Energy band/level

Fig. 3.6 A schematic representation of semiconductor energy band levels and energy distribution of the electrolyte redox system.

To test the device model we used two different small molecule organic materials N,. V -bisgi-iiK i liylpli( iiyl i-.V. IV -diphenyl-l, 1 -biphenyl-4, 4 diamine (TPD) and 3,4,9,10-perylenetetracarboxylic bis-benzimidazole (PTCBI), whose absorption spectra and approximate energy band levels are depicted in Fig. 5.18. TPD (H.W. Sands) is a common hole transport material used in organic LEDs, making it suitable for use as the CTL. PTCBI (Sensient... 

Fig. 5.18. Absorption spectra, chemical structure, and proposed energy band levels of the materials used in the bi-layer hetero junction photoconductor N, N -bis(3-methylphenyl)-W,W -diphenyl-l,l/-biphenyl-4,4 -diamine (TPD, solid) and 3,4,9,10-perylenetetracarboxylic bis-benzimidazole (PTCBI, dashes). Also shown is the emission profile of the green LED (green, Apeak 532 nm) operated with a forward current of 2 A and an intensity of approximately 40 mW cnT (dotted)...

Figure 3.104 Energy band levels of components of the Ti02/CdS/CuSCN cell. Reprinted with permission from Larramona et al., 2006 . Copyright (2006) American Chemical Society...

Figure Al.3.7. Evolution of energy bands in the Kronig-Penney model as the separation between wells, b (figure A 1,3.61 is deereased from (a) to (d). In (a) the wells are separated by a large distanee (large value of b) and the energy bands resemble diserete levels of an isolated well. In (d) the wells are quite elose together (small value of b) and the energy bands are free-eleetron-like.

Several factors detennine how efficient impurity atoms will be in altering the electronic properties of a semiconductor. For example, the size of the band gap, the shape of the energy bands near the gap and the ability of the valence electrons to screen the impurity atom are all important. The process of adding controlled impurity atoms to semiconductors is called doping. The ability to produce well defined doping levels in semiconductors is one reason for the revolutionary developments in the construction of solid-state electronic devices. 

Instead of plotting tire electron distribution function in tire energy band diagram, it is convenient to indicate tire position of tire Fenni level. In a semiconductor of high purity, tire Fenni level is close to mid-gap. In p type (n type) semiconductors, it lies near tire VB (CB). In very heavily doped semiconductors tire Fenni level can move into eitlier tire CB or VB, depending on tire doping type. 

Figure C2.16.7. A schematic energy band diagram of a p-n junction witliout external bias (a) and under forward bias (b). Electrons and holes are indicated witli - and + signs, respectively. It should be remembered tliat tlie energy of electrons increases by moving up, holes by moving down. Electrons injected into tlie p side of tlie junction become minority carriers. Approximate positions of donor and acceptor levels and tlie Feniii level, are indicated.

Figure C2.16.8. Schematic energy band diagram for an n-p-n bipolar junction transistor. Positions of quasi-Fenni levels and bias voltages are indicated.

Simply doing electronic structure computations at the M, K, X, and T points in the Brillouin zone is not necessarily sufficient to yield a band gap. This is because the minimum and maximum energies reached by any given energy band sometimes fall between these points. Such limited calculations are sometimes done when the computational method is very CPU-intensive. For example, this type of spot check might be done at a high level of theory to determine whether complete calculations are necessary at that level. 

One important question is how many orbitals are available at any given energy level. This is shown using a density of states (DOS) diagram as in Figure 34.2. It is typical to include the Fermi level as denoted by the dotted line in this figure. A material with a half-filled energy band is a conductor, but it may be a... 

Fig. 1. Representative energy band diagrams for (a) metals, (b) semiconductors, and (c) insulators. The dashed line represents the Fermi Level, and the shaded areas represent filled states of the bands. denotes the band gap of the material.

MetaUic behavior is observed for those soHds that have partially filled bands (Fig. lb), that is, for materials that have their Fermi level within a band. Since the energy bands are delocalized throughout the crystal, electrons in partially filled bands are free to move in the presence of an electric field, and large conductivity results. Conduction in metals shows a decrease in conductivity at higher temperatures, since scattering mechanisms (lattice phonons, etc) are frozen out at lower temperatures, but become more important as the temperature is raised. 

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.

The most extensive calculations of the electronic structure of fullerenes so far have been done for Ceo- Representative results for the energy levels of the free Ceo molecule are shown in Fig. 5(a) [60]. Because of the molecular nature of solid C o, the electronic structure for the solid phase is expected to be closely related to that of the free molecule [61]. An LDA calculation for the crystalline phase is shown in Fig. 5(b) for the energy bands derived from the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) for Cgo, and the band gap between the LUMO and HOMO-derived energy bands is shown on the figure. The LDA calculations are one-electron treatments which tend to underestimate the actual bandgap. Nevertheless, such calculations are widely used in the fullerene literature to provide physical insights about many of the physical properties. 

Calculations for Ceo in the LDA approximation [62, 60] yield a narrow band (- 0.4 0.6 eV bandwidth) solid, with a HOMO-LUMO-derived direct band gap of - 1.5 eV at the X point of the fee Brillouin zone. The narrow energy bands and the molecular nature of the electronic structure of fullerenes are indicative of a highly correlated electron system. Since the HOMO and LUMO levels both have the same odd parity, electric dipole transitions between these levels are symmetry forbidden in the free Ceo moleeule. In the crystalline solid, transitions between the direct bandgap states at the T and X points in the cubic Brillouin zone arc also forbidden, but are allowed at the lower symmetry points in the Brillouin zone. The allowed electric dipole... 

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