Forbidden gap

Fig. 1. The energy levels in a semiconductor. Shown are the valence and conduction bands and the forbidden gap in between where represents an occupied level, ie, electrons are present O, an unoccupied level and -3- an energy level arising from a chemical defect D and occurring within the forbidden gap. The electrons in each band are somewhat independent, (a) A cold semiconductor in pitch darkness where the valence band levels are filled and conduction band levels are empty, (b) The same semiconductor exposed to intense light or some other form of excitation showing the quasi-Fermi level for each band. The energy levels are occupied up to the available voltage for that band. There is a population inversion between conduction and valence bands which can lead to optical gain and possible lasing. Conversely, the chemical potential difference between the quasi-Fermi levels can be connected as the output voltage of a solar cell. Fquilihrium is reestabUshed by stepwise recombination at the defect levels D within the forbidden gap.

ZnS is a broad band semiconductor, the electron in the fully occupied valence band is difficult to be excited up to the conduction band. There is less free electron in ZnS, and then it is not easy to accelerate the electrochemistry oxidation of surface. That is to say, the dissolution of ZnS from mineral surface is difficult and has little chance to react with thio-collectors. When substituted by Cu or Fe ions, the forbidden gap of doped ZnS will decrease and the quantity of free electrons in ZnS will increase. This variation will enhance the electrochemistry activity of ZnS. 

At equilibrium in the dark, the Fermi levels for electrons and holes in a particular sample of semiconductor are coincident, being near the top of the forbidden gap in an n-type and near the bottom of the gap in a p-type semiconductor. Figure 4 illustrates the region near the surface of an n-type semiconductor, the Fermi levels for electrons and holes, coincident... 

The excited electron may also recombine with an activator, with the following luminescence, or a trap, with the following electron capturing, within the forbidden gap. Traps and activator energy levels are caused by defects in the crystal lattice (Fig. 2.6b). 

An important aspect of semiconductor films in general with regard to electronic properties is the effect of intrabandgap states, and particularly surface states, on these properties. Surface states are electronic states in the forbidden gap that exist because the perfect periodicity of the semiconductor crystal, on which band theory is based, is broken at the surface. Change of chemistry due to bonding of various adsorbates at the surface is often an important factor in this respect. For CD semiconductor films, which are usually nanocrystalline, the surface-to-volume ratio may be very high (several tens of percent of all the atoms may be situated at the surface for 5 mn crystals), and the effects of such surface states are expected to be particularly high. Some aspects of surface states probed by photoluminescence studies are discussed in the previous section. 

For a semiconductor like Ge, the pattern of electronic interaction between the surface and an adsorbate is more complex than that for a metal. Semiconductors possess a forbidden gap between the filled band (valence band) and the conduction band. Fig. 6a shows the energy levels for a semiconductor where Er represents the energy of the top of the valence band, Ec the bottom of the conduction band, and Ey is the Fermi energy level. The clean Ge surface is characterized by the presence of unfilled orbitals which trap electrons from the bulk, and the free bonds give rise to a space-charge layer S and hence a substantial dipole moment. Furthermore, an appreciable field is produced inside the semiconductor, as distinct from a metal, and positive charges may be distributed over several hundred A. 

Most monomeric organic dyes have a conductivity of the order of 10-10 to 10-14 ohm-1cm 1 because the relatively broad forbidden gap between the valence and conduction bands limits the generation rate z to low values ... 

As mentioned above, with broad forbidden gaps a carrier injection from the electrodes may contribute to the dark current. Because the energetic conditions are... 

This observation may result from an usual acceptor effect according to which AE can be identified with the energetic position of acceptors in the forbidden gap. It should be mentioned here that, according to Lyons 75>, AE is connected by Eqs. (52) and (53) with the electrostatic polarization energy P. 

