Insulators electron band structure

Louie S G 1987 Theory of quasiparticle energies and excitation spectra of semiconductors and insulators Electronic Band Structure and Its Applications (Lecture Notes in Physics vol 283) ed M Youssouf (Berlin Springer)... 

Figure 7.7a shows the extended-zone electronic band structure for a one-dimensional crystal - an atom chain with a real-space unit cell parameter a and reciprocal lattice vector Tr/n - containing a half-filled (metallic) band. In this diagram, both values of the wave vector, +k, are shown. The wave vector is the reciprocal unit cell dimension. The Fermi surface is a pair of points in the first BZ (Fig. 7.7c). When areas on the Fermi surface can be made to coincide by mere translation of a wave vector, q, the Fermi surface is said to be nested. The instability of the material towards the Peierls distortion is due to this nesting. In one dimension, nesting is complete and a one-dimensional metal is converted to an insulator because of a Peierls distortion. This is shown in Figure 7.7b, where the real-space unit cell parameter of the distorted lattice is 2a and a band gap opens at values of the wave vector equal to half the original values, 7r/2a.

Gallium arsenide s native oxide is found to be a mixture of nonstoichiometric galhum and arsenic oxides and elemental arsenic. Thus, the electronic band structure is found to be severely disrupted, causing a breakdown in normal semiconductor behavior on the GaAs surface. As a consequence, the GaAs MISFET (metal insulator semiconductor field-effect transistor) equivalent to the technologically important Si-based MOSFET (metal-oxide semiconductor field-effect transistor) is, therefore, presently unavailable. 

In condensed-phase molecular systems, and particularly insulating molecular crystals, infrared and Raman spectroscopies are well-established tools for investigating molecular and crystalline structural properties. On the other hand, in inorganic semiconductors and metals the same spectroscopic methods are widely used to evaluate electronic band structure parameters. Organic charge transfer (CT) crystals, as molecular conductors and semiconductors, share some properties of both the above classes of solids, and, therefore, new spectroscopic phenomena are expected, and indeed observed for these materials. ... 

The electrical properties of conventional materials depend on the electronic band structure and on the distribution of available electrons in the bands. When the bands are filled or empty, no conduction occurs. If the band gap is narrow compared with thermal excitation energies (i.e. kT), electrons are excited to the conduction band and the conductivity increases. When the band gap is too wide, thermal excitation is insufficient to excite electrons to the conduction band and the material is an insulator. 

Electronic properties of nanocrystals critically depend on size. This aspect is aptly put forth in the quest How many atoms make a metal . It is clear that as the size of metal nanocrystals is reduced, the accompanjung changes in the electronic structure render them insulating. This transition, called the size-induced metal-insulator transition (SIMIT), has evoked much interest from chemists and physicists alike. A SIMIT is manifested in experiments that measure the electronic band structure and atomistic properties such as ionization energy. 

Potter et al. (1992) reviewed the literature on the microstructure of semiconductors in a composite structure with an insulating matrix. These composites offer insight into the electronic band structure and the optical properties of the materials. Simmons et al. (1991) discussed the electronic band structure of composites formed from semiconductors and glass components. 

Figure 3.1 Schematics of the electronic band structures in insulators, metals and semiconductors...

FIGURE 3.55 Electronic band structure for metals, semiconductors, and insulators. 

We attempt to extend the Hard-Soft Acid-Base (HSAB) principle for the reactions in solutions to interactions in solids. First we point out the important link between the absolute hardness of acid-and-base and the average energy gap. Then we discuss the electronic band structures of various solids, e.g., metals, semimetals, semiconductors and insulators. On the basis of energy gaps, we elaborate various consequences of the acid-base interactions in solids. The applications of HSAB principle and the frontier orbital concept to the solid adhesion and surface interactions between metals and polymers will be verified by experimental results reported in the literature. The new findings reported in this paper should be beneficial to those who are carrying out research in or processing thin-film microelectronic devices or thick-film multilayer structures. 

Solids can be classified as metals, semimetals, intrinsic semiconductors and insulators. The band structures of solids can be illustrated in Fig. 3. Monovalent metals, e.g., Na , have a partially filled valence band, the lower half of which is occupied. The Fermi level is in the valence band but at the top of the occupied orbitals. Furthermore, there is still an energy gap between the valence band and the conduction band (unoccupied MO). In some metals, such as the bivalent metals, the valence band is full but overlaps a higher unoccupied conduction band. In this case, the Fermi level is in the conduction band and the overlapped valence band. Thus, the electrons close to the Fermi level are still free to move as the extra bands supply the unoccupied states. In the latter case, there appears to be no minimum energy gap. Eg" y which is generally reported in the literature. However, it is not... 

Figure 18.4 The various possible electron band structures in solids at 0 K. (a) The electron band structure found in metals such as copper, in which there are available electron states above and adjacent to filled states, in the same band, b) The electron band structure of metals such as magnesium, in which there is an overlap of filled and empty outer bands, (c) The electron band structure characteristic of insulators the filled valence band is separated from the empty conduction band by a relatively large band gap (>2 eV). d) The electron band structure found in the semiconductors, which is the same as for insulators except that the band gap is relatively narrow (<2 eV).

Fig. 6.16. Probing the transient electronic structure of TbTes in the course of its ultrafast insulator-to-metal transition induced by femtosecond-laser excitation (a) Time- and angle-resolved photoemission spectroscopy. A TbTcs sample was excited by an IR pulse (hi Pump = I.SeV, about 50 fs duration) and probed after a time delay At with a UV pulse (hi/pump = 6 eV, about 90 fs duration). The photoelectron intensity and kinetic energy E ,i were measured as a function of the emission angles (a, 9). (b) Insulator-to-metal transition Above the critical temperature Tc (or 100fsafterlaserexcitation)the band gap of the CDW phase closes, (c) "Snapshots" of the electronic band structure E(k)in TbTej fordifferenttimedelaysAt.Afterlaserexcitation, the gap has closed and the band dispersion near the Eermi level, Ep, changed after a time delay of 100 fs. Such a delayed collapse of the band gap is characteristic of the "Peierls type" mechanism (see text).

It is well known that metallic electronic structure is not generally realised in low-dimensional materials on account of metal-insulator transition (or Peierls transition [14]). This transition is formally required by energetical stabilisation and often accompanied with the bond alternation, an example of which is illustrated in Fig. 4 for metallic polyacetylene [15]. This kind of metal-insulator transition should also be checked for CNT satisfying 2a + b = 3N, since CNT is considered to belong to also low-dimensional materials. Representative bond-alternation patterns are shown in Fig. 5. Expression of band structures of any isodistant tubes (a, b) is equal to those in Eq.(2). Those for bond-alternation patterned tube a, b) are given by. 

The description derived above gives useful insight into the general characteristics of the band structure in solids. In reality, band structure is far more complex than suggested by Fig. 6.16, as a result of the inclusion of three dimensions, and due to the presence of many types of orbitals that form bands. The detailed electronic structure determines the physical and chemical properties of the solids, in particular whether a solid is a conductor, semiconductor, or insulator (Fig. 6.17). 

Accepting that the electronic structure of the metal clusters is in between the discreet electronic levels of the isolated atoms and the band structure of the metals, it is expectable that under a certain size the particle becomes nonmetallic. Indeed, theoretical estimations [102,105] suggest that the gap between the filled and empty electron states becomes comparable with the energy of the thermal excitations in clusters smaller than 50-100 atoms or 1 nm in size, where the particles start to behave as insulators. A... 

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