Concentration of Electrons and Holes

The applied voltage determines the difference in the electrochemical potential of the electrons or the ratio of the concentrations of the electronic species on both sides of the electrolyte  

The difference in the charge transfers in the two experiments (AQ) is given by the difference in the areas of the two triangles in Fig. 14  

The charge-transfer technique [48] is an electrochemical method for determination of the concentrations of electronic species. As in the case of DC-polarization and 

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In an undoped, intrinsic semiconductor the equiHbrium concentrations of electrons, and holes,/), are described by a lever rule derived from the law of mass action (eq. 3) ... 

It is important to realize that the migration in an electric field depends on the magnitude of the concentration of the charged species, whereas the diffusion process depends only on the concentration gradient, but not on the concentration itself. Accordingly, the mobility rather than the concentration of electrons and holes has to be small in practically useful solid electrolytes. This has been confirmed for several compounds which have been investigated in this regard so far [13]. 

Here we make use of the same designations n(.x) and pix) for concentrations of electrons and holes in SCR rq and po their concentrations in volume outside SCR. It is assumed that the thickness and the average size of an adsorbent microcrystal / are much larger than the shielding radius, x is the coordinate plotted from the surface inside the semiconductor. 

These surface concentrations of electrons and holes are important in electrochemistry. 

When electronic equilibrium is established in the space charge layer, the concentration of interfacial electrons is given by n, = n exp (- e A /k T) and the concentration of interfacial holes is given by Pt = p exp(e A lk T) n and p are the concentrations of electrons and holes, respectively, in the semiconductor interior. In general, the ionization of surface atoms (Eqn. 9-24) is in quasiequilibrium so that the concentration of surface ions depends on the overvoltage... 

The concentrations of electrons and holes in the conduction and valence bands, n and p, in the photostationary state under photon irradiation are expressed, respectively, in Eqn. 10-1 ... 

For semiconductor electrodes in which the concentration of impurities is relatively high (.No, Ni, lO cm ), the photopotential has been derived as a function of the concentration of electrons and holes to obtain Eqns. 10-10 and 10-11 [Myamlin-Pleskov, 1967] ... 

Furthermore, V > 0 is the voltage drop in the system (between x = 0 — 0 and x — L + 0) 0 < Co 1 is the external concentration of univalent electrolyte (equilibrium concentration of electrons and holes), maintained fixed at the outer boundaries of the multilayered arrangement. 

On the other hand, the concentrations of electrons and holes, n and p, respectively, in the conduction band and valence band of the semiconductors, which contribute to the electrical conductivity, are expressed by the following equations ... 

Photopotential transients have also been studied [181]. The light pulse will generate a non-stationary concentration of electrons and holes analysis reveals that these separate rapidly in the depletion layer (type semiconductor) and an exponential concentration of electrons at the inner edge of the depletion layer, as discussed above. This new charge distribution will alter the potential distribution and numerical integration for an n-type wide bandgap material shows that, if... 

H. J. Engell in this volume). An important consequence is that concentrations of electrons and holes in the surface can change with polarization by several orders of magnitude in a metal surface the concentration of electrons remains relatively constant and only their potential energy changes with polarization. 

If, however, the electrode is a semiconductor, the distribution of charges in the solid will be similar to that in the electrolyte, for the concentration of carriers in semiconductors is significantly smaller than in metals, hi pure germanium for example the concentration of electrons and holes at room temperature is 2.5 x 10 cm or 4 x 10 mole/1 i.e., the... 

To describe the conductivity of an intrinsic semiconductor sample quantitatively, we need to calculate the concentrations of both types of charge carriers in the solid. The key quantity that controls the equilibrium concentration of electrons and holes in an intrinsic semiconductor is the band gap. Because the thermal excitation energy required to produce an electron and a hole is equal to Eg, the intrinsic carrier concentrations can be related to Eg using the Boltzmann relationship ... 

Figure 12.3 Fermi energy at the flat-band potential, referenced to the valence band energy, as a function of doping level for an n-type GaAs semiconductor. The corresponding concentrations of electrons and holes are presented in Figure 12.2.

The mathematicEil development presented here is intended to emphasize the similarities between the analysis of transport in semiconductors and that in electrolytic systems as presented in Chapter 5. In doing so, concentrations of electrons and holes, typically presented on an atomistic basis, e.g., in units of cm , are given in a molar basis. 

As shown by curve b in Figure 12.7, illumination at the open-circuit condition produces electron-hole pairs that are separated by the potential gradient associated with the interface. The concentration of holes increases at all positions within the semiconductor, and the concentration of electrons increases in the space-charge region, thus straightening the equilibrium potential variation. As the system approaches the short-circuit condition under illumination (curve c in Figure 12.7), the concentrations of electrons and holes tends toward the equilibrium distributions. 

Even in a doped semiconductor, mobile electrons and holes are both present, although one carrier type is predominant. For example, in a sample of silicon doped with arsenic (w-type doping), the concentrations of mobile electrons are slightly less than the concentration of arsenic atoms (usually expressed in terms of atoms/cm ), and the concentrations of mobile holes are extremely low. Interestingly, the concentrations of electrons and holes always follow an equilibrium expression that is entirely analogous to that for the autodissociation of water into H and OH ions (Chapter 18) that is,... 

The charge conservation law requires that the concentration of electrons and holes trapped in colour centres during irradiation in vacuo under steady-state conditions (since the concentration of free charge carriers can be neglected compared with that of trapped carriers) or after irradiation must be equal. That is... 

Two parameters that affect the selectivity stand out (1) the ratio ox/ ed of the rate constants for oxidation and reduction, and (2) the parameter y= [es ]/[hs ] which expresses the ratio between the surface concentrations of electrons and holes. 

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