Positive hole

According to the electron-transfer mechanism of spectral sensitization (92,93), the transfer of an electron from the excited sensitizer molecule to the silver haHde and the injection of photoelectrons into the conduction band ate the primary processes. Thus, the lowest vacant level of the sensitizer dye is situated higher than the bottom of the conduction band. The regeneration of the sensitizer is possible by reactions of the positive hole to form radical dications (94). If the highest filled level of the dye is situated below the top of the valence band, desensitization occurs because of hole production. 

One feature of oxides is drat, like all substances, they contain point defects which are most usually found on the cation lattice as interstitial ions, vacancies or ions with a higher charge than dre bulk of the cations, refened to as positive holes because their effect of oxygen partial pressure on dre electrical conductivity is dre opposite of that on free electron conductivity. The interstitial ions are usually considered to have a lower valency than the normal lattice ions, e.g. Zn+ interstitial ions in the zinc oxide ZnO structure. 

Usually tills is not tire case and Table 5.2 shows values for Eg, jig and ptp for a number of semiconductors having the diamond structure. It will generally be observed from this table that the mobilities of electrons are greater than those of positive holes making these materials n-type semiconductors. 

Generally speaking tire mobilities of elecU ons and positive holes decrease and the band gaps increase as the bonding in the semiconductors becomes more... 

The relative contributions of ions, electrons and positive holes to the conductivity is described drrough the transport number which is related to a partial conductivity defined by... 

At the other end of the conduction spectrum, many oxides have conductivities dominated by electron and positive hole contributions to the extent that some, such as Re03, SnOa and tire perovskite LaCrOs have conductivities at the level of metallic conduction. High levels of p-type semiconduction are found in some transition metal perovskites especially those containing alio-valent ions. Thus the lanthairum-based perovskites containing transition metal ions, e.g. LaMOs (M-Cr, Mn, Fe, Co, Ni) have eirlranced p-type semiconduction due to the dependence of the transition metal ion valencies on the ambient... 

Here Oq represents the oxide ion which is incorporated, IT represents the Ni + ion which is a positive hole, and an exU a negative charge being indicated by the superscript dot, thus V/,j is the vacant cation site where tire double dot represents the absence of two positive charges at that site. 

The analysis of oxidation processes to which diffusion control and interfacial equilibrium applied has been analysed by Wagner (1933) who used the Einstein mobility equation as a starting point. To describe the oxidation for example of nickel to the monoxide NiO, consideration must be given to tire respective fluxes of cations, anions and positive holes. These fluxes must be balanced to preserve local electroneutrality tliroughout the growing oxide. The flux equation for each species includes a term due to a chemical potential gradient plus a term due to the elecuic potential gradient... 

The ionic and elecU oii or positive hole chemical potentials are related tluough thermodynamic relations such as... 

If there is more than one type of carrier, i.e. electrons and positive holes, as in MWCNT, the contribution of each type of carrier should be taken into account. In that case, the total electrical conductivity is given by the sum of the partial conductivities. 

If n is the concentration of defects (cation vacancies or positive holes) at equilibrium, then, applying the law of mass action to equation 1.157... 

We note that is positive and goes through a maximum as a increases. If the positive holes were localised on the cations, they would give an entropy contribution exactly equal to. The positive holes have, however, considerable mobility (see below), and are perhaps best treated as an ideal gas consisting of particles of effective mass m. In this case ... 

Motion of a cation vacancy Fig. 1.73 Motion of positive holes and cation vacancies... 

The reason for this can be seen as follows. In a perfect crystal with the ions held fixed, a positive hole would move about like a free particle with a mass m depending on the nature of the crystal. In an applied electric field, the hole would be uniformly accelerated, and a mobility could not be defined. The existence of a mobility in a real crystal derives from the fact that the uniform acceleration is continually disturbed by deviations from a perfect lattice structure. Among such deviations, the thermal motions of the ions, and in particular, the longitudinal polarisation vibrations, are most important in obstructing the uniform acceleration of the hole. Since the amplitude of the lattice vibrations increases with temperature, we see how the mobility of a... 

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