The electronic and hole conductivity

Fig. 2 Scheme representing the general principle of a photoelectrochemical system. Electrons are photoexdted in the absorber. The electron and hole are selectively transferred to an electron conductor (usually a metal or a semiconductor) and to a hole conductor (a redox system in a liquid electrolyte). The photovoltage is the difference between the electrochemical potentials in the electron and hole conducting phases thus Mh-... 

Fig. 5. The electronic and hole conductivity of Zro.85Yo.15O1 925 (Park and Blumental, 1989), Lao.gSro iGao -Mgo.2O2.85 (LSGM9182), (Yamaji et al., 1997 Kim and Yoo, 2001) and Ceo sGdo oOi 9 (GDC), (Xiong et al., 2004) measured by the ion blocking method at 1273 K.

The relatively high mobilities of conducting electrons and electron holes contribute appreciably to electrical conductivity. In some cases, metallic levels of conductivity result ia others, the electronic contribution is extremely small. In all cases the electrical conductivity can be iaterpreted ia terms of carrier concentration and carrier mobiUties. Including all modes of conduction, the electronic and ionic conductivity is given by the general equation ... 

Where b is Planck s constant and m and are the effective masses of the electron and hole which may be larger or smaller than the rest mass of the electron. The effective mass reflects the strength of the interaction between the electron or hole and the periodic lattice and potentials within the crystal stmcture. In an ideal covalent semiconductor, electrons in the conduction band and holes in the valence band may be considered as quasi-free particles. The carriers have high drift mobilities in the range of 10 to 10 cm /(V-s) at room temperature. As shown in Table 4, this is the case for both metallic oxides and covalent semiconductors at room temperature. 

Therefore, there could exist rich defects in Ba3BP30i2, BaBPOs and Ba3BP07 powders. From the point of energy-band theory, these defects will create defect energy levels in the band gap. It can be suggested that the electrons and holes introduced by X-ray excitation in the host might be mobile and lead to transitions within the conduction band, acceptor levels, donor levels and valence band. Consequently, some X-ray-excited luminescence bands may come into being. 

In semiconductors, which have a bandgap, recombination of the excited carriers— return of the electrons from the conduction band to vacancies in the valence band—is greatly delayed, and the lifetime of the excited state is much longer than in metals. Moreover, in n-type semiconductors with band edges bent upward, excess electrons in the conduction band will be driven away from the surface into the semiconductor by the electrostatic held, while positive holes in the valence band will be pushed against the solution boundary (Fig. 29.3). The electrons and holes in the pairs produced are thus separated in space. This leads to an additional stabihzation of the excited state, to the creation of some steady concentration of excess electrons in the conduction band inside the semiconductor, and to the creation of excess holes in the valence band at the semiconductor-solution interface. 

The most fundamental transition that can take place is the transfer of an electron from the valence band to the conduction band. This creates a mobile electron and a mobile hole, both of which can often be treated as defects. Transitions of this type, and the reverse, when an electron in the conduction band drops to the valence band, eliminating a hole in the process and liberating energy, are called interband transitions. Apart from the electrons and holes themselves, interband transitions do not involve defects. All other transitions do. 

Mobility data on bipolar charge-transport materials are still rare. Some bipolar molecules with balanced mobilities have been developed [267], but the mobilities are low (10 6—10 8 cm2/Vs). Up to now, no low molecular material is known that exhibits both high electron and hole conductivity in the amorphous state, but it is believed that it will be only a matter of time. One alternative approach, however, is to use blends of hole and electron transporting materials [268]. 

Figures 2.13(a) and 2.13(b) illustrate the basis of a semiconductor diode laser. The laser action is produced by electronic transitions between the conduction and the valence bands at the p-n junction of a diode. When an electric current is sent in the forward direction through a p-n semiconductor diode, the electrons and holes can recombine within the p-n junction and may emit the recombination energy as electromagnetic radiation. Above a certain threshold current, the radiation field in the junction becomes sufficiently intense to make the stimulated emission rate exceed the spontaneous processes.

For metal electrodes, the concentrations of both electrons and holes in the electrode are sufficiently high at the Fermi level that the eneigy of electrons and holes, which participate in the electrode reaction, may be represented by the Fermi level namely by the electron level corresponding to the electrode potential. For semiconductor electrodes, in contrast, the electrons and holes that participate in the electrode reaction are not at the Fermi level, but at the levels of the conduction and valence bands different finm the Fermi level of the electrode, i. e. from the electron level corresponding to the electrode potential. For example, as shown in Fig. 10-13, the anodic OJ gen reaction at n-iype semiconductor electrodes proceeds with interfacial holes in the valence band, whose energy — Cy (—Cv =... 

The properties of the band gap in semiconductors often control the applicability of these materials in practical applications. To give just one example, Si is of great importance as a material for solar cells. The basic phenomenon that allows Si to be used in this way is that a photon can excite an electron in Si from the valence band into the conduction band. The unoccupied state created in the valence band is known as a hole, so this process has created an electron-hole pair. If the electron and hole can be physically separated, then they can create net electrical current. If, on the other hand, the electron and hole recombine before they are separated, no current will flow. One effect that can increase this recombination rate is the presence of metal impurities within a Si solar cell. This effect is illustrated in Fig. 8.4, which compares the DOS of bulk Si with the DOS of a large supercell of Si containing a single Au atom impurity. In the latter supercell, one Si atom in the pure material was replaced with a Au atom,... 

The mechanism operating within a polymer LED involves injection, via a metal electrode, of electrons into the conduction band and holes into the valence band of the polymeric semi-conductor. The electrons and holes diffuse towards each other and then combine to form an exciton, which can move along the polymer chain. These excited states then decay to the ground state with a characteristic fluorescence. 

Person 1 Use the data to write a relationship for the intrinsic conductivity of this substance as a function of the electron and hole mobilities. 

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