Phase transitions insulator-semiconductor

As has been pointed out previously, ionic compounds are characterized by a Fermi level EF that is located within an s-p-state energy gap Ef. It is for this reason that ionic compounds are usually insulators. However, if the ionic compound contains transition element cations, electrical conductivity can take place via the d electrons. Two situations have been distinguished the case where Ru > Rc(n,d) and that where Rlt < Rc(n,d). Compounds corresponding to the first alternative have been discussed in Chapter III, Section I, where it was pointed out that the presence of similar atoms on similar lattice sites, but in different valence states, leads to low or intermediate mobility semiconduction via a hopping of d electrons over a lattice-polarization barrier from cations of lower valence to cations of higher valence. In this section it is shown how compounds that illustrate the second alternative, Rtt < 72c(n,d), may lead to intermediate mobility, metallic conduction and to martensitic semiconductor metallic phase transitions. 

In elemental semiconductors and the polar faces of compound semiconductors, an odd number of electrons is formed per surface atom by the creation of a surface. The solid therefore undergoes a metal—insulator phase transition [82] to produce an even number of electrons per surface unit cell, thus reducing its symmetry in the plane of the surface. For non-polar faces of compound semiconductors, the simple truncated bulk geometry is already insulating in character because anionic and cationic species are electronically inequivalent. No distortions which reduce the symmetry are therefore necessary to provide stability, but the unbalanced ionic forces and unsaturated covalencies can produce quite large ( 0.5 A) atomic movements ( surface relaxation ). 

Among the phase transitions where electronic factors play a major role, the most well-known are the metal-insulator transitions exhibited by transition-metal oxides, sulfides, and so on. This subject has been discussed at length. A recent observation of some interest is that the metal-nonmetal transition occurs at a critical electron concentration as given by the particular form of the Mott criterion, n / aH = 0.26 0.05. The Verwey transition in Fe304 is associated with a marked jump in conductivity, but the material remains a semiconductor both above and below the transition temperature (123 K) below 123 K, there is... 

Depending on the crystal structure of the one-dimensional stacks and on whether a Peierls transition occurs or not (more on this subject wiU be given in Sect. 9.3), the states in the one-dimensional bands are wholly or partiaUy fUled. The CT crystals can therefore be semiconductors or metalHc conductors. If at high temperature metallic conductivity is present and at a lower temperature Tp a Peierls phase transition occurs, the metal becomes a semiconductor at T< Tp, or an insulator. 

Complete dispersion curves along symmetry directions in the Brillouin zone are obtained from calculated force constants. Calculations of enharmonic terms and phonon-phonon interaction matrix elements are also presented. In Sec. IIIC, results for solid-solid phase transitions are presented. The stability of group IV covalent materials under pressure is discussed. Also presented is a calculation on the temperature- and pressure-induced crystal phase transitions in Be. In Sec. IV, we discuss the application of pseudopotential calculations to surface studies. Silicon and diamond surfaces will be used as the prototypes for the covalent semiconductor and insulator cases while surfaces of niobium and palladium will serve as representatives of the transition metal cases. In Sec. V, the validity of the local density approximation is examined. The results of a nonlocal density functional calculation for Si and... 

The first solution to this problem was produced phenomenologically by Mooser and Pearson. The solution for A B compounds is reproduced in Figure 9. Similar solutions apply not only to A"B semiconductors and insulators, but also to many intermetallic compounds including transition metals. This work provides the first step toward explaining structural and phase transitions in chemically homologous families of binary crystals. It has made the question of the proper treatment of chemical bonding in crystals susceptible to theoretical analysis, whereas formerly work based on mechanical models (ionic compounds) or quantum mechanical perturbation theory (nearly-free-electron metals) made the same problem appear insoluble. 

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