KCl-RbCl exhibits purely ionic conduction. The transport numbers of electronic charge carriers are negligibly small. Secondly, a finite transport of anions occurs. Because of these facts, the atomic mechanism of the solid state reaction between KCl and RbCl is essentially of a different sort than that between NiO and MgO. Once again, the diffusion profile exhibits an asymmetry (see Fig. 6-1). However, in this case the asymmetry arises not so much because of the variation of the defect concentration with composition, but rather because of the different mobilities of the ions at given concentration. Were the transport number of the chloride ions negligible, then the diffusion potential (which would be set up because of the different diffusion velocities of potassium and rubidium) would ensure that the motion of the two cations is coupled. If, on the contrary, the transference number of the chloride ions is one, then there is no diffusion potential, and the motion of the two cations is decoupled. 

The integral effect exerted by such profiles, is what is generally measured or perceived in a specific application. A conductance experiment is a well-suited example, because the local specific conductivity is proportional and sensitive to the charge carrier concentration. (See Section 6.6.2 for diffusion through boundary layers, and Section 7.3.3 for the capacitance effects.)... 

At this point, it is instructive to discuss the behaviour of the minority charge carrier [255]. Let us assume that the adequately mobile minority charge carrier 3 (e.g. the conduction electrons in the example in Fig. 5.72) is also enriched, which is the case if Z1Z3 > 0. We obtain its concentration profile via Cs = Ci ) according to Eq. (5.215). For Z3 = zi we obviously get, after integration, a result which is analogous to Eq. (5.237), namely... 

We assume that a conductance measurement is used to monitor the stoichiometric change. We consider a thin rectangular sheet of isotropic material, which has been equilibrated under a partial pressure of oxygen Pi (=M20n-6j). We suddenly alter the partial pressure to the value P2 and follow the relaxation process to the final state (=M20i+i2) (Fig. 6.27). The initial homogeneous profile is described by Ci, (here c denotes the concentration of the charge carrier measured in the conductance... 

In the case of the Mott-Schottky boundary layer (majority charge carrier immobile, counterdefect depleted), we obtained a simple result for high depletion and could ap-proximate the space charge profile by means of a rectangular function of width A oc Ay l o total surface charge is approximately obtained by multiplication of A with the constant doping concentration m resulting in ... 

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