Insulators, energy bands

Figure Al.3.8. Schematic energy bands illustrating an insulator (large band gap), a semiconductor (small band gap), a metal (no gap) and a semimetal. In a semimetal, one band is almost filled and another band is almost empty.

Louie S G 1987 Theory of quasiparticle energies and excitation spectra of semiconductors and insulators Eleotronio Band Struoture and Its Applioations (Leoture Notes in Physios vol 283) ed M Youssouf (Berlin Springer)... 

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.

Semiconductors. The basic material employed in LEDs is the semiconductor, a soHd which possesses a conductivity intermediate between that of a conductor and an insulator. Unlike conductors, semiconductors and insulators possess an energy gap, E, between two energy bands, the... 

S2.3 Point Defects and Energy Bands in Semiconductors and Insulators... 

With insulators or semiconductors, the valence band is completely filled and is separated from the next highest allowable energy band (conduction band) by a gap (or forbidden band). In order for valence electrons to be raised into the conduction band, they must be given a sizable amount of energy. With insulators this gap corresponds to several electron volts. For semiconductors the gap is sufficiently small so that a significant number of electrons can acquire the necessary additional energy by thermal means at room temperature. 

Figure 4.6 The filling of energy bands in a metal (sodium) and in an insulator (sodium chloride).

Fig. 2-6. Electron occupation in energy bands classified into (a) metals, (b) insulators, and (c) semiconductors FOB = fully occupied band FOB = partially occupied band CB = conduction band VB = valence band.

Figure 3.12. Schematic electron occupancy of allowed energy bands for a metal (a), an insulator (b), and a semiconductor (c). The shaded areas indicate the regions filled with electrons. The vertical extent of the boxes indicates the energy regions allowed.

As shown by Ruderman and Kittel (77) and Bloembergen and Rowland (78), Aij in a solid is dependent on the nature of the energy bands in the solid. For metals A is proportional to the product of the square of the electron density of Fermi surface electrons at the nucleus and the effective mass, and decreases as the inverse cube of the internuclear distance. Insulators have been treated by the energy band method (78) and by a molecular method (79) where each atom is considered to be bonded to its nearest neighbors. Unfortunately, both of these methods involve approximations in the evaluation of An which are quite crude at present. 

To give an example of a wide band gap material, Fig. 8.5 shows the calculated DOS of bulk quartz (Si02). The band gap from the calculation shown in this figure is 5.9 eV. Even remembering that DFT typically underestimates the band gap, it is clear that quartz is an insulator. Unlike Si, the valence band of quartz includes several separate energy bands with distinct energy gaps between them. We will return to these bands when we discuss the local density of states in Section 8.2. 

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