Carrier concentration effect

Compared to preceding two strategies, the synergistic optimization of Seebeck coefficient and electrical conductivity is more difficult due to the inverse coupling of the two parameters, which are directly related to the carrier concentration, effective mass, and mobility. However, thanks to the unremitting efforts of scientists, a series of encouraging progress has been made in this field. 

In an intrinsic semiconductor, charge conservation gives n = p = where is the intrinsic carrier concentration as shown in Table 1. Ai, and are the effective densities of states per unit volume for the conduction and valence bands. In terms of these densities of states, n andp are given in equations 4 and... 

A method for quantification of the CL, the so-called MAS corrections, in analogy with the ZAP correction method for X rays (see the article on EPMA), has been proposed to account for the effects of the excess carrier concentration, absorption and surface recombination. In addition, a total internal reflection correction should also be included in the analysis, which leads to the MARS set of corrections. This method can be used for further quantification efforts that also should involve Monte Carlo calculations of the generation of excess carriers. 

How can such problems be counterbalanced Since a large capacitance of a semiconductor/electrolyte junction will not negatively affect the PMC transient measurement, a large area electrode (nanostructured materials) should be selected to decrease the effective excess charge carrier concentration (excess carriers per surface area) in the interface. PMC transient measurements have been performed at a sensitized nanostructured Ti02 liquidjunction solar cell.40 With a 10-ns laser pulse excitation, only the slow decay processes can be studied. The very fast rise time cannot be resolved, but this should be the aim of picosecond studies. Such experiments are being prepared in our laboratory, but using nanostructured... 

A typical featnre of semicondnctor electrodes is the space charge present in a relatively thick surface layer (see Section 10.6), which canses a potential drop across this layer (i.e., the appearance of a snrface potential %). This potential drop affects the rate of an electrochemical charge-transfer reaction in exactly the same way as the potential drop across the diffnse EDL part (the / -potential) hrst, through a change in carrier concentration in the snrface layer, and second, throngh a change in the effect of potential on the reaction s activation energy. 

It is not overly difficult to include the effects of interconversion of hydrogen among its charge states if these are equilibrated with the local carrier concentrations and if we continue to neglect complex formation and assume that the spatial scale of the diffusion-migration phenomena is large... 

The rate of an electrode reaction is a function of three principle types of species charge carriers on the surface, active surface atoms and reactant species in the solution as illustrated in Figure 23. That is, r cc [h] [Siactive] [A]. Carrier concentration and reactant concentration do not, in general, depend on surface orientation while active surface atoms may be a function of surface orientation. Anisotropic effect occurs when the rate determining step depends on the active surface atoms that vary with crystal orientation of the surface. On the other hand, reactions are isotropic when the concentration of active surface atoms is not a function of surface orientation or when the rate determining step does not involve active surface atoms. 

Figure 4.22 Schematic diagram of a field effect transistor. The silicon-silicon dioxide system exhibits good semiconductor characteristics for use in FETs. The free charge carrier concentration, and hence the conductivity, of silicon can be increased by doping with impurities such as boron. This results in p-type silicon, the p describing the presence of excess positive mobile charges present. Silicon can also be doped with other impurities to form n-type silicon with an excess of negative mobile charges.

In materials that have high ionic conductivity, effects such as the above are undoubtedly very important. They show up particularly in materials that have a high concentration of mobile ions and in experimental values of the ac conductivity measured as a function of frequency. In materials with a high carrier concentration, mobile ions are inevitably quite close together, separated by at most a few angstroms. Consequently, ions cannot hop in isolation but are influenced by the distribution of mobile ions in their vicinity. This contrasts with the behaviour of dilute defect systems with low carrier concentrations. In these, the mobile ions are well separated from each other and their conduction can largely be treated in terms of isolated hops. 

The work of Mensfoort et al. is a striking test of the importance of charge carrier density effects in space-charge-limited transport studies. For a given applied voltage the space charge concentration is inversely proportional to the device thickness. This explains why in Fig. 9 the deviation from the In cx... 

Fig. 20 Charge carrier mobility in P3HT as a function of the charge carrier concentration. Squares refer to an experiment performed on a field effect transistor while circles refer to experiments done on an electrochemically doped sample. In the latter case the mobility is inferred from the steady state current at a given doping level. Solid and dashed lines have been fitted using the theory of [101]. The fit parameters are the site separation a, the prefactor Vq in the Miller-Abrahams-type hopping rate, the inverse wavefunction decay parameter y and the dielectric constant e. From [101] with permission. Copyright (2005) by the American Institute of Physics...

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