Therefore, we are able to discuss the existence of defect states (recombination centers and traps) in the forbidden gap of solid organic dyes characterized by different trapping probabilities (ranging from 10-12 cm2 to 10-20 cm2) for electrons and holes. Hence, asymmetric trapping of electrons and holes leading to n- and -photoconductivity is very probable. 

In most semiconductors, there are, in addition to the allowed energy levels for electrons in the conduction and filled bands of the ideal crystal, discrete levels with energies in the forbidden gap which correspond to electrons localized at impurity atoms or imperfections. In zinc oxide, such levels arise when there are excess zinc atoms located interstitially in the lattice. At very low temperatures the interstitial zinc is in the form of neutral atoms. However, the ionization energy of the interstitial atoms in the crystal is small and at room temperature most are singly ionized, their electrons being thermally excited into the conduction band. These electrons give rise to the observed A-type conductivity. 

The absorption of light increases as the concentration of interstitial zinc increases. Scharowski subtracts the intrinsic absorption, as found in relatively stoichiometric crystals, from the total absorption in a highly doped sample, and considers the excess absorption to arise from the double ionization of interstitial zinc. This excess absorption peaks at about 3.2 e.v., and from this Scharowski concludes that the energy of ionization of interstitial Zn+ is 3.2 e.v. The fact that this is equal to the forbidden gap width is considered to be coincidental. 

Figure 1 is an energy level diagram showing a proposed model for the band structure of zinc oxide. The valence band and conduction band are shown separated by a forbidden gap. Two levels which correspond to the trapping of two electrons by the interstitial zinc are indicated in the forbidden gap. Surface levels associated with adsorbed oxygen are shown. 

The threshold of the photocurrent is at the energy of 1 eV. This value is less than the absorption edge enagy, what proves the existence of deep levels inside the forbidden gap. The absence of the structure at the beginning of the interband transitions excludes the possibility that the photocurrent is due to the surface exciton dissociation. Attempts to observe good photoconduction in ris-(CH) were unsuccessful. The photocunent in cis-(CH)n was three orders of magnitude lower than in trans-(CH) . 

The main scheme is shown in Fig. 17. The photogenerated electron hole pairs transfer to the soliton-antisoliton pairs in 10 13s. Two kinks appeared in the polymer structure, which separates the degenerated regions. Due to the degeneration, two charged solitons may move without energy dissipation in the electric field and cause the photoconductivity. The size of the soliton was defined as 15 monomer links with the mass equal to the mass of the free electron. In the scheme in Fig. 17, the localized electron levels in the forbidden gap correspond to the free ( + ) and twice occupied ( — ) solitons. The theory shows the suppression of the interband transitions in the presence of the soliton. For cis-(CH)n the degeneration is absent, the soliton cannot be formed and photoconductivity practically does not exist. 

Fig. 17a, b. Band scheme (a) and chemical structure (b) of trans-(CH) . The polymer chain contains the charged soliton-antisoliton pair. In the middle of the forbidden gap there are levels connected with two solitons not occupied ( + ) and twice occupied ( —) [106]... 

Schottky photovoltaic elements were proposed because of the good conformity of the solar spectrum with the polyacetylene forbidden gap. The photovoltaic spectra for (CH)n-Al structure and volt-current characteristic for (CH) -nCdS heterojunction are presented in Fig. 19 and Fig. 20 respectively. 

However, in the last two decades it has been shown experimentally [1,7, 8,12-14] and theoretically [15-18] that in many wide-gap insulators including alkali halides the primary mechanism of the Frenkel defect formation is subthreshold, i.e., lattice defects arise from the non-radiative decay of excitons whose formation energy is less than the forbidden gap of solids, typically 10 eV. These excitons are created easily by X-rays and UV light. Under ionic or electron beam irradiations the main portion of the incident particle... 

According to the band theory model, this process corresponds to thermal excitation across the forbidden gap and as such the law of mass action may be applied to the equilibrium between creation and recombination of holes and electrons. 

